%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : COL015-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n027.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 : 600s % DateTime : Fri Jul 15 00:36:50 EDT 2022 % Result : Unsatisfiable 0.67s 0.84s % Output : Proof 0.67s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : COL015-1 : TPTP v8.1.0. Released v1.0.0. % 0.03/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n027.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 : 600 % 0.13/0.34 % DateTime : Tue May 31 04:24:17 EDT 2022 % 0.13/0.34 % CPUTime : % 0.67/0.84 % SZS status Unsatisfiable % 0.67/0.84 % SZS output start Proof % 0.67/0.84 The input problem is unsatisfiable because % 0.67/0.84 % 0.67/0.84 [1] the following set of Horn clauses is unsatisfiable: % 0.67/0.84 % 0.67/0.84 apply(m, X) = apply(X, X) % 0.67/0.84 apply(apply(apply(q, X), Y), Z) = apply(Y, apply(X, Z)) % 0.67/0.84 Y = apply(combinator, Y) ==> \bottom % 0.67/0.84 % 0.67/0.84 This holds because % 0.67/0.84 % 0.67/0.84 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.67/0.84 % 0.67/0.84 E: % 0.67/0.84 apply(apply(apply(q, X), Y), Z) = apply(Y, apply(X, Z)) % 0.67/0.84 apply(m, X) = apply(X, X) % 0.67/0.84 f1(Y, Y) = true__ % 0.67/0.84 f1(apply(combinator, Y), Y) = false__ % 0.67/0.84 G: % 0.67/0.84 true__ = false__ % 0.67/0.84 % 0.67/0.84 This holds because % 0.67/0.84 % 0.67/0.84 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.67/0.84 % 0.67/0.84 apply(X1, apply(X0, apply(Y1, apply(apply(q, Y1), apply(apply(q, X0), X1))))) = apply(m, apply(apply(q, Y1), apply(apply(q, X0), X1))) % 0.67/0.84 apply(Y0, apply(X1, apply(X0, apply(apply(q, apply(apply(q, X0), X1)), Y0)))) = apply(m, apply(apply(q, apply(apply(q, X0), X1)), Y0)) % 0.67/0.84 apply(Y0, apply(apply(q, X0), apply(X0, apply(apply(q, apply(m, apply(q, X0))), Y0)))) = apply(m, apply(apply(q, apply(m, apply(q, X0))), Y0)) % 0.67/0.84 apply(apply(m, apply(apply(q, X1), apply(q, Y0))), Y2) = apply(apply(X1, apply(apply(q, X1), apply(q, Y0))), apply(Y0, Y2)) % 0.67/0.84 apply(apply(m, apply(m, apply(apply(q, X1), q))), Y1) = apply(apply(q, apply(X1, apply(apply(q, X1), q))), apply(apply(X1, apply(apply(q, X1), q)), Y1)) % 0.67/0.84 apply(apply(q, X0), apply(X0, apply(Y1, apply(apply(q, Y1), apply(m, apply(q, X0)))))) = apply(m, apply(apply(q, Y1), apply(m, apply(q, X0)))) % 0.67/0.84 apply(apply(q, Y1), apply(Y1, apply(m, apply(q, Y1)))) = apply(m, apply(apply(q, Y1), apply(q, Y1))) % 0.67/0.84 apply(m, X) = apply(X, X) % 0.67/0.84 apply(m, apply(apply(q, Y0), Y1)) = apply(Y1, apply(Y0, apply(apply(q, Y0), Y1))) % 0.67/0.84 apply(m, apply(m, apply(q, Y0))) = apply(apply(q, Y0), apply(Y0, apply(apply(q, Y0), apply(q, Y0)))) % 0.67/0.84 apply(m, apply(m, apply(q, Y0))) = apply(apply(q, Y0), apply(Y0, apply(m, apply(q, Y0)))) % 0.67/0.84 apply(apply(apply(m, apply(apply(q, X1), q)), Y1), Y2) -> apply(Y1, apply(apply(X1, apply(apply(q, X1), q)), Y2)) % 0.67/0.84 apply(apply(apply(q, X), Y), Z) -> apply(Y, apply(X, Z)) % 0.67/0.84 apply(apply(m, apply(apply(q, q), m)), Y1) -> apply(apply(q, apply(apply(q, q), m)), apply(m, apply(q, Y1))) % 0.67/0.84 apply(apply(m, apply(q, Y0)), Y2) -> apply(apply(q, Y0), apply(Y0, Y2)) % 0.67/0.84 f1(Y, Y) -> true__ % 0.67/0.84 f1(apply(combinator, Y), Y) -> false__ % 0.67/0.84 f1(apply(m, apply(apply(q, X1), combinator)), apply(X1, apply(apply(q, X1), combinator))) -> false__ % 0.67/0.84 f1(apply(m, apply(apply(q, apply(apply(q, X0), X1)), combinator)), apply(X1, apply(X0, apply(apply(q, apply(apply(q, X0), X1)), combinator)))) -> false__ % 0.67/0.84 true__ -> false__ % 0.67/0.84 with the LPO induced by % 0.67/0.84 m > f1 > apply > q > combinator > true__ > false__ % 0.67/0.84 % 0.67/0.84 % SZS output end Proof % 0.67/0.84 %------------------------------------------------------------------------------