0.047/0.047 NO 0.047/0.047 0.047/0.047 Problem 1: 0.047/0.047 0.047/0.047 0.047/0.047 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.047/0.047 Confluence Problem: 0.047/0.047 (VAR vNonEmpty x y) 0.047/0.047 (REPLACEMENT-MAP 0.047/0.047 (a) 0.047/0.047 (b) 0.047/0.047 (c) 0.047/0.047 (d) 0.047/0.047 (f 1) 0.047/0.047 (g 1, 2, 3) 0.047/0.047 (h 1, 2) 0.047/0.047 (k) 0.047/0.047 (A) 0.047/0.047 (e) 0.047/0.047 (fSNonEmpty) 0.047/0.047 (l) 0.047/0.047 (m) 0.047/0.047 ) 0.047/0.047 (RULES 0.047/0.047 a -> c 0.047/0.047 a -> d 0.047/0.047 b -> c 0.047/0.047 b -> d 0.047/0.047 c -> e 0.047/0.047 c -> l 0.047/0.047 d -> m 0.047/0.047 f(x) -> x | x ->* e 0.047/0.047 g(d,x,y) -> A | y ->* x 0.047/0.047 h(x,y) -> g(x,y,f(k)) | y ->* x 0.047/0.047 k -> l 0.047/0.047 k -> m 0.047/0.047 ) 0.047/0.047 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.047/0.047 0.047/0.047 0.047/0.047 Problem 1: 0.047/0.047 0.047/0.047 Inlining of Conditions Processor [STERN17]: 0.047/0.047 0.047/0.047 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.047/0.047 Confluence Problem: 0.047/0.047 (VAR vNonEmpty x y) 0.047/0.047 (REPLACEMENT-MAP 0.047/0.047 (a) 0.047/0.047 (b) 0.047/0.047 (c) 0.047/0.047 (d) 0.047/0.047 (f 1) 0.047/0.047 (g 1, 2, 3) 0.047/0.047 (h 1, 2) 0.047/0.047 (k) 0.047/0.047 (A) 0.047/0.047 (e) 0.047/0.047 (fSNonEmpty) 0.047/0.047 (l) 0.047/0.047 (m) 0.047/0.047 ) 0.047/0.047 (RULES 0.047/0.047 a -> c 0.047/0.047 a -> d 0.047/0.047 b -> c 0.047/0.047 b -> d 0.047/0.047 c -> e 0.047/0.047 c -> l 0.047/0.047 d -> m 0.047/0.047 f(x) -> x | x ->* e 0.047/0.047 g(d,x,y) -> A | y ->* x 0.047/0.047 h(x,y) -> g(x,y,f(k)) | y ->* x 0.047/0.047 k -> l 0.047/0.047 k -> m 0.047/0.047 ) 0.047/0.047 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.047/0.047 0.047/0.047 0.047/0.047 Problem 1: 0.047/0.047 0.047/0.047 Clean CTRS Processor: 0.047/0.047 0.047/0.047 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.047/0.047 Confluence Problem: 0.047/0.047 (VAR x y) 0.047/0.047 (REPLACEMENT-MAP 0.047/0.047 (a) 0.047/0.047 (b) 0.047/0.047 (c) 0.047/0.047 (d) 0.047/0.047 (f 1) 0.047/0.047 (g 1, 2, 3) 0.047/0.047 (h 1, 2) 0.047/0.047 (k) 0.047/0.047 (A) 0.047/0.047 (e) 0.047/0.047 (fSNonEmpty) 0.047/0.047 (l) 0.047/0.047 (m) 0.047/0.047 ) 0.047/0.047 (RULES 0.047/0.047 a -> c 0.047/0.047 a -> d 0.047/0.047 b -> c 0.047/0.047 b -> d 0.047/0.047 c -> e 0.047/0.047 c -> l 0.047/0.047 d -> m 0.047/0.047 f(x) -> x | x ->* e 0.047/0.047 g(d,x,y) -> A | y ->* x 0.047/0.047 h(x,y) -> g(x,y,f(k)) | y ->* x 0.047/0.047 k -> l 0.047/0.047 k -> m 0.047/0.047 ) 0.047/0.047 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.047/0.047 0.047/0.047 CRule InfChecker Info: 0.047/0.047 a -> c 0.047/0.047 Rule remains 0.047/0.047 Proof: 0.047/0.047 NO_CONDS 0.047/0.047 0.047/0.047 CRule InfChecker Info: 0.047/0.047 a -> d 0.047/0.047 Rule remains 0.047/0.047 Proof: 0.047/0.047 NO_CONDS 0.047/0.047 0.047/0.047 CRule InfChecker Info: 0.047/0.047 b -> c 0.047/0.047 Rule remains 0.047/0.047 Proof: 0.047/0.047 NO_CONDS 0.047/0.047 0.047/0.047 CRule InfChecker Info: 0.047/0.047 b -> d 0.047/0.047 Rule remains 0.047/0.047 Proof: 0.047/0.047 NO_CONDS 0.047/0.047 0.047/0.047 CRule InfChecker Info: 0.047/0.047 c -> e 0.047/0.047 Rule remains 0.047/0.047 Proof: 0.047/0.047 NO_CONDS 0.047/0.047 0.047/0.047 CRule InfChecker Info: 0.047/0.047 c -> l 0.047/0.047 Rule remains 0.047/0.047 Proof: 0.047/0.047 NO_CONDS 0.047/0.047 0.047/0.047 CRule InfChecker Info: 0.047/0.047 d -> m 0.047/0.047 Rule remains 0.047/0.047 Proof: 0.047/0.047 NO_CONDS 0.047/0.047 0.047/0.047 CRule InfChecker Info: 0.047/0.047 f(x) -> x | x ->* e 0.047/0.047 Rule remains 0.047/0.047 Proof: 0.047/0.047 NO 0.047/0.047 0.047/0.047 Problem 1: 0.047/0.047 0.047/0.047 Infeasibility Problem: 0.047/0.047 [(VAR vNonEmpty x y vNonEmpty x) 0.047/0.047 (STRATEGY CONTEXTSENSITIVE 0.047/0.047 (a) 0.047/0.047 (b) 0.047/0.047 (c) 0.047/0.047 (d) 0.047/0.047 (f 1) 0.047/0.047 (g 1 2 3) 0.047/0.047 (h 1 2) 0.047/0.047 (k) 0.047/0.047 (A) 0.047/0.047 (e) 0.047/0.047 (fSNonEmpty) 0.047/0.047 (l) 0.047/0.047 (m) 0.047/0.047 ) 0.047/0.047 (RULES 0.047/0.047 a -> c 0.047/0.047 a -> d 0.047/0.047 b -> c 0.047/0.047 b -> d 0.047/0.047 c -> e 0.047/0.047 c -> l 0.047/0.047 d -> m 0.047/0.047 f(x) -> x | x ->* e 0.047/0.047 g(d,x,y) -> A | y ->* x 0.047/0.047 h(x,y) -> g(x,y,f(k)) | y ->* x 0.047/0.047 k -> l 0.047/0.047 k -> m 0.047/0.047 )] 0.047/0.047 0.047/0.047 Infeasibility Conditions: 0.047/0.047 x ->* e 0.047/0.047 0.047/0.047 Problem 1: 0.047/0.047 0.047/0.047 Obtaining a proof using Prover9: 0.047/0.047 0.047/0.047 -> Prover9 Output: 0.047/0.047 ============================== Prover9 =============================== 0.047/0.047 Prover9 (64) version 2009-11A, November 2009. 0.047/0.047 Process 11704 was started by ubuntu on ubuntu, 0.047/0.047 Wed Mar 9 09:17:41 2022 0.047/0.047 The command was "./prover9 -f /tmp/prover911697-0.in". 0.047/0.047 ============================== end of head =========================== 0.047/0.047 0.047/0.047 ============================== INPUT ================================= 0.047/0.047 0.047/0.047 % Reading from file /tmp/prover911697-0.in 0.047/0.047 0.047/0.047 assign(max_seconds,20). 0.047/0.047 0.047/0.047 formulas(assumptions). 0.047/0.047 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence). 0.047/0.047 ->_s0(x1,y) -> ->_s0(g(x1,x2,x3),g(y,x2,x3)) # label(congruence). 0.047/0.047 ->_s0(x2,y) -> ->_s0(g(x1,x2,x3),g(x1,y,x3)) # label(congruence). 0.047/0.047 ->_s0(x3,y) -> ->_s0(g(x1,x2,x3),g(x1,x2,y)) # label(congruence). 0.047/0.047 ->_s0(x1,y) -> ->_s0(h(x1,x2),h(y,x2)) # label(congruence). 0.047/0.047 ->_s0(x2,y) -> ->_s0(h(x1,x2),h(x1,y)) # label(congruence). 0.047/0.047 ->_s0(a,c) # label(replacement). 0.047/0.047 ->_s0(a,d) # label(replacement). 0.047/0.047 ->_s0(b,c) # label(replacement). 0.047/0.047 ->_s0(b,d) # label(replacement). 0.047/0.047 ->_s0(c,e) # label(replacement). 0.047/0.047 ->_s0(c,l) # label(replacement). 0.047/0.047 ->_s0(d,m) # label(replacement). 0.047/0.047 ->*_s0(x1,e) -> ->_s0(f(x1),x1) # label(replacement). 0.047/0.047 ->*_s0(x2,x1) -> ->_s0(g(d,x1,x2),A) # label(replacement). 0.047/0.047 ->*_s0(x2,x1) -> ->_s0(h(x1,x2),g(x1,x2,f(k))) # label(replacement). 0.047/0.047 ->_s0(k,l) # label(replacement). 0.047/0.047 ->_s0(k,m) # label(replacement). 0.047/0.047 ->*_s0(x,x) # label(reflexivity). 0.047/0.047 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 0.047/0.047 end_of_list. 0.047/0.047 0.047/0.047 formulas(goals). 0.047/0.047 (exists x4 ->*_s0(x4,e)) # label(goal). 