17.029/17.029 NO 17.029/17.029 17.029/17.029 Problem 1: 17.029/17.029 17.029/17.029 17.029/17.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 17.029/17.029 Confluence Problem: 17.029/17.029 (VAR vNonEmpty:S x:S y:S) 17.029/17.029 (STRATEGY CONTEXTSENSITIVE 17.029/17.029 (a) 17.029/17.029 (b) 17.029/17.029 (f 1) 17.029/17.029 (g 1 2) 17.029/17.029 (s 1) 17.029/17.029 (c) 17.029/17.029 (d) 17.029/17.029 (fSNonEmpty) 17.029/17.029 (h 1 2) 17.029/17.029 (k) 17.029/17.029 (l) 17.029/17.029 (pair 1 2) 17.029/17.029 (t 1) 17.029/17.029 ) 17.029/17.029 (RULES 17.029/17.029 a -> c 17.029/17.029 a -> d 17.029/17.029 b -> c 17.029/17.029 b -> d 17.029/17.029 f(x:S) -> pair(x:S,y:S) | s(x:S) ->* t(y:S) 17.029/17.029 g(x:S,x:S) -> h(x:S,x:S) 17.029/17.029 s(c) -> t(k) 17.029/17.029 s(c) -> t(l) 17.029/17.029 ) 17.029/17.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 17.029/17.029 17.029/17.029 17.029/17.029 Problem 1: 17.029/17.029 17.029/17.029 Inlining of Conditions Processor [STERN17]: 17.029/17.029 17.029/17.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 17.029/17.029 Confluence Problem: 17.029/17.029 (VAR vNonEmpty:S x:S y:S) 17.029/17.029 (STRATEGY CONTEXTSENSITIVE 17.029/17.029 (a) 17.029/17.029 (b) 17.029/17.029 (f 1) 17.029/17.029 (g 1 2) 17.029/17.029 (s 1) 17.029/17.029 (c) 17.029/17.029 (d) 17.029/17.029 (fSNonEmpty) 17.029/17.029 (h 1 2) 17.029/17.029 (k) 17.029/17.029 (l) 17.029/17.029 (pair 1 2) 17.029/17.029 (t 1) 17.029/17.029 ) 17.029/17.029 (RULES 17.029/17.029 a -> c 17.029/17.029 a -> d 17.029/17.029 b -> c 17.029/17.029 b -> d 17.029/17.029 f(x:S) -> pair(x:S,y:S) | s(x:S) ->* t(y:S) 17.029/17.029 g(x:S,x:S) -> h(x:S,x:S) 17.029/17.029 s(c) -> t(k) 17.029/17.029 s(c) -> t(l) 17.029/17.029 ) 17.029/17.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 17.029/17.029 17.029/17.029 17.029/17.029 Problem 1: 17.029/17.029 17.029/17.029 Clean CTRS Processor: 17.029/17.029 17.029/17.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 17.029/17.029 Confluence Problem: 17.029/17.029 (VAR x:S y:S) 17.029/17.029 (STRATEGY CONTEXTSENSITIVE 17.029/17.029 (a) 17.029/17.029 (b) 17.029/17.029 (f 1) 17.029/17.029 (g 1 2) 17.029/17.029 (s 1) 17.029/17.029 (c) 17.029/17.029 (d) 17.029/17.029 (fSNonEmpty) 17.029/17.029 (h 1 2) 17.029/17.029 (k) 17.029/17.029 (l) 17.029/17.029 (pair 1 2) 17.029/17.029 (t 1) 17.029/17.029 ) 17.029/17.029 (RULES 17.029/17.029 a -> c 17.029/17.029 a -> d 17.029/17.029 b -> c 17.029/17.029 b -> d 17.029/17.029 f(x:S) -> pair(x:S,y:S) | s(x:S) ->* t(y:S) 17.029/17.029 g(x:S,x:S) -> h(x:S,x:S) 17.029/17.029 s(c) -> t(k) 17.029/17.029 s(c) -> t(l) 17.029/17.029 ) 17.029/17.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 17.029/17.029 17.029/17.029 CRule InfChecker Info: 17.029/17.029 a -> c 17.029/17.029 Rule remains 17.029/17.029 Proof: 17.029/17.029 NO_CONDS 17.029/17.029 17.029/17.029 CRule InfChecker Info: 17.029/17.029 a -> d 17.029/17.029 Rule remains 17.029/17.029 Proof: 17.029/17.029 NO_CONDS 17.029/17.029 17.029/17.029 CRule InfChecker Info: 17.029/17.029 b -> c 17.029/17.029 Rule remains 17.029/17.029 Proof: 17.029/17.029 NO_CONDS 17.029/17.029 17.029/17.029 CRule InfChecker Info: 17.029/17.029 b -> d 17.029/17.029 Rule remains 17.029/17.029 Proof: 17.029/17.029 NO_CONDS 17.029/17.029 17.029/17.029 CRule InfChecker Info: 17.029/17.029 f(x:S) -> pair(x:S,y:S) | s(x:S) ->* t(y:S) 17.029/17.029 Rule remains 17.029/17.029 Proof: 17.029/17.029 NO 17.029/17.029 17.029/17.029 Problem 1: 17.029/17.029 17.029/17.029 Infeasibility Problem: 17.029/17.029 [(VAR vNonEmpty:S vNonEmpty:S:S x:S:S y:S:S) 17.029/17.029 (STRATEGY CONTEXTSENSITIVE 17.029/17.029 (a) 17.029/17.029 (b) 17.029/17.029 (f 1) 17.029/17.029 (g 1 2) 17.029/17.029 (s 1) 17.029/17.029 (c) 17.029/17.029 (d) 17.029/17.029 (fSNonEmpty) 17.029/17.029 (h 1 2) 17.029/17.029 (k) 17.029/17.029 (l) 17.029/17.029 (pair 1 2) 17.029/17.029 (t 1) 17.029/17.029 ) 17.029/17.029 (RULES 17.029/17.029 a -> c 17.029/17.029 a -> d 17.029/17.029 b -> c 17.029/17.029 b -> d 17.029/17.029 f(x:S:S) -> pair(x:S:S,y:S:S) | s(x:S:S) ->* t(y:S:S) 17.029/17.029 g(x:S:S,x:S:S) -> h(x:S:S,x:S:S) 17.029/17.029 s(c) -> t(k) 17.029/17.029 s(c) -> t(l) 17.029/17.029 )] 17.029/17.029 17.029/17.029 Infeasibility Conditions: 17.029/17.029 s(x:S:S) ->* t(y:S:S) 17.029/17.029 17.029/17.029 Problem 1: 17.029/17.029 17.029/17.029 Obtaining a proof using Prover9: 17.029/17.029 17.029/17.029 -> Prover9 Output: 17.029/17.029 ============================== Prover9 =============================== 17.029/17.029 Prover9 (64) version 2009-11A, November 2009. 17.029/17.029 Process 109755 was started by ubuntu on ubuntu, 17.029/17.029 Fri Jul 16 15:05:44 2021 17.029/17.029 The command was "./prover9 -f /tmp/prover9109748-0.in". 