%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SET845-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n006.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 03:45:08 EDT 2022 % Result : Unsatisfiable 1.36s 1.46s % Output : Proof 1.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : SET845-2 : TPTP v8.1.0. Released v3.2.0. % 0.08/0.14 % Command : moca.sh %s % 0.14/0.35 % Computer : n006.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 600 % 0.14/0.35 % DateTime : Mon Jul 11 08:24:50 EDT 2022 % 0.14/0.35 % CPUTime : % 1.36/1.46 % SZS status Unsatisfiable % 1.36/1.46 % SZS output start Proof % 1.36/1.46 The input problem is unsatisfiable because % 1.36/1.46 % 1.36/1.46 [1] the following set of Horn clauses is unsatisfiable: % 1.36/1.46 % 1.36/1.46 c_in(V_B, V_A, tc_set(T_a)) ==> c_lessequals(V_B, c_Union(V_A, T_a), tc_set(T_a)) % 1.36/1.46 c_lessequals(V_B, V_A, tc_set(T_a)) & c_lessequals(V_A, V_B, tc_set(T_a)) ==> V_A = V_B % 1.36/1.46 c_lessequals(V_x, c_Zorn_Osucc(V_S, V_x, T_a), tc_set(tc_set(T_a))) % 1.36/1.46 c_in(V_x, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))) ==> c_in(c_Zorn_Osucc(V_S, V_x, T_a), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))) % 1.36/1.46 c_in(v_m, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))) % 1.36/1.46 v_m = c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)) % 1.36/1.46 v_m = c_Zorn_Osucc(v_S, v_m, t_a) ==> \bottom % 1.36/1.46 % 1.36/1.46 This holds because % 1.36/1.46 % 1.36/1.46 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 1.36/1.46 % 1.36/1.46 E: % 1.36/1.46 c_in(v_m, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))) = true__ % 1.36/1.46 c_lessequals(V_x, c_Zorn_Osucc(V_S, V_x, T_a), tc_set(tc_set(T_a))) = true__ % 1.36/1.46 f1(c_in(V_B, V_A, tc_set(T_a)), V_B, V_A, T_a) = true__ % 1.36/1.46 f1(true__, V_B, V_A, T_a) = c_lessequals(V_B, c_Union(V_A, T_a), tc_set(T_a)) % 1.36/1.46 f2(true__, V_A, V_B) = V_A % 1.36/1.46 f3(c_lessequals(V_A, V_B, tc_set(T_a)), V_B, V_A, T_a) = V_B % 1.36/1.46 f3(true__, V_B, V_A, T_a) = f2(c_lessequals(V_B, V_A, tc_set(T_a)), V_A, V_B) % 1.36/1.46 f4(c_in(V_x, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))), V_S, V_x, T_a) = true__ % 1.36/1.46 f4(true__, V_S, V_x, T_a) = c_in(c_Zorn_Osucc(V_S, V_x, T_a), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))) % 1.36/1.46 f5(c_Zorn_Osucc(v_S, v_m, t_a)) = false__ % 1.36/1.46 f5(v_m) = true__ % 1.36/1.46 v_m = c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)) % 1.36/1.46 G: % 1.36/1.46 true__ = false__ % 1.36/1.46 % 1.36/1.46 This holds because % 1.36/1.46 % 1.36/1.46 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 