0.047/0.047 end_of_list. 0.047/0.047 0.047/0.047 ============================== end of input ========================== 0.047/0.047 0.047/0.047 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.047/0.047 0.047/0.047 % Formulas that are not ordinary clauses: 0.047/0.047 1 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 0.047/0.047 2 ->_s0(x1,y) -> ->_s0(g(x1,x2,x3),g(y,x2,x3)) # label(congruence) # label(non_clause). [assumption]. 0.047/0.047 3 ->_s0(x2,y) -> ->_s0(g(x1,x2,x3),g(x1,y,x3)) # label(congruence) # label(non_clause). [assumption]. 0.047/0.047 4 ->_s0(x3,y) -> ->_s0(g(x1,x2,x3),g(x1,x2,y)) # label(congruence) # label(non_clause). [assumption]. 0.047/0.047 5 ->_s0(x1,y) -> ->_s0(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.047/0.047 6 ->_s0(x2,y) -> ->_s0(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.047/0.047 7 ->*_s0(x1,e) -> ->_s0(f(x1),x1) # label(replacement) # label(non_clause). [assumption]. 0.047/0.047 8 ->*_s0(x2,x1) -> ->_s0(g(d,x1,x2),A) # label(replacement) # label(non_clause). [assumption]. 0.047/0.047 9 ->*_s0(x2,x1) -> ->_s0(h(x1,x2),g(x1,x2,f(k))) # label(replacement) # label(non_clause). [assumption]. 0.047/0.047 10 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 0.047/0.047 11 (exists x4 ->*_s0(x4,e)) # label(goal) # label(non_clause) # label(goal). [goal]. 0.047/0.047 0.047/0.047 ============================== end of process non-clausal formulas === 0.047/0.047 0.047/0.047 ============================== PROCESS INITIAL CLAUSES =============== 0.047/0.047 0.047/0.047 % Clauses before input processing: 0.047/0.047 0.047/0.047 formulas(usable). 0.047/0.047 end_of_list. 0.047/0.047 0.047/0.047 formulas(sos). 0.047/0.047 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(1)]. 0.047/0.047 -->_s0(x,y) | ->_s0(g(x,z,u),g(y,z,u)) # label(congruence). [clausify(2)]. 0.047/0.047 -->_s0(x,y) | ->_s0(g(z,x,u),g(z,y,u)) # label(congruence). [clausify(3)]. 0.047/0.047 -->_s0(x,y) | ->_s0(g(z,u,x),g(z,u,y)) # label(congruence). [clausify(4)]. 0.047/0.047 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(5)]. 0.047/0.047 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(6)]. 0.047/0.047 ->_s0(a,c) # label(replacement). [assumption]. 0.047/0.047 ->_s0(a,d) # label(replacement). [assumption]. 0.047/0.047 ->_s0(b,c) # label(replacement). [assumption]. 0.047/0.047 ->_s0(b,d) # label(replacement). [assumption]. 0.047/0.047 ->_s0(c,e) # label(replacement). [assumption]. 0.047/0.047 ->_s0(c,l) # label(replacement). [assumption]. 0.047/0.047 ->_s0(d,m) # label(replacement). [assumption]. 0.047/0.047 -->*_s0(x,e) | ->_s0(f(x),x) # label(replacement). [clausify(7)]. 0.047/0.047 -->*_s0(x,y) | ->_s0(g(d,y,x),A) # label(replacement). [clausify(8)]. 0.047/0.047 -->*_s0(x,y) | ->_s0(h(y,x),g(y,x,f(k))) # label(replacement). [clausify(9)]. 0.047/0.047 ->_s0(k,l) # label(replacement). [assumption]. 0.047/0.047 ->_s0(k,m) # label(replacement). [assumption]. 0.047/0.047 ->*_s0(x,x) # label(reflexivity). [assumption]. 0.047/0.047 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(10)]. 0.047/0.047 -->*_s0(x,e) # label(goal). [deny(11)]. 0.047/0.047 end_of_list. 0.047/0.047 0.047/0.047 formulas(demodulators). 0.047/0.047 end_of_list. 0.047/0.047 0.047/0.047 ============================== PREDICATE ELIMINATION ================= 0.047/0.047 0.047/0.047 No predicates eliminated. 0.047/0.047 0.047/0.047 ============================== end predicate elimination ============= 0.047/0.047 0.047/0.047 Auto_denials: 0.047/0.047 % copying label goal to answer in negative clause 0.047/0.047 0.047/0.047 Term ordering decisions: 0.047/0.047 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 0.047/0.047 Function symbol precedence: function_order([ c, d, k, e, l, m, a, b, A, h, f, g ]). 0.047/0.047 After inverse_order: (no changes). 0.047/0.047 Unfolding symbols: (none). 0.047/0.047 0.047/0.047 Auto_inference settings: 0.047/0.047 % set(neg_binary_resolution). % (HNE depth_diff=-10) 0.047/0.047 % clear(ordered_res). % (HNE depth_diff=-10) 0.047/0.047 % set(ur_resolution). % (HNE depth_diff=-10) 0.047/0.047 % set(ur_resolution) -> set(pos_ur_resolution). 0.047/0.047 % set(ur_resolution) -> set(neg_ur_resolution). 0.047/0.047 0.047/0.047 Auto_process settings: (no changes). 0.047/0.047 0.047/0.047 kept: 12 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(1)]. 0.047/0.047 kept: 13 -->_s0(x,y) | ->_s0(g(x,z,u),g(y,z,u)) # label(congruence). [clausify(2)]. 0.047/0.047 kept: 14 -->_s0(x,y) | ->_s0(g(z,x,u),g(z,y,u)) # label(congruence). [clausify(3)]. 0.047/0.047 kept: 15 -->_s0(x,y) | ->_s0(g(z,u,x),g(z,u,y)) # label(congruence). [clausify(4)]. 0.047/0.047 kept: 16 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(5)]. 0.047/0.047 kept: 17 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(6)]. 0.047/0.047 kept: 18 ->_s0(a,c) # label(replacement). [assumption]. 0.047/0.047 kept: 19 ->_s0(a,d) # label(replacement). [assumption]. 0.047/0.047 kept: 20 ->_s0(b,c) # label(replacement). [assumption]. 0.047/0.047 kept: 21 ->_s0(b,d) # label(replacement). [assumption]. 0.047/0.047 kept: 22 ->_s0(c,e) # label(replacement). [assumption]. 0.047/0.047 kept: 23 ->_s0(c,l) # label(replacement). [assumption]. 0.047/0.047 kept: 24 ->_s0(d,m) # label(replacement). [assumption]. 0.047/0.047 kept: 25 -->*_s0(x,e) | ->_s0(f(x),x) # label(replacement). [clausify(7)]. 0.047/0.047 kept: 26 -->*_s0(x,y) | ->_s0(g(d,y,x),A) # label(replacement). [clausify(8)]. 0.047/0.047 kept: 27 -->*_s0(x,y) | ->_s0(h(y,x),g(y,x,f(k))) # label(replacement). [clausify(9)]. 0.047/0.047 kept: 28 ->_s0(k,l) # label(replacement). [assumption]. 0.047/0.047 kept: 29 ->_s0(k,m) # label(replacement). [assumption]. 0.047/0.047 kept: 30 ->*_s0(x,x) # label(reflexivity). [assumption]. 0.047/0.047 kept: 31 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(10)]. 0.047/0.047 kept: 32 -->*_s0(x,e) # label(goal) # answer(goal). [deny(11)]. 0.047/0.047 0.047/0.047 ============================== PROOF ================================= 0.047/0.047 0.047/0.047 % Proof 1 at 0.00 (+ 0.00) seconds: goal. 0.047/0.047 % Length of proof is 4. 0.047/0.047 % Level of proof is 2. 0.047/0.047 % Maximum clause weight is 3.000. 0.047/0.047 % Given clauses 0. 0.047/0.047 0.047/0.047 11 (exists x4 ->*_s0(x4,e)) # label(goal) # label(non_clause) # label(goal). [goal]. 0.047/0.047 30 ->*_s0(x,x) # label(reflexivity). [assumption]. 0.047/0.047 32 -->*_s0(x,e) # label(goal) # answer(goal). [deny(11)]. 0.047/0.047 33 $F # answer(goal). [resolve(32,a,30,a)]. 0.047/0.047 0.047/0.047 ============================== end of proof ========================== 0.047/0.047 0.047/0.047 ============================== STATISTICS ============================ 0.047/0.047 0.047/0.047 Given=0. Generated=21. Kept=21. proofs=1. 