17.029/17.029 ============================== end of head =========================== 17.029/17.029 17.029/17.029 ============================== INPUT ================================= 17.029/17.029 17.029/17.029 % Reading from file /tmp/prover9109748-0.in 17.029/17.029 17.029/17.029 assign(max_seconds,20). 17.029/17.029 17.029/17.029 formulas(assumptions). 17.029/17.029 ->*_s0(x,x) # label(reflexivity). 17.029/17.029 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 17.029/17.029 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence). 17.029/17.029 ->_s0(x1,y) -> ->_s0(g(x1,x2),g(y,x2)) # label(congruence). 17.029/17.029 ->_s0(x2,y) -> ->_s0(g(x1,x2),g(x1,y)) # label(congruence). 17.029/17.029 ->_s0(x1,y) -> ->_s0(s(x1),s(y)) # label(congruence). 17.029/17.029 ->_s0(x1,y) -> ->_s0(h(x1,x2),h(y,x2)) # label(congruence). 17.029/17.029 ->_s0(x2,y) -> ->_s0(h(x1,x2),h(x1,y)) # label(congruence). 17.029/17.029 ->_s0(x1,y) -> ->_s0(pair(x1,x2),pair(y,x2)) # label(congruence). 17.029/17.029 ->_s0(x2,y) -> ->_s0(pair(x1,x2),pair(x1,y)) # label(congruence). 17.029/17.029 ->_s0(x1,y) -> ->_s0(t(x1),t(y)) # label(congruence). 17.029/17.029 ->_s0(a,c) # label(replacement). 17.029/17.029 ->_s0(a,d) # label(replacement). 17.029/17.029 ->_s0(b,c) # label(replacement). 17.029/17.029 ->_s0(b,d) # label(replacement). 17.029/17.029 ->*_s0(s(x2),t(x3)) -> ->_s0(f(x2),pair(x2,x3)) # label(replacement). 17.029/17.029 ->_s0(g(x2,x2),h(x2,x2)) # label(replacement). 17.029/17.029 ->_s0(s(c),t(k)) # label(replacement). 17.029/17.029 ->_s0(s(c),t(l)) # label(replacement). 17.029/17.029 end_of_list. 17.029/17.029 17.029/17.029 formulas(goals). 17.029/17.029 (exists x2 exists x3 ->*_s0(s(x2),t(x3))) # label(goal). 17.029/17.029 end_of_list. 17.029/17.029 17.029/17.029 ============================== end of input ========================== 17.029/17.029 17.029/17.029 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 17.029/17.029 17.029/17.029 % Formulas that are not ordinary clauses: 17.029/17.029 1 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 17.029/17.029 2 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 17.029/17.029 3 ->_s0(x1,y) -> ->_s0(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 17.029/17.029 4 ->_s0(x2,y) -> ->_s0(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 17.029/17.029 5 ->_s0(x1,y) -> ->_s0(s(x1),s(y)) # label(congruence) # label(non_clause). [assumption]. 17.029/17.029 6 ->_s0(x1,y) -> ->_s0(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 17.029/17.029 7 ->_s0(x2,y) -> ->_s0(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 17.029/17.029 8 ->_s0(x1,y) -> ->_s0(pair(x1,x2),pair(y,x2)) # label(congruence) # label(non_clause). [assumption]. 17.029/17.029 9 ->_s0(x2,y) -> ->_s0(pair(x1,x2),pair(x1,y)) # label(congruence) # label(non_clause). [assumption]. 17.029/17.029 10 ->_s0(x1,y) -> ->_s0(t(x1),t(y)) # label(congruence) # label(non_clause). [assumption]. 17.029/17.029 11 ->*_s0(s(x2),t(x3)) -> ->_s0(f(x2),pair(x2,x3)) # label(replacement) # label(non_clause). [assumption]. 17.029/17.029 12 (exists x2 exists x3 ->*_s0(s(x2),t(x3))) # label(goal) # label(non_clause) # label(goal). [goal]. 17.029/17.029 17.029/17.029 ============================== end of process non-clausal formulas === 17.029/17.029 17.029/17.029 ============================== PROCESS INITIAL CLAUSES =============== 17.029/17.029 17.029/17.029 % Clauses before input processing: 17.029/17.029 17.029/17.029 formulas(usable). 17.029/17.029 end_of_list. 17.029/17.029 17.029/17.029 formulas(sos). 17.029/17.029 ->*_s0(x,x) # label(reflexivity). [assumption]. 17.029/17.029 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 17.029/17.029 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)]. 17.029/17.029 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(3)]. 17.029/17.029 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(4)]. 17.029/17.029 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(5)]. 17.029/17.029 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(6)]. 17.029/17.029 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(7)]. 17.029/17.029 -->_s0(x,y) | ->_s0(pair(x,z),pair(y,z)) # label(congruence). [clausify(8)]. 17.029/17.029 -->_s0(x,y) | ->_s0(pair(z,x),pair(z,y)) # label(congruence). [clausify(9)]. 17.029/17.029 -->_s0(x,y) | ->_s0(t(x),t(y)) # label(congruence). [clausify(10)]. 17.029/17.029 ->_s0(a,c) # label(replacement). [assumption]. 17.029/17.029 ->_s0(a,d) # label(replacement). [assumption]. 17.029/17.029 ->_s0(b,c) # label(replacement). [assumption]. 17.029/17.029 ->_s0(b,d) # label(replacement). [assumption]. 