%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : COL022-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n024.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 00:36:53 EDT 2022 % Result : Unsatisfiable 15.30s 15.44s % Output : Proof 15.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : COL022-1 : TPTP v8.1.0. Released v1.0.0. % 0.03/0.13 % Command : moca.sh %s % 0.12/0.34 % Computer : n024.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Tue May 31 12:11:06 EDT 2022 % 0.12/0.34 % CPUTime : % 15.30/15.44 % SZS status Unsatisfiable % 15.30/15.44 % SZS output start Proof % 15.30/15.44 The input problem is unsatisfiable because % 15.30/15.44 % 15.30/15.44 [1] the following set of Horn clauses is unsatisfiable: % 15.30/15.44 % 15.30/15.44 apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)) % 15.30/15.44 apply(m, X) = apply(X, X) % 15.30/15.44 apply(apply(o, X), Y) = apply(Y, apply(X, Y)) % 15.30/15.44 Y = apply(combinator, Y) ==> \bottom % 15.30/15.44 % 15.30/15.44 This holds because % 15.30/15.44 % 15.30/15.44 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 15.30/15.44 % 15.30/15.44 E: % 15.30/15.44 apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)) % 15.30/15.44 apply(apply(o, X), Y) = apply(Y, apply(X, Y)) % 15.30/15.44 apply(m, X) = apply(X, X) % 15.30/15.44 f1(Y, Y) = true__ % 15.30/15.44 f1(apply(combinator, Y), Y) = false__ % 15.30/15.44 G: % 15.30/15.44 true__ = false__ % 15.30/15.44 % 15.30/15.44 This holds because % 15.30/15.44 % 15.30/15.44 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 15.30/15.44 % 15.30/15.44 apply(Y0, apply(X0, apply(X1, Y0))) = apply(apply(o, apply(apply(b, X0), X1)), Y0) % 15.30/15.44 apply(Y0, apply(X0, apply(apply(b, X0), Y0))) = apply(apply(o, apply(m, apply(b, X0))), Y0) % 15.30/15.44 apply(Y0, apply(Y0, Y0)) = apply(apply(o, m), Y0) % 15.30/15.44 apply(Y0, apply(Y0, apply(X0, Y0))) = apply(apply(o, apply(o, X0)), Y0) % 15.30/15.44 apply(Y0, apply(Y0, apply(Y0, Y0))) = apply(apply(o, apply(o, m)), Y0) % 15.30/15.44 apply(Y0, apply(Y0, apply(Y0, apply(X0, Y0)))) = apply(apply(o, apply(o, apply(o, X0))), Y0) % 15.30/15.44 apply(Y0, apply(Y0, apply(Y0, apply(Y0, Y0)))) = apply(apply(o, apply(o, apply(o, m))), Y0) % 15.30/15.44 apply(Y0, apply(Y0, apply(Y0, apply(o, Y0)))) = apply(apply(o, apply(o, apply(m, o))), Y0) % 15.30/15.44 apply(Y0, apply(Y1, apply(Y0, Y0))) = apply(apply(o, apply(apply(b, Y1), m)), Y0) % 15.30/15.44 apply(Y0, apply(apply(Y0, Y0), apply(m, Y0))) = apply(apply(o, apply(apply(b, m), m)), Y0) % 15.30/15.44 apply(Y0, apply(apply(Y2, Y0), apply(Y2, Y0))) = apply(apply(o, apply(apply(b, m), Y2)), Y0) % 15.30/15.44 apply(Y0, apply(b, apply(X0, Y0))) = apply(apply(o, apply(apply(m, b), X0)), Y0) % 15.30/15.44 apply(Y0, apply(b, apply(Y0, Y0))) = apply(apply(o, apply(apply(m, b), m)), Y0) % 15.30/15.44 apply(Y0, apply(b, apply(apply(m, b), Y0))) = apply(apply(o, apply(m, apply(m, b))), Y0) % 15.30/15.44 apply(Y0, apply(m, apply(o, apply(b, Y0)))) = apply(m, apply(apply(m, o), apply(b, Y0))) % 15.30/15.44 apply(apply(X1, Y1), apply(apply(o, X1), Y1)) = apply(apply(o, Y1), apply(X1, Y1)) % 15.30/15.44 apply(apply(Y1, Y1), apply(apply(o, m), Y1)) = apply(apply(m, Y1), apply(Y1, apply(Y1, Y1))) % 