%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : COL020-1 : 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 : n011.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 04:44:48 EDT 2024 % Result : Unsatisfiable 58.52s 58.67s % Output : CNFRefutation 58.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : COL020-1 : TPTP v8.2.0. Released v1.0.0. % 0.08/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.34 % Computer : n011.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 15:37:54 EDT 2024 % 0.12/0.34 % CPUTime : % 0.20/0.57 start to proof:theBenchmark % 58.52/58.65 %------------------------------------------- % 58.52/58.65 % File :CSE---1.7 % 58.52/58.65 % Problem :theBenchmark % 58.52/58.65 % Transform :cnf % 58.52/58.65 % Format :tptp:raw % 58.52/58.65 % Command :java -jar mcs_scs.jar %d %s % 58.52/58.65 % 58.52/58.65 % Result :Theorem 58.000000s % 58.52/58.65 % Output :CNFRefutation 58.000000s % 58.52/58.65 %------------------------------------------- % 58.52/58.67 %-------------------------------------------------------------------------- % 58.52/58.67 % File : COL020-1 : TPTP v8.2.0. Released v1.0.0. % 58.52/58.67 % Domain : Combinatory Logic % 58.52/58.67 % Problem : Weak fixed point for B, S, and C % 58.52/58.67 % Version : [WM88] (equality) axioms. % 58.52/58.67 % English : The weak fixed point property holds for the set P consisting % 58.52/58.67 % of the combinators B, S, and C, where ((Sx)y)z = (xz)(yz), % 58.52/58.67 % ((Bx)y)z = x(yz), ((Cx)y)z = (xz)y. % 58.52/58.67 % 58.52/58.67 % Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi % 58.52/58.67 % : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem % 58.52/58.67 % : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq % 58.52/58.67 % : [MW88] McCune & Wos (1988), Some Fixed Point Problems in Comb % 58.52/58.67 % Source : [MW88] % 58.52/58.67 % Names : - [MW88] % 58.52/58.67 % 58.52/58.67 % Status : Unsatisfiable % 58.52/58.67 % Rating : 0.14 v8.2.0, 0.21 v8.1.0, 0.25 v7.5.0, 0.29 v7.4.0, 0.35 v7.3.0, 0.37 v7.1.0, 0.28 v7.0.0, 0.26 v6.4.0, 0.37 v6.3.0, 0.41 v6.2.0, 0.43 v6.1.0, 0.12 v6.0.0, 0.19 v5.5.0, 0.16 v5.4.0, 0.13 v5.3.0, 0.17 v5.2.0, 0.14 v5.1.0, 0.13 v5.0.0, 0.14 v4.1.0, 0.09 v4.0.1, 0.21 v4.0.0, 0.23 v3.7.0, 0.11 v3.4.0, 0.12 v3.3.0, 0.07 v3.1.0, 0.11 v2.7.0, 0.00 v2.6.0, 0.17 v2.5.0, 0.00 v2.4.0, 0.33 v2.3.0, 0.00 v2.0.0 % 58.52/58.67 % Syntax : Number of clauses : 4 ( 4 unt; 0 nHn; 1 RR) % 58.52/58.67 % Number of literals : 4 ( 4 equ; 1 neg) % 58.52/58.67 % Maximal clause size : 1 ( 1 avg) % 58.52/58.67 % Maximal term depth : 4 ( 2 avg) % 58.52/58.67 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty) % 58.52/58.67 % Number of functors : 5 ( 5 usr; 4 con; 0-2 aty) % 58.52/58.67 % Number of variables : 10 ( 0 sgn) % 58.52/58.67 % SPC : CNF_UNS_RFO_PEQ_UEQ % 58.52/58.67 % 58.52/58.67 % Comments : % 58.52/58.67 %-------------------------------------------------------------------------- % 58.52/58.67 cnf(s_definition,axiom, % 58.52/58.67 apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)) ). % 58.52/58.67 % 58.52/58.67 cnf(b_definition,axiom, % 58.52/58.67 apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ). % 58.52/58.67 % 58.52/58.67 cnf(c_definition,axiom, % 58.52/58.67 apply(apply(apply(c,X),Y),Z) = apply(apply(X,Z),Y) ). % 58.52/58.67 % 58.52/58.67 cnf(prove_fixed_point,negated_conjecture, % 58.52/58.67 Y != apply(combinator,Y) ). % 58.52/58.67 % 58.52/58.67 %-------------------------------------------------------------------------- % 58.52/58.67 %------------------------------------------- % 58.52/58.67 % Proof found % 58.52/58.67 % SZS status Theorem for theBenchmark % 58.52/58.67 % SZS output start Proof % 58.52/58.69 %ClaNum:9(EqnAxiom:5) % 58.52/58.69 %VarNum:21(SingletonVarNum:10) % 58.52/58.69 %MaxLitNum:1 % 58.52/58.69 %MaxfuncDepth:3 % 58.52/58.69 %SharedTerms:4 % 58.52/58.69 %goalClause: 9 % 58.52/58.69 %singleGoalClaCount:1 % 58.52/58.69 [9]~E(f2(a5,x91),x91) % 58.52/58.69 [6]E(f2(f2(f2(a1,x61),x62),x63),f2(x61,f2(x62,x63))) % 58.52/58.69 [7]E(f2(f2(f2(a3,x71),x72),x73),f2(f2(x71,x73),x72)) % 58.52/58.69 [8]E(f2(f2(f2(a4,x81),x82),x83),f2(f2(x81,x83),f2(x82,x83))) % 58.52/58.69 %EqnAxiom % 58.52/58.69 [1]E(x11,x11) % 58.52/58.69 [2]E(x22,x21)+~E(x21,x22) % 58.52/58.69 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 58.52/58.69 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43)) % 58.52/58.69 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52)) % 58.52/58.69 % 58.52/58.69 %------------------------------------------- % 58.52/58.70 cnf(11,plain, % 58.52/58.70 (E(f2(x111,f2(x112,x113)),f2(f2(f2(a1,x111),x112),x113))), % 58.52/58.70 inference(scs_inference,[],[6,2])). % 58.52/58.70 cnf(14,plain, % 58.52/58.70 (~E(f2(f2(f2(a1,a5),x141),x142),f2(x141,x142))), % 58.52/58.70 inference(scs_inference,[],[9,11,2,3])). % 58.52/58.70 cnf(17,plain, % 58.52/58.70 (~E(f2(x171,x172),f2(f2(f2(a1,a5),x171),x172))), % 58.52/58.70 inference(scs_inference,[],[14,2])). % 58.52/58.70 cnf(18,plain, % 58.52/58.70 ($false), % 58.52/58.70 inference(scs_inference,[],[8,17,7,3]), % 58.52/58.70 ['proof']). % 58.52/58.70 % SZS output end Proof % 58.52/58.70 % Total time :58.000000s %------------------------------------------------------------------------------