17.029/17.029 -->*_s0(s(x),t(y)) | ->_s0(f(x),pair(x,y)) # label(replacement). [clausify(11)]. 17.029/17.029 ->_s0(g(x,x),h(x,x)) # label(replacement). [assumption]. 17.029/17.029 ->_s0(s(c),t(k)) # label(replacement). [assumption]. 17.029/17.029 ->_s0(s(c),t(l)) # label(replacement). [assumption]. 17.029/17.029 -->*_s0(s(x),t(y)) # label(goal). [deny(12)]. 17.029/17.029 end_of_list. 17.029/17.029 17.029/17.029 formulas(demodulators). 17.029/17.029 end_of_list. 17.029/17.029 17.029/17.029 ============================== PREDICATE ELIMINATION ================= 17.029/17.029 17.029/17.029 No predicates eliminated. 17.029/17.029 17.029/17.029 ============================== end predicate elimination ============= 17.029/17.029 17.029/17.029 Auto_denials: 17.029/17.029 % copying label goal to answer in negative clause 17.029/17.029 17.029/17.029 Term ordering decisions: 17.029/17.029 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 17.029/17.029 Function symbol precedence: function_order([ c, a, b, d, k, l, h, pair, g, t, s, f ]). 17.029/17.029 After inverse_order: (no changes). 17.029/17.029 Unfolding symbols: (none). 17.029/17.029 17.029/17.029 Auto_inference settings: 17.029/17.029 % set(neg_binary_resolution). % (HNE depth_diff=-9) 17.029/17.029 % clear(ordered_res). % (HNE depth_diff=-9) 17.029/17.029 % set(ur_resolution). % (HNE depth_diff=-9) 17.029/17.029 % set(ur_resolution) -> set(pos_ur_resolution). 17.029/17.029 % set(ur_resolution) -> set(neg_ur_resolution). 17.029/17.029 17.029/17.029 Auto_process settings: (no changes). 17.029/17.029 17.029/17.029 kept: 13 ->*_s0(x,x) # label(reflexivity). [assumption]. 17.029/17.029 kept: 14 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 17.029/17.029 kept: 15 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)]. 17.029/17.029 kept: 16 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(3)]. 17.029/17.029 kept: 17 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(4)]. 17.029/17.029 kept: 18 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(5)]. 17.029/17.029 kept: 19 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(6)]. 17.029/17.029 kept: 20 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(7)]. 17.029/17.029 kept: 21 -->_s0(x,y) | ->_s0(pair(x,z),pair(y,z)) # label(congruence). [clausify(8)]. 17.029/17.029 kept: 22 -->_s0(x,y) | ->_s0(pair(z,x),pair(z,y)) # label(congruence). [clausify(9)]. 17.029/17.029 kept: 23 -->_s0(x,y) | ->_s0(t(x),t(y)) # label(congruence). [clausify(10)]. 17.029/17.029 kept: 24 ->_s0(a,c) # label(replacement). [assumption]. 17.029/17.029 kept: 25 ->_s0(a,d) # label(replacement). [assumption]. 17.029/17.029 kept: 26 ->_s0(b,c) # label(replacement). [assumption]. 17.029/17.029 kept: 27 ->_s0(b,d) # label(replacement). [assumption]. 17.029/17.029 kept: 28 -->*_s0(s(x),t(y)) | ->_s0(f(x),pair(x,y)) # label(replacement). [clausify(11)]. 17.029/17.029 kept: 29 ->_s0(g(x,x),h(x,x)) # label(replacement). [assumption]. 17.029/17.029 kept: 30 ->_s0(s(c),t(k)) # label(replacement). [assumption]. 17.029/17.029 kept: 31 ->_s0(s(c),t(l)) # label(replacement). [assumption]. 17.029/17.029 kept: 32 -->*_s0(s(x),t(y)) # label(goal) # answer(goal). [deny(12)]. 17.029/17.029 17.029/17.029 ============================== end of process initial clauses ======== 17.029/17.029 17.029/17.029 ============================== CLAUSES FOR SEARCH ==================== 17.029/17.029 17.029/17.029 % Clauses after input processing: 17.029/17.029 17.029/17.029 formulas(usable). 17.029/17.029 end_of_list. 17.029/17.029 17.029/17.029 formulas(sos). 17.029/17.029 13 ->*_s0(x,x) # label(reflexivity). [assumption]. 17.029/17.029 14 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 17.029/17.029 15 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)]. 17.029/17.029 16 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(3)]. 17.029/17.029 17 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(4)]. 17.029/17.029 18 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(5)]. 17.029/17.029 19 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(6)]. 17.029/17.029 20 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(7)]. 17.029/17.029 21 -->_s0(x,y) | ->_s0(pair(x,z),pair(y,z)) # label(congruence). [clausify(8)]. 17.029/17.029 22 -->_s0(x,y) | ->_s0(pair(z,x),pair(z,y)) # label(congruence). [clausify(9)]. 17.029/17.029 23 -->_s0(x,y) | ->_s0(t(x),t(y)) # label(congruence). [clausify(10)]. 17.029/17.029 24 ->_s0(a,c) # label(replacement). [assumption]. 17.029/17.029 25 ->_s0(a,d) # label(replacement). [assumption]. 17.029/17.029 26 ->_s0(b,c) # label(replacement). [assumption]. 17.029/17.029 27 ->_s0(b,d) # label(replacement). [assumption]. 17.029/17.029 29 ->_s0(g(x,x),h(x,x)) # label(replacement). [assumption]. 