36.014/36.014 NO 36.014/36.014 36.014/36.014 Problem 1: 36.014/36.014 36.014/36.014 36.014/36.014 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 36.014/36.014 Confluence Problem: 36.014/36.014 (VAR vNonEmpty:S x:S y:S) 36.014/36.014 (STRATEGY CONTEXTSENSITIVE 36.014/36.014 (a) 36.014/36.014 (b) 36.014/36.014 (f 1 2) 36.014/36.014 (g 1 2) 36.014/36.014 (s 1) 36.014/36.014 (c) 36.014/36.014 (d) 36.014/36.014 (fSNonEmpty) 36.014/36.014 (h 1 2) 36.014/36.014 (k) 36.014/36.014 (l) 36.014/36.014 (t 1) 36.014/36.014 ) 36.014/36.014 (RULES 36.014/36.014 a -> c 36.014/36.014 a -> d 36.014/36.014 b -> c 36.014/36.014 b -> d 36.014/36.014 f(x:S,y:S) -> y:S | s(x:S) ->* t(y:S) 36.014/36.014 g(x:S,x:S) -> h(x:S,x:S) 36.014/36.014 s(k) -> t(a) 36.014/36.014 s(l) -> t(a) 36.014/36.014 ) 36.014/36.014 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 36.014/36.014 36.014/36.014 36.014/36.014 Problem 1: 36.014/36.014 36.014/36.014 Inlining of Conditions Processor [STERN17]: 36.014/36.014 36.014/36.014 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 36.014/36.014 Confluence Problem: 36.014/36.014 (VAR vNonEmpty:S x:S y:S) 36.014/36.014 (STRATEGY CONTEXTSENSITIVE 36.014/36.014 (a) 36.014/36.014 (b) 36.014/36.014 (f 1 2) 36.014/36.014 (g 1 2) 36.014/36.014 (s 1) 36.014/36.014 (c) 36.014/36.014 (d) 36.014/36.014 (fSNonEmpty) 36.014/36.014 (h 1 2) 36.014/36.014 (k) 36.014/36.014 (l) 36.014/36.014 (t 1) 36.014/36.014 ) 36.014/36.014 (RULES 36.014/36.014 a -> c 36.014/36.014 a -> d 36.014/36.014 b -> c 36.014/36.014 b -> d 36.014/36.014 f(x:S,y:S) -> y:S | s(x:S) ->* t(y:S) 36.014/36.014 g(x:S,x:S) -> h(x:S,x:S) 36.014/36.014 s(k) -> t(a) 36.014/36.014 s(l) -> t(a) 36.014/36.014 ) 36.014/36.014 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 36.014/36.014 36.014/36.014 36.014/36.014 Problem 1: 36.014/36.014 36.014/36.014 Clean CTRS Processor: 36.014/36.014 36.014/36.014 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 36.014/36.014 Confluence Problem: 36.014/36.014 (VAR x:S y:S) 36.014/36.014 (STRATEGY CONTEXTSENSITIVE 36.014/36.014 (a) 36.014/36.014 (b) 36.014/36.014 (f 1 2) 36.014/36.014 (g 1 2) 36.014/36.014 (s 1) 36.014/36.014 (c) 36.014/36.014 (d) 36.014/36.014 (fSNonEmpty) 36.014/36.014 (h 1 2) 36.014/36.014 (k) 36.014/36.014 (l) 36.014/36.014 (t 1) 36.014/36.014 ) 36.014/36.014 (RULES 36.014/36.014 a -> c 36.014/36.014 a -> d 36.014/36.014 b -> c 36.014/36.014 b -> d 36.014/36.014 f(x:S,y:S) -> y:S | s(x:S) ->* t(y:S) 36.014/36.014 g(x:S,x:S) -> h(x:S,x:S) 36.014/36.014 s(k) -> t(a) 36.014/36.014 s(l) -> t(a) 36.014/36.014 ) 36.014/36.014 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 36.014/36.014 36.014/36.014 CRule InfChecker Info: 36.014/36.014 a -> c 36.014/36.014 Rule remains 36.014/36.014 Proof: 36.014/36.014 NO_CONDS 36.014/36.014 36.014/36.014 CRule InfChecker Info: 36.014/36.014 a -> d 36.014/36.014 Rule remains 36.014/36.014 Proof: 36.014/36.014 NO_CONDS 36.014/36.014 36.014/36.014 CRule InfChecker Info: 36.014/36.014 b -> c 36.014/36.014 Rule remains 36.014/36.014 Proof: 36.014/36.014 NO_CONDS 36.014/36.014 36.014/36.014 CRule InfChecker Info: 36.014/36.014 b -> d 36.014/36.014 Rule remains 36.014/36.014 Proof: 36.014/36.014 NO_CONDS 36.014/36.014 36.014/36.014 CRule InfChecker Info: 36.014/36.014 f(x:S,y:S) -> y:S | s(x:S) ->* t(y:S) 36.014/36.014 Rule remains 36.014/36.014 Proof: 36.014/36.014 NO 36.014/36.014 36.014/36.014 Problem 1: 36.014/36.014 36.014/36.014 Infeasibility Problem: 36.014/36.014 [(VAR vNonEmpty:S vNonEmpty:S:S x:S:S y:S:S) 36.014/36.014 (STRATEGY CONTEXTSENSITIVE 36.014/36.014 (a) 36.014/36.014 (b) 36.014/36.014 (f 1 2) 36.014/36.014 (g 1 2) 36.014/36.014 (s 1) 36.014/36.014 (c) 36.014/36.014 (d) 36.014/36.014 (fSNonEmpty) 36.014/36.014 (h 1 2) 36.014/36.014 (k) 36.014/36.014 (l) 36.014/36.014 (t 1) 36.014/36.014 ) 36.014/36.014 (RULES 36.014/36.014 a -> c 36.014/36.014 a -> d 36.014/36.014 b -> c 36.014/36.014 b -> d 36.014/36.014 f(x:S:S,y:S:S) -> y:S:S | s(x:S:S) ->* t(y:S:S) 36.014/36.014 g(x:S:S,x:S:S) -> h(x:S:S,x:S:S) 36.014/36.014 s(k) -> t(a) 36.014/36.014 s(l) -> t(a) 36.014/36.014 )] 36.014/36.014 36.014/36.014 Infeasibility Conditions: 36.014/36.014 s(x:S:S) ->* t(y:S:S) 36.014/36.014 36.014/36.014 Problem 1: 36.014/36.014 36.014/36.014 Obtaining a proof using Prover9: 36.014/36.014 36.014/36.014 -> Prover9 Output: 36.014/36.014 ============================== Prover9 =============================== 36.014/36.014 Prover9 (64) version 2009-11A, November 2009. 