0.018/0.018 NO 0.018/0.018 0.018/0.018 Problem 1: 0.018/0.018 0.018/0.018 0.018/0.018 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.018/0.018 Confluence Problem: 0.018/0.018 (VAR vNonEmpty x) 0.018/0.018 (REPLACEMENT-MAP 0.018/0.018 (a) 0.018/0.018 (b) 0.018/0.018 (c) 0.018/0.018 (d) 0.018/0.018 (f 1) 0.018/0.018 (g 1, 2, 3) 0.018/0.018 (h 1, 2) 0.018/0.018 (k) 0.018/0.018 (A) 0.018/0.018 (e) 0.018/0.018 (e') 0.018/0.018 (fSNonEmpty) 0.018/0.018 (l) 0.018/0.018 (m) 0.018/0.018 ) 0.018/0.018 (RULES 0.018/0.018 a -> c 0.018/0.018 a -> d 0.018/0.018 b -> c 0.018/0.018 b -> d 0.018/0.018 c -> e 0.018/0.018 c -> e' 0.018/0.018 c -> l 0.018/0.018 d -> m 0.018/0.018 f(x) -> x | x ->* e, x ->* e' 0.018/0.018 g(d,x,x) -> A 0.018/0.018 h(x,x) -> g(x,x,f(k)) 0.018/0.018 k -> l 0.018/0.018 k -> m 0.018/0.018 ) 0.018/0.018 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.018/0.018 0.018/0.018 0.018/0.018 Problem 1: 0.018/0.018 0.018/0.018 Inlining of Conditions Processor [STERN17]: 0.018/0.018 0.018/0.018 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.018/0.018 Confluence Problem: 0.018/0.018 (VAR vNonEmpty x) 0.018/0.018 (REPLACEMENT-MAP 0.018/0.018 (a) 0.018/0.018 (b) 0.018/0.018 (c) 0.018/0.018 (d) 0.018/0.018 (f 1) 0.018/0.018 (g 1, 2, 3) 0.018/0.018 (h 1, 2) 0.018/0.018 (k) 0.018/0.018 (A) 0.018/0.018 (e) 0.018/0.018 (e') 0.018/0.018 (fSNonEmpty) 0.018/0.018 (l) 0.018/0.018 (m) 0.018/0.018 ) 0.018/0.018 (RULES 0.018/0.018 a -> c 0.018/0.018 a -> d 0.018/0.018 b -> c 0.018/0.018 b -> d 0.018/0.018 c -> e 0.018/0.018 c -> e' 0.018/0.018 c -> l 0.018/0.018 d -> m 0.018/0.018 f(x) -> x | x ->* e, x ->* e' 0.018/0.018 g(d,x,x) -> A 0.018/0.018 h(x,x) -> g(x,x,f(k)) 0.018/0.018 k -> l 0.018/0.018 k -> m 0.018/0.018 ) 0.018/0.018 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.018/0.018 0.018/0.018 0.018/0.018 Problem 1: 0.018/0.018 0.018/0.018 Clean CTRS Processor: 0.018/0.018 0.018/0.018 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.018/0.018 Confluence Problem: 0.018/0.018 (VAR x) 0.018/0.018 (REPLACEMENT-MAP 0.018/0.018 (a) 0.018/0.018 (b) 0.018/0.018 (c) 0.018/0.018 (d) 0.018/0.018 (f 1) 0.018/0.018 (g 1, 2, 3) 0.018/0.018 (h 1, 2) 0.018/0.018 (k) 0.018/0.018 (A) 0.018/0.018 (e) 0.018/0.018 (e') 0.018/0.018 (fSNonEmpty) 0.018/0.018 (l) 0.018/0.018 (m) 0.018/0.018 ) 0.018/0.018 (RULES 0.018/0.018 a -> c 0.018/0.018 a -> d 0.018/0.018 b -> c 0.018/0.018 b -> d 0.018/0.018 c -> e 0.018/0.018 c -> e' 0.018/0.018 c -> l 0.018/0.018 d -> m 0.018/0.018 f(x) -> x | x ->* e, x ->* e' 0.018/0.018 g(d,x,x) -> A 0.018/0.018 h(x,x) -> g(x,x,f(k)) 0.018/0.018 k -> l 0.018/0.018 k -> m 0.018/0.018 ) 0.018/0.018 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.018/0.018 0.018/0.018 CRule InfChecker Info: 0.018/0.018 a -> c 0.018/0.018 Rule remains 0.018/0.018 Proof: 0.018/0.018 NO_CONDS 0.018/0.018 0.018/0.018 CRule InfChecker Info: 0.018/0.018 a -> d 0.018/0.018 Rule remains 0.018/0.018 Proof: 0.018/0.018 NO_CONDS 0.018/0.018 0.018/0.018 CRule InfChecker Info: 0.018/0.018 b -> c 0.018/0.018 Rule remains 0.018/0.018 Proof: 0.018/0.018 NO_CONDS 0.018/0.018 0.018/0.018 CRule InfChecker Info: 0.018/0.018 b -> d 0.018/0.018 Rule remains 0.018/0.018 Proof: 0.018/0.018 NO_CONDS 0.018/0.018 0.018/0.018 CRule InfChecker Info: 0.018/0.018 c -> e 0.018/0.018 Rule remains 0.018/0.018 Proof: 0.018/0.018 NO_CONDS 0.018/0.018 0.018/0.018 CRule InfChecker Info: 0.018/0.018 c -> e' 0.018/0.018 Rule remains 0.018/0.018 Proof: 0.018/0.018 NO_CONDS 0.018/0.018 0.018/0.018 CRule InfChecker Info: 0.018/0.018 c -> l 0.018/0.018 Rule remains 0.018/0.018 Proof: 0.018/0.018 NO_CONDS 0.018/0.018 0.018/0.018 CRule InfChecker Info: 0.018/0.018 d -> m 0.018/0.018 Rule remains 0.018/0.018 Proof: 0.018/0.018 NO_CONDS 0.018/0.018 0.018/0.018 CRule InfChecker Info: 0.018/0.018 f(x) -> x | x ->* e, x ->* e' 0.018/0.018 Rule remains 0.018/0.018 Proof: 0.018/0.018 NO 0.018/0.018 0.018/0.018 Problem 1: 0.018/0.018 0.018/0.018 Infeasibility Problem: 0.018/0.018 [(VAR vNonEmpty x vNonEmpty x) 0.018/0.018 (STRATEGY CONTEXTSENSITIVE 0.018/0.018 (a) 0.018/0.018 (b) 0.018/0.018 (c) 0.018/0.018 (d) 0.018/0.018 (f 1) 0.018/0.018 (g 1 2 3) 0.018/0.018 (h 1 2) 0.018/0.018 (k) 0.018/0.018 (A) 0.018/0.018 (e) 0.018/0.018 (e') 0.018/0.018 (fSNonEmpty) 0.018/0.018 (l) 0.018/0.018 (m) 0.018/0.018 ) 0.018/0.018 (RULES 0.018/0.018 a -> c 0.018/0.018 a -> d 0.018/0.018 b -> c 0.018/0.018 b -> d 0.018/0.018 c -> e 0.018/0.018 c -> e' 0.018/0.018 c -> l 0.018/0.018 d -> m 0.018/0.018 f(x) -> x | x ->* e, x ->* e' 0.018/0.018 g(d,x,x) -> A 0.018/0.018 h(x,x) -> g(x,x,f(k)) 0.018/0.018 k -> l 0.018/0.018 k -> m 0.018/0.018 )] 0.018/0.018 0.018/0.018 Infeasibility Conditions: 0.018/0.018 x ->* e, x ->* e' 0.018/0.018 0.018/0.018 Problem 1: 0.018/0.018 0.018/0.018 Obtaining a proof using Prover9: 0.018/0.018 0.018/0.018 -> Prover9 Output: 0.018/0.018 ============================== Prover9 =============================== 0.018/0.018 Prover9 (64) version 2009-11A, November 2009. 