0.047/0.047 Usable=0. Sos=0. Demods=0. Limbo=20, Disabled=21. Hints=0. 0.047/0.047 Kept_by_rule=0, Deleted_by_rule=0. 0.047/0.047 Forward_subsumed=0. Back_subsumed=0. 0.047/0.047 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 0.047/0.047 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 0.047/0.047 Demod_attempts=0. Demod_rewrites=0. 0.047/0.047 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 0.047/0.047 Nonunit_fsub_feature_tests=4. Nonunit_bsub_feature_tests=0. 0.047/0.047 Megabytes=0.07. 0.047/0.047 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 0.047/0.047 0.047/0.047 ============================== end of statistics ===================== 0.047/0.047 0.047/0.047 ============================== end of search ========================= 0.047/0.047 0.047/0.047 THEOREM PROVED 0.047/0.047 0.047/0.047 Exiting with 1 proof. 0.047/0.047 0.047/0.047 Process 11704 exit (max_proofs) Wed Mar 9 09:17:41 2022 0.047/0.047 0.047/0.047 0.047/0.047 The problem is feasible. 0.047/0.047 0.047/0.047 0.047/0.047 CRule InfChecker Info: 0.047/0.047 g(d,x,y) -> A | y ->* x 0.047/0.047 Rule remains 0.047/0.047 Proof: 0.047/0.047 NO 0.047/0.047 0.047/0.047 Problem 1: 0.047/0.047 0.047/0.047 Infeasibility Problem: 0.047/0.047 [(VAR vNonEmpty x y vNonEmpty x y) 0.047/0.047 (STRATEGY CONTEXTSENSITIVE 0.047/0.047 (a) 0.047/0.047 (b) 0.047/0.047 (c) 0.047/0.047 (d) 0.047/0.047 (f 1) 0.047/0.047 (g 1 2 3) 0.047/0.047 (h 1 2) 0.047/0.047 (k) 0.047/0.047 (A) 0.047/0.047 (e) 0.047/0.047 (fSNonEmpty) 0.047/0.047 (l) 0.047/0.047 (m) 0.047/0.047 ) 0.047/0.047 (RULES 0.047/0.047 a -> c 0.047/0.047 a -> d 0.047/0.047 b -> c 0.047/0.047 b -> d 0.047/0.047 c -> e 0.047/0.047 c -> l 0.047/0.047 d -> m 0.047/0.047 f(x) -> x | x ->* e 0.047/0.047 g(d,x,y) -> A | y ->* x 0.047/0.047 h(x,y) -> g(x,y,f(k)) | y ->* x 0.047/0.047 k -> l 0.047/0.047 k -> m 0.047/0.047 )] 0.047/0.047 0.047/0.047 Infeasibility Conditions: 0.047/0.047 y ->* x 0.047/0.047 0.047/0.047 Problem 1: 0.047/0.047 0.047/0.047 Obtaining a proof using Prover9: 0.047/0.047 0.047/0.047 -> Prover9 Output: 0.047/0.047 ============================== Prover9 =============================== 0.047/0.047 Prover9 (64) version 2009-11A, November 2009. 0.047/0.047 Process 11728 was started by ubuntu on ubuntu, 0.047/0.047 Wed Mar 9 09:17:41 2022 0.047/0.047 The command was "./prover9 -f /tmp/prover911719-0.in". 0.047/0.047 ============================== end of head =========================== 0.047/0.047 0.047/0.047 ============================== INPUT ================================= 0.047/0.047 0.047/0.047 % Reading from file /tmp/prover911719-0.in 0.047/0.047 0.047/0.047 assign(max_seconds,20). 0.047/0.047 0.047/0.047 formulas(assumptions). 0.047/0.047 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence). 0.047/0.047 ->_s0(x1,y) -> ->_s0(g(x1,x2,x3),g(y,x2,x3)) # label(congruence). 0.047/0.047 ->_s0(x2,y) -> ->_s0(g(x1,x2,x3),g(x1,y,x3)) # label(congruence). 0.047/0.047 ->_s0(x3,y) -> ->_s0(g(x1,x2,x3),g(x1,x2,y)) # label(congruence). 0.047/0.047 ->_s0(x1,y) -> ->_s0(h(x1,x2),h(y,x2)) # label(congruence). 0.047/0.047 ->_s0(x2,y) -> ->_s0(h(x1,x2),h(x1,y)) # label(congruence). 0.047/0.047 ->_s0(a,c) # label(replacement). 0.047/0.047 ->_s0(a,d) # label(replacement). 0.047/0.047 ->_s0(b,c) # label(replacement). 0.047/0.047 ->_s0(b,d) # label(replacement). 0.047/0.047 ->_s0(c,e) # label(replacement). 0.047/0.047 ->_s0(c,l) # label(replacement). 0.047/0.047 ->_s0(d,m) # label(replacement). 0.047/0.047 ->*_s0(x1,e) -> ->_s0(f(x1),x1) # label(replacement). 0.047/0.047 ->*_s0(x2,x1) -> ->_s0(g(d,x1,x2),A) # label(replacement). 0.047/0.047 ->*_s0(x2,x1) -> ->_s0(h(x1,x2),g(x1,x2,f(k))) # label(replacement). 0.047/0.047 ->_s0(k,l) # label(replacement). 0.047/0.047 ->_s0(k,m) # label(replacement). 0.047/0.047 ->*_s0(x,x) # label(reflexivity). 0.047/0.047 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 0.047/0.047 end_of_list. 0.047/0.047 0.047/0.047 formulas(goals). 0.047/0.047 (exists x4 exists x5 ->*_s0(x5,x4)) # label(goal). 0.047/0.047 end_of_list. 0.047/0.047 0.047/0.047 ============================== end of input ========================== 0.047/0.047 0.047/0.047 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.047/0.047 0.047/0.047 % Formulas that are not ordinary clauses: 0.047/0.047 1 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 0.047/0.047 2 ->_s0(x1,y) -> ->_s0(g(x1,x2,x3),g(y,x2,x3)) # label(congruence) # label(non_clause). [assumption]. 0.047/0.047 3 ->_s0(x2,y) -> ->_s0(g(x1,x2,x3),g(x1,y,x3)) # label(congruence) # label(non_clause). [assumption]. 0.047/0.047 4 ->_s0(x3,y) -> ->_s0(g(x1,x2,x3),g(x1,x2,y)) # label(congruence) # label(non_clause). [assumption]. 0.047/0.047 5 ->_s0(x1,y) -> ->_s0(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.047/0.047 6 ->_s0(x2,y) -> ->_s0(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.047/0.047 7 ->*_s0(x1,e) -> ->_s0(f(x1),x1) # label(replacement) # label(non_clause). [assumption]. 0.047/0.047 8 ->*_s0(x2,x1) -> ->_s0(g(d,x1,x2),A) # label(replacement) # label(non_clause). [assumption]. 0.047/0.047 9 ->*_s0(x2,x1) -> ->_s0(h(x1,x2),g(x1,x2,f(k))) # label(replacement) # label(non_clause). [assumption]. 0.047/0.047 10 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 0.047/0.047 11 (exists x4 exists x5 ->*_s0(x5,x4)) # label(goal) # label(non_clause) # label(goal). [goal]. 0.047/0.047 0.047/0.047 ============================== end of process non-clausal formulas === 0.047/0.047 0.047/0.047 ============================== PROCESS INITIAL CLAUSES =============== 0.047/0.047 0.047/0.047 % Clauses before input processing: 0.047/0.047 0.047/0.047 formulas(usable). 0.047/0.047 end_of_list. 0.047/0.047 0.047/0.047 formulas(sos). 0.047/0.047 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(1)]. 0.047/0.047 -->_s0(x,y) | ->_s0(g(x,z,u),g(y,z,u)) # label(congruence). [clausify(2)]. 0.047/0.047 -->_s0(x,y) | ->_s0(g(z,x,u),g(z,y,u)) # label(congruence). [clausify(3)]. 0.047/0.047 -->_s0(x,y) | ->_s0(g(z,u,x),g(z,u,y)) # label(congruence). [clausify(4)]. 0.047/0.047 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(5)]. 0.047/0.047 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(6)]. 0.047/0.047 ->_s0(a,c) # label(replacement). [assumption]. 0.047/0.047 ->_s0(a,d) # label(replacement). [assumption]. 0.047/0.047 ->_s0(b,c) # label(replacement). [assumption]. 0.047/0.047 ->_s0(b,d) # label(replacement). [assumption]. 0.047/0.047 ->_s0(c,e) # label(replacement). [assumption]. 0.047/0.047 ->_s0(c,l) # label(replacement). [assumption]. 