0.00/0.19 YES 0.00/0.19 0.00/0.19 Problem 1: 0.00/0.19 0.00/0.19 (VAR v_NonEmpty:S X:S) 0.00/0.19 (RULES 0.00/0.19 b -> c 0.00/0.19 f(X:S,X:S) -> f(a,b) 0.00/0.19 ) 0.00/0.19 (STRATEGY INNERMOST) 0.00/0.19 0.00/0.19 Problem 1: 0.00/0.19 0.00/0.19 Dependency Pairs Processor: 0.00/0.19 -> Pairs: 0.00/0.19 F(X:S,X:S) -> B 0.00/0.19 F(X:S,X:S) -> F(a,b) 0.00/0.19 -> Rules: 0.00/0.19 b -> c 0.00/0.19 f(X:S,X:S) -> f(a,b) 0.00/0.19 0.00/0.19 Problem 1: 0.00/0.19 0.00/0.19 SCC Processor: 0.00/0.19 -> Pairs: 0.00/0.19 F(X:S,X:S) -> B 0.00/0.19 F(X:S,X:S) -> F(a,b) 0.00/0.19 -> Rules: 0.00/0.19 b -> c 0.00/0.19 f(X:S,X:S) -> f(a,b) 0.00/0.19 ->Strongly Connected Components: 0.00/0.19 ->->Cycle: 0.00/0.19 ->->-> Pairs: 0.00/0.19 F(X:S,X:S) -> F(a,b) 0.00/0.19 ->->-> Rules: 0.00/0.19 b -> c 0.00/0.19 f(X:S,X:S) -> f(a,b) 0.00/0.19 0.00/0.19 Problem 1: 0.00/0.19 0.00/0.19 Reduction Pair Processor: 0.00/0.19 -> Pairs: 0.00/0.19 F(X:S,X:S) -> F(a,b) 0.00/0.19 -> Rules: 0.00/0.19 b -> c 0.00/0.19 f(X:S,X:S) -> f(a,b) 0.00/0.19 -> Usable rules: 0.00/0.19 b -> c 0.00/0.19 ->Mace4 Output: 0.00/0.19 ============================== Mace4 ================================= 0.00/0.19 Mace4 (64) version 2009-11A, November 2009. 0.00/0.19 Process 58069 was started by sandbox on n140.star.cs.uiowa.edu, 0.00/0.19 Thu Mar 28 22:14:43 2019 0.00/0.19 The command was "./mace4 -c -f /tmp/mace4336465782861021530.in". 0.00/0.19 ============================== end of head =========================== 0.00/0.19 0.00/0.19 ============================== INPUT ================================= 0.00/0.19 0.00/0.19 % Reading from file /tmp/mace4336465782861021530.in 0.00/0.19 0.00/0.19 assign(max_seconds,20). 0.00/0.19 0.00/0.19 formulas(assumptions). 0.00/0.19 gtrsim_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility). 0.00/0.19 succeq_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility). 0.00/0.19 gtrsim_s0(x,y) & succeq_s0(y,z) -> gtrsim_s0(x,z) # label(compatibility). 0.00/0.19 arrow_s0(x1,y) -> arrow_s0(f3(x1,x2),f3(y,x2)) # label(congruence). 0.00/0.19 arrow_s0(x2,y) -> arrow_s0(f3(x1,x2),f3(x1,y)) # label(congruence). 0.00/0.19 arrow_s0(x1,y) -> arrow_s0(f9(x1,x2),f9(y,x2)) # label(congruence). 0.00/0.19 arrow_s0(x2,y) -> arrow_s0(f9(x1,x2),f9(x1,y)) # label(congruence). 0.00/0.19 arrow_s0(f2,f5) # label(replacement). 0.00/0.19 arrow_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion). 0.00/0.19 sqsupset_s0(f9(x1,x1),f9(f4,f2)) # label(replacement). 0.00/0.19 sqsupset_s0(x,y) -> sqsupsetStar_s0(x,y) # label(inclusion). 0.00/0.19 sqsupset_s0(x,y) & sqsupsetStar_s0(y,z) -> sqsupsetStar_s0(x,z) # label(compatibility). 0.00/0.19 end_of_list. 0.00/0.19 0.00/0.19 formulas(goals). 0.00/0.19 (exists x sqsupsetStar_s0(x,x)) # label(wellfoundedness). 