%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : LDA002-1 : TPTP v8.1.0. Released v1.0.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n029.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 4.07s 4.19s % Output : Proof 4.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : LDA002-1 : TPTP v8.1.0. Released v1.0.0. % 0.03/0.12 % Command : moca.sh %s % 0.13/0.33 % Computer : n029.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Mon May 30 03:07:29 EDT 2022 % 0.13/0.33 % CPUTime : % 4.07/4.19 % SZS status Unsatisfiable % 4.07/4.19 % SZS output start Proof % 4.07/4.19 The input problem is unsatisfiable because % 4.07/4.19 % 4.07/4.19 [1] the following set of Horn clauses is unsatisfiable: % 4.07/4.19 % 4.07/4.19 f(X, f(Y, Z)) = f(f(X, Y), f(X, Z)) % 4.07/4.19 n2 = f(n1, n1) % 4.07/4.19 n3 = f(n2, n1) % 4.07/4.19 u = f(n2, n2) % 4.07/4.19 u1 = f(u, n1) % 4.07/4.19 u2 = f(u, n2) % 4.07/4.19 u3 = f(u, n3) % 4.07/4.19 uu = f(u, u) % 4.07/4.19 a = f(f(n3, n2), u2) % 4.07/4.19 b = f(u1, u3) % 4.07/4.19 v = f(uu, uu) % 4.07/4.19 f(a, v) = f(b, v) ==> \bottom % 4.07/4.19 % 4.07/4.19 This holds because % 4.07/4.19 % 4.07/4.19 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 4.07/4.19 % 4.07/4.19 E: % 4.07/4.19 a = f(f(n3, n2), u2) % 4.07/4.19 b = f(u1, u3) % 4.07/4.19 f(X, f(Y, Z)) = f(f(X, Y), f(X, Z)) % 4.07/4.19 f1(f(a, v)) = true__ % 4.07/4.19 f1(f(b, v)) = false__ % 4.07/4.19 n2 = f(n1, n1) % 4.07/4.19 n3 = f(n2, n1) % 4.07/4.19 u = f(n2, n2) % 4.07/4.19 u1 = f(u, n1) % 4.07/4.19 u2 = f(u, n2) % 4.07/4.19 u3 = f(u, n3) % 4.07/4.19 uu = f(u, u) % 4.07/4.19 v = f(uu, uu) % 4.07/4.19 G: % 4.07/4.19 true__ = false__ % 4.07/4.19 % 4.07/4.19 This holds because % 4.07/4.19 % 4.07/4.19 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 4.07/4.19 % 4.07/4.19 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)) % 4.07/4.19 f(f(Y1, f(X1, Y2)), f(f(f(f(Y1, X1), Y1), f(Y1, X1)), Y3)) = f(f(f(f(Y1, X1), Y1), f(Y1, X1)), f(f(f(f(Y1, X1), Y1), Y2), Y3)) % 4.07/4.20 f(f(f(Y0, Y1), Y0), f(f(Y0, f(Y1, X2)), Y3)) = f(f(Y0, f(Y1, f(Y0, X2))), f(f(f(Y0, Y1), Y0), Y3)) % 4.07/4.20 f(f(f(Y1, X1), f(X2, f(Y1, X3))), f(f(f(f(Y1, X1), X2), Y1), Y3)) = f(f(f(f(Y1, X1), X2), Y1), f(f(f(f(Y1, X1), X2), f(X1, X3)), Y3)) % 4.07/4.20 a -> f(f(n3, n2), u2) % 4.07/4.20 b -> f(u1, u3) % 4.07/4.20 f(f(X, Y), f(X, Z)) -> f(X, f(Y, Z)) % 4.07/4.20 f(f(X0, f(X1, X2)), f(f(X0, X1), Y2)) -> f(f(X0, X1), f(f(X0, X2), Y2)) % 4.07/4.20 f(f(X0, f(f(X1, X2), X1)), f(f(f(X0, f(X1, X2)), Y2), Y3)) -> f(f(f(X0, X1), f(f(X0, X2), Y2)), f(f(X0, f(f(X1, X2), X1)), Y3)) % 