%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : COL052-2 : 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 : n010.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 9.42s 9.50s % Output : CNFRefutation 9.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : COL052-2 : TPTP v8.2.0. Released v1.0.0. % 0.03/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.14/0.34 % Computer : n010.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Tue Jun 18 16:28:39 EDT 2024 % 0.14/0.34 % CPUTime : % 0.44/0.63 start to proof:theBenchmark % 9.39/9.49 %------------------------------------------- % 9.39/9.49 % File :CSE---1.7 % 9.39/9.49 % Problem :theBenchmark % 9.39/9.49 % Transform :cnf % 9.39/9.49 % Format :tptp:raw % 9.39/9.49 % Command :java -jar mcs_scs.jar %d %s % 9.39/9.49 % 9.39/9.49 % Result :Theorem 8.800000s % 9.42/9.49 % Output :CNFRefutation 8.800000s % 9.42/9.49 %------------------------------------------- % 9.42/9.49 %-------------------------------------------------------------------------- % 9.42/9.49 % File : COL052-2 : TPTP v8.2.0. Released v1.0.0. % 9.42/9.49 % Domain : Combinatory Logic % 9.42/9.49 % Problem : A Question on Agreeable Birds % 9.42/9.49 % Version : Especial. % 9.42/9.49 % Theorem formulation : Explicit definition of agreeable. % 9.42/9.49 % English : For all birds x and y, there exists a bird z that composes % 9.42/9.49 % x with y for all birds w. Prove that if C is agreeable then % 9.42/9.49 % A is agreeable. % 9.42/9.49 % 9.42/9.49 % Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi % 9.42/9.49 % Source : [ANL] % 9.42/9.49 % Names : bird4.ver2.in [ANL] % 9.42/9.49 % 9.42/9.49 % Status : Unsatisfiable % 9.42/9.49 % Rating : 0.12 v8.2.0, 0.08 v8.1.0, 0.11 v7.5.0, 0.10 v7.4.0, 0.22 v7.2.0, 0.25 v7.1.0, 0.29 v6.3.0, 0.00 v6.0.0, 0.11 v5.5.0, 0.12 v5.4.0, 0.13 v5.3.0, 0.33 v5.2.0, 0.12 v5.1.0, 0.14 v5.0.0, 0.00 v4.1.0, 0.11 v4.0.1, 0.00 v3.3.0, 0.14 v3.2.0, 0.00 v2.4.0, 0.00 v2.0.0 % 9.42/9.49 % Syntax : Number of clauses : 6 ( 4 unt; 0 nHn; 4 RR) % 9.42/9.49 % Number of literals : 8 ( 4 equ; 3 neg) % 9.42/9.49 % Maximal clause size : 2 ( 1 avg) % 9.42/9.49 % Maximal term depth : 3 ( 2 avg) % 9.42/9.49 % Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty) % 9.42/9.49 % Number of functors : 7 ( 7 usr; 3 con; 0-2 aty) % 9.42/9.49 % Number of variables : 7 ( 0 sgn) % 9.42/9.49 % SPC : CNF_UNS_RFO_SEQ_HRN % 9.42/9.49 % 9.42/9.49 % Comments : % 9.42/9.49 %-------------------------------------------------------------------------- % 9.42/9.49 %----For all birds x and y, there exists a bird z that composes x with % 9.42/9.49 %----y for all birds w. % 9.42/9.49 %---- FAx FAy TEz FAw [response(z,w) = response(x,response(y,w))]. % 9.42/9.49 %---- response(comp(x,y),w) = response(x,response(y,w)). % 9.42/9.49 cnf(composer_exists,axiom, % 9.42/9.49 response(compose(X,Y),W) = response(X,response(Y,W)) ). % 9.42/9.49 % 9.42/9.49 %----Definition of agreeable: A bird x is agreeable if and only if for all % 9.42/9.49 %----birds y there exists a bird z such that xz = yz. % 9.42/9.49 %---- 1) If agreeable(x) then FAy TEz [response(x,z) = % 9.42/9.49 %---- response(y,z)] and % 9.42/9.49 %---- 2) if TEx FAy TEz [response(x,z) = response(y,z)] then % 9.42/9.49 %---- agreeable(x). % 9.42/9.49 %---- 1) -agreeable(x) | response(x,common_bird(y)) = % 9.42/9.49 %---- response(y,common_bird(y)). % 9.42/9.49 %---- 2) FAx TEy FAz -[response(x,z) = response(y,z)] | % 9.42/9.49 %---- agreeable(x). % 9.42/9.49 %---- -[response(x,z) = response(compatible(x),z)] | % 9.42/9.49 %---- agreeable(x). % 9.42/9.49 cnf(agreeable1,axiom, % 9.42/9.49 ( ~ agreeable(X) % 9.42/9.49 | response(X,common_bird(Y)) = response(Y,common_bird(Y)) ) ). % 9.42/9.49 % 9.42/9.49 cnf(agreeable2,axiom, % 9.42/9.49 ( response(X,Z) != response(compatible(X),Z) % 9.42/9.50 | agreeable(X) ) ). % 9.42/9.50 % 9.42/9.50 %----Hypothesis: If C is agreeable then A is agreeable. % 9.42/9.50 %---- - [ If agreeable(C) then agreeable(A) ]. % 9.42/9.50 %---- - [ -agreeable(C) | agreeable(A) ]. % 9.42/9.50 %---- agreeable(C) and -agreeable(A). % 9.42/9.50 cnf(c_is_agreeable,hypothesis, % 9.42/9.50 agreeable(c) ). % 9.42/9.50 % 9.42/9.50 cnf(prove_a_is_agreeable,negated_conjecture, % 9.42/9.50 ~ agreeable(a) ). % 9.42/9.50 % 9.42/9.50 %----C composes A with B. WHY IS THIS HERE?? % 9.42/9.50 cnf(c_composes_a_with_b,hypothesis, % 9.42/9.50 c = compose(a,b) ). % 9.42/9.50 % 9.42/9.50 %-------------------------------------------------------------------------- % 9.42/9.50 %------------------------------------------- % 9.42/9.50 % Proof found % 9.42/9.50 % SZS status Theorem for theBenchmark % 9.42/9.50 % SZS output start Proof % 9.42/9.50 %ClaNum:16(EqnAxiom:10) % 9.42/9.50 %VarNum:16(SingletonVarNum:7) % 9.42/9.50 %MaxLitNum:2 % 9.42/9.50 %MaxfuncDepth:2 % 9.42/9.50 %SharedTerms:7 % 9.42/9.50 %goalClause: 14 % 9.42/9.50 %singleGoalClaCount:1 % 9.42/9.50 [11]P1(a1) % 9.42/9.50 [14]~P1(a2) % 9.42/9.50 [12]E(f4(a2,a3),a1) % 9.42/9.50 [13]E(f7(f4(x131,x132),x133),f7(x131,f7(x132,x133))) % 9.42/9.50 [15]~P1(x151)+E(f7(x151,f5(x152)),f7(x152,f5(x152))) % 9.42/9.50 [16]P1(x161)+~E(f7(f6(x161),x162),f7(x161,x162)) % 9.42/9.50 %EqnAxiom % 9.42/9.50 [1]E(x11,x11) % 9.42/9.50 [2]E(x22,x21)+~E(x21,x22) % 9.42/9.50 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 9.42/9.50 [4]~E(x41,x42)+E(f4(x41,x43),f4(x42,x43)) % 9.42/9.50 [5]~E(x51,x52)+E(f4(x53,x51),f4(x53,x52)) % 9.42/9.50 [6]~E(x61,x62)+E(f7(x61,x63),f7(x62,x63)) % 9.42/9.50 [7]~E(x71,x72)+E(f7(x73,x71),f7(x73,x72)) % 9.42/9.50 [8]~E(x81,x82)+E(f6(x81),f6(x82)) % 9.42/9.50 [9]~E(x91,x92)+E(f5(x91),f5(x92)) % 9.42/9.50 [10]~P1(x101)+P1(x102)+~E(x101,x102) % 9.42/9.50 % 9.42/9.50 %------------------------------------------- % 9.42/9.50 cnf(17,plain, % 9.42/9.50 (E(f7(x171,f7(x172,x173)),f7(f4(x171,x172),x173))), % 9.42/9.50 inference(scs_inference,[],[13,2])). % 9.42/9.50 cnf(19,plain, % 9.42/9.50 (E(x191,a1)+~E(x191,f4(a2,a3))), % 9.42/9.50 inference(scs_inference,[],[13,12,2,10,3])). % 9.42/9.50 cnf(71,plain, % 9.42/9.50 (~E(f7(a2,x711),f7(f6(a2),x711))), % 9.42/9.50 inference(scs_inference,[],[14,2,16])). % 9.42/9.50 cnf(136,plain, % 9.42/9.50 (~E(f7(f6(a2),f7(x1361,x1362)),f7(f4(a2,x1361),x1362))), % 9.42/9.50 inference(scs_inference,[],[71,13,2,3])). % 9.42/9.50 cnf(308,plain, % 9.42/9.50 (~E(x3081,a2)+E(f4(x3081,a3),a1)), % 9.42/9.50 inference(scs_inference,[],[19,4])). % 9.42/9.50 cnf(551,plain, % 9.42/9.50 (E(a1,f4(x5511,a3))+~E(x5511,a2)), % 9.42/9.50 inference(scs_inference,[],[308,2])). % 9.42/9.50 cnf(774,plain, % 9.42/9.50 (P1(f4(x7741,a3))+~E(x7741,a2)), % 9.42/9.50 inference(scs_inference,[],[11,551,10])). % 9.42/9.50 cnf(776,plain, % 9.42/9.50 (~E(x7761,a2)+E(f7(f4(x7761,a3),f5(x7762)),f7(x7762,f5(x7762)))), % 9.42/9.50 inference(scs_inference,[],[774,15])). % 9.42/9.50 cnf(777,plain, % 9.42/9.50 (E(f7(f4(a2,a3),f5(x7771)),f7(x7771,f5(x7771)))), % 9.42/9.50 inference(equality_inference,[],[776])). % 9.42/9.50 cnf(779,plain, % 9.42/9.50 ($false), % 9.42/9.50 inference(scs_inference,[],[17,777,136,2,3]), % 9.42/9.50 ['proof']). % 9.42/9.50 % SZS output end Proof % 9.42/9.50 % Total time :8.800000s %------------------------------------------------------------------------------