21.042/21.042 NO 21.042/21.042 21.042/21.042 Problem 1: 21.042/21.042 21.042/21.042 21.042/21.042 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 21.042/21.042 Confluence Problem: 21.042/21.042 (VAR vNonEmpty:S x:S y:S) 21.042/21.042 (STRATEGY CONTEXTSENSITIVE 21.042/21.042 (a) 21.042/21.042 (b) 21.042/21.042 (f 1) 21.042/21.042 (g 1 2) 21.042/21.042 (s 1) 21.042/21.042 (c) 21.042/21.042 (d) 21.042/21.042 (fSNonEmpty) 21.042/21.042 (h 1 2) 21.042/21.042 (k) 21.042/21.042 (l) 21.042/21.042 (pair 1 2) 21.042/21.042 (t 1) 21.042/21.042 ) 21.042/21.042 (RULES 21.042/21.042 a -> c 21.042/21.042 a -> d 21.042/21.042 b -> c 21.042/21.042 b -> d 21.042/21.042 f(x:S) -> pair(x:S,y:S) | s(x:S) ->* t(y:S) 21.042/21.042 g(x:S,x:S) -> h(x:S,x:S) 21.042/21.042 s(c) -> t(k) 21.042/21.042 s(c) -> t(l) 21.042/21.042 ) 21.042/21.042 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 21.042/21.042 21.042/21.042 21.042/21.042 Problem 1: 21.042/21.042 21.042/21.042 Inlining of Conditions Processor [STERN17]: 21.042/21.042 21.042/21.042 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 21.042/21.042 Confluence Problem: 21.042/21.042 (VAR vNonEmpty:S x:S y:S) 21.042/21.042 (STRATEGY CONTEXTSENSITIVE 21.042/21.042 (a) 21.042/21.042 (b) 21.042/21.042 (f 1) 21.042/21.042 (g 1 2) 21.042/21.042 (s 1) 21.042/21.042 (c) 21.042/21.042 (d) 21.042/21.042 (fSNonEmpty) 21.042/21.042 (h 1 2) 21.042/21.042 (k) 21.042/21.042 (l) 21.042/21.042 (pair 1 2) 21.042/21.042 (t 1) 21.042/21.042 ) 21.042/21.042 (RULES 21.042/21.042 a -> c 21.042/21.042 a -> d 21.042/21.042 b -> c 21.042/21.042 b -> d 21.042/21.042 f(x:S) -> pair(x:S,y:S) | s(x:S) ->* t(y:S) 21.042/21.042 g(x:S,x:S) -> h(x:S,x:S) 21.042/21.042 s(c) -> t(k) 21.042/21.042 s(c) -> t(l) 21.042/21.042 ) 21.042/21.042 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 21.042/21.042 21.042/21.042 21.042/21.042 Problem 1: 21.042/21.042 21.042/21.042 Clean CTRS Processor: 21.042/21.042 21.042/21.042 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 21.042/21.042 Confluence Problem: 21.042/21.042 (VAR x:S y:S) 21.042/21.042 (STRATEGY CONTEXTSENSITIVE 21.042/21.042 (a) 21.042/21.042 (b) 21.042/21.042 (f 1) 21.042/21.042 (g 1 2) 21.042/21.042 (s 1) 21.042/21.042 (c) 21.042/21.042 (d) 21.042/21.042 (fSNonEmpty) 21.042/21.042 (h 1 2) 21.042/21.042 (k) 21.042/21.042 (l) 21.042/21.042 (pair 1 2) 21.042/21.042 (t 1) 21.042/21.042 ) 21.042/21.042 (RULES 21.042/21.042 a -> c 21.042/21.042 a -> d 21.042/21.042 b -> c 21.042/21.042 b -> d 21.042/21.042 f(x:S) -> pair(x:S,y:S) | s(x:S) ->* t(y:S) 21.042/21.042 g(x:S,x:S) -> h(x:S,x:S) 21.042/21.042 s(c) -> t(k) 21.042/21.042 s(c) -> t(l) 21.042/21.042 ) 21.042/21.042 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 21.042/21.042 21.042/21.042 CRule InfChecker Info: 21.042/21.042 a -> c 21.042/21.042 Rule remains 21.042/21.042 Proof: 21.042/21.042 NO_CONDS 21.042/21.042 21.042/21.042 CRule InfChecker Info: 21.042/21.042 a -> d 21.042/21.042 Rule remains 21.042/21.042 Proof: 21.042/21.042 NO_CONDS 21.042/21.042 21.042/21.042 CRule InfChecker Info: 21.042/21.042 b -> c 21.042/21.042 Rule remains 21.042/21.042 Proof: 21.042/21.042 NO_CONDS 21.042/21.042 21.042/21.042 CRule InfChecker Info: 21.042/21.042 b -> d 21.042/21.042 Rule remains 21.042/21.042 Proof: 21.042/21.042 NO_CONDS 21.042/21.042 21.042/21.042 CRule InfChecker Info: 21.042/21.042 f(x:S) -> pair(x:S,y:S) | s(x:S) ->* t(y:S) 21.042/21.042 Rule remains 21.042/21.042 Proof: 21.042/21.042 NO 21.042/21.042 21.042/21.042 Problem 1: 21.042/21.042 21.042/21.042 Infeasibility Problem: 21.042/21.042 [(VAR vNonEmpty:S vNonEmpty:S:S x:S:S y:S:S) 21.042/21.042 (STRATEGY CONTEXTSENSITIVE 21.042/21.042 (a) 21.042/21.042 (b) 21.042/21.042 (f 1) 21.042/21.042 (g 1 2) 21.042/21.042 (s 1) 21.042/21.042 (c) 21.042/21.042 (d) 21.042/21.042 (fSNonEmpty) 21.042/21.042 (h 1 2) 21.042/21.042 (k) 21.042/21.042 (l) 21.042/21.042 (pair 1 2) 21.042/21.042 (t 1) 21.042/21.042 ) 21.042/21.042 (RULES 21.042/21.042 a -> c 21.042/21.042 a -> d 21.042/21.042 b -> c 21.042/21.042 b -> d 21.042/21.042 f(x:S:S) -> pair(x:S:S,y:S:S) | s(x:S:S) ->* t(y:S:S) 21.042/21.042 g(x:S:S,x:S:S) -> h(x:S:S,x:S:S) 21.042/21.042 s(c) -> t(k) 21.042/21.042 s(c) -> t(l) 21.042/21.042 )] 21.042/21.042 21.042/21.042 Infeasibility Conditions: 21.042/21.042 s(x:S:S) ->* t(y:S:S) 21.042/21.042 21.042/21.042 Problem 1: 21.042/21.042 21.042/21.042 Obtaining a proof using Prover9: 21.042/21.042 21.042/21.042 -> Prover9 Output: 21.042/21.042 ============================== Prover9 =============================== 21.042/21.042 Prover9 (64) version 2009-11A, November 2009. 