%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SYN333-1 : TPTP v8.1.0. Released v1.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n023.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 : Thu Jul 21 09:15:24 EDT 2022 % Result : Unsatisfiable 0.19s 0.39s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SYN333-1 : TPTP v8.1.0. Released v1.2.0. % 0.07/0.13 % Command : moca.sh %s % 0.12/0.34 % Computer : n023.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 Jul 12 05:11:24 EDT 2022 % 0.12/0.34 % CPUTime : % 0.19/0.39 % SZS status Unsatisfiable % 0.19/0.39 % SZS output start Proof % 0.19/0.39 The input problem is unsatisfiable because % 0.19/0.39 % 0.19/0.39 [1] the following set of Horn clauses is unsatisfiable: % 0.19/0.39 % 0.19/0.39 f(X, Y) % 0.19/0.39 f(Y, z(X, Y)) & f(z(X, Y), z(X, Y)) ==> g(X, Y) % 0.19/0.39 f(Y, z(X, Y)) & f(z(X, Y), z(X, Y)) & g(X, z(X, Y)) & g(z(X, Y), z(X, Y)) ==> \bottom % 0.19/0.39 % 0.19/0.39 This holds because % 0.19/0.39 % 0.19/0.39 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.19/0.39 % 0.19/0.39 E: % 0.19/0.39 f(X, Y) = true__ % 0.19/0.39 f1(true__, X, Y) = g(X, Y) % 0.19/0.39 f2(f(z(X, Y), z(X, Y)), Y, X) = true__ % 0.19/0.39 f2(true__, Y, X) = f1(f(Y, z(X, Y)), X, Y) % 0.19/0.39 f3(true__) = false__ % 0.19/0.39 f4(true__, Y, X) = f3(f(Y, z(X, Y))) % 0.19/0.39 f5(true__, X, Y) = f4(f(z(X, Y), z(X, Y)), Y, X) % 0.19/0.39 f6(g(z(X, Y), z(X, Y)), X, Y) = true__ % 0.19/0.39 f6(true__, X, Y) = f5(g(X, z(X, Y)), X, Y) % 0.19/0.39 G: % 0.19/0.39 true__ = false__ % 0.19/0.39 % 0.19/0.39 This holds because % 0.19/0.39 % 0.19/0.39 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.19/0.39 % 0.19/0.39 % 0.19/0.39 f(X, Y) -> true__ % 0.19/0.39 f1(true__, Y0, Y1) -> true__ % 0.19/0.39 f2(f(z(X, Y), z(X, Y)), Y, X) -> true__ % 0.19/0.39 f2(true__, Y, X) -> f1(f(Y, z(X, Y)), X, Y) % 0.19/0.39 f3(true__) -> false__ % 0.19/0.39 f4(true__, Y, X) -> f3(f(Y, z(X, Y))) % 0.19/0.39 f5(true__, X, Y) -> f4(f(z(X, Y), z(X, Y)), Y, X) % 0.19/0.39 f6(f1(true__, z(Y0, Y1), z(Y0, Y1)), Y0, Y1) -> true__ % 0.19/0.39 f6(g(z(X, Y), z(X, Y)), X, Y) -> true__ % 0.19/0.39 f6(true__, X, Y) -> f5(g(X, z(X, Y)), X, Y) % 0.19/0.39 false__ -> true__ % 0.19/0.39 g(X, Y) -> f1(true__, X, Y) % 0.19/0.39 with the LPO induced by % 0.19/0.39 f2 > f6 > f5 > f4 > f > f3 > g > z > f1 > false__ > true__ % 0.19/0.39 % 0.19/0.39 % SZS output end Proof % 0.19/0.39 %------------------------------------------------------------------------------