0.018/0.018 Process 12597 was started by ubuntu on ubuntu, 0.018/0.018 Wed Mar 9 09:20:26 2022 0.018/0.018 The command was "./prover9 -f /tmp/prover912590-0.in". 0.018/0.018 ============================== end of head =========================== 0.018/0.018 0.018/0.018 ============================== INPUT ================================= 0.018/0.018 0.018/0.018 % Reading from file /tmp/prover912590-0.in 0.018/0.018 0.018/0.018 assign(max_seconds,20). 0.018/0.018 0.018/0.018 formulas(assumptions). 0.018/0.018 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence). 0.018/0.018 ->_s0(x1,y) -> ->_s0(g(x1,x2,x3),g(y,x2,x3)) # label(congruence). 0.018/0.018 ->_s0(x2,y) -> ->_s0(g(x1,x2,x3),g(x1,y,x3)) # label(congruence). 0.018/0.018 ->_s0(x3,y) -> ->_s0(g(x1,x2,x3),g(x1,x2,y)) # label(congruence). 0.018/0.018 ->_s0(x1,y) -> ->_s0(h(x1,x2),h(y,x2)) # label(congruence). 0.018/0.018 ->_s0(x2,y) -> ->_s0(h(x1,x2),h(x1,y)) # label(congruence). 0.018/0.018 ->_s0(a,c) # label(replacement). 0.018/0.018 ->_s0(a,d) # label(replacement). 0.018/0.018 ->_s0(b,c) # label(replacement). 0.018/0.018 ->_s0(b,d) # label(replacement). 0.018/0.018 ->_s0(c,e) # label(replacement). 0.018/0.018 ->_s0(c,e') # label(replacement). 0.018/0.018 ->_s0(c,l) # label(replacement). 0.018/0.018 ->_s0(d,m) # label(replacement). 0.018/0.018 ->*_s0(x1,e) & ->*_s0(x1,e') -> ->_s0(f(x1),x1) # label(replacement). 0.018/0.018 ->_s0(g(d,x1,x1),A) # label(replacement). 0.018/0.018 ->_s0(h(x1,x1),g(x1,x1,f(k))) # label(replacement). 0.018/0.018 ->_s0(k,l) # label(replacement). 0.018/0.018 ->_s0(k,m) # label(replacement). 0.018/0.018 ->*_s0(x,x) # label(reflexivity). 0.018/0.018 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 0.018/0.018 end_of_list. 0.018/0.018 0.018/0.018 formulas(goals). 0.018/0.018 (exists x3 (->*_s0(x3,e) & ->*_s0(x3,e'))) # label(goal). 0.018/0.018 end_of_list. 0.018/0.018 0.018/0.018 ============================== end of input ========================== 0.018/0.018 0.018/0.018 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.018/0.018 0.018/0.018 % Formulas that are not ordinary clauses: 0.018/0.018 1 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 0.018/0.018 2 ->_s0(x1,y) -> ->_s0(g(x1,x2,x3),g(y,x2,x3)) # label(congruence) # label(non_clause). [assumption]. 0.018/0.018 3 ->_s0(x2,y) -> ->_s0(g(x1,x2,x3),g(x1,y,x3)) # label(congruence) # label(non_clause). [assumption]. 0.018/0.018 4 ->_s0(x3,y) -> ->_s0(g(x1,x2,x3),g(x1,x2,y)) # label(congruence) # label(non_clause). [assumption]. 0.018/0.018 5 ->_s0(x1,y) -> ->_s0(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.018/0.018 6 ->_s0(x2,y) -> ->_s0(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.018/0.018 7 ->*_s0(x1,e) & ->*_s0(x1,e') -> ->_s0(f(x1),x1) # label(replacement) # label(non_clause). [assumption]. 0.018/0.018 8 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 0.018/0.018 9 (exists x3 (->*_s0(x3,e) & ->*_s0(x3,e'))) # label(goal) # label(non_clause) # label(goal). [goal]. 0.018/0.018 0.018/0.018 ============================== end of process non-clausal formulas === 0.018/0.018 0.018/0.018 ============================== PROCESS INITIAL CLAUSES =============== 0.018/0.018 0.018/0.018 % Clauses before input processing: 0.018/0.018 0.018/0.018 formulas(usable). 0.018/0.018 end_of_list. 0.018/0.018 0.018/0.018 formulas(sos). 0.018/0.018 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(1)]. 0.018/0.018 -->_s0(x,y) | ->_s0(g(x,z,u),g(y,z,u)) # label(congruence). [clausify(2)]. 0.018/0.018 -->_s0(x,y) | ->_s0(g(z,x,u),g(z,y,u)) # label(congruence). [clausify(3)]. 0.018/0.018 -->_s0(x,y) | ->_s0(g(z,u,x),g(z,u,y)) # label(congruence). [clausify(4)]. 0.018/0.018 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(5)]. 0.018/0.018 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(6)]. 0.018/0.018 ->_s0(a,c) # label(replacement). [assumption]. 0.018/0.018 ->_s0(a,d) # label(replacement). [assumption]. 0.018/0.018 ->_s0(b,c) # label(replacement). [assumption]. 0.018/0.018 ->_s0(b,d) # label(replacement). [assumption]. 0.018/0.018 ->_s0(c,e) # label(replacement). [assumption]. 0.018/0.018 ->_s0(c,e') # label(replacement). [assumption]. 0.018/0.018 ->_s0(c,l) # label(replacement). [assumption]. 0.018/0.018 ->_s0(d,m) # label(replacement). [assumption]. 0.018/0.018 -->*_s0(x,e) | -->*_s0(x,e') | ->_s0(f(x),x) # label(replacement). [clausify(7)]. 0.018/0.018 ->_s0(g(d,x,x),A) # label(replacement). [assumption]. 0.018/0.018 ->_s0(h(x,x),g(x,x,f(k))) # label(replacement). [assumption]. 0.018/0.018 ->_s0(k,l) # label(replacement). [assumption]. 0.018/0.018 ->_s0(k,m) # label(replacement). [assumption]. 