17.029/17.029 30 ->_s0(s(c),t(k)) # label(replacement). [assumption]. 17.029/17.029 31 ->_s0(s(c),t(l)) # label(replacement). [assumption]. 17.029/17.029 32 -->*_s0(s(x),t(y)) # label(goal) # answer(goal). [deny(12)]. 17.029/17.029 end_of_list. 17.029/17.029 17.029/17.029 formulas(demodulators). 17.029/17.029 end_of_list. 17.029/17.029 17.029/17.029 ============================== end of clauses for search ============= 17.029/17.029 17.029/17.029 ============================== SEARCH ================================ 17.029/17.029 17.029/17.029 % Starting search at 0.00 seconds. 17.029/17.029 17.029/17.029 given #1 (I,wt=3): 13 ->*_s0(x,x) # label(reflexivity). [assumption]. 17.029/17.029 17.029/17.029 given #2 (I,wt=9): 14 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 17.029/17.029 17.029/17.029 given #3 (I,wt=8): 15 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)]. 17.029/17.029 17.029/17.029 given #4 (I,wt=10): 16 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(3)]. 17.029/17.029 17.029/17.029 given #5 (I,wt=10): 17 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(4)]. 17.029/17.029 17.029/17.029 given #6 (I,wt=8): 18 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(5)]. 17.029/17.029 17.029/17.029 given #7 (I,wt=10): 19 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(6)]. 17.029/17.029 17.029/17.029 given #8 (I,wt=10): 20 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(7)]. 17.029/17.029 17.029/17.029 given #9 (I,wt=10): 21 -->_s0(x,y) | ->_s0(pair(x,z),pair(y,z)) # label(congruence). [clausify(8)]. 17.029/17.029 17.029/17.029 given #10 (I,wt=10): 22 -->_s0(x,y) | ->_s0(pair(z,x),pair(z,y)) # label(congruence). [clausify(9)]. 17.029/17.029 17.029/17.029 given #11 (I,wt=8): 23 -->_s0(x,y) | ->_s0(t(x),t(y)) # label(congruence). [clausify(10)]. 17.029/17.029 17.029/17.029 given #12 (I,wt=3): 24 ->_s0(a,c) # label(replacement). [assumption]. 17.029/17.029 17.029/17.029 given #13 (I,wt=3): 25 ->_s0(a,d) # label(replacement). [assumption]. 17.029/17.029 17.029/17.029 given #14 (I,wt=3): 26 ->_s0(b,c) # label(replacement). [assumption]. 17.029/17.029 17.029/17.029 given #15 (I,wt=3): 27 ->_s0(b,d) # label(replacement). [assumption]. 17.029/17.029 17.029/17.029 given #16 (I,wt=7): 29 ->_s0(g(x,x),h(x,x)) # label(replacement). [assumption]. 17.029/17.029 17.029/17.029 given #17 (I,wt=5): 30 ->_s0(s(c),t(k)) # label(replacement). [assumption]. 17.029/17.029 17.029/17.029 ============================== PROOF ================================= 17.029/17.029 17.029/17.029 % Proof 1 at 0.00 (+ 0.00) seconds: goal. 17.029/17.029 % Length of proof is 8. 17.029/17.029 % Level of proof is 3. 17.029/17.029 % Maximum clause weight is 9.000. 17.029/17.029 % Given clauses 17. 17.029/17.029 17.029/17.029 1 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 17.029/17.029 12 (exists x2 exists x3 ->*_s0(s(x2),t(x3))) # label(goal) # label(non_clause) # label(goal). [goal]. 17.029/17.029 13 ->*_s0(x,x) # label(reflexivity). [assumption]. 17.029/17.029 14 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 17.029/17.029 30 ->_s0(s(c),t(k)) # label(replacement). [assumption]. 17.029/17.029 32 -->*_s0(s(x),t(y)) # label(goal) # answer(goal). [deny(12)]. 17.029/17.029 92 ->*_s0(s(c),t(k)). [ur(14,a,30,a,b,13,a)]. 17.029/17.029 93 $F # answer(goal). [resolve(92,a,32,a)]. 17.029/17.029 17.029/17.029 ============================== end of proof ========================== 17.029/17.029 17.029/17.029 ============================== STATISTICS ============================ 17.029/17.029 17.029/17.029 Given=17. Generated=80. Kept=80. proofs=1. 17.029/17.029 Usable=17. Sos=52. Demods=0. Limbo=9, Disabled=21. Hints=0. 17.029/17.029 Kept_by_rule=0, Deleted_by_rule=0. 17.029/17.029 Forward_subsumed=0. Back_subsumed=1. 17.029/17.029 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 17.029/17.029 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 17.029/17.029 Demod_attempts=0. Demod_rewrites=0. 17.029/17.029 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 17.029/17.029 Nonunit_fsub_feature_tests=3. Nonunit_bsub_feature_tests=19. 17.029/17.029 Megabytes=0.16. 17.029/17.029 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 17.029/17.029 17.029/17.029 ============================== end of statistics ===================== 17.029/17.029 17.029/17.029 ============================== end of search ========================= 17.029/17.029 17.029/17.029 THEOREM PROVED 17.029/17.029 17.029/17.029 Exiting with 1 proof. 17.029/17.029 17.029/17.029 Process 109755 exit (max_proofs) Fri Jul 16 15:05:44 2021 17.029/17.029 17.029/17.029 17.029/17.029 The problem is feasible. 