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 x y z) 21.042/21.042 (REPLACEMENT-MAP 21.042/21.042 (gcd 1, 2) 21.042/21.042 (iadd 1) 21.042/21.042 (u1 1) 21.042/21.042 (0) 21.042/21.042 (add 1, 2) 21.042/21.042 (fSNonEmpty) 21.042/21.042 (s 1) 21.042/21.042 (tp2 1, 2) 21.042/21.042 ) 21.042/21.042 (RULES 21.042/21.042 gcd(0,x) -> x 21.042/21.042 gcd(x,0) -> x 21.042/21.042 gcd(y,z) -> gcd(x,y) | iadd(z) ->* tp2(x,y) 21.042/21.042 gcd(z,y) -> gcd(x,y) | iadd(z) ->* tp2(x,y) 21.042/21.042 iadd(add(x,y)) -> tp2(x,y) 21.042/21.042 iadd(s(z)) -> u1(iadd(z)) 21.042/21.042 iadd(y) -> tp2(0,y) 21.042/21.042 u1(tp2(x,y)) -> tp2(s(x),y) 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 x y z) 21.042/21.042 (REPLACEMENT-MAP 21.042/21.042 (gcd 1, 2) 21.042/21.042 (iadd 1) 21.042/21.042 (u1 1) 21.042/21.042 (0) 21.042/21.042 (add 1, 2) 21.042/21.042 (fSNonEmpty) 21.042/21.042 (s 1) 21.042/21.042 (tp2 1, 2) 21.042/21.042 ) 21.042/21.042 (RULES 21.042/21.042 gcd(0,x) -> x 21.042/21.042 gcd(x,0) -> x 21.042/21.042 gcd(y,z) -> gcd(x,y) | iadd(z) ->* tp2(x,y) 21.042/21.042 gcd(z,y) -> gcd(x,y) | iadd(z) ->* tp2(x,y) 21.042/21.042 iadd(add(x,y)) -> tp2(x,y) 21.042/21.042 iadd(s(z)) -> u1(iadd(z)) 21.042/21.042 iadd(y) -> tp2(0,y) 21.042/21.042 u1(tp2(x,y)) -> tp2(s(x),y) 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 y z) 21.042/21.042 (REPLACEMENT-MAP 21.042/21.042 (gcd 1, 2) 21.042/21.042 (iadd 1) 21.042/21.042 (u1 1) 21.042/21.042 (0) 21.042/21.042 (add 1, 2) 21.042/21.042 (fSNonEmpty) 21.042/21.042 (s 1) 21.042/21.042 (tp2 1, 2) 21.042/21.042 ) 21.042/21.042 (RULES 21.042/21.042 gcd(0,x) -> x 21.042/21.042 gcd(x,0) -> x 21.042/21.042 gcd(y,z) -> gcd(x,y) | iadd(z) ->* tp2(x,y) 21.042/21.042 gcd(z,y) -> gcd(x,y) | iadd(z) ->* tp2(x,y) 21.042/21.042 iadd(add(x,y)) -> tp2(x,y) 21.042/21.042 iadd(s(z)) -> u1(iadd(z)) 21.042/21.042 iadd(y) -> tp2(0,y) 21.042/21.042 u1(tp2(x,y)) -> tp2(s(x),y) 21.042/21.042 ) 21.042/21.042 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 21.042/21.042 21.042/21.042 CRule InfChecker Info: 21.042/21.042 gcd(0,x) -> x 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 gcd(x,0) -> x 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 gcd(y,z) -> gcd(x,y) | iadd(z) ->* tp2(x,y) 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 x y z vNonEmpty x y z) 21.042/21.042 (STRATEGY CONTEXTSENSITIVE 21.042/21.042 (gcd 1 2) 21.042/21.042 (iadd 1) 21.042/21.042 (u1 1) 21.042/21.042 (0) 21.042/21.042 (add 1 2) 21.042/21.042 (fSNonEmpty) 21.042/21.042 (s 1) 21.042/21.042 (tp2 1 2) 21.042/21.042 ) 21.042/21.042 (RULES 21.042/21.042 gcd(0,x) -> x 21.042/21.042 gcd(x,0) -> x 21.042/21.042 gcd(y,z) -> gcd(x,y) | iadd(z) ->* tp2(x,y) 21.042/21.042 gcd(z,y) -> gcd(x,y) | iadd(z) ->* tp2(x,y) 21.042/21.042 iadd(add(x,y)) -> tp2(x,y) 21.042/21.042 iadd(s(z)) -> u1(iadd(z)) 21.042/21.042 iadd(y) -> tp2(0,y) 21.042/21.042 u1(tp2(x,y)) -> tp2(s(x),y) 21.042/21.042 )] 21.042/21.042 21.042/21.042 Infeasibility Conditions: 21.042/21.042 iadd(z) ->* tp2(x,y) 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 10774 was started by ubuntu on ubuntu, 21.042/21.042 Wed Mar 9 09:14:42 2022 21.042/21.042 The command was "./prover9 -f /tmp/prover910767-0.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/prover910767-0.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(x1,y) -> ->_s0(gcd(x1,x2),gcd(y,x2)) # label(congruence). 21.042/21.042 ->_s0(x2,y) -> ->_s0(gcd(x1,x2),gcd(x1,y)) # label(congruence). 21.042/21.042 ->_s0(x1,y) -> ->_s0(iadd(x1),iadd(y)) # label(congruence). 21.042/21.042 ->_s0(x1,y) -> ->_s0(u1(x1),u1(y)) # label(congruence). 21.042/21.042 ->_s0(x1,y) -> ->_s0(add(x1,x2),add(y,x2)) # label(congruence). 21.042/21.042 ->_s0(x2,y) -> ->_s0(add(x1,x2),add(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(tp2(x1,x2),tp2(y,x2)) # label(congruence). 21.042/21.042 ->_s0(x2,y) -> ->_s0(tp2(x1,x2),tp2(x1,y)) # label(congruence). 21.042/21.042 ->_s0(gcd(0,x1),x1) # label(replacement). 21.042/21.042 ->_s0(gcd(x1,0),x1) # label(replacement). 21.042/21.042 ->*_s0(iadd(x3),tp2(x1,x2)) -> ->_s0(gcd(x2,x3),gcd(x1,x2)) # label(replacement). 21.042/21.042 ->*_s0(iadd(x3),tp2(x1,x2)) -> ->_s0(gcd(x3,x2),gcd(x1,x2)) # label(replacement). 21.042/21.042 ->_s0(iadd(add(x1,x2)),tp2(x1,x2)) # label(replacement). 21.042/21.042 ->_s0(iadd(s(x3)),u1(iadd(x3))) # label(replacement). 21.042/21.042 ->_s0(iadd(x2),tp2(0,x2)) # label(replacement). 21.042/21.042 ->_s0(u1(tp2(x1,x2)),tp2(s(x1),x2)) # label(replacement). 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 end_of_list. 21.042/21.042 21.042/21.042 formulas(goals). 