0.018/0.018 ->*_s0(x,x) # label(reflexivity). [assumption]. 0.018/0.018 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(8)]. 0.018/0.018 -->*_s0(x,e) | -->*_s0(x,e') # label(goal). [deny(9)]. 0.018/0.018 end_of_list. 0.018/0.018 0.018/0.018 formulas(demodulators). 0.018/0.018 end_of_list. 0.018/0.018 0.018/0.018 ============================== PREDICATE ELIMINATION ================= 0.018/0.018 0.018/0.018 No predicates eliminated. 0.018/0.018 0.018/0.018 ============================== end predicate elimination ============= 0.018/0.018 0.018/0.018 Auto_denials: 0.018/0.018 % copying label goal to answer in negative clause 0.018/0.018 0.018/0.018 Term ordering decisions: 0.018/0.018 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 0.018/0.018 Function symbol precedence: function_order([ c, d, k, e, e', l, m, a, b, A, h, f, g ]). 0.018/0.018 After inverse_order: (no changes). 0.018/0.018 Unfolding symbols: (none). 0.018/0.018 0.018/0.018 Auto_inference settings: 0.018/0.018 % set(neg_binary_resolution). % (HNE depth_diff=-7) 0.018/0.018 % clear(ordered_res). % (HNE depth_diff=-7) 0.018/0.018 % set(ur_resolution). % (HNE depth_diff=-7) 0.018/0.018 % set(ur_resolution) -> set(pos_ur_resolution). 0.018/0.018 % set(ur_resolution) -> set(neg_ur_resolution). 0.018/0.018 0.018/0.018 Auto_process settings: 0.018/0.018 % set(unit_deletion). % (Horn set with negative nonunits) 0.018/0.018 0.018/0.018 kept: 10 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(1)]. 0.018/0.018 kept: 11 -->_s0(x,y) | ->_s0(g(x,z,u),g(y,z,u)) # label(congruence). [clausify(2)]. 0.018/0.018 kept: 12 -->_s0(x,y) | ->_s0(g(z,x,u),g(z,y,u)) # label(congruence). [clausify(3)]. 0.018/0.018 kept: 13 -->_s0(x,y) | ->_s0(g(z,u,x),g(z,u,y)) # label(congruence). [clausify(4)]. 0.018/0.018 kept: 14 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(5)]. 0.018/0.018 kept: 15 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(6)]. 0.018/0.018 kept: 16 ->_s0(a,c) # label(replacement). [assumption]. 0.018/0.018 kept: 17 ->_s0(a,d) # label(replacement). [assumption]. 0.018/0.018 kept: 18 ->_s0(b,c) # label(replacement). [assumption]. 0.018/0.018 kept: 19 ->_s0(b,d) # label(replacement). [assumption]. 0.018/0.018 kept: 20 ->_s0(c,e) # label(replacement). [assumption]. 0.018/0.018 kept: 21 ->_s0(c,e') # label(replacement). [assumption]. 0.018/0.018 kept: 22 ->_s0(c,l) # label(replacement). [assumption]. 0.018/0.018 kept: 23 ->_s0(d,m) # label(replacement). [assumption]. 0.018/0.018 kept: 24 -->*_s0(x,e) | -->*_s0(x,e') | ->_s0(f(x),x) # label(replacement). [clausify(7)]. 0.018/0.018 kept: 25 ->_s0(g(d,x,x),A) # label(replacement). [assumption]. 0.018/0.018 kept: 26 ->_s0(h(x,x),g(x,x,f(k))) # label(replacement). [assumption]. 0.018/0.018 kept: 27 ->_s0(k,l) # label(replacement). [assumption]. 0.018/0.018 kept: 28 ->_s0(k,m) # label(replacement). [assumption]. 0.018/0.018 kept: 29 ->*_s0(x,x) # label(reflexivity). [assumption]. 0.018/0.018 kept: 30 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(8)]. 0.018/0.018 kept: 31 -->*_s0(x,e) | -->*_s0(x,e') # label(goal) # answer(goal). [deny(9)]. 0.018/0.018 0.018/0.018 ============================== end of process initial clauses ======== 0.018/0.018 0.018/0.018 ============================== CLAUSES FOR SEARCH ==================== 0.018/0.018 0.018/0.018 % Clauses after input processing: 0.018/0.018 0.018/0.018 formulas(usable). 0.018/0.018 end_of_list. 0.018/0.018 0.018/0.018 formulas(sos). 0.018/0.018 10 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(1)]. 0.018/0.018 11 -->_s0(x,y) | ->_s0(g(x,z,u),g(y,z,u)) # label(congruence). [clausify(2)]. 0.018/0.018 12 -->_s0(x,y) | ->_s0(g(z,x,u),g(z,y,u)) # label(congruence). [clausify(3)]. 0.018/0.018 13 -->_s0(x,y) | ->_s0(g(z,u,x),g(z,u,y)) # label(congruence). [clausify(4)]. 0.018/0.018 14 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(5)]. 0.018/0.018 15 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(6)]. 0.018/0.018 16 ->_s0(a,c) # label(replacement). [assumption]. 0.018/0.018 17 ->_s0(a,d) # label(replacement). [assumption]. 0.018/0.018 18 ->_s0(b,c) # label(replacement). [assumption]. 0.018/0.018 19 ->_s0(b,d) # label(replacement). [assumption]. 0.018/0.018 20 ->_s0(c,e) # label(replacement). [assumption]. 0.018/0.018 21 ->_s0(c,e') # label(replacement). [assumption]. 0.018/0.018 22 ->_s0(c,l) # label(replacement). [assumption]. 0.018/0.018 23 ->_s0(d,m) # label(replacement). [assumption]. 0.018/0.018 25 ->_s0(g(d,x,x),A) # label(replacement). [assumption]. 0.018/0.018 26 ->_s0(h(x,x),g(x,x,f(k))) # label(replacement). [assumption]. 0.018/0.018 27 ->_s0(k,l) # label(replacement). [assumption]. 0.018/0.018 28 ->_s0(k,m) # label(replacement). [assumption]. 0.018/0.018 29 ->*_s0(x,x) # label(reflexivity). [assumption]. 