%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : COL008-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n032.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 00:36:47 EDT 2022 % Result : Unsatisfiable 0.53s 0.77s % Output : Proof 0.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : COL008-1 : TPTP v8.1.0. Released v1.0.0. % 0.00/0.11 % Command : moca.sh %s % 0.11/0.30 % Computer : n032.cluster.edu % 0.11/0.30 % Model : x86_64 x86_64 % 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.30 % Memory : 8042.1875MB % 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.31 % CPULimit : 300 % 0.11/0.31 % WCLimit : 600 % 0.11/0.31 % DateTime : Tue May 31 12:23:58 EDT 2022 % 0.11/0.31 % CPUTime : % 0.53/0.77 % SZS status Unsatisfiable % 0.53/0.77 % SZS output start Proof % 0.53/0.77 The input problem is unsatisfiable because % 0.53/0.77 % 0.53/0.77 [1] the following set of Horn clauses is unsatisfiable: % 0.53/0.77 % 0.53/0.77 apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)) % 0.53/0.77 apply(m, X) = apply(X, X) % 0.53/0.77 Y = apply(combinator, Y) ==> \bottom % 0.53/0.77 % 0.53/0.77 This holds because % 0.53/0.77 % 0.53/0.77 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.53/0.77 % 0.53/0.77 E: % 0.53/0.77 apply(apply(apply(b, X), Y), Z) = apply(X, apply(Y, Z)) % 0.53/0.77 apply(m, X) = apply(X, X) % 0.53/0.77 f1(Y, Y) = true__ % 0.53/0.77 f1(apply(combinator, Y), Y) = false__ % 0.53/0.77 G: % 0.53/0.77 true__ = false__ % 0.53/0.77 % 0.53/0.77 This holds because % 0.53/0.77 % 0.53/0.77 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.53/0.77 % 0.53/0.77 apply(X0, apply(X1, apply(Y1, apply(apply(b, apply(apply(b, X0), X1)), Y1)))) = apply(m, apply(apply(b, apply(apply(b, X0), X1)), Y1)) % 0.53/0.77 apply(Y0, apply(X0, apply(X1, apply(apply(b, Y0), apply(apply(b, X0), X1))))) = apply(m, apply(apply(b, Y0), apply(apply(b, X0), X1))) % 0.53/0.77 apply(apply(m, apply(apply(b, apply(b, Y0)), X1)), Y2) = apply(Y0, apply(apply(X1, apply(apply(b, apply(b, Y0)), X1)), Y2)) % 0.53/0.77 apply(m, X) = apply(X, X) % 0.53/0.77 apply(m, apply(apply(b, Y0), Y1)) = apply(Y0, apply(Y1, apply(apply(b, Y0), Y1))) % 0.53/0.77 apply(Y0, apply(apply(b, Y0), apply(m, apply(b, Y0)))) -> apply(m, apply(m, apply(b, Y0))) % 0.53/0.77 apply(Y0, apply(b, apply(X0, apply(apply(b, Y0), apply(apply(m, b), X0))))) -> apply(m, apply(apply(b, Y0), apply(apply(m, b), X0))) % 0.53/0.77 apply(apply(apply(b, X), Y), Z) -> apply(X, apply(Y, Z)) % 0.53/0.77 apply(apply(apply(m, apply(apply(m, b), X1)), Y1), Y2) -> apply(apply(X1, apply(apply(m, b), X1)), apply(Y1, Y2)) % 0.53/0.77 apply(apply(apply(m, b), Y1), Y2) -> apply(b, apply(Y1, Y2)) % 0.53/0.77 apply(apply(m, apply(b, Y0)), Y2) -> apply(Y0, apply(apply(b, Y0), Y2)) % 0.53/0.77 apply(apply(m, apply(m, b)), Y1) -> apply(b, apply(apply(m, b), Y1)) % 0.53/0.77 apply(b, apply(X0, apply(X1, apply(apply(m, b), apply(apply(b, X0), X1))))) -> apply(m, apply(apply(m, b), apply(apply(b, X0), X1))) % 0.53/0.77 apply(b, apply(X0, apply(Y1, apply(apply(b, apply(apply(m, b), X0)), Y1)))) -> apply(m, apply(apply(b, apply(apply(m, b), X0)), Y1)) % 0.53/0.77 apply(b, apply(Y0, apply(apply(m, b), Y0))) -> apply(m, apply(apply(m, b), Y0)) % 0.53/0.77 apply(b, apply(apply(m, b), apply(m, apply(m, b)))) -> apply(m, apply(m, apply(m, b))) % 0.53/0.77 f1(Y, Y) -> true__ % 0.53/0.77 f1(apply(combinator, Y), Y) -> false__ % 0.53/0.77 f1(apply(m, apply(apply(b, combinator), X1)), apply(X1, apply(apply(b, combinator), X1))) -> false__ % 0.53/0.77 f1(apply(m, apply(m, apply(b, combinator))), apply(apply(b, combinator), apply(m, apply(b, combinator)))) -> false__ % 0.53/0.77 true__ -> false__ % 0.53/0.77 with the LPO induced by % 0.53/0.77 b > f1 > apply > m > combinator > true__ > false__ % 0.53/0.77 % 0.53/0.77 % SZS output end Proof % 0.53/0.77 %------------------------------------------------------------------------------