21.042/21.042 (exists x5 exists x6 exists x7 ->*_s0(iadd(x7),tp2(x5,x6))) # 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(x1,y) -> ->_s0(gcd(x1,x2),gcd(y,x2)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 2 ->_s0(x2,y) -> ->_s0(gcd(x1,x2),gcd(x1,y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 3 ->_s0(x1,y) -> ->_s0(iadd(x1),iadd(y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 4 ->_s0(x1,y) -> ->_s0(u1(x1),u1(y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 5 ->_s0(x1,y) -> ->_s0(add(x1,x2),add(y,x2)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 6 ->_s0(x2,y) -> ->_s0(add(x1,x2),add(x1,y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 7 ->_s0(x1,y) -> ->_s0(s(x1),s(y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 8 ->_s0(x1,y) -> ->_s0(tp2(x1,x2),tp2(y,x2)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 9 ->_s0(x2,y) -> ->_s0(tp2(x1,x2),tp2(x1,y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 10 ->*_s0(iadd(x3),tp2(x1,x2)) -> ->_s0(gcd(x2,x3),gcd(x1,x2)) # label(replacement) # label(non_clause). [assumption]. 21.042/21.042 11 ->*_s0(iadd(x3),tp2(x1,x2)) -> ->_s0(gcd(x3,x2),gcd(x1,x2)) # label(replacement) # label(non_clause). [assumption]. 21.042/21.042 12 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 21.042/21.042 13 (exists x5 exists x6 exists x7 ->*_s0(iadd(x7),tp2(x5,x6))) # 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,y) | ->_s0(gcd(x,z),gcd(y,z)) # label(congruence). [clausify(1)]. 21.042/21.042 -->_s0(x,y) | ->_s0(gcd(z,x),gcd(z,y)) # label(congruence). [clausify(2)]. 21.042/21.042 -->_s0(x,y) | ->_s0(iadd(x),iadd(y)) # label(congruence). [clausify(3)]. 21.042/21.042 -->_s0(x,y) | ->_s0(u1(x),u1(y)) # label(congruence). [clausify(4)]. 21.042/21.042 -->_s0(x,y) | ->_s0(add(x,z),add(y,z)) # label(congruence). [clausify(5)]. 21.042/21.042 -->_s0(x,y) | ->_s0(add(z,x),add(z,y)) # label(congruence). [clausify(6)]. 21.042/21.042 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(7)]. 21.042/21.042 -->_s0(x,y) | ->_s0(tp2(x,z),tp2(y,z)) # label(congruence). [clausify(8)]. 21.042/21.042 -->_s0(x,y) | ->_s0(tp2(z,x),tp2(z,y)) # label(congruence). [clausify(9)]. 21.042/21.042 ->_s0(gcd(0,x),x) # label(replacement). [assumption]. 21.042/21.042 ->_s0(gcd(x,0),x) # label(replacement). [assumption]. 21.042/21.042 -->*_s0(iadd(x),tp2(y,z)) | ->_s0(gcd(z,x),gcd(y,z)) # label(replacement). [clausify(10)]. 21.042/21.042 -->*_s0(iadd(x),tp2(y,z)) | ->_s0(gcd(x,z),gcd(y,z)) # label(replacement). [clausify(11)]. 21.042/21.042 ->_s0(iadd(add(x,y)),tp2(x,y)) # label(replacement). [assumption]. 21.042/21.042 ->_s0(iadd(s(x)),u1(iadd(x))) # label(replacement). [assumption]. 21.042/21.042 ->_s0(iadd(x),tp2(0,x)) # label(replacement). [assumption]. 21.042/21.042 ->_s0(u1(tp2(x,y)),tp2(s(x),y)) # label(replacement). [assumption]. 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(12)]. 21.042/21.042 -->*_s0(iadd(x),tp2(y,z)) # label(goal). [deny(13)]. 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([ 0, gcd, tp2, add, iadd, u1, s ]). 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: 14 -->_s0(x,y) | ->_s0(gcd(x,z),gcd(y,z)) # label(congruence). [clausify(1)]. 21.042/21.042 kept: 15 -->_s0(x,y) | ->_s0(gcd(z,x),gcd(z,y)) # label(congruence). [clausify(2)]. 21.042/21.042 kept: 16 -->_s0(x,y) | ->_s0(iadd(x),iadd(y)) # label(congruence). [clausify(3)]. 21.042/21.042 kept: 17 -->_s0(x,y) | ->_s0(u1(x),u1(y)) # label(congruence). [clausify(4)]. 21.042/21.042 kept: 18 -->_s0(x,y) | ->_s0(add(x,z),add(y,z)) # label(congruence). [clausify(5)]. 21.042/21.042 kept: 19 -->_s0(x,y) | ->_s0(add(z,x),add(z,y)) # label(congruence). [clausify(6)]. 21.042/21.042 kept: 20 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(7)]. 21.042/21.042 kept: 21 -->_s0(x,y) | ->_s0(tp2(x,z),tp2(y,z)) # label(congruence). [clausify(8)]. 21.042/21.042 kept: 22 -->_s0(x,y) | ->_s0(tp2(z,x),tp2(z,y)) # label(congruence). [clausify(9)]. 21.042/21.042 kept: 23 ->_s0(gcd(0,x),x) # label(replacement). [assumption]. 21.042/21.042 kept: 24 ->_s0(gcd(x,0),x) # label(replacement). [assumption]. 21.042/21.042 kept: 25 -->*_s0(iadd(x),tp2(y,z)) | ->_s0(gcd(z,x),gcd(y,z)) # label(replacement). [clausify(10)]. 21.042/21.042 kept: 26 -->*_s0(iadd(x),tp2(y,z)) | ->_s0(gcd(x,z),gcd(y,z)) # label(replacement). [clausify(11)]. 21.042/21.042 kept: 27 ->_s0(iadd(add(x,y)),tp2(x,y)) # label(replacement). [assumption]. 21.042/21.042 kept: 28 ->_s0(iadd(s(x)),u1(iadd(x))) # label(replacement). [assumption]. 21.042/21.042 kept: 29 ->_s0(iadd(x),tp2(0,x)) # label(replacement). [assumption]. 21.042/21.042 kept: 30 ->_s0(u1(tp2(x,y)),tp2(s(x),y)) # label(replacement). [assumption]. 21.042/21.042 kept: 31 ->*_s0(x,x) # label(reflexivity). [assumption]. 21.042/21.042 kept: 32 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(12)]. 