%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : ANA020-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n015.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 19:15:37 EDT 2022 % Result : Unsatisfiable 13.58s 13.41s % Output : Proof 13.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.14 % Problem : ANA020-2 : TPTP v8.1.0. Released v3.2.0. % 0.14/0.14 % Command : moca.sh %s % 0.15/0.36 % Computer : n015.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 600 % 0.15/0.36 % DateTime : Fri Jul 8 06:23:35 EDT 2022 % 0.15/0.36 % CPUTime : % 13.58/13.41 % SZS status Unsatisfiable % 13.58/13.41 % SZS output start Proof % 13.58/13.41 The input problem is unsatisfiable because % 13.58/13.41 % 13.58/13.41 [1] the following set of Horn clauses is unsatisfiable: % 13.58/13.41 % 13.58/13.41 v_f(c_0) = c_0 % 13.58/13.41 c_less(c_0, v_c, t_a) % 13.58/13.41 v_x = c_0 % 13.58/13.41 c_lessequals(c_HOL_Oabs(v_f(v_x), t_a), c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a) ==> \bottom % 13.58/13.41 class_Ring__and__Field_Oordered__idom(t_a) % 13.58/13.41 class_OrderedGroup_Olordered__ab__group__abs(T_a) ==> c_HOL_Oabs(c_0, T_a) = c_0 % 13.58/13.41 class_OrderedGroup_Olordered__ab__group__abs(T_a) ==> c_lessequals(c_0, c_HOL_Oabs(V_a, T_a), T_a) % 13.58/13.41 class_Orderings_Oorder(T_a) & c_less(V_x, V_y, T_a) ==> c_lessequals(V_x, V_y, T_a) % 13.58/13.41 class_Ring__and__Field_Opordered__cancel__semiring(T_a) & c_lessequals(c_0, V_b, T_a) & c_lessequals(c_0, V_a, T_a) ==> c_lessequals(c_0, c_times(V_a, V_b, T_a), T_a) % 13.58/13.41 class_Ring__and__Field_Oordered__idom(T) ==> class_Ring__and__Field_Opordered__cancel__semiring(T) % 13.58/13.41 class_Ring__and__Field_Oordered__idom(T) ==> class_Orderings_Oorder(T) % 13.58/13.41 class_Ring__and__Field_Oordered__idom(T) ==> class_OrderedGroup_Olordered__ab__group__abs(T) % 13.58/13.41 % 13.58/13.41 This holds because % 13.58/13.41 % 13.58/13.41 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 13.58/13.41 % 13.58/13.41 E: % 13.58/13.41 c_less(c_0, v_c, t_a) = true__ % 13.58/13.41 class_Ring__and__Field_Oordered__idom(t_a) = true__ % 13.58/13.41 f1(c_lessequals(c_HOL_Oabs(v_f(v_x), t_a), c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a)) = true__ % 13.58/13.41 f1(true__) = false__ % 13.58/13.41 f10(class_Ring__and__Field_Oordered__idom(T), T) = true__ % 13.58/13.41 f10(true__, T) = class_Orderings_Oorder(T) % 13.58/13.41 f11(class_Ring__and__Field_Oordered__idom(T), T) = true__ % 13.58/13.41 f11(true__, T) = class_OrderedGroup_Olordered__ab__group__abs(T) % 13.58/13.41 f2(class_OrderedGroup_Olordered__ab__group__abs(T_a), T_a) = c_0 % 13.58/13.41 f2(true__, T_a) = c_HOL_Oabs(c_0, T_a) % 13.58/13.41 f3(class_OrderedGroup_Olordered__ab__group__abs(T_a), V_a, T_a) = true__ % 13.58/13.41 f3(true__, V_a, T_a) = c_lessequals(c_0, c_HOL_Oabs(V_a, T_a), T_a) % 13.58/13.41 f4(true__, V_x, V_y, T_a) = c_lessequals(V_x, V_y, T_a) % 13.58/13.41 f5(c_less(V_x, V_y, T_a), T_a, V_x, V_y) = true__ % 13.58/13.41 f5(true__, T_a, V_x, V_y) = f4(class_Orderings_Oorder(T_a), V_x, V_y, T_a) % 13.58/13.41 f6(true__, V_a, V_b, T_a) = c_lessequals(c_0, c_times(V_a, V_b, T_a), T_a) % 13.58/13.41 f7(true__, T_a, V_a, V_b) = f6(class_Ring__and__Field_Opordered__cancel__semiring(T_a), V_a, V_b, T_a) % 13.58/13.41 f8(c_lessequals(c_0, V_a, T_a), V_b, T_a, V_a) = true__ % 13.58/13.41 f8(true__, V_b, T_a, V_a) = f7(c_lessequals(c_0, V_b, T_a), T_a, V_a, V_b) % 13.58/13.41 f9(class_Ring__and__Field_Oordered__idom(T), T) = true__ % 13.58/13.41 f9(true__, T) = class_Ring__and__Field_Opordered__cancel__semiring(T) % 13.58/13.41 v_f(c_0) = c_0 % 13.58/13.41 v_x = c_0 % 13.58/13.41 G: % 13.58/13.41 true__ = false__ % 13.58/13.41 % 13.58/13.41 This holds because % 13.58/13.41 % 13.58/13.41 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 13.58/13.41 % 13.58/13.41 % 13.58/13.41 c_0 -> v_x % 13.58/13.41 