36.014/36.014 Process 49168 was started by ubuntu on ubuntu, 36.014/36.014 Wed Jul 14 10:49:11 2021 36.014/36.014 The command was "./prover9 -f /tmp/prover949161-0.in". 36.014/36.014 ============================== end of head =========================== 36.014/36.014 36.014/36.014 ============================== INPUT ================================= 36.014/36.014 36.014/36.014 % Reading from file /tmp/prover949161-0.in 36.014/36.014 36.014/36.014 assign(max_seconds,20). 36.014/36.014 36.014/36.014 formulas(assumptions). 36.014/36.014 ->*_s0(x,x) # label(reflexivity). 36.014/36.014 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 36.014/36.014 ->_s0(x1,y) -> ->_s0(f(x1,x2),f(y,x2)) # label(congruence). 36.014/36.014 ->_s0(x2,y) -> ->_s0(f(x1,x2),f(x1,y)) # label(congruence). 36.014/36.014 ->_s0(x1,y) -> ->_s0(g(x1,x2),g(y,x2)) # label(congruence). 36.014/36.014 ->_s0(x2,y) -> ->_s0(g(x1,x2),g(x1,y)) # label(congruence). 36.014/36.014 ->_s0(x1,y) -> ->_s0(s(x1),s(y)) # label(congruence). 36.014/36.014 ->_s0(x1,y) -> ->_s0(h(x1,x2),h(y,x2)) # label(congruence). 36.014/36.014 ->_s0(x2,y) -> ->_s0(h(x1,x2),h(x1,y)) # label(congruence). 36.014/36.014 ->_s0(x1,y) -> ->_s0(t(x1),t(y)) # label(congruence). 36.014/36.014 ->_s0(a,c) # label(replacement). 36.014/36.014 ->_s0(a,d) # label(replacement). 36.014/36.014 ->_s0(b,c) # label(replacement). 36.014/36.014 ->_s0(b,d) # label(replacement). 36.014/36.014 ->*_s0(s(x2),t(x3)) -> ->_s0(f(x2,x3),x3) # label(replacement). 36.014/36.014 ->_s0(g(x2,x2),h(x2,x2)) # label(replacement). 36.014/36.014 ->_s0(s(k),t(a)) # label(replacement). 36.014/36.014 ->_s0(s(l),t(a)) # label(replacement). 36.014/36.014 end_of_list. 36.014/36.014 36.014/36.014 formulas(goals). 36.014/36.014 (exists x2 exists x3 ->*_s0(s(x2),t(x3))) # label(goal). 36.014/36.014 end_of_list. 36.014/36.014 36.014/36.014 ============================== end of input ========================== 36.014/36.014 36.014/36.014 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 36.014/36.014 36.014/36.014 % Formulas that are not ordinary clauses: 36.014/36.014 1 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 36.014/36.014 2 ->_s0(x1,y) -> ->_s0(f(x1,x2),f(y,x2)) # label(congruence) # label(non_clause). [assumption]. 36.014/36.014 3 ->_s0(x2,y) -> ->_s0(f(x1,x2),f(x1,y)) # label(congruence) # label(non_clause). [assumption]. 36.014/36.014 4 ->_s0(x1,y) -> ->_s0(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 36.014/36.014 5 ->_s0(x2,y) -> ->_s0(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 36.014/36.014 6 ->_s0(x1,y) -> ->_s0(s(x1),s(y)) # label(congruence) # label(non_clause). [assumption]. 36.014/36.014 7 ->_s0(x1,y) -> ->_s0(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 36.014/36.014 8 ->_s0(x2,y) -> ->_s0(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 36.014/36.014 9 ->_s0(x1,y) -> ->_s0(t(x1),t(y)) # label(congruence) # label(non_clause). [assumption]. 36.014/36.014 10 ->*_s0(s(x2),t(x3)) -> ->_s0(f(x2,x3),x3) # label(replacement) # label(non_clause). [assumption]. 36.014/36.014 11 (exists x2 exists x3 ->*_s0(s(x2),t(x3))) # label(goal) # label(non_clause) # label(goal). [goal]. 36.014/36.014 36.014/36.014 ============================== end of process non-clausal formulas === 36.014/36.014 36.014/36.014 ============================== PROCESS INITIAL CLAUSES =============== 36.014/36.014 36.014/36.014 % Clauses before input processing: 36.014/36.014 36.014/36.014 formulas(usable). 36.014/36.014 end_of_list. 36.014/36.014 36.014/36.014 formulas(sos). 36.014/36.014 ->*_s0(x,x) # label(reflexivity). [assumption]. 36.014/36.014 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 36.014/36.014 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(2)]. 36.014/36.014 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(3)]. 36.014/36.014 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(4)]. 36.014/36.014 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(5)]. 36.014/36.014 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(6)]. 36.014/36.014 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(7)]. 36.014/36.014 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(8)]. 36.014/36.014 -->_s0(x,y) | ->_s0(t(x),t(y)) # label(congruence). [clausify(9)]. 36.014/36.014 ->_s0(a,c) # label(replacement). [assumption]. 36.014/36.014 ->_s0(a,d) # label(replacement). [assumption]. 36.014/36.014 ->_s0(b,c) # label(replacement). [assumption]. 36.014/36.014 ->_s0(b,d) # label(replacement). [assumption]. 