21.042/21.042 Process 48673 was started by ubuntu on ubuntu, 21.042/21.042 Wed Jul 14 10:48:14 2021 21.042/21.042 The command was "./prover9 -f /tmp/prover948666-0.in". 21.042/21.042 ============================== end of head =========================== 21.042/21.042 21.042/21.042 ============================== INPUT ================================= 21.042/21.042 21.042/21.042 % Reading from file /tmp/prover948666-0.in 21.042/21.042 21.042/21.042 assign(max_seconds,20). 21.042/21.042 21.042/21.042 formulas(assumptions). 21.042/21.042 ->*_s0(x,x) # label(reflexivity). 21.042/21.042 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 21.042/21.042 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence). 21.042/21.042 ->_s0(x1,y) -> ->_s0(g(x1,x2),g(y,x2)) # label(congruence). 21.042/21.042 ->_s0(x2,y) -> ->_s0(g(x1,x2),g(x1,y)) # label(congruence). 21.042/21.042 ->_s0(x1,y) -> ->_s0(s(x1),s(y)) # label(congruence). 21.042/21.042 ->_s0(x1,y) -> ->_s0(h(x1,x2),h(y,x2)) # label(congruence). 21.042/21.042 ->_s0(x2,y) -> ->_s0(h(x1,x2),h(x1,y)) # label(congruence). 21.042/21.042 ->_s0(x1,y) -> ->_s0(pair(x1,x2),pair(y,x2)) # label(congruence). 21.042/21.042 ->_s0(x2,y) -> ->_s0(pair(x1,x2),pair(x1,y)) # label(congruence). 21.042/21.042 ->_s0(x1,y) -> ->_s0(t(x1),t(y)) # label(congruence). 21.042/21.042 ->_s0(a,c) # label(replacement). 21.042/21.042 ->_s0(a,d) # label(replacement). 21.042/21.042 ->_s0(b,c) # label(replacement). 21.042/21.042 ->_s0(b,d) # label(replacement). 21.042/21.042 ->*_s0(s(x2),t(x3)) -> ->_s0(f(x2),pair(x2,x3)) # label(replacement). 21.042/21.042 ->_s0(g(x2,x2),h(x2,x2)) # label(replacement). 21.042/21.042 ->_s0(s(c),t(k)) # label(replacement). 21.042/21.042 ->_s0(s(c),t(l)) # label(replacement). 21.042/21.042 end_of_list. 21.042/21.042 21.042/21.042 formulas(goals). 21.042/21.042 (exists x2 exists x3 ->*_s0(s(x2),t(x3))) # label(goal). 21.042/21.042 end_of_list. 21.042/21.042 21.042/21.042 ============================== end of input ========================== 21.042/21.042 21.042/21.042 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 21.042/21.042 21.042/21.042 % Formulas that are not ordinary clauses: 21.042/21.042 1 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 21.042/21.042 2 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 3 ->_s0(x1,y) -> ->_s0(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 4 ->_s0(x2,y) -> ->_s0(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 5 ->_s0(x1,y) -> ->_s0(s(x1),s(y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 6 ->_s0(x1,y) -> ->_s0(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 7 ->_s0(x2,y) -> ->_s0(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 8 ->_s0(x1,y) -> ->_s0(pair(x1,x2),pair(y,x2)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 9 ->_s0(x2,y) -> ->_s0(pair(x1,x2),pair(x1,y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 10 ->_s0(x1,y) -> ->_s0(t(x1),t(y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 11 ->*_s0(s(x2),t(x3)) -> ->_s0(f(x2),pair(x2,x3)) # label(replacement) # label(non_clause). [assumption]. 21.042/21.042 12 (exists x2 exists x3 ->*_s0(s(x2),t(x3))) # label(goal) # label(non_clause) # label(goal). [goal]. 21.042/21.042 21.042/21.042 ============================== end of process non-clausal formulas === 21.042/21.042 21.042/21.042 ============================== PROCESS INITIAL CLAUSES =============== 21.042/21.042 21.042/21.042 % Clauses before input processing: 21.042/21.042 21.042/21.042 formulas(usable). 21.042/21.042 end_of_list. 21.042/21.042 21.042/21.042 formulas(sos). 21.042/21.042 ->*_s0(x,x) # label(reflexivity). [assumption]. 21.042/21.042 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 21.042/21.042 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)]. 21.042/21.042 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(3)]. 21.042/21.042 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(4)]. 21.042/21.042 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(5)]. 21.042/21.042 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(6)]. 21.042/21.042 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(7)]. 21.042/21.042 -->_s0(x,y) | ->_s0(pair(x,z),pair(y,z)) # label(congruence). [clausify(8)]. 21.042/21.042 -->_s0(x,y) | ->_s0(pair(z,x),pair(z,y)) # label(congruence). [clausify(9)]. 21.042/21.042 -->_s0(x,y) | ->_s0(t(x),t(y)) # label(congruence). [clausify(10)]. 21.042/21.042 ->_s0(a,c) # label(replacement). [assumption]. 21.042/21.042 ->_s0(a,d) # label(replacement). [assumption]. 21.042/21.042 ->_s0(b,c) # label(replacement). [assumption]. 21.042/21.042 ->_s0(b,d) # label(replacement). [assumption]. 21.042/21.042 -->*_s0(s(x),t(y)) | ->_s0(f(x),pair(x,y)) # label(replacement). [clausify(11)]. 