%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : COL010-1 : 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 : n026.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 04:44:47 EDT 2024 % Result : Unsatisfiable 0.54s 0.61s % Output : CNFRefutation 0.57s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : COL010-1 : 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 % 0.13/0.33 % Computer : n026.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Tue Jun 18 16:13:09 EDT 2024 % 0.13/0.34 % CPUTime : % 0.20/0.58 start to proof:theBenchmark % 0.54/0.60 %------------------------------------------- % 0.54/0.60 % File :CSE---1.7 % 0.54/0.60 % Problem :theBenchmark % 0.54/0.60 % Transform :cnf % 0.54/0.60 % Format :tptp:raw % 0.54/0.60 % Command :java -jar mcs_scs.jar %d %s % 0.54/0.60 % 0.54/0.61 % Result :Theorem 0.000000s % 0.54/0.61 % Output :CNFRefutation 0.000000s % 0.54/0.61 %------------------------------------------- % 0.54/0.61 %-------------------------------------------------------------------------- % 0.54/0.61 % File : COL010-1 : TPTP v8.2.0. Released v1.0.0. % 0.54/0.61 % Domain : Combinatory Logic % 0.54/0.61 % Problem : Weak fixed point for B and S2 % 0.54/0.61 % Version : [WM88] (equality) axioms. % 0.54/0.61 % English : The weak fixed point property holds for the set P consisting % 0.54/0.61 % of the combinators B and S2, where ((Bx)y)z = x(yz), % 0.54/0.61 % ((S2x)y)z = (xz)(yy). % 0.54/0.61 % 0.54/0.61 % Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi % 0.54/0.61 % : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem % 0.54/0.61 % : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq % 0.54/0.61 % : [MW88] McCune & Wos (1988), Some Fixed Point Problems in Comb % 0.54/0.61 % Source : [MW88] % 0.54/0.61 % Names : - [MW88] % 0.54/0.61 % 0.54/0.61 % Status : Unsatisfiable % 0.54/0.61 % Rating : 0.14 v8.2.0, 0.21 v8.1.0, 0.25 v7.4.0, 0.26 v7.1.0, 0.17 v7.0.0, 0.16 v6.4.0, 0.21 v6.3.0, 0.18 v6.2.0, 0.14 v6.1.0, 0.06 v6.0.0, 0.14 v5.5.0, 0.11 v5.4.0, 0.07 v5.3.0, 0.08 v5.2.0, 0.07 v5.1.0, 0.13 v5.0.0, 0.14 v4.1.0, 0.09 v4.0.1, 0.14 v4.0.0, 0.15 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 v2.0.0 % 0.54/0.61 % Syntax : Number of clauses : 3 ( 3 unt; 0 nHn; 1 RR) % 0.54/0.61 % Number of literals : 3 ( 3 equ; 1 neg) % 0.54/0.61 % Maximal clause size : 1 ( 1 avg) % 0.54/0.61 % Maximal term depth : 4 ( 2 avg) % 0.54/0.61 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty) % 0.54/0.61 % Number of functors : 4 ( 4 usr; 3 con; 0-2 aty) % 0.54/0.61 % Number of variables : 7 ( 0 sgn) % 0.54/0.61 % SPC : CNF_UNS_RFO_PEQ_UEQ % 0.54/0.61 % 0.54/0.61 % Comments : % 0.54/0.61 %-------------------------------------------------------------------------- % 0.54/0.61 cnf(b_definition,axiom, % 0.54/0.61 apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ). % 0.54/0.61 % 0.54/0.61 cnf(s2_definition,axiom, % 0.54/0.61 apply(apply(apply(s2,X),Y),Z) = apply(apply(X,Z),apply(Y,Y)) ). % 0.54/0.61 % 0.54/0.61 cnf(prove_fixed_point,negated_conjecture, % 0.54/0.61 Y != apply(combinator,Y) ). % 0.54/0.61 % 0.54/0.61 %-------------------------------------------------------------------------- % 0.54/0.61 %------------------------------------------- % 0.54/0.61 % Proof found % 0.54/0.61 % SZS status Theorem for theBenchmark % 0.54/0.61 % SZS output start Proof % 0.54/0.61 %ClaNum:8(EqnAxiom:5) % 0.57/0.61 %VarNum:15(SingletonVarNum:7) % 0.57/0.61 %MaxLitNum:1 % 0.57/0.61 %MaxfuncDepth:3 % 0.57/0.61 %SharedTerms:3 % 0.57/0.61 %goalClause: 8 % 0.57/0.61 %singleGoalClaCount:1 % 0.57/0.61 [8]~E(f2(a4,x81),x81) % 0.57/0.61 [6]E(f2(f2(f2(a1,x61),x62),x63),f2(x61,f2(x62,x63))) % 0.57/0.61 [7]E(f2(f2(f2(a3,x71),x72),x73),f2(f2(x71,x73),f2(x72,x72))) % 0.57/0.61 %EqnAxiom % 0.57/0.61 [1]E(x11,x11) % 0.57/0.61 [2]E(x22,x21)+~E(x21,x22) % 0.57/0.61 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.57/0.61 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43)) % 0.57/0.61 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52)) % 0.57/0.61 % 0.57/0.61 %------------------------------------------- % 0.57/0.62 cnf(9,plain, % 0.57/0.62 (E(f2(f2(x91,x92),f2(x93,x93)),f2(f2(f2(a3,x91),x93),x92))), % 0.57/0.62 inference(scs_inference,[],[7,2])). % 0.57/0.62 cnf(11,plain, % 0.57/0.62 ($false), % 0.57/0.62 inference(scs_inference,[],[8,9,6,2,3]), % 0.57/0.62 ['proof']). % 0.57/0.62 % SZS output end Proof % 0.57/0.62 % Total time :0.000000s %------------------------------------------------------------------------------