0.047/0.047 ->_s0(d,m) # label(replacement). [assumption]. 0.047/0.047 -->*_s0(x,e) | ->_s0(f(x),x) # label(replacement). [clausify(7)]. 0.047/0.047 -->*_s0(x,y) | ->_s0(g(d,y,x),A) # label(replacement). [clausify(8)]. 0.047/0.047 -->*_s0(x,y) | ->_s0(h(y,x),g(y,x,f(k))) # label(replacement). [clausify(9)]. 0.047/0.047 ->_s0(k,l) # label(replacement). [assumption]. 0.047/0.047 ->_s0(k,m) # label(replacement). [assumption]. 0.047/0.047 ->*_s0(x,x) # label(reflexivity). [assumption]. 0.047/0.047 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(10)]. 0.047/0.047 -->*_s0(x,y) # label(goal). [deny(11)]. 0.047/0.047 end_of_list. 0.047/0.047 0.047/0.047 formulas(demodulators). 0.047/0.047 end_of_list. 0.047/0.047 0.047/0.047 ============================== PREDICATE ELIMINATION ================= 0.047/0.047 0.047/0.047 No predicates eliminated. 0.047/0.047 0.047/0.047 ============================== end predicate elimination ============= 0.047/0.047 0.047/0.047 Auto_denials: 0.047/0.047 % copying label goal to answer in negative clause 0.047/0.047 0.047/0.047 Term ordering decisions: 0.047/0.047 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 0.047/0.047 Function symbol precedence: function_order([ c, d, k, e, l, m, a, b, A, h, f, g ]). 0.047/0.047 After inverse_order: (no changes). 0.047/0.047 Unfolding symbols: (none). 0.047/0.047 0.047/0.047 Auto_inference settings: 0.047/0.047 % set(neg_binary_resolution). % (HNE depth_diff=-10) 0.047/0.047 % clear(ordered_res). % (HNE depth_diff=-10) 0.047/0.047 % set(ur_resolution). % (HNE depth_diff=-10) 0.047/0.047 % set(ur_resolution) -> set(pos_ur_resolution). 0.047/0.047 % set(ur_resolution) -> set(neg_ur_resolution). 0.047/0.047 0.047/0.047 Auto_process settings: (no changes). 0.047/0.047 0.047/0.047 kept: 12 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(1)]. 0.047/0.047 kept: 13 -->_s0(x,y) | ->_s0(g(x,z,u),g(y,z,u)) # label(congruence). [clausify(2)]. 0.047/0.047 kept: 14 -->_s0(x,y) | ->_s0(g(z,x,u),g(z,y,u)) # label(congruence). [clausify(3)]. 0.047/0.047 kept: 15 -->_s0(x,y) | ->_s0(g(z,u,x),g(z,u,y)) # label(congruence). [clausify(4)]. 0.047/0.047 kept: 16 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(5)]. 0.047/0.047 kept: 17 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(6)]. 0.047/0.047 kept: 18 ->_s0(a,c) # label(replacement). [assumption]. 0.047/0.047 kept: 19 ->_s0(a,d) # label(replacement). [assumption]. 0.047/0.047 kept: 20 ->_s0(b,c) # label(replacement). [assumption]. 0.047/0.047 kept: 21 ->_s0(b,d) # label(replacement). [assumption]. 0.047/0.047 kept: 22 ->_s0(c,e) # label(replacement). [assumption]. 0.047/0.047 kept: 23 ->_s0(c,l) # label(replacement). [assumption]. 0.047/0.047 kept: 24 ->_s0(d,m) # label(replacement). [assumption]. 0.047/0.047 kept: 25 -->*_s0(x,e) | ->_s0(f(x),x) # label(replacement). [clausify(7)]. 0.047/0.047 kept: 26 -->*_s0(x,y) | ->_s0(g(d,y,x),A) # label(replacement). [clausify(8)]. 0.047/0.047 kept: 27 -->*_s0(x,y) | ->_s0(h(y,x),g(y,x,f(k))) # label(replacement). [clausify(9)]. 0.047/0.047 kept: 28 ->_s0(k,l) # label(replacement). [assumption]. 0.047/0.047 kept: 29 ->_s0(k,m) # label(replacement). [assumption]. 0.047/0.047 kept: 30 ->*_s0(x,x) # label(reflexivity). [assumption]. 0.047/0.047 kept: 31 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(10)]. 0.047/0.047 kept: 32 -->*_s0(x,y) # label(goal) # answer(goal). [deny(11)]. 0.047/0.047 0.047/0.047 ============================== PROOF ================================= 0.047/0.047 0.047/0.047 % Proof 1 at 0.00 (+ 0.00) seconds: goal. 0.047/0.047 % Length of proof is 4. 0.047/0.047 % Level of proof is 2. 0.047/0.047 % Maximum clause weight is 3.000. 0.047/0.047 % Given clauses 0. 0.047/0.047 0.047/0.047 11 (exists x4 exists x5 ->*_s0(x5,x4)) # label(goal) # label(non_clause) # label(goal). [goal]. 0.047/0.047 30 ->*_s0(x,x) # label(reflexivity). [assumption]. 0.047/0.047 32 -->*_s0(x,y) # label(goal) # answer(goal). [deny(11)]. 0.047/0.047 33 $F # answer(goal). [resolve(32,a,30,a)]. 0.047/0.047 0.047/0.047 ============================== end of proof ========================== 0.047/0.047 0.047/0.047 ============================== STATISTICS ============================ 0.047/0.047 0.047/0.047 Given=0. Generated=21. Kept=21. proofs=1. 0.047/0.047 Usable=0. Sos=0. Demods=0. Limbo=20, Disabled=21. Hints=0. 0.047/0.047 Kept_by_rule=0, Deleted_by_rule=0. 0.047/0.047 Forward_subsumed=0. Back_subsumed=0. 0.047/0.047 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 0.047/0.047 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 0.047/0.047 Demod_attempts=0. Demod_rewrites=0. 0.047/0.047 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 0.047/0.047 Nonunit_fsub_feature_tests=4. Nonunit_bsub_feature_tests=0. 0.047/0.047 Megabytes=0.07. 0.047/0.047 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 0.047/0.047 0.047/0.047 ============================== end of statistics ===================== 0.047/0.047 0.047/0.047 ============================== end of search ========================= 0.047/0.047 0.047/0.047 THEOREM PROVED 0.047/0.047 0.047/0.047 Exiting with 1 proof. 0.047/0.047 0.047/0.047 Process 11728 exit (max_proofs) Wed Mar 9 09:17:41 2022 0.047/0.047 0.047/0.047 0.047/0.047 The problem is feasible. 0.047/0.047 0.047/0.047 0.047/0.047 CRule InfChecker Info: 0.047/0.047 h(x,y) -> g(x,y,f(k)) | y ->* x 0.047/0.047 Rule remains 0.047/0.047 Proof: 0.047/0.047 NO 0.047/0.047 0.047/0.047 Problem 1: 0.047/0.047 0.047/0.047 Infeasibility Problem: 0.047/0.047 [(VAR vNonEmpty x y vNonEmpty x y) 0.047/0.047 (STRATEGY CONTEXTSENSITIVE 0.047/0.047 (a) 0.047/0.047 (b) 0.047/0.047 (c) 0.047/0.047 (d) 0.047/0.047 (f 1) 0.047/0.047 (g 1 2 3) 0.047/0.047 (h 1 2) 0.047/0.047 (k) 0.047/0.047 (A) 0.047/0.047 (e) 0.047/0.047 (fSNonEmpty) 0.047/0.047 (l) 0.047/0.047 (m) 0.047/0.047 ) 0.047/0.047 (RULES 0.047/0.047 a -> c 0.047/0.047 a -> d 0.047/0.047 b -> c 0.047/0.047 b -> d 0.047/0.047 c -> e 0.047/0.047 c -> l 0.047/0.047 d -> m 0.047/0.047 f(x) -> x | x ->* e 0.047/0.047 g(d,x,y) -> A | y ->* x 0.047/0.047 h(x,y) -> g(x,y,f(k)) | y ->* x 0.047/0.047 k -> l 0.047/0.047 k -> m 0.047/0.047 )] 0.047/0.047 0.047/0.047 Infeasibility Conditions: 0.047/0.047 y ->* x 0.047/0.047 0.047/0.047 Problem 1: 0.047/0.047 0.047/0.047 Obtaining a proof using Prover9: 0.047/0.047 0.047/0.047 -> Prover9 Output: 0.047/0.047 ============================== Prover9 =============================== 0.047/0.047 Prover9 (64) version 2009-11A, November 2009. 0.047/0.047 Process 11750 was started by ubuntu on ubuntu, 0.047/0.047 Wed Mar 9 09:17:41 2022 0.047/0.047 The command was "./prover9 -f /tmp/prover911743-0.in". 