%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : COL051-1 : 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 : n002.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 0.63s % Output : CNFRefutation 0.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : COL051-1 : TPTP v8.2.0. Released v1.0.0. % 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.34 % Computer : n002.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Tue Jun 18 16:06:23 EDT 2024 % 0.12/0.35 % CPUTime : % 0.53/0.59 start to proof:theBenchmark % 0.56/0.63 %------------------------------------------- % 0.56/0.63 % File :CSE---1.7 % 0.56/0.63 % Problem :theBenchmark % 0.56/0.63 % Transform :cnf % 0.56/0.63 % Format :tptp:raw % 0.56/0.63 % Command :java -jar mcs_scs.jar %d %s % 0.56/0.63 % 0.56/0.63 % Result :Theorem 0.010000s % 0.56/0.63 % Output :CNFRefutation 0.010000s % 0.56/0.63 %------------------------------------------- % 0.56/0.63 %-------------------------------------------------------------------------- % 0.56/0.63 % File : COL051-1 : TPTP v8.2.0. Released v1.0.0. % 0.56/0.63 % Domain : Combinatory Logic % 0.56/0.63 % Problem : Egocentric mocking bird? % 0.56/0.63 % Version : Especial. % 0.56/0.63 % English : There exists a mocking bird. For all birds x and y, there % 0.56/0.63 % exists a bird z that composes x with y for all birds w. Prove % 0.56/0.63 % that there exists a bird x that is fond of itself. % 0.56/0.63 % 0.56/0.63 % Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi % 0.56/0.63 % Source : [ANL] % 0.56/0.63 % Names : bird2.ver1.in [ANL] % 0.56/0.63 % 0.56/0.63 % Status : Unsatisfiable % 0.56/0.63 % Rating : 0.09 v8.2.0, 0.08 v8.1.0, 0.10 v7.5.0, 0.08 v7.4.0, 0.13 v7.3.0, 0.11 v7.1.0, 0.06 v7.0.0, 0.00 v6.0.0, 0.10 v5.5.0, 0.05 v5.4.0, 0.00 v5.1.0, 0.07 v5.0.0, 0.00 v2.0.0 % 0.56/0.63 % Syntax : Number of clauses : 3 ( 3 unt; 0 nHn; 1 RR) % 0.56/0.63 % Number of literals : 3 ( 3 equ; 1 neg) % 0.56/0.63 % Maximal clause size : 1 ( 1 avg) % 0.56/0.63 % Maximal term depth : 3 ( 1 avg) % 0.56/0.63 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty) % 0.56/0.63 % Number of functors : 3 ( 3 usr; 1 con; 0-2 aty) % 0.56/0.63 % Number of variables : 5 ( 0 sgn) % 0.56/0.63 % SPC : CNF_UNS_RFO_PEQ_UEQ % 0.56/0.63 % 0.56/0.63 % Comments : % 0.56/0.63 %-------------------------------------------------------------------------- % 0.56/0.63 %---- There exists a mocking bird (Mock). % 0.56/0.63 %---- TEx FAy [response(x,y) = response(y,y)]. % 0.56/0.63 %---- response(Mock,y) = response(y,y). % 0.56/0.63 cnf(mocking_bird_exists,axiom, % 0.56/0.63 response(mocking_bird,Y) = response(Y,Y) ). % 0.56/0.63 % 0.56/0.63 %---- For all birds x and y, there exists a bird z that composes % 0.56/0.63 %---- x with y for all birds w. % 0.56/0.63 %---- FAx FAy TEz FAw [response(z,w) = response(x,response(y,w))] % 0.56/0.63 %---- response(comp(x,y),w) = response(x,response(y,w)). % 0.56/0.63 cnf(composer_exists,hypothesis, % 0.56/0.63 response(compose(X,Y),W) = response(X,response(Y,W)) ). % 0.56/0.63 % 0.56/0.63 %---- Hypothesis: There exists a bird x that is fond of itself. % 0.56/0.63 %---- -TEx [response(x,x) = x]. % 0.56/0.63 %---- FAx -[response(x,x) = x]. % 0.56/0.63 cnf(prove_the_bird_exists,negated_conjecture, % 0.56/0.63 response(X,X) != X ). % 0.56/0.63 % 0.56/0.63 %-------------------------------------------------------------------------- % 0.56/0.63 %------------------------------------------- % 0.56/0.63 % Proof found % 0.56/0.63 % SZS status Theorem for theBenchmark % 0.56/0.63 % SZS output start Proof % 0.56/0.63 %ClaNum:10(EqnAxiom:7) % 0.56/0.63 %VarNum:12(SingletonVarNum:5) % 0.56/0.63 %MaxLitNum:1 % 0.56/0.64 %MaxfuncDepth:2 % 0.56/0.64 %SharedTerms:1 % 0.56/0.64 %goalClause: 10 % 0.56/0.64 %singleGoalClaCount:1 % 0.56/0.64 [8]E(f3(a1,x81),f3(x81,x81)) % 0.56/0.64 [10]~E(f3(x101,x101),x101) % 0.56/0.64 [9]E(f3(f2(x91,x92),x93),f3(x91,f3(x92,x93))) % 0.56/0.64 %EqnAxiom % 0.56/0.64 [1]E(x11,x11) % 0.56/0.64 [2]E(x22,x21)+~E(x21,x22) % 0.56/0.64 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.56/0.64 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43)) % 0.56/0.64 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52)) % 0.56/0.64 [6]~E(x61,x62)+E(f2(x61,x63),f2(x62,x63)) % 0.56/0.64 [7]~E(x71,x72)+E(f2(x73,x71),f2(x73,x72)) % 0.56/0.64 % 0.56/0.64 %------------------------------------------- % 0.56/0.64 cnf(11,plain, % 0.56/0.64 (E(f3(x111,x111),f3(a1,x111))), % 0.56/0.64 inference(scs_inference,[],[8,2])). % 0.56/0.64 cnf(14,plain, % 0.56/0.64 (E(f3(x141,f3(x142,x143)),f3(f2(x141,x142),x143))), % 0.56/0.64 inference(scs_inference,[],[9,2])). % 0.56/0.64 cnf(15,plain, % 0.56/0.64 (~E(f3(f3(a1,x151),f3(a1,x151)),f3(x151,x151))), % 0.56/0.64 inference(scs_inference,[],[10,11,9,2,3])). % 0.56/0.64 cnf(17,plain, % 0.56/0.64 ($false), % 0.56/0.64 inference(scs_inference,[],[15,14,11,3]), % 0.56/0.64 ['proof']). % 0.56/0.64 % SZS output end Proof % 0.56/0.64 % Total time :0.010000s %------------------------------------------------------------------------------