21.042/21.042 kept: 33 -->*_s0(iadd(x),tp2(y,z)) # label(goal) # answer(goal). [deny(13)]. 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 14 -->_s0(x,y) | ->_s0(gcd(x,z),gcd(y,z)) # label(congruence). [clausify(1)]. 21.042/21.042 15 -->_s0(x,y) | ->_s0(gcd(z,x),gcd(z,y)) # label(congruence). [clausify(2)]. 21.042/21.042 16 -->_s0(x,y) | ->_s0(iadd(x),iadd(y)) # label(congruence). [clausify(3)]. 21.042/21.042 17 -->_s0(x,y) | ->_s0(u1(x),u1(y)) # label(congruence). [clausify(4)]. 21.042/21.042 18 -->_s0(x,y) | ->_s0(add(x,z),add(y,z)) # label(congruence). [clausify(5)]. 21.042/21.042 19 -->_s0(x,y) | ->_s0(add(z,x),add(z,y)) # label(congruence). [clausify(6)]. 21.042/21.042 20 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(7)]. 21.042/21.042 21 -->_s0(x,y) | ->_s0(tp2(x,z),tp2(y,z)) # label(congruence). [clausify(8)]. 21.042/21.042 22 -->_s0(x,y) | ->_s0(tp2(z,x),tp2(z,y)) # label(congruence). [clausify(9)]. 21.042/21.042 23 ->_s0(gcd(0,x),x) # label(replacement). [assumption]. 21.042/21.042 24 ->_s0(gcd(x,0),x) # label(replacement). [assumption]. 21.042/21.042 27 ->_s0(iadd(add(x,y)),tp2(x,y)) # label(replacement). [assumption]. 21.042/21.042 28 ->_s0(iadd(s(x)),u1(iadd(x))) # label(replacement). [assumption]. 21.042/21.042 29 ->_s0(iadd(x),tp2(0,x)) # label(replacement). [assumption]. 21.042/21.042 30 ->_s0(u1(tp2(x,y)),tp2(s(x),y)) # label(replacement). [assumption]. 21.042/21.042 31 ->*_s0(x,x) # label(reflexivity). [assumption]. 21.042/21.042 32 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(12)]. 21.042/21.042 33 -->*_s0(iadd(x),tp2(y,z)) # label(goal) # answer(goal). [deny(13)]. 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=10): 14 -->_s0(x,y) | ->_s0(gcd(x,z),gcd(y,z)) # label(congruence). [clausify(1)]. 21.042/21.042 21.042/21.042 given #2 (I,wt=10): 15 -->_s0(x,y) | ->_s0(gcd(z,x),gcd(z,y)) # label(congruence). [clausify(2)]. 21.042/21.042 21.042/21.042 given #3 (I,wt=8): 16 -->_s0(x,y) | ->_s0(iadd(x),iadd(y)) # label(congruence). [clausify(3)]. 21.042/21.042 21.042/21.042 given #4 (I,wt=8): 17 -->_s0(x,y) | ->_s0(u1(x),u1(y)) # label(congruence). [clausify(4)]. 21.042/21.042 21.042/21.042 given #5 (I,wt=10): 18 -->_s0(x,y) | ->_s0(add(x,z),add(y,z)) # label(congruence). [clausify(5)]. 21.042/21.042 21.042/21.042 given #6 (I,wt=10): 19 -->_s0(x,y) | ->_s0(add(z,x),add(z,y)) # label(congruence). [clausify(6)]. 21.042/21.042 21.042/21.042 given #7 (I,wt=8): 20 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(7)]. 21.042/21.042 21.042/21.042 given #8 (I,wt=10): 21 -->_s0(x,y) | ->_s0(tp2(x,z),tp2(y,z)) # label(congruence). [clausify(8)]. 21.042/21.042 21.042/21.042 given #9 (I,wt=10): 22 -->_s0(x,y) | ->_s0(tp2(z,x),tp2(z,y)) # label(congruence). [clausify(9)]. 21.042/21.042 21.042/21.042 given #10 (I,wt=5): 23 ->_s0(gcd(0,x),x) # label(replacement). [assumption]. 21.042/21.042 21.042/21.042 given #11 (I,wt=5): 24 ->_s0(gcd(x,0),x) # label(replacement). [assumption]. 21.042/21.042 21.042/21.042 given #12 (I,wt=8): 27 ->_s0(iadd(add(x,y)),tp2(x,y)) # label(replacement). [assumption]. 21.042/21.042 21.042/21.042 given #13 (I,wt=7): 28 ->_s0(iadd(s(x)),u1(iadd(x))) # label(replacement). [assumption]. 21.042/21.042 21.042/21.042 given #14 (I,wt=6): 29 ->_s0(iadd(x),tp2(0,x)) # label(replacement). [assumption]. 21.042/21.042 21.042/21.042 given #15 (I,wt=9): 30 ->_s0(u1(tp2(x,y)),tp2(s(x),y)) # label(replacement). [assumption]. 21.042/21.042 21.042/21.042 given #16 (I,wt=3): 31 ->*_s0(x,x) # label(reflexivity). [assumption]. 21.042/21.042 21.042/21.042 given #17 (I,wt=9): 32 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(12)]. 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 12 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 21.042/21.042 13 (exists x5 exists x6 exists x7 ->*_s0(iadd(x7),tp2(x5,x6))) # label(goal) # label(non_clause) # label(goal). [goal]. 21.042/21.042 29 ->_s0(iadd(x),tp2(0,x)) # label(replacement). [assumption]. 21.042/21.042 31 ->*_s0(x,x) # label(reflexivity). [assumption]. 21.042/21.042 32 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(12)]. 21.042/21.042 33 -->*_s0(iadd(x),tp2(y,z)) # label(goal) # answer(goal). [deny(13)]. 21.042/21.042 89 ->*_s0(iadd(x),tp2(0,x)). [ur(32,a,29,a,b,31,a)]. 21.042/21.042 90 $F # answer(goal). [resolve(89,a,33,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=76. Kept=76. proofs=1. 21.042/21.042 Usable=17. Sos=55. Demods=0. Limbo=1, Disabled=22. Hints=0. 21.042/21.042 Kept_by_rule=0, Deleted_by_rule=0. 21.042/21.042 Forward_subsumed=0. Back_subsumed=2. 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=4. Nonunit_bsub_feature_tests=23. 21.042/21.042 Megabytes=0.20. 