c_HOL_Oabs(v_x, t_a) -> v_x % 13.58/13.41 c_less(c_0, v_c, t_a) -> true__ % 13.58/13.41 c_less(v_x, v_c, t_a) -> true__ % 13.58/13.41 c_lessequals(V_x, V_y, T_a) -> f4(true__, V_x, V_y, T_a) % 13.58/13.41 class_OrderedGroup_Olordered__ab__group__abs(T) -> f11(true__, T) % 13.58/13.41 class_Orderings_Oorder(T) -> f10(true__, T) % 13.58/13.41 class_Ring__and__Field_Oordered__idom(t_a) -> true__ % 13.58/13.41 class_Ring__and__Field_Opordered__cancel__semiring(T) -> f9(true__, T) % 13.58/13.41 f1(c_lessequals(c_HOL_Oabs(v_f(v_x), t_a), c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a)) -> true__ % 13.58/13.41 f1(f4(true__, c_HOL_Oabs(v_x, t_a), c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a)) -> true__ % 13.58/13.41 f1(f4(true__, v_x, c_times(v_c, c_HOL_Oabs(v_h(v_x), t_a), t_a), t_a)) -> true__ % 13.58/13.41 f1(true__) -> false__ % 13.58/13.41 f10(class_Ring__and__Field_Oordered__idom(T), T) -> true__ % 13.58/13.41 f10(true__, t_a) -> true__ % 13.58/13.41 f11(class_Ring__and__Field_Oordered__idom(T), T) -> true__ % 13.58/13.41 f11(true__, t_a) -> true__ % 13.58/13.41 f2(class_OrderedGroup_Olordered__ab__group__abs(T_a), T_a) -> c_0 % 13.58/13.41 f2(f11(true__, Y0), Y0) -> v_x % 13.58/13.41 f2(true__, T_a) -> c_HOL_Oabs(c_0, T_a) % 13.58/13.41 f3(class_OrderedGroup_Olordered__ab__group__abs(T_a), V_a, T_a) -> true__ % 13.58/13.41 f3(f11(true__, Y0), Y1, Y0) -> true__ % 13.58/13.41 f3(true__, V_a, T_a) -> c_lessequals(c_0, c_HOL_Oabs(V_a, T_a), T_a) % 13.58/13.41 f4(true__, v_x, c_HOL_Oabs(Y1, t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_HOL_Oabs(Y1, t_a), c_HOL_Oabs(X0, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_HOL_Oabs(Y1, t_a), c_times(c_HOL_Oabs(X0, t_a), v_c, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_HOL_Oabs(Y1, t_a), c_times(c_HOL_Oabs(X0, t_a), v_x, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_HOL_Oabs(Y1, t_a), c_times(c_times(v_c, v_c, t_a), v_c, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_HOL_Oabs(Y1, t_a), c_times(c_times(v_c, v_c, t_a), v_x, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_HOL_Oabs(Y1, t_a), c_times(c_times(v_c, v_x, t_a), v_c, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_HOL_Oabs(Y1, t_a), c_times(c_times(v_c, v_x, t_a), v_x, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_HOL_Oabs(Y1, t_a), c_times(c_times(v_x, v_c, t_a), v_c, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_HOL_Oabs(Y1, t_a), c_times(v_c, c_HOL_Oabs(X0, t_a), t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_HOL_Oabs(Y1, t_a), c_times(v_c, c_times(v_c, v_c, t_a), t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_HOL_Oabs(Y1, t_a), c_times(v_c, c_times(v_c, v_x, t_a), t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_HOL_Oabs(Y1, t_a), c_times(v_c, c_times(v_x, v_c, t_a), t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_HOL_Oabs(Y1, t_a), c_times(v_c, c_times(v_x, v_x, t_a), t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_HOL_Oabs(Y1, t_a), c_times(v_c, v_c, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_HOL_Oabs(Y1, t_a), c_times(v_c, v_x, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_HOL_Oabs(Y1, t_a), c_times(v_x, c_HOL_Oabs(X0, t_a), t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_HOL_Oabs(Y1, t_a), c_times(v_x, c_times(v_c, v_c, t_a), t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_HOL_Oabs(Y1, t_a), c_times(v_x, c_times(v_c, v_x, t_a), t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_HOL_Oabs(Y1, t_a), c_times(v_x, c_times(v_x, v_c, t_a), t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_HOL_Oabs(Y1, t_a), c_times(v_x, c_times(v_x, v_x, t_a), t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_HOL_Oabs(Y1, t_a), c_times(v_x, v_c, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_HOL_Oabs(Y1, t_a), c_times(v_x, v_x, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_HOL_Oabs(Y1, t_a), v_c, t