%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : ANA010-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n020.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 19:15:30 EDT 2022 % Result : Unsatisfiable 9.96s 9.94s % Output : Proof 9.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : ANA010-2 : TPTP v8.1.0. Released v3.2.0. % 0.03/0.11 % Command : moca.sh %s % 0.11/0.31 % Computer : n020.cluster.edu % 0.11/0.31 % Model : x86_64 x86_64 % 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.31 % Memory : 8042.1875MB % 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.31 % CPULimit : 300 % 0.11/0.31 % WCLimit : 600 % 0.11/0.31 % DateTime : Fri Jul 8 03:53:13 EDT 2022 % 0.11/0.31 % CPUTime : % 9.96/9.94 % SZS status Unsatisfiable % 9.96/9.94 % SZS output start Proof % 9.96/9.94 The input problem is unsatisfiable because % 9.96/9.94 % 9.96/9.94 [1] the following set of Horn clauses is unsatisfiable: % 9.96/9.94 % 9.96/9.94 class_OrderedGroup_Olordered__ab__group__abs(T_a) & c_lessequals(c_0, V_y, T_a) ==> c_HOL_Oabs(V_y, T_a) = V_y % 9.96/9.94 class_Orderings_Oorder(T_a) & c_lessequals(V_y, V_z, T_a) & c_lessequals(V_x, V_y, T_a) ==> c_lessequals(V_x, V_z, T_a) % 9.96/9.94 class_Ring__and__Field_Oordered__idom(T_a) ==> c_HOL_Oabs(c_times(V_a, V_b, T_a), T_a) = c_times(c_HOL_Oabs(V_a, T_a), c_HOL_Oabs(V_b, T_a), T_a) % 9.96/9.94 c_lessequals(c_0, v_f(V_U), t_b) % 9.96/9.94 c_lessequals(v_f(V_U), c_times(v_c, v_g(V_U), t_b), t_b) % 9.96/9.94 c_lessequals(v_f(v_x(V_U)), c_times(V_U, c_HOL_Oabs(v_g(v_x(V_U)), t_b), t_b), t_b) ==> \bottom % 9.96/9.94 class_OrderedGroup_Olordered__ab__group__abs(T) ==> class_Orderings_Oorder(T) % 9.96/9.94 class_Ring__and__Field_Oordered__idom(T) ==> class_OrderedGroup_Olordered__ab__group__abs(T) % 9.96/9.94 class_Ring__and__Field_Oordered__idom(t_b) % 9.96/9.94 % 9.96/9.94 This holds because % 9.96/9.94 % 9.96/9.94 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 9.96/9.95 % 9.96/9.95 E: % 9.96/9.95 c_lessequals(c_0, v_f(V_U), t_b) = true__ % 9.96/9.95 c_lessequals(v_f(V_U), c_times(v_c, v_g(V_U), t_b), t_b) = true__ % 9.96/9.95 class_Ring__and__Field_Oordered__idom(t_b) = true__ % 9.96/9.95 f1(true__, V_y, T_a) = c_HOL_Oabs(V_y, T_a) % 9.96/9.95 f2(c_lessequals(c_0, V_y, T_a), T_a, V_y) = V_y % 9.96/9.95 f2(true__, T_a, V_y) = f1(class_OrderedGroup_Olordered__ab__group__abs(T_a), V_y, T_a) % 9.96/9.95 f3(true__, V_x, V_z, T_a) = c_lessequals(V_x, V_z, T_a) % 9.96/9.95 f4(true__, T_a, V_x, V_z) = f3(class_Orderings_Oorder(T_a), V_x, V_z, T_a) % 9.96/9.95 f5(c_lessequals(V_x, V_y, T_a), V_y, V_z, T_a, V_x) = true__ % 9.96/9.95 f5(true__, V_y, V_z, T_a, V_x) = f4(c_lessequals(V_y, V_z, T_a), T_a, V_x, V_z) % 9.96/9.95 f6(class_Ring__and__Field_Oordered__idom(T_a), V_a, V_b, T_a) = c_times(c_HOL_Oabs(V_a, T_a), c_HOL_Oabs(V_b, T_a), T_a) % 9.96/9.95 f6(true__, V_a, V_b, T_a) = c_HOL_Oabs(c_times(V_a, V_b, T_a), T_a) % 9.96/9.95 