17.029/17.029 17.029/17.029 17.029/17.029 CRule InfChecker Info: 17.029/17.029 g(x:S,x:S) -> h(x:S,x:S) 17.029/17.029 Rule remains 17.029/17.029 Proof: 17.029/17.029 NO_CONDS 17.029/17.029 17.029/17.029 CRule InfChecker Info: 17.029/17.029 s(c) -> t(k) 17.029/17.029 Rule remains 17.029/17.029 Proof: 17.029/17.029 NO_CONDS 17.029/17.029 17.029/17.029 CRule InfChecker Info: 17.029/17.029 s(c) -> t(l) 17.029/17.029 Rule remains 17.029/17.029 Proof: 17.029/17.029 NO_CONDS 17.029/17.029 17.029/17.029 Problem 1: 17.029/17.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 17.029/17.029 Confluence Problem: 17.029/17.029 (VAR x:S y:S) 17.029/17.029 (STRATEGY CONTEXTSENSITIVE 17.029/17.029 (a) 17.029/17.029 (b) 17.029/17.029 (f 1) 17.029/17.029 (g 1 2) 17.029/17.029 (s 1) 17.029/17.029 (c) 17.029/17.029 (d) 17.029/17.029 (fSNonEmpty) 17.029/17.029 (h 1 2) 17.029/17.029 (k) 17.029/17.029 (l) 17.029/17.029 (pair 1 2) 17.029/17.029 (t 1) 17.029/17.029 ) 17.029/17.029 (RULES 17.029/17.029 a -> c 17.029/17.029 a -> d 17.029/17.029 b -> c 17.029/17.029 b -> d 17.029/17.029 f(x:S) -> pair(x:S,y:S) | s(x:S) ->* t(y:S) 17.029/17.029 g(x:S,x:S) -> h(x:S,x:S) 17.029/17.029 s(c) -> t(k) 17.029/17.029 s(c) -> t(l) 17.029/17.029 ) 17.029/17.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 17.029/17.029 17.029/17.029 Critical Pairs Processor: 17.029/17.029 -> Rules: 17.029/17.029 a -> c 17.029/17.029 a -> d 17.029/17.029 b -> c 17.029/17.029 b -> d 17.029/17.029 f(x:S) -> pair(x:S,y:S) | s(x:S) ->* t(y:S) 17.029/17.029 g(x:S,x:S) -> h(x:S,x:S) 17.029/17.029 s(c) -> t(k) 17.029/17.029 s(c) -> t(l) 17.029/17.029 -> Vars: 17.029/17.029 "x", "y", "x" 17.029/17.029 -> FVars: 17.029/17.029 "x3", "x4", "x5" 17.029/17.029 -> PVars: 17.029/17.029 "x": ["x3", "x5"], "y": ["x4"] 17.029/17.029 17.029/17.029 -> Rlps: 17.029/17.029 crule: a -> c, id: 1, possubterms: a-> [] 17.029/17.029 crule: a -> d, id: 2, possubterms: a-> [] 17.029/17.029 crule: b -> c, id: 3, possubterms: b-> [] 17.029/17.029 crule: b -> d, id: 4, possubterms: b-> [] 17.029/17.029 crule: f(x3:S) -> pair(x3:S,x4:S) | s(x3:S) ->* t(x4:S), id: 5, possubterms: f(x3:S)-> [] 17.029/17.029 crule: g(x5:S,x5:S) -> h(x5:S,x5:S), id: 6, possubterms: g(x5:S,x5:S)-> [] 17.029/17.029 crule: s(c) -> t(k), id: 7, possubterms: s(c)-> [], c-> [1] 17.029/17.029 crule: s(c) -> t(l), id: 8, possubterms: s(c)-> [], c-> [1] 17.029/17.029 17.029/17.029 -> Unifications: 17.029/17.029 R2 unifies with R1 at p: [], l: a, lp: a, conds: {}, sig: {}, l': a, r: d, r': c 17.029/17.029 R4 unifies with R3 at p: [], l: b, lp: b, conds: {}, sig: {}, l': b, r: d, r': c 17.029/17.029 R8 unifies with R7 at p: [], l: s(c), lp: s(c), conds: {}, sig: {}, l': s(c), r: t(l), r': t(k) 17.029/17.029 17.029/17.029 -> Critical pairs info: 17.029/17.029 => Not trivial, Overlay, N1 17.029/17.029 => Not trivial, Overlay, N2 17.029/17.029 17.029/17.029 -> Problem conclusions: 17.029/17.029 Not left linear, Not right linear, Not linear 17.029/17.029 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 17.029/17.029 CTRS Type: 3 17.029/17.029 Deterministic, Strongly deterministic 17.029/17.029 Oriented CTRS, Properly oriented CTRS, Not join CTRS 17.029/17.029 Maybe right-stable CTRS, Overlay CTRS 17.029/17.029 Maybe normal CTRS, Maybe almost normal CTRS 17.029/17.029 Maybe terminating CTRS, Maybe joinable CCPs 17.029/17.029 Maybe level confluent 17.029/17.029 Maybe confluent 17.029/17.029 17.029/17.029 Problem 1: 17.029/17.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 17.029/17.029 Confluence Problem: 17.029/17.029 (VAR x:S y:S) 17.029/17.029 (STRATEGY CONTEXTSENSITIVE 17.029/17.029 (a) 17.029/17.029 (b) 17.029/17.029 (f 1) 17.029/17.029 (g 1 2) 17.029/17.029 (s 1) 17.029/17.029 (c) 17.029/17.029 (d) 17.029/17.029 (fSNonEmpty) 17.029/17.029 (h 1 2) 17.029/17.029 (k) 17.029/17.029 (l) 17.029/17.029 (pair 1 2) 17.029/17.029 (t 1) 17.029/17.029 ) 17.029/17.029 (RULES 17.029/17.029 a -> c 17.029/17.029 a -> d 17.029/17.029 b -> c 17.029/17.029 b -> d 17.029/17.029 f(x:S) -> pair(x:S,y:S) | s(x:S) ->* t(y:S) 17.029/17.029 g(x:S,x:S) -> h(x:S,x:S) 17.029/17.029 s(c) -> t(k) 17.029/17.029 s(c) -> t(l) 17.029/17.029 ) 17.029/17.029 Critical Pairs: 17.029/17.029 => Not trivial, Overlay, N1 17.029/17.029 => Not trivial, Overlay, N2 17.029/17.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 17.029/17.029 17.029/17.029 Conditional Critical Pairs Distributor Processor 17.029/17.029 17.029/17.029 Problem 1: 17.029/17.