0.018/0.018 30 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(8)]. 0.018/0.018 31 -->*_s0(x,e) | -->*_s0(x,e') # label(goal) # answer(goal). [deny(9)]. 0.018/0.018 end_of_list. 0.018/0.018 0.018/0.018 formulas(demodulators). 0.018/0.018 end_of_list. 0.018/0.018 0.018/0.018 ============================== end of clauses for search ============= 0.018/0.018 0.018/0.018 ============================== SEARCH ================================ 0.018/0.018 0.018/0.018 % Starting search at 0.00 seconds. 0.018/0.018 0.018/0.018 given #1 (I,wt=8): 10 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(1)]. 0.018/0.018 0.018/0.018 given #2 (I,wt=12): 11 -->_s0(x,y) | ->_s0(g(x,z,u),g(y,z,u)) # label(congruence). [clausify(2)]. 0.018/0.018 0.018/0.018 given #3 (I,wt=12): 12 -->_s0(x,y) | ->_s0(g(z,x,u),g(z,y,u)) # label(congruence). [clausify(3)]. 0.018/0.018 0.018/0.018 given #4 (I,wt=12): 13 -->_s0(x,y) | ->_s0(g(z,u,x),g(z,u,y)) # label(congruence). [clausify(4)]. 0.018/0.018 0.018/0.018 given #5 (I,wt=10): 14 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(5)]. 0.018/0.018 0.018/0.018 given #6 (I,wt=10): 15 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(6)]. 0.018/0.018 0.018/0.018 given #7 (I,wt=3): 16 ->_s0(a,c) # label(replacement). [assumption]. 0.018/0.018 0.018/0.018 given #8 (I,wt=3): 17 ->_s0(a,d) # label(replacement). [assumption]. 0.018/0.018 0.018/0.018 given #9 (I,wt=3): 18 ->_s0(b,c) # label(replacement). [assumption]. 0.018/0.018 0.018/0.018 given #10 (I,wt=3): 19 ->_s0(b,d) # label(replacement). [assumption]. 0.018/0.018 0.018/0.018 given #11 (I,wt=3): 20 ->_s0(c,e) # label(replacement). [assumption]. 0.018/0.018 0.018/0.018 given #12 (I,wt=3): 21 ->_s0(c,e') # label(replacement). [assumption]. 0.018/0.018 0.018/0.018 given #13 (I,wt=3): 22 ->_s0(c,l) # label(replacement). [assumption]. 0.018/0.018 0.018/0.018 given #14 (I,wt=3): 23 ->_s0(d,m) # label(replacement). [assumption]. 0.018/0.018 0.018/0.018 given #15 (I,wt=6): 25 ->_s0(g(d,x,x),A) # label(replacement). [assumption]. 0.018/0.018 0.018/0.018 given #16 (I,wt=9): 26 ->_s0(h(x,x),g(x,x,f(k))) # label(replacement). [assumption]. 0.018/0.018 0.018/0.018 given #17 (I,wt=3): 27 ->_s0(k,l) # label(replacement). [assumption]. 0.018/0.018 0.018/0.018 given #18 (I,wt=3): 28 ->_s0(k,m) # label(replacement). [assumption]. 0.018/0.018 0.018/0.018 given #19 (I,wt=3): 29 ->*_s0(x,x) # label(reflexivity). [assumption]. 0.018/0.018 0.018/0.018 given #20 (I,wt=9): 30 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(8)]. 0.018/0.018 0.018/0.018 given #21 (I,wt=6): 31 -->*_s0(x,e) | -->*_s0(x,e') # label(goal) # answer(goal). [deny(9)]. 0.018/0.018 0.018/0.018 given #22 (A,wt=7): 32 ->_s0(h(x,a),h(x,c)). [ur(15,a,16,a)]. 0.018/0.018 0.018/0.018 given #23 (F,wt=3): 117 -->*_s0(e,e') # answer(goal). [resolve(31,a,29,a)]. 0.018/0.018 0.018/0.018 given #24 (F,wt=3): 119 -->*_s0(e',e) # answer(goal). [resolve(31,b,29,a)]. 0.018/0.018 0.018/0.018 given #25 (F,wt=3): 128 -->_s0(e,e') # answer(goal). [ur(30,b,29,a,c,117,a)]. 0.018/0.018 0.018/0.018 given #26 (F,wt=3): 130 -->_s0(e',e) # answer(goal). [ur(30,b,29,a,c,119,a)]. 0.018/0.018 0.018/0.018 given #27 (T,wt=3): 104 ->*_s0(k,m). [ur(30,a,28,a,b,29,a)]. 0.018/0.018 0.018/0.018 given #28 (T,wt=3): 105 ->*_s0(k,l). [ur(30,a,27,a,b,29,a)]. 0.018/0.018 0.018/0.018 given #29 (T,wt=3): 108 ->*_s0(d,m). [ur(30,a,23,a,b,29,a)]. 0.018/0.018 0.018/0.018 given #30 (T,wt=3): 109 ->*_s0(c,l). [ur(30,a,22,a,b,29,a)]. 0.018/0.018 0.018/0.018 given #31 (A,wt=7): 33 ->_s0(h(a,x),h(c,x)). [ur(14,a,16,a)]. 0.018/0.018 0.018/0.018 given #32 (F,wt=6): 127 -->_s0(e,x) | -->*_s0(x,e') # answer(goal). [resolve(117,a,30,c)]. 0.018/0.018 0.018/0.018 given #33 (F,wt=6): 129 -->_s0(e',x) | -->*_s0(x,e) # answer(goal). [resolve(119,a,30,c)]. 0.018/0.018 0.018/0.018 given #34 (F,wt=9): 116 -->*_s0(x,e') | -->_s0(x,y) | -->*_s0(y,e) # answer(goal). [resolve(31,a,30,c)]. 0.018/0.018 0.018/0.018 ============================== PROOF ================================= 0.018/0.018 0.018/0.018 % Proof 1 at 0.00 (+ 0.00) seconds: goal. 0.018/0.018 % Length of proof is 10. 0.018/0.018 % Level of proof is 3. 0.018/0.018 % Maximum clause weight is 9.000. 0.018/0.018 % Given clauses 34. 0.018/0.018 0.018/0.018 8 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 0.018/0.018 9 (exists x3 (->*_s0(x3,e) & ->*_s0(x3,e'))) # label(goal) # label(non_clause) # label(goal). [goal]. 0.018/0.018 20 ->_s0(c,e) # label(replacement). [assumption]. 0.018/0.018 21 ->_s0(c,e') # label(replacement). [assumption]. 0.018/0.018 29 ->*_s0(x,x) # label(reflexivity). [assumption]. 0.018/0.018 30 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(8)]. 0.018/0.018 31 -->*_s0(x,e) | -->*_s0(x,e') # label(goal) # answer(goal). [deny(9)]. 0.018/0.018 110 ->*_s0(c,e'). [ur(30,a,21,a,b,29,a)]. 