21.042/21.042 ->_s0(g(x,x),h(x,x)) # label(replacement). [assumption]. 21.042/21.042 ->_s0(s(c),t(k)) # label(replacement). [assumption]. 21.042/21.042 ->_s0(s(c),t(l)) # label(replacement). [assumption]. 21.042/21.042 -->*_s0(s(x),t(y)) # label(goal). [deny(12)]. 21.042/21.042 end_of_list. 21.042/21.042 21.042/21.042 formulas(demodulators). 21.042/21.042 end_of_list. 21.042/21.042 21.042/21.042 ============================== PREDICATE ELIMINATION ================= 21.042/21.042 21.042/21.042 No predicates eliminated. 21.042/21.042 21.042/21.042 ============================== end predicate elimination ============= 21.042/21.042 21.042/21.042 Auto_denials: 21.042/21.042 % copying label goal to answer in negative clause 21.042/21.042 21.042/21.042 Term ordering decisions: 21.042/21.042 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 21.042/21.042 Function symbol precedence: function_order([ c, a, b, d, k, l, h, pair, g, t, s, f ]). 21.042/21.042 After inverse_order: (no changes). 21.042/21.042 Unfolding symbols: (none). 21.042/21.042 21.042/21.042 Auto_inference settings: 21.042/21.042 % set(neg_binary_resolution). % (HNE depth_diff=-9) 21.042/21.042 % clear(ordered_res). % (HNE depth_diff=-9) 21.042/21.042 % set(ur_resolution). % (HNE depth_diff=-9) 21.042/21.042 % set(ur_resolution) -> set(pos_ur_resolution). 21.042/21.042 % set(ur_resolution) -> set(neg_ur_resolution). 21.042/21.042 21.042/21.042 Auto_process settings: (no changes). 21.042/21.042 21.042/21.042 kept: 13 ->*_s0(x,x) # label(reflexivity). [assumption]. 21.042/21.042 kept: 14 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 21.042/21.042 kept: 15 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)]. 21.042/21.042 kept: 16 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(3)]. 21.042/21.042 kept: 17 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(4)]. 21.042/21.042 kept: 18 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(5)]. 21.042/21.042 kept: 19 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(6)]. 21.042/21.042 kept: 20 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(7)]. 21.042/21.042 kept: 21 -->_s0(x,y) | ->_s0(pair(x,z),pair(y,z)) # label(congruence). [clausify(8)]. 21.042/21.042 kept: 22 -->_s0(x,y) | ->_s0(pair(z,x),pair(z,y)) # label(congruence). [clausify(9)]. 21.042/21.042 kept: 23 -->_s0(x,y) | ->_s0(t(x),t(y)) # label(congruence). [clausify(10)]. 21.042/21.042 kept: 24 ->_s0(a,c) # label(replacement). [assumption]. 21.042/21.042 kept: 25 ->_s0(a,d) # label(replacement). [assumption]. 21.042/21.042 kept: 26 ->_s0(b,c) # label(replacement). [assumption]. 21.042/21.042 kept: 27 ->_s0(b,d) # label(replacement). [assumption]. 21.042/21.042 kept: 28 -->*_s0(s(x),t(y)) | ->_s0(f(x),pair(x,y)) # label(replacement). [clausify(11)]. 21.042/21.042 kept: 29 ->_s0(g(x,x),h(x,x)) # label(replacement). [assumption]. 21.042/21.042 kept: 30 ->_s0(s(c),t(k)) # label(replacement). [assumption]. 21.042/21.042 kept: 31 ->_s0(s(c),t(l)) # label(replacement). [assumption]. 21.042/21.042 kept: 32 -->*_s0(s(x),t(y)) # label(goal) # answer(goal). [deny(12)]. 21.042/21.042 21.042/21.042 ============================== end of process initial clauses ======== 21.042/21.042 21.042/21.042 ============================== CLAUSES FOR SEARCH ==================== 21.042/21.042 21.042/21.042 % Clauses after input processing: 21.042/21.042 21.042/21.042 formulas(usable). 21.042/21.042 end_of_list. 21.042/21.042 21.042/21.042 formulas(sos). 21.042/21.042 13 ->*_s0(x,x) # label(reflexivity). [assumption]. 21.042/21.042 14 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 21.042/21.042 15 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)]. 21.042/21.042 16 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(3)]. 21.042/21.042 17 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(4)]. 21.042/21.042 18 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(5)]. 21.042/21.042 19 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(6)]. 21.042/21.042 20 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(7)]. 21.042/21.042 21 -->_s0(x,y) | ->_s0(pair(x,z),pair(y,z)) # label(congruence). [clausify(8)]. 21.042/21.042 22 -->_s0(x,y) | ->_s0(pair(z,x),pair(z,y)) # label(congruence). [clausify(9)]. 21.042/21.042 23 -->_s0(x,y) | ->_s0(t(x),t(y)) # label(congruence). [clausify(10)]. 21.042/21.042 24 ->_s0(a,c) # label(replacement). [assumption]. 21.042/21.042 25 ->_s0(a,d) # label(replacement). [assumption]. 21.042/21.042 26 ->_s0(b,c) # label(replacement). [assumption]. 21.042/21.042 27 ->_s0(b,d) # label(replacement). [assumption]. 21.042/21.042 29 ->_s0(g(x,x),h(x,x)) # label(replacement). [assumption]. 