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 17.029/17.029 Confluence Problem: 17.029/17.029 (VAR x:S y:S) 17.029/17.029 (STRATEGY CONTEXTSENSITIVE 17.029/17.029 (a) 17.029/17.029 (b) 17.029/17.029 (f 1) 17.029/17.029 (g 1 2) 17.029/17.029 (s 1) 17.029/17.029 (c) 17.029/17.029 (d) 17.029/17.029 (fSNonEmpty) 17.029/17.029 (h 1 2) 17.029/17.029 (k) 17.029/17.029 (l) 17.029/17.029 (pair 1 2) 17.029/17.029 (t 1) 17.029/17.029 ) 17.029/17.029 (RULES 17.029/17.029 a -> c 17.029/17.029 a -> d 17.029/17.029 b -> c 17.029/17.029 b -> d 17.029/17.029 f(x:S) -> pair(x:S,y:S) | s(x:S) ->* t(y:S) 17.029/17.029 g(x:S,x:S) -> h(x:S,x:S) 17.029/17.029 s(c) -> t(k) 17.029/17.029 s(c) -> t(l) 17.029/17.029 ) 17.029/17.029 Critical Pairs: 17.029/17.029 => Not trivial, Overlay, N1 17.029/17.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 17.029/17.029 17.029/17.029 InfChecker Different Ground and Normal No Conditions CCP Terms Processor: 17.029/17.029 Proof: 17.029/17.029 YES 17.029/17.029 17.029/17.029 Problem 1: 17.029/17.029 17.029/17.029 Infeasibility Problem: 17.029/17.029 [(VAR vNonEmpty:S x:S y:S) 17.029/17.029 (STRATEGY CONTEXTSENSITIVE 17.029/17.029 (a) 17.029/17.029 (b) 17.029/17.029 (f 1) 17.029/17.029 (g 1 2) 17.029/17.029 (s 1) 17.029/17.029 (c) 17.029/17.029 (d) 17.029/17.029 (fSNonEmpty) 17.029/17.029 (h 1 2) 17.029/17.029 (k) 17.029/17.029 (l) 17.029/17.029 (pair 1 2) 17.029/17.029 (t 1) 17.029/17.029 ) 17.029/17.029 (RULES 17.029/17.029 a -> c 17.029/17.029 a -> d 17.029/17.029 b -> c 17.029/17.029 b -> d 17.029/17.029 f(x:S) -> pair(x:S,y:S) | s(x:S) ->* t(y:S) 17.029/17.029 g(x:S,x:S) -> h(x:S,x:S) 17.029/17.029 s(c) -> t(k) 17.029/17.029 s(c) -> t(l) 17.029/17.029 )] 17.029/17.029 17.029/17.029 Infeasibility Conditions: 17.029/17.029 t(k) -> y:S 17.029/17.029 17.029/17.029 Problem 1: 17.029/17.029 17.029/17.029 Obtaining a model using Mace4: 17.029/17.029 17.029/17.029 -> Usable Rules: 17.029/17.029 Empty 17.029/17.029 17.029/17.029 -> Mace4 Output: 17.029/17.029 ============================== Mace4 ================================= 17.029/17.029 Mace4 (64) version 2009-11A, November 2009. 17.029/17.029 Process 109798 was started by ubuntu on ubuntu, 17.029/17.029 Fri Jul 16 15:05:44 2021 17.029/17.029 The command was "./mace4 -c -f /tmp/mace4109773-2.in". 17.029/17.029 ============================== end of head =========================== 17.029/17.029 17.029/17.029 ============================== INPUT ================================= 17.029/17.029 17.029/17.029 % Reading from file /tmp/mace4109773-2.in 17.029/17.029 17.029/17.029 assign(max_seconds,3). 17.029/17.029 17.029/17.029 formulas(assumptions). 17.029/17.029 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence). 17.029/17.029 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence). 17.029/17.029 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence). 17.029/17.029 ->(x1,y) -> ->(s(x1),s(y)) # label(congruence). 17.029/17.029 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence). 17.029/17.029 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence). 17.029/17.029 ->(x1,y) -> ->(pair(x1,x2),pair(y,x2)) # label(congruence). 17.029/17.029 ->(x2,y) -> ->(pair(x1,x2),pair(x1,y)) # label(congruence). 17.029/17.029 ->(x1,y) -> ->(t(x1),t(y)) # label(congruence). 17.029/17.029 end_of_list. 17.029/17.029 17.029/17.029 formulas(goals). 17.029/17.029 (exists x2 ->(t(k),x2)) # label(goal). 17.029/17.029 end_of_list. 17.029/17.029 17.029/17.029 ============================== end of input ========================== 17.029/17.029 17.029/17.029 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 17.029/17.029 17.029/17.029 % Formulas that are not ordinary clauses: 17.029/17.029 1 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 17.029/17.029 2 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 17.029/17.029 3 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 17.029/17.029 4 ->(x1,y) -> ->(s(x1),s(y)) # label(congruence) # label(non_clause). [assumption]. 17.029/17.029 5 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 17.029/17.029 6 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 17.029/17.029 7 ->(x1,y) -> ->(pair(x1,x2),pair(y,x2)) # label(congruence) # label(non_clause). [assumption]. 17.029/17.029 8 ->(x2,y) -> ->(pair(x1,x2),pair(x1,y)) # label(congruence) # label(non_clause). [assumption]. 17.029/17.029 9 ->(x1,y) -> ->(t(x1),t(y)) # label(congruence) # label(non_clause). [assumption]. 17.029/17.029 10 (exists x2 ->(t(k),x2)) # label(goal) # label(non_clause) # label(goal). [goal]. 17.029/17.029 17.029/17.029 ============================== end of process non-clausal formulas === 17.029/17.029 17.029/17.029 ============================== CLAUSES FOR SEARCH ==================== 17.029/17.029 17.029/17.029 formulas(mace4_clauses). 17.029/17.029 -->(x,y) | ->(f(x),f(y)) # label(congruence). 17.029/17.029 -->(x,y) | ->(g(x,z),g(y,z)) # label(congruence). 17.029/17.029 -->(x,y) | ->(g(z,x),g(z,y)) # label(congruence). 