%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : COL066-2 : TPTP v8.2.0. Bugfixed v1.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n032.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 04:45:02 EDT 2024 % Result : Unsatisfiable 0.68s 0.85s % Output : CNFRefutation 0.68s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.07 % Problem : COL066-2 : TPTP v8.2.0. Bugfixed v1.2.0. % 0.00/0.07 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.06/0.26 % Computer : n032.cluster.edu % 0.06/0.26 % Model : x86_64 x86_64 % 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.06/0.26 % Memory : 8042.1875MB % 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64 % 0.06/0.26 % CPULimit : 300 % 0.06/0.26 % WCLimit : 300 % 0.06/0.26 % DateTime : Tue Jun 18 15:35:23 EDT 2024 % 0.06/0.26 % CPUTime : % 0.11/0.45 start to proof:theBenchmark % 0.68/0.85 %------------------------------------------- % 0.68/0.85 % File :CSE---1.7 % 0.68/0.85 % Problem :theBenchmark % 0.68/0.85 % Transform :cnf % 0.68/0.85 % Format :tptp:raw % 0.68/0.85 % Command :java -jar mcs_scs.jar %d %s % 0.68/0.85 % 0.68/0.85 % Result :Theorem 0.360000s % 0.68/0.85 % Output :CNFRefutation 0.360000s % 0.68/0.85 %------------------------------------------- % 0.68/0.85 %-------------------------------------------------------------------------- % 0.68/0.85 % File : COL066-2 : TPTP v8.2.0. Bugfixed v1.2.0. % 0.68/0.85 % Domain : Combinatory Logic % 0.68/0.85 % Problem : Find combinator equivalent to P from B, Q and W % 0.68/0.85 % Version : [WM88] (equality) axioms. % 0.68/0.85 % Theorem formulation : The combinator is provided and checked. % 0.68/0.85 % English : Construct from B, Q and W alone a combinator that behaves as % 0.68/0.85 % the combinator P does, where ((Bx)y)z = x(yz), ((Qx)y)z = % 0.68/0.85 % y(xz), (Wx)y = (xy)y, (((Px)y)y)z = (xy)((xy)z) % 0.68/0.85 % 0.68/0.85 % Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq % 0.68/0.85 % : [WW+90] Wos et al. (1990), Automated Reasoning Contributes to % 0.68/0.85 % Source : [TPTP] % 0.68/0.85 % Names : % 0.68/0.85 % 0.68/0.85 % Status : Unsatisfiable % 0.68/0.85 % Rating : 0.05 v8.2.0, 0.12 v8.1.0, 0.15 v7.5.0, 0.12 v7.4.0, 0.17 v7.3.0, 0.11 v7.1.0, 0.00 v7.0.0, 0.05 v6.4.0, 0.11 v6.3.0, 0.06 v6.2.0, 0.07 v6.1.0, 0.06 v6.0.0, 0.24 v5.5.0, 0.16 v5.4.0, 0.07 v5.3.0, 0.00 v5.2.0, 0.07 v5.1.0, 0.00 v5.0.0, 0.07 v4.1.0, 0.09 v4.0.1, 0.07 v4.0.0, 0.08 v3.7.0, 0.11 v3.4.0, 0.12 v3.3.0, 0.00 v2.7.0, 0.09 v2.6.0, 0.00 v2.1.0, 0.29 v2.0.0 % 0.68/0.85 % Syntax : Number of clauses : 4 ( 4 unt; 0 nHn; 1 RR) % 0.68/0.85 % Number of literals : 4 ( 4 equ; 1 neg) % 0.68/0.85 % Maximal clause size : 1 ( 1 avg) % 0.68/0.85 % Maximal term depth : 9 ( 2 avg) % 0.68/0.85 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty) % 0.68/0.85 % Number of functors : 7 ( 7 usr; 6 con; 0-2 aty) % 0.68/0.85 % Number of variables : 8 ( 0 sgn) % 0.68/0.85 % SPC : CNF_UNS_RFO_PEQ_UEQ % 0.68/0.85 % 0.68/0.85 % Comments : % 0.68/0.85 % Bugfixes : v1.2.0 : Redundant [fgh]_substitution axioms removed. % 0.68/0.85 %-------------------------------------------------------------------------- % 0.68/0.85 cnf(b_definition,axiom, % 0.68/0.85 apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ). % 0.68/0.85 % 0.68/0.85 cnf(q_definition,axiom, % 0.68/0.85 apply(apply(apply(q,X),Y),Z) = apply(Y,apply(X,Z)) ). % 0.68/0.85 % 0.68/0.85 cnf(w_definition,axiom, % 0.68/0.85 apply(apply(w,X),Y) = apply(apply(X,Y),Y) ). % 0.68/0.85 % 0.68/0.85 %----This is the P equivalent % 0.68/0.85 cnf(prove_p_combinator,negated_conjecture, % 0.68/0.85 apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)) ). % 0.68/0.85 % 0.68/0.85 %-------------------------------------------------------------------------- % 0.68/0.85 %------------------------------------------- % 0.68/0.85 % Proof found % 0.68/0.85 % SZS status Theorem for theBenchmark % 0.68/0.85 % SZS output start Proof % 0.68/0.85 %ClaNum:9(EqnAxiom:5) % 0.68/0.85 %VarNum:17(SingletonVarNum:8) % 0.68/0.85 %MaxLitNum:1 % 0.68/0.85 %MaxfuncDepth:8 % 0.68/0.85 %SharedTerms:18 % 0.68/0.85 %goalClause: 9 % 0.68/0.85 %singleGoalClaCount:1 % 0.68/0.85 [9]~E(f2(f2(f2(f2(f2(f2(a4,a4),f2(a1,f2(a4,f2(a4,a4)))),a5),a6),a6),a7),f2(f2(a5,a6),f2(f2(a5,a6),a7))) % 0.68/0.85 [6]E(f2(f2(a1,x61),x62),f2(f2(x61,x62),x62)) % 0.68/0.85 [7]E(f2(f2(f2(a3,x71),x72),x73),f2(x71,f2(x72,x73))) % 0.68/0.85 [8]E(f2(f2(f2(a4,x81),x82),x83),f2(x82,f2(x81,x83))) % 0.68/0.85 %EqnAxiom % 0.68/0.85 [1]E(x11,x11) % 0.68/0.85 [2]E(x22,x21)+~E(x21,x22) % 0.68/0.85 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.68/0.85 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43)) % 0.68/0.85 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52)) % 0.68/0.85 % 0.68/0.85 %------------------------------------------- % 0.68/0.86 cnf(17,plain, % 0.68/0.86 (~E(f2(f2(f2(f2(f2(a4,a4),f2(a1,f2(a4,f2(a4,a4)))),a5),a6),a6),f2(f2(a4,f2(a5,a6)),f2(a5,a6)))), % 0.68/0.86 inference(scs_inference,[],[9,8,2,3,4])). % 0.68/0.86 cnf(34,plain, % 0.68/0.86 (~E(f2(f2(f2(f2(a4,a4),f2(a1,f2(a4,f2(a4,a4)))),a5),a6),f2(f2(a4,a5),f2(a4,f2(a5,a6))))), % 0.68/0.86 inference(scs_inference,[],[17,8,3,4])). % 0.68/0.86 cnf(53,plain, % 0.68/0.86 (~E(f2(f2(f2(f2(a4,a4),f2(a1,f2(a4,f2(a4,a4)))),a5),a6),f2(f2(f2(a4,a4),f2(a4,a5)),f2(a5,a6)))), % 0.68/0.86 inference(scs_inference,[],[34,8,3])). % 0.68/0.86 cnf(86,plain, % 0.68/0.86 (~E(f2(f2(f2(a4,a4),f2(a1,f2(a4,f2(a4,a4)))),a5),f2(f2(a3,f2(f2(a4,a4),f2(a4,a5))),a5))), % 0.68/0.86 inference(scs_inference,[],[53,7,3,4])). % 0.68/0.86 cnf(88,plain, % 0.68/0.86 (~E(f2(f2(f2(f2(a4,a4),f2(a1,f2(a4,f2(a4,a4)))),a5),a6),f2(f2(f2(a4,a5),f2(f2(a4,a4),f2(a4,a5))),a6))), % 0.68/0.86 inference(scs_inference,[],[53,86,8,4,3])). % 0.68/0.86 cnf(90,plain, % 0.68/0.86 (~E(f2(f2(f2(a4,a4),f2(a1,f2(a4,f2(a4,a4)))),a5),f2(f2(a4,a5),f2(f2(a4,a4),f2(a4,a5))))), % 0.68/0.86 inference(scs_inference,[],[88,4])). % 0.68/0.86 cnf(125,plain, % 0.68/0.86 (~E(f2(f2(f2(a4,a4),f2(a1,f2(a4,f2(a4,a4)))),a5),f2(f2(f2(a4,f2(a4,a4)),f2(a4,a5)),f2(a4,a5)))), % 0.68/0.86 inference(scs_inference,[],[90,8,3])). % 0.68/0.86 cnf(127,plain, % 0.68/0.86 ($false), % 0.68/0.86 inference(scs_inference,[],[125,6,8,3]), % 0.68/0.86 ['proof']). % 0.68/0.86 % SZS output end Proof % 0.68/0.86 % Total time :0.360000s %------------------------------------------------------------------------------