21.042/21.042 30 ->_s0(s(c),t(k)) # label(replacement). [assumption]. 21.042/21.042 31 ->_s0(s(c),t(l)) # label(replacement). [assumption]. 21.042/21.042 32 -->*_s0(s(x),t(y)) # label(goal) # answer(goal). [deny(12)]. 21.042/21.042 end_of_list. 21.042/21.042 21.042/21.042 formulas(demodulators). 21.042/21.042 end_of_list. 21.042/21.042 21.042/21.042 ============================== end of clauses for search ============= 21.042/21.042 21.042/21.042 ============================== SEARCH ================================ 21.042/21.042 21.042/21.042 % Starting search at 0.00 seconds. 21.042/21.042 21.042/21.042 given #1 (I,wt=3): 13 ->*_s0(x,x) # label(reflexivity). [assumption]. 21.042/21.042 21.042/21.042 given #2 (I,wt=9): 14 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 21.042/21.042 21.042/21.042 given #3 (I,wt=8): 15 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)]. 21.042/21.042 21.042/21.042 given #4 (I,wt=10): 16 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(3)]. 21.042/21.042 21.042/21.042 given #5 (I,wt=10): 17 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(4)]. 21.042/21.042 21.042/21.042 given #6 (I,wt=8): 18 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(5)]. 21.042/21.042 21.042/21.042 given #7 (I,wt=10): 19 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(6)]. 21.042/21.042 21.042/21.042 given #8 (I,wt=10): 20 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(7)]. 21.042/21.042 21.042/21.042 given #9 (I,wt=10): 21 -->_s0(x,y) | ->_s0(pair(x,z),pair(y,z)) # label(congruence). [clausify(8)]. 21.042/21.042 21.042/21.042 given #10 (I,wt=10): 22 -->_s0(x,y) | ->_s0(pair(z,x),pair(z,y)) # label(congruence). [clausify(9)]. 21.042/21.042 21.042/21.042 given #11 (I,wt=8): 23 -->_s0(x,y) | ->_s0(t(x),t(y)) # label(congruence). [clausify(10)]. 21.042/21.042 21.042/21.042 given #12 (I,wt=3): 24 ->_s0(a,c) # label(replacement). [assumption]. 21.042/21.042 21.042/21.042 given #13 (I,wt=3): 25 ->_s0(a,d) # label(replacement). [assumption]. 21.042/21.042 21.042/21.042 given #14 (I,wt=3): 26 ->_s0(b,c) # label(replacement). [assumption]. 21.042/21.042 21.042/21.042 given #15 (I,wt=3): 27 ->_s0(b,d) # label(replacement). [assumption]. 21.042/21.042 21.042/21.042 given #16 (I,wt=7): 29 ->_s0(g(x,x),h(x,x)) # label(replacement). [assumption]. 21.042/21.042 21.042/21.042 given #17 (I,wt=5): 30 ->_s0(s(c),t(k)) # label(replacement). [assumption]. 21.042/21.042 21.042/21.042 ============================== PROOF ================================= 21.042/21.042 21.042/21.042 % Proof 1 at 0.00 (+ 0.00) seconds: goal. 21.042/21.042 % Length of proof is 8. 21.042/21.042 % Level of proof is 3. 21.042/21.042 % Maximum clause weight is 9.000. 21.042/21.042 % Given clauses 17. 21.042/21.042 21.042/21.042 1 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 21.042/21.042 12 (exists x2 exists x3 ->*_s0(s(x2),t(x3))) # label(goal) # label(non_clause) # label(goal). [goal]. 21.042/21.042 13 ->*_s0(x,x) # label(reflexivity). [assumption]. 21.042/21.042 14 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 21.042/21.042 30 ->_s0(s(c),t(k)) # label(replacement). [assumption]. 21.042/21.042 32 -->*_s0(s(x),t(y)) # label(goal) # answer(goal). [deny(12)]. 21.042/21.042 92 ->*_s0(s(c),t(k)). [ur(14,a,30,a,b,13,a)]. 21.042/21.042 93 $F # answer(goal). [resolve(92,a,32,a)]. 21.042/21.042 21.042/21.042 ============================== end of proof ========================== 21.042/21.042 21.042/21.042 ============================== STATISTICS ============================ 21.042/21.042 21.042/21.042 Given=17. Generated=80. Kept=80. proofs=1. 21.042/21.042 Usable=17. Sos=52. Demods=0. Limbo=9, Disabled=21. Hints=0. 21.042/21.042 Kept_by_rule=0, Deleted_by_rule=0. 21.042/21.042 Forward_subsumed=0. Back_subsumed=1. 21.042/21.042 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 21.042/21.042 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 21.042/21.042 Demod_attempts=0. Demod_rewrites=0. 21.042/21.042 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 21.042/21.042 Nonunit_fsub_feature_tests=3. Nonunit_bsub_feature_tests=19. 21.042/21.042 Megabytes=0.16. 21.042/21.042 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 21.042/21.042 21.042/21.042 ============================== end of statistics ===================== 21.042/21.042 21.042/21.042 ============================== end of search ========================= 21.042/21.042 21.042/21.042 THEOREM PROVED 21.042/21.042 21.042/21.042 Exiting with 1 proof. 21.042/21.042 21.042/21.042 Process 48673 exit (max_proofs) Wed Jul 14 10:48:14 2021 21.042/21.042 21.042/21.042 21.042/21.042 The problem is feasible. 