0.018/0.018 116 -->*_s0(x,e') | -->_s0(x,y) | -->*_s0(y,e) # answer(goal). [resolve(31,a,30,c)]. 0.018/0.018 153 $F # answer(goal). [resolve(116,b,20,a),unit_del(a,110),unit_del(b,29)]. 0.018/0.018 0.018/0.018 ============================== end of proof ========================== 0.018/0.018 0.018/0.018 ============================== STATISTICS ============================ 0.018/0.018 0.018/0.018 Given=34. Generated=152. Kept=143. proofs=1. 0.018/0.018 Usable=34. Sos=99. Demods=0. Limbo=9, Disabled=23. Hints=0. 0.018/0.018 Kept_by_rule=0, Deleted_by_rule=0. 0.018/0.018 Forward_subsumed=8. Back_subsumed=1. 0.018/0.018 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 0.018/0.018 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 0.018/0.018 Demod_attempts=0. Demod_rewrites=0. 0.018/0.018 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 0.018/0.018 Nonunit_fsub_feature_tests=29. Nonunit_bsub_feature_tests=46. 0.018/0.018 Megabytes=0.24. 0.018/0.018 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 0.018/0.018 0.018/0.018 ============================== end of statistics ===================== 0.018/0.018 0.018/0.018 ============================== end of search ========================= 0.018/0.018 0.018/0.018 THEOREM PROVED 0.018/0.018 0.018/0.018 Exiting with 1 proof. 0.018/0.018 0.018/0.018 Process 12597 exit (max_proofs) Wed Mar 9 09:20:26 2022 0.018/0.018 0.018/0.018 0.018/0.018 The problem is feasible. 0.018/0.018 0.018/0.018 0.018/0.018 CRule InfChecker Info: 0.018/0.018 g(d,x,x) -> A 0.018/0.018 Rule remains 0.018/0.018 Proof: 0.018/0.018 NO_CONDS 0.018/0.018 0.018/0.018 CRule InfChecker Info: 0.018/0.018 h(x,x) -> g(x,x,f(k)) 0.018/0.018 Rule remains 0.018/0.018 Proof: 0.018/0.018 NO_CONDS 0.018/0.018 0.018/0.018 CRule InfChecker Info: 0.018/0.018 k -> l 0.018/0.018 Rule remains 0.018/0.018 Proof: 0.018/0.018 NO_CONDS 0.018/0.018 0.018/0.018 CRule InfChecker Info: 0.018/0.018 k -> m 0.018/0.018 Rule remains 0.018/0.018 Proof: 0.018/0.018 NO_CONDS 0.018/0.018 0.018/0.018 Problem 1: 0.018/0.018 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.018/0.018 Confluence Problem: 0.018/0.018 (VAR x) 0.018/0.018 (REPLACEMENT-MAP 0.018/0.018 (a) 0.018/0.018 (b) 0.018/0.018 (c) 0.018/0.018 (d) 0.018/0.018 (f 1) 0.018/0.018 (g 1, 2, 3) 0.018/0.018 (h 1, 2) 0.018/0.018 (k) 0.018/0.018 (A) 0.018/0.018 (e) 0.018/0.018 (e') 0.018/0.018 (fSNonEmpty) 0.018/0.018 (l) 0.018/0.018 (m) 0.018/0.018 ) 0.018/0.018 (RULES 0.018/0.018 a -> c 0.018/0.018 a -> d 0.018/0.018 b -> c 0.018/0.018 b -> d 0.018/0.018 c -> e 0.018/0.018 c -> e' 0.018/0.018 c -> l 0.018/0.018 d -> m 0.018/0.018 f(x) -> x | x ->* e, x ->* e' 0.018/0.018 g(d,x,x) -> A 0.018/0.018 h(x,x) -> g(x,x,f(k)) 0.018/0.018 k -> l 0.018/0.018 k -> m 0.018/0.018 ) 0.018/0.018 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.018/0.018 0.018/0.018 Critical Pairs Processor: 0.018/0.018 -> Rules: 0.018/0.018 a -> c 0.018/0.018 a -> d 0.018/0.018 b -> c 0.018/0.018 b -> d 0.018/0.018 c -> e 0.018/0.018 c -> e' 0.018/0.018 c -> l 0.018/0.018 d -> m 0.018/0.018 f(x) -> x | x ->* e, x ->* e' 0.018/0.018 g(d,x,x) -> A 0.018/0.018 h(x,x) -> g(x,x,f(k)) 0.018/0.018 k -> l 0.018/0.018 k -> m 0.018/0.018 -> Vars: 0.018/0.018 "x" 0.018/0.018 0.018/0.018 -> Rlps: 0.018/0.018 crule: a -> c, id: 1, possubterms: a-> [] 0.018/0.018 crule: a -> d, id: 2, possubterms: a-> [] 0.018/0.018 crule: b -> c, id: 3, possubterms: b-> [] 0.018/0.018 crule: b -> d, id: 4, possubterms: b-> [] 0.018/0.018 crule: c -> e, id: 5, possubterms: c-> [] 0.018/0.018 crule: c -> e', id: 6, possubterms: c-> [] 0.018/0.018 crule: c -> l, id: 7, possubterms: c-> [] 0.018/0.018 crule: d -> m, id: 8, possubterms: d-> [] 0.018/0.018 crule: f(x) -> x | x ->* e, x ->* e', id: 9, possubterms: f(x)-> [] 0.018/0.018 crule: g(d,x,x) -> A, id: 10, possubterms: g(d,x,x)-> [], d-> [1] 0.018/0.018 crule: h(x,x) -> g(x,x,f(k)), id: 11, possubterms: h(x,x)-> [] 0.018/0.018 crule: k -> l, id: 12, possubterms: k-> [] 0.018/0.018 crule: k -> m, id: 13, possubterms: k-> [] 0.018/0.018 0.018/0.018 -> Unifications: 0.018/0.018 R2 unifies with R1 at p: [], l: a, lp: a, conds: {}, sig: {}, l': a, r: d, r': c 0.018/0.018 R4 unifies with R3 at p: [], l: b, lp: b, conds: {}, sig: {}, l': b, r: d, r': c 0.018/0.018 R6 unifies with R5 at p: [], l: c, lp: c, conds: {}, sig: {}, l': c, r: e', r': e 0.018/0.018 R7 unifies with R5 at p: [], l: c, lp: c, conds: {}, sig: {}, l': c, r: l, r': e 0.018/0.018 R7 unifies with R6 at p: [], l: c, lp: c, conds: {}, sig: {}, l': c, r: l, r': e' 0.018/0.018 R10 unifies with R8 at p: [1], l: g(d,x,x), lp: d, conds: {}, sig: {}, l': d, r: A, r': m 0.018/0.018 R13 unifies with R12 at p: [], l: k, lp: k, conds: {}, sig: {}, l': k, r: m, r': l 0.018/0.018 0.018/0.018 -> Critical pairs info: 0.018/0.018 => Not trivial, Overlay, NW2, N1 0.018/0.018 => Not