%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : COL016-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n020.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 00:36:51 EDT 2022 % Result : Unsatisfiable 0.60s 0.79s % Output : Proof 0.60s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : COL016-1 : TPTP v8.1.0. Released v1.0.0. % 0.11/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n020.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 14:13:08 EDT 2022 % 0.12/0.33 % CPUTime : % 0.60/0.79 % SZS status Unsatisfiable % 0.60/0.79 % SZS output start Proof % 0.60/0.79 The input problem is unsatisfiable because % 0.60/0.79 % 0.60/0.79 [1] the following set of Horn clauses is unsatisfiable: % 0.60/0.79 % 0.60/0.79 apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)) % 0.60/0.79 apply(apply(l, X), Y) = apply(X, apply(Y, Y)) % 0.60/0.79 apply(m, X) = apply(X, X) % 0.60/0.79 Y = apply(combinator, Y) ==> \bottom % 0.60/0.79 % 0.60/0.79 This holds because % 0.60/0.79 % 0.60/0.79 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.60/0.79 % 0.60/0.79 E: % 0.60/0.79 apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)) % 0.60/0.79 apply(apply(l, X), Y) = apply(X, apply(Y, Y)) % 0.60/0.79 apply(m, X) = apply(X, X) % 0.60/0.79 f1(Y, Y) = true__ % 0.60/0.79 f1(apply(combinator, Y), Y) = false__ % 0.60/0.79 G: % 0.60/0.79 true__ = false__ % 0.60/0.79 % 0.60/0.79 This holds because % 0.60/0.79 % 0.60/0.79 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.60/0.79 % 0.60/0.79 apply(X0, apply(apply(Y1, Y1), apply(Y1, Y1))) = apply(X0, apply(m, apply(m, Y1))) % 0.60/0.79 apply(apply(Y0, Y0), apply(m, Y0)) = apply(m, apply(m, Y0)) % 0.60/0.79 apply(apply(Y1, Y1), apply(Y1, Y1)) = apply(apply(l, m), Y1) % 0.60/0.79 apply(apply(Y1, Y1), apply(Y1, Y1)) = apply(m, apply(m, Y1)) % 0.60/0.79 apply(apply(apply(X1, X1), apply(X1, X1)), apply(m, apply(m, X1))) = apply(m, apply(apply(X1, X1), apply(X1, X1))) % 0.60/0.79 apply(apply(apply(X1, X1), apply(X1, X1)), apply(m, apply(m, X1))) = apply(m, apply(m, apply(X1, X1))) % 0.60/0.79 apply(apply(l, X), Y) = apply(X, apply(Y, Y)) % 0.60/0.79 apply(apply(m, l), Y1) = apply(l, apply(Y1, Y1)) % 0.60/0.79 apply(m, X) = apply(X, X) % 0.60/0.79 apply(m, apply(Y0, Y0)) = apply(apply(Y0, Y0), apply(m, Y0)) % 0.60/0.79 apply(m, apply(apply(b, Y0), Y1)) = apply(Y0, apply(Y1, apply(apply(b, Y0), Y1))) % 0.60/0.79 apply(m, apply(m, apply(m, X1))) = apply(apply(apply(X1, X1), apply(X1, X1)), apply(apply(X1, X1), apply(X1, X1))) % 0.60/0.79 apply(m, apply(m, apply(m, X1))) = apply(apply(apply(X1, X1), apply(X1, X1)), apply(m, apply(X1, X1))) % 0.60/0.79 apply(Y0, apply(m, apply(l, Y0))) -> apply(m, apply(l, Y0)) % 0.60/0.79 apply(apply(apply(b, X), Y), Z) -> apply(X, apply(Y, Z)) % 0.60/0.79 apply(apply(apply(m, b), Y1), Y2) -> apply(b, apply(Y1, Y2)) % 0.60/0.79 apply(apply(l, Y0), Y1) -> apply(Y0, apply(m, Y1)) % 0.60/0.79 apply(apply(m, Y0), apply(Y0, Y0)) -> apply(m, apply(m, Y0)) % 0.60/0.79 apply(apply(m, apply(b, Y0)), Y2) -> apply(Y0, apply(apply(b, Y0), Y2)) % 0.60/0.79 apply(apply(m, apply(m, X0)), apply(apply(X0, X0), apply(X0, X0))) -> apply(m, apply(m, apply(X0, X0))) % 0.60/0.79 apply(apply(m, apply(m, b)), Y1) -> apply(b, apply(apply(m, b), Y1)) % 0.60/0.79 apply(apply(m, apply(m, l)), apply(m, apply(m, apply(m, l)))) -> apply(m, apply(m, apply(m, l))) % 0.60/0.79 apply(apply(m, l), Y0) -> apply(l, apply(m, Y0)) % 0.60/0.79 apply(b, apply(Y0, apply(apply(m, b), Y0))) -> apply(m, apply(apply(m, b), Y0)) % 0.60/0.79 apply(l, apply(l, apply(m, apply(m, l)))) -> apply(l, apply(m, apply(m, l))) % 0.60/0.79 apply(l, apply(m, apply(m, l))) -> apply(m, apply(m, l)) % 0.60/0.79 f1(Y, Y) -> true__ % 0.60/0.79 f1(apply(combinator, Y), Y) -> false__ % 0.60/0.79 f1(apply(combinator, apply(m, X1)), apply(X1, X1)) -> false__ % 0.60/0.79 f1(apply(combinator, apply(m, apply(X0, X0))), apply(m, apply(m, X0))) -> false__ % 0.60/0.79 f1(apply(combinator, apply(m, apply(m, X1))), apply(apply(X1, X1), apply(X1, X1))) -> false__ % 0.60/0.79 f1(apply(m, combinator), combinator) -> false__ % 0.60/0.79 true__ -> false__ % 0.60/0.79 with the LPO induced by % 0.60/0.79 l > combinator > b > m > apply > f1 > true__ > false__ % 0.60/0.79 % 0.60/0.79 % SZS output end Proof % 0.60/0.79 %------------------------------------------------------------------------------