21.042/21.042 21.042/21.042 21.042/21.042 CRule InfChecker Info: 21.042/21.042 g(x:S,x:S) -> h(x:S,x:S) 21.042/21.042 Rule remains 21.042/21.042 Proof: 21.042/21.042 NO_CONDS 21.042/21.042 21.042/21.042 CRule InfChecker Info: 21.042/21.042 s(c) -> t(k) 21.042/21.042 Rule remains 21.042/21.042 Proof: 21.042/21.042 NO_CONDS 21.042/21.042 21.042/21.042 CRule InfChecker Info: 21.042/21.042 s(c) -> t(l) 21.042/21.042 Rule remains 21.042/21.042 Proof: 21.042/21.042 NO_CONDS 21.042/21.042 21.042/21.042 Problem 1: 21.042/21.042 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 21.042/21.042 Confluence Problem: 21.042/21.042 (VAR x:S y:S) 21.042/21.042 (STRATEGY CONTEXTSENSITIVE 21.042/21.042 (a) 21.042/21.042 (b) 21.042/21.042 (f 1) 21.042/21.042 (g 1 2) 21.042/21.042 (s 1) 21.042/21.042 (c) 21.042/21.042 (d) 21.042/21.042 (fSNonEmpty) 21.042/21.042 (h 1 2) 21.042/21.042 (k) 21.042/21.042 (l) 21.042/21.042 (pair 1 2) 21.042/21.042 (t 1) 21.042/21.042 ) 21.042/21.042 (RULES 21.042/21.042 a -> c 21.042/21.042 a -> d 21.042/21.042 b -> c 21.042/21.042 b -> d 21.042/21.042 f(x:S) -> pair(x:S,y:S) | s(x:S) ->* t(y:S) 21.042/21.042 g(x:S,x:S) -> h(x:S,x:S) 21.042/21.042 s(c) -> t(k) 21.042/21.042 s(c) -> t(l) 21.042/21.042 ) 21.042/21.042 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 21.042/21.042 21.042/21.042 Critical Pairs Processor: 21.042/21.042 -> Rules: 21.042/21.042 a -> c 21.042/21.042 a -> d 21.042/21.042 b -> c 21.042/21.042 b -> d 21.042/21.042 f(x:S) -> pair(x:S,y:S) | s(x:S) ->* t(y:S) 21.042/21.042 g(x:S,x:S) -> h(x:S,x:S) 21.042/21.042 s(c) -> t(k) 21.042/21.042 s(c) -> t(l) 21.042/21.042 -> Vars: 21.042/21.042 "x", "y", "x" 21.042/21.042 -> FVars: 21.042/21.042 "x3", "x4", "x5" 21.042/21.042 -> PVars: 21.042/21.042 "x": ["x3", "x5"], "y": ["x4"] 21.042/21.042 21.042/21.042 -> Rlps: 21.042/21.042 crule: a -> c, id: 1, possubterms: a-> [] 21.042/21.042 crule: a -> d, id: 2, possubterms: a-> [] 21.042/21.042 crule: b -> c, id: 3, possubterms: b-> [] 21.042/21.042 crule: b -> d, id: 4, possubterms: b-> [] 21.042/21.042 crule: f(x3:S) -> pair(x3:S,x4:S) | s(x3:S) ->* t(x4:S), id: 5, possubterms: f(x3:S)-> [] 21.042/21.042 crule: g(x5:S,x5:S) -> h(x5:S,x5:S), id: 6, possubterms: g(x5:S,x5:S)-> [] 21.042/21.042 crule: s(c) -> t(k), id: 7, possubterms: s(c)-> [], c-> [1] 21.042/21.042 crule: s(c) -> t(l), id: 8, possubterms: s(c)-> [], c-> [1] 21.042/21.042 21.042/21.042 -> Unifications: 21.042/21.042 R2 unifies with R1 at p: [], l: a, lp: a, conds: {}, sig: {}, l': a, r: d, r': c 21.042/21.042 R4 unifies with R3 at p: [], l: b, lp: b, conds: {}, sig: {}, l': b, r: d, r': c 21.042/21.042 R8 unifies with R7 at p: [], l: s(c), lp: s(c), conds: {}, sig: {}, l': s(c), r: t(l), r': t(k) 21.042/21.042 21.042/21.042 -> Critical pairs info: 21.042/21.042 => Not trivial, Overlay, N1 21.042/21.042 => Not trivial, Overlay, N2 21.042/21.042 21.042/21.042 -> Problem conclusions: 21.042/21.042 Not left linear, Not right linear, Not linear 21.042/21.042 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 21.042/21.042 CTRS Type: 3 21.042/21.042 Deterministic, Strongly deterministic 21.042/21.042 Oriented CTRS, Properly oriented CTRS, Not join CTRS 21.042/21.042 Maybe right-stable CTRS, Overlay CTRS 21.042/21.042 Maybe normal CTRS, Maybe almost normal CTRS 21.042/21.042 Maybe terminating CTRS, Maybe joinable CCPs 21.042/21.042 Maybe level confluent 21.042/21.042 Maybe confluent 21.042/21.042 21.042/21.042 Problem 1: 21.042/21.042 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 21.042/21.042 Confluence Problem: 21.042/21.042 (VAR x:S y:S) 21.042/21.042 (STRATEGY CONTEXTSENSITIVE 21.042/21.042 (a) 21.042/21.042 (b) 21.042/21.042 (f 1) 21.042/21.042 (g 1 2) 21.042/21.042 (s 1) 21.042/21.042 (c) 21.042/21.042 (d) 21.042/21.042 (fSNonEmpty) 21.042/21.042 (h 1 2) 21.042/21.042 (k) 21.042/21.042 (l) 21.042/21.042 (pair 1 2) 21.042/21.042 (t 1) 21.042/21.042 ) 21.042/21.042 (RULES 21.042/21.042 a -> c 21.042/21.042 a -> d 21.042/21.042 b -> c 21.042/21.042 b -> d 21.042/21.042 f(x:S) -> pair(x:S,y:S) | s(x:S) ->* t(y:S) 21.042/21.042 g(x:S,x:S) -> h(x:S,x:S) 21.042/21.042 s(c) -> t(k) 21.042/21.042 s(c) -> t(l) 21.042/21.042 ) 21.042/21.042 Critical Pairs: 21.042/21.042 => Not trivial, Overlay, N1 21.042/21.042 => Not trivial, Overlay, N2 21.042/21.042 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 21.042/21.042 21.042/21.042 Conditional Critical Pairs Distributor Processor 21.042/21.042 21.042/21.042 Problem 1: 21.042/21.042 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 21.042/21.042 Confluence Problem: 21.042/21.042 (VAR x:S y:S) 21.042/21.042 (STRATEGY CONTEXTSENSITIVE 