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 10774 exit (max_proofs) Wed Mar 9 09:14:42 2022 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 gcd(z,y) -> gcd(x,y) | iadd(z) ->* tp2(x,y) 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 x y z vNonEmpty x y z) 21.042/21.042 (STRATEGY CONTEXTSENSITIVE 21.042/21.042 (gcd 1 2) 21.042/21.042 (iadd 1) 21.042/21.042 (u1 1) 21.042/21.042 (0) 21.042/21.042 (add 1 2) 21.042/21.042 (fSNonEmpty) 21.042/21.042 (s 1) 21.042/21.042 (tp2 1 2) 21.042/21.042 ) 21.042/21.042 (RULES 21.042/21.042 gcd(0,x) -> x 21.042/21.042 gcd(x,0) -> x 21.042/21.042 gcd(y,z) -> gcd(x,y) | iadd(z) ->* tp2(x,y) 21.042/21.042 gcd(z,y) -> gcd(x,y) | iadd(z) ->* tp2(x,y) 21.042/21.042 iadd(add(x,y)) -> tp2(x,y) 21.042/21.042 iadd(s(z)) -> u1(iadd(z)) 21.042/21.042 iadd(y) -> tp2(0,y) 21.042/21.042 u1(tp2(x,y)) -> tp2(s(x),y) 21.042/21.042 )] 21.042/21.042 21.042/21.042 Infeasibility Conditions: 21.042/21.042 iadd(z) ->* tp2(x,y) 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 10796 was started by ubuntu on ubuntu, 21.042/21.042 Wed Mar 9 09:14:42 2022 21.042/21.042 The command was "./prover9 -f /tmp/prover910789-0.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/prover910789-0.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(x1,y) -> ->_s0(gcd(x1,x2),gcd(y,x2)) # label(congruence). 21.042/21.042 ->_s0(x2,y) -> ->_s0(gcd(x1,x2),gcd(x1,y)) # label(congruence). 21.042/21.042 ->_s0(x1,y) -> ->_s0(iadd(x1),iadd(y)) # label(congruence). 21.042/21.042 ->_s0(x1,y) -> ->_s0(u1(x1),u1(y)) # label(congruence). 21.042/21.042 ->_s0(x1,y) -> ->_s0(add(x1,x2),add(y,x2)) # label(congruence). 21.042/21.042 ->_s0(x2,y) -> ->_s0(add(x1,x2),add(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(tp2(x1,x2),tp2(y,x2)) # label(congruence). 21.042/21.042 ->_s0(x2,y) -> ->_s0(tp2(x1,x2),tp2(x1,y)) # label(congruence). 21.042/21.042 ->_s0(gcd(0,x1),x1) # label(replacement). 21.042/21.042 ->_s0(gcd(x1,0),x1) # label(replacement). 21.042/21.042 ->*_s0(iadd(x3),tp2(x1,x2)) -> ->_s0(gcd(x2,x3),gcd(x1,x2)) # label(replacement). 21.042/21.042 ->*_s0(iadd(x3),tp2(x1,x2)) -> ->_s0(gcd(x3,x2),gcd(x1,x2)) # label(replacement). 21.042/21.042 ->_s0(iadd(add(x1,x2)),tp2(x1,x2)) # label(replacement). 21.042/21.042 ->_s0(iadd(s(x3)),u1(iadd(x3))) # label(replacement). 21.042/21.042 ->_s0(iadd(x2),tp2(0,x2)) # label(replacement). 21.042/21.042 ->_s0(u1(tp2(x1,x2)),tp2(s(x1),x2)) # label(replacement). 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 end_of_list. 21.042/21.042 21.042/21.042 formulas(goals). 21.042/21.042 (exists x5 exists x6 exists x7 ->*_s0(iadd(x7),tp2(x5,x6))) # 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(x1,y) -> ->_s0(gcd(x1,x2),gcd(y,x2)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 2 ->_s0(x2,y) -> ->_s0(gcd(x1,x2),gcd(x1,y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 3 ->_s0(x1,y) -> ->_s0(iadd(x1),iadd(y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 4 ->_s0(x1,y) -> ->_s0(u1(x1),u1(y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 5 ->_s0(x1,y) -> ->_s0(add(x1,x2),add(y,x2)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 6 ->_s0(x2,y) -> ->_s0(add(x1,x2),add(x1,y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 7 ->_s0(x1,y) -> ->_s0(s(x1),s(y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 8 ->_s0(x1,y) -> ->_s0(tp2(x1,x2),tp2(y,x2)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 9 ->_s0(x2,y) -> ->_s0(tp2(x1,x2),tp2(x1,y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 10 ->*_s0(iadd(x3),tp2(x1,x2)) -> ->_s0(gcd(x2,x3),gcd(x1,x2)) # label(replacement) # label(non_clause). [assumption]. 21.042/21.042 11 ->*_s0(iadd(x3),tp2(x1,x2)) -> ->_s0(gcd(x3,x2),gcd(x1,x2)) # label(replacement) # label(non_clause). [assumption]. 21.042/21.042 12 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 21.042/21.042 13 (exists x5 exists x6 exists x7 ->*_s0(iadd(x7),tp2(x5,x6))) # 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,y) | ->_s0(gcd(x,z),gcd(y,z)) # label(congruence). [clausify(1)]. 21.042/21.042 -->_s0(x,y) | ->_s0(gcd(z,x),gcd(z,y)) # label(congruence). [clausify(2)]. 21.042/21.042 -->_s0(x,y) | ->_s0(iadd(x),iadd(y)) # label(congruence). [clausify(3)]. 21.042/21.042 -->_s0(x,y) | ->_s0(u1(x),u1(y)) # label(congruence). [clausify(4)]. 21.042/21.042 -->_s0(x,y) | ->_s0(add(x,z),add(y,z)) # label(congruence). [clausify(5)]. 21.042/21.042 -->_s0(x,y) | ->_s0(add(z,x),add(z,y)) # label(congruence). [clausify(6)]. 21.042/21.042 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(7)]. 21.042/21.042 -->_s0(x,y) | ->_s0(tp2(x,z),tp2(y,z)) # label(congruence). [clausify(8)]. 21.042/21.042 -->_s0(x,y) | ->_s0(tp2(z,x),tp2(z,y)) # label(congruence). [clausify(9)]. 