%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : ANA045-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n007.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 : Thu Jul 14 19:15:54 EDT 2022 % Result : Unsatisfiable 0.96s 1.10s % Output : Proof 0.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : ANA045-2 : TPTP v8.1.0. Released v3.2.0. % 0.03/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n007.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Fri Jul 8 05:18:45 EDT 2022 % 0.13/0.34 % CPUTime : % 0.96/1.10 % SZS status Unsatisfiable % 0.96/1.10 % SZS output start Proof % 0.96/1.10 The input problem is unsatisfiable because % 0.96/1.10 % 0.96/1.10 [1] the following set of Horn clauses is unsatisfiable: % 0.96/1.10 % 0.96/1.10 c_lessequals(c_0, c_times(V_U, c_HOL_Oabs(v_g(v_x(V_U)), t_b), t_b), t_b) ==> \bottom % 0.96/1.10 class_Ring__and__Field_Oordered__idom(t_b) % 0.96/1.10 class_OrderedGroup_Olordered__ab__group__abs(T_a) ==> c_lessequals(c_0, c_HOL_Oabs(V_a, T_a), T_a) % 0.96/1.10 class_Ring__and__Field_Oordered__idom(T_a) ==> V_c = c_times(c_1, V_c, T_a) % 0.96/1.10 class_Ring__and__Field_Oordered__idom(T) ==> class_OrderedGroup_Olordered__ab__group__abs(T) % 0.96/1.10 % 0.96/1.10 This holds because % 0.96/1.10 % 0.96/1.10 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.96/1.10 % 0.96/1.10 E: % 0.96/1.10 class_Ring__and__Field_Oordered__idom(t_b) = true__ % 0.96/1.10 f1(c_lessequals(c_0, c_times(V_U, c_HOL_Oabs(v_g(v_x(V_U)), t_b), t_b), t_b)) = true__ % 0.96/1.10 f1(true__) = false__ % 0.96/1.10 f2(class_OrderedGroup_Olordered__ab__group__abs(T_a), V_a, T_a) = true__ % 0.96/1.10 f2(true__, V_a, T_a) = c_lessequals(c_0, c_HOL_Oabs(V_a, T_a), T_a) % 0.96/1.10 f3(class_Ring__and__Field_Oordered__idom(T_a), V_c, T_a) = c_times(c_1, V_c, T_a) % 0.96/1.10 f3(true__, V_c, T_a) = V_c % 0.96/1.10 f4(class_Ring__and__Field_Oordered__idom(T), T) = true__ % 0.96/1.10 f4(true__, T) = class_OrderedGroup_Olordered__ab__group__abs(T) % 0.96/1.10 G: % 0.96/1.10 true__ = false__ % 0.96/1.10 % 0.96/1.10 This holds because % 0.96/1.10 % 0.96/1.10 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.96/1.10 % 0.96/1.10 % 0.96/1.10 c_lessequals(c_0, c_HOL_Oabs(V_a, T_a), T_a) -> f2(true__, V_a, T_a) % 0.96/1.10 c_times(c_1, Y1, t_b) -> Y1 % 0.96/1.10 class_OrderedGroup_Olordered__ab__group__abs(T) -> f4(true__, T) % 0.96/1.10 class_Ring__and__Field_Oordered__idom(t_b) -> true__ % 0.96/1.10 f1(c_lessequals(c_0, c_times(V_U, c_HOL_Oabs(v_g(v_x(V_U)), t_b), t_b), t_b)) -> true__ % 0.96/1.10 f1(f2(true__, v_g(v_x(c_1)), t_b)) -> true__ % 0.96/1.10 f1(true__) -> false__ % 0.96/1.10 f2(class_OrderedGroup_Olordered__ab__group__abs(T_a), V_a, T_a) -> true__ % 0.96/1.10 f2(f4(true__, Y0), Y1, Y0) -> true__ % 0.96/1.10 f2(true__, Y1, t_b) -> true__ % 0.96/1.10 f3(class_Ring__and__Field_Oordered__idom(T_a), V_c, T_a) -> c_times(c_1, V_c, T_a) % 0.96/1.10 f3(true__, V_c, T_a) -> V_c % 0.96/1.10 f4(class_Ring__and__Field_Oordered__idom(T), T) -> true__ % 0.96/1.10 f4(true__, t_b) -> true__ % 0.96/1.10 false__ -> true__ % 0.96/1.10 with the LPO induced by % 0.96/1.10 class_OrderedGroup_Olordered__ab__group__abs > f4 > class_Ring__and__Field_Oordered__idom > c_1 > f3 > v_x > c_times > c_lessequals > f2 > c_HOL_Oabs > c_0 > t_b > v_g > f1 > false__ > true__ % 0.96/1.10 % 0.96/1.10 % SZS output end Proof % 0.96/1.10 %------------------------------------------------------------------------------