%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SET864-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n021.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 03:45:21 EDT 2022 % Result : Unsatisfiable 6.62s 6.54s % Output : Proof 6.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SET864-2 : TPTP v8.1.0. Released v3.2.0. % 0.06/0.12 % Command : moca.sh %s % 0.12/0.34 % Computer : n021.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 Jul 11 02:20:23 EDT 2022 % 0.12/0.34 % CPUTime : % 6.62/6.54 % SZS status Unsatisfiable % 6.62/6.54 % SZS output start Proof % 6.62/6.54 The input problem is unsatisfiable because % 6.62/6.54 % 6.62/6.54 [1] the following set of Horn clauses is unsatisfiable: % 6.62/6.54 % 6.62/6.54 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 % 6.62/6.54 c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))) % 6.62/6.54 c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)) % 6.62/6.54 c_in(V_U, v_S, tc_set(t_a)) ==> c_in(v_x(V_U), v_S, tc_set(t_a)) % 6.62/6.54 c_in(V_U, v_S, tc_set(t_a)) ==> c_lessequals(V_U, v_x(V_U), tc_set(t_a)) % 6.62/6.54 V_U = v_x(V_U) & c_in(V_U, v_S, tc_set(t_a)) ==> \bottom % 6.62/6.54 % 6.62/6.54 This holds because % 6.62/6.54 % 6.62/6.54 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 6.62/6.54 % 6.62/6.54 E: % 6.62/6.54 c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)) = true__ % 6.62/6.54 c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))) = true__ % 6.62/6.54 f1(true__, V_c, T_a, V_u) = c_Union(V_c, T_a) % 6.62/6.54 f2(true__, V_u, V_S, T_a, V_c) = f1(c_in(V_u, V_S, tc_set(T_a)), V_c, T_a, V_u) % 6.62/6.54 f3(c_lessequals(c_Union(V_c, T_a), V_u, tc_set(T_a)), V_c, V_S, T_a, V_u) = V_u % 6.62/6.54 f3(true__, V_c, V_S, T_a, V_u) = f2(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) % 6.62/6.54 f4(c_in(V_U, v_S, tc_set(t_a)), V_U) = true__ % 6.62/6.54 f4(true__, V_U) = c_in(v_x(V_U), v_S, tc_set(t_a)) % 6.62/6.54 f5(c_in(V_U, v_S, tc_set(t_a)), V_U) = true__ % 6.62/6.54 f5(true__, V_U) = c_lessequals(V_U, v_x(V_U), tc_set(t_a)) % 6.62/6.54 f6(v_x(V_U), V_U) = false__ % 6.62/6.54 f7(c_in(V_U, v_S, tc_set(t_a)), V_U) = true__ % 6.62/6.54 f7(true__, V_U) = f6(V_U, V_U) % 6.62/6.54 G: % 6.62/6.54 true__ = false__ % 6.62/6.54 % 6.62/6.54 This holds because % 6.62/6.54 % 6.62/6.54 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 6.62/6.54 % 6.62/6.54 % 6.62/6.54 c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)) -> true__ % 6.62/6.54 c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))) -> true__ % 6.62/6.54 c_in(v_x(V_U), v_S, tc_set(t_a)) -> f4(true__, V_U) % 6.62/6.54 c_lessequals(c_Union(v_c, t_a), c_Union(v_c, t_a), tc_set(t_a)) -> true__ % 6.62/6.54 c_lessequals(c_Union(v_c, t_a), v_x(c_Union(v_c, t_a)), tc_set(t_a)) -> true__ % 6.62/6.54 c_lessequals(v_x(c_Union(v_c, t_a)), v_x(v_x(c_Union(v_c, t_a))), tc_set(t_a)) -> true__ % 6.62/6.54 c_lessequals(v_x(v_x(c_Union(v_c, t_a))), v_x(v_x(v_x(c_Union(v_c, t_a)))), tc_set(t_a)) -> true__ % 6.62/6.54 c_lessequals(v_x(v_x(v_x(c_Union(v_c, t_a)))), v_x(v_x(v_x(v_x(c_Union(v_c, t_a))))), tc_set(t_a)) -> true__ % 6.62/6.54 f1(c_in(V_u, V_S, tc_set(T_a)), V_c, T_a, V_u) -> f2(true__, V_u, V_S, T_a, V_c) % 6.62/6.54 f1(f4(true__, X0), Y3, t_a, v_x(X0)) -> f2(true__, v_x(X0), v_S, t_a, Y3) % 6.62/6.54 f1(true__, V_c, T_a, V_u) -> c_Union(V_c, T_a) % 6.62/6.54 f2(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) -> f3(true__, V_c, V_S, T_a, V_u) % 6.62/6.54 f2(true__, Y3, v_S, t_a, v_c) -> f3(true__, v_c, v_S, t_a, Y3) % 6.62/6.54 f2(true__, c_Union(v_c, t_a), v_S, t_a, Y3) -> c_Union(Y3, t_a) % 6.62/6.54 f2(true__, v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(t_a), Y3) -> c_Union(Y3, tc_set(t_a)) % 6.62/6.54 f2(true__, v_x(c_Union(v_c, t_a)), v_S, t_a, Y1) -> c_Union(Y1, t_a) % 6.62/6.54 f2(true__, v_x(v_x(c_Union(v_c, t_a))), v_S, t_a, Y1) -> c_Union(Y1, t_a) % 6.62/6.54 f2(true__, v_x(v_x(v_x(c_Union(v_c, t_a)))), v_S, t_a, Y1) -> c_Union(Y1, t_a) % 6.62/6.54 f3(c_lessequals(c_Union(V_c, T_a), V_u, tc_set(T_a)), V_c, V_S, T_a, V_u) -> V_u % 6.62/6.54 f3(true__, v_c, Y0, t_a, c_Union(v_c, t_a)) -> c_Union(v_c, t_a) % 6.62/6.54 f3(true__, v_c, Y3, t_a, v_x(c_Union(v_c, t_a))) -> v_x(c_Union(v_c, t_a)) % 6.62/6.54 f3(true__, v_c, v_S, t_a, c_Union(v_c, t_a)) -> c_Union(v_c, t_a) % 6.62/6.54 f3(true__, v_c, v_S, t_a, v_x(v_x(c_Union(v_c, t_a)))) -> c_Union(v_c, t_a) % 6.62/6.54 f4(c_in(V_U, v_S, tc_set(t_a)), V_U) -> true__ % 6.62/6.54 f4(f4(true__, X0), v_x(X0)) -> true__ % 6.62/6.54 f4(true__, c_Union(v_c, t_a)) -> true__ % 6.62/6.54 f4(true__, v_x(c_Union(v_c, t_a))) -> true__ % 6.62/6.54 f4(true__, v_x(v_x(c_Union(v_c, t_a)))) -> true__ % 6.62/6.54 f4(true__, v_x(v_x(v_x(c_Union(v_c, t_a))))) -> true__ % 6.62/6.54 f5(c_in(V_U, v_S, tc_set(t_a)), V_U) -> true__ % 6.62/6.54 f5(f4(true__, X0), v_x(X0)) -> true__ % 6.62/6.54 f5(true__, V_U) -> c_lessequals(V_U, v_x(V_U), tc_set(t_a)) % 6.62/6.54 f6(V_U, V_U) -> f7(true__, V_U) % 6.62/6.54 f6(v_x(V_U), V_U) -> false__ % 6.62/6.54 f7(c_in(V_U, v_S, tc_set(t_a)), V_U) -> true__ % 6.62/6.54 f7(f4(true__, X0), v_x(X0)) -> true__ % 6.62/6.54 f7(true__, c_Union(v_c, t_a)) -> true__ % 6.62/6.54 f7(true__, v_x(c_Union(v_c, t_a))) -> true__ % 6.62/6.54 f7(true__, v_x(v_x(c_Union(v_c, t_a)))) -> true__ % 6.62/6.54 f7(true__, v_x(v_x(v_x(c_Union(v_c, t_a))))) -> true__ % 6.62/6.54 false__ -> true__ % 6.62/6.54 v_x(c_Union(v_c, t_a)) -> c_Union(v_c, t_a) % 6.62/6.54 with the LPO induced by % 6.62/6.54 f6 > f7 > f5 > v_x > f4 > t_a > c_lessequals > f1 > f2 > f3 > c_in > v_S > v_c > c_Zorn_Omaxchain > tc_set > c_Union > false__ > true__ % 6.62/6.54 % 6.62/6.54 % SZS output end Proof % 6.62/6.54 %------------------------------------------------------------------------------