17.029/17.029 -->(x,y) | ->(s(x),s(y)) # label(congruence). 17.029/17.029 -->(x,y) | ->(h(x,z),h(y,z)) # label(congruence). 17.029/17.029 -->(x,y) | ->(h(z,x),h(z,y)) # label(congruence). 17.029/17.029 -->(x,y) | ->(pair(x,z),pair(y,z)) # label(congruence). 17.029/17.029 -->(x,y) | ->(pair(z,x),pair(z,y)) # label(congruence). 17.029/17.029 -->(x,y) | ->(t(x),t(y)) # label(congruence). 17.029/17.029 -->(t(k),x) # label(goal). 17.029/17.029 end_of_list. 17.029/17.029 17.029/17.029 ============================== end of clauses for search ============= 17.029/17.029 17.029/17.029 % There are no natural numbers in the input. 17.029/17.029 17.029/17.029 ============================== DOMAIN SIZE 2 ========================= 17.029/17.029 17.029/17.029 ============================== MODEL ================================= 17.029/17.029 17.029/17.029 interpretation( 2, [number=1, seconds=0], [ 17.029/17.029 17.029/17.029 function(k, [ 0 ]), 17.029/17.029 17.029/17.029 function(t(_), [ 0, 0 ]), 17.029/17.029 17.029/17.029 function(f(_), [ 0, 0 ]), 17.029/17.029 17.029/17.029 function(s(_), [ 0, 0 ]), 17.029/17.029 17.029/17.029 function(h(_,_), [ 17.029/17.029 0, 0, 17.029/17.029 0, 0 ]), 17.029/17.029 17.029/17.029 function(pair(_,_), [ 17.029/17.029 0, 0, 17.029/17.029 0, 0 ]), 17.029/17.029 17.029/17.029 function(g(_,_), [ 17.029/17.029 0, 0, 17.029/17.029 0, 0 ]), 17.029/17.029 17.029/17.029 relation(->(_,_), [ 17.029/17.029 0, 0, 17.029/17.029 0, 0 ]) 17.029/17.029 ]). 17.029/17.029 17.029/17.029 ============================== end of model ========================== 17.029/17.029 17.029/17.029 ============================== STATISTICS ============================ 17.029/17.029 17.029/17.029 For domain size 2. 17.029/17.029 17.029/17.029 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 17.029/17.029 Ground clauses: seen=62, kept=62. 17.029/17.029 Selections=19, assignments=19, propagations=4, current_models=1. 17.029/17.029 Rewrite_terms=124, rewrite_bools=65, indexes=4. 17.029/17.029 Rules_from_neg_clauses=0, cross_offs=0. 17.029/17.029 17.029/17.029 ============================== end of statistics ===================== 17.029/17.029 17.029/17.029 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 17.029/17.029 17.029/17.029 Exiting with 1 model. 17.029/17.029 17.029/17.029 Process 109798 exit (max_models) Fri Jul 16 15:05:44 2021 17.029/17.029 The process finished Fri Jul 16 15:05:44 2021 17.029/17.029 17.029/17.029 17.029/17.029 Mace4 cooked interpretation: 17.029/17.029 17.029/17.029 17.029/17.029 17.029/17.029 The problem is infeasible. 17.029/17.029 YES 17.029/17.029 17.029/17.029 Problem 1: 17.029/17.029 17.029/17.029 Infeasibility Problem: 17.029/17.029 [(VAR vNonEmpty:S x:S y:S) 17.029/17.029 (STRATEGY CONTEXTSENSITIVE 17.029/17.029 (a) 17.029/17.029 (b) 17.029/17.029 (f 1) 17.029/17.029 (g 1 2) 17.029/17.029 (s 1) 17.029/17.029 (c) 17.029/17.029 (d) 17.029/17.029 (fSNonEmpty) 17.029/17.029 (h 1 2) 17.029/17.029 (k) 17.029/17.029 (l) 17.029/17.029 (pair 1 2) 17.029/17.029 (t 1) 17.029/17.029 ) 17.029/17.029 (RULES 17.029/17.029 a -> c 17.029/17.029 a -> d 17.029/17.029 b -> c 17.029/17.029 b -> d 17.029/17.029 f(x:S) -> pair(x:S,y:S) | s(x:S) ->* t(y:S) 17.029/17.029 g(x:S,x:S) -> h(x:S,x:S) 17.029/17.029 s(c) -> t(k) 17.029/17.029 s(c) -> t(l) 17.029/17.029 )] 17.029/17.029 17.029/17.029 Infeasibility Conditions: 17.029/17.029 t(l) -> x:S 17.029/17.029 17.029/17.029 Problem 1: 17.029/17.029 17.029/17.029 Obtaining a model using Mace4: 17.029/17.029 17.029/17.029 -> Usable Rules: 17.029/17.029 Empty 17.029/17.029 17.029/17.029 -> Mace4 Output: 17.029/17.029 ============================== Mace4 ================================= 17.029/17.029 Mace4 (64) version 2009-11A, November 2009. 17.029/17.029 Process 109838 was started by ubuntu on ubuntu, 17.029/17.029 Fri Jul 16 15:05:54 2021 17.029/17.029 The command was "./mace4 -c -f /tmp/mace4109825-2.in". 17.029/17.029 ============================== end of head =========================== 17.029/17.029 17.029/17.029 ============================== INPUT ================================= 17.029/17.029 17.029/17.029 % Reading from file /tmp/mace4109825-2.in 17.029/17.029 17.029/17.029 assign(max_seconds,3). 17.029/17.029 17.029/17.029 formulas(assumptions). 17.029/17.029 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence). 17.029/17.029 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence). 17.029/17.029 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence). 17.029/17.029 ->(x1,y) -> ->(s(x1),s(y)) # label(congruence). 17.029/17.029 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence). 17.029/17.029 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence). 