%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : COL029-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n018.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 00:36:56 EDT 2022 % Result : Unsatisfiable 0.19s 0.43s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : COL029-1 : TPTP v8.1.0. Released v1.0.0. % 0.12/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n018.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Tue May 31 15:28:58 EDT 2022 % 0.13/0.35 % CPUTime : % 0.19/0.43 % SZS status Unsatisfiable % 0.19/0.43 % SZS output start Proof % 0.19/0.43 The input problem is unsatisfiable because % 0.19/0.43 % 0.19/0.43 [1] the following set of Horn clauses is unsatisfiable: % 0.19/0.43 % 0.19/0.43 apply(apply(u, X), Y) = apply(Y, apply(apply(X, X), Y)) % 0.19/0.43 apply(Y, f(Y)) = apply(f(Y), apply(Y, f(Y))) ==> \bottom % 0.19/0.43 % 0.19/0.43 This holds because % 0.19/0.43 % 0.19/0.43 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.19/0.43 % 0.19/0.43 E: % 0.19/0.43 apply(apply(u, X), Y) = apply(Y, apply(apply(X, X), Y)) % 0.19/0.43 f1(apply(Y, f(Y)), Y) = true__ % 0.19/0.43 f1(apply(f(Y), apply(Y, f(Y))), Y) = false__ % 0.19/0.43 G: % 0.19/0.43 true__ = false__ % 0.19/0.43 % 0.19/0.43 This holds because % 0.19/0.43 % 0.19/0.43 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.19/0.43 % 0.19/0.43 apply(apply(apply(X1, X1), apply(Y1, Y1)), apply(apply(u, X1), apply(Y1, Y1))) = apply(apply(u, Y1), apply(apply(X1, X1), apply(Y1, Y1))) % 0.19/0.43 apply(apply(u, X), Y) = apply(Y, apply(apply(X, X), Y)) % 0.19/0.43 apply(Y0, apply(apply(apply(u, X1), apply(apply(u, u), apply(X1, X1))), Y0)) -> apply(apply(u, apply(apply(u, u), apply(X1, X1))), Y0) % 0.19/0.43 apply(apply(apply(apply(apply(X1, X1), u), apply(apply(X1, X1), u)), apply(Y1, Y1)), apply(apply(apply(u, X1), u), apply(Y1, Y1))) -> apply(apply(u, Y1), apply(apply(apply(apply(X1, X1), u), apply(apply(X1, X1), u)), apply(Y1, Y1))) % 0.19/0.43 apply(apply(apply(u, X0), apply(X0, X0)), apply(apply(u, X0), apply(apply(X0, X0), apply(X0, X0)))) -> apply(apply(u, apply(X0, X0)), apply(apply(u, X0), apply(X0, X0))) % 0.19/0.43 apply(apply(apply(u, X1), apply(X1, X1)), apply(apply(u, X1), apply(apply(X1, X1), apply(X1, X1)))) -> apply(apply(u, apply(X1, X1)), apply(apply(X1, X1), apply(apply(X1, X1), apply(X1, X1)))) % 0.19/0.43 apply(apply(u, apply(u, u)), apply(apply(u, u), apply(u, u))) -> apply(apply(u, u), apply(u, u)) % 0.19/0.43 f1(apply(Y, f(Y)), Y) -> true__ % 0.19/0.43 f1(apply(apply(apply(u, X1), u), f(apply(apply(apply(X1, X1), u), apply(apply(X1, X1), u)))), apply(apply(apply(X1, X1), u), apply(apply(X1, X1), u))) -> false__ % 0.19/0.43 f1(apply(apply(u, X1), f(apply(X1, X1))), apply(X1, X1)) -> false__ % 0.19/0.43 f1(apply(f(Y), apply(Y, f(Y))), Y) -> false__ % 0.19/0.43 false__ -> true__ % 0.19/0.43 with the LPO induced by % 0.19/0.43 u > f > apply > f1 > false__ > true__ % 0.19/0.43 % 0.19/0.43 % SZS output end Proof % 0.19/0.43 %------------------------------------------------------------------------------