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_HOL_Oabs(Y1, t_a), v_x, t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_times(v_c, v_c, t_a), c_HOL_Oabs(X0, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_times(v_c, v_c, t_a), c_times(v_c, v_c, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_times(v_c, v_c, t_a), c_times(v_c, v_x, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_times(v_c, v_c, t_a), c_times(v_x, v_c, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_times(v_c, v_c, t_a), c_times(v_x, v_x, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_times(v_c, v_c, t_a), v_c, t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_times(v_c, v_c, t_a), v_x, t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_times(v_c, v_x, t_a), c_HOL_Oabs(X0, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_times(v_c, v_x, t_a), c_times(v_c, v_c, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_times(v_c, v_x, t_a), c_times(v_c, v_x, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_times(v_c, v_x, t_a), c_times(v_x, v_c, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_times(v_c, v_x, t_a), c_times(v_x, v_x, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_times(v_c, v_x, t_a), v_c, t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_times(v_c, v_x, t_a), v_x, t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_times(v_x, v_c, t_a), c_HOL_Oabs(X0, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_times(v_x, v_c, t_a), c_times(v_c, v_c, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_times(v_x, v_c, t_a), c_times(v_c, v_x, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_times(v_x, v_c, t_a), c_times(v_x, v_c, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_times(v_x, v_c, t_a), c_times(v_x, v_x, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_times(v_x, v_c, t_a), v_c, t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_times(v_x, v_c, t_a), v_x, t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_times(v_x, v_x, t_a), c_HOL_Oabs(X0, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_times(v_x, v_x, t_a), c_times(v_c, v_c, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_times(v_x, v_x, t_a), c_times(v_c, v_x, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_times(v_x, v_x, t_a), c_times(v_x, v_c, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_times(v_x, v_x, t_a), c_times(v_x, v_x, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_times(v_x, v_x, t_a), v_c, t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(c_times(v_x, v_x, t_a), v_x, t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_c, c_HOL_Oabs(X0, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_c, c_times(c_HOL_Oabs(X0, t_a), c_HOL_Oabs(X1, t_a), t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_c, c_times(c_HOL_Oabs(X0, t_a), v_c, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_c, c_times(c_HOL_Oabs(X0, t_a), v_x, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_c, c_times(c_times(v_c, v_c, t_a), v_c, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_c, c_times(c_times(v_c, v_c, t_a), v_x, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_c, c_times(c_times(v_c, v_x, t_a), v_c, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_c, c_times(c_times(v_c, v_x, t_a), v_x, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_c, c_times(c_times(v_x, v_c, t_a), v_c, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_c, c_times(c_times(v_x, v_c, t_a), v_x, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_c, c_times(c_times(v_x, v_x, t_a), v_c, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_c, c_times(c_times(v_x, v_x, t_a), v_x, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_c, c_times(v_c, c_HOL_Oabs(X0, t_a), t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_c, c_times(v_c, c_times(v_c, v_c, t_a), t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