%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : COL056-1 : 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 : n007.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 04:44:57 EDT 2024 % Result : Unsatisfiable 58.63s 58.71s % Output : CNFRefutation 58.63s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : COL056-1 : TPTP v8.2.0. Released v1.0.0. % 0.03/0.11 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.11/0.33 % Computer : n007.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 300 % 0.11/0.33 % DateTime : Tue Jun 18 16:09:54 EDT 2024 % 0.11/0.33 % CPUTime : % 0.48/0.62 start to proof:theBenchmark % 58.63/58.69 %------------------------------------------- % 58.63/58.69 % File :CSE---1.7 % 58.63/58.69 % Problem :theBenchmark % 58.63/58.69 % Transform :cnf % 58.63/58.69 % Format :tptp:raw % 58.63/58.69 % Command :java -jar mcs_scs.jar %d %s % 58.63/58.69 % 58.63/58.69 % Result :Theorem 58.000000s % 58.63/58.69 % Output :CNFRefutation 58.000000s % 58.63/58.69 %------------------------------------------- % 58.63/58.71 %-------------------------------------------------------------------------- % 58.63/58.71 % File : COL056-1 : TPTP v8.2.0. Released v1.0.0. % 58.63/58.71 % Domain : Combinatory Logic % 58.63/58.71 % Problem : Normal Birds % 58.63/58.71 % Version : Especial. % 58.63/58.71 % English : For all birds x and y, there exists a bird z that composes % 58.63/58.71 % x with y for all birds w. Prove that if there exists a happy % 58.63/58.71 % bird then there exists a normal bird. % 58.63/58.71 % 58.63/58.71 % Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi % 58.63/58.71 % Source : [ANL] % 58.63/58.71 % Names : bird8.ver1.in [ANL] % 58.63/58.71 % 58.63/58.71 % Status : Unsatisfiable % 58.63/58.71 % Rating : 0.09 v8.2.0, 0.08 v8.1.0, 0.00 v7.5.0, 0.04 v7.4.0, 0.09 v7.3.0, 0.05 v7.1.0, 0.06 v7.0.0, 0.05 v6.3.0, 0.06 v6.2.0, 0.07 v6.1.0, 0.06 v6.0.0, 0.05 v5.4.0, 0.07 v5.3.0, 0.08 v5.2.0, 0.07 v4.1.0, 0.09 v4.0.1, 0.07 v4.0.0, 0.08 v3.7.0, 0.11 v3.4.0, 0.12 v3.3.0, 0.07 v3.1.0, 0.00 v2.7.0, 0.09 v2.6.0, 0.17 v2.5.0, 0.00 v2.0.0 % 58.63/58.71 % Syntax : Number of clauses : 4 ( 4 unt; 0 nHn; 3 RR) % 58.63/58.71 % Number of literals : 4 ( 4 equ; 1 neg) % 58.63/58.71 % Maximal clause size : 1 ( 1 avg) % 58.63/58.71 % Maximal term depth : 3 ( 1 avg) % 58.63/58.71 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty) % 58.63/58.71 % Number of functors : 5 ( 5 usr; 3 con; 0-2 aty) % 58.63/58.71 % Number of variables : 5 ( 1 sgn) % 58.63/58.71 % SPC : CNF_UNS_RFO_PEQ_UEQ % 58.63/58.71 % 58.63/58.71 % Comments : % 58.63/58.71 %-------------------------------------------------------------------------- % 58.63/58.71 %----For all birds x and y, there exists a bird z that composes x with % 58.63/58.71 %----y for all birds w. % 58.63/58.71 %---- FAx FAy TEz FAw [response(z,w) = response(x,response(y,w))]. % 58.63/58.71 %---- response(comp(x,y),w) = response(x,response(y,w)). % 58.63/58.71 cnf(composer_exists,axiom, % 