%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : COL054-1 : TPTP v8.2.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % Computer : n018.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 0.56s 0.68s % Output : CNFRefutation 0.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : COL054-1 : TPTP v8.2.0. Released v1.0.0. % 0.12/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n018.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 : Tue Jun 18 16:08:24 EDT 2024 % 0.12/0.33 % CPUTime : % 0.53/0.61 start to proof:theBenchmark % 0.56/0.67 %------------------------------------------- % 0.56/0.67 % File :CSE---1.7 % 0.56/0.67 % Problem :theBenchmark % 0.56/0.67 % Transform :cnf % 0.56/0.67 % Format :tptp:raw % 0.56/0.67 % Command :java -jar mcs_scs.jar %d %s % 0.56/0.67 % 0.56/0.67 % Result :Theorem 0.000000s % 0.56/0.67 % Output :CNFRefutation 0.000000s % 0.56/0.67 %------------------------------------------- % 0.56/0.68 %-------------------------------------------------------------------------- % 0.56/0.68 % File : COL054-1 : TPTP v8.2.0. Released v1.0.0. % 0.56/0.68 % Domain : Combinatory Logic % 0.56/0.68 % Problem : Compatible Birds % 0.56/0.68 % Version : Especial. % 0.56/0.68 % English : There exists a mockingbird. For all birds x and y, there % 0.56/0.68 % exists a bird z that composes x with y for all birds w. Prove % 0.56/0.68 % that any two birds are compatible. % 0.56/0.68 % 0.56/0.68 % Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi % 0.56/0.68 % Source : [ANL] % 0.56/0.68 % Names : bird6.ver1.in [ANL] % 0.56/0.68 % 0.56/0.68 % Status : Unsatisfiable % 0.56/0.68 % Rating : 0.07 v8.2.0, 0.12 v8.1.0, 0.11 v7.5.0, 0.12 v7.4.0, 0.18 v7.3.0, 0.15 v7.2.0, 0.17 v7.1.0, 0.09 v7.0.0, 0.08 v6.4.0, 0.21 v6.3.0, 0.10 v6.2.0, 0.20 v6.1.0, 0.18 v6.0.0, 0.14 v5.5.0, 0.25 v5.4.0, 0.11 v5.3.0, 0.20 v5.2.0, 0.12 v5.1.0, 0.11 v5.0.0, 0.10 v4.1.0, 0.11 v4.0.1, 0.12 v4.0.0, 0.00 v3.3.0, 0.11 v3.2.0, 0.00 v2.0.0 % 0.56/0.68 % Syntax : Number of clauses : 3 ( 2 unt; 0 nHn; 1 RR) % 0.56/0.68 % Number of literals : 4 ( 4 equ; 2 neg) % 0.56/0.68 % Maximal clause size : 2 ( 1 avg) % 0.56/0.68 % Maximal term depth : 3 ( 1 avg) % 0.56/0.68 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty) % 0.56/0.68 % Number of functors : 5 ( 5 usr; 3 con; 0-2 aty) % 0.56/0.68 % Number of variables : 6 ( 0 sgn) % 0.56/0.68 % SPC : CNF_UNS_RFO_PEQ_NUE % 0.56/0.68 % 0.56/0.68 % Comments : % 0.56/0.68 %-------------------------------------------------------------------------- % 0.56/0.68 %---- There exists a mocking bird (Mock). % 0.56/0.68 %---- TEx FAy [response(x,y) = response(y,y)]. % 0.56/0.68 %---- response(Mock,y) = response(y,y). % 0.56/0.68 cnf(mocking_bird_exists,axiom, % 0.56/0.68 response(mocking_bird,Y) = response(Y,Y) ). % 