%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : COL010-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n022.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 00:36:48 EDT 2022 % Result : Unsatisfiable 1.89s 2.08s % Output : Proof 1.89s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : COL010-1 : TPTP v8.1.0. Released v1.0.0. % 0.06/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n022.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 12:04:07 EDT 2022 % 0.12/0.33 % CPUTime : % 1.89/2.08 % SZS status Unsatisfiable % 1.89/2.08 % SZS output start Proof % 1.89/2.08 The input problem is unsatisfiable because % 1.89/2.08 % 1.89/2.08 [1] the following set of Horn clauses is unsatisfiable: % 1.89/2.08 % 1.89/2.08 apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)) % 1.89/2.08 apply(apply(apply(s2, X), Y), Z) = apply(apply(X, Z), apply(Y, Y)) % 1.89/2.08 Y = apply(combinator, Y) ==> \bottom % 1.89/2.08 % 1.89/2.08 This holds because % 1.89/2.08 % 1.89/2.08 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 1.89/2.08 % 1.89/2.08 E: % 1.89/2.08 apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)) % 1.89/2.08 apply(apply(apply(s2, X), Y), Z) = apply(apply(X, Z), apply(Y, Y)) % 1.89/2.08 f1(Y, Y) = true__ % 1.89/2.08 f1(apply(combinator, Y), Y) = false__ % 1.89/2.08 G: % 1.89/2.08 true__ = false__ % 1.89/2.08 % 1.89/2.08 This holds because % 1.89/2.08 % 1.89/2.08 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 1.89/2.08 % 1.89/2.08 apply(X0, apply(X1, apply(Y1, apply(Y2, Y2)))) = apply(apply(apply(s2, apply(b, apply(apply(b, X0), X1))), Y2), Y1) % 1.89/2.08 apply(X0, apply(Y1, apply(Y2, Y2))) = apply(apply(apply(s2, apply(b, X0)), Y2), Y1) % 1.89/2.08 apply(Y0, apply(X0, apply(X1, apply(Y2, Y2)))) = apply(apply(apply(s2, apply(b, Y0)), Y2), apply(apply(b, X0), X1)) % 1.89/2.08 apply(Y0, apply(Y1, apply(X0, apply(X1, apply(apply(b, X0), X1))))) = apply(apply(apply(s2, apply(b, Y0)), apply(apply(b, X0), X1)), Y1) % 1.89/2.08 apply(Y0, apply(apply(X0, apply(Y2, Y2)), apply(X1, X1))) = apply(apply(apply(s2, apply(b, Y0)), Y2), apply(apply(s2, X0), X1)) % 1.89/2.08 apply(Y0, apply(apply(apply(s2, X0), Y2), X1)) = apply(apply(apply(s2, apply(b, Y0)), Y2), apply(X0, X1)) % 1.89/2.08 apply(apply(X0, apply(X1, Y1)), apply(Y2, Y2)) = apply(apply(apply(s2, apply(apply(b, X0), X1)), Y2), Y1) % 1.89/2.08 apply(apply(X0, apply(Y1, apply(Y2, Y2))), apply(X1, X1)) = apply(apply(apply(s2, apply(b, apply(apply(s2, X0), X1))), Y2), Y1) % 1.89/2.08 apply(apply(X0, apply(Y2, Y2)), apply(Y1, Y1)) = apply(apply(apply(s2, apply(s2, X0)), Y2), Y1) % 1.89/2.08 apply(apply(Y0, Y1), apply(X0, apply(X1, apply(apply(b, X0), X1)))) = apply(apply(apply(s2, Y0), apply(apply(b, X0), X1)), Y1) % 1.89/2.08 apply(apply(apply(X0, Y1), apply(X1, X1)), apply(Y2, Y2)) = apply(apply(apply(s2, apply(apply(s2, X0), X1)), Y2), Y1) % 1.89/2.08 apply(apply(apply(apply(apply(s2, apply(b, s2)), X2), X1), Y1), Y2) = apply(apply(apply(X1, apply(X2, X2)), Y2), apply(Y1, Y1)) % 1.89/2.08 apply(apply(apply(apply(s2, X0), X2), X1), apply(Y2, Y2)) = apply(apply(apply(s2, apply(X0, X1)), Y2), apply(X2, X2)) % 1.89/2.08 apply(apply(apply(apply(s2, apply(b, apply(b, Y0))), X2), X1), Y2) = apply(Y0, apply(apply(X1, apply(X2, X2)), Y2)) % 1.89/2.08 apply(apply(apply(apply(s2, apply(b, apply(s2, Y0))), X2), X1), Y2) = apply(apply(Y0, Y2), apply(apply(X1, apply(X2, X2)), apply(X1, apply(X2, X2)))) % 1.89/2.08 apply(apply(apply(apply(s2, s2), X2), Y0), Y2) = apply(apply(Y0, Y2), apply(apply(X2, X2), apply(X2, X2))) % 1.89/2.08 apply(apply(apply(s2, X), Y), Z) = apply(apply(X, Z), apply(Y, Y)) % 1.89/2.08 apply(apply(apply(s2, X0), apply(Y2, Y2)), X1) = apply(apply(apply(s2, apply(b, apply(X0, X1))), Y2), apply(Y2, Y2)) % 1.89/2.08 apply(apply(apply(apply(apply(s2, apply(b, b)), X2), X1), Y1), Y2) -> apply(apply(X1, apply(X2, X2)), apply(Y1, Y2)) % 1.89/2.08 apply(apply(apply(apply(s2, b), X2), Y0), Y2) -> apply(Y0, apply(apply(X2, X2), Y2)) % 1.89/2.08 apply(apply(apply(b, X), Y), Z) -> apply(X, apply(Y, Z)) % 1.89/2.08 f1(Y, Y) -> true__ % 1.89/2.08 f1(apply(apply(apply(s2, apply(b, combinator)), X2), X1), apply(X1, apply(X2, X2))) -> false__ % 1.89/2.08 f1(apply(combinator, Y), Y) -> false__ % 1.89/2.08 true__ -> false__ % 1.89/2.08 with the LPO induced by % 1.89/2.08 b > f1 > apply > s2 > combinator > true__ > false__ % 1.89/2.08 % 1.89/2.08 % SZS output end Proof % 1.89/2.08 %------------------------------------------------------------------------------