%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : COL048-1 : 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 00:37:10 EDT 2022 % Result : Unsatisfiable 9.46s 9.58s % Output : Proof 9.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : COL048-1 : TPTP v8.1.0. Released v1.0.0. % 0.11/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n017.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 03:57:25 EDT 2022 % 0.12/0.33 % CPUTime : % 9.46/9.58 % SZS status Unsatisfiable % 9.46/9.58 % SZS output start Proof % 9.46/9.58 The input problem is unsatisfiable because % 9.46/9.58 % 9.46/9.58 [1] the following set of Horn clauses is unsatisfiable: % 9.46/9.58 % 9.46/9.58 apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)) % 9.46/9.58 apply(apply(w, X), Y) = apply(apply(X, Y), Y) % 9.46/9.58 apply(m, X) = apply(X, X) % 9.46/9.58 Y = apply(combinator, Y) ==> \bottom % 9.46/9.58 % 9.46/9.58 This holds because % 9.46/9.58 % 9.46/9.58 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 9.46/9.58 % 9.46/9.58 E: % 9.46/9.58 apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)) % 9.46/9.58 apply(apply(w, X), Y) = apply(apply(X, Y), Y) % 9.46/9.58 apply(m, X) = apply(X, X) % 9.46/9.58 f1(Y, Y) = true__ % 9.46/9.58 f1(apply(combinator, Y), Y) = false__ % 9.46/9.58 G: % 9.46/9.58 true__ = false__ % 9.46/9.58 % 9.46/9.58 This holds because % 9.46/9.58 % 9.46/9.58 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 9.46/9.58 % 9.46/9.58 apply(apply(X0, apply(X1, Y1)), Y1) = apply(apply(w, apply(apply(b, X0), X1)), Y1) % 9.46/9.58 apply(apply(X0, apply(X1, apply(apply(b, X0), X1))), apply(apply(b, X0), X1)) = apply(apply(m, w), apply(apply(b, X0), X1)) % 9.46/9.58 apply(apply(X0, apply(Y1, Y1)), Y1) = apply(apply(w, apply(w, apply(b, X0))), Y1) % 9.46/9.58 apply(apply(X0, apply(Y1, Y1)), apply(Y1, Y1)) = apply(apply(w, X0), apply(m, Y1)) % 9.46/9.58 apply(apply(X0, apply(Y1, Y1)), apply(Y1, Y1)) = apply(apply(w, apply(b, apply(w, X0))), Y1) % 9.46/9.58 apply(apply(Y1, Y1), Y1) = apply(apply(m, w), Y1) % 9.46/9.58 apply(apply(Y1, Y1), Y1) = apply(apply(w, m), Y1) % 9.46/9.58 apply(apply(Y1, Y1), apply(Y1, Y1)) = apply(apply(w, apply(b, m)), Y1) % 9.46/9.58 apply(apply(Y1, Y1), apply(Y1, Y1)) = apply(m, apply(m, Y1)) % 9.46/9.58 apply(apply(apply(X0, Y1), Y1), Y1) = apply(apply(w, apply(w, X0)), Y1) % 9.46/9.58 apply(apply(apply(Y1, Y1), Y1), Y1) = apply(apply(w, apply(m, w)), Y1) % 9.46/9.58 apply(apply(apply(Y1, Y1), Y1), Y1) = apply(apply(w, apply(w, m)), Y1) % 9.46/9.58 apply(apply(apply(apply(X0, Y1), Y1), Y1), Y1) = apply(apply(w, apply(w, apply(w, X0))), Y1) % 9.46/9.58 apply(apply(apply(apply(m, Y1), Y1), Y1), Y1) = apply(apply(w, apply(w, apply(m, w))), Y1) % 9.46/9.58 apply(apply(apply(m, Y1), Y1), Y1) = apply(apply(w, apply(m, w)), Y1) % 9.46/9.58 apply(apply(apply(m, Y1), Y1), Y1) = apply(apply(w, apply(w, Y1)), Y1) % 9.46/9.58 apply(apply(apply(w, apply(b, w)), X1), Y1) = apply(apply(apply(X1, X1), Y1), Y1) % 