_c, c_times(v_c, c_times(v_c, v_x, t_a), t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_c, c_times(v_c, c_times(v_x, v_c, t_a), t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_c, c_times(v_c, c_times(v_x, v_x, t_a), t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_c, c_times(v_c, v_c, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_c, c_times(v_c, v_x, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_c, c_times(v_x, c_HOL_Oabs(X0, t_a), t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_c, c_times(v_x, c_times(v_c, v_c, t_a), t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_c, c_times(v_x, c_times(v_c, v_x, t_a), t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_c, c_times(v_x, c_times(v_x, v_c, t_a), t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_c, c_times(v_x, c_times(v_x, v_x, t_a), t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_c, c_times(v_x, v_c, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_c, c_times(v_x, v_x, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_c, v_c, t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_c, v_x, t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_x, c_HOL_Oabs(Y1, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_x, c_times(c_HOL_Oabs(X0, t_a), c_HOL_Oabs(X1, t_a), t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_x, c_times(c_HOL_Oabs(X0, t_a), v_c, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_x, c_times(c_HOL_Oabs(X0, t_a), v_x, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_x, c_times(c_times(v_c, v_c, t_a), v_c, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_x, c_times(c_times(v_c, v_c, t_a), v_x, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_x, c_times(c_times(v_c, v_x, t_a), v_c, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_x, c_times(c_times(v_c, v_x, t_a), v_x, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_x, c_times(c_times(v_x, v_c, t_a), v_c, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_x, c_times(c_times(v_x, v_c, t_a), v_x, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_x, c_times(c_times(v_x, v_x, t_a), v_c, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_x, c_times(c_times(v_x, v_x, t_a), v_x, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_x, c_times(v_c, c_HOL_Oabs(X0, t_a), t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_x, c_times(v_c, c_times(v_c, v_c, t_a), t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_x, c_times(v_c, c_times(v_c, v_x, t_a), t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_x, c_times(v_c, c_times(v_x, v_c, t_a), t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_x, c_times(v_c, c_times(v_x, v_x, t_a), t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_x, c_times(v_c, v_c, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_x, c_times(v_c, v_x, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_x, c_times(v_x, c_HOL_Oabs(X0, t_a), t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_x, c_times(v_x, c_times(v_c, v_c, t_a), t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_x, c_times(v_x, c_times(v_c, v_x, t_a), t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_x, c_times(v_x, c_times(v_x, v_c, t_a), t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_x, c_times(v_x, c_times(v_x, v_x, t_a), t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_x, c_times(v_x, v_c, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_x, c_times(v_x, v_x, t_a), t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_x, v_c, t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, c_times(v_x, v_x, t_a), t_a) -> true__ % 13.58/13.41 f4(true__, v_x, v_c, t_a) -> true__ % 13.58/13.41 f4(true__, v_x, v_x, t_a) -> true__ % 13.58/13.41 f5(c_less(V_x, V_y, T_a), T_a, V_x, V_y) -> true__ % 13.58/13.41 f5(true__, T_a, V_x, V_y) -> f4(class_Orderings_Oorder(T_a), V_x, V_y, T_a) % 13.58/13.41 