%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : COL053-1 : TPTP v8.2.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n027.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 04:44:56 EDT 2024 % Result : Unsatisfiable 0.55s 0.61s % Output : CNFRefutation 0.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : COL053-1 : TPTP v8.2.0. Released v1.0.0. % 0.03/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.13/0.33 % Computer : n027.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Tue Jun 18 15:36:54 EDT 2024 % 0.13/0.34 % CPUTime : % 0.47/0.57 start to proof:theBenchmark % 0.55/0.60 %------------------------------------------- % 0.55/0.60 % File :CSE---1.7 % 0.55/0.60 % Problem :theBenchmark % 0.55/0.60 % Transform :cnf % 0.55/0.60 % Format :tptp:raw % 0.55/0.60 % Command :java -jar mcs_scs.jar %d %s % 0.55/0.60 % 0.55/0.60 % Result :Theorem 0.000000s % 0.55/0.60 % Output :CNFRefutation 0.000000s % 0.55/0.60 %------------------------------------------- % 0.55/0.60 %-------------------------------------------------------------------------- % 0.55/0.60 % File : COL053-1 : TPTP v8.2.0. Released v1.0.0. % 0.55/0.60 % Domain : Combinatory Logic % 0.55/0.60 % Problem : An Exercise in Composition % 0.55/0.60 % Version : Especial. % 0.55/0.60 % English : For all birds x and y, there exists a bird z that composes % 0.55/0.60 % x with y for all birds w. Prove that for all birds x, y, and % 0.55/0.60 % z, there exists a bird u such that for all w, uw = x(y(zw)). % 0.55/0.60 % 0.55/0.60 % Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi % 0.55/0.60 % Source : [ANL] % 0.55/0.60 % Names : bird5.ver1.in [ANL] % 0.55/0.60 % 0.55/0.60 % Status : Unsatisfiable % 0.55/0.60 % Rating : 0.09 v8.2.0, 0.08 v8.1.0, 0.15 v7.5.0, 0.08 v7.4.0, 0.13 v7.3.0, 0.11 v7.1.0, 0.00 v6.4.0, 0.05 v6.3.0, 0.06 v6.2.0, 0.07 v6.1.0, 0.00 v6.0.0, 0.05 v5.5.0, 0.00 v2.0.0 % 0.55/0.60 % Syntax : Number of clauses : 2 ( 2 unt; 0 nHn; 1 RR) % 0.55/0.60 % Number of literals : 2 ( 2 equ; 1 neg) % 0.55/0.60 % Maximal clause size : 1 ( 1 avg) % 0.55/0.60 % Maximal term depth : 5 ( 2 avg) % 0.55/0.60 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty) % 0.55/0.60 % Number of functors : 6 ( 6 usr; 3 con; 0-2 aty) % 0.55/0.60 % Number of variables : 4 ( 0 sgn) % 0.55/0.60 % SPC : CNF_UNS_RFO_PEQ_UEQ % 0.55/0.61 % 0.55/0.61 % Comments : % 0.55/0.61 %-------------------------------------------------------------------------- % 0.55/0.61 %----For all birds x and y, there exists a bird z that composes x with % 0.55/0.61 %----y for all birds w. % 0.55/0.61 %---- FAx FAy TEz FAw [response(z,w) = response(x,response(y,w))]. % 0.55/0.61 %---- response(comp(x,y),w) = response(x,response(y,w)). % 0.55/0.61 cnf(composer_exists,axiom, % 0.55/0.61 response(compose(X,Y),W) = response(X,response(Y,W)) ). % 0.55/0.61 % 0.55/0.61 %----Hypothesis: For all birds x, y, and z, there exists a bird u such % 0.55/0.61 %----that for all w, uw = x(y(zw)). % 0.55/0.61 %----Finding clause (using xy to replace response(x,y)): % 0.55/0.61 %---- - (FAx FAy FAz TEu FAw (uw = x(y(zw)))). % 0.55/0.61 %---- TEx TEy TEz FAu TEw -(uw = x(y(zw))). % 0.55/0.61 %---- Letting w = f(u), x = A, y = B, and z = C, % 0.55/0.61 %---- -[(u)f(u) = A(B((C)f(u)))]. % 0.55/0.61 cnf(prove_bird_exists,negated_conjecture, % 0.55/0.61 response(U,f(U)) != response(a,response(b,response(c,f(U)))) ). % 0.55/0.61 % 0.55/0.61 %-------------------------------------------------------------------------- % 0.55/0.61 %------------------------------------------- % 0.55/0.61 % Proof found % 0.55/0.61 % SZS status Theorem for theBenchmark % 0.55/0.61 % SZS output start Proof % 0.55/0.61 %ClaNum:10(EqnAxiom:8) % 0.55/0.61 %VarNum:9(SingletonVarNum:4) % 0.55/0.61 %MaxLitNum:1 % 0.55/0.61 %MaxfuncDepth:4 % 0.55/0.61 %SharedTerms:3 % 0.55/0.61 %goalClause: 10 % 0.55/0.61 %singleGoalClaCount:1 % 0.55/0.61 [10]~E(f5(x101,f6(x101)),f5(a2,f5(a3,f5(a4,f6(x101))))) % 0.55/0.61 [9]E(f5(f1(x91,x92),x93),f5(x91,f5(x92,x93))) % 0.55/0.61 %EqnAxiom % 0.55/0.61 [1]E(x11,x11) % 0.55/0.61 [2]E(x22,x21)+~E(x21,x22) % 0.55/0.61 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.55/0.61 [4]~E(x41,x42)+E(f1(x41,x43),f1(x42,x43)) % 0.55/0.61 [5]~E(x51,x52)+E(f1(x53,x51),f1(x53,x52)) % 0.55/0.61 [6]~E(x61,x62)+E(f5(x61,x63),f5(x62,x63)) % 0.55/0.61 [7]~E(x71,x72)+E(f5(x73,x71),f5(x73,x72)) % 0.55/0.61 [8]~E(x81,x82)+E(f6(x81),f6(x82)) % 0.55/0.61 % 0.55/0.61 %------------------------------------------- % 0.55/0.61 cnf(13,plain, % 0.55/0.61 (~E(f5(x131,f6(x131)),f5(a2,f5(a3,f5(a4,f6(x131)))))), % 0.55/0.61 inference(rename_variables,[],[10])). % 0.55/0.61 cnf(14,plain, % 0.55/0.61 (~E(f5(x141,f6(x141)),f5(f1(a2,a3),f5(a4,f6(x141))))), % 0.55/0.61 inference(scs_inference,[],[10,13,9,2,7,3])). % 0.55/0.61 cnf(16,plain, % 0.55/0.61 ($false), % 0.55/0.61 inference(scs_inference,[],[14,9]), % 0.55/0.61 ['proof']). % 0.55/0.61 % SZS output end Proof % 0.55/0.61 % Total time :0.000000s %------------------------------------------------------------------------------