%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : COL031-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n019.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 00:36:57 EDT 2022 % Result : Unsatisfiable 2.37s 2.52s % Output : Proof 2.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : COL031-1 : TPTP v8.1.0. Released v1.0.0. % 0.08/0.13 % Command : moca.sh %s % 0.14/0.35 % Computer : n019.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 600 % 0.14/0.35 % DateTime : Tue May 31 11:18:55 EDT 2022 % 0.14/0.35 % CPUTime : % 2.37/2.52 % SZS status Unsatisfiable % 2.37/2.52 % SZS output start Proof % 2.37/2.52 The input problem is unsatisfiable because % 2.37/2.52 % 2.37/2.52 [1] the following set of Horn clauses is unsatisfiable: % 2.37/2.52 % 2.37/2.52 apply(apply(l, X), Y) = apply(X, apply(Y, Y)) % 2.37/2.52 apply(apply(o, X), Y) = apply(Y, apply(X, Y)) % 2.37/2.52 apply(Y, f(Y)) = apply(f(Y), apply(Y, f(Y))) ==> \bottom % 2.37/2.52 % 2.37/2.52 This holds because % 2.37/2.52 % 2.37/2.52 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 2.37/2.52 % 2.37/2.52 E: % 2.37/2.52 apply(apply(l, X), Y) = apply(X, apply(Y, Y)) % 2.37/2.52 apply(apply(o, X), Y) = apply(Y, apply(X, Y)) % 2.37/2.52 f1(apply(Y, f(Y)), Y) = true__ % 2.37/2.52 f1(apply(f(Y), apply(Y, f(Y))), Y) = false__ % 2.37/2.52 G: % 2.37/2.52 true__ = false__ % 2.37/2.52 % 2.37/2.52 This holds because % 2.37/2.52 % 2.37/2.52 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 2.37/2.52 % 2.37/2.52 apply(X0, apply(apply(Y1, Y1), apply(Y1, Y1))) = apply(apply(l, apply(l, X0)), Y1) % 2.37/2.52 apply(Y0, apply(X0, apply(Y0, Y0))) = apply(apply(o, apply(l, X0)), Y0) % 2.37/2.52 apply(Y0, apply(Y0, apply(X0, Y0))) = apply(apply(o, apply(o, X0)), Y0) % 2.37/2.52 apply(Y0, apply(Y0, apply(X0, apply(Y0, Y0)))) = apply(apply(o, apply(o, apply(l, X0))), Y0) % 2.37/2.52 apply(Y0, apply(Y0, apply(Y0, apply(X0, Y0)))) = apply(apply(o, apply(o, apply(o, X0))), Y0) % 2.37/2.52 apply(Y0, apply(Y0, apply(apply(X0, X0), Y0))) = apply(apply(o, apply(apply(l, o), X0)), Y0) % 2.37/2.52 apply(Y0, apply(apply(X0, X0), apply(Y0, Y0))) = apply(apply(o, apply(apply(l, l), X0)), Y0) % 2.37/2.52 apply(Y0, apply(apply(apply(l, l), X0), X0)) = apply(apply(l, Y0), apply(X0, X0)) % 2.37/2.52 apply(Y0, apply(apply(apply(l, l), X0), Y0)) = apply(apply(o, apply(l, apply(X0, X0))), Y0) % 2.37/2.52 apply(Y0, apply(apply(apply(l, l), Y1), Y1)) = apply(apply(l, apply(l, Y0)), Y1) % 2.37/2.52 apply(Y0, apply(apply(apply(l, o), X1), Y0)) = apply(apply(o, apply(o, apply(X1, X1))), Y0) % 2.37/2.52 apply(apply(X1, X1), apply(apply(l, Y1), X1)) = apply(apply(o, Y1), apply(X1, X1)) % 2.37/2.52 apply(apply(X1, Y1), apply(apply(o, X1), Y1)) = apply(apply(o, Y1), apply(X1, Y1)) % 2.37/2.52 apply(apply(Y0, Y0), apply(apply(l, Y1), Y0)) = apply(apply(l, apply(o, Y1)), Y0) % 2.37/2.52 apply(apply(Y1, Y1), apply(X0, apply(Y1, Y1))) = apply(apply(l, apply(o, X0)), Y1) % 2.37/2.52 apply(apply(Y1, Y1), apply(o, apply(Y1, Y1))) = apply(apply(apply(l, l), o), Y1) % 2.37/2.52 apply(apply(apply(apply(l, o), X1), l), Y1) = apply(apply(apply(X1, X1), l), apply(Y1, Y1)) % 2.37/2.52 apply(apply(apply(apply(l, o), X1), o), Y1) = apply(Y1, apply(apply(apply(X1, X1), o), Y1)) % 2.37/2.52 apply(apply(apply(l, l), X0), apply(Y1, Y1)) = apply(apply(l, apply(l, apply(X0, X0))), Y1) % 2.37/2.52 apply(apply(apply(l, l), X1), Y1) = apply(apply(X1, X1), apply(Y1, Y1)) % 2.37/2.52 apply(apply(apply(l, l), o), Y1) = apply(apply(Y1, Y1), apply(apply(l, o), Y1)) % 2.37/2.52 apply(apply(apply(l, o), X1), Y1) = apply(Y1, apply(apply(X1, X1), Y1)) % 2.37/2.52 apply(apply(apply(o, X1), l), Y1) = apply(apply(X1, l), apply(Y1, Y1)) % 2.37/2.52 apply(apply(l, X), Y) = apply(X, apply(Y, Y)) % 2.37/2.52 apply(apply(o, X), Y) = apply(Y, apply(X, Y)) % 2.37/2.52 apply(apply(apply(l, o), X0), apply(X0, X0)) -> apply(apply(apply(l, l), X0), apply(X0, X0)) % 2.37/2.52 f1(apply(Y, f(Y)), Y) -> true__ % 2.37/2.52 f1(apply(apply(apply(l, o), X1), f(apply(X1, X1))), apply(X1, X1)) -> false__ % 2.37/2.52 f1(apply(apply(o, Y0), f(Y0)), Y0) -> false__ % 2.37/2.52 f1(apply(apply(o, apply(Y0, Y0)), f(apply(Y0, Y0))), apply(Y0, Y0)) -> false__ % 2.37/2.52 f1(apply(f(Y), apply(Y, f(Y))), Y) -> false__ % 2.37/2.52 false__ -> true__ % 2.37/2.52 with the LPO induced by % 2.37/2.52 o > l > f > apply > f1 > false__ > true__ % 2.37/2.52 % 2.37/2.52 % SZS output end Proof % 2.37/2.52 %------------------------------------------------------------------------------