0.047/0.047 ============================== end of head =========================== 0.047/0.047 0.047/0.047 ============================== INPUT ================================= 0.047/0.047 0.047/0.047 % Reading from file /tmp/prover911743-0.in 0.047/0.047 0.047/0.047 assign(max_seconds,20). 0.047/0.047 0.047/0.047 formulas(assumptions). 0.047/0.047 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence). 0.047/0.047 ->_s0(x1,y) -> ->_s0(g(x1,x2,x3),g(y,x2,x3)) # label(congruence). 0.047/0.047 ->_s0(x2,y) -> ->_s0(g(x1,x2,x3),g(x1,y,x3)) # label(congruence). 0.047/0.047 ->_s0(x3,y) -> ->_s0(g(x1,x2,x3),g(x1,x2,y)) # label(congruence). 0.047/0.047 ->_s0(x1,y) -> ->_s0(h(x1,x2),h(y,x2)) # label(congruence). 0.047/0.047 ->_s0(x2,y) -> ->_s0(h(x1,x2),h(x1,y)) # label(congruence). 0.047/0.047 ->_s0(a,c) # label(replacement). 0.047/0.047 ->_s0(a,d) # label(replacement). 0.047/0.047 ->_s0(b,c) # label(replacement). 0.047/0.047 ->_s0(b,d) # label(replacement). 0.047/0.047 ->_s0(c,e) # label(replacement). 0.047/0.047 ->_s0(c,l) # label(replacement). 0.047/0.047 ->_s0(d,m) # label(replacement). 0.047/0.047 ->*_s0(x1,e) -> ->_s0(f(x1),x1) # label(replacement). 0.047/0.047 ->*_s0(x2,x1) -> ->_s0(g(d,x1,x2),A) # label(replacement). 0.047/0.047 ->*_s0(x2,x1) -> ->_s0(h(x1,x2),g(x1,x2,f(k))) # label(replacement). 0.047/0.047 ->_s0(k,l) # label(replacement). 0.047/0.047 ->_s0(k,m) # label(replacement). 0.047/0.047 ->*_s0(x,x) # label(reflexivity). 0.047/0.047 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 0.047/0.047 end_of_list. 0.047/0.047 0.047/0.047 formulas(goals). 0.047/0.047 (exists x4 exists x5 ->*_s0(x5,x4)) # label(goal). 0.047/0.047 end_of_list. 0.047/0.047 0.047/0.047 ============================== end of input ========================== 0.047/0.047 0.047/0.047 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.047/0.047 0.047/0.047 % Formulas that are not ordinary clauses: 0.047/0.047 1 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 0.047/0.047 2 ->_s0(x1,y) -> ->_s0(g(x1,x2,x3),g(y,x2,x3)) # label(congruence) # label(non_clause). [assumption]. 0.047/0.047 3 ->_s0(x2,y) -> ->_s0(g(x1,x2,x3),g(x1,y,x3)) # label(congruence) # label(non_clause). [assumption]. 0.047/0.047 4 ->_s0(x3,y) -> ->_s0(g(x1,x2,x3),g(x1,x2,y)) # label(congruence) # label(non_clause). [assumption]. 0.047/0.047 5 ->_s0(x1,y) -> ->_s0(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.047/0.047 6 ->_s0(x2,y) -> ->_s0(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.047/0.047 7 ->*_s0(x1,e) -> ->_s0(f(x1),x1) # label(replacement) # label(non_clause). [assumption]. 0.047/0.047 8 ->*_s0(x2,x1) -> ->_s0(g(d,x1,x2),A) # label(replacement) # label(non_clause). [assumption]. 0.047/0.047 9 ->*_s0(x2,x1) -> ->_s0(h(x1,x2),g(x1,x2,f(k))) # label(replacement) # label(non_clause). [assumption]. 0.047/0.047 10 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 0.047/0.047 11 (exists x4 exists x5 ->*_s0(x5,x4)) # label(goal) # label(non_clause) # label(goal). [goal]. 0.047/0.047 0.047/0.047 ============================== end of process non-clausal formulas === 0.047/0.047 0.047/0.047 ============================== PROCESS INITIAL CLAUSES =============== 0.047/0.047 0.047/0.047 % Clauses before input processing: 0.047/0.047 0.047/0.047 formulas(usable). 0.047/0.047 end_of_list. 0.047/0.047 0.047/0.047 formulas(sos). 0.047/0.047 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(1)]. 0.047/0.047 -->_s0(x,y) | ->_s0(g(x,z,u),g(y,z,u)) # label(congruence). [clausify(2)]. 0.047/0.047 -->_s0(x,y) | ->_s0(g(z,x,u),g(z,y,u)) # label(congruence). [clausify(3)]. 0.047/0.047 -->_s0(x,y) | ->_s0(g(z,u,x),g(z,u,y)) # label(congruence). [clausify(4)]. 0.047/0.047 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(5)]. 0.047/0.047 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(6)]. 0.047/0.047 ->_s0(a,c) # label(replacement). [assumption]. 0.047/0.047 ->_s0(a,d) # label(replacement). [assumption]. 0.047/0.047 ->_s0(b,c) # label(replacement). [assumption]. 0.047/0.047 ->_s0(b,d) # label(replacement). [assumption]. 0.047/0.047 ->_s0(c,e) # label(replacement). [assumption]. 0.047/0.047 ->_s0(c,l) # label(replacement). [assumption]. 0.047/0.047 ->_s0(d,m) # label(replacement). [assumption]. 0.047/0.047 -->*_s0(x,e) | ->_s0(f(x),x) # label(replacement). [clausify(7)]. 0.047/0.047 -->*_s0(x,y) | ->_s0(g(d,y,x),A) # label(replacement). [clausify(8)]. 0.047/0.047 -->*_s0(x,y) | ->_s0(h(y,x),g(y,x,f(k))) # label(replacement). [clausify(9)]. 0.047/0.047 ->_s0(k,l) # label(replacement). [assumption]. 0.047/0.047 ->_s0(k,m) # label(replacement). [assumption]. 0.047/0.047 ->*_s0(x,x) # label(reflexivity). [assumption]. 0.047/0.047 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(10)]. 0.047/0.047 -->*_s0(x,y) # label(goal). [deny(11)]. 0.047/0.047 end_of_list. 0.047/0.047 0.047/0.047 formulas(demodulators). 0.047/0.047 end_of_list. 0.047/0.047 0.047/0.047 ============================== PREDICATE ELIMINATION ================= 0.047/0.047 0.047/0.047 No predicates eliminated. 0.047/0.047 0.047/0.047 ============================== end predicate elimination ============= 0.047/0.047 0.047/0.047 Auto_denials: 0.047/0.047 % copying label goal to answer in negative clause 0.047/0.047 0.047/0.047 Term ordering decisions: 0.047/0.047 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 0.047/0.047 Function symbol precedence: function_order([ c, d, k, e, l, m, a, b, A, h, f, g ]). 0.047/0.047 After inverse_order: (no changes). 0.047/0.047 Unfolding symbols: (none). 0.047/0.047 0.047/0.047 Auto_inference settings: 0.047/0.047 % set(neg_binary_resolution). % (HNE depth_diff=-10) 0.047/0.047 % clear(ordered_res). % (HNE depth_diff=-10) 0.047/0.047 % set(ur_resolution). % (HNE depth_diff=-10) 0.047/0.047 % set(ur_resolution) -> set(pos_ur_resolution). 0.047/0.047 % set(ur_resolution) -> set(neg_ur_resolution). 0.047/0.047 0.047/0.047 Auto_process settings: (no changes). 0.047/0.047 0.047/0.047 kept: 12 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(1)]. 0.047/0.047 kept: 13 -->_s0(x,y) | ->_s0(g(x,z,u),g(y,z,u)) # label(congruence). [clausify(2)]. 0.047/0.047 kept: 14 -->_s0(x,y) | ->_s0(g(z,x,u),g(z,y,u)) # label(congruence). [clausify(3)]. 0.047/0.047 kept: 15 -->_s0(x,y) | ->_s0(g(z,u,x),g(z,u,y)) # label(congruence). [clausify(4)]. 0.047/0.047 kept: 16 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(5)]. 0.047/0.047 kept: 17 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(6)]. 0.047/0.047 kept: 18 ->_s0(a,c) # label(replacement). [assumption]. 0.047/0.047 kept: 19 ->_s0(a,d) # label(replacement). [assumption]. 