21.042/21.042 ->_s0(gcd(0,x),x) # label(replacement). [assumption]. 21.042/21.042 ->_s0(gcd(x,0),x) # label(replacement). [assumption]. 21.042/21.042 -->*_s0(iadd(x),tp2(y,z)) | ->_s0(gcd(z,x),gcd(y,z)) # label(replacement). [clausify(10)]. 21.042/21.042 -->*_s0(iadd(x),tp2(y,z)) | ->_s0(gcd(x,z),gcd(y,z)) # label(replacement). [clausify(11)]. 21.042/21.042 ->_s0(iadd(add(x,y)),tp2(x,y)) # label(replacement). [assumption]. 21.042/21.042 ->_s0(iadd(s(x)),u1(iadd(x))) # label(replacement). [assumption]. 21.042/21.042 ->_s0(iadd(x),tp2(0,x)) # label(replacement). [assumption]. 21.042/21.042 ->_s0(u1(tp2(x,y)),tp2(s(x),y)) # label(replacement). [assumption]. 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(12)]. 21.042/21.042 -->*_s0(iadd(x),tp2(y,z)) # label(goal). [deny(13)]. 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([ 0, gcd, tp2, add, iadd, u1, s ]). 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: 14 -->_s0(x,y) | ->_s0(gcd(x,z),gcd(y,z)) # label(congruence). [clausify(1)]. 21.042/21.042 kept: 15 -->_s0(x,y) | ->_s0(gcd(z,x),gcd(z,y)) # label(congruence). [clausify(2)]. 21.042/21.042 kept: 16 -->_s0(x,y) | ->_s0(iadd(x),iadd(y)) # label(congruence). [clausify(3)]. 21.042/21.042 kept: 17 -->_s0(x,y) | ->_s0(u1(x),u1(y)) # label(congruence). [clausify(4)]. 21.042/21.042 kept: 18 -->_s0(x,y) | ->_s0(add(x,z),add(y,z)) # label(congruence). [clausify(5)]. 21.042/21.042 kept: 19 -->_s0(x,y) | ->_s0(add(z,x),add(z,y)) # label(congruence). [clausify(6)]. 21.042/21.042 kept: 20 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(7)]. 21.042/21.042 kept: 21 -->_s0(x,y) | ->_s0(tp2(x,z),tp2(y,z)) # label(congruence). [clausify(8)]. 21.042/21.042 kept: 22 -->_s0(x,y) | ->_s0(tp2(z,x),tp2(z,y)) # label(congruence). [clausify(9)]. 21.042/21.042 kept: 23 ->_s0(gcd(0,x),x) # label(replacement). [assumption]. 21.042/21.042 kept: 24 ->_s0(gcd(x,0),x) # label(replacement). [assumption]. 21.042/21.042 kept: 25 -->*_s0(iadd(x),tp2(y,z)) | ->_s0(gcd(z,x),gcd(y,z)) # label(replacement). [clausify(10)]. 21.042/21.042 kept: 26 -->*_s0(iadd(x),tp2(y,z)) | ->_s0(gcd(x,z),gcd(y,z)) # label(replacement). [clausify(11)]. 21.042/21.042 kept: 27 ->_s0(iadd(add(x,y)),tp2(x,y)) # label(replacement). [assumption]. 21.042/21.042 kept: 28 ->_s0(iadd(s(x)),u1(iadd(x))) # label(replacement). [assumption]. 21.042/21.042 kept: 29 ->_s0(iadd(x),tp2(0,x)) # label(replacement). [assumption]. 21.042/21.042 kept: 30 ->_s0(u1(tp2(x,y)),tp2(s(x),y)) # label(replacement). [assumption]. 21.042/21.042 kept: 31 ->*_s0(x,x) # label(reflexivity). [assumption]. 21.042/21.042 kept: 32 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(12)]. 21.042/21.042 kept: 33 -->*_s0(iadd(x),tp2(y,z)) # label(goal) # answer(goal). [deny(13)]. 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 14 -->_s0(x,y) | ->_s0(gcd(x,z),gcd(y,z)) # label(congruence). [clausify(1)]. 21.042/21.042 15 -->_s0(x,y) | ->_s0(gcd(z,x),gcd(z,y)) # label(congruence). [clausify(2)]. 21.042/21.042 16 -->_s0(x,y) | ->_s0(iadd(x),iadd(y)) # label(congruence). [clausify(3)]. 21.042/21.042 17 -->_s0(x,y) | ->_s0(u1(x),u1(y)) # label(congruence). [clausify(4)]. 21.042/21.042 18 -->_s0(x,y) | ->_s0(add(x,z),add(y,z)) # label(congruence). [clausify(5)]. 21.042/21.042 19 -->_s0(x,y) | ->_s0(add(z,x),add(z,y)) # label(congruence). [clausify(6)]. 21.042/21.042 20 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(7)]. 21.042/21.042 21 -->_s0(x,y) | ->_s0(tp2(x,z),tp2(y,z)) # label(congruence). [clausify(8)]. 21.042/21.042 22 -->_s0(x,y) | ->_s0(tp2(z,x),tp2(z,y)) # label(congruence). [clausify(9)]. 21.042/21.042 23 ->_s0(gcd(0,x),x) # label(replacement). [assumption]. 21.042/21.042 24 ->_s0(gcd(x,0),x) # label(replacement). [assumption]. 21.042/21.042 27 ->_s0(iadd(add(x,y)),tp2(x,y)) # label(replacement). [assumption]. 21.042/21.042 28 ->_s0(iadd(s(x)),u1(iadd(x))) # label(replacement). [assumption]. 21.042/21.042 29 ->_s0(iadd(x),tp2(0,x)) # label(replacement). [assumption]. 21.042/21.042 30 ->_s0(u1(tp2(x,y)),tp2(s(x),y)) # label(replacement). [assumption]. 21.042/21.042 31 ->*_s0(x,x) # label(reflexivity). [assumption]. 21.042/21.042 32 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(12)]. 21.042/21.042 33 -->*_s0(iadd(x),tp2(y,z)) # label(goal) # answer(goal). [deny(13)]. 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=10): 14 -->_s0(x,y) | ->_s0(gcd(x,z),gcd(y,z)) # label(congruence). [clausify(1)]. 21.042/21.042 21.042/21.042 given #2 (I,wt=10): 15 -->_s0(x,y) | ->_s0(gcd(z,x),gcd(z,y)) # label(congruence). [clausify(2)]. 21.042/21.042 21.042/21.042 given #3 (I,wt=8): 16 -->_s0(x,y) | ->_s0(iadd(x),iadd(y)) # label(congruence). [clausify(3)]. 