4.07/4.20 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)) % 4.07/4.20 f(f(Y0, f(f(X0, X1), f(f(X0, X2), X3))), f(f(Y0, f(X0, f(X1, X2))), Y3)) -> f(f(Y0, f(X0, f(X1, X2))), f(f(Y0, f(f(X0, X1), X3)), Y3)) % 4.07/4.20 f(f(Y0, f(f(X1, X2), Y2)), f(f(Y0, X1), f(f(Y0, X2), X3))) -> f(f(Y0, f(X1, X2)), f(f(Y0, Y2), f(f(Y0, X1), X3))) % 4.07/4.20 f(f(f(X0, X1), Y1), f(X0, f(X1, X2))) -> f(f(X0, X1), f(Y1, f(X0, X2))) % 4.07/4.20 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)) % 4.07/4.20 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))) % 4.07/4.20 f(f(f(X0, f(X1, X2)), f(f(f(X0, X1), X3), Y2)), f(f(f(X0, X1), f(f(X0, X2), X3)), Y3)) -> f(f(f(X0, X1), f(f(X0, X2), X3)), f(f(f(X0, f(X1, X2)), Y2), Y3)) % 4.07/4.20 f(f(f(X0, f(f(X1, X2), X1)), Y2), f(f(X0, X1), f(f(X0, X2), Y3))) -> f(f(X0, f(f(X1, X2), X1)), f(Y2, f(f(X0, f(X1, X2)), Y3))) % 4.07/4.20 f(f(f(Y0, X1), f(f(Y0, X2), X3)), f(Y0, f(f(X1, X2), Y3))) -> f(f(Y0, f(X1, X2)), f(f(f(Y0, X1), X3), f(Y0, Y3))) % 4.07/4.20 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)))) % 4.07/4.20 f(f(f(Y0, f(X0, f(X1, X2))), Y2), f(Y0, f(f(X0, X1), f(f(X0, X2), X3)))) -> f(f(Y0, f(X0, f(X1, X2))), f(Y2, f(Y0, f(f(X0, X1), X3)))) % 4.07/4.20 f(f(f(f(X0, X1), X2), f(f(X0, f(X1, X3)), Y2)), f(f(f(X0, X1), f(X2, f(X0, X3))), Y3)) -> f(f(f(X0, X1), f(X2, f(X0, X3))), f(f(f(f(X0, X1), X2), Y2), Y3)) % 4.07/4.20 f(f(f(f(X0, X1), f(f(X0, X2), X3)), Y2), f(f(X0, f(X1, X2)), f(f(f(X0, X1), X3), Y3))) -> f(f(f(X0, X1), f(f(X0, X2), X3)), f(Y2, f(f(X0, f(X1, X2)), Y3))) % 4.07/4.20 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))) % 4.07/4.20 f1(f(a, v)) -> true__ % 4.07/4.20 f1(f(b, v)) -> false__ % 4.07/4.20 f1(f(f(f(f(f(n1, n1), n1), f(n1, n1)), f(n1, f(f(n1, n1), n1))), f(n1, f(n1, f(n1, f(n1, n1)))))) -> true__ % 4.07/4.20 f1(f(n1, f(f(f(n1, n1), f(f(n1, n1), n1)), f(n1, f(n1, f(n1, n1)))))) -> false__ % 4.07/4.20 f1(f(n1, f(n1, f(n1, f(n1, f(n1, n1)))))) -> false__ % 4.07/4.20 f1(f(n1, f(n1, f(n1, f(n1, f(n1, n1)))))) -> true__ % 4.07/4.20 n2 -> f(n1, n1) % 4.07/4.20 n3 -> f(n2, n1) % 4.07/4.20 true__ -> false__ % 4.07/4.20 u -> f(n2, n2) % 4.07/4.20 u1 -> f(u, n1) % 4.07/4.20 u2 -> f(u, n2) % 4.07/4.20 u3 -> f(u, n3) % 4.07/4.20 uu -> f(u, u) % 4.07/4.20 v -> f(uu, uu) % 4.07/4.20 with the LPO induced by % 4.07/4.20 f1 > b > u1 > v > uu > a > u3 > n3 > u2 > u > n2 > f > n1 > true__ > false__ % 4.07/4.20 % 4.07/4.20 % SZS output end Proof % 4.07/4.20 %------------------------------------------------------------------------------