%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : COL001-2 : 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 : n020.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 04:44:42 EDT 2024 % Result : Unsatisfiable 1.00s 1.13s % Output : CNFRefutation 1.00s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : COL001-2 : TPTP v8.2.0. Released v1.0.0. % 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.34 % Computer : n020.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 16:03:39 EDT 2024 % 0.12/0.34 % CPUTime : % 0.20/0.58 start to proof:theBenchmark % 1.00/1.12 %------------------------------------------- % 1.00/1.12 % File :CSE---1.7 % 1.00/1.12 % Problem :theBenchmark % 1.00/1.12 % Transform :cnf % 1.00/1.12 % Format :tptp:raw % 1.00/1.12 % Command :java -jar mcs_scs.jar %d %s % 1.00/1.12 % 1.00/1.12 % Result :Theorem 0.510000s % 1.00/1.12 % Output :CNFRefutation 0.510000s % 1.00/1.12 %------------------------------------------- % 1.00/1.13 %-------------------------------------------------------------------------- % 1.00/1.13 % File : COL001-2 : TPTP v8.2.0. Released v1.0.0. % 1.00/1.13 % Domain : Combinatory Logic % 1.00/1.13 % Problem : Weak fixed point for S and K % 1.00/1.13 % Version : [WM88] (equality) axioms : Augmented. % 1.00/1.13 % English : The weak fixed point property holds for the set P consisting % 1.00/1.13 % of the combinators S and K alone, where ((Sx)y)z = (xz)(yz) % 1.00/1.13 % and (Kx)y = x. % 1.00/1.13 % 1.00/1.13 % Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq % 1.00/1.13 % Source : [TPTP] % 1.00/1.13 % Names : % 1.00/1.13 % 1.00/1.13 % Status : Unsatisfiable % 1.00/1.13 % Rating : 0.14 v8.2.0, 0.21 v8.1.0, 0.20 v7.5.0, 0.25 v7.4.0, 0.30 v7.3.0, 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, 0.21 v6.1.0, 0.12 v6.0.0, 0.24 v5.5.0, 0.21 v5.4.0, 0.13 v5.3.0, 0.17 v5.2.0, 0.21 v5.1.0, 0.27 v5.0.0, 0.29 v4.1.0, 0.18 v4.0.1, 0.21 v4.0.0, 0.31 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 v2.1.0, 0.13 v2.0.0 % 1.00/1.13 % Syntax : Number of clauses : 6 ( 6 unt; 0 nHn; 1 RR) % 1.00/1.13 % Number of literals : 6 ( 6 equ; 1 neg) % 1.00/1.13 % Maximal clause size : 1 ( 1 avg) % 1.00/1.13 % Maximal term depth : 6 ( 2 avg) % 1.00/1.13 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty) % 1.00/1.13 % Number of functors : 7 ( 7 usr; 6 con; 0-2 aty) % 1.00/1.13 % Number of variables : 11 ( 1 sgn) % 1.00/1.13 % SPC : CNF_UNS_RFO_PEQ_UEQ % 1.00/1.13 % 1.00/1.13 % Comments : This allows the use of B and I in the proof, as done in the % 1.00/1.13 % "Proof of Theorem C1" in [WM88]. % 1.00/1.13 %-------------------------------------------------------------------------- % 1.00/1.13 cnf(s_definition,axiom, % 1.00/1.13 apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)) ). % 1.00/1.13 % 1.00/1.13 cnf(k_definition,axiom, % 1.00/1.13 apply(apply(k,X),Y) = X ). % 1.00/1.13 % 1.00/1.13 cnf(b_definition,axiom, % 1.00/1.13 apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ). % 1.00/1.13 % 1.00/1.13 cnf(i_definition,axiom, % 1.00/1.13 apply(i,X) = X ). % 1.00/1.13 % 1.00/1.13 cnf(sb_property,axiom, % 1.00/1.13 apply(apply(apply(s,apply(b,X)),i),apply(apply(s,apply(b,X)),i)) = apply(x,apply(apply(apply(s,apply(b,X)),i),apply(apply(s,apply(b,X)),i))) ). % 1.00/1.13 % 1.00/1.13 cnf(prove_fixed_point,negated_conjecture, % 1.00/1.13 Y != apply(combinator,Y) ). % 1.00/1.13 % 1.00/1.13 %-------------------------------------------------------------------------- % 1.00/1.13 %------------------------------------------- % 1.00/1.13 % Proof found % 1.00/1.13 % SZS status Theorem for theBenchmark % 1.00/1.13 % SZS output start Proof % 1.00/1.13 %ClaNum:11(EqnAxiom:5) % 1.00/1.13 %VarNum:24(SingletonVarNum:11) % 1.00/1.13 %MaxLitNum:1 % 1.00/1.13 %MaxfuncDepth:5 % 1.00/1.13 %SharedTerms:6 % 1.00/1.13 %goalClause: 11 % 1.00/1.13 %singleGoalClaCount:1 % 1.00/1.13 [6]E(f2(a1,x61),x61) % 1.00/1.13 [11]~E(f2(a4,x111),x111) % 1.00/1.13 [10]E(f2(a7,f2(f2(f2(a6,f2(a3,x101)),a1),f2(f2(a6,f2(a3,x101)),a1))),f2(f2(f2(a6,f2(a3,x101)),a1),f2(f2(a6,f2(a3,x101)),a1))) % 1.00/1.13 [7]E(f2(f2(a5,x71),x72),x71) % 1.00/1.13 [8]E(f2(f2(f2(a3,x81),x82),x83),f2(x81,f2(x82,x83))) % 1.00/1.13 [9]E(f2(f2(f2(a6,x91),x92),x93),f2(f2(x91,x93),f2(x92,x93))) % 1.00/1.13 %EqnAxiom % 1.00/1.13 [1]E(x11,x11) % 1.00/1.13 [2]E(x22,x21)+~E(x21,x22) % 1.00/1.13 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 1.00/1.13 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43)) % 1.00/1.13 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52)) % 1.00/1.13 % 1.00/1.13 %------------------------------------------- % 1.00/1.14 cnf(12,plain, % 1.00/1.14 (E(x121,f2(a1,x121))), % 1.00/1.14 inference(scs_inference,[],[6,2])). % 1.00/1.14 cnf(20,plain, % 1.00/1.14 (E(f2(f2(x201,x202),f2(x203,x202)),f2(f2(f2(a6,x201),x203),x202))), % 1.00/1.14 inference(scs_inference,[],[9,2])). % 1.00/1.14 cnf(25,plain, % 1.00/1.14 (E(f2(x251,f2(x252,x253)),f2(f2(f2(a3,x251),x252),x253))), % 1.00/1.14 inference(scs_inference,[],[8,2])). % 1.00/1.14 cnf(26,plain, % 1.00/1.14 (~E(f2(a4,f2(f2(f2(a6,x261),x262),x263)),f2(f2(x261,x263),f2(x262,x263)))), % 1.00/1.14 inference(scs_inference,[],[11,20,8,2,3])). % 1.00/1.14 cnf(195,plain, % 1.00/1.14 (~E(f2(f2(f2(a6,f2(a3,a4)),x1951),x1952),f2(x1952,f2(x1951,x1952)))), % 1.00/1.14 inference(scs_inference,[],[26,25,3,5])). % 1.00/1.14 cnf(196,plain, % 1.00/1.14 ($false), % 1.00/1.14 inference(scs_inference,[],[12,195,5]), % 1.00/1.14 ['proof']). % 1.00/1.14 % SZS output end Proof % 1.00/1.14 % Total time :0.510000s %------------------------------------------------------------------------------