0.00/0.19 end_of_list. 0.00/0.19 0.00/0.19 ============================== end of input ========================== 0.00/0.19 0.00/0.19 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.00/0.19 0.00/0.19 % Formulas that are not ordinary clauses: 0.00/0.19 1 gtrsim_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 0.00/0.19 2 succeq_s0(x,y) & sqsupset_s0(y,z) -> sqsupset_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 0.00/0.19 3 gtrsim_s0(x,y) & succeq_s0(y,z) -> gtrsim_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 0.00/0.19 4 arrow_s0(x1,y) -> arrow_s0(f3(x1,x2),f3(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.19 5 arrow_s0(x2,y) -> arrow_s0(f3(x1,x2),f3(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.19 6 arrow_s0(x1,y) -> arrow_s0(f9(x1,x2),f9(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.19 7 arrow_s0(x2,y) -> arrow_s0(f9(x1,x2),f9(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.00/0.19 8 arrow_s0(x,y) -> gtrsim_s0(x,y) # label(inclusion) # label(non_clause). [assumption]. 0.00/0.19 9 sqsupset_s0(x,y) -> sqsupsetStar_s0(x,y) # label(inclusion) # label(non_clause). [assumption]. 0.00/0.19 10 sqsupset_s0(x,y) & sqsupsetStar_s0(y,z) -> sqsupsetStar_s0(x,z) # label(compatibility) # label(non_clause). [assumption]. 0.00/0.19 11 (exists x sqsupsetStar_s0(x,x)) # label(wellfoundedness) # label(non_clause) # label(goal). [goal]. 0.00/0.19 0.00/0.19 ============================== end of process non-clausal formulas === 0.00/0.19 0.00/0.19 ============================== CLAUSES FOR SEARCH ==================== 0.00/0.19 0.00/0.19 formulas(mace4_clauses). 0.00/0.19 -gtrsim_s0(x,y) | -sqsupset_s0(y,z) | sqsupset_s0(x,z) # label(compatibility). 0.00/0.19 -succeq_s0(x,y) | -sqsupset_s0(y,z) | sqsupset_s0(x,z) # label(compatibility). 0.00/0.19 -gtrsim_s0(x,y) | -succeq_s0(y,z) | gtrsim_s0(x,z) # label(compatibility). 0.00/0.19 -arrow_s0(x,y) | arrow_s0(f3(x,z),f3(y,z)) # label(congruence). 0.00/0.19 -arrow_s0(x,y) | arrow_s0(f3(z,x),f3(z,y)) # label(congruence). 0.00/0.19 -arrow_s0(x,y) | arrow_s0(f9(x,z),f9(y,z)) # label(congruence). 0.00/0.19 -arrow_s0(x,y) | arrow_s0(f9(z,x),f9(z,y)) # label(congruence). 0.00/0.19 arrow_s0(f2,f5) # label(replacement). 0.00/0.19 -arrow_s0(x,y) | gtrsim_s0(x,y) # label(inclusion). 0.00/0.19 sqsupset_s0(f9(x,x),f9(f4,f2)) # label(replacement). 0.00/0.19 -sqsupset_s0(x,y) | sqsupsetStar_s0(x,y) # label(inclusion). 0.00/0.19 -sqsupset_s0(x,y) | -sqsupsetStar_s0(y,z) | sqsupsetStar_s0(x,z) # label(compatibility). 0.00/0.19 -sqsupsetStar_s0(x,x) # label(wellfoundedness). 0.00/0.19 end_of_list. 0.00/0.19 0.00/0.19 ============================== end of clauses for search ============= 0.00/0.19 0.00/0.19 % There are no natural numbers in the input. 