36.014/36.014 -->*_s0(s(x),t(y)) | ->_s0(f(x,y),y) # label(replacement). [clausify(10)]. 36.014/36.014 ->_s0(g(x,x),h(x,x)) # label(replacement). [assumption]. 36.014/36.014 ->_s0(s(k),t(a)) # label(replacement). [assumption]. 36.014/36.014 ->_s0(s(l),t(a)) # label(replacement). [assumption]. 36.014/36.014 -->*_s0(s(x),t(y)) # label(goal). [deny(11)]. 36.014/36.014 end_of_list. 36.014/36.014 36.014/36.014 formulas(demodulators). 36.014/36.014 end_of_list. 36.014/36.014 36.014/36.014 ============================== PREDICATE ELIMINATION ================= 36.014/36.014 36.014/36.014 No predicates eliminated. 36.014/36.014 36.014/36.014 ============================== end predicate elimination ============= 36.014/36.014 36.014/36.014 Auto_denials: 36.014/36.014 % copying label goal to answer in negative clause 36.014/36.014 36.014/36.014 Term ordering decisions: 36.014/36.014 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 36.014/36.014 Function symbol precedence: function_order([ a, b, c, d, k, l, h, f, g, t, s ]). 36.014/36.014 After inverse_order: (no changes). 36.014/36.014 Unfolding symbols: (none). 36.014/36.014 36.014/36.014 Auto_inference settings: 36.014/36.014 % set(neg_binary_resolution). % (HNE depth_diff=-8) 36.014/36.014 % clear(ordered_res). % (HNE depth_diff=-8) 36.014/36.014 % set(ur_resolution). % (HNE depth_diff=-8) 36.014/36.014 % set(ur_resolution) -> set(pos_ur_resolution). 36.014/36.014 % set(ur_resolution) -> set(neg_ur_resolution). 36.014/36.014 36.014/36.014 Auto_process settings: (no changes). 36.014/36.014 36.014/36.014 kept: 12 ->*_s0(x,x) # label(reflexivity). [assumption]. 36.014/36.014 kept: 13 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 36.014/36.014 kept: 14 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(2)]. 36.014/36.014 kept: 15 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(3)]. 36.014/36.014 kept: 16 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(4)]. 36.014/36.014 kept: 17 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(5)]. 36.014/36.014 kept: 18 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(6)]. 36.014/36.014 kept: 19 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(7)]. 36.014/36.014 kept: 20 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(8)]. 36.014/36.014 kept: 21 -->_s0(x,y) | ->_s0(t(x),t(y)) # label(congruence). [clausify(9)]. 36.014/36.014 kept: 22 ->_s0(a,c) # label(replacement). [assumption]. 36.014/36.014 kept: 23 ->_s0(a,d) # label(replacement). [assumption]. 36.014/36.014 kept: 24 ->_s0(b,c) # label(replacement). [assumption]. 36.014/36.014 kept: 25 ->_s0(b,d) # label(replacement). [assumption]. 36.014/36.014 kept: 26 -->*_s0(s(x),t(y)) | ->_s0(f(x,y),y) # label(replacement). [clausify(10)]. 36.014/36.014 kept: 27 ->_s0(g(x,x),h(x,x)) # label(replacement). [assumption]. 36.014/36.014 kept: 28 ->_s0(s(k),t(a)) # label(replacement). [assumption]. 36.014/36.014 kept: 29 ->_s0(s(l),t(a)) # label(replacement). [assumption]. 36.014/36.014 kept: 30 -->*_s0(s(x),t(y)) # label(goal) # answer(goal). [deny(11)]. 36.014/36.014 36.014/36.014 ============================== end of process initial clauses ======== 36.014/36.014 36.014/36.014 ============================== CLAUSES FOR SEARCH ==================== 36.014/36.014 36.014/36.014 % Clauses after input processing: 36.014/36.014 36.014/36.014 formulas(usable). 36.014/36.014 end_of_list. 36.014/36.014 36.014/36.014 formulas(sos). 36.014/36.014 12 ->*_s0(x,x) # label(reflexivity). [assumption]. 36.014/36.014 13 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 36.014/36.014 14 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(2)]. 36.014/36.014 15 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(3)]. 36.014/36.014 16 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(4)]. 36.014/36.014 17 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(5)]. 36.014/36.014 18 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(6)]. 36.014/36.014 19 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(7)]. 36.014/36.014 20 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(8)]. 36.014/36.014 21 -->_s0(x,y) | ->_s0(t(x),t(y)) # label(congruence). [clausify(9)]. 36.014/36.014 22 ->_s0(a,c) # label(replacement). [assumption]. 36.014/36.014 23 ->_s0(a,d) # label(replacement). [assumption]. 36.014/36.014 24 ->_s0(b,c) # label(replacement). [assumption]. 36.014/36.014 25 ->_s0(b,d) # label(replacement). [assumption]. 36.014/36.014 27 ->_s0(g(x,x),h(x,x)) # label(replacement). [assumption]. 