21.042/21.042 21.042/21.042 given #4 (I,wt=8): 17 -->_s0(x,y) | ->_s0(u1(x),u1(y)) # label(congruence). [clausify(4)]. 21.042/21.042 21.042/21.042 given #5 (I,wt=10): 18 -->_s0(x,y) | ->_s0(add(x,z),add(y,z)) # label(congruence). [clausify(5)]. 21.042/21.042 21.042/21.042 given #6 (I,wt=10): 19 -->_s0(x,y) | ->_s0(add(z,x),add(z,y)) # label(congruence). [clausify(6)]. 21.042/21.042 21.042/21.042 given #7 (I,wt=8): 20 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(7)]. 21.042/21.042 21.042/21.042 given #8 (I,wt=10): 21 -->_s0(x,y) | ->_s0(tp2(x,z),tp2(y,z)) # label(congruence). [clausify(8)]. 21.042/21.042 21.042/21.042 given #9 (I,wt=10): 22 -->_s0(x,y) | ->_s0(tp2(z,x),tp2(z,y)) # label(congruence). [clausify(9)]. 21.042/21.042 21.042/21.042 given #10 (I,wt=5): 23 ->_s0(gcd(0,x),x) # label(replacement). [assumption]. 21.042/21.042 21.042/21.042 given #11 (I,wt=5): 24 ->_s0(gcd(x,0),x) # label(replacement). [assumption]. 21.042/21.042 21.042/21.042 given #12 (I,wt=8): 27 ->_s0(iadd(add(x,y)),tp2(x,y)) # label(replacement). [assumption]. 21.042/21.042 21.042/21.042 given #13 (I,wt=7): 28 ->_s0(iadd(s(x)),u1(iadd(x))) # label(replacement). [assumption]. 21.042/21.042 21.042/21.042 given #14 (I,wt=6): 29 ->_s0(iadd(x),tp2(0,x)) # label(replacement). [assumption]. 21.042/21.042 21.042/21.042 given #15 (I,wt=9): 30 ->_s0(u1(tp2(x,y)),tp2(s(x),y)) # label(replacement). [assumption]. 21.042/21.042 21.042/21.042 given #16 (I,wt=3): 31 ->*_s0(x,x) # label(reflexivity). [assumption]. 21.042/21.042 21.042/21.042 given #17 (I,wt=9): 32 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(12)]. 21.042/21.042 21.042/21.042 ============================== PROOF ================================= 21.042/21.042 21.042/21.042 % Proof 1 at 0.01 (+ 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 12 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 21.042/21.042 13 (exists x5 exists x6 exists x7 ->*_s0(iadd(x7),tp2(x5,x6))) # label(goal) # label(non_clause) # label(goal). [goal]. 21.042/21.042 29 ->_s0(iadd(x),tp2(0,x)) # label(replacement). [assumption]. 21.042/21.042 31 ->*_s0(x,x) # label(reflexivity). [assumption]. 21.042/21.042 32 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(12)]. 21.042/21.042 33 -->*_s0(iadd(x),tp2(y,z)) # label(goal) # answer(goal). [deny(13)]. 21.042/21.042 89 ->*_s0(iadd(x),tp2(0,x)). [ur(32,a,29,a,b,31,a)]. 21.042/21.042 90 $F # answer(goal). [resolve(89,a,33,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=76. Kept=76. proofs=1. 21.042/21.042 Usable=17. Sos=55. Demods=0. Limbo=1, Disabled=22. Hints=0. 21.042/21.042 Kept_by_rule=0, Deleted_by_rule=0. 21.042/21.042 Forward_subsumed=0. Back_subsumed=2. 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=4. Nonunit_bsub_feature_tests=23. 21.042/21.042 Megabytes=0.20. 21.042/21.042 User_CPU=0.01, 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 10796 exit (max_proofs) Wed Mar 9 09:14:42 2022 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 iadd(add(x,y)) -> tp2(x,y) 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 iadd(s(z)) -> u1(iadd(z)) 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 iadd(y) -> tp2(0,y) 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 u1(tp2(x,y)) -> tp2(s(x),y) 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 y z) 21.042/21.042 (REPLACEMENT-MAP 21.042/21.042 (gcd 1, 2) 21.042/21.042 (iadd 1) 21.042/21.042 (u1 1) 21.042/21.042 (0) 21.042/21.042 (add 1, 2) 21.042/21.042 (fSNonEmpty) 21.042/21.042 (s 1) 21.042/21.042 (tp2 1, 2) 21.042/21.042 ) 21.042/21.042 (RULES 21.042/21.042 gcd(0,x) -> x 21.042/21.042 gcd(x,0) -> x 21.042/21.042 gcd(y,z) -> gcd(x,y) | iadd(z) ->* tp2(x,y) 21.042/21.042 gcd(z,y) -> gcd(x,y) | iadd(z) ->* tp2(x,y) 21.042/21.042 iadd(add(x,y)) -> tp2(x,y) 21.042/21.042 iadd(s(z)) -> u1(iadd(z)) 21.042/21.042 iadd(y) -> tp2(0,y) 21.042/21.042 u1(tp2(x,y)) -> tp2(s(x),y) 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 gcd(0,x) -> x 21.042/21.042 gcd(x,0) -> x 21.042/21.042 gcd(y,z) -> gcd(x,y) | iadd(z) ->* tp2(x,y) 21.042/21.042 gcd(z,y) -> gcd(x,y) | iadd(z) ->* tp2(x,y) 21.042/21.042 iadd(add(x,y)) -> tp2(x,y) 21.042/21.042 iadd(s(z)) -> u1(iadd(z)) 21.042/21.042 iadd(y) -> tp2(0,y) 21.042/21.042 u1(tp2(x,y)) -> tp2(s(x),y) 21.042/21.042 -> Vars: 21.042/21.042 "x", "y", "z" 21.042/21.042 21.042/21.042 -> Rlps: 21.042/21.042 crule: gcd(0,x) -> x, id: 1, possubterms: gcd(0,x)-> [], 0-> [1] 21.042/21.042 crule: gcd(x,0) -> x, id: 2, possubterms: gcd(x,0)-> [], 0-> [2] 21.042/21.042 crule: gcd(y,z) -> gcd(x,y) | iadd(z) ->* tp2(x,y), id: 3, possubterms: gcd(y,z)-> [] 21.042/21.042 crule: gcd(z,y) -> gcd(x,y) | iadd(z) ->* tp2(x,y), id: 4, possubterms: gcd(z,y)-> [] 21.042/21.042 crule: iadd(add(x,y)) -> tp2(x,y), id: 