%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : COL013-1 : 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 00:36:50 EDT 2022 % Result : Unsatisfiable 0.20s 0.42s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : COL013-1 : TPTP v8.1.0. Released v1.0.0. % 0.07/0.14 % Command : moca.sh %s % 0.13/0.35 % Computer : n019.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Tue May 31 14:30:10 EDT 2022 % 0.13/0.35 % CPUTime : % 0.20/0.42 % SZS status Unsatisfiable % 0.20/0.42 % SZS output start Proof % 0.20/0.42 The input problem is unsatisfiable because % 0.20/0.42 % 0.20/0.42 [1] the following set of Horn clauses is unsatisfiable: % 0.20/0.42 % 0.20/0.42 apply(apply(apply(s, X), Y), Z) = apply(apply(X, Z), apply(Y, Z)) % 0.20/0.42 apply(apply(l, X), Y) = apply(X, apply(Y, Y)) % 0.20/0.42 Y = apply(combinator, Y) ==> \bottom % 0.20/0.42 % 0.20/0.42 This holds because % 0.20/0.42 % 0.20/0.42 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.20/0.42 % 0.20/0.42 E: % 0.20/0.42 apply(apply(apply(s, X), Y), Z) = apply(apply(X, Z), apply(Y, Z)) % 0.20/0.42 apply(apply(l, X), Y) = apply(X, apply(Y, Y)) % 0.20/0.42 f1(Y, Y) = true__ % 0.20/0.42 f1(apply(combinator, Y), Y) = false__ % 0.20/0.42 G: % 0.20/0.42 true__ = false__ % 0.20/0.42 % 0.20/0.42 This holds because % 0.20/0.42 % 0.20/0.42 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.20/0.42 % 0.20/0.42 apply(X0, apply(apply(Y1, Y1), apply(Y1, Y1))) = apply(apply(l, apply(l, X0)), Y1) % 0.20/0.42 apply(Y1, apply(apply(Y2, Y1), apply(Y2, Y1))) = apply(apply(apply(s, l), Y2), Y1) % 0.20/0.42 apply(apply(X0, apply(Y1, Y1)), apply(Y2, Y1)) = apply(apply(apply(s, apply(l, X0)), Y2), Y1) % 0.20/0.42 apply(apply(Y0, Y1), apply(X0, apply(Y1, Y1))) = apply(apply(apply(s, Y0), apply(l, X0)), Y1) % 0.20/0.42 apply(apply(apply(apply(l, s), X1), Y1), Y2) = apply(apply(apply(X1, X1), Y2), apply(Y1, Y2)) % 0.20/0.42 apply(apply(apply(l, Y0), X1), apply(Y2, apply(X1, X1))) = apply(apply(apply(s, Y0), Y2), apply(X1, X1)) % 0.20/0.42 apply(apply(apply(l, apply(l, l)), X1), Y1) = apply(apply(apply(X1, X1), apply(X1, X1)), apply(Y1, Y1)) % 0.20/0.42 apply(apply(apply(l, apply(s, Y0)), X1), Y2) = apply(apply(Y0, Y2), apply(apply(X1, X1), Y2)) % 0.20/0.42 apply(apply(apply(l, l), X1), Y1) = apply(apply(X1, X1), apply(Y1, Y1)) % 0.20/0.42 apply(apply(apply(s, X), Y), Z) = apply(apply(X, Z), apply(Y, Z)) % 0.20/0.42 apply(apply(l, X), Y) = apply(X, apply(Y, Y)) % 0.20/0.42 apply(apply(l, apply(apply(l, l), Y0)), X1) = apply(apply(Y0, Y0), apply(apply(X1, X1), apply(X1, X1))) % 0.20/0.42 apply(apply(l, apply(apply(s, Y0), Y1)), X1) = apply(apply(Y0, apply(X1, X1)), apply(Y1, apply(X1, X1))) % 0.20/0.42 f1(Y, Y) -> true__ % 0.20/0.42 f1(apply(apply(l, apply(l, combinator)), X1), apply(apply(X1, X1), apply(X1, X1))) -> false__ % 0.20/0.42 f1(apply(apply(l, combinator), X1), apply(X1, X1)) -> false__ % 0.20/0.42 f1(apply(combinator, Y), Y) -> false__ % 0.20/0.42 true__ -> false__ % 0.20/0.42 with the LPO induced by % 0.20/0.42 s > f1 > apply > l > combinator > true__ > false__ % 0.20/0.42 % 0.20/0.42 % SZS output end Proof % 0.20/0.42 %------------------------------------------------------------------------------