36.014/36.014 28 ->_s0(s(k),t(a)) # label(replacement). [assumption]. 36.014/36.014 29 ->_s0(s(l),t(a)) # label(replacement). [assumption]. 36.014/36.014 30 -->*_s0(s(x),t(y)) # label(goal) # answer(goal). [deny(11)]. 36.014/36.014 end_of_list. 36.014/36.014 36.014/36.014 formulas(demodulators). 36.014/36.014 end_of_list. 36.014/36.014 36.014/36.014 ============================== end of clauses for search ============= 36.014/36.014 36.014/36.014 ============================== SEARCH ================================ 36.014/36.014 36.014/36.014 % Starting search at 0.00 seconds. 36.014/36.014 36.014/36.014 given #1 (I,wt=3): 12 ->*_s0(x,x) # label(reflexivity). [assumption]. 36.014/36.014 36.014/36.014 given #2 (I,wt=9): 13 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 36.014/36.014 36.014/36.014 given #3 (I,wt=10): 14 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(2)]. 36.014/36.014 36.014/36.014 given #4 (I,wt=10): 15 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(3)]. 36.014/36.014 36.014/36.014 given #5 (I,wt=10): 16 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(4)]. 36.014/36.014 36.014/36.014 given #6 (I,wt=10): 17 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(5)]. 36.014/36.014 36.014/36.014 given #7 (I,wt=8): 18 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(6)]. 36.014/36.014 36.014/36.014 given #8 (I,wt=10): 19 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(7)]. 36.014/36.014 36.014/36.014 given #9 (I,wt=10): 20 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(8)]. 36.014/36.014 36.014/36.014 given #10 (I,wt=8): 21 -->_s0(x,y) | ->_s0(t(x),t(y)) # label(congruence). [clausify(9)]. 36.014/36.014 36.014/36.014 given #11 (I,wt=3): 22 ->_s0(a,c) # label(replacement). [assumption]. 36.014/36.014 36.014/36.014 given #12 (I,wt=3): 23 ->_s0(a,d) # label(replacement). [assumption]. 36.014/36.014 36.014/36.014 given #13 (I,wt=3): 24 ->_s0(b,c) # label(replacement). [assumption]. 36.014/36.014 36.014/36.014 given #14 (I,wt=3): 25 ->_s0(b,d) # label(replacement). [assumption]. 36.014/36.014 36.014/36.014 given #15 (I,wt=7): 27 ->_s0(g(x,x),h(x,x)) # label(replacement). [assumption]. 36.014/36.014 36.014/36.014 given #16 (I,wt=5): 28 ->_s0(s(k),t(a)) # label(replacement). [assumption]. 36.014/36.014 36.014/36.014 ============================== PROOF ================================= 36.014/36.014 36.014/36.014 % Proof 1 at 0.00 (+ 0.00) seconds: goal. 36.014/36.014 % Length of proof is 8. 36.014/36.014 % Level of proof is 3. 36.014/36.014 % Maximum clause weight is 9.000. 36.014/36.014 % Given clauses 16. 36.014/36.014 36.014/36.014 1 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 36.014/36.014 11 (exists x2 exists x3 ->*_s0(s(x2),t(x3))) # label(goal) # label(non_clause) # label(goal). [goal]. 36.014/36.014 12 ->*_s0(x,x) # label(reflexivity). [assumption]. 36.014/36.014 13 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 36.014/36.014 28 ->_s0(s(k),t(a)) # label(replacement). [assumption]. 36.014/36.014 30 -->*_s0(s(x),t(y)) # label(goal) # answer(goal). [deny(11)]. 36.014/36.014 84 ->*_s0(s(k),t(a)). [ur(13,a,28,a,b,12,a)]. 36.014/36.014 85 $F # answer(goal). [resolve(84,a,30,a)]. 36.014/36.014 36.014/36.014 ============================== end of proof ========================== 36.014/36.014 36.014/36.014 ============================== STATISTICS ============================ 36.014/36.014 36.014/36.014 Given=16. Generated=73. Kept=73. proofs=1. 36.014/36.014 Usable=16. Sos=47. Demods=0. Limbo=8, Disabled=20. Hints=0. 36.014/36.014 Kept_by_rule=0, Deleted_by_rule=0. 36.014/36.014 Forward_subsumed=0. Back_subsumed=1. 36.014/36.014 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 36.014/36.014 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 36.014/36.014 Demod_attempts=0. Demod_rewrites=0. 36.014/36.014 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 36.014/36.014 Nonunit_fsub_feature_tests=3. Nonunit_bsub_feature_tests=18. 36.014/36.014 Megabytes=0.15. 36.014/36.014 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 36.014/36.014 36.014/36.014 ============================== end of statistics ===================== 36.014/36.014 36.014/36.014 ============================== end of search ========================= 36.014/36.014 36.014/36.014 THEOREM PROVED 36.014/36.014 36.014/36.014 Exiting with 1 proof. 36.014/36.014 36.014/36.014 Process 49168 exit (max_proofs) Wed Jul 14 10:49:11 2021 36.014/36.014 36.014/36.014 36.014/36.014 The problem is feasible. 