trivial, Overlay, NW2, N2 0.018/0.018 => Not trivial, Overlay, NW2, N3 0.018/0.018 => Not trivial, Overlay, NW2, N4 0.018/0.018 => Not trivial, Not overlay, NW2, N5 0.018/0.018 => Not trivial, Overlay, NW0, N6 0.018/0.018 0.018/0.018 -> Problem conclusions: 0.018/0.018 Not left linear, Not right linear, Not linear 0.018/0.018 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 0.018/0.018 CTRS Type: 1 0.018/0.018 Deterministic, Strongly deterministic 0.018/0.018 Oriented CTRS, Properly oriented CTRS, Not join CTRS, Not semiequational CTRS 0.018/0.018 Maybe right-stable CTRS, Not overlay CTRS 0.018/0.018 Maybe normal CTRS, Maybe almost normal CTRS 0.018/0.018 Maybe terminating CTRS, Maybe operational terminating CTRS, Maybe joinable CCPs 0.018/0.018 Maybe level confluent 0.018/0.018 Maybe confluent 0.018/0.018 0.018/0.018 Problem 1: 0.018/0.018 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.018/0.018 Confluence Problem: 0.018/0.018 (VAR x) 0.018/0.018 (REPLACEMENT-MAP 0.018/0.018 (a) 0.018/0.018 (b) 0.018/0.018 (c) 0.018/0.018 (d) 0.018/0.018 (f 1) 0.018/0.018 (g 1, 2, 3) 0.018/0.018 (h 1, 2) 0.018/0.018 (k) 0.018/0.018 (A) 0.018/0.018 (e) 0.018/0.018 (e') 0.018/0.018 (fSNonEmpty) 0.018/0.018 (l) 0.018/0.018 (m) 0.018/0.018 ) 0.018/0.018 (RULES 0.018/0.018 a -> c 0.018/0.018 a -> d 0.018/0.018 b -> c 0.018/0.018 b -> d 0.018/0.018 c -> e 0.018/0.018 c -> e' 0.018/0.018 c -> l 0.018/0.018 d -> m 0.018/0.018 f(x) -> x | x ->* e, x ->* e' 0.018/0.018 g(d,x,x) -> A 0.018/0.018 h(x,x) -> g(x,x,f(k)) 0.018/0.018 k -> l 0.018/0.018 k -> m 0.018/0.018 ) 0.018/0.018 Critical Pairs: 0.018/0.018 => Not trivial, Overlay, NW2, N1 0.018/0.018 => Not trivial, Overlay, NW2, N2 0.018/0.018 => Not trivial, Overlay, NW2, N3 0.018/0.018 => Not trivial, Overlay, NW2, N4 0.018/0.018 => Not trivial, Not overlay, NW2, N5 0.018/0.018 => Not trivial, Overlay, NW0, N6 0.018/0.018 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.018/0.018 0.018/0.018 Conditional Critical Pairs Distributor Processor 0.018/0.018 0.018/0.018 Problem 1: 0.018/0.018 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.018/0.018 Confluence Problem: 0.018/0.018 (VAR x) 0.018/0.018 (REPLACEMENT-MAP 0.018/0.018 (a) 0.018/0.018 (b) 0.018/0.018 (c) 0.018/0.018 (d) 0.018/0.018 (f 1) 0.018/0.018 (g 1, 2, 3) 0.018/0.018 (h 1, 2) 0.018/0.018 (k) 0.018/0.018 (A) 0.018/0.018 (e) 0.018/0.018 (e') 0.018/0.018 (fSNonEmpty) 0.018/0.018 (l) 0.018/0.018 (m) 0.018/0.018 ) 0.018/0.018 (RULES 0.018/0.018 a -> c 0.018/0.018 a -> d 0.018/0.018 b -> c 0.018/0.018 b -> d 0.018/0.018 c -> e 0.018/0.018 c -> e' 0.018/0.018 c -> l 0.018/0.018 d -> m 0.018/0.018 f(x) -> x | x ->* e, x ->* e' 0.018/0.018 g(d,x,x) -> A 0.018/0.018 h(x,x) -> g(x,x,f(k)) 0.018/0.018 k -> l 0.018/0.018 k -> m 0.018/0.018 ) 0.018/0.018 Critical Pairs: 0.018/0.018 => Not trivial, Overlay, NW2, N1 0.018/0.018 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.018/0.018 0.018/0.018 InfChecker Different Ground and Normal No Conditions CCP Terms Processor: 0.018/0.018 Proof: 0.018/0.018 YES 0.018/0.018 0.018/0.018 Problem 1: 0.018/0.018 0.018/0.018 Infeasibility Problem: 0.018/0.018 [(VAR vNonEmpty x vNonEmpty y) 0.018/0.018 (STRATEGY CONTEXTSENSITIVE 0.018/0.018 (a) 0.018/0.018 (b) 0.018/0.018 (c) 0.018/0.018 (d) 0.018/0.018 (f 1) 0.018/0.018 (g 1 2 3) 0.018/0.018 (h 1 2) 0.018/0.018 (k) 0.018/0.018 (A) 0.018/0.018 (e) 0.018/0.018 (e1) 0.018/0.018 (fSNonEmpty) 0.018/0.018 (l) 0.018/0.018 (m) 0.018/0.018 ) 0.018/0.018 (RULES 0.018/0.018 a -> c 0.018/0.018 a -> d 0.018/0.018 b -> c 0.018/0.018 b -> d 0.018/0.018 c -> e 0.018/0.018 c -> e1 0.018/0.018 c -> l 0.018/0.018 d -> m 0.018/0.018 f(x) -> x | x ->* e, x ->* e1 0.018/0.018 g(d,x,x) -> A 0.018/0.018 h(x,x) -> g(x,x,f(k)) 0.018/0.018 k -> l 0.018/0.018 k -> m 0.018/0.018 )] 0.018/0.018 0.018/0.018 Infeasibility Conditions: 0.018/0.018 e -> y 0.018/0.018 0.018/0.018 Problem 1: 0.018/0.018 0.018/0.018 Obtaining a model using Mace4: 0.018/0.018 0.018/0.018 -> Usable Rules: 0.018/0.018 Empty 0.018/0.018 0.018/0.018 -> Mace4 Output: 0.018/0.018 ============================== Mace4 ================================= 0.018/0.018 Mace4 (64) version 2009-11A, November 2009. 0.018/0.018 Process 12639 was started by ubuntu on ubuntu, 0.018/0.018 Wed Mar 9 09:20:26 2022 0.018/0.018 The command was "./mace4 -c -f /tmp/mace412616-2.in". 0.018/0.018 ============================== end of head =========================== 0.018/0.018 0.018/0.018 ============================== INPUT ================================= 0.018/0.018 0.018/0.018 % Reading from file /tmp/mace412616-2.in 0.018/0.018 0.018/0.018 assign(max_seconds,6). 0.018/0.018 0.018/0.018 formulas(assumptions). 0.018/0.018 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence). 0.018/0.018 ->(x1,y) -> ->(g(x1,x2,x3),g(y,x2,x3)) # label(congruence). 