%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : LDA001-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n027.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 16:45:01 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 % 0.04/0.12 % Problem : LDA001-1 : TPTP v8.1.0. Released v1.0.0. % 0.04/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n027.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 : Mon May 30 02:22:16 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, f(Y, Z)) = f(f(X, Y), f(X, Z)) % 0.19/0.39 n2 = f(n1, n1) % 0.19/0.39 n3 = f(n2, n1) % 0.19/0.39 u = f(n2, n2) % 0.19/0.39 f(f(n3, n2), u) = f(f(u, u), u) ==> \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, f(Y, Z)) = f(f(X, Y), f(X, Z)) % 0.19/0.39 f1(f(f(n3, n2), u)) = true__ % 0.19/0.39 f1(f(f(u, u), u)) = false__ % 0.19/0.39 n2 = f(n1, n1) % 0.19/0.39 n3 = f(n2, n1) % 0.19/0.39 u = f(n2, n2) % 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 f(f(Y1, f(X1, Y2)), f(f(f(Y1, X1), Y1), Y3)) = f(f(f(Y1, X1), Y1), f(f(f(Y1, X1), Y2), Y3)) % 0.19/0.39 f(f(X, Y), f(X, Z)) -> f(X, f(Y, Z)) % 0.19/0.39 f(f(X0, f(X1, X2)), f(f(X0, X1), Y2)) -> f(f(X0, X1), f(f(X0, X2), Y2)) % 0.19/0.39 f(f(Y0, f(X0, f(X1, X2))), f(f(Y0, f(X0, X1)), Y3)) -> f(f(Y0, f(X0, X1)), f(f(Y0, f(X0, X2)), Y3)) % 0.19/0.39 f(f(f(X0, X1), Y1), f(X0, f(X1, X2))) -> f(f(X0, X1), f(Y1, f(X0, X2))) % 0.19/0.39 f(f(f(X0, X1), f(f(X0, X2), Y2)), f(f(X0, f(X1, X2)), Y3)) -> f(f(X0, f(X1, X2)), f(f(f(X0, X1), Y2), Y3)) % 0.19/0.39 f(f(f(X0, f(X1, X2)), Y1), f(f(X0, X1), f(f(X0, X2), X3))) -> f(f(X0, f(X1, X2)), f(Y1, f(f(X0, X1), X3))) % 0.19/0.39 f(f(f(Y0, f(X0, X1)), Y2), f(Y0, f(X0, f(X1, X2)))) -> f(f(Y0, f(X0, X1)), f(Y2, f(Y0, f(X0, X2)))) % 0.19/0.39 f(f(f(f(Y1, X1), Y1), Y2), f(Y1, f(X1, Y3))) -> f(f(f(Y1, X1), Y1), f(Y2, f(f(Y1, X1), Y3))) % 0.19/0.39 f1(f(f(f(f(n1, n1), n1), f(n1, n1)), f(n1, f(n1, n1)))) -> true__ % 0.19/0.39 f1(f(f(n3, n2), u)) -> true__ % 0.19/0.39 f1(f(f(u, u), u)) -> false__ % 0.19/0.39 f1(f(n1, f(n1, f(f(n1, n1), n1)))) -> false__ % 0.19/0.39 n2 -> f(n1, n1) % 0.19/0.39 n3 -> f(n2, n1) % 0.19/0.39 true__ -> false__ % 0.19/0.39 u -> f(n2, n2) % 0.19/0.39 with the LPO induced by % 0.19/0.39 f1 > n3 > u > n2 > n1 > f > true__ > false__ % 0.19/0.39 % 0.19/0.39 % SZS output end Proof % 0.19/0.39 %------------------------------------------------------------------------------