36.014/36.014 36.014/36.014 36.014/36.014 CRule InfChecker Info: 36.014/36.014 g(x:S,x:S) -> h(x:S,x:S) 36.014/36.014 Rule remains 36.014/36.014 Proof: 36.014/36.014 NO_CONDS 36.014/36.014 36.014/36.014 CRule InfChecker Info: 36.014/36.014 s(k) -> t(a) 36.014/36.014 Rule remains 36.014/36.014 Proof: 36.014/36.014 NO_CONDS 36.014/36.014 36.014/36.014 CRule InfChecker Info: 36.014/36.014 s(l) -> t(a) 36.014/36.014 Rule remains 36.014/36.014 Proof: 36.014/36.014 NO_CONDS 36.014/36.014 36.014/36.014 Problem 1: 36.014/36.014 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 36.014/36.014 Confluence Problem: 36.014/36.014 (VAR x:S y:S) 36.014/36.014 (STRATEGY CONTEXTSENSITIVE 36.014/36.014 (a) 36.014/36.014 (b) 36.014/36.014 (f 1 2) 36.014/36.014 (g 1 2) 36.014/36.014 (s 1) 36.014/36.014 (c) 36.014/36.014 (d) 36.014/36.014 (fSNonEmpty) 36.014/36.014 (h 1 2) 36.014/36.014 (k) 36.014/36.014 (l) 36.014/36.014 (t 1) 36.014/36.014 ) 36.014/36.014 (RULES 36.014/36.014 a -> c 36.014/36.014 a -> d 36.014/36.014 b -> c 36.014/36.014 b -> d 36.014/36.014 f(x:S,y:S) -> y:S | s(x:S) ->* t(y:S) 36.014/36.014 g(x:S,x:S) -> h(x:S,x:S) 36.014/36.014 s(k) -> t(a) 36.014/36.014 s(l) -> t(a) 36.014/36.014 ) 36.014/36.014 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 36.014/36.014 36.014/36.014 Critical Pairs Processor: 36.014/36.014 -> Rules: 36.014/36.014 a -> c 36.014/36.014 a -> d 36.014/36.014 b -> c 36.014/36.014 b -> d 36.014/36.014 f(x:S,y:S) -> y:S | s(x:S) ->* t(y:S) 36.014/36.014 g(x:S,x:S) -> h(x:S,x:S) 36.014/36.014 s(k) -> t(a) 36.014/36.014 s(l) -> t(a) 36.014/36.014 -> Vars: 36.014/36.014 "x", "y", "x" 36.014/36.014 -> FVars: 36.014/36.014 "x3", "x4", "x5" 36.014/36.014 -> PVars: 36.014/36.014 "x": ["x3", "x5"], "y": ["x4"] 36.014/36.014 36.014/36.014 -> Rlps: 36.014/36.014 crule: a -> c, id: 1, possubterms: a-> [] 36.014/36.014 crule: a -> d, id: 2, possubterms: a-> [] 36.014/36.014 crule: b -> c, id: 3, possubterms: b-> [] 36.014/36.014 crule: b -> d, id: 4, possubterms: b-> [] 36.014/36.014 crule: f(x3:S,x4:S) -> x4:S | s(x3:S) ->* t(x4:S), id: 5, possubterms: f(x3:S,x4:S)-> [] 36.014/36.014 crule: g(x5:S,x5:S) -> h(x5:S,x5:S), id: 6, possubterms: g(x5:S,x5:S)-> [] 36.014/36.014 crule: s(k) -> t(a), id: 7, possubterms: s(k)-> [], k-> [1] 36.014/36.014 crule: s(l) -> t(a), id: 8, possubterms: s(l)-> [], l-> [1] 36.014/36.014 36.014/36.014 -> Unifications: 36.014/36.014 R2 unifies with R1 at p: [], l: a, lp: a, conds: {}, sig: {}, l': a, r: d, r': c 36.014/36.014 R4 unifies with R3 at p: [], l: b, lp: b, conds: {}, sig: {}, l': b, r: d, r': c 36.014/36.014 36.014/36.014 -> Critical pairs info: 36.014/36.014 => Not trivial, Overlay, N1 36.014/36.014 36.014/36.014 -> Problem conclusions: 36.014/36.014 Not left linear, Not right linear, Not linear 36.014/36.014 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 36.014/36.014 CTRS Type: 1 36.014/36.014 Deterministic, Strongly deterministic 36.014/36.014 Oriented CTRS, Properly oriented CTRS, Not join CTRS 36.014/36.014 Maybe right-stable CTRS, Overlay CTRS 36.014/36.014 Maybe normal CTRS, Maybe almost normal CTRS 36.014/36.014 Maybe terminating CTRS, Maybe joinable CCPs 36.014/36.014 Maybe level confluent 36.014/36.014 Maybe confluent 36.014/36.014 36.014/36.014 Problem 1: 36.014/36.014 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 36.014/36.014 Confluence Problem: 36.014/36.014 (VAR x:S y:S) 36.014/36.014 (STRATEGY CONTEXTSENSITIVE 36.014/36.014 (a) 36.014/36.014 (b) 36.014/36.014 (f 1 2) 36.014/36.014 (g 1 2) 36.014/36.014 (s 1) 36.014/36.014 (c) 36.014/36.014 (d) 36.014/36.014 (fSNonEmpty) 36.014/36.014 (h 1 2) 36.014/36.014 (k) 36.014/36.014 (l) 36.014/36.014 (t 1) 36.014/36.014 ) 36.014/36.014 (RULES 36.014/36.014 a -> c 36.014/36.014 a -> d 36.014/36.014 b -> c 36.014/36.014 b -> d 36.014/36.014 f(x:S,y:S) -> y:S | s(x:S) ->* t(y:S) 36.014/36.014 g(x:S,x:S) -> h(x:S,x:S) 36.014/36.014 s(k) -> t(a) 36.014/36.014 s(l) -> t(a) 36.014/36.014 ) 36.014/36.014 Critical Pairs: 36.014/36.014 => Not trivial, Overlay, N1 36.014/36.014 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 36.014/36.014 36.014/36.014 Conditional Critical Pairs Distributor Processor 36.014/36.014 36.014/36.014 Problem 1: 36.014/36.014 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 36.014/36.014 Confluence Problem: 36.014/36.014 (VAR x:S y:S) 36.014/36.014 (STRATEGY CONTEXTSENSITIVE 36.014/36.014 (a) 36.014/36.014 (b) 36.014/36.014 (f 1 2) 36.014/36.014 (g 1 2) 