%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : SET855-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n003.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 03:45:15 EDT 2022 % Result : Unsatisfiable 0.19s 0.63s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.11 % Problem : SET855-2 : TPTP v8.1.0. Released v3.2.0. % 0.10/0.12 % Command : moca.sh %s % 0.13/0.33 % Computer : n003.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 : Sun Jul 10 10:45:59 EDT 2022 % 0.13/0.33 % CPUTime : % 0.19/0.63 % SZS status Unsatisfiable % 0.19/0.63 % SZS output start Proof % 0.19/0.63 The input problem is unsatisfiable because % 0.19/0.63 % 0.19/0.63 [1] the following set of Horn clauses is unsatisfiable: % 0.19/0.63 % 0.19/0.63 c_lessequals(V_B, V_A, tc_set(T_a)) & c_lessequals(V_A, V_B, tc_set(T_a)) ==> V_A = V_B % 0.19/0.63 c_lessequals(v_n, c_Union(v_Y, tc_set(t_a)), tc_set(tc_set(t_a))) % 0.19/0.63 c_lessequals(c_Union(v_Y, tc_set(t_a)), v_n, tc_set(tc_set(t_a))) % 0.19/0.63 v_n = c_Union(v_Y, tc_set(t_a)) ==> \bottom % 0.19/0.63 % 0.19/0.63 This holds because % 0.19/0.63 % 0.19/0.63 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.19/0.63 % 0.19/0.63 E: % 0.19/0.63 c_lessequals(c_Union(v_Y, tc_set(t_a)), v_n, tc_set(tc_set(t_a))) = true__ % 0.19/0.63 c_lessequals(v_n, c_Union(v_Y, tc_set(t_a)), tc_set(tc_set(t_a))) = true__ % 0.19/0.63 f1(true__, V_A, V_B) = V_A % 0.19/0.63 f2(c_lessequals(V_A, V_B, tc_set(T_a)), V_B, V_A, T_a) = V_B % 0.19/0.63 f2(true__, V_B, V_A, T_a) = f1(c_lessequals(V_B, V_A, tc_set(T_a)), V_A, V_B) % 0.19/0.63 f3(c_Union(v_Y, tc_set(t_a))) = false__ % 0.19/0.63 f3(v_n) = true__ % 0.19/0.63 G: % 0.19/0.63 true__ = false__ % 0.19/0.63 % 0.19/0.63 This holds because % 0.19/0.63 % 0.19/0.63 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.19/0.63 % 0.19/0.63 % 0.19/0.63 c_Union(v_Y, tc_set(t_a)) -> v_n % 0.19/0.63 c_lessequals(c_Union(v_Y, tc_set(t_a)), v_n, tc_set(tc_set(t_a))) -> true__ % 0.19/0.63 c_lessequals(v_n, c_Union(v_Y, tc_set(t_a)), tc_set(tc_set(t_a))) -> true__ % 0.19/0.63 c_lessequals(v_n, v_n, tc_set(tc_set(t_a))) -> true__ % 0.19/0.63 f1(c_lessequals(V_B, V_A, tc_set(T_a)), V_A, V_B) -> f2(true__, V_B, V_A, T_a) % 0.19/0.63 f1(true__, V_A, V_B) -> V_A % 0.19/0.63 f2(c_lessequals(V_A, V_B, tc_set(T_a)), V_B, V_A, T_a) -> V_B % 0.19/0.63 f2(true__, c_Union(v_Y, tc_set(t_a)), v_n, tc_set(t_a)) -> c_Union(v_Y, tc_set(t_a)) % 0.19/0.63 f2(true__, c_Union(v_Y, tc_set(t_a)), v_n, tc_set(t_a)) -> v_n % 0.19/0.63 f2(true__, v_n, c_Union(v_Y, tc_set(t_a)), tc_set(t_a)) -> c_Union(v_Y, tc_set(t_a)) % 0.19/0.63 f2(true__, v_n, c_Union(v_Y, tc_set(t_a)), tc_set(t_a)) -> v_n % 0.19/0.63 f2(true__, v_n, v_n, tc_set(t_a)) -> v_n % 0.19/0.63 f3(c_Union(v_Y, tc_set(t_a))) -> false__ % 0.19/0.63 f3(v_n) -> true__ % 0.19/0.63 false__ -> true__ % 0.19/0.63 with the LPO induced by % 0.19/0.63 f3 > t_a > v_Y > c_Union > v_n > f1 > f2 > tc_set > c_lessequals > false__ > true__ % 0.19/0.63 % 0.19/0.63 % SZS output end Proof % 0.19/0.63 %------------------------------------------------------------------------------