0.047/0.047 kept: 20 ->_s0(b,c) # label(replacement). [assumption]. 0.047/0.047 kept: 21 ->_s0(b,d) # label(replacement). [assumption]. 0.047/0.047 kept: 22 ->_s0(c,e) # label(replacement). [assumption]. 0.047/0.047 kept: 23 ->_s0(c,l) # label(replacement). [assumption]. 0.047/0.047 kept: 24 ->_s0(d,m) # label(replacement). [assumption]. 0.047/0.047 kept: 25 -->*_s0(x,e) | ->_s0(f(x),x) # label(replacement). [clausify(7)]. 0.047/0.047 kept: 26 -->*_s0(x,y) | ->_s0(g(d,y,x),A) # label(replacement). [clausify(8)]. 0.047/0.047 kept: 27 -->*_s0(x,y) | ->_s0(h(y,x),g(y,x,f(k))) # label(replacement). [clausify(9)]. 0.047/0.047 kept: 28 ->_s0(k,l) # label(replacement). [assumption]. 0.047/0.047 kept: 29 ->_s0(k,m) # label(replacement). [assumption]. 0.047/0.047 kept: 30 ->*_s0(x,x) # label(reflexivity). [assumption]. 0.047/0.047 kept: 31 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(10)]. 0.047/0.047 kept: 32 -->*_s0(x,y) # label(goal) # answer(goal). [deny(11)]. 0.047/0.047 0.047/0.047 ============================== PROOF ================================= 0.047/0.047 0.047/0.047 % Proof 1 at 0.00 (+ 0.00) seconds: goal. 0.047/0.047 % Length of proof is 4. 0.047/0.047 % Level of proof is 2. 0.047/0.047 % Maximum clause weight is 3.000. 0.047/0.047 % Given clauses 0. 0.047/0.047 0.047/0.047 11 (exists x4 exists x5 ->*_s0(x5,x4)) # label(goal) # label(non_clause) # label(goal). [goal]. 0.047/0.047 30 ->*_s0(x,x) # label(reflexivity). [assumption]. 0.047/0.047 32 -->*_s0(x,y) # label(goal) # answer(goal). [deny(11)]. 0.047/0.047 33 $F # answer(goal). [resolve(32,a,30,a)]. 0.047/0.047 0.047/0.047 ============================== end of proof ========================== 0.047/0.047 0.047/0.047 ============================== STATISTICS ============================ 0.047/0.047 0.047/0.047 Given=0. Generated=21. Kept=21. proofs=1. 0.047/0.047 Usable=0. Sos=0. Demods=0. Limbo=20, Disabled=21. Hints=0. 0.047/0.047 Kept_by_rule=0, Deleted_by_rule=0. 0.047/0.047 Forward_subsumed=0. Back_subsumed=0. 0.047/0.047 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 0.047/0.047 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 0.047/0.047 Demod_attempts=0. Demod_rewrites=0. 0.047/0.047 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 0.047/0.047 Nonunit_fsub_feature_tests=4. Nonunit_bsub_feature_tests=0. 0.047/0.047 Megabytes=0.07. 0.047/0.047 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 0.047/0.047 0.047/0.047 ============================== end of statistics ===================== 0.047/0.047 0.047/0.047 ============================== end of search ========================= 0.047/0.047 0.047/0.047 THEOREM PROVED 0.047/0.047 0.047/0.047 Exiting with 1 proof. 0.047/0.047 0.047/0.047 Process 11750 exit (max_proofs) Wed Mar 9 09:17:41 2022 0.047/0.047 0.047/0.047 0.047/0.047 The problem is feasible. 0.047/0.047 0.047/0.047 0.047/0.047 CRule InfChecker Info: 0.047/0.047 k -> l 0.047/0.047 Rule remains 0.047/0.047 Proof: 0.047/0.047 NO_CONDS 0.047/0.047 0.047/0.047 CRule InfChecker Info: 0.047/0.047 k -> m 0.047/0.047 Rule remains 0.047/0.047 Proof: 0.047/0.047 NO_CONDS 0.047/0.047 0.047/0.047 Problem 1: 0.047/0.047 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.047/0.047 Confluence Problem: 0.047/0.047 (VAR x y) 0.047/0.047 (REPLACEMENT-MAP 0.047/0.047 (a) 0.047/0.047 (b) 0.047/0.047 (c) 0.047/0.047 (d) 0.047/0.047 (f 1) 0.047/0.047 (g 1, 2, 3) 0.047/0.047 (h 1, 2) 0.047/0.047 (k) 0.047/0.047 (A) 0.047/0.047 (e) 0.047/0.047 (fSNonEmpty) 0.047/0.047 (l) 0.047/0.047 (m) 0.047/0.047 ) 0.047/0.047 (RULES 0.047/0.047 a -> c 0.047/0.047 a -> d 0.047/0.047 b -> c 0.047/0.047 b -> d 0.047/0.047 c -> e 0.047/0.047 c -> l 0.047/0.047 d -> m 0.047/0.047 f(x) -> x | x ->* e 0.047/0.047 g(d,x,y) -> A | y ->* x 0.047/0.047 h(x,y) -> g(x,y,f(k)) | y ->* x 0.047/0.047 k -> l 0.047/0.047 k -> m 0.047/0.047 ) 0.047/0.047 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.047/0.047 0.047/0.047 Critical Pairs Processor: 0.047/0.047 -> Rules: 0.047/0.047 a -> c 0.047/0.047 a -> d 0.047/0.047 b -> c 0.047/0.047 b -> d 0.047/0.047 c -> e 0.047/0.047 c -> l 0.047/0.047 d -> m 0.047/0.047 f(x) -> x | x ->* e 0.047/0.047 g(d,x,y) -> A | y ->* x 0.047/0.047 h(x,y) -> g(x,y,f(k)) | y ->* x 0.047/0.047 k -> l 0.047/0.047 k -> m 0.047/0.047 -> Vars: 0.047/0.047 "x", "y" 0.047/0.047 0.047/0.047 -> Rlps: 0.047/0.047 crule: a -> c, id: 1, possubterms: a-> [] 0.047/0.047 crule: a -> d, id: 2, possubterms: a-> [] 0.047/0.047 crule: b -> c, id: 3, possubterms: b-> [] 0.047/0.047 crule: b -> d, id: 4, possubterms: b-> [] 0.047/0.047 crule: c -> e, id: 5, possubterms: c-> [] 0.047/0.047 crule: c -> l, id: 6, possubterms: c-> [] 0.047/0.047 crule: d -> m, id: 7, possubterms: d-> [] 0.047/0.047 crule: f(x) -> x | x ->* e, id: 8, possubterms: f(x)-> [] 0.047/0.047 crule: g(d,x,y) -> A | y ->* x, id: 9, possubterms: g(d,x,y)-> [], d-> [1] 0.047/0.047 crule: h(x,y) -> g(x,y,f(k)) | y ->* x, id: 10, possubterms: h(x,y)-> [] 0.047/0.047 crule: k -> l, id: 11, possubterms: k-> [] 0.047/0.047 crule: k -> m, id: 12, possubterms: k-> [] 0.047/0.047 0.047/0.047 -> Unifications: 0.047/0.047 R2 unifies with R1 at p: [], l: a, lp: a, conds: {}, sig: {}, l': a, r: d, r': c 0.047/0.047 R4 unifies with R3 at p: [], l: b, lp: b, conds: {}, sig: {}, l': b, r: d, r': c 0.047/0.047 R6 unifies with R5 at p: [], l: c, lp: c, conds: {}, sig: {}, l': c, r: l, r': e 0.047/0.047 R9 unifies with R7 at p: [1], l: g(d,x,y), lp: d, conds: {y ->* x}, sig: {}, l': d, r: A, r': m 0.047/0.047 R12 unifies with R11 at p: [], l: k, lp: k, conds: {}, sig: {}, l': k, r: m, r': l 0.047/0.047 0.047/0.047 -> Critical pairs info: 0.047/0.047 => Not trivial, Overlay, NW2, N1 0.047/0.047 | y ->* x => Not trivial, Not overlay, NW2, N2 0.047/0.047 => Not trivial, Overlay, NW2, N3 0.047/0.047 => Not trivial, Overlay, NW0, N4 0.047/0.047 0.047/0.047 -> Problem conclusions: 0.047/0.047 Left linear, Right linear, Linear 0.047/0.047 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 0.047/0.047 CTRS Type: 1 0.047/0.047 Deterministic, Maybe strongly deterministic 0.047/0.047 Oriented CTRS, Properly oriented CTRS, Not join CTRS, Not semiequational CTRS 0.047/0.047 Maybe right-stable CTRS, Not overlay CTRS 0.047/0.047 Maybe normal CTRS, Maybe almost normal CTRS 0.047/0.047 Maybe terminating CTRS, Maybe operational terminating CTRS, Maybe joinable CCPs 0.047/0.047 Maybe level confluent 0.047/0.047 Maybe confluent 0.047/0.047 0.047/0.047 Problem 1: 0.047/0.047 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.047/0.047 Confluence Problem: 0.047/0.047 (VAR x y) 0.047/0.047 (REPLACEMENT-MAP 0.047/0.047 (a) 0.047/0.047 (b) 0.047/0.047 (c) 0.047/0.047 (d) 0.047/0.047 (f 1) 0.047/0.047 (g 1, 2, 3) 0.047/0.047 (h 1, 2) 0.047/0.047 (k) 0.047/0.047 (A) 0.047/0.047 (e) 0.047/0.047 (fSNonEmpty) 0.047/0.047 (l) 0.047/0.047 (m) 0.047/0.047 ) 0.047/0.047 (RULES 0.047/0.047 a -> c 0.047/0.047 a -> d 0.047/0.047 b -> c 0.047/0.047 b -> d 0.047/0.047 c -> e 0.047/0.047 c -> l 0.047/0.047 d -> m 0.047/0.047 f(x) -> x | x ->* e 0.047/0.047 g(d,x,y) -> A | y ->* x 0.047/0.047 h(x,y) -> g(x,y,f(k)) | y ->* x 0.047/0.047 k -> l 0.047/0.047 k -> m 0.047/0.047 ) 0.047/0.047 Critical Pairs: 0.047/0.047 => Not trivial, Overlay, NW2, N1 0.047/0.047 | y ->* x => Not trivial, Not overlay, NW2, N2 0.047/0.047 => Not trivial, Overlay, NW2, N3 0.047/0.047 => Not trivial, Overlay, NW0, N4 0.047/0.047 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.047/0.047 0.047/0.047 Conditional Critical Pairs Distributor Processor 0.047/0.047 0.047/0.047 Problem 1: 0.047/0.047 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.047/0.047 Confluence Problem: 0.047/0.047 (VAR x y) 0.047/0.047 (REPLACEMENT-MAP 0.047/0.047 (a) 0.047/0.047 (b) 0.047/0.047 (c) 0.047/0.047 (d) 0.047/0.047 (f 1) 0.047/0.047 (g 1, 2, 3) 0.047/0.047 (h 1, 2) 0.047/0.047 (k) 0.047/0.047 (A) 0.047/0.047 (e) 0.047/0.047 (fSNonEmpty) 0.047/0.047 (l) 0.047/0.047 (m) 0.047/0.047 ) 0.047/0.047 (RULES 0.047/0.047 a -> c 0.047/0.047 a -> d 0.047/0.047 b -> c 0.047/0.047 b -> d 0.047/0.047 c -> e 0.047/0.047 c -> l 0.047/0.047 d -> m 0.047/0.047 f(x) -> x | x ->* e 0.047/0.047 g(d,x,y) -> A | y ->* x 0.047/0.047 h(x,y) -> g(x,y,f(k)) | y ->* x 0.047/0.047 k -> l 0.047/0.047 k -> m 0.047/0.047 ) 0.047/0.047 Critical Pairs: 0.047/0.047 => Not trivial, Overlay, NW2, N1 0.047/0.047 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.047/0.047 0.047/0.047 InfChecker Different Ground and Normal No Conditions CCP Terms Processor: 0.047/0.047 Proof: 0.047/0.047 YES 0.047/0.047 0.047/0.047 Problem 1: 0.047/0.047 0.047/0.047 Infeasibility Problem: 0.047/0.047 [(VAR vNonEmpty x y vNonEmpty y) 0.047/0.047 (STRATEGY CONTEXTSENSITIVE 0.047/0.047 (a) 0.047/0.047 (b) 0.047/0.047 (c) 0.047/0.047 (d) 0.047/0.047 (f 1) 0.047/0.047 (g 1 2 3) 0.047/0.047 (h 1 2) 0.047/0.047 (k) 0.047/0.047 (A) 0.047/0.047 (e) 0.047/0.047 (fSNonEmpty) 0.047/0.047 (l) 0.047/0.047 (m) 0.047/0.047 ) 0.047/0.047 (RULES 0.047/0.047 a -> c 0.047/0.047 a -> d 0.047/0.047 b -> c 0.047/0.047 b -> d 0.047/0.047 c -> e 0.047/0.047 c -> l 0.047/0.047 d -> m 0.047/0.047 f(x) -> x | x ->* e 0.047/0.047 g(d,x,y) -> A | y ->* x 0.047/0.047 h(x,y) -> g(x,y,f(k)) | y ->* x 0.047/0.047 k -> l 0.047/0.047 k -> m 0.047/0.047 )] 0.047/0.047 0.047/0.047 Infeasibility Conditions: 0.047/0.047 l -> y 0.047/0.047 0.047/0.047 Problem 1: 0.047/0.047 0.047/0.047 Obtaining a model using Mace4: 0.047/0.047 0.047/0.047 -> Usable Rules: 0.047/0.047 Empty 0.047/0.047 0.047/0.047 -> Mace4 Output: 0.047/0.047 ============================== Mace4 ================================= 0.047/0.047 Mace4 (64) version 2009-11A, November 2009. 0.047/0.047 Process 11796 was started by ubuntu on ubuntu, 0.047/0.047 Wed Mar 9 09:17:41 2022 0.047/0.047 The command was "./mace4 -c -f /tmp/mace411768-2.in". 0.047/0.047 ============================== end of head =========================== 0.047/0.047 0.047/0.047 ============================== INPUT ================================= 0.047/0.047 0.047/0.047 % Reading from file /tmp/mace411768-2.in 0.047/0.047 0.047/0.047 assign(max_seconds,6). 0.047/0.047 0.047/0.047 formulas(assumptions). 0.047/0.047 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence). 0.047/0.047 ->(x1,y) -> ->(g(x1,x2,x3),g(y,x2,x3)) # label(congruence). 0.047/0.047 ->(x2,y) -> ->(g(x1,x2,x3),g(x1,y,x3)) # label(congruence). 0.047/0.047 ->(x3,y) -> ->(g(x1,x2,x3),g(x1,x2,y)) # label(congruence). 0.047/0.047 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence). 0.047/0.047 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence). 0.047/0.047 end_of_list. 0.047/0.047 0.047/0.047 formulas(goals). 0.047/0.047 (exists x4 ->(l,x4)) # label(goal). 0.047/0.047 end_of_list. 0.047/0.047 0.047/0.047 ============================== end of input ========================== 0.047/0.047 0.047/0.047 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.047/0.047 0.047/0.047 % Formulas that are not ordinary clauses: 0.047/0.047 1 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 0.047/0.047 2 ->(x1,y) -> ->(g(x1,x2,x3),g(y,x2,x3)) # label(congruence) # label(non_clause). [assumption]. 0.047/0.047 3 ->(x2,y) -> ->(g(x1,x2,x3),g(x1,y,x3)) # label(congruence) # label(non_clause). [assumption]. 0.047/0.047 4 ->(x3,y) -> ->(g(x1,x2,x3),g(x1,x2,y)) # label(congruence) # label(non_clause). [assumption]. 0.047/0.047 5 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.047/0.047 6 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.047/0.047 7 (exists x4 ->(l,x4)) # label(goal) # label(non_clause) # label(goal). [goal]. 0.047/0.047 0.047/0.047 ============================== end of process non-clausal formulas === 0.047/0.047 0.047/0.047 ============================== CLAUSES FOR SEARCH ==================== 0.047/0.047 0.047/0.047 formulas(mace4_clauses). 0.047/0.047 -->(x,y) | ->(f(x),f(y)) # label(congruence). 0.047/0.047 -->(x,y) | ->(g(x,z,u),g(y,z,u)) # label(congruence). 0.047/0.047 -->(x,y) | ->(g(z,x,u),g(z,y,u)) # label(congruence). 0.047/0.047 -->(x,y) | ->(g(z,u,x),g(z,u,y)) # label(congruence). 0.047/0.047 -->(x,y) | ->(h(x,z),h(y,z)) # label(congruence). 0.047/0.047 -->(x,y) | ->(h(z,x),h(z,y)) # label(congruence). 0.047/0.047 -->(l,x) # label(goal). 0.047/0.047 end_of_list. 0.047/0.047 0.047/0.047 ============================== end of clauses for search ============= 0.047/0.047 0.047/0.047 % There are no natural numbers in the input. 0.047/0.047 0.047/0.047 ============================== DOMAIN SIZE 2 ========================= 0.047/0.047 0.047/0.047 ============================== MODEL ================================= 0.047/0.047 0.047/0.047 interpretation( 2, [number=1, seconds=0], [ 0.047/0.047 0.047/0.047 function(l, [ 0 ]), 0.047/0.047 0.047/0.047 function(f(_), [ 0, 0 ]), 0.047/0.047 0.047/0.047 function(h(_,_), [ 0.047/0.047 0, 0, 0.047/0.047 0, 0 ]), 0.047/0.047 0.047/0.047 function(g(_,_,_), [ 0.047/0.047 0, 0, 0.047/0.047 0, 0, 0.047/0.047 0, 0, 0.047/0.047 0, 0 ]), 0.047/0.047 0.047/0.047 relation(->(_,_), [ 0.047/0.047 0, 0, 0.047/0.047 0, 0 ]) 0.047/0.047 ]). 0.047/0.047 0.047/0.047 ============================== end of model ========================== 0.047/0.047 0.047/0.047 ============================== STATISTICS ============================ 0.047/0.047 0.047/0.047 For domain size 2. 