36.014/36.014 (s 1) 36.014/36.014 (c) 36.014/36.014 (d) 36.014/36.014 (fSNonEmpty) 36.014/36.014 (h 1 2) 36.014/36.014 (k) 36.014/36.014 (l) 36.014/36.014 (t 1) 36.014/36.014 ) 36.014/36.014 (RULES 36.014/36.014 a -> c 36.014/36.014 a -> d 36.014/36.014 b -> c 36.014/36.014 b -> d 36.014/36.014 f(x:S,y:S) -> y:S | s(x:S) ->* t(y:S) 36.014/36.014 g(x:S,x:S) -> h(x:S,x:S) 36.014/36.014 s(k) -> t(a) 36.014/36.014 s(l) -> t(a) 36.014/36.014 ) 36.014/36.014 Critical Pairs: 36.014/36.014 => Not trivial, Overlay, N1 36.014/36.014 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 36.014/36.014 36.014/36.014 InfChecker Different Ground and Normal No Conditions CCP Terms Processor: 36.014/36.014 Proof: 36.014/36.014 YES 36.014/36.014 36.014/36.014 Problem 1: 36.014/36.014 36.014/36.014 Infeasibility Problem: 36.014/36.014 [(VAR vNonEmpty:S x:S y:S) 36.014/36.014 (STRATEGY CONTEXTSENSITIVE 36.014/36.014 (a) 36.014/36.014 (b) 36.014/36.014 (f 1 2) 36.014/36.014 (g 1 2) 36.014/36.014 (s 1) 36.014/36.014 (c) 36.014/36.014 (d) 36.014/36.014 (fSNonEmpty) 36.014/36.014 (h 1 2) 36.014/36.014 (k) 36.014/36.014 (l) 36.014/36.014 (t 1) 36.014/36.014 ) 36.014/36.014 (RULES 36.014/36.014 a -> c 36.014/36.014 a -> d 36.014/36.014 b -> c 36.014/36.014 b -> d 36.014/36.014 f(x:S,y:S) -> y:S | s(x:S) ->* t(y:S) 36.014/36.014 g(x:S,x:S) -> h(x:S,x:S) 36.014/36.014 s(k) -> t(a) 36.014/36.014 s(l) -> t(a) 36.014/36.014 )] 36.014/36.014 36.014/36.014 Infeasibility Conditions: 36.014/36.014 c -> y:S 36.014/36.014 36.014/36.014 Problem 1: 36.014/36.014 36.014/36.014 Obtaining a model using Mace4: 36.014/36.014 36.014/36.014 -> Usable Rules: 36.014/36.014 Empty 36.014/36.014 36.014/36.014 -> Mace4 Output: 36.014/36.014 ============================== Mace4 ================================= 36.014/36.014 Mace4 (64) version 2009-11A, November 2009. 36.014/36.014 Process 49202 was started by ubuntu on ubuntu, 36.014/36.014 Wed Jul 14 10:49:11 2021 36.014/36.014 The command was "./mace4 -c -f /tmp/mace449183-2.in". 36.014/36.014 ============================== end of head =========================== 36.014/36.014 36.014/36.014 ============================== INPUT ================================= 36.014/36.014 36.014/36.014 % Reading from file /tmp/mace449183-2.in 36.014/36.014 36.014/36.014 assign(max_seconds,6). 36.014/36.014 36.014/36.014 formulas(assumptions). 36.014/36.014 ->(x1,y) -> ->(f(x1,x2),f(y,x2)) # label(congruence). 36.014/36.014 ->(x2,y) -> ->(f(x1,x2),f(x1,y)) # label(congruence). 36.014/36.014 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence). 36.014/36.014 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence). 36.014/36.014 ->(x1,y) -> ->(s(x1),s(y)) # label(congruence). 36.014/36.014 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence). 36.014/36.014 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence). 36.014/36.014 ->(x1,y) -> ->(t(x1),t(y)) # label(congruence). 36.014/36.014 end_of_list. 36.014/36.014 36.014/36.014 formulas(goals). 36.014/36.014 (exists x2 ->(c,x2)) # label(goal). 36.014/36.014 end_of_list. 36.014/36.014 36.014/36.014 ============================== end of input ========================== 36.014/36.014 36.014/36.014 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 36.014/36.014 36.014/36.014 % Formulas that are not ordinary clauses: 36.014/36.014 1 ->(x1,y) -> ->(f(x1,x2),f(y,x2)) # label(congruence) # label(non_clause). [assumption]. 36.014/36.014 2 ->(x2,y) -> ->(f(x1,x2),f(x1,y)) # label(congruence) # label(non_clause). [assumption]. 36.014/36.014 3 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 36.014/36.014 4 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 36.014/36.014 5 ->(x1,y) -> ->(s(x1),s(y)) # label(congruence) # label(non_clause). [assumption]. 36.014/36.014 6 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 36.014/36.014 7 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 36.014/36.014 8 ->(x1,y) -> ->(t(x1),t(y)) # label(congruence) # label(non_clause). [assumption]. 36.014/36.014 9 (exists x2 ->(c,x2)) # label(goal) # label(non_clause) # label(goal). [goal]. 36.014/36.014 36.014/36.014 ============================== end of process non-clausal formulas === 36.014/36.014 36.014/36.014 ============================== CLAUSES FOR SEARCH ==================== 36.014/36.014 36.014/36.014 formulas(mace4_clauses). 36.014/36.014 -->(x,y) | ->(f(x,z),f(y,z)) # label(congruence). 36.014/36.014 -->(x,y) | ->(f(z,x),f(z,y)) # label(congruence). 