1.36/1.46 % 1.36/1.46 c_lessequals(Y0, v_m, tc_set(tc_set(t_a))) = f1(true__, Y0, c_Zorn_OTFin(v_S, t_a), tc_set(t_a)) % 1.36/1.46 c_Union(c_Zorn_OTFin(v_S, t_a), tc_set(t_a)) -> v_m % 1.36/1.46 c_Zorn_Osucc(v_S, v_m, t_a) -> v_m % 1.36/1.46 c_in(c_Zorn_Osucc(V_S, V_x, T_a), c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))) -> f4(true__, V_S, V_x, T_a) % 1.36/1.46 c_in(v_m, c_Zorn_OTFin(v_S, t_a), tc_set(tc_set(t_a))) -> true__ % 1.36/1.46 c_lessequals(V_B, c_Union(V_A, T_a), tc_set(T_a)) -> f1(true__, V_B, V_A, T_a) % 1.36/1.47 c_lessequals(V_x, c_Zorn_Osucc(V_S, V_x, T_a), tc_set(tc_set(T_a))) -> true__ % 1.36/1.47 c_lessequals(v_m, v_m, tc_set(tc_set(t_a))) -> true__ % 1.36/1.47 f1(c_in(V_B, V_A, tc_set(T_a)), V_B, V_A, T_a) -> true__ % 1.36/1.47 f1(f4(true__, X0, X1, X2), c_Zorn_Osucc(X0, X1, X2), c_Zorn_OTFin(X0, X2), tc_set(X2)) -> true__ % 1.36/1.47 f1(true__, c_Zorn_Osucc(v_S, v_m, t_a), c_Zorn_OTFin(v_S, t_a), tc_set(t_a)) -> true__ % 1.36/1.47 f1(true__, v_m, c_Zorn_OTFin(v_S, t_a), tc_set(t_a)) -> true__ % 1.36/1.47 f2(c_lessequals(V_B, V_A, tc_set(T_a)), V_A, V_B) -> f3(true__, V_B, V_A, T_a) % 1.36/1.47 f2(f1(true__, Y0, X1, Y2), c_Union(X1, Y2), Y0) -> f3(true__, Y0, c_Union(X1, Y2), Y2) % 1.36/1.47 f2(f1(true__, Y0, c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), v_m, Y0) -> f3(true__, Y0, v_m, tc_set(t_a)) % 1.36/1.47 f2(true__, V_A, V_B) -> V_A % 1.36/1.47 f3(c_lessequals(V_A, V_B, tc_set(T_a)), V_B, V_A, T_a) -> V_B % 1.36/1.47 f3(f1(true__, Y0, X1, Y2), c_Union(X1, Y2), Y0, Y2) -> c_Union(X1, Y2) % 1.36/1.47 f3(f1(true__, Y0, c_Zorn_OTFin(v_S, t_a), tc_set(t_a)), v_m, Y0, tc_set(t_a)) -> v_m % 1.36/1.47 f3(true__, Y0, c_Zorn_Osucc(X1, Y0, X2), tc_set(X2)) -> c_Zorn_Osucc(X1, Y0, X2) % 1.36/1.47 f3(true__, c_Zorn_Osucc(X1, Y0, X2), Y0, tc_set(X2)) -> c_Zorn_Osucc(X1, Y0, X2) % 1.36/1.47 f3(true__, v_m, v_m, tc_set(t_a)) -> v_m % 1.36/1.47 f4(c_in(V_x, c_Zorn_OTFin(V_S, T_a), tc_set(tc_set(T_a))), V_S, V_x, T_a) -> true__ % 1.36/1.47 f4(f4(true__, Y1, X1, Y2), Y1, c_Zorn_Osucc(Y1, X1, Y2), Y2) -> true__ % 1.36/1.47 f4(true__, v_S, c_Zorn_Osucc(v_S, v_m, t_a), t_a) -> true__ % 1.36/1.47 f4(true__, v_S, v_m, t_a) -> true__ % 1.36/1.47 f5(c_Zorn_Osucc(v_S, v_m, t_a)) -> false__ % 1.36/1.47 f5(v_m) -> true__ % 1.36/1.47 false__ -> true__ % 1.36/1.47 with the LPO induced by % 1.36/1.47 f5 > c_in > f4 > c_Zorn_Osucc > v_S > c_Zorn_OTFin > v_m > f2 > f3 > c_lessequals > f1 > c_Union > t_a > tc_set > false__ > true__ % 1.36/1.47 % 1.36/1.47 % SZS output end Proof % 1.36/1.47 %------------------------------------------------------------------------------