5, possubterms: iadd(add(x,y))-> [], add(x,y)-> [1] 21.042/21.042 crule: iadd(s(z)) -> u1(iadd(z)), id: 6, possubterms: iadd(s(z))-> [], s(z)-> [1] 21.042/21.042 crule: iadd(y) -> tp2(0,y), id: 7, possubterms: iadd(y)-> [] 21.042/21.042 crule: u1(tp2(x,y)) -> tp2(s(x),y), id: 8, possubterms: u1(tp2(x,y))-> [], tp2(x,y)-> [1] 21.042/21.042 21.042/21.042 -> Unifications: 21.042/21.042 R2 unifies with R1 at p: [], l: gcd(x,0), lp: gcd(x,0), conds: {}, sig: {x -> 0,x' -> 0}, l': gcd(0,x'), r: x, r': x' 21.042/21.042 R3 unifies with R1 at p: [], l: gcd(y,z), lp: gcd(y,z), conds: {iadd(z) ->* tp2(x,y)}, sig: {y -> 0,z -> x'}, l': gcd(0,x'), r: gcd(x,y), r': x' 21.042/21.042 R3 unifies with R2 at p: [], l: gcd(y,z), lp: gcd(y,z), conds: {iadd(z) ->* tp2(x,y)}, sig: {y -> x',z -> 0}, l': gcd(x',0), r: gcd(x,y), r': x' 21.042/21.042 R4 unifies with R1 at p: [], l: gcd(z,y), lp: gcd(z,y), conds: {iadd(z) ->* tp2(x,y)}, sig: {y -> x',z -> 0}, l': gcd(0,x'), r: gcd(x,y), r': x' 21.042/21.042 R4 unifies with R2 at p: [], l: gcd(z,y), lp: gcd(z,y), conds: {iadd(z) ->* tp2(x,y)}, sig: {y -> 0,z -> x'}, l': gcd(x',0), r: gcd(x,y), r': x' 21.042/21.042 R4 unifies with R3 at p: [], l: gcd(z,y), lp: gcd(z,y), conds: {iadd(z) ->* tp2(x,y), iadd(z') ->* tp2(x',y')}, sig: {y -> z',z -> y'}, l': gcd(y',z'), r: gcd(x,y), r': gcd(x',y') 21.042/21.042 R7 unifies with R5 at p: [], l: iadd(y), lp: iadd(y), conds: {}, sig: {y -> add(x,y')}, l': iadd(add(x,y')), r: tp2(0,y), r': tp2(x,y') 21.042/21.042 R7 unifies with R6 at p: [], l: iadd(y), lp: iadd(y), conds: {}, sig: {y -> s(z)}, l': iadd(s(z)), r: tp2(0,y), r': u1(iadd(z)) 21.042/21.042 21.042/21.042 -> Critical pairs info: 21.042/21.042 => Not trivial, Overlay, NW2, N1 21.042/21.042 <0,0> => Trivial, Overlay, NW2, N2 21.042/21.042 | iadd(x') ->* tp2(x,0) => Not trivial, Overlay, NW1, N3 21.042/21.042 | iadd(0) ->* tp2(x,x') => Not trivial, Overlay, NW1, N4 21.042/21.042 => Not trivial, Overlay, NW1, N5 21.042/21.042 | iadd(y') ->* tp2(x,z'), iadd(z') ->* tp2(x',y') => Not trivial, Overlay, NW0, N6 21.042/21.042 21.042/21.042 -> Problem conclusions: 21.042/21.042 Left linear, Right linear, 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, Not semiequational 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 operational 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 y z x y' z) 21.042/21.042 (REPLACEMENT-MAP 21.042/21.042 (gcd 1, 2) 21.042/21.042 (iadd 1) 21.042/21.042 (u1 1) 21.042/21.042 (0) 21.042/21.042 (add 1, 2) 21.042/21.042 (fSNonEmpty) 21.042/21.042 (s 1) 21.042/21.042 (tp2 1, 2) 21.042/21.042 ) 21.042/21.042 (RULES 21.042/21.042 gcd(0,x) -> x 21.042/21.042 gcd(x,0) -> x 21.042/21.042 gcd(y,z) -> gcd(x,y) | iadd(z) ->* tp2(x,y) 21.042/21.042 gcd(z,y) -> gcd(x,y) | iadd(z) ->* tp2(x,y) 21.042/21.042 iadd(add(x,y)) -> tp2(x,y) 21.042/21.042 iadd(s(z)) -> u1(iadd(z)) 21.042/21.042 iadd(y) -> tp2(0,y) 21.042/21.042 u1(tp2(x,y)) -> tp2(s(x),y) 21.042/21.042 ) 21.042/21.042 Critical Pairs: 21.042/21.042 => Not trivial, Overlay, NW2, N1 21.042/21.042 | iadd(x') ->* tp2(x,0) => Not trivial, Overlay, NW1, N3 21.042/21.042 | iadd(0) ->* tp2(x,x') => Not trivial, Overlay, NW1, N4 21.042/21.042 => Not trivial, Overlay, NW1, N5 21.042/21.042 | iadd(y') ->* tp2(x,z'), iadd(z') ->* tp2(x',y') => Not trivial, Overlay, NW0, N6 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 y z x y' z) 21.042/21.042 (REPLACEMENT-MAP 21.042/21.042 (gcd 1, 2) 21.042/21.042 (iadd 1) 21.042/21.042 (u1 1) 21.042/21.042 (0) 21.042/21.042 (add 1, 2) 21.042/21.042 (fSNonEmpty) 21.042/21.042 (s 1) 21.042/21.042 (tp2 1, 2) 21.042/21.042 ) 21.042/21.042 (RULES 21.042/21.042 gcd(0,x) -> x 21.042/21.042 gcd(x,0) -> x 21.042/21.042 gcd(y,z) -> gcd(x,y) | iadd(z) ->* tp2(x,y) 21.042/21.042 gcd(z,y) -> gcd(x,y) | iadd(z) ->* tp2(x,y) 21.042/21.042 iadd(add(x,y)) -> tp2(x,y) 21.042/21.042 iadd(s(z)) -> u1(iadd(z)) 21.042/21.042 iadd(y) -> tp2(0,y) 21.042/21.042 u1(tp2(x,y)) -> tp2(s(x),y) 21.042/21.042 ) 21.042/21.042 Critical Pairs: 21.042/21.042 => Not trivial, Overlay, NW2, N1 21.042/21.042 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 21.042/21.042 21.042/21.042 Infeasible Convergence No Conditions CCP Processor: 21.042/21.042 Infeasible convergence? 