0.018/0.018 ->(x2,y) -> ->(g(x1,x2,x3),g(x1,y,x3)) # label(congruence). 0.018/0.018 ->(x3,y) -> ->(g(x1,x2,x3),g(x1,x2,y)) # label(congruence). 0.018/0.018 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence). 0.018/0.018 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence). 0.018/0.018 end_of_list. 0.018/0.018 0.018/0.018 formulas(goals). 0.018/0.018 (exists x3 ->(e,x3)) # label(goal). 0.018/0.018 end_of_list. 0.018/0.018 0.018/0.018 ============================== end of input ========================== 0.018/0.018 0.018/0.018 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.018/0.018 0.018/0.018 % Formulas that are not ordinary clauses: 0.018/0.018 1 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 0.018/0.018 2 ->(x1,y) -> ->(g(x1,x2,x3),g(y,x2,x3)) # label(congruence) # label(non_clause). [assumption]. 0.018/0.018 3 ->(x2,y) -> ->(g(x1,x2,x3),g(x1,y,x3)) # label(congruence) # label(non_clause). [assumption]. 0.018/0.018 4 ->(x3,y) -> ->(g(x1,x2,x3),g(x1,x2,y)) # label(congruence) # label(non_clause). [assumption]. 0.018/0.018 5 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.018/0.018 6 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.018/0.018 7 (exists x3 ->(e,x3)) # label(goal) # label(non_clause) # label(goal). [goal]. 0.018/0.018 0.018/0.018 ============================== end of process non-clausal formulas === 0.018/0.018 0.018/0.018 ============================== CLAUSES FOR SEARCH ==================== 0.018/0.018 0.018/0.018 formulas(mace4_clauses). 0.018/0.018 -->(x,y) | ->(f(x),f(y)) # label(congruence). 0.018/0.018 -->(x,y) | ->(g(x,z,u),g(y,z,u)) # label(congruence). 0.018/0.018 -->(x,y) | ->(g(z,x,u),g(z,y,u)) # label(congruence). 0.018/0.018 -->(x,y) | ->(g(z,u,x),g(z,u,y)) # label(congruence). 0.018/0.018 -->(x,y) | ->(h(x,z),h(y,z)) # label(congruence). 0.018/0.018 -->(x,y) | ->(h(z,x),h(z,y)) # label(congruence). 0.018/0.018 -->(e,x) # label(goal). 0.018/0.018 end_of_list. 0.018/0.018 0.018/0.018 ============================== end of clauses for search ============= 0.018/0.018 0.018/0.018 % There are no natural numbers in the input. 0.018/0.018 0.018/0.018 ============================== DOMAIN SIZE 2 ========================= 0.018/0.018 0.018/0.018 ============================== MODEL ================================= 0.018/0.018 0.018/0.018 interpretation( 2, [number=1, seconds=0], [ 0.018/0.018 0.018/0.018 function(e, [ 0 ]), 0.018/0.018 0.018/0.018 function(f(_), [ 0, 0 ]), 0.018/0.018 0.018/0.018 function(h(_,_), [ 0.018/0.018 0, 0, 0.018/0.018 0, 0 ]), 0.018/0.018 0.018/0.018 function(g(_,_,_), [ 0.018/0.018 0, 0, 0.018/0.018 0, 0, 0.018/0.018 0, 0, 0.018/0.018 0, 0 ]), 0.018/0.018 0.018/0.018 relation(->(_,_), [ 0.018/0.018 0, 0, 0.018/0.018 0, 0 ]) 0.018/0.018 ]). 0.018/0.018 0.018/0.018 ============================== end of model ========================== 0.018/0.018 0.018/0.018 ============================== STATISTICS ============================ 0.018/0.018 0.018/0.018 For domain size 2. 0.018/0.018 0.018/0.018 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 0.018/0.018 Ground clauses: seen=70, kept=70. 0.018/0.018 Selections=15, assignments=15, propagations=4, current_models=1. 0.018/0.018 Rewrite_terms=138, rewrite_bools=72, indexes=2. 0.018/0.018 Rules_from_neg_clauses=0, cross_offs=0. 0.018/0.018 0.018/0.018 ============================== end of statistics ===================== 0.018/0.018 0.018/0.018 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 0.018/0.018 0.018/0.018 Exiting with 1 model. 0.018/0.018 0.018/0.018 Process 12639 exit (max_models) Wed Mar 9 09:20:26 2022 0.018/0.018 The process finished Wed Mar 9 09:20:26 2022 0.018/0.018 0.018/0.018 0.018/0.018 Mace4 cooked interpretation: 0.018/0.018 0.018/0.018 0.018/0.018 0.018/0.018 The problem is infeasible. 0.018/0.018 YES 0.018/0.018 0.018/0.018 Problem 1: 0.018/0.018 0.018/0.018 Infeasibility Problem: 0.018/0.018 [(VAR vNonEmpty x vNonEmpty x) 0.018/0.018 (STRATEGY CONTEXTSENSITIVE 0.018/0.018 (a) 0.018/0.018 (b) 0.018/0.018 (c) 0.018/0.018 (d) 0.018/0.018 (f 1) 0.018/0.018 (g 1 2 3) 0.018/0.018 (h 1 2) 0.018/0.018 (k) 0.018/0.018 (A) 0.018/0.018 (e) 0.018/0.018 (e1) 0.018/0.018 (fSNonEmpty) 0.018/0.018 (l) 0.018/0.018 (m) 0.018/0.018 ) 0.018/0.018 (RULES 0.018/0.018 a -> c 0.018/0.018 a -> d 0.018/0.018 b -> c 0.018/0.018 b -> d 0.018/0.018 c -> e 0.018/0.018 c -> e1 0.018/0.018 c -> l 0.018/0.018 d -> m 0.018/0.018 f(x) -> x | x ->* e, x ->* e1 0.018/0.018 g(d,x,x) -> A 0.018/0.018 h(x,x) -> g(x,x,f(k)) 0.018/0.018 k -> l 0.018/0.018 k -> m 0.018/0.018 )] 0.018/0.018 0.018/0.018 Infeasibility Conditions: 0.018/0.018 l -> x 0.018/0.018 0.018/0.018 Problem 1: 0.018/0.018 0.018/0.018 Obtaining a model using Mace4: 0.018/0.018 0.018/0.018 -> Usable Rules: 0.018/0.018 Empty 0.018/0.018 0.018/0.018 -> Mace4 Output: 0.018/0.018 ============================== Mace4 ================================= 0.018/0.018 Mace4 (64) version 2009-11A, November 2009. 