%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : LDA003-1 : TPTP v8.1.0. Released v1.0.0. % 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 : Sun Jul 17 16:45:02 EDT 2022 % Result : Unsatisfiable 0.20s 0.40s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : LDA003-1 : TPTP v8.1.0. Released v1.0.0. % 0.06/0.13 % 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 : Mon May 30 04:29:57 EDT 2022 % 0.12/0.34 % CPUTime : % 0.20/0.40 % SZS status Unsatisfiable % 0.20/0.40 % SZS output start Proof % 0.20/0.40 The input problem is unsatisfiable because % 0.20/0.40 % 0.20/0.40 [1] the following set of Horn clauses is unsatisfiable: % 0.20/0.40 % 0.20/0.40 f(X, f(Y, Z)) = f(f(X, Y), f(X, Z)) % 0.20/0.40 left(X, f(X, Y)) % 0.20/0.40 left(X, Y) & left(Y, Z) ==> left(X, Z) % 0.20/0.40 n2 = f(n1, n1) % 0.20/0.40 n3 = f(n2, n1) % 0.20/0.40 u = f(n2, n2) % 0.20/0.40 left(n3, u) ==> \bottom % 0.20/0.40 % 0.20/0.40 This holds because % 0.20/0.40 % 0.20/0.40 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.20/0.40 % 0.20/0.40 E: % 0.20/0.40 f(X, f(Y, Z)) = f(f(X, Y), f(X, Z)) % 0.20/0.40 f1(true__, X, Z) = left(X, Z) % 0.20/0.40 f2(left(Y, Z), X, Y, Z) = true__ % 0.20/0.40 f2(true__, X, Y, Z) = f1(left(X, Y), X, Z) % 0.20/0.40 f3(left(n3, u)) = true__ % 0.20/0.40 f3(true__) = false__ % 0.20/0.40 left(X, f(X, Y)) = true__ % 0.20/0.40 n2 = f(n1, n1) % 0.20/0.40 n3 = f(n2, n1) % 0.20/0.40 u = f(n2, n2) % 0.20/0.40 G: % 0.20/0.40 true__ = false__ % 0.20/0.40 % 0.20/0.40 This holds because % 0.20/0.40 % 0.20/0.40 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.20/0.40 % 0.20/0.40 % 0.20/0.40 f(f(X, Y), f(X, Z)) -> f(X, f(Y, Z)) % 0.20/0.40 f(f(X0, f(X1, X2)), f(f(X0, X1), Y2)) -> f(f(X0, X1), f(f(X0, X2), Y2)) % 0.20/0.40 f(f(f(X0, X1), Y1), f(X0, f(X1, X2))) -> f(f(X0, X1), f(Y1, f(X0, X2))) % 0.20/0.40 f1(f1(true__, Y2, Y0), Y2, f(Y0, X1)) -> true__ % 0.20/0.40 f1(f1(true__, Y2, f(X0, X1)), Y2, f(X0, f(X1, X2))) -> true__ % 0.20/0.40 f1(true__, Y0, f(Y0, X1)) -> true__ % 0.20/0.40 f1(true__, Y0, f(f(Y0, X1), Y2)) -> true__ % 0.20/0.40 f1(true__, f(X0, X1), f(X0, f(X1, X2))) -> true__ % 0.20/0.40 f1(true__, f(X0, X1), f(f(X0, f(X1, X2)), Y2)) -> true__ % 0.20/0.40 f1(true__, f(X0, f(X1, X2)), f(f(X0, X1), f(f(X0, X2), X3))) -> true__ % 0.20/0.40 f1(true__, f(Y0, f(X0, X1)), f(Y0, f(X0, f(X1, X2)))) -> true__ % 0.20/0.40 f1(true__, f(f(Y1, X1), Y1), f(Y1, f(X1, Y2))) -> true__ % 0.20/0.40 f2(f1(true__, Y0, Y1), Y2, Y0, Y1) -> true__ % 0.20/0.40 f2(left(Y, Z), X, Y, Z) -> true__ % 0.20/0.40 f2(true__, X, Y, Z) -> f1(left(X, Y), X, Z) % 0.20/0.40 f3(f1(true__, f(f(n1, n1), n1), f(n1, f(n1, n1)))) -> true__ % 0.20/0.40 f3(left(n3, u)) -> true__ % 0.20/0.40 f3(true__) -> false__ % 0.20/0.40 false__ -> true__ % 0.20/0.40 left(X, Z) -> f1(true__, X, Z) % 0.20/0.40 left(X, f(X, Y)) -> true__ % 0.20/0.40 n2 -> f(n1, n1) % 0.20/0.40 n3 -> f(n2, n1) % 0.20/0.40 u -> f(n2, n2) % 0.20/0.40 with the LPO induced by % 0.20/0.40 f3 > n3 > f2 > left > f1 > u > n2 > n1 > f > false__ > true__ % 0.20/0.40 % 0.20/0.40 % SZS output end Proof % 0.20/0.40 %------------------------------------------------------------------------------