36.014/36.014 -->(x,y) | ->(g(x,z),g(y,z)) # label(congruence). 36.014/36.014 -->(x,y) | ->(g(z,x),g(z,y)) # label(congruence). 36.014/36.014 -->(x,y) | ->(s(x),s(y)) # label(congruence). 36.014/36.014 -->(x,y) | ->(h(x,z),h(y,z)) # label(congruence). 36.014/36.014 -->(x,y) | ->(h(z,x),h(z,y)) # label(congruence). 36.014/36.014 -->(x,y) | ->(t(x),t(y)) # label(congruence). 36.014/36.014 -->(c,x) # label(goal). 36.014/36.014 end_of_list. 36.014/36.014 36.014/36.014 ============================== end of clauses for search ============= 36.014/36.014 36.014/36.014 % There are no natural numbers in the input. 36.014/36.014 36.014/36.014 ============================== DOMAIN SIZE 2 ========================= 36.014/36.014 36.014/36.014 ============================== MODEL ================================= 36.014/36.014 36.014/36.014 interpretation( 2, [number=1, seconds=0], [ 36.014/36.014 36.014/36.014 function(c, [ 0 ]), 36.014/36.014 36.014/36.014 function(t(_), [ 0, 0 ]), 36.014/36.014 36.014/36.014 function(s(_), [ 0, 0 ]), 36.014/36.014 36.014/36.014 function(h(_,_), [ 36.014/36.014 0, 0, 36.014/36.014 0, 0 ]), 36.014/36.014 36.014/36.014 function(f(_,_), [ 36.014/36.014 0, 0, 36.014/36.014 0, 0 ]), 36.014/36.014 36.014/36.014 function(g(_,_), [ 36.014/36.014 0, 0, 36.014/36.014 0, 0 ]), 36.014/36.014 36.014/36.014 relation(->(_,_), [ 36.014/36.014 0, 0, 36.014/36.014 0, 0 ]) 36.014/36.014 ]). 36.014/36.014 36.014/36.014 ============================== end of model ========================== 36.014/36.014 36.014/36.014 ============================== STATISTICS ============================ 36.014/36.014 36.014/36.014 For domain size 2. 36.014/36.014 36.014/36.014 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 36.014/36.014 Ground clauses: seen=58, kept=58. 36.014/36.014 Selections=17, assignments=17, propagations=4, current_models=1. 36.014/36.014 Rewrite_terms=114, rewrite_bools=60, indexes=2. 36.014/36.014 Rules_from_neg_clauses=0, cross_offs=0. 36.014/36.014 36.014/36.014 ============================== end of statistics ===================== 36.014/36.014 36.014/36.014 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 36.014/36.014 36.014/36.014 Exiting with 1 model. 36.014/36.014 36.014/36.014 Process 49202 exit (max_models) Wed Jul 14 10:49:11 2021 36.014/36.014 The process finished Wed Jul 14 10:49:11 2021 36.014/36.014 36.014/36.014 36.014/36.014 Mace4 cooked interpretation: 36.014/36.014 36.014/36.014 36.014/36.014 36.014/36.014 The problem is infeasible. 36.014/36.014 YES 36.014/36.014 36.014/36.014 Problem 1: 36.014/36.014 36.014/36.014 Infeasibility Problem: 36.014/36.014 [(VAR vNonEmpty:S x:S y:S) 36.014/36.014 (STRATEGY CONTEXTSENSITIVE 36.014/36.014 (a) 36.014/36.014 (b) 36.014/36.014 (f 1 2) 36.014/36.014 (g 1 2) 36.014/36.014 (s 1) 36.014/36.014 (c) 36.014/36.014 (d) 36.014/36.014 (fSNonEmpty) 36.014/36.014 (h 1 2) 36.014/36.014 (k) 36.014/36.014 (l) 36.014/36.014 (t 1) 36.014/36.014 ) 36.014/36.014 (RULES 36.014/36.014 a -> c 36.014/36.014 a -> d 36.014/36.014 b -> c 36.014/36.014 b -> d 36.014/36.014 f(x:S,y:S) -> y:S | s(x:S) ->* t(y:S) 36.014/36.014 g(x:S,x:S) -> h(x:S,x:S) 36.014/36.014 s(k) -> t(a) 36.014/36.014 s(l) -> t(a) 36.014/36.014 )] 36.014/36.014 36.014/36.014 Infeasibility Conditions: 36.014/36.014 d -> x:S 36.014/36.014 36.014/36.014 Problem 1: 36.014/36.014 36.014/36.014 Obtaining a model using Mace4: 36.014/36.014 36.014/36.014 -> Usable Rules: 36.014/36.014 Empty 36.014/36.014 36.014/36.014 -> Mace4 Output: 36.014/36.014 ============================== Mace4 ================================= 36.014/36.014 Mace4 (64) version 2009-11A, November 2009. 36.014/36.014 Process 49257 was started by ubuntu on ubuntu, 36.014/36.014 Wed Jul 14 10:49:30 2021 36.014/36.014 The command was "./mace4 -c -f /tmp/mace449244-2.in". 36.014/36.014 ============================== end of head =========================== 36.014/36.014 36.014/36.014 ============================== INPUT ================================= 36.014/36.014 36.014/36.014 % Reading from file /tmp/mace449244-2.in 36.014/36.014 36.014/36.014 assign(max_seconds,6). 36.014/36.014 36.014/36.014 formulas(assumptions). 36.014/36.014 ->(x1,y) -> ->(f(x1,x2),f(y,x2)) # label(congruence). 36.014/36.014 ->(x2,y) -> ->(f(x1,x2),f(x1,y)) # label(congruence). 36.014/36.014 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence). 36.014/36.014 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence). 36.014/36.014 ->(x1,y) -> ->(s(x1),s(y)) # label(congruence). 