%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : COL012-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n025.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 00:36:49 EDT 2022 % Result : Unsatisfiable 0.19s 0.42s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : COL012-1 : TPTP v8.1.0. Released v1.0.0. % 0.04/0.13 % Command : moca.sh %s % 0.12/0.34 % Computer : n025.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 : 600 % 0.12/0.34 % DateTime : Tue May 31 10:04:58 EDT 2022 % 0.12/0.34 % CPUTime : % 0.19/0.42 % SZS status Unsatisfiable % 0.19/0.42 % SZS output start Proof % 0.19/0.42 The input problem is unsatisfiable because % 0.19/0.42 % 0.19/0.42 [1] the following set of Horn clauses is unsatisfiable: % 0.19/0.42 % 0.19/0.42 apply(apply(u, X), Y) = apply(Y, apply(apply(X, X), Y)) % 0.19/0.42 Y = apply(combinator, Y) ==> \bottom % 0.19/0.42 % 0.19/0.42 This holds because % 0.19/0.42 % 0.19/0.42 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.19/0.42 % 0.19/0.42 E: % 0.19/0.42 apply(apply(u, X), Y) = apply(Y, apply(apply(X, X), Y)) % 0.19/0.42 f1(Y, Y) = true__ % 0.19/0.42 f1(apply(combinator, Y), Y) = false__ % 0.19/0.42 G: % 0.19/0.42 true__ = false__ % 0.19/0.42 % 0.19/0.42 This holds because % 0.19/0.42 % 0.19/0.42 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.19/0.42 % 0.19/0.42 apply(apply(apply(X1, X1), apply(Y1, Y1)), apply(apply(u, X1), apply(Y1, Y1))) = apply(apply(u, Y1), apply(apply(X1, X1), apply(Y1, Y1))) % 0.19/0.42 apply(apply(u, X), Y) = apply(Y, apply(apply(X, X), Y)) % 0.19/0.42 apply(Y0, apply(apply(apply(u, X1), apply(apply(u, u), apply(X1, X1))), Y0)) -> apply(apply(u, apply(apply(u, u), apply(X1, X1))), Y0) % 0.19/0.42 apply(apply(apply(apply(apply(X1, X1), u), apply(apply(X1, X1), u)), apply(Y1, Y1)), apply(apply(apply(u, X1), u), apply(Y1, Y1))) -> apply(apply(u, Y1), apply(apply(apply(apply(X1, X1), u), apply(apply(X1, X1), u)), apply(Y1, Y1))) % 0.19/0.42 apply(apply(apply(u, X0), apply(X0, X0)), apply(apply(u, X0), apply(apply(X0, X0), apply(X0, X0)))) -> apply(apply(u, apply(X0, X0)), apply(apply(u, X0), apply(X0, X0))) % 0.19/0.42 apply(apply(apply(u, X1), apply(X1, X1)), apply(apply(u, X1), apply(apply(X1, X1), apply(X1, X1)))) -> apply(apply(u, apply(X1, X1)), apply(apply(X1, X1), apply(apply(X1, X1), apply(X1, X1)))) % 0.19/0.42 apply(apply(u, apply(u, u)), apply(apply(u, u), apply(u, u))) -> apply(apply(u, u), apply(u, u)) % 0.19/0.42 f1(Y, Y) -> true__ % 0.19/0.42 f1(apply(apply(apply(u, X1), u), combinator), apply(apply(apply(apply(X1, X1), u), apply(apply(X1, X1), u)), combinator)) -> false__ % 0.19/0.42 f1(apply(apply(u, X1), combinator), apply(apply(X1, X1), combinator)) -> false__ % 0.19/0.42 f1(apply(combinator, Y), Y) -> false__ % 0.19/0.42 false__ -> true__ % 0.19/0.42 with the LPO induced by % 0.19/0.42 u > combinator > apply > f1 > false__ > true__ % 0.19/0.42 % 0.19/0.42 % SZS output end Proof % 0.19/0.42 %------------------------------------------------------------------------------