%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : COL060-1 : 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 : n010.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 04:44:58 EDT 2024 % Result : Unsatisfiable 58.44s 58.58s % Output : CNFRefutation 58.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : COL060-1 : TPTP v8.2.0. Released v1.0.0. % 0.03/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.13/0.34 % Computer : n010.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 15:57:09 EDT 2024 % 0.13/0.34 % CPUTime : % 0.60/0.64 start to proof:theBenchmark % 58.44/58.56 %------------------------------------------- % 58.44/58.56 % File :CSE---1.7 % 58.44/58.56 % Problem :theBenchmark % 58.44/58.56 % Transform :cnf % 58.44/58.56 % Format :tptp:raw % 58.44/58.56 % Command :java -jar mcs_scs.jar %d %s % 58.44/58.56 % 58.44/58.56 % Result :Theorem 57.820000s % 58.44/58.56 % Output :CNFRefutation 57.820000s % 58.44/58.56 %------------------------------------------- % 58.44/58.58 %-------------------------------------------------------------------------- % 58.44/58.58 % File : COL060-1 : TPTP v8.2.0. Released v1.0.0. % 58.44/58.58 % Domain : Combinatory Logic % 58.44/58.58 % Problem : Find combinator equivalent to Q from B and T % 58.44/58.58 % Version : [WM88] (equality) axioms. % 58.44/58.58 % English : Construct from B and T alone a combinator that behaves as the % 58.44/58.58 % combinator Q does, where ((Bx)y)z = x(yz), (Tx)y = yx, % 58.44/58.58 % ((Qx)y)z = y(xz). % 58.44/58.58 % 58.44/58.58 % Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq % 58.44/58.58 % : [WW+90] Wos et al. (1990), Automated Reasoning Contributes to % 58.44/58.58 % Source : [WW+90] % 58.44/58.58 % Names : CL-1 [WW+90] % 58.44/58.58 % 58.44/58.58 % Status : Unsatisfiable % 58.44/58.58 % Rating : 0.27 v8.2.0, 0.33 v8.1.0, 0.30 v7.5.0, 0.33 v7.4.0, 0.48 v7.3.0, 0.37 v7.1.0, 0.28 v7.0.0, 0.32 v6.4.0, 0.37 v6.3.0, 0.35 v6.2.0, 0.36 v6.1.0, 0.31 v6.0.0, 0.43 v5.5.0, 0.37 v5.4.0, 0.27 v5.3.0, 0.33 v5.2.0, 0.29 v5.1.0, 0.33 v5.0.0, 0.29 v4.1.0, 0.27 v4.0.1, 0.29 v4.0.0, 0.31 v3.7.0, 0.33 v3.4.0, 0.38 v3.3.0, 0.36 v3.1.0, 0.33 v2.7.0, 0.36 v2.6.0, 0.17 v2.5.0, 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.62 v2.0.0 % 58.44/58.58 % Syntax : Number of clauses : 3 ( 3 unt; 0 nHn; 1 RR) % 58.44/58.58 % Number of literals : 3 ( 3 equ; 1 neg) % 58.44/58.58 % Maximal clause size : 1 ( 1 avg) % 58.44/58.58 % Maximal term depth : 5 ( 2 avg) % 58.44/58.58 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty) % 58.44/58.58 % Number of functors : 6 ( 6 usr; 2 con; 0-2 aty) % 58.44/58.58 % Number of variables : 6 ( 0 sgn) % 58.44/58.58 % SPC : CNF_UNS_RFO_PEQ_UEQ % 58.44/58.58 % 58.44/58.58 % Comments : % 58.44/58.58 %-------------------------------------------------------------------------- % 58.44/58.58 cnf(b_definition,axiom, % 58.44/58.58 apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ). % 58.44/58.58 % 58.44/58.58 cnf(t_definition,axiom, % 58.44/58.58 apply(apply(t,X),Y) = apply(Y,X) ). % 58.44/58.58 % 58.44/58.58 cnf(prove_q_combinator,negated_conjecture, % 58.44/58.58 apply(apply(apply(X,f(X)),g(X)),h(X)) != apply(g(X),apply(f(X),h(X))) ). % 58.44/58.58 % 58.44/58.58 %-------------------------------------------------------------------------- % 58.44/58.58 %------------------------------------------- % 58.44/58.58 % Proof found % 58.44/58.58 % SZS status Theorem for theBenchmark % 58.44/58.58 % SZS output start Proof % 58.52/58.59 %ClaNum:11(EqnAxiom:8) % 58.52/58.59 %VarNum:17(SingletonVarNum:6) % 58.52/58.59 %MaxLitNum:1 % 58.52/58.59 %MaxfuncDepth:3 % 58.52/58.59 %SharedTerms:2 % 58.52/58.59 %goalClause: 11 % 58.52/58.59 %singleGoalClaCount:1 % 58.52/58.59 [11]~E(f2(f2(f2(x111,f4(x111)),f5(x111)),f6(x111)),f2(f5(x111),f2(f4(x111),f6(x111)))) % 58.52/58.59 [9]E(f2(f2(a1,x91),x92),f2(x92,x91)) % 58.52/58.59 [10]E(f2(f2(f2(a3,x101),x102),x103),f2(x101,f2(x102,x103))) % 58.52/58.59 %EqnAxiom % 58.52/58.59 [1]E(x11,x11) % 58.52/58.59 [2]E(x22,x21)+~E(x21,x22) % 58.52/58.59 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 58.52/58.59 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43)) % 58.52/58.59 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52)) % 58.52/58.59 [6]~E(x61,x62)+E(f6(x61),f6(x62)) % 58.52/58.59 [7]~E(x71,x72)+E(f4(x71),f4(x72)) % 58.52/58.59 [8]~E(x81,x82)+E(f5(x81),f5(x82)) % 58.52/58.59 % 58.52/58.59 %------------------------------------------- % 58.52/58.61 cnf(15,plain, % 58.52/58.61 (E(f2(x151,f2(x152,x153)),f2(f2(f2(a3,x151),x152),x153))), % 58.52/58.61 inference(scs_inference,[],[10,2])). % 58.52/58.61 cnf(18,plain, % 58.52/58.61 (~E(f2(f2(x181,f4(x181)),f5(x181)),f2(f2(a3,f5(x181)),f4(x181)))), % 58.52/58.61 inference(scs_inference,[],[11,10,2,3,4])). % 58.52/58.61 cnf(19,plain, % 58.52/58.61 (~E(f2(f2(x191,f4(x191)),f5(x191)),f2(f2(a1,f4(x191)),f2(a3,f5(x191))))), % 58.52/58.61 inference(scs_inference,[],[18,9,3])). % 58.52/58.61 cnf(36,plain, % 58.52/58.61 (~E(f2(x361,f4(x361)),f2(f2(a3,f2(a1,f4(x361))),a3))), % 58.52/58.61 inference(scs_inference,[],[19,10,3,4])). % 58.52/58.61 cnf(47,plain, % 58.52/58.61 (~E(f2(x471,f4(x471)),f2(f2(a1,a3),f2(a3,f2(a1,f4(x471)))))), % 58.52/58.61 inference(scs_inference,[],[36,9,3])). % 58.52/58.61 cnf(54,plain, % 58.52/58.61 ($false), % 58.52/58.61 inference(scs_inference,[],[47,15,10,3,2]), % 58.52/58.61 ['proof']). % 58.52/58.61 % SZS output end Proof % 58.52/58.61 % Total time :57.820000s %------------------------------------------------------------------------------