0.018/0.018 Process 12677 was started by ubuntu on ubuntu, 0.018/0.018 Wed Mar 9 09:20:26 2022 0.018/0.018 The command was "./mace4 -c -f /tmp/mace412662-2.in". 0.018/0.018 ============================== end of head =========================== 0.018/0.018 0.018/0.018 ============================== INPUT ================================= 0.018/0.018 0.018/0.018 % Reading from file /tmp/mace412662-2.in 0.018/0.018 0.018/0.018 assign(max_seconds,6). 0.018/0.018 0.018/0.018 formulas(assumptions). 0.018/0.018 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence). 0.018/0.018 ->(x1,y) -> ->(g(x1,x2,x3),g(y,x2,x3)) # label(congruence). 0.018/0.018 ->(x2,y) -> ->(g(x1,x2,x3),g(x1,y,x3)) # label(congruence). 0.018/0.018 ->(x3,y) -> ->(g(x1,x2,x3),g(x1,x2,y)) # label(congruence). 0.018/0.018 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence). 0.018/0.018 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence). 0.018/0.018 end_of_list. 0.018/0.018 0.018/0.018 formulas(goals). 0.018/0.018 (exists x3 ->(l,x3)) # label(goal). 0.018/0.018 end_of_list. 0.018/0.018 0.018/0.018 ============================== end of input ========================== 0.018/0.018 0.018/0.018 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.018/0.018 0.018/0.018 % Formulas that are not ordinary clauses: 0.018/0.018 1 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 0.018/0.018 2 ->(x1,y) -> ->(g(x1,x2,x3),g(y,x2,x3)) # label(congruence) # label(non_clause). [assumption]. 0.018/0.018 3 ->(x2,y) -> ->(g(x1,x2,x3),g(x1,y,x3)) # label(congruence) # label(non_clause). [assumption]. 0.018/0.018 4 ->(x3,y) -> ->(g(x1,x2,x3),g(x1,x2,y)) # label(congruence) # label(non_clause). [assumption]. 0.018/0.018 5 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.018/0.018 6 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.018/0.018 7 (exists x3 ->(l,x3)) # label(goal) # label(non_clause) # label(goal). [goal]. 0.018/0.018 0.018/0.018 ============================== end of process non-clausal formulas === 0.018/0.018 0.018/0.018 ============================== CLAUSES FOR SEARCH ==================== 0.018/0.018 0.018/0.018 formulas(mace4_clauses). 0.018/0.018 -->(x,y) | ->(f(x),f(y)) # label(congruence). 0.018/0.018 -->(x,y) | ->(g(x,z,u),g(y,z,u)) # label(congruence). 0.018/0.018 -->(x,y) | ->(g(z,x,u),g(z,y,u)) # label(congruence). 0.018/0.018 -->(x,y) | ->(g(z,u,x),g(z,u,y)) # label(congruence). 0.018/0.018 -->(x,y) | ->(h(x,z),h(y,z)) # label(congruence). 0.018/0.018 -->(x,y) | ->(h(z,x),h(z,y)) # label(congruence). 0.018/0.018 -->(l,x) # label(goal). 0.018/0.018 end_of_list. 0.018/0.018 0.018/0.018 ============================== end of clauses for search ============= 0.018/0.018 0.018/0.018 % There are no natural numbers in the input. 0.018/0.018 0.018/0.018 ============================== DOMAIN SIZE 2 ========================= 0.018/0.018 0.018/0.018 ============================== MODEL ================================= 0.018/0.018 0.018/0.018 interpretation( 2, [number=1, seconds=0], [ 0.018/0.018 0.018/0.018 function(l, [ 0 ]), 0.018/0.018 0.018/0.018 function(f(_), [ 0, 0 ]), 0.018/0.018 0.018/0.018 function(h(_,_), [ 0.018/0.018 0, 0, 0.018/0.018 0, 0 ]), 0.018/0.018 0.018/0.018 function(g(_,_,_), [ 0.018/0.018 0, 0, 0.018/0.018 0, 0, 0.018/0.018 0, 0, 0.018/0.018 0, 0 ]), 0.018/0.018 0.018/0.018 relation(->(_,_), [ 0.018/0.018 0, 0, 0.018/0.018 0, 0 ]) 0.018/0.018 ]). 0.018/0.018 0.018/0.018 ============================== end of model ========================== 0.018/0.018 0.018/0.018 ============================== STATISTICS ============================ 0.018/0.018 0.018/0.018 For domain size 2. 0.018/0.018 0.018/0.018 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 0.018/0.018 Ground clauses: seen=70, kept=70. 0.018/0.018 Selections=15, assignments=15, propagations=4, current_models=1. 0.018/0.018 Rewrite_terms=138, rewrite_bools=72, indexes=2. 0.018/0.018 Rules_from_neg_clauses=0, cross_offs=0. 0.018/0.018 0.018/0.018 ============================== end of statistics ===================== 0.018/0.018 0.018/0.018 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 0.018/0.018 0.018/0.018 Exiting with 1 model. 0.018/0.018 0.018/0.018 Process 12677 exit (max_models) Wed Mar 9 09:20:26 2022 0.018/0.018 The process finished Wed Mar 9 09:20:26 2022 0.018/0.018 0.018/0.018 0.018/0.018 Mace4 cooked interpretation: 0.018/0.018 0.018/0.018 0.018/0.018 0.018/0.018 The problem is infeasible. 0.018/0.018 0.018/0.018 0.018/0.018 The problem is not joinable. 0.018/0.018 0.12user 0.01system 0:00.18elapsed 78%CPU (0avgtext+0avgdata 12128maxresident)k 0.018/0.018 8inputs+0outputs (0major+9852minor)pagefaults 0swaps