0.00/0.19 0.00/0.19 ============================== DOMAIN SIZE 2 ========================= 0.00/0.19 0.00/0.19 ============================== MODEL ================================= 0.00/0.19 0.00/0.19 interpretation( 2, [number=1, seconds=0], [ 0.00/0.19 0.00/0.19 function(f2, [ 0 ]), 0.00/0.19 0.00/0.19 function(f4, [ 1 ]), 0.00/0.19 0.00/0.19 function(f5, [ 0 ]), 0.00/0.19 0.00/0.19 function(f3(_,_), [ 0.00/0.19 0, 0, 0.00/0.19 0, 0 ]), 0.00/0.19 0.00/0.19 function(f9(_,_), [ 0.00/0.19 0, 0, 0.00/0.19 1, 0 ]), 0.00/0.19 0.00/0.19 relation(arrow_s0(_,_), [ 0.00/0.19 1, 0, 0.00/0.19 0, 1 ]), 0.00/0.19 0.00/0.19 relation(gtrsim_s0(_,_), [ 0.00/0.19 1, 0, 0.00/0.19 0, 1 ]), 0.00/0.19 0.00/0.19 relation(sqsupsetStar_s0(_,_), [ 0.00/0.19 0, 1, 0.00/0.19 0, 0 ]), 0.00/0.19 0.00/0.19 relation(sqsupset_s0(_,_), [ 0.00/0.19 0, 1, 0.00/0.19 0, 0 ]), 0.00/0.19 0.00/0.19 relation(succeq_s0(_,_), [ 0.00/0.19 0, 0, 0.00/0.19 0, 0 ]) 0.00/0.19 ]). 0.00/0.19 0.00/0.19 ============================== end of model ========================== 0.00/0.19 0.00/0.19 ============================== STATISTICS ============================ 0.00/0.19 0.00/0.19 For domain size 2. 0.00/0.19 0.00/0.19 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 0.00/0.19 Ground clauses: seen=77, kept=77. 0.00/0.19 Selections=19, assignments=27, propagations=26, current_models=1. 0.00/0.19 Rewrite_terms=134, rewrite_bools=191, indexes=18. 0.00/0.19 Rules_from_neg_clauses=2, cross_offs=2. 0.00/0.19 0.00/0.19 ============================== end of statistics ===================== 0.00/0.19 0.00/0.19 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 0.00/0.19 0.00/0.19 Exiting with 1 model. 0.00/0.19 0.00/0.19 Process 58069 exit (max_models) Thu Mar 28 22:14:43 2019 0.00/0.19 The process finished Thu Mar 28 22:14:43 2019 0.00/0.19 0.00/0.19 0.00/0.19 Mace4 cooked interpretation: 0.00/0.19 0.00/0.19 % number = 1 0.00/0.19 % seconds = 0 0.00/0.19 0.00/0.19 % Interpretation of size 2 0.00/0.19 0.00/0.19 f2 = 0. 0.00/0.19 0.00/0.19 f4 = 1. 0.00/0.19 0.00/0.19 f5 = 0. 0.00/0.19 0.00/0.19 f3(0,0) = 0. 0.00/0.19 f3(0,1) = 0. 0.00/0.19 f3(1,0) = 0. 0.00/0.19 f3(1,1) = 0. 0.00/0.19 0.00/0.19 f9(0,0) = 0. 0.00/0.19 f9(0,1) = 0. 0.00/0.19 f9(1,0) = 1. 0.00/0.19 f9(1,1) = 0. 0.00/0.19 0.00/0.19 arrow_s0(0,0). 0.00/0.19 - arrow_s0(0,1). 0.00/0.19 - arrow_s0(1,0). 0.00/0.19 arrow_s0(1,1). 0.00/0.19 0.00/0.19 gtrsim_s0(0,0). 0.00/0.19 - gtrsim_s0(0,1). 0.00/0.19 - gtrsim_s0(1,0). 0.00/0.19 gtrsim_s0(1,1). 0.00/0.19 0.00/0.19 - sqsupsetStar_s0(0,0). 0.00/0.19 sqsupsetStar_s0(0,1). 0.00/0.19 - sqsupsetStar_s0(1,0). 0.00/0.19 - sqsupsetStar_s0(1,1). 0.00/0.19 0.00/0.19 - sqsupset_s0(0,0). 0.00/0.19 sqsupset_s0(0,1). 0.00/0.19 - sqsupset_s0(1,0). 0.00/0.19 - sqsupset_s0(1,1). 0.00/0.19 0.00/0.19 - succeq_s0(0,0). 0.00/0.19 - succeq_s0(0,1). 0.00/0.19 - succeq_s0(1,0). 0.00/0.19 - succeq_s0(1,1). 0.00/0.19 0.00/0.19 0.00/0.19 Problem 1: 0.00/0.19 0.00/0.19 SCC Processor: 0.00/0.19 -> Pairs: 0.00/0.19 Empty 0.00/0.19 -> Rules: 0.00/0.19 b -> c 0.00/0.19 f(X:S,X:S) -> f(a,b) 0.00/0.19 ->Strongly Connected Components: 0.00/0.19 There is no strongly connected component 0.00/0.19 0.00/0.19 The problem is finite. 0.00/0.19 EOF