%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : COL027-1 : 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 : n008.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 04:44:50 EDT 2024 % Result : Unsatisfiable 58.36s 58.51s % Output : CNFRefutation 58.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : COL027-1 : TPTP v8.2.0. Released v1.0.0. % 0.12/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.34 % Computer : n008.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 16:32:54 EDT 2024 % 0.12/0.34 % CPUTime : % 0.55/0.60 start to proof:theBenchmark % 58.36/58.49 %------------------------------------------- % 58.36/58.49 % File :CSE---1.7 % 58.36/58.49 % Problem :theBenchmark % 58.36/58.49 % Transform :cnf % 58.36/58.49 % Format :tptp:raw % 58.36/58.49 % Command :java -jar mcs_scs.jar %d %s % 58.36/58.49 % 58.36/58.49 % Result :Theorem 57.810000s % 58.36/58.49 % Output :CNFRefutation 57.810000s % 58.36/58.49 %------------------------------------------- % 58.36/58.50 %-------------------------------------------------------------------------- % 58.36/58.50 % File : COL027-1 : TPTP v8.2.0. Released v1.0.0. % 58.36/58.50 % Domain : Combinatory Logic % 58.36/58.50 % Problem : Weak fixed point for B and H % 58.36/58.50 % Version : [WM88] (equality) axioms. % 58.36/58.50 % English : The weak fixed point property holds for the set P consisting % 58.36/58.50 % of the combinators B and H, where ((Bx)y)z = x(yz), ((Hx)y)z % 58.36/58.50 % = ((xy)z)y. % 58.36/58.50 % 58.36/58.50 % Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi % 58.36/58.50 % : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem % 58.36/58.50 % : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq % 58.36/58.50 % : [MW88] McCune & Wos (1988), Some Fixed Point Problems in Comb % 58.36/58.50 % Source : [MW88] % 58.36/58.50 % Names : - [MW88] % 58.36/58.50 % 58.36/58.50 % Status : Unsatisfiable % 58.36/58.51 % Rating : 0.18 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, 0.12 v6.2.0, 0.07 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.05 v5.4.0, 0.00 v5.1.0, 0.13 v5.0.0, 0.14 v4.1.0, 0.09 v4.0.1, 0.14 v4.0.0, 0.23 v3.7.0, 0.11 v3.4.0, 0.12 v3.3.0, 0.00 v2.0.0 % 58.36/58.51 % Syntax : Number of clauses : 3 ( 3 unt; 0 nHn; 1 RR) % 58.36/58.51 % Number of literals : 3 ( 3 equ; 1 neg) % 58.36/58.51 % Maximal clause size : 1 ( 1 avg) % 58.36/58.51 % Maximal term depth : 4 ( 2 avg) % 58.36/58.51 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty) % 58.36/58.51 % Number of functors : 4 ( 4 usr; 3 con; 0-2 aty) % 58.36/58.51 % Number of variables : 7 ( 0 sgn) % 58.36/58.51 % SPC : CNF_UNS_RFO_PEQ_UEQ % 58.36/58.51 % 58.36/58.51 % Comments : % 58.36/58.51 %-------------------------------------------------------------------------- % 58.36/58.51 cnf(b_definition,axiom, % 58.36/58.51 apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ). % 58.36/58.51 % 58.36/58.51 cnf(h_definition,axiom, % 58.36/58.51 apply(apply(apply(h,X),Y),Z) = apply(apply(apply(X,Y),Z),Y) ). % 58.36/58.51 % 58.36/58.51 cnf(prove_fixed_point,negated_conjecture, % 58.36/58.51 Y != apply(combinator,Y) ). % 58.36/58.51 % 58.36/58.51 %-------------------------------------------------------------------------- % 58.36/58.51 %------------------------------------------- % 58.36/58.51 % Proof found % 58.36/58.51 % SZS status Theorem for theBenchmark % 58.36/58.51 % SZS output start Proof % 58.36/58.51 %ClaNum:8(EqnAxiom:5) % 58.36/58.51 %VarNum:15(SingletonVarNum:7) % 58.36/58.51 %MaxLitNum:1 % 58.36/58.51 %MaxfuncDepth:3 % 58.36/58.51 %SharedTerms:3 % 58.36/58.51 %goalClause: 8 % 58.36/58.51 %singleGoalClaCount:1 % 58.36/58.51 [8]~E(f2(a4,x81),x81) % 58.36/58.52 [6]E(f2(f2(f2(a1,x61),x62),x63),f2(x61,f2(x62,x63))) % 58.36/58.52 [7]E(f2(f2(f2(a3,x71),x72),x73),f2(f2(f2(x71,x72),x73),x72)) % 58.36/58.52 %EqnAxiom % 58.36/58.52 [1]E(x11,x11) % 58.36/58.52 [2]E(x22,x21)+~E(x21,x22) % 58.36/58.52 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 58.36/58.52 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43)) % 58.36/58.52 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52)) % 58.36/58.52 % 58.36/58.52 %------------------------------------------- % 58.45/58.53 cnf(9,plain, % 58.45/58.53 (E(f2(f2(f2(x91,x92),x93),x92),f2(f2(f2(a3,x91),x92),x93))), % 58.45/58.53 inference(scs_inference,[],[7,2])). % 58.45/58.53 cnf(12,plain, % 58.45/58.53 (E(f2(x121,f2(x122,x123)),f2(f2(f2(a1,x121),x122),x123))), % 58.45/58.53 inference(scs_inference,[],[6,2])). % 58.45/58.53 cnf(15,plain, % 58.45/58.53 (~E(f2(f2(f2(a1,a4),x151),x152),f2(x151,x152))), % 58.45/58.53 inference(scs_inference,[],[8,6,2,3,5])). % 58.45/58.53 cnf(83,plain, % 58.45/58.53 (~E(f2(f2(f2(a1,a4),f2(f2(a3,x831),x832)),x833),f2(f2(f2(x831,x832),x833),x832))), % 58.45/58.53 inference(scs_inference,[],[15,9,3])). % 58.45/58.53 cnf(87,plain, % 58.45/58.53 ($false), % 58.45/58.53 inference(scs_inference,[],[12,83,4]), % 58.45/58.53 ['proof']). % 58.45/58.53 % SZS output end Proof % 58.45/58.53 % Total time :57.810000s %------------------------------------------------------------------------------