0.047/0.047 0.047/0.047 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 0.047/0.047 Ground clauses: seen=70, kept=70. 0.047/0.047 Selections=15, assignments=15, propagations=4, current_models=1. 0.047/0.047 Rewrite_terms=138, rewrite_bools=72, indexes=2. 0.047/0.047 Rules_from_neg_clauses=0, cross_offs=0. 0.047/0.047 0.047/0.047 ============================== end of statistics ===================== 0.047/0.047 0.047/0.047 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 0.047/0.047 0.047/0.047 Exiting with 1 model. 0.047/0.047 0.047/0.047 Process 11796 exit (max_models) Wed Mar 9 09:17:41 2022 0.047/0.047 The process finished Wed Mar 9 09:17:41 2022 0.047/0.047 0.047/0.047 0.047/0.047 Mace4 cooked interpretation: 0.047/0.047 0.047/0.047 0.047/0.047 0.047/0.047 The problem is infeasible. 0.047/0.047 YES 0.047/0.047 0.047/0.047 Problem 1: 0.047/0.047 0.047/0.047 Infeasibility Problem: 0.047/0.047 [(VAR vNonEmpty x y vNonEmpty x) 0.047/0.047 (STRATEGY CONTEXTSENSITIVE 0.047/0.047 (a) 0.047/0.047 (b) 0.047/0.047 (c) 0.047/0.047 (d) 0.047/0.047 (f 1) 0.047/0.047 (g 1 2 3) 0.047/0.047 (h 1 2) 0.047/0.047 (k) 0.047/0.047 (A) 0.047/0.047 (e) 0.047/0.047 (fSNonEmpty) 0.047/0.047 (l) 0.047/0.047 (m) 0.047/0.047 ) 0.047/0.047 (RULES 0.047/0.047 a -> c 0.047/0.047 a -> d 0.047/0.047 b -> c 0.047/0.047 b -> d 0.047/0.047 c -> e 0.047/0.047 c -> l 0.047/0.047 d -> m 0.047/0.047 f(x) -> x | x ->* e 0.047/0.047 g(d,x,y) -> A | y ->* x 0.047/0.047 h(x,y) -> g(x,y,f(k)) | y ->* x 0.047/0.047 k -> l 0.047/0.047 k -> m 0.047/0.047 )] 0.047/0.047 0.047/0.047 Infeasibility Conditions: 0.047/0.047 m -> x 0.047/0.047 0.047/0.047 Problem 1: 0.047/0.047 0.047/0.047 Obtaining a model using Mace4: 0.047/0.047 0.047/0.047 -> Usable Rules: 0.047/0.047 Empty 0.047/0.047 0.047/0.047 -> Mace4 Output: 0.047/0.047 ============================== Mace4 ================================= 0.047/0.047 Mace4 (64) version 2009-11A, November 2009. 0.047/0.047 Process 11826 was started by ubuntu on ubuntu, 0.047/0.047 Wed Mar 9 09:17:41 2022 0.047/0.047 The command was "./mace4 -c -f /tmp/mace411814-2.in". 0.047/0.047 ============================== end of head =========================== 0.047/0.047 0.047/0.047 ============================== INPUT ================================= 0.047/0.047 0.047/0.047 % Reading from file /tmp/mace411814-2.in 0.047/0.047 0.047/0.047 assign(max_seconds,6). 0.047/0.047 0.047/0.047 formulas(assumptions). 0.047/0.047 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence). 0.047/0.047 ->(x1,y) -> ->(g(x1,x2,x3),g(y,x2,x3)) # label(congruence). 0.047/0.047 ->(x2,y) -> ->(g(x1,x2,x3),g(x1,y,x3)) # label(congruence). 0.047/0.047 ->(x3,y) -> ->(g(x1,x2,x3),g(x1,x2,y)) # label(congruence). 0.047/0.047 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence). 0.047/0.047 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence). 0.047/0.047 end_of_list. 0.047/0.047 0.047/0.047 formulas(goals). 0.047/0.047 (exists x4 ->(m,x4)) # label(goal). 0.047/0.047 end_of_list. 0.047/0.047 0.047/0.047 ============================== end of input ========================== 0.047/0.047 0.047/0.047 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.047/0.047 0.047/0.047 % Formulas that are not ordinary clauses: 0.047/0.047 1 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 0.047/0.047 2 ->(x1,y) -> ->(g(x1,x2,x3),g(y,x2,x3)) # label(congruence) # label(non_clause). [assumption]. 0.047/0.047 3 ->(x2,y) -> ->(g(x1,x2,x3),g(x1,y,x3)) # label(congruence) # label(non_clause). [assumption]. 0.047/0.047 4 ->(x3,y) -> ->(g(x1,x2,x3),g(x1,x2,y)) # label(congruence) # label(non_clause). [assumption]. 0.047/0.047 5 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.047/0.047 6 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.047/0.047 7 (exists x4 ->(m,x4)) # label(goal) # label(non_clause) # label(goal). [goal]. 0.047/0.047 0.047/0.047 ============================== end of process non-clausal formulas === 0.047/0.047 0.047/0.047 ============================== CLAUSES FOR SEARCH ==================== 0.047/0.047 0.047/0.047 formulas(mace4_clauses). 0.047/0.047 -->(x,y) | ->(f(x),f(y)) # label(congruence). 0.047/0.047 -->(x,y) | ->(g(x,z,u),g(y,z,u)) # label(congruence). 0.047/0.047 -->(x,y) | ->(g(z,x,u),g(z,y,u)) # label(congruence). 0.047/0.047 -->(x,y) | ->(g(z,u,x),g(z,u,y)) # label(congruence). 0.047/0.047 -->(x,y) | ->(h(x,z),h(y,z)) # label(congruence). 0.047/0.047 -->(x,y) | ->(h(z,x),h(z,y)) # label(congruence). 0.047/0.047 -->(m,x) # label(goal). 0.047/0.047 end_of_list. 0.047/0.047 0.047/0.047 ============================== end of clauses for search ============= 0.047/0.047 0.047/0.047 % There are no natural numbers in the input. 0.047/0.047 0.047/0.047 ============================== DOMAIN SIZE 2 ========================= 0.047/0.047 0.047/0.047 ============================== MODEL ================================= 0.047/0.047 0.047/0.047 interpretation( 2, [number=1, seconds=0], [ 0.047/0.047 0.047/0.047 function(m, [ 0 ]), 0.047/0.047 0.047/0.047 function(f(_), [ 0, 0 ]), 0.047/0.047 0.047/0.047 function(h(_,_), [ 0.047/0.047 0, 0, 0.047/0.047 0, 0 ]), 0.047/0.047 0.047/0.047 function(g(_,_,_), [ 0.047/0.047 0, 0, 0.047/0.047 0, 0, 0.047/0.047 0, 0, 0.047/0.047 0, 0 ]), 0.047/0.047 0.047/0.047 relation(->(_,_), [ 0.047/0.047 0, 0, 0.047/0.047 0, 0 ]) 0.047/0.047 ]). 0.047/0.047 0.047/0.047 ============================== end of model ========================== 0.047/0.047 0.047/0.047 ============================== STATISTICS ============================ 0.047/0.047 0.047/0.047 For domain size 2. 0.047/0.047 0.047/0.047 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 0.047/0.047 Ground clauses: seen=70, kept=70. 0.047/0.047 Selections=15, assignments=15, propagations=4, current_models=1. 0.047/0.047 Rewrite_terms=138, rewrite_bools=72, indexes=2. 0.047/0.047 Rules_from_neg_clauses=0, cross_offs=0. 0.047/0.047 0.047/0.047 ============================== end of statistics ===================== 0.047/0.047 0.047/0.047 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 0.047/0.047 0.047/0.047 Exiting with 1 model. 0.047/0.047 0.047/0.047 Process 11826 exit (max_models) Wed Mar 9 09:17:41 2022 0.047/0.047 The process finished Wed Mar 9 09:17:41 2022 0.047/0.047 0.047/0.047 0.047/0.047 Mace4 cooked interpretation: 0.047/0.047 0.047/0.047 0.047/0.047 0.047/0.047 The problem is infeasible. 0.047/0.047 0.047/0.047 0.047/0.047 The problem is not joinable. 0.047/0.047 0.13user 0.06system 0:00.47elapsed 42%CPU (0avgtext+0avgdata 12984maxresident)k 0.047/0.047 8inputs+0outputs (0major+13372minor)pagefaults 0swaps