21.042/21.042 (a) 21.042/21.042 (b) 21.042/21.042 (f 1) 21.042/21.042 (g 1 2) 21.042/21.042 (s 1) 21.042/21.042 (c) 21.042/21.042 (d) 21.042/21.042 (fSNonEmpty) 21.042/21.042 (h 1 2) 21.042/21.042 (k) 21.042/21.042 (l) 21.042/21.042 (pair 1 2) 21.042/21.042 (t 1) 21.042/21.042 ) 21.042/21.042 (RULES 21.042/21.042 a -> c 21.042/21.042 a -> d 21.042/21.042 b -> c 21.042/21.042 b -> d 21.042/21.042 f(x:S) -> pair(x:S,y:S) | s(x:S) ->* t(y:S) 21.042/21.042 g(x:S,x:S) -> h(x:S,x:S) 21.042/21.042 s(c) -> t(k) 21.042/21.042 s(c) -> t(l) 21.042/21.042 ) 21.042/21.042 Critical Pairs: 21.042/21.042 => Not trivial, Overlay, N1 21.042/21.042 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 21.042/21.042 21.042/21.042 InfChecker Different Ground and Normal No Conditions CCP Terms Processor: 21.042/21.042 Proof: 21.042/21.042 YES 21.042/21.042 21.042/21.042 Problem 1: 21.042/21.042 21.042/21.042 Infeasibility Problem: 21.042/21.042 [(VAR vNonEmpty:S x:S y:S) 21.042/21.042 (STRATEGY CONTEXTSENSITIVE 21.042/21.042 (a) 21.042/21.042 (b) 21.042/21.042 (f 1) 21.042/21.042 (g 1 2) 21.042/21.042 (s 1) 21.042/21.042 (c) 21.042/21.042 (d) 21.042/21.042 (fSNonEmpty) 21.042/21.042 (h 1 2) 21.042/21.042 (k) 21.042/21.042 (l) 21.042/21.042 (pair 1 2) 21.042/21.042 (t 1) 21.042/21.042 ) 21.042/21.042 (RULES 21.042/21.042 a -> c 21.042/21.042 a -> d 21.042/21.042 b -> c 21.042/21.042 b -> d 21.042/21.042 f(x:S) -> pair(x:S,y:S) | s(x:S) ->* t(y:S) 21.042/21.042 g(x:S,x:S) -> h(x:S,x:S) 21.042/21.042 s(c) -> t(k) 21.042/21.042 s(c) -> t(l) 21.042/21.042 )] 21.042/21.042 21.042/21.042 Infeasibility Conditions: 21.042/21.042 t(k) -> y:S 21.042/21.042 21.042/21.042 Problem 1: 21.042/21.042 21.042/21.042 Obtaining a model using Mace4: 21.042/21.042 21.042/21.042 -> Usable Rules: 21.042/21.042 Empty 21.042/21.042 21.042/21.042 -> Mace4 Output: 21.042/21.042 ============================== Mace4 ================================= 21.042/21.042 Mace4 (64) version 2009-11A, November 2009. 21.042/21.042 Process 48715 was started by ubuntu on ubuntu, 21.042/21.042 Wed Jul 14 10:48:14 2021 21.042/21.042 The command was "./mace4 -c -f /tmp/mace448691-2.in". 21.042/21.042 ============================== end of head =========================== 21.042/21.042 21.042/21.042 ============================== INPUT ================================= 21.042/21.042 21.042/21.042 % Reading from file /tmp/mace448691-2.in 21.042/21.042 21.042/21.042 assign(max_seconds,6). 21.042/21.042 21.042/21.042 formulas(assumptions). 21.042/21.042 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence). 21.042/21.042 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence). 21.042/21.042 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence). 21.042/21.042 ->(x1,y) -> ->(s(x1),s(y)) # label(congruence). 21.042/21.042 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence). 21.042/21.042 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence). 21.042/21.042 ->(x1,y) -> ->(pair(x1,x2),pair(y,x2)) # label(congruence). 21.042/21.042 ->(x2,y) -> ->(pair(x1,x2),pair(x1,y)) # label(congruence). 21.042/21.042 ->(x1,y) -> ->(t(x1),t(y)) # label(congruence). 21.042/21.042 end_of_list. 21.042/21.042 21.042/21.042 formulas(goals). 21.042/21.042 (exists x2 ->(t(k),x2)) # label(goal). 21.042/21.042 end_of_list. 21.042/21.042 21.042/21.042 ============================== end of input ========================== 21.042/21.042 21.042/21.042 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 21.042/21.042 21.042/21.042 % Formulas that are not ordinary clauses: 21.042/21.042 1 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 2 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 3 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 4 ->(x1,y) -> ->(s(x1),s(y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 5 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 6 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 7 ->(x1,y) -> ->(pair(x1,x2),pair(y,x2)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 8 ->(x2,y) -> ->(pair(x1,x2),pair(x1,y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 9 ->(x1,y) -> ->(t(x1),t(y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 10 (exists x2 ->(t(k),x2)) # label(goal) # label(non_clause) # label(goal). [goal]. 21.042/21.042 21.042/21.042 ============================== end of process non-clausal formulas === 21.042/21.042 21.042/21.042 ============================== CLAUSES FOR SEARCH ==================== 21.042/21.042 21.042/21.042 formulas(mace4_clauses). 21.042/21.042 -->(x,y) | ->(f(x),f(y)) # label(congruence). 21.042/21.042 -->(x,y) | ->(g(x,z),g(y,z)) # label(congruence). 