%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : LAT014-1 : TPTP v8.2.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % Computer : n023.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Jun 24 10:17:58 EDT 2024 % Result : Unsatisfiable 0.53s 0.60s % Output : CNFRefutation 0.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : LAT014-1 : TPTP v8.2.0. Released v2.2.0. % 0.12/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n023.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Fri Jun 21 22:13:39 EDT 2024 % 0.12/0.34 % CPUTime : % 0.20/0.57 start to proof:theBenchmark % 0.53/0.60 %------------------------------------------- % 0.53/0.60 % File :CSE---1.7 % 0.53/0.60 % Problem :theBenchmark % 0.53/0.60 % Transform :cnf % 0.53/0.60 % Format :tptp:raw % 0.53/0.60 % Command :java -jar mcs_scs.jar %d %s % 0.53/0.60 % 0.53/0.60 % Result :Theorem 0.000000s % 0.53/0.60 % Output :CNFRefutation 0.000000s % 0.53/0.60 %------------------------------------------- % 0.53/0.60 %-------------------------------------------------------------------------- % 0.53/0.60 % File : LAT014-1 : TPTP v8.2.0. Released v2.2.0. % 0.53/0.60 % Domain : Lattice Theory % 0.53/0.60 % Problem : McKenzie's 4-basis for lattice theory, part 3 (of 3) % 0.53/0.60 % Version : [MP96] (equality) axioms. % 0.53/0.60 % English : This is part of a proof that McKenzie's 4-basis axiomatizes % 0.53/0.60 % lattice theory. We prove half of the standard basis. % 0.53/0.60 % The other half follows by duality. In this part we prove % 0.53/0.60 % absorbtion of meet. % 0.53/0.60 % 0.53/0.60 % Refs : [McC98] McCune (1998), Email to G. Sutcliffe % 0.53/0.60 % : [MP96] McCune & Padmanabhan (1996), Automated Deduction in Eq % 0.53/0.60 % Source : [McC98] % 0.53/0.60 % Names : LT-9 [MP96] % 0.53/0.60 % 0.53/0.60 % Status : Unsatisfiable % 0.53/0.60 % Rating : 0.00 v7.4.0, 0.04 v7.3.0, 0.00 v6.0.0, 0.10 v5.5.0, 0.05 v5.4.0, 0.00 v5.1.0, 0.13 v5.0.0, 0.07 v4.1.0, 0.09 v4.0.1, 0.07 v4.0.0, 0.08 v3.7.0, 0.00 v2.2.1 % 0.53/0.60 % Syntax : Number of clauses : 5 ( 5 unt; 0 nHn; 1 RR) % 0.53/0.60 % Number of literals : 5 ( 5 equ; 1 neg) % 0.53/0.60 % Maximal clause size : 1 ( 1 avg) % 0.53/0.60 % Maximal term depth : 4 ( 2 avg) % 0.53/0.60 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty) % 0.53/0.60 % Number of functors : 4 ( 4 usr; 2 con; 0-2 aty) % 0.53/0.60 % Number of variables : 12 ( 8 sgn) % 0.53/0.60 % SPC : CNF_UNS_RFO_PEQ_UEQ % 0.53/0.60 % 0.53/0.60 % Comments : % 0.53/0.60 %-------------------------------------------------------------------------- % 0.53/0.60 %----McKenzie's self-dual (independent) absorptive 4-basis for lattice theory. % 0.53/0.60 cnf(mckenzie1,axiom, % 0.53/0.60 join(X,meet(Y,meet(X,Z))) = X ). % 0.53/0.60 % 0.53/0.60 cnf(mckenzie2,axiom, % 0.53/0.60 meet(X,join(Y,join(X,Z))) = X ). % 0.53/0.60 % 0.53/0.60 cnf(mckenzie3,axiom, % 0.53/0.60 join(join(meet(X,Y),meet(Y,Z)),Y) = Y ). % 0.53/0.60 % 0.53/0.60 cnf(mckenzie4,axiom, % 0.53/0.60 meet(meet(join(X,Y),join(Y,Z)),Y) = Y ). % 0.53/0.60 % 0.53/0.60 %----Denial of conclusion: % 0.53/0.60 cnf(prove_absorbtion,negated_conjecture, % 0.53/0.60 meet(a,join(a,b)) != a ). % 0.53/0.60 % 0.53/0.60 %-------------------------------------------------------------------------- % 0.53/0.60 %------------------------------------------- % 0.53/0.60 % Proof found % 0.53/0.60 % SZS status Theorem for theBenchmark % 0.53/0.60 % SZS output start Proof % 0.53/0.60 %ClaNum:12(EqnAxiom:7) % 0.53/0.60 %VarNum:22(SingletonVarNum:12) % 0.53/0.60 %MaxLitNum:1 % 0.53/0.60 %MaxfuncDepth:3 % 0.53/0.60 %SharedTerms:5 % 0.53/0.60 %goalClause: 12 % 0.53/0.60 %singleGoalClaCount:1 % 0.53/0.60 [12]~E(f4(a2,f1(a2,a3)),a2) % 0.53/0.60 [8]E(f4(x81,f1(x82,f1(x81,x83))),x81) % 0.53/0.60 [9]E(f1(x91,f4(x92,f4(x91,x93))),x91) % 0.53/0.60 [10]E(f4(f4(f1(x101,x102),f1(x102,x103)),x102),x102) % 0.53/0.60 [11]E(f1(f1(f4(x111,x112),f4(x112,x113)),x112),x112) % 0.53/0.60 %EqnAxiom % 0.53/0.60 [1]E(x11,x11) % 0.53/0.60 [2]E(x22,x21)+~E(x21,x22) % 0.53/0.60 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.53/0.60 [4]~E(x41,x42)+E(f1(x41,x43),f1(x42,x43)) % 0.53/0.60 [5]~E(x51,x52)+E(f1(x53,x51),f1(x53,x52)) % 0.53/0.60 [6]~E(x61,x62)+E(f4(x61,x63),f4(x62,x63)) % 0.53/0.60 [7]~E(x71,x72)+E(f4(x73,x71),f4(x73,x72)) % 0.53/0.60 % 0.53/0.60 %------------------------------------------- % 0.53/0.61 cnf(16,plain, % 0.53/0.61 (E(x161,f1(f1(f4(x162,x161),f4(x161,x163)),x161))), % 0.53/0.61 inference(scs_inference,[],[11,2])). % 0.53/0.61 cnf(22,plain, % 0.53/0.61 ($false), % 0.53/0.61 inference(scs_inference,[],[12,16,8,2,3,7]), % 0.53/0.61 ['proof']). % 0.53/0.61 % SZS output end Proof % 0.53/0.61 % Total time :0.000000s %------------------------------------------------------------------------------