%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : PUZ063-2 : 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 : Mon Jul 18 18:21:40 EDT 2022 % Result : Unsatisfiable 0.18s 0.37s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : PUZ063-2 : TPTP v8.1.0. Released v3.2.0. % 0.03/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n021.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 May 28 20:49:57 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.37 % SZS status Unsatisfiable % 0.18/0.37 % SZS output start Proof % 0.18/0.37 The input problem is unsatisfiable because % 0.18/0.37 % 0.18/0.37 [1] the following set of Horn clauses is unsatisfiable: % 0.18/0.37 % 0.18/0.37 c_in(v_u, c_Mutil_Otiling(v_A, t_a), tc_set(t_a)) % 0.18/0.37 c_in(c_union(c_emptyset, v_u, t_a), c_Mutil_Otiling(v_A, t_a), tc_set(t_a)) ==> \bottom % 0.18/0.37 c_union(c_emptyset, V_y, T_a) = V_y % 0.18/0.37 % 0.18/0.37 This holds because % 0.18/0.37 % 0.18/0.37 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.18/0.37 % 0.18/0.37 E: % 0.18/0.37 c_in(v_u, c_Mutil_Otiling(v_A, t_a), tc_set(t_a)) = true__ % 0.18/0.37 c_union(c_emptyset, V_y, T_a) = V_y % 0.18/0.37 f1(c_in(c_union(c_emptyset, v_u, t_a), c_Mutil_Otiling(v_A, t_a), tc_set(t_a))) = true__ % 0.18/0.37 f1(true__) = false__ % 0.18/0.37 G: % 0.18/0.37 true__ = false__ % 0.18/0.37 % 0.18/0.37 This holds because % 0.18/0.37 % 0.18/0.37 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.18/0.37 % 0.18/0.37 % 0.18/0.37 c_in(v_u, c_Mutil_Otiling(v_A, t_a), tc_set(t_a)) -> true__ % 0.18/0.37 c_union(c_emptyset, V_y, T_a) -> V_y % 0.18/0.37 f1(c_in(c_union(c_emptyset, v_u, t_a), c_Mutil_Otiling(v_A, t_a), tc_set(t_a))) -> true__ % 0.18/0.37 f1(true__) -> false__ % 0.18/0.37 false__ -> true__ % 0.18/0.37 with the LPO induced by % 0.18/0.37 c_emptyset > c_union > f1 > tc_set > t_a > v_A > c_Mutil_Otiling > v_u > c_in > false__ > true__ % 0.18/0.37 % 0.18/0.37 % SZS output end Proof % 0.18/0.37 %------------------------------------------------------------------------------