f7(c_lessequals(v_f(v_x(V_U)), c_times(V_U, c_HOL_Oabs(v_g(v_x(V_U)), t_b), t_b), t_b)) = true__ % 9.96/9.95 f7(true__) = false__ % 9.96/9.95 f8(class_OrderedGroup_Olordered__ab__group__abs(T), T) = true__ % 9.96/9.95 f8(true__, T) = class_Orderings_Oorder(T) % 9.96/9.95 f9(class_Ring__and__Field_Oordered__idom(T), T) = true__ % 9.96/9.95 f9(true__, T) = class_OrderedGroup_Olordered__ab__group__abs(T) % 9.96/9.95 G: % 9.96/9.95 true__ = false__ % 9.96/9.95 % 9.96/9.95 This holds because % 9.96/9.95 % 9.96/9.95 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 9.96/9.95 % 9.96/9.95 % 9.96/9.95 c_HOL_Oabs(V_y, T_a) -> f1(true__, V_y, T_a) % 9.96/9.95 c_lessequals(V_x, V_z, T_a) -> f3(true__, V_x, V_z, T_a) % 9.96/9.95 c_times(f1(true__, v_c, t_b), f1(true__, v_g(X0), t_b), t_b) -> c_times(v_c, v_g(X0), t_b) % 9.96/9.95 class_OrderedGroup_Olordered__ab__group__abs(T) -> f9(true__, T) % 9.96/9.95 class_Orderings_Oorder(T) -> f8(true__, T) % 9.96/9.95 class_Ring__and__Field_Oordered__idom(t_b) -> true__ % 9.96/9.95 f1(true__, c_times(Y1, Y2, t_b), t_b) -> c_times(f1(true__, Y1, t_b), f1(true__, Y2, t_b), t_b) % 9.96/9.95 f1(true__, v_f(Y0), t_b) -> v_f(Y0) % 9.96/9.95 f2(f3(true__, c_0, Y0, Y1), Y1, Y0) -> Y0 % 9.96/9.95 f2(true__, T_a, V_y) -> f1(f9(true__, T_a), V_y, T_a) % 9.96/9.95 f3(true__, c_0, c_times(v_c, v_g(Y0), t_b), t_b) -> true__ % 9.96/9.95 f3(true__, c_0, v_f(X0), t_b) -> true__ % 9.96/9.95 f3(true__, v_f(Y0), c_times(v_c, v_g(Y0), t_b), t_b) -> true__ % 9.96/9.95 f4(f3(true__, c_times(v_c, v_g(X0), t_b), Y3, t_b), t_b, c_0, Y3) -> true__ % 9.96/9.95 f4(f3(true__, c_times(v_c, v_g(X0), t_b), Y3, t_b), t_b, v_f(X0), Y3) -> true__ % 9.96/9.95 f4(f3(true__, v_f(X0), Y3, t_b), t_b, c_0, Y3) -> true__ % 9.96/9.95 f4(true__, T_a, V_x, V_z) -> f3(f8(true__, T_a), V_x, V_z, T_a) % 9.96/9.95 f5(f3(true__, Y0, Y1, Y2), Y1, Y3, Y2, Y0) -> true__ % 9.96/9.95 f5(true__, V_y, V_z, T_a, V_x) -> f4(f3(true__, V_y, V_z, T_a), T_a, V_x, V_z) % 9.96/9.95 f6(class_Ring__and__Field_Oordered__idom(T_a), V_a, V_b, T_a) -> c_times(f1(true__, V_a, T_a), f1(true__, V_b, T_a), T_a) % 9.96/9.95 f6(true__, V_a, V_b, T_a) -> f1(true__, c_times(V_a, V_b, T_a), T_a) % 9.96/9.95 f7(f3(true__, v_f(v_x(Y0)), c_times(Y0, f1(true__, v_g(v_x(Y0)), t_b), t_b), t_b)) -> true__ % 9.96/9.95 f7(true__) -> false__ % 9.96/9.95 f8(f9(true__, Y0), Y0) -> true__ % 9.96/9.95 f8(true__, t_b) -> true__ % 9.96/9.95 f9(class_Ring__and__Field_Oordered__idom(T), T) -> true__ % 9.96/9.95 f9(true__, t_b) -> true__ % 9.96/9.95 false__ -> true__ % 9.96/9.95 with the LPO induced by % 9.96/9.95 v_x > f2 > f6 > c_HOL_Oabs > f1 > c_times > class_Ring__and__Field_Oordered__idom > class_OrderedGroup_Olordered__ab__group__abs > f9 > f5 > f4 > v_c > c_lessequals > f3 > v_f > class_Orderings_Oorder > f8 > v_g > c_0 > t_b > f7 > false__ > true__ % 9.96/9.95 % 9.96/9.95 % SZS output end Proof % 9.96/9.95 %------------------------------------------------------------------------------