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 x y z y1 vNonEmpty z) 21.042/21.042 (STRATEGY CONTEXTSENSITIVE 21.042/21.042 (gcd 1 2) 21.042/21.042 (iadd 1) 21.042/21.042 (u1 1) 21.042/21.042 (0) 21.042/21.042 (add 1 2) 21.042/21.042 (c_x) 21.042/21.042 (c_y1) 21.042/21.042 (fSNonEmpty) 21.042/21.042 (s 1) 21.042/21.042 (tp2 1 2) 21.042/21.042 ) 21.042/21.042 (RULES 21.042/21.042 gcd(0,x) -> x 21.042/21.042 gcd(x,0) -> x 21.042/21.042 gcd(y,z) -> gcd(x,y) | iadd(z) ->* tp2(x,y) 21.042/21.042 gcd(z,y) -> gcd(x,y) | iadd(z) ->* tp2(x,y) 21.042/21.042 iadd(add(x,y)) -> tp2(x,y) 21.042/21.042 iadd(s(z)) -> u1(iadd(z)) 21.042/21.042 iadd(y) -> tp2(0,y) 21.042/21.042 u1(tp2(x,y)) -> tp2(s(x),y) 21.042/21.042 )] 21.042/21.042 21.042/21.042 Infeasibility Conditions: 21.042/21.042 tp2(c_x,c_y1) ->* z, tp2(0,add(c_x,c_y1)) ->* z 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 10824 was started by ubuntu on ubuntu, 21.042/21.042 Wed Mar 9 09:14:42 2022 21.042/21.042 The command was "./mace4 -c -f /tmp/mace410811-2.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/mace410811-2.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 ->(x1,y) -> ->(gcd(x1,x2),gcd(y,x2)) # label(congruence). 21.042/21.042 ->(x2,y) -> ->(gcd(x1,x2),gcd(x1,y)) # label(congruence). 21.042/21.042 ->(x1,y) -> ->(iadd(x1),iadd(y)) # label(congruence). 21.042/21.042 ->(x1,y) -> ->(u1(x1),u1(y)) # label(congruence). 21.042/21.042 ->(x1,y) -> ->(add(x1,x2),add(y,x2)) # label(congruence). 21.042/21.042 ->(x2,y) -> ->(add(x1,x2),add(x1,y)) # label(congruence). 21.042/21.042 ->(x1,y) -> ->(s(x1),s(y)) # label(congruence). 21.042/21.042 ->(x1,y) -> ->(tp2(x1,x2),tp2(y,x2)) # label(congruence). 21.042/21.042 ->(x2,y) -> ->(tp2(x1,x2),tp2(x1,y)) # label(congruence). 21.042/21.042 ->*(x,x) # label(reflexivity). 21.042/21.042 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity). 21.042/21.042 end_of_list. 21.042/21.042 21.042/21.042 formulas(goals). 21.042/21.042 (exists x6 (->*(tp2(c_x,c_y1),x6) & ->*(tp2(0,add(c_x,c_y1)),x6))) # 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) -> ->(gcd(x1,x2),gcd(y,x2)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 2 ->(x2,y) -> ->(gcd(x1,x2),gcd(x1,y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 3 ->(x1,y) -> ->(iadd(x1),iadd(y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 4 ->(x1,y) -> ->(u1(x1),u1(y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 5 ->(x1,y) -> ->(add(x1,x2),add(y,x2)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 6 ->(x2,y) -> ->(add(x1,x2),add(x1,y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 7 ->(x1,y) -> ->(s(x1),s(y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 8 ->(x1,y) -> ->(tp2(x1,x2),tp2(y,x2)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 9 ->(x2,y) -> ->(tp2(x1,x2),tp2(x1,y)) # label(congruence) # label(non_clause). [assumption]. 21.042/21.042 10 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause). [assumption]. 21.042/21.042 11 (exists x6 (->*(tp2(c_x,c_y1),x6) & ->*(tp2(0,add(c_x,c_y1)),x6))) # 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) | ->(gcd(x,z),gcd(y,z)) # label(congruence). 21.042/21.042 -->(x,y) | ->(gcd(z,x),gcd(z,y)) # label(congruence). 21.042/21.042 -->(x,y) | ->(iadd(x),iadd(y)) # label(congruence). 21.042/21.042 -->(x,y) | ->(u1(x),u1(y)) # label(congruence). 21.042/21.042 -->(x,y) | ->(add(x,z),add(y,z)) # label(congruence). 21.042/21.042 -->(x,y) | ->(add(z,x),add(z,y)) # label(congruence). 21.042/21.042 -->(x,y) | ->(s(x),s(y)) # label(congruence). 21.042/21.042 -->(x,y) | ->(tp2(x,z),tp2(y,z)) # label(congruence). 21.042/21.042 -->(x,y) | ->(tp2(z,x),tp2(z,y)) # label(congruence). 21.042/21.042 ->*(x,x) # label(reflexivity). 21.042/21.042 -->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity). 21.042/21.042 -->*(tp2(c_x,c_y1),x) | -->*(tp2(0,add(c_x,c_y1)),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(0, [ 0 ]), 21.042/21.042 21.042/21.042 function(c_x, [ 0 ]), 21.042/21.042 21.042/21.042 function(c_y1, [ 0 ]), 21.042/21.042 21.042/21.042 function(s(_), [ 0, 0 ]), 21.042/21.042 21.042/21.042 function(iadd(_), [ 0, 0 ]), 21.042/21.042 21.042/21.042 function(u1(_), [ 0, 0 ]), 21.042/21.042 21.042/21.042 function(tp2(_,_), [ 21.042/21.042 0, 1, 21.042/21.042 0, 0 ]), 21.042/21.042 21.042/21.042 function(gcd(_,_), [ 21.042/21.042 0, 0, 21.042/21.042 0, 0 ]), 21.042/21.042 21.042/21.042 function(add(_,_), [ 21.042/21.042 1, 0, 21.042/21.042 0, 0 ]), 21.042/21.042 21.042/21.042 relation(->*(_,_), [ 21.042/21.042 1, 0, 21.042/21.042 0, 1 ]), 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=72, kept=68. 21.042/21.042 Selections=21, assignments=22, propagations=8, current_models=1. 21.042/21.042 Rewrite_terms=138, rewrite_bools=86, indexes=21. 21.042/21.042 Rules_from_neg_clauses=1, cross_offs=1. 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 10824 exit (max_models) Wed Mar 9 09:14:42 2022 21.042/21.042 The process finished Wed Mar 9 09:14:42 2022 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 27.49user 0.98system 0:21.42elapsed 132%CPU (0avgtext+0avgdata 445280maxresident)k 21.042/21.042 8inputs+0outputs (0major+167438minor)pagefaults 0swaps