36.014/36.014 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence). 36.014/36.014 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence). 36.014/36.014 ->(x1,y) -> ->(t(x1),t(y)) # label(congruence). 36.014/36.014 end_of_list. 36.014/36.014 36.014/36.014 formulas(goals). 36.014/36.014 (exists x1 ->(d,x1)) # label(goal). 36.014/36.014 end_of_list. 36.014/36.014 36.014/36.014 ============================== end of input ========================== 36.014/36.014 36.014/36.014 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 36.014/36.014 36.014/36.014 % Formulas that are not ordinary clauses: 36.014/36.014 1 ->(x1,y) -> ->(f(x1,x2),f(y,x2)) # label(congruence) # label(non_clause). [assumption]. 36.014/36.014 2 ->(x2,y) -> ->(f(x1,x2),f(x1,y)) # label(congruence) # label(non_clause). [assumption]. 36.014/36.014 3 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 36.014/36.014 4 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 36.014/36.014 5 ->(x1,y) -> ->(s(x1),s(y)) # label(congruence) # label(non_clause). [assumption]. 36.014/36.014 6 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 36.014/36.014 7 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 36.014/36.014 8 ->(x1,y) -> ->(t(x1),t(y)) # label(congruence) # label(non_clause). [assumption]. 36.014/36.014 9 (exists x1 ->(d,x1)) # label(goal) # label(non_clause) # label(goal). [goal]. 36.014/36.014 36.014/36.014 ============================== end of process non-clausal formulas === 36.014/36.014 36.014/36.014 ============================== CLAUSES FOR SEARCH ==================== 36.014/36.014 36.014/36.014 formulas(mace4_clauses). 36.014/36.014 -->(x,y) | ->(f(x,z),f(y,z)) # label(congruence). 36.014/36.014 -->(x,y) | ->(f(z,x),f(z,y)) # label(congruence). 36.014/36.014 -->(x,y) | ->(g(x,z),g(y,z)) # label(congruence). 36.014/36.014 -->(x,y) | ->(g(z,x),g(z,y)) # label(congruence). 36.014/36.014 -->(x,y) | ->(s(x),s(y)) # label(congruence). 36.014/36.014 -->(x,y) | ->(h(x,z),h(y,z)) # label(congruence). 36.014/36.014 -->(x,y) | ->(h(z,x),h(z,y)) # label(congruence). 36.014/36.014 -->(x,y) | ->(t(x),t(y)) # label(congruence). 36.014/36.014 -->(d,x) # label(goal). 36.014/36.014 end_of_list. 36.014/36.014 36.014/36.014 ============================== end of clauses for search ============= 36.014/36.014 36.014/36.014 % There are no natural numbers in the input. 36.014/36.014 36.014/36.014 ============================== DOMAIN SIZE 2 ========================= 36.014/36.014 36.014/36.014 ============================== MODEL ================================= 36.014/36.014 36.014/36.014 interpretation( 2, [number=1, seconds=0], [ 36.014/36.014 36.014/36.014 function(d, [ 0 ]), 36.014/36.014 36.014/36.014 function(t(_), [ 0, 0 ]), 36.014/36.014 36.014/36.014 function(s(_), [ 0, 0 ]), 36.014/36.014 36.014/36.014 function(h(_,_), [ 36.014/36.014 0, 0, 36.014/36.014 0, 0 ]), 36.014/36.014 36.014/36.014 function(f(_,_), [ 36.014/36.014 0, 0, 36.014/36.014 0, 0 ]), 36.014/36.014 36.014/36.014 function(g(_,_), [ 36.014/36.014 0, 0, 36.014/36.014 0, 0 ]), 36.014/36.014 36.014/36.014 relation(->(_,_), [ 36.014/36.014 0, 0, 36.014/36.014 0, 0 ]) 36.014/36.014 ]). 36.014/36.014 36.014/36.014 ============================== end of model ========================== 36.014/36.014 36.014/36.014 ============================== STATISTICS ============================ 36.014/36.014 36.014/36.014 For domain size 2. 36.014/36.014 36.014/36.014 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 36.014/36.014 Ground clauses: seen=58, kept=58. 36.014/36.014 Selections=17, assignments=17, propagations=4, current_models=1. 36.014/36.014 Rewrite_terms=114, rewrite_bools=60, indexes=2. 36.014/36.014 Rules_from_neg_clauses=0, cross_offs=0. 36.014/36.014 36.014/36.014 ============================== end of statistics ===================== 36.014/36.014 36.014/36.014 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 36.014/36.014 36.014/36.014 Exiting with 1 model. 36.014/36.014 36.014/36.014 Process 49257 exit (max_models) Wed Jul 14 10:49:30 2021 36.014/36.014 The process finished Wed Jul 14 10:49:30 2021 36.014/36.014 36.014/36.014 36.014/36.014 Mace4 cooked interpretation: 36.014/36.014 36.014/36.014 36.014/36.014 36.014/36.014 The problem is infeasible. 36.014/36.014 36.014/36.014 36.014/36.014 The problem is not joinable. 36.014/36.014 58.19user 4.26system 0:36.14elapsed 172%CPU (0avgtext+0avgdata 998228maxresident)k 36.014/36.014 0inputs+0outputs (0major+679846minor)pagefaults 0swaps