21.042/21.042 -->(x,y) | ->(g(z,x),g(z,y)) # label(congruence). 21.042/21.042 -->(x,y) | ->(s(x),s(y)) # label(congruence). 21.042/21.042 -->(x,y) | ->(h(x,z),h(y,z)) # label(congruence). 21.042/21.042 -->(x,y) | ->(h(z,x),h(z,y)) # label(congruence). 21.042/21.042 -->(x,y) | ->(pair(x,z),pair(y,z)) # label(congruence). 21.042/21.042 -->(x,y) | ->(pair(z,x),pair(z,y)) # label(congruence). 21.042/21.042 -->(x,y) | ->(t(x),t(y)) # label(congruence). 21.042/21.042 -->(t(k),x) # label(goal). 21.042/21.042 end_of_list. 21.042/21.042 21.042/21.042 ============================== end of clauses for search ============= 21.042/21.042 21.042/21.042 % There are no natural numbers in the input. 21.042/21.042 21.042/21.042 ============================== DOMAIN SIZE 2 ========================= 21.042/21.042 21.042/21.042 ============================== MODEL ================================= 21.042/21.042 21.042/21.042 interpretation( 2, [number=1, seconds=0], [ 21.042/21.042 21.042/21.042 function(k, [ 0 ]), 21.042/21.042 21.042/21.042 function(t(_), [ 0, 0 ]), 21.042/21.042 21.042/21.042 function(f(_), [ 0, 0 ]), 21.042/21.042 21.042/21.042 function(s(_), [ 0, 0 ]), 21.042/21.042 21.042/21.042 function(h(_,_), [ 21.042/21.042 0, 0, 21.042/21.042 0, 0 ]), 21.042/21.042 21.042/21.042 function(pair(_,_), [ 21.042/21.042 0, 0, 21.042/21.042 0, 0 ]), 21.042/21.042 21.042/21.042 function(g(_,_), [ 21.042/21.042 0, 0, 21.042/21.042 0, 0 ]), 21.042/21.042 21.042/21.042 relation(->(_,_), [ 21.042/21.042 0, 0, 21.042/21.042 0, 0 ]) 21.042/21.042 ]). 21.042/21.042 21.042/21.042 ============================== end of model ========================== 21.042/21.042 21.042/21.042 ============================== STATISTICS ============================ 21.042/21.042 21.042/21.042 For domain size 2. 21.042/21.042 21.042/21.042 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 21.042/21.042 Ground clauses: seen=62, kept=62. 21.042/21.042 Selections=19, assignments=19, propagations=4, current_models=1. 21.042/21.042 Rewrite_terms=124, rewrite_bools=65, indexes=4. 21.042/21.042 Rules_from_neg_clauses=0, cross_offs=0. 21.042/21.042 21.042/21.042 ============================== end of statistics ===================== 21.042/21.042 21.042/21.042 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 21.042/21.042 21.042/21.042 Exiting with 1 model. 21.042/21.042 21.042/21.042 Process 48715 exit (max_models) Wed Jul 14 10:48:14 2021 21.042/21.042 The process finished Wed Jul 14 10:48:14 2021 21.042/21.042 21.042/21.042 21.042/21.042 Mace4 cooked interpretation: 21.042/21.042 21.042/21.042 21.042/21.042 21.042/21.042 The problem is infeasible. 21.042/21.042 YES 21.042/21.042 21.042/21.042 Problem 1: 21.042/21.042 21.042/21.042 Infeasibility Problem: 21.042/21.042 [(VAR vNonEmpty:S x:S y:S) 21.042/21.042 (STRATEGY CONTEXTSENSITIVE 21.042/21.042 (a) 21.042/21.042 (b) 21.042/21.042 (f 1) 21.042/21.042 (g 1 2) 21.042/21.042 (s 1) 21.042/21.042 (c) 21.042/21.042 (d) 21.042/21.042 (fSNonEmpty) 21.042/21.042 (h 1 2) 21.042/21.042 (k) 21.042/21.042 (l) 21.042/21.042 (pair 1 2) 21.042/21.042 (t 1) 21.042/21.042 ) 21.042/21.042 (RULES 21.042/21.042 a -> c 21.042/21.042 a -> d 21.042/21.042 b -> c 21.042/21.042 b -> d 21.042/21.042 f(x:S) -> pair(x:S,y:S) | s(x:S) ->* t(y:S) 21.042/21.042 g(x:S,x:S) -> h(x:S,x:S) 21.042/21.042 s(c) -> t(k) 21.042/21.042 s(c) -> t(l) 21.042/21.042 )] 21.042/21.042 21.042/21.042 Infeasibility Conditions: 21.042/21.042 t(l) -> x:S 21.042/21.042 21.042/21.042 Problem 1: 21.042/21.042 21.042/21.042 Obtaining a model using Mace4: 21.042/21.042 21.042/21.042 -> Usable Rules: 21.042/21.042 Empty 21.042/21.042 21.042/21.042 -> Mace4 Output: 21.042/21.042 ============================== Mace4 ================================= 21.042/21.042 Mace4 (64) version 2009-11A, November 2009. 21.042/21.042 Process 48760 was started by ubuntu on ubuntu, 21.042/21.042 Wed Jul 14 10:48:26 2021 21.042/21.042 The command was "./mace4 -c -f /tmp/mace448746-2.in". 21.042/21.042 ============================== end of head =========================== 21.042/21.042 21.042/21.042 ============================== INPUT ================================= 21.042/21.042 21.042/21.042 % Reading from file /tmp/mace448746-2.in 21.042/21.042 21.042/21.042 assign(max_seconds,6). 21.042/21.042 21.042/21.042 formulas(assumptions). 21.042/21.042 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence). 21.042/21.042 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence). 21.042/21.042 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence). 21.042/21.042 ->(x1,y) -> ->(s(x1),s(y)) # label(congruence). 21.042/21.042 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence). 