17.029/17.029 ->(x1,y) -> ->(pair(x1,x2),pair(y,x2)) # label(congruence). 17.029/17.029 ->(x2,y) -> ->(pair(x1,x2),pair(x1,y)) # label(congruence). 17.029/17.029 ->(x1,y) -> ->(t(x1),t(y)) # label(congruence). 17.029/17.029 end_of_list. 17.029/17.029 17.029/17.029 formulas(goals). 17.029/17.029 (exists x1 ->(t(l),x1)) # label(goal). 17.029/17.029 end_of_list. 17.029/17.029 17.029/17.029 ============================== end of input ========================== 17.029/17.029 17.029/17.029 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 17.029/17.029 17.029/17.029 % Formulas that are not ordinary clauses: 17.029/17.029 1 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 17.029/17.029 2 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 17.029/17.029 3 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 17.029/17.029 4 ->(x1,y) -> ->(s(x1),s(y)) # label(congruence) # label(non_clause). [assumption]. 17.029/17.029 5 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 17.029/17.029 6 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 17.029/17.029 7 ->(x1,y) -> ->(pair(x1,x2),pair(y,x2)) # label(congruence) # label(non_clause). [assumption]. 17.029/17.029 8 ->(x2,y) -> ->(pair(x1,x2),pair(x1,y)) # label(congruence) # label(non_clause). [assumption]. 17.029/17.029 9 ->(x1,y) -> ->(t(x1),t(y)) # label(congruence) # label(non_clause). [assumption]. 17.029/17.029 10 (exists x1 ->(t(l),x1)) # label(goal) # label(non_clause) # label(goal). [goal]. 17.029/17.029 17.029/17.029 ============================== end of process non-clausal formulas === 17.029/17.029 17.029/17.029 ============================== CLAUSES FOR SEARCH ==================== 17.029/17.029 17.029/17.029 formulas(mace4_clauses). 17.029/17.029 -->(x,y) | ->(f(x),f(y)) # label(congruence). 17.029/17.029 -->(x,y) | ->(g(x,z),g(y,z)) # label(congruence). 17.029/17.029 -->(x,y) | ->(g(z,x),g(z,y)) # label(congruence). 17.029/17.029 -->(x,y) | ->(s(x),s(y)) # label(congruence). 17.029/17.029 -->(x,y) | ->(h(x,z),h(y,z)) # label(congruence). 17.029/17.029 -->(x,y) | ->(h(z,x),h(z,y)) # label(congruence). 17.029/17.029 -->(x,y) | ->(pair(x,z),pair(y,z)) # label(congruence). 17.029/17.029 -->(x,y) | ->(pair(z,x),pair(z,y)) # label(congruence). 17.029/17.029 -->(x,y) | ->(t(x),t(y)) # label(congruence). 17.029/17.029 -->(t(l),x) # label(goal). 17.029/17.029 end_of_list. 17.029/17.029 17.029/17.029 ============================== end of clauses for search ============= 17.029/17.029 17.029/17.029 % There are no natural numbers in the input. 17.029/17.029 17.029/17.029 ============================== DOMAIN SIZE 2 ========================= 17.029/17.029 17.029/17.029 ============================== MODEL ================================= 17.029/17.029 17.029/17.029 interpretation( 2, [number=1, seconds=0], [ 17.029/17.029 17.029/17.029 function(l, [ 0 ]), 17.029/17.029 17.029/17.029 function(t(_), [ 0, 0 ]), 17.029/17.029 17.029/17.029 function(f(_), [ 0, 0 ]), 17.029/17.029 17.029/17.029 function(s(_), [ 0, 0 ]), 17.029/17.029 17.029/17.029 function(h(_,_), [ 17.029/17.029 0, 0, 17.029/17.029 0, 0 ]), 17.029/17.029 17.029/17.029 function(pair(_,_), [ 17.029/17.029 0, 0, 17.029/17.029 0, 0 ]), 17.029/17.029 17.029/17.029 function(g(_,_), [ 17.029/17.029 0, 0, 17.029/17.029 0, 0 ]), 17.029/17.029 17.029/17.029 relation(->(_,_), [ 17.029/17.029 0, 0, 17.029/17.029 0, 0 ]) 17.029/17.029 ]). 17.029/17.029 17.029/17.029 ============================== end of model ========================== 17.029/17.029 17.029/17.029 ============================== STATISTICS ============================ 17.029/17.029 17.029/17.029 For domain size 2. 17.029/17.029 17.029/17.029 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 17.029/17.029 Ground clauses: seen=62, kept=62. 17.029/17.029 Selections=19, assignments=19, propagations=4, current_models=1. 17.029/17.029 Rewrite_terms=124, rewrite_bools=65, indexes=4. 17.029/17.029 Rules_from_neg_clauses=0, cross_offs=0. 17.029/17.029 17.029/17.029 ============================== end of statistics ===================== 17.029/17.029 17.029/17.029 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 17.029/17.029 17.029/17.029 Exiting with 1 model. 17.029/17.029 17.029/17.029 Process 109838 exit (max_models) Fri Jul 16 15:05:54 2021 17.029/17.029 The process finished Fri Jul 16 15:05:54 2021 17.029/17.029 17.029/17.029 17.029/17.029 Mace4 cooked interpretation: 17.029/17.029 17.029/17.029 17.029/17.029 17.029/17.029 The problem is infeasible. 17.029/17.029 17.029/17.029 17.029/17.029 The problem is not joinable. 17.029/17.029 18.34user 2.02system 0:17.29elapsed 117%CPU (0avgtext+0avgdata 434872maxresident)k 17.029/17.029 8inputs+0outputs (0major+296568minor)pagefaults 0swaps