0.56/0.68 % 0.56/0.68 %----For all birds x and y, there exists a bird z that composes x with % 0.56/0.68 %----y for all birds w. % 0.56/0.68 %---- FAx FAy TEz FAw [response(z,w) = response(x,response(y,w))]. % 0.56/0.68 %---- response(comp(x,y),w) = response(x,response(y,w)). % 0.56/0.68 cnf(composer_exists,hypothesis, % 0.56/0.68 response(compose(X,Y),W) = response(X,response(Y,W)) ). % 0.56/0.68 % 0.56/0.68 %----Hypothesis: Any two birds are compatible. % 0.56/0.68 %----Finding clause (using xy to replace response(x,y)): % 0.56/0.68 %---- -FAx FAy TEw TEz [(xw = z) and (yz = w)]. % 0.56/0.68 %---- TEx TEy FAw FAz -[(xw = z) and (yz = w)]. % 0.56/0.68 %---- Letting A = x, B = y, x = w, and y = z, % 0.56/0.68 %---- -(Ax = y) | -(By = x). % 0.56/0.68 cnf(prove_birds_are_compatible,negated_conjecture, % 0.56/0.68 ( response(a,X) != Y % 0.56/0.68 | response(b,Y) != X ) ). % 0.56/0.68 % 0.56/0.68 %-------------------------------------------------------------------------- % 0.56/0.68 %------------------------------------------- % 0.56/0.68 % Proof found % 0.56/0.68 % SZS status Theorem for theBenchmark % 0.56/0.68 % SZS output start Proof % 0.56/0.68 %ClaNum:10(EqnAxiom:7) % 0.56/0.68 %VarNum:13(SingletonVarNum:6) % 0.56/0.68 %MaxLitNum:2 % 0.56/0.68 %MaxfuncDepth:2 % 0.56/0.68 %SharedTerms:3 % 0.56/0.68 %goalClause: 10 % 0.56/0.68 [8]E(f5(a1,x81),f5(x81,x81)) % 0.56/0.68 [9]E(f5(f2(x91,x92),x93),f5(x91,f5(x92,x93))) % 0.56/0.68 [10]~E(f5(a4,x102),x101)+~E(f5(a3,x101),x102) % 0.56/0.68 %EqnAxiom % 0.56/0.68 [1]E(x11,x11) % 0.56/0.68 [2]E(x22,x21)+~E(x21,x22) % 0.56/0.68 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.56/0.68 [4]~E(x41,x42)+E(f5(x41,x43),f5(x42,x43)) % 0.56/0.68 [5]~E(x51,x52)+E(f5(x53,x51),f5(x53,x52)) % 0.56/0.68 [6]~E(x61,x62)+E(f2(x61,x63),f2(x62,x63)) % 0.56/0.68 [7]~E(x71,x72)+E(f2(x73,x71),f2(x73,x72)) % 0.56/0.68 % 0.56/0.68 %------------------------------------------- % 0.56/0.68 cnf(11,plain, % 0.56/0.68 (E(f5(x111,x111),f5(a1,x111))), % 0.56/0.68 inference(scs_inference,[],[8,2])). % 0.56/0.68 cnf(16,plain, % 0.56/0.68 (E(f5(x161,f5(x162,x163)),f5(f2(x161,x162),x163))), % 0.56/0.69 inference(scs_inference,[],[9,2])). % 0.56/0.69 cnf(17,plain, % 0.56/0.69 (~E(f5(a4,f5(f2(a3,x171),x172)),f5(x171,x172))), % 0.56/0.69 inference(scs_inference,[],[9,2,10])). % 0.56/0.69 cnf(23,plain, % 0.56/0.69 (~E(f5(a4,f5(f2(a3,x231),x232)),f5(x231,x232))), % 0.56/0.69 inference(rename_variables,[],[17])). % 0.56/0.69 cnf(24,plain, % 0.56/0.69 ($false), % 0.56/0.69 inference(scs_inference,[],[17,23,16,11,5,3]), % 0.56/0.69 ['proof']). % 0.56/0.69 % SZS output end Proof % 0.56/0.69 % Total time :0.000000s %------------------------------------------------------------------------------