15.30/15.44 apply(apply(Y1, Y1), apply(apply(o, m), Y1)) = apply(apply(o, Y1), apply(m, Y1)) % 15.30/15.44 apply(apply(m, o), Y1) = apply(Y1, apply(o, Y1)) % 15.30/15.44 apply(apply(o, X), Y) = apply(Y, apply(X, Y)) % 15.30/15.44 apply(apply(o, apply(m, o)), Y1) = apply(Y1, apply(Y1, apply(o, Y1))) % 15.30/15.44 apply(m, X) = apply(X, X) % 15.30/15.44 apply(m, apply(apply(b, Y0), Y1)) = apply(Y0, apply(Y1, apply(apply(b, Y0), Y1))) % 15.30/15.44 apply(Y0, apply(apply(o, apply(b, Y0)), Y1)) -> apply(m, apply(apply(b, Y0), Y1)) % 15.30/15.44 apply(Y0, apply(apply(o, m), apply(b, Y0))) -> apply(m, apply(m, apply(b, Y0))) % 15.30/15.44 apply(apply(Y1, apply(o, Y1)), apply(apply(o, apply(m, o)), Y1)) -> apply(m, apply(o, Y1)) % 15.30/15.44 apply(apply(apply(apply(m, o), b), Y1), Y2) -> apply(apply(o, b), apply(Y1, Y2)) % 15.30/15.44 apply(apply(apply(apply(o, X1), b), Y1), Y2) -> apply(apply(X1, b), apply(Y1, Y2)) % 15.30/15.44 apply(apply(apply(b, X), Y), Z) -> apply(X, apply(Y, Z)) % 15.30/15.44 apply(apply(apply(m, b), Y1), Y2) -> apply(b, apply(Y1, Y2)) % 15.30/15.44 apply(apply(apply(m, o), Y1), apply(Y1, apply(Y1, apply(o, Y1)))) -> apply(m, apply(o, Y1)) % 15.30/15.44 apply(apply(apply(m, o), apply(b, Y0)), Y2) -> apply(Y0, apply(apply(o, apply(b, Y0)), Y2)) % 15.30/15.44 apply(apply(apply(m, o), apply(m, b)), Y1) -> apply(b, apply(apply(o, apply(m, b)), Y1)) % 15.30/15.44 apply(apply(apply(o, X1), apply(b, Y0)), Y2) -> apply(Y0, apply(apply(X1, apply(b, Y0)), Y2)) % 15.30/15.44 apply(apply(apply(o, X1), apply(m, b)), Y1) -> apply(b, apply(apply(X1, apply(m, b)), Y1)) % 15.30/15.44 apply(apply(m, apply(b, Y0)), Y2) -> apply(Y0, apply(apply(b, Y0), Y2)) % 15.30/15.44 apply(apply(m, apply(m, b)), Y1) -> apply(b, apply(apply(m, b), Y1)) % 15.30/15.44 apply(apply(o, Y1), apply(Y1, Y1)) -> apply(apply(m, Y1), apply(Y1, apply(Y1, Y1))) % 15.30/15.44 apply(apply(o, Y1), apply(apply(m, o), Y1)) -> apply(m, apply(o, Y1)) % 15.30/15.44 apply(apply(o, apply(o, o)), m) -> apply(apply(o, apply(o, m)), apply(apply(o, o), m)) % 15.30/15.44 apply(b, apply(Y0, apply(apply(m, b), Y0))) -> apply(m, apply(apply(m, b), Y0)) % 15.30/15.44 apply(b, apply(apply(o, m), apply(m, b))) -> apply(m, apply(m, apply(m, b))) % 15.30/15.44 f1(Y, Y) -> true__ % 15.30/15.44 f1(apply(apply(m, o), combinator), apply(o, combinator)) -> false__ % 15.30/15.44 f1(apply(apply(o, X1), combinator), apply(X1, combinator)) -> false__ % 15.30/15.44 f1(apply(combinator, Y), Y) -> false__ % 15.30/15.44 f1(apply(m, apply(apply(b, combinator), X1)), apply(X1, apply(apply(b, combinator), X1))) -> false__ % 15.30/15.44 f1(apply(m, apply(apply(b, combinator), Y0)), apply(apply(o, apply(b, combinator)), Y0)) -> false__ % 15.30/15.44 f1(apply(m, apply(m, apply(b, combinator))), apply(apply(o, m), apply(b, combinator))) -> false__ % 15.30/15.44 f1(apply(m, combinator), combinator) -> false__ % 15.30/15.44 false__ -> true__ % 15.30/15.44 with the LPO induced by % 15.30/15.44 b > apply > o > m > combinator > f1 > false__ > true__ % 15.30/15.44 % 15.30/15.44 % SZS output end Proof % 15.30/15.44 %------------------------------------------------------------------------------