%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : COL018-1 : 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 : n023.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 0.54s 0.62s % Output : CNFRefutation 0.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.13 % Problem : COL018-1 : TPTP v8.2.0. Released v1.0.0. % 0.13/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.13/0.34 % Computer : n023.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Tue Jun 18 15:45:09 EDT 2024 % 0.13/0.34 % CPUTime : % 0.52/0.58 start to proof:theBenchmark % 0.54/0.61 %------------------------------------------- % 0.54/0.61 % File :CSE---1.7 % 0.54/0.61 % Problem :theBenchmark % 0.54/0.61 % Transform :cnf % 0.54/0.61 % Format :tptp:raw % 0.54/0.61 % Command :java -jar mcs_scs.jar %d %s % 0.54/0.61 % 0.54/0.61 % Result :Theorem 0.000000s % 0.54/0.61 % Output :CNFRefutation 0.000000s % 0.54/0.61 %------------------------------------------- % 0.54/0.62 %-------------------------------------------------------------------------- % 0.54/0.62 % File : COL018-1 : TPTP v8.2.0. Released v1.0.0. % 0.54/0.62 % Domain : Combinatory Logic % 0.54/0.62 % Problem : Weak fixed point for W, Q, and L % 0.54/0.62 % Version : [WM88] (equality) axioms. % 0.54/0.62 % English : The weak fixed point property holds for the set P consisting % 0.54/0.62 % of the combinators W, Q, and L, where (Lx)y = x(yy), (Wx)y % 0.54/0.62 % = (xy)y, ((Qx)y)z = y(xz). % 0.54/0.62 % 0.54/0.62 % Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi % 0.54/0.62 % : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem % 0.54/0.62 % : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq % 0.54/0.62 % : [MW88] McCune & Wos (1988), Some Fixed Point Problems in Comb % 0.54/0.62 % Source : [MW88] % 0.54/0.62 % Names : - [MW88] % 0.54/0.62 % 0.54/0.62 % Status : Unsatisfiable % 0.54/0.62 % Rating : 0.09 v8.2.0, 0.08 v8.1.0, 0.15 v7.5.0, 0.12 v7.4.0, 0.17 v7.3.0, 0.16 v7.1.0, 0.06 v7.0.0, 0.00 v6.4.0, 0.11 v6.3.0, 0.12 v6.2.0, 0.07 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 v5.0.0, 0.00 v2.0.0 % 0.54/0.62 % Syntax : Number of clauses : 4 ( 4 unt; 0 nHn; 1 RR) % 0.54/0.62 % Number of literals : 4 ( 4 equ; 1 neg) % 0.54/0.62 % Maximal clause size : 1 ( 1 avg) % 0.54/0.62 % Maximal term depth : 4 ( 2 avg) % 0.54/0.62 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty) % 0.54/0.62 % Number of functors : 5 ( 5 usr; 4 con; 0-2 aty) % 0.54/0.62 % Number of variables : 8 ( 0 sgn) % 0.54/0.62 % SPC : CNF_UNS_RFO_PEQ_UEQ % 0.54/0.62 % 0.54/0.62 % Comments : % 0.54/0.62 %-------------------------------------------------------------------------- % 0.54/0.62 cnf(l_definition,axiom, % 0.54/0.62 apply(apply(l,X),Y) = apply(X,apply(Y,Y)) ). % 0.54/0.62 % 0.54/0.62 cnf(w_definition,axiom, % 0.54/0.62 apply(apply(w,X),Y) = apply(apply(X,Y),Y) ). % 0.54/0.62 % 0.54/0.62 cnf(q_definition,axiom, % 0.54/0.62 apply(apply(apply(q,X),Y),Z) = apply(Y,apply(X,Z)) ). % 0.54/0.62 % 0.54/0.62 cnf(prove_fixed_point,negated_conjecture, % 0.54/0.62 Y != apply(combinator,Y) ). % 0.54/0.62 % 0.54/0.62 %-------------------------------------------------------------------------- % 0.54/0.62 %------------------------------------------- % 0.54/0.62 % Proof found % 0.54/0.62 % SZS status Theorem for theBenchmark % 0.54/0.62 % SZS output start Proof % 0.54/0.62 %ClaNum:9(EqnAxiom:5) % 0.54/0.62 %VarNum:18(SingletonVarNum:8) % 0.54/0.62 %MaxLitNum:1 % 0.54/0.62 %MaxfuncDepth:3 % 0.54/0.62 %SharedTerms:4 % 0.54/0.62 %goalClause: 9 % 0.54/0.62 %singleGoalClaCount:1 % 0.54/0.62 [9]~E(f2(a3,x91),x91) % 0.54/0.62 [6]E(f2(f2(a1,x61),x62),f2(x61,f2(x62,x62))) % 0.54/0.62 [7]E(f2(f2(a4,x71),x72),f2(f2(x71,x72),x72)) % 0.54/0.62 [8]E(f2(f2(f2(a5,x81),x82),x83),f2(x82,f2(x81,x83))) % 0.54/0.62 %EqnAxiom % 0.54/0.62 [1]E(x11,x11) % 0.54/0.62 [2]E(x22,x21)+~E(x21,x22) % 0.54/0.62 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.54/0.62 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43)) % 0.54/0.62 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52)) % 0.54/0.62 % 0.54/0.62 %------------------------------------------- % 0.54/0.62 cnf(10,plain, % 0.54/0.62 ($false), % 0.54/0.62 inference(scs_inference,[],[9,6,2]), % 0.54/0.62 ['proof']). % 0.54/0.62 % SZS output end Proof % 0.54/0.62 % Total time :0.000000s %------------------------------------------------------------------------------