9.46/9.58 apply(apply(b, apply(X0, Y1)), Y1) = apply(apply(w, apply(apply(m, b), X0)), Y1) % 9.46/9.58 apply(apply(m, apply(Y1, Y1)), apply(Y1, Y1)) = apply(apply(m, w), apply(m, Y1)) % 9.46/9.58 apply(apply(m, w), Y1) = apply(apply(m, Y1), Y1) % 9.46/9.58 apply(apply(m, w), apply(b, Y0)) = apply(Y0, apply(m, apply(b, Y0))) % 9.46/9.58 apply(apply(w, X), Y) = apply(apply(X, Y), Y) % 9.46/9.58 apply(apply(w, apply(b, Y0)), Y2) = apply(Y0, apply(Y2, Y2)) % 9.46/9.58 apply(apply(w, apply(m, X1)), Y1) = apply(apply(apply(X1, X1), Y1), Y1) % 9.46/9.58 apply(apply(w, apply(m, b)), Y1) = apply(b, apply(Y1, Y1)) % 9.46/9.58 apply(apply(w, apply(m, w)), Y1) = apply(apply(w, apply(Y1, Y1)), Y1) % 9.46/9.58 apply(apply(w, apply(m, w)), Y1) = apply(apply(w, apply(m, Y1)), Y1) % 9.46/9.58 apply(apply(w, apply(w, X0)), Y1) = apply(apply(w, apply(X0, Y1)), Y1) % 9.46/9.58 apply(apply(w, apply(w, apply(w, m))), Y1) = apply(apply(w, apply(w, apply(Y1, Y1))), Y1) % 9.46/9.58 apply(apply(w, apply(w, m)), Y1) = apply(apply(w, apply(Y1, Y1)), Y1) % 9.46/9.58 apply(m, X) = apply(X, X) % 9.46/9.58 apply(m, apply(apply(b, Y0), Y1)) = apply(Y0, apply(Y1, apply(apply(b, Y0), Y1))) % 9.46/9.58 apply(m, apply(apply(w, b), Y0)) = apply(Y0, apply(Y0, apply(apply(w, b), Y0))) % 9.46/9.58 apply(apply(apply(b, X), Y), Z) -> apply(X, apply(Y, Z)) % 9.46/9.58 apply(apply(apply(m, b), Y1), Y2) -> apply(b, apply(Y1, Y2)) % 9.46/9.58 apply(apply(apply(w, b), Y1), Y2) -> apply(Y1, apply(Y1, Y2)) % 9.46/9.58 apply(apply(m, apply(b, Y0)), Y2) -> apply(Y0, apply(apply(b, Y0), Y2)) % 9.46/9.58 apply(apply(m, apply(m, b)), Y1) -> apply(b, apply(apply(m, b), Y1)) % 9.46/9.58 apply(apply(m, apply(w, b)), Y1) -> apply(apply(w, b), apply(apply(w, b), Y1)) % 9.46/9.58 apply(apply(m, w), apply(w, m)) -> apply(m, apply(w, m)) % 9.46/9.58 apply(apply(w, Y1), Y1) -> apply(apply(m, Y1), Y1) % 9.46/9.58 apply(apply(w, Y1), Y1) -> apply(apply(m, w), Y1) % 9.46/9.58 apply(apply(w, apply(b, Y0)), Y1) -> apply(Y0, apply(m, Y1)) % 9.46/9.58 apply(apply(w, apply(m, b)), Y0) -> apply(b, apply(m, Y0)) % 9.46/9.58 apply(apply(w, apply(m, w)), apply(w, m)) -> apply(apply(m, w), apply(w, m)) % 9.46/9.58 apply(apply(w, apply(w, Y1)), Y1) -> apply(apply(w, apply(m, w)), Y1) % 9.46/9.58 apply(apply(w, apply(w, m)), Y1) -> apply(apply(w, apply(m, w)), Y1) % 9.46/9.58 apply(apply(w, m), Y0) -> apply(apply(m, w), Y0) % 9.46/9.58 apply(b, apply(Y0, apply(apply(m, b), Y0))) -> apply(m, apply(apply(m, b), Y0)) % 9.46/9.58 f1(Y, Y) -> true__ % 9.46/9.58 f1(apply(apply(w, apply(b, combinator)), X1), apply(X1, X1)) -> false__ % 9.46/9.58 f1(apply(combinator, Y), Y) -> false__ % 9.46/9.58 f1(apply(m, combinator), combinator) -> false__ % 9.46/9.58 true__ -> false__ % 9.46/9.58 with the LPO induced by % 9.46/9.58 w > combinator > b > m > apply > f1 > true__ > false__ % 9.46/9.58 % 9.46/9.58 % SZS output end Proof % 9.46/9.58 %------------------------------------------------------------------------------