%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : COL014-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n022.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 0.18s 0.39s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : COL014-1 : TPTP v8.1.0. Released v1.0.0. % 0.03/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n022.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Tue May 31 08:17:22 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.39 % SZS status Unsatisfiable % 0.18/0.39 % SZS output start Proof % 0.18/0.39 The input problem is unsatisfiable because % 0.18/0.39 % 0.18/0.39 [1] the following set of Horn clauses is unsatisfiable: % 0.18/0.39 % 0.18/0.39 apply(apply(l, X), Y) = apply(X, apply(Y, Y)) % 0.18/0.39 apply(apply(o, X), Y) = apply(Y, apply(X, Y)) % 0.18/0.39 Y = apply(combinator, Y) ==> \bottom % 0.18/0.39 % 0.18/0.39 This holds because % 0.18/0.39 % 0.18/0.39 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.18/0.39 % 0.18/0.39 E: % 0.18/0.39 apply(apply(l, X), Y) = apply(X, apply(Y, Y)) % 0.18/0.39 apply(apply(o, X), Y) = apply(Y, apply(X, Y)) % 0.18/0.39 f1(Y, Y) = true__ % 0.18/0.39 f1(apply(combinator, Y), Y) = false__ % 0.18/0.39 G: % 0.18/0.39 true__ = false__ % 0.18/0.39 % 0.18/0.39 This holds because % 0.18/0.39 % 0.18/0.39 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.18/0.39 % 0.18/0.39 apply(X0, apply(apply(Y1, Y1), apply(Y1, Y1))) = apply(apply(l, apply(l, X0)), Y1) % 0.18/0.39 apply(Y0, apply(X0, apply(Y0, Y0))) = apply(apply(o, apply(l, X0)), Y0) % 0.18/0.39 apply(Y0, apply(X0, apply(apply(Y0, Y0), apply(Y0, Y0)))) = apply(apply(o, apply(l, apply(l, X0))), Y0) % 0.18/0.39 apply(Y0, apply(Y0, apply(X0, Y0))) = apply(apply(o, apply(o, X0)), Y0) % 0.18/0.39 apply(Y0, apply(apply(Y0, Y0), apply(X0, apply(Y0, Y0)))) = apply(apply(o, apply(l, apply(o, X0))), Y0) % 0.18/0.39 apply(apply(X1, X1), apply(apply(l, Y1), X1)) = apply(apply(o, Y1), apply(X1, X1)) % 0.18/0.39 apply(apply(X1, Y1), apply(apply(o, X1), Y1)) = apply(apply(o, Y1), apply(X1, Y1)) % 0.18/0.39 apply(apply(Y1, Y1), apply(X0, apply(Y1, Y1))) = apply(apply(l, apply(o, X0)), Y1) % 0.18/0.39 apply(apply(apply(l, l), X1), Y1) = apply(apply(X1, X1), apply(Y1, Y1)) % 0.18/0.39 apply(apply(apply(l, o), X1), Y1) = apply(Y1, apply(apply(X1, X1), Y1)) % 0.18/0.39 apply(apply(apply(o, X1), l), Y1) = apply(apply(X1, l), apply(Y1, Y1)) % 0.18/0.39 apply(apply(l, X), Y) = apply(X, apply(Y, Y)) % 0.18/0.39 apply(apply(o, X), Y) = apply(Y, apply(X, Y)) % 0.18/0.39 f1(Y, Y) -> true__ % 0.18/0.39 f1(apply(apply(l, apply(l, combinator)), X1), apply(apply(X1, X1), apply(X1, X1))) -> false__ % 0.18/0.39 f1(apply(apply(l, combinator), X1), apply(X1, X1)) -> false__ % 0.18/0.39 f1(apply(combinator, Y), Y) -> false__ % 0.18/0.39 true__ -> false__ % 0.18/0.39 with the LPO induced by % 0.18/0.39 l > f1 > apply > o > combinator > true__ > false__ % 0.18/0.39 % 0.18/0.39 % SZS output end Proof % 0.18/0.39 %------------------------------------------------------------------------------