%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : COL018-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n017.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 00:36:52 EDT 2022 % Result : Unsatisfiable 0.20s 0.40s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : COL018-1 : TPTP v8.1.0. Released v1.0.0. % 0.03/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n017.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Tue May 31 05:57:56 EDT 2022 % 0.13/0.34 % CPUTime : % 0.20/0.40 % SZS status Unsatisfiable % 0.20/0.40 % SZS output start Proof % 0.20/0.40 The input problem is unsatisfiable because % 0.20/0.40 % 0.20/0.40 [1] the following set of Horn clauses is unsatisfiable: % 0.20/0.40 % 0.20/0.40 apply(apply(l, X), Y) = apply(X, apply(Y, Y)) % 0.20/0.40 apply(apply(w, X), Y) = apply(apply(X, Y), Y) % 0.20/0.40 apply(apply(apply(q, X), Y), Z) = apply(Y, apply(X, Z)) % 0.20/0.40 Y = apply(combinator, Y) ==> \bottom % 0.20/0.40 % 0.20/0.40 This holds because % 0.20/0.40 % 0.20/0.40 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.20/0.40 % 0.20/0.40 E: % 0.20/0.40 apply(apply(apply(q, X), Y), Z) = apply(Y, apply(X, Z)) % 0.20/0.40 apply(apply(l, X), Y) = apply(X, apply(Y, Y)) % 0.20/0.40 apply(apply(w, X), Y) = apply(apply(X, Y), Y) % 0.20/0.40 f1(Y, Y) = true__ % 0.20/0.40 f1(apply(combinator, Y), Y) = false__ % 0.20/0.40 G: % 0.20/0.40 true__ = false__ % 0.20/0.40 % 0.20/0.40 This holds because % 0.20/0.40 % 0.20/0.40 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.20/0.40 % 0.20/0.40 apply(X0, apply(apply(Y1, Y1), apply(Y1, Y1))) = apply(apply(l, apply(l, X0)), Y1) % 0.20/0.40 apply(Y1, apply(Y1, Y1)) = apply(apply(w, l), Y1) % 0.20/0.40 apply(apply(X0, apply(Y1, Y1)), Y1) = apply(apply(w, apply(l, X0)), Y1) % 0.20/0.40 apply(apply(X0, apply(Y1, Y1)), apply(Y1, Y1)) = apply(apply(l, apply(w, X0)), Y1) % 0.20/0.40 apply(apply(Y1, Y1), Y1) = apply(apply(w, w), Y1) % 0.20/0.40 apply(apply(apply(X0, Y1), Y1), Y1) = apply(apply(w, apply(w, X0)), Y1) % 0.20/0.40 apply(apply(apply(l, Y0), X1), apply(X1, X1)) = apply(apply(w, Y0), apply(X1, X1)) % 0.20/0.40 apply(apply(apply(l, l), X1), Y1) = apply(apply(X1, X1), apply(Y1, Y1)) % 0.20/0.40 apply(apply(apply(l, w), X1), Y1) = apply(apply(apply(X1, X1), Y1), Y1) % 0.20/0.40 apply(apply(l, X), Y) = apply(X, apply(Y, Y)) % 0.20/0.40 apply(apply(l, apply(w, l)), X1) = apply(apply(X1, X1), apply(apply(X1, X1), apply(X1, X1))) % 0.20/0.40 apply(apply(w, X), Y) = apply(apply(X, Y), Y) % 0.20/0.40 apply(apply(w, apply(w, X0)), Y1) = apply(apply(w, apply(X0, Y1)), Y1) % 0.20/0.40 apply(apply(apply(q, X), Y), Z) -> apply(Y, apply(X, Z)) % 0.20/0.40 apply(apply(apply(w, l), Y0), apply(Y0, Y0)) -> apply(apply(w, Y0), apply(Y0, Y0)) % 0.20/0.40 f1(Y, Y) -> true__ % 0.20/0.40 f1(apply(apply(l, combinator), X1), apply(X1, X1)) -> false__ % 0.20/0.40 f1(apply(combinator, Y), Y) -> false__ % 0.20/0.40 true__ -> false__ % 0.20/0.40 with the LPO induced by % 0.20/0.40 w > combinator > l > q > apply > f1 > true__ > false__ % 0.20/0.40 % 0.20/0.40 % SZS output end Proof % 0.20/0.40 %------------------------------------------------------------------------------