%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : COL023-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n021.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 00:36:54 EDT 2022 % Result : Unsatisfiable 27.48s 27.66s % Output : Proof 27.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : COL023-1 : TPTP v8.1.0. Released v1.0.0. % 0.03/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n021.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 15:28:30 EDT 2022 % 0.12/0.33 % CPUTime : % 27.48/27.66 % SZS status Unsatisfiable % 27.48/27.66 % SZS output start Proof % 27.48/27.66 The input problem is unsatisfiable because % 27.48/27.66 % 27.48/27.66 [1] the following set of Horn clauses is unsatisfiable: % 27.48/27.66 % 27.48/27.66 apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)) % 27.48/27.66 apply(apply(apply(n, X), Y), Z) = apply(apply(apply(X, Z), Y), Z) % 27.48/27.66 Y = apply(combinator, Y) ==> \bottom % 27.48/27.66 % 27.48/27.66 This holds because % 27.48/27.66 % 27.48/27.66 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 27.48/27.66 % 27.48/27.66 E: % 27.48/27.66 apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)) % 27.48/27.66 apply(apply(apply(n, X), Y), Z) = apply(apply(apply(X, Z), Y), Z) % 27.48/27.66 f1(Y, Y) = true__ % 27.48/27.66 f1(apply(combinator, Y), Y) = false__ % 27.48/27.66 G: % 27.48/27.66 true__ = false__ % 27.48/27.66 % 27.48/27.66 This holds because % 27.48/27.66 % 27.48/27.66 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 27.48/27.66 % 27.48/27.66 apply(X0, apply(apply(Y1, Y2), Y1)) = apply(apply(apply(n, apply(b, apply(b, X0))), Y2), Y1) % 27.48/27.66 apply(Y0, apply(X0, apply(X1, Y0))) = apply(apply(apply(n, b), apply(apply(b, X0), X1)), Y0) % 27.48/27.66 apply(Y0, apply(Y0, apply(X0, Y0))) = apply(apply(apply(n, b), apply(apply(n, b), X0)), Y0) % 27.48/27.66 apply(Y1, apply(Y2, Y1)) = apply(apply(apply(n, b), Y2), Y1) % 27.48/27.66 apply(Y1, apply(apply(Y1, Y2), Y1)) = apply(apply(apply(n, apply(b, apply(n, b))), Y2), Y1) % 27.48/27.66 apply(apply(X0, apply(Y1, Y2)), Y1) = apply(apply(apply(n, apply(b, X0)), Y2), Y1) % 27.48/27.66 apply(apply(Y2, apply(Y1, Y2)), Y1) = apply(apply(apply(n, apply(n, b)), Y2), Y1) % 27.48/27.66 apply(apply(apply(Y1, Y1), Y2), Y1) = apply(apply(apply(n, n), Y2), Y1) % 27.48/27.66 apply(apply(apply(apply(n, apply(b, b)), X2), Y1), Y2) = apply(apply(Y1, X2), apply(Y1, Y2)) % 27.48/27.66 apply(apply(apply(apply(n, apply(b, b)), b), Y1), Y2) = apply(apply(Y1, b), apply(Y1, Y2)) % 27.48/27.66 apply(apply(apply(n, X), Y), Z) = apply(apply(apply(X, Z), Y), Z) % 27.48/27.66 apply(apply(apply(n, apply(X0, Y2)), Y2), Y1) = apply(apply(apply(n, apply(n, X0)), Y2), Y1) % 27.48/27.66 apply(apply(apply(n, apply(n, apply(b, b))), Y0), b) = apply(apply(Y0, b), apply(Y0, b)) % 27.48/27.66 apply(apply(apply(n, apply(n, apply(b, b))), Y1), Y2) = apply(apply(Y1, Y2), apply(Y1, Y2)) % 27.48/27.66 apply(apply(apply(n, apply(n, n)), Y2), Y1) = apply(apply(apply(n, apply(Y2, Y2)), Y2), Y1) % 27.48/27.66 apply(apply(apply(b, X), Y), Z) -> apply(X, apply(Y, Z)) % 27.48/27.66 f1(Y, Y) -> true__ % 27.48/27.66 f1(apply(apply(apply(n, apply(b, apply(b, combinator))), X2), X1), apply(apply(X1, X2), X1)) -> false__ % 27.48/27.66 f1(apply(apply(apply(n, apply(b, apply(n, b))), X2), combinator), apply(apply(combinator, X2), combinator)) -> false__ % 27.48/27.66 f1(apply(apply(apply(n, b), X1), combinator), apply(X1, combinator)) -> false__ % 27.48/27.66 f1(apply(apply(apply(n, b), apply(apply(b, X0), X1)), combinator), apply(X0, apply(X1, combinator))) -> false__ % 27.48/27.66 f1(apply(apply(apply(n, b), apply(apply(n, b), X0)), combinator), apply(combinator, apply(X0, combinator))) -> false__ % 27.48/27.66 f1(apply(combinator, Y), Y) -> false__ % 27.48/27.66 f1(apply(combinator, apply(apply(apply(X0, combinator), X2), combinator)), apply(apply(apply(n, X0), X2), combinator)) -> false__ % 27.48/27.66 f1(apply(combinator, apply(apply(apply(n, b), Y0), combinator)), apply(combinator, apply(Y0, combinator))) -> false__ % 27.48/27.66 f1(apply(combinator, apply(combinator, apply(X0, combinator))), apply(apply(apply(n, b), X0), combinator)) -> false__ % 27.48/27.66 true__ -> false__ % 27.48/27.66 with the LPO induced by % 27.48/27.66 combinator > f1 > apply > n > b > true__ > false__ % 27.48/27.66 % 27.48/27.66 % SZS output end Proof % 27.48/27.66 %------------------------------------------------------------------------------