%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SET865-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n026.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 : Tue Jul 19 03:45:22 EDT 2022 % Result : Unsatisfiable 6.81s 6.80s % Output : Proof 6.81s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SET865-2 : TPTP v8.1.0. Released v3.2.0. % 0.10/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n026.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 : Sat Jul 9 17:51:56 EDT 2022 % 0.12/0.33 % CPUTime : % 6.81/6.80 % SZS status Unsatisfiable % 6.81/6.80 % SZS output start Proof % 6.81/6.80 The input problem is unsatisfiable because % 6.81/6.80 % 6.81/6.80 [1] the following set of Horn clauses is unsatisfiable: % 6.81/6.80 % 6.81/6.80 c_in(V_U, c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))) ==> c_in(c_Union(V_U, t_a), v_S, tc_set(t_a)) % 6.81/6.80 c_in(V_U, v_S, tc_set(t_a)) ==> c_in(v_x(V_U), v_S, tc_set(t_a)) % 6.81/6.80 c_in(V_U, v_S, tc_set(t_a)) ==> c_lessequals(V_U, v_x(V_U), tc_set(t_a)) % 6.81/6.80 V_U = v_x(V_U) & c_in(V_U, v_S, tc_set(t_a)) ==> \bottom % 6.81/6.80 c_in(V_c, V_A, T_a) & c_lessequals(V_A, V_B, tc_set(T_a)) ==> c_in(V_c, V_B, T_a) % 6.81/6.80 c_in(c_Zorn_OHausdorff__1(V_S, T_a), c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a))) % 6.81/6.80 c_in(V_u, V_S, tc_set(T_a)) & c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a))) & c_lessequals(c_Union(V_c, T_a), V_u, tc_set(T_a)) ==> c_Union(V_c, T_a) = V_u % 6.81/6.80 c_lessequals(c_Zorn_Omaxchain(V_S, T_a), c_Zorn_Ochain(V_S, T_a), tc_set(tc_set(tc_set(T_a)))) % 6.81/6.80 % 6.81/6.80 This holds because % 6.81/6.80 % 6.81/6.80 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 6.81/6.80 % 6.81/6.80 E: % 6.81/6.80 c_in(c_Zorn_OHausdorff__1(V_S, T_a), c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a))) = true__ % 6.81/6.80 c_lessequals(c_Zorn_Omaxchain(V_S, T_a), c_Zorn_Ochain(V_S, T_a), tc_set(tc_set(tc_set(T_a)))) = true__ % 6.81/6.80 f1(c_in(V_U, c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))), V_U) = true__ % 6.81/6.80 f1(true__, V_U) = c_in(c_Union(V_U, t_a), v_S, tc_set(t_a)) % 6.81/6.80 f10(c_lessequals(c_Union(V_c, T_a), V_u, tc_set(T_a)), V_c, V_S, T_a, V_u) = V_u % 6.81/6.80 f10(true__, V_c, V_S, T_a, V_u) = f9(c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a))), V_u, V_S, T_a, V_c) % 6.81/6.80 f2(c_in(V_U, v_S, tc_set(t_a)), V_U) = true__ % 6.81/6.80 f2(true__, V_U) = c_in(v_x(V_U), v_S, tc_set(t_a)) % 6.81/6.80 f3(c_in(V_U, v_S, tc_set(t_a)), V_U) = true__ % 6.81/6.80 f3(true__, V_U) = c_lessequals(V_U, v_x(V_U), tc_set(t_a)) % 6.81/6.80 f4(v_x(V_U), V_U) = false__ % 6.81/6.80 f5(c_in(V_U, v_S, tc_set(t_a)), V_U) = true__ % 6.81/6.80 f5(true__, V_U) = f4(V_U, V_U) % 6.81/6.80 f6(true__, V_c, V_B, T_a) = c_in(V_c, V_B, T_a) % 6.81/6.80 f7(c_lessequals(V_A, V_B, tc_set(T_a)), V_c, V_A, T_a, V_B) = true__ % 6.81/6.80 f7(true__, V_c, V_A, T_a, V_B) = f6(c_in(V_c, V_A, T_a), V_c, V_B, T_a) % 6.81/6.80 f8(true__, V_c, T_a, V_u) = c_Union(V_c, T_a) % 6.81/6.80 f9(true__, V_u, V_S, T_a, V_c) = f8(c_in(V_u, V_S, tc_set(T_a)), V_c, T_a, V_u) % 6.81/6.80 G: % 6.81/6.80 true__ = false__ % 6.81/6.80 % 6.81/6.80 This holds because % 6.81/6.80 % 6.81/6.80 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 6.81/6.80 % 6.81/6.80 % 6.81/6.80 c_in(V_c, V_B, T_a) -> f6(true__, V_c, V_B, T_a) % 6.81/6.80 c_in(c_Zorn_OHausdorff__1(V_S, T_a), c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a))) -> true__ % 6.81/6.80 c_lessequals(V_U, v_x(V_U), tc_set(t_a)) -> f3(true__, V_U) % 6.81/6.80 c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), tc_set(t_a)) -> true__ % 6.81/6.80 c_lessequals(c_Zorn_Omaxchain(V_S, T_a), c_Zorn_Ochain(V_S, T_a), tc_set(tc_set(tc_set(T_a)))) -> true__ % 6.81/6.80 f1(c_in(V_U, c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))), V_U) -> true__ % 6.81/6.80 f1(f6(true__, Y0, c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))), Y0) -> true__ % 6.81/6.80 f1(true__, V_U) -> c_in(c_Union(V_U, t_a), v_S, tc_set(t_a)) % 6.81/6.80 f10(c_lessequals(c_Union(V_c, T_a), V_u, tc_set(T_a)), V_c, V_S, T_a, V_u) -> V_u % 6.81/6.80 f10(f3(true__, c_Union(Y0, t_a)), Y0, Y3, t_a, v_x(c_Union(Y0, t_a))) -> v_x(c_Union(Y0, t_a)) % 6.81/6.80 f10(true__, V_c, V_S, T_a, V_u) -> f9(c_in(V_c, c_Zorn_Omaxchain(V_S, T_a), tc_set(tc_set(T_a))), V_u, V_S, T_a, V_c) % 6.81/6.80 f2(c_in(V_U, v_S, tc_set(t_a)), V_U) -> true__ % 6.81/6.80 f2(f6(true__, Y0, v_S, tc_set(t_a)), Y0) -> true__ % 6.81/6.80 f2(true__, V_U) -> c_in(v_x(V_U), v_S, tc_set(t_a)) % 6.81/6.80 f3(c_in(V_U, v_S, tc_set(t_a)), V_U) -> true__ % 6.81/6.80 f3(f6(true__, Y0, v_S, tc_set(t_a)), Y0) -> true__ % 6.81/6.80 f3(true__, c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)) -> true__ % 6.81/6.80 f3(true__, v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))) -> true__ % 6.81/6.80 f3(true__, v_x(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)))) -> true__ % 6.81/6.80 f4(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)) -> true__ % 6.81/6.80 f4(v_x(V_U), V_U) -> false__ % 6.81/6.80 f4(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))) -> true__ % 6.81/6.80 f4(v_x(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), v_x(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)))) -> true__ % 6.81/6.80 f5(c_in(V_U, v_S, tc_set(t_a)), V_U) -> true__ % 6.81/6.80 f5(f6(true__, Y0, v_S, tc_set(t_a)), Y0) -> true__ % 6.81/6.80 f5(true__, V_U) -> f4(V_U, V_U) % 6.81/6.80 f6(f6(true__, Y1, c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), t_a), Y1, c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), t_a) -> true__ % 6.81/6.80 f6(f6(true__, Y1, c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), t_a), Y1, v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), t_a) -> true__ % 6.81/6.80 f6(f6(true__, Y1, v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), t_a), Y1, v_x(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), t_a) -> true__ % 6.81/6.80 f6(f6(true__, Y3, c_Zorn_Omaxchain(X0, X1), tc_set(tc_set(X1))), Y3, c_Zorn_Ochain(X0, X1), tc_set(tc_set(X1))) -> true__ % 6.81/6.80 f6(true__, c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a)) -> true__ % 6.81/6.80 f6(true__, c_Zorn_OHausdorff__1(Y0, Y1), c_Zorn_Omaxchain(Y0, Y1), tc_set(tc_set(Y1))) -> true__ % 6.81/6.80 f6(true__, c_Zorn_OHausdorff__1(Y1, Y2), c_Zorn_Ochain(Y1, Y2), tc_set(tc_set(Y2))) -> true__ % 6.81/6.80 f6(true__, v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_S, tc_set(t_a)) -> true__ % 6.81/6.80 f6(true__, v_x(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), v_S, tc_set(t_a)) -> true__ % 6.81/6.80 f6(true__, v_x(v_x(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)))), v_S, tc_set(t_a)) -> true__ % 6.81/6.80 f7(c_lessequals(V_A, V_B, tc_set(T_a)), V_c, V_A, T_a, V_B) -> true__ % 6.81/6.80 f7(f3(true__, Y0), Y3, Y0, t_a, v_x(Y0)) -> true__ % 6.81/6.80 f7(true__, V_c, V_A, T_a, V_B) -> f6(c_in(V_c, V_A, T_a), V_c, V_B, T_a) % 6.81/6.80 f8(true__, V_c, T_a, V_u) -> c_Union(V_c, T_a) % 6.81/6.80 f9(f6(true__, c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(Y1, t_a), tc_set(tc_set(t_a))), c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), Y1, t_a, c_Zorn_OHausdorff__1(v_S, t_a)) -> c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a) % 6.81/6.80 f9(f6(true__, c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(Y1, t_a), tc_set(tc_set(t_a))), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), Y1, t_a, c_Zorn_OHausdorff__1(v_S, t_a)) -> v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)) % 6.81/6.80 f9(true__, V_u, V_S, T_a, V_c) -> f8(c_in(V_u, V_S, tc_set(T_a)), V_c, T_a, V_u) % 6.81/6.80 false__ -> true__ % 6.81/6.80 v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)) -> c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a) % 6.81/6.80 with the LPO induced by % 6.81/6.80 f10 > f9 > f8 > f1 > c_Union > c_Zorn_Omaxchain > c_Zorn_OHausdorff__1 > f2 > v_S > c_lessequals > f3 > tc_set > t_a > f7 > c_in > f6 > f5 > f4 > v_x > c_Zorn_Ochain > false__ > true__ % 6.81/6.80 % 6.81/6.80 % SZS output end Proof % 6.81/6.80 %------------------------------------------------------------------------------