f6(true__, V_a, V_b, T_a) -> c_lessequals(c_0, c_times(V_a, V_b, T_a), T_a) % 13.58/13.41 f7(f4(true__, v_x, Y0, t_a), t_a, v_x, Y0) -> true__ % 13.58/13.41 f7(f4(true__, v_x, Y2, t_a), t_a, c_HOL_Oabs(X0, t_a), Y2) -> true__ % 13.58/13.41 f7(f4(true__, v_x, Y2, t_a), t_a, c_times(c_HOL_Oabs(X0, t_a), c_HOL_Oabs(X1, t_a), t_a), Y2) -> true__ % 13.58/13.41 f7(f4(true__, v_x, Y2, t_a), t_a, c_times(c_HOL_Oabs(X0, t_a), v_c, t_a), Y2) -> true__ % 13.58/13.41 f7(f4(true__, v_x, Y2, t_a), t_a, c_times(c_HOL_Oabs(X0, t_a), v_x, t_a), Y2) -> true__ % 13.58/13.41 f7(f4(true__, v_x, Y2, t_a), t_a, c_times(c_times(v_c, v_c, t_a), v_c, t_a), Y2) -> true__ % 13.58/13.41 f7(f4(true__, v_x, Y2, t_a), t_a, c_times(c_times(v_c, v_c, t_a), v_x, t_a), Y2) -> true__ % 13.58/13.41 f7(f4(true__, v_x, Y2, t_a), t_a, c_times(c_times(v_c, v_x, t_a), v_c, t_a), Y2) -> true__ % 13.58/13.41 f7(f4(true__, v_x, Y2, t_a), t_a, c_times(c_times(v_c, v_x, t_a), v_x, t_a), Y2) -> true__ % 13.58/13.41 f7(f4(true__, v_x, Y2, t_a), t_a, c_times(c_times(v_x, v_c, t_a), v_c, t_a), Y2) -> true__ % 13.58/13.41 f7(f4(true__, v_x, Y2, t_a), t_a, c_times(c_times(v_x, v_c, t_a), v_x, t_a), Y2) -> true__ % 13.58/13.41 f7(f4(true__, v_x, Y2, t_a), t_a, c_times(c_times(v_x, v_x, t_a), v_c, t_a), Y2) -> true__ % 13.58/13.41 f7(f4(true__, v_x, Y2, t_a), t_a, c_times(c_times(v_x, v_x, t_a), v_x, t_a), Y2) -> true__ % 13.58/13.41 f7(f4(true__, v_x, Y2, t_a), t_a, c_times(v_c, c_HOL_Oabs(X0, t_a), t_a), Y2) -> true__ % 13.58/13.41 f7(f4(true__, v_x, Y2, t_a), t_a, c_times(v_c, c_times(v_c, v_c, t_a), t_a), Y2) -> true__ % 13.58/13.41 f7(f4(true__, v_x, Y2, t_a), t_a, c_times(v_c, c_times(v_c, v_x, t_a), t_a), Y2) -> true__ % 13.58/13.41 f7(f4(true__, v_x, Y2, t_a), t_a, c_times(v_c, c_times(v_x, v_c, t_a), t_a), Y2) -> true__ % 13.58/13.41 f7(f4(true__, v_x, Y2, t_a), t_a, c_times(v_c, c_times(v_x, v_x, t_a), t_a), Y2) -> true__ % 13.58/13.41 f7(f4(true__, v_x, Y2, t_a), t_a, c_times(v_c, v_c, t_a), Y2) -> true__ % 13.58/13.41 f7(f4(true__, v_x, Y2, t_a), t_a, c_times(v_c, v_x, t_a), Y2) -> true__ % 13.58/13.41 f7(f4(true__, v_x, Y2, t_a), t_a, c_times(v_x, c_HOL_Oabs(X0, t_a), t_a), Y2) -> true__ % 13.58/13.41 f7(f4(true__, v_x, Y2, t_a), t_a, c_times(v_x, c_times(v_c, v_c, t_a), t_a), Y2) -> true__ % 13.58/13.41 f7(f4(true__, v_x, Y2, t_a), t_a, c_times(v_x, c_times(v_c, v_x, t_a), t_a), Y2) -> true__ % 13.58/13.41 f7(f4(true__, v_x, Y2, t_a), t_a, c_times(v_x, c_times(v_x, v_c, t_a), t_a), Y2) -> true__ % 13.58/13.41 f7(f4(true__, v_x, Y2, t_a), t_a, c_times(v_x, c_times(v_x, v_x, t_a), t_a), Y2) -> true__ % 13.58/13.42 f7(f4(true__, v_x, Y2, t_a), t_a, c_times(v_x, v_c, t_a), Y2) -> true__ % 13.58/13.42 f7(f4(true__, v_x, Y2, t_a), t_a, c_times(v_x, v_x, t_a), Y2) -> true__ % 13.58/13.42 f7(f4(true__, v_x, Y2, t_a), t_a, v_c, Y2) -> true__ % 13.58/13.42 f7(true__, T_a, V_a, V_b) -> f6(class_Ring__and__Field_Opordered__cancel__semiring(T_a), V_a, V_b, T_a) % 13.58/13.42 f8(c_lessequals(c_0, V_a, T_a), V_b, T_a, V_a) -> true__ % 13.58/13.42 f8(f4(true__, v_x, Y0, Y1), Y2, Y1, Y0) -> true__ % 13.58/13.42 f8(true__, V_b, T_a, V_a) -> f7(c_lessequals(c_0, V_b, T_a), T_a, V_a, V_b) % 13.58/13.42 f9(class_Ring__and__Field_Oordered__idom(T), T) -> true__ % 13.58/13.42 f9(true__, t_a) -> true__ % 13.58/13.42 false__ -> true__ % 13.58/13.42 v_f(c_0) -> c_0 % 13.58/13.42 v_f(v_x) -> v_x % 13.58/13.42 with the LPO induced by % 13.58/13.42 f5 > f8 > f3 > c_less > f2 > f7 > class_Ring__and__Field_Opordered__cancel__semiring > f9 > f6 > c_0 > class_OrderedGroup_Olordered__ab__group__abs > class_Orderings_Oorder > f10 > f11 > c_lessequals > f4 > class_Ring__and__Field_Oordered__idom > v_h > c_times > c_HOL_Oabs > f1 > v_x > t_a > v_c > v_f > false__ > true__ % 13.58/13.42 % 13.58/13.42 % SZS output end Proof % 13.58/13.42 %------------------------------------------------------------------------------