%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : COL019-1 : 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 : n022.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 0.55s 0.70s % Output : CNFRefutation 0.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : COL019-1 : TPTP v8.2.0. Released v1.0.0. % 0.07/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.34 % Computer : n022.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 16:23:39 EDT 2024 % 0.12/0.34 % CPUTime : % 0.47/0.58 start to proof:theBenchmark % 0.55/0.69 %------------------------------------------- % 0.55/0.69 % File :CSE---1.7 % 0.55/0.69 % Problem :theBenchmark % 0.55/0.69 % Transform :cnf % 0.55/0.69 % Format :tptp:raw % 0.55/0.69 % Command :java -jar mcs_scs.jar %d %s % 0.55/0.69 % 0.55/0.69 % Result :Theorem 0.070000s % 0.55/0.69 % Output :CNFRefutation 0.070000s % 0.55/0.69 %------------------------------------------- % 0.55/0.69 %-------------------------------------------------------------------------- % 0.55/0.69 % File : COL019-1 : TPTP v8.2.0. Released v1.0.0. % 0.55/0.69 % Domain : Combinatory Logic % 0.55/0.69 % Problem : Weak fixed point for B, S, and T % 0.55/0.69 % Version : [WM88] (equality) axioms. % 0.55/0.69 % English : The weak fixed point property holds for the set P consisting % 0.55/0.69 % of the combinators B, S, and T, where ((Sx)y)z = (xz)(yz), % 0.55/0.69 % ((Bx)y)z = x(yz), (Tx)y = yx. % 0.55/0.69 % 0.55/0.69 % Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi % 0.55/0.69 % : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem % 0.55/0.69 % : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq % 0.55/0.69 % : [MW88] McCune & Wos (1988), Some Fixed Point Problems in Comb % 0.55/0.69 % Source : [MW88] % 0.55/0.69 % Names : - [MW88] % 0.55/0.69 % 0.55/0.69 % Status : Unsatisfiable % 0.55/0.69 % Rating : 0.14 v8.2.0, 0.21 v8.1.0, 0.25 v7.5.0, 0.21 v7.4.0, 0.30 v7.3.0, 0.21 v7.1.0, 0.11 v6.4.0, 0.16 v6.3.0, 0.18 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 0.10 v5.5.0, 0.05 v5.4.0, 0.00 v5.1.0, 0.07 v4.1.0, 0.09 v4.0.1, 0.07 v4.0.0, 0.15 v3.7.0, 0.11 v3.4.0, 0.12 v3.3.0, 0.00 v2.1.0, 0.13 v2.0.0 % 0.55/0.69 % Syntax : Number of clauses : 4 ( 4 unt; 0 nHn; 1 RR) % 0.55/0.70 % Number of literals : 4 ( 4 equ; 1 neg) % 0.55/0.70 % Maximal clause size : 1 ( 1 avg) % 0.55/0.70 % Maximal term depth : 4 ( 2 avg) % 0.55/0.70 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty) % 0.55/0.70 % Number of functors : 5 ( 5 usr; 4 con; 0-2 aty) % 0.55/0.70 % Number of variables : 9 ( 0 sgn) % 0.55/0.70 % SPC : CNF_UNS_RFO_PEQ_UEQ % 0.55/0.70 % 0.55/0.70 % Comments : % 0.55/0.70 %-------------------------------------------------------------------------- % 0.55/0.70 cnf(s_definition,axiom, % 0.55/0.70 apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)) ). % 0.55/0.70 % 0.55/0.70 cnf(b_definition,axiom, % 0.55/0.70 apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ). % 0.55/0.70 % 0.55/0.70 cnf(t_definition,axiom, % 0.55/0.70 apply(apply(t,X),Y) = apply(Y,X) ). % 0.55/0.70 % 0.55/0.70 cnf(prove_fixed_point,negated_conjecture, % 0.55/0.70 Y != apply(combinator,Y) ). % 0.55/0.70 % 0.55/0.70 %-------------------------------------------------------------------------- % 0.55/0.70 %------------------------------------------- % 0.55/0.70 % Proof found % 0.55/0.70 % SZS status Theorem for theBenchmark % 0.55/0.70 % SZS output start Proof % 0.55/0.70 %ClaNum:9(EqnAxiom:5) % 0.55/0.70 %VarNum:19(SingletonVarNum:9) % 0.55/0.70 %MaxLitNum:1 % 0.55/0.70 %MaxfuncDepth:3 % 0.55/0.70 %SharedTerms:4 % 0.55/0.70 %goalClause: 9 % 0.55/0.70 %singleGoalClaCount:1 % 0.55/0.70 [9]~E(f2(a5,x91),x91) % 0.55/0.70 [6]E(f2(f2(a1,x61),x62),f2(x62,x61)) % 0.55/0.70 [7]E(f2(f2(f2(a3,x71),x72),x73),f2(x71,f2(x72,x73))) % 0.55/0.70 [8]E(f2(f2(f2(a4,x81),x82),x83),f2(f2(x81,x83),f2(x82,x83))) % 0.55/0.70 %EqnAxiom % 0.55/0.70 [1]E(x11,x11) % 0.55/0.70 [2]E(x22,x21)+~E(x21,x22) % 0.55/0.70 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.55/0.70 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43)) % 0.55/0.70 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52)) % 0.55/0.70 % 0.55/0.70 %------------------------------------------- % 0.55/0.70 cnf(10,plain, % 0.55/0.70 (E(f2(x101,x102),f2(f2(a1,x102),x101))), % 0.55/0.70 inference(scs_inference,[],[6,2])). % 0.55/0.70 cnf(13,plain, % 0.55/0.70 (E(f2(f2(x131,x132),f2(x133,x132)),f2(f2(f2(a4,x131),x133),x132))), % 0.55/0.70 inference(scs_inference,[],[8,2])). % 0.55/0.70 cnf(14,plain, % 0.55/0.70 (~E(f2(a5,f2(f2(a1,x141),x142)),f2(x142,x141))), % 0.55/0.70 inference(scs_inference,[],[9,10,8,2,3])). % 0.55/0.70 cnf(18,plain, % 0.55/0.70 (E(f2(x181,f2(x182,x183)),f2(f2(f2(a3,x181),x182),x183))), % 0.55/0.70 inference(scs_inference,[],[7,2])). % 0.55/0.70 cnf(22,plain, % 0.55/0.70 (~E(f2(a5,f2(f2(a1,x221),f2(a1,x222))),f2(x221,x222))), % 0.55/0.70 inference(scs_inference,[],[14,10,3])). % 0.55/0.70 cnf(41,plain, % 0.55/0.70 ($false), % 0.55/0.70 inference(scs_inference,[],[22,13,18,3]), % 0.55/0.70 ['proof']). % 0.55/0.70 % SZS output end Proof % 0.55/0.70 % Total time :0.070000s %------------------------------------------------------------------------------