58.63/58.71 response(compose(X,Y),W) = response(X,response(Y,W)) ). % 58.63/58.71 % 58.63/58.71 %----Hypothesis: If there exists a happy bird then there exists a normal % 58.63/58.71 %----bird. % 58.63/58.71 %----Finding clause (using xy to replace response(x,y)): % 58.63/58.71 %---- -[ If TEx TEy TEz (xy = z) and (xz = y) % 58.63/58.71 %---- then TEw TEv (wv = v) ]. % 58.63/58.71 %---- -[ FAx FAy FAz -((xy = z) and (xz = y)) | TEw TEv (wv = v) ] % 58.63/58.71 %---- TEx TEy TEz [(xy = z) and (xz = y)] and FAw FAv -(wv = v). % 58.63/58.71 %---- (AB = C) and (AC = B) and -(wv = v). % 58.63/58.71 cnf(a_to_b_responds_c,hypothesis, % 58.63/58.71 response(a,b) = c ). % 58.63/58.71 % 58.63/58.71 cnf(a_to_c_responds_b,hypothesis, % 58.63/58.71 response(a,c) = b ). % 58.63/58.71 % 58.63/58.71 cnf(prove_there_exists_a_happy_bird,negated_conjecture, % 58.63/58.71 response(W,V) != V ). % 58.63/58.71 % 58.63/58.71 %-------------------------------------------------------------------------- % 58.63/58.71 %------------------------------------------- % 58.63/58.71 % Proof found % 58.63/58.71 % SZS status Theorem for theBenchmark % 58.63/58.71 % SZS output start Proof % 58.63/58.72 %ClaNum:11(EqnAxiom:7) % 58.63/58.72 %VarNum:9(SingletonVarNum:5) % 58.63/58.72 %MaxLitNum:1 % 58.63/58.72 %MaxfuncDepth:2 % 58.63/58.72 %SharedTerms:7 % 58.63/58.72 %goalClause: 11 % 58.63/58.72 %singleGoalClaCount:1 % 58.63/58.72 [8]E(f3(a1,a2),a4) % 58.63/58.72 [9]E(f3(a1,a4),a2) % 58.63/58.72 [11]~E(f3(x111,x112),x112) % 58.63/58.72 [10]E(f3(f5(x101,x102),x103),f3(x101,f3(x102,x103))) % 58.63/58.72 %EqnAxiom % 58.63/58.72 [1]E(x11,x11) % 58.63/58.72 [2]E(x22,x21)+~E(x21,x22) % 58.63/58.72 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 58.63/58.72 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43)) % 58.63/58.72 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52)) % 58.63/58.72 [6]~E(x61,x62)+E(f5(x61,x63),f5(x62,x63)) % 58.63/58.72 [7]~E(x71,x72)+E(f5(x73,x71),f5(x73,x72)) % 58.63/58.72 % 58.63/58.72 %------------------------------------------- % 58.63/58.73 cnf(13,plain, % 58.63/58.73 (~E(f3(x131,a4),f3(a1,a2))), % 58.63/58.73 inference(scs_inference,[],[11,10,8,2,3])). % 58.63/58.73 cnf(16,plain, % 58.63/58.73 (E(a2,f3(a1,a4))), % 58.63/58.73 inference(scs_inference,[],[9,2])). % 58.63/58.73 cnf(20,plain, % 58.63/58.73 (E(a4,f3(a1,a2))), % 58.63/58.73 inference(scs_inference,[],[8,2])). % 58.63/58.73 cnf(32,plain, % 58.63/58.73 (~E(f3(x321,f3(x322,a4)),f3(a1,a2))), % 58.63/58.73 inference(scs_inference,[],[8,13,10,4,6,7,5,2,3])). % 58.63/58.73 cnf(38,plain, % 58.63/58.73 (E(f3(x381,a2),f3(x381,f3(a1,a4)))), % 58.63/58.73 inference(scs_inference,[],[16,6,7,4,5])). % 58.63/58.73 cnf(47,plain, % 58.63/58.73 ($false), % 58.63/58.73 inference(scs_inference,[],[32,38,20,7,6,4,5,2]), % 58.63/58.73 ['proof']). % 58.63/58.73 % SZS output end Proof % 58.63/58.73 % Total time :58.000000s %------------------------------------------------------------------------------