21.042/21.042 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence). 21.042/21.042 ->(x1,y) -> ->(pair(x1,x2),pair(y,x2)) # label(congruence). 21.042/21.042 ->(x2,y) -> ->(pair(x1,x2),pair(x1,y)) # label(congruence). 21.042/21.042 ->(x1,y) -> ->(t(x1),t(y)) # label(congruence). 21.042/21.042 end_of_list. 21.042/21.042 21.042/21.042 formulas(goals). 21.042/21.042 (exists x1 ->(t(l),x1)) # label(goal). 21.042/21.042 end_of_list. 21.042/21.042 21.042/21.042 ============================== end of input ========================== 21.042/21.042 21.042/21.042 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 21.042/21.042 21.042/21.042 % Formulas that are not ordinary clauses: 21.042/21.042 1 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 2 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 3 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 4 ->(x1,y) -> ->(s(x1),s(y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 5 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 6 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 7 ->(x1,y) -> ->(pair(x1,x2),pair(y,x2)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 8 ->(x2,y) -> ->(pair(x1,x2),pair(x1,y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 9 ->(x1,y) -> ->(t(x1),t(y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 10 (exists x1 ->(t(l),x1)) # label(goal) # label(non_clause) # label(goal). [goal]. 21.042/21.042 21.042/21.042 ============================== end of process non-clausal formulas === 21.042/21.042 21.042/21.042 ============================== CLAUSES FOR SEARCH ==================== 21.042/21.042 21.042/21.042 formulas(mace4_clauses). 21.042/21.042 -->(x,y) | ->(f(x),f(y)) # label(congruence). 21.042/21.042 -->(x,y) | ->(g(x,z),g(y,z)) # label(congruence). 21.042/21.042 -->(x,y) | ->(g(z,x),g(z,y)) # label(congruence). 21.042/21.042 -->(x,y) | ->(s(x),s(y)) # label(congruence). 21.042/21.042 -->(x,y) | ->(h(x,z),h(y,z)) # label(congruence). 21.042/21.042 -->(x,y) | ->(h(z,x),h(z,y)) # label(congruence). 21.042/21.042 -->(x,y) | ->(pair(x,z),pair(y,z)) # label(congruence). 21.042/21.042 -->(x,y) | ->(pair(z,x),pair(z,y)) # label(congruence). 21.042/21.042 -->(x,y) | ->(t(x),t(y)) # label(congruence). 21.042/21.042 -->(t(l),x) # label(goal). 21.042/21.042 end_of_list. 21.042/21.042 21.042/21.042 ============================== end of clauses for search ============= 21.042/21.042 21.042/21.042 % There are no natural numbers in the input. 21.042/21.042 21.042/21.042 ============================== DOMAIN SIZE 2 ========================= 21.042/21.042 21.042/21.042 ============================== MODEL ================================= 21.042/21.042 21.042/21.042 interpretation( 2, [number=1, seconds=0], [ 21.042/21.042 21.042/21.042 function(l, [ 0 ]), 21.042/21.042 21.042/21.042 function(t(_), [ 0, 0 ]), 21.042/21.042 21.042/21.042 function(f(_), [ 0, 0 ]), 21.042/21.042 21.042/21.042 function(s(_), [ 0, 0 ]), 21.042/21.042 21.042/21.042 function(h(_,_), [ 21.042/21.042 0, 0, 21.042/21.042 0, 0 ]), 21.042/21.042 21.042/21.042 function(pair(_,_), [ 21.042/21.042 0, 0, 21.042/21.042 0, 0 ]), 21.042/21.042 21.042/21.042 function(g(_,_), [ 21.042/21.042 0, 0, 21.042/21.042 0, 0 ]), 21.042/21.042 21.042/21.042 relation(->(_,_), [ 21.042/21.042 0, 0, 21.042/21.042 0, 0 ]) 21.042/21.042 ]). 21.042/21.042 21.042/21.042 ============================== end of model ========================== 21.042/21.042 21.042/21.042 ============================== STATISTICS ============================ 21.042/21.042 21.042/21.042 For domain size 2. 21.042/21.042 21.042/21.042 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 21.042/21.042 Ground clauses: seen=62, kept=62. 21.042/21.042 Selections=19, assignments=19, propagations=4, current_models=1. 21.042/21.042 Rewrite_terms=124, rewrite_bools=65, indexes=4. 21.042/21.042 Rules_from_neg_clauses=0, cross_offs=0. 21.042/21.042 21.042/21.042 ============================== end of statistics ===================== 21.042/21.042 21.042/21.042 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 21.042/21.042 21.042/21.042 Exiting with 1 model. 21.042/21.042 21.042/21.042 Process 48760 exit (max_models) Wed Jul 14 10:48:26 2021 21.042/21.042 The process finished Wed Jul 14 10:48:26 2021 21.042/21.042 21.042/21.042 21.042/21.042 Mace4 cooked interpretation: 21.042/21.042 21.042/21.042 21.042/21.042 21.042/21.042 The problem is infeasible. 21.042/21.042 21.042/21.042 21.042/21.042 The problem is not joinable. 21.042/21.042 49.31user 3.87system 0:21.42elapsed 248%CPU (0avgtext+0avgdata 435136maxresident)k 21.042/21.042 0inputs+0outputs (0major+391717minor)pagefaults 0swaps