%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : ANA044-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n017.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 4.67s 4.66s % Output : Proof 4.67s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.13 % Problem : ANA044-2 : TPTP v8.1.0. Released v3.2.0. % 0.09/0.14 % Command : moca.sh %s % 0.15/0.36 % Computer : n017.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 05:11:00 EDT 2022 % 0.15/0.36 % CPUTime : % 4.67/4.66 % SZS status Unsatisfiable % 4.67/4.66 % SZS output start Proof % 4.67/4.66 The input problem is unsatisfiable because % 4.67/4.66 % 4.67/4.66 [1] the following set of Horn clauses is unsatisfiable: % 4.67/4.66 % 4.67/4.66 c_lessequals(c_0, v_l(V_U, V_V), t_b) % 4.67/4.66 c_lessequals(c_0, v_h(V_U), t_b) % 4.67/4.66 c_times(v_l(v_x, v_xa), v_h(v_k(v_x, v_xa)), t_b) = c_HOL_Oabs(c_times(v_l(v_x, v_xa), v_h(v_k(v_x, v_xa)), t_b), t_b) ==> \bottom % 4.67/4.66 class_Ring__and__Field_Oordered__idom(t_b) % 4.67/4.66 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 % 4.67/4.66 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) % 4.67/4.66 class_Ring__and__Field_Oordered__idom(T) ==> class_Ring__and__Field_Opordered__cancel__semiring(T) % 4.67/4.66 class_Ring__and__Field_Oordered__idom(T) ==> class_OrderedGroup_Olordered__ab__group__abs(T) % 4.67/4.66 % 4.67/4.66 This holds because % 4.67/4.66 % 4.67/4.66 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 4.67/4.66 % 4.67/4.66 E: % 4.67/4.66 c_lessequals(c_0, v_h(V_U), t_b) = true__ % 4.67/4.66 c_lessequals(c_0, v_l(V_U, V_V), t_b) = true__ % 4.67/4.66 class_Ring__and__Field_Oordered__idom(t_b) = true__ % 4.67/4.66 f1(c_HOL_Oabs(c_times(v_l(v_x, v_xa), v_h(v_k(v_x, v_xa)), t_b), t_b)) = false__ % 4.67/4.66 f1(c_times(v_l(v_x, v_xa), v_h(v_k(v_x, v_xa)), t_b)) = true__ % 4.67/4.66 f2(true__, V_y, T_a) = c_HOL_Oabs(V_y, T_a) % 4.67/4.66 f3(c_lessequals(c_0, V_y, T_a), T_a, V_y) = V_y % 4.67/4.66 f3(true__, T_a, V_y) = f2(class_OrderedGroup_Olordered__ab__group__abs(T_a), V_y, T_a) % 4.67/4.66 f4(true__, V_a, V_b, T_a) = c_lessequals(c_0, c_times(V_a, V_b, T_a), T_a) % 4.67/4.66 f5(true__, T_a, V_a, V_b) = f4(class_Ring__and__Field_Opordered__cancel__semiring(T_a), V_a, V_b, T_a) % 4.67/4.66 f6(c_lessequals(c_0, V_a, T_a), V_b, T_a, V_a) = true__ % 4.67/4.66 f6(true__, V_b, T_a, V_a) = f5(c_lessequals(c_0, V_b, T_a), T_a, V_a, V_b) % 4.67/4.66 f7(class_Ring__and__Field_Oordered__idom(T), T) = true__ % 4.67/4.66 f7(true__, T) = class_Ring__and__Field_Opordered__cancel__semiring(T) % 4.67/4.66 f8(class_Ring__and__Field_Oordered__idom(T), T) = true__ % 4.67/4.66 f8(true__, T) = class_OrderedGroup_Olordered__ab__group__abs(T) % 4.67/4.66 G: % 4.67/4.66 true__ = false__ % 4.67/4.66 % 4.67/4.66 This holds because % 4.67/4.66 % 4.67/4.66 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 4.67/4.66 % 4.67/4.66 % 4.67/4.66 c_HOL_Oabs(V_y, T_a) -> f2(true__, V_y, T_a) % 4.67/4.66 c_lessequals(c_0, c_times(v_h(X1), v_h(Y0), t_b), t_b) -> true__ % 4.67/4.66 c_lessequals(c_0, c_times(v_h(X1), v_l(Y0, Y1), t_b), t_b) -> true__ % 4.67/4.66 c_lessequals(c_0, c_times(v_l(X1, X2), v_h(Y0), t_b), t_b) -> true__ % 4.67/4.66 c_lessequals(c_0, c_times(v_l(X1, X2), v_l(Y0, Y1), t_b), t_b) -> true__ % 4.67/4.66 c_lessequals(c_0, v_h(V_U), t_b) -> true__ % 4.67/4.66 c_lessequals(c_0, v_l(V_U, V_V), t_b) -> true__ % 4.67/4.66 class_OrderedGroup_Olordered__ab__group__abs(T) -> f8(true__, T) % 4.67/4.66 class_Ring__and__Field_Oordered__idom(t_b) -> true__ % 4.67/4.66 class_Ring__and__Field_Opordered__cancel__semiring(T) -> f7(true__, T) % 4.67/4.66 f1(c_times(v_l(v_x, v_xa), v_h(v_k(v_x, v_xa)), t_b)) -> true__ % 4.67/4.66 f1(f2(true__, c_times(v_l(v_x, v_xa), v_h(v_k(v_x, v_xa)), t_b), t_b)) -> false__ % 4.67/4.66 f2(true__, c_times(v_h(X0), v_h(X1), t_b), t_b) -> c_times(v_h(X0), v_h(X1), t_b) % 4.67/4.66 f2(true__, c_times(v_h(X0), v_l(X1, X2), t_b), t_b) -> c_times(v_h(X0), v_l(X1, X2), t_b) % 4.67/4.66 f2(true__, c_times(v_l(X0, X1), v_h(X2), t_b), t_b) -> c_times(v_l(X0, X1), v_h(X2), t_b) % 4.67/4.66 f2(true__, c_times(v_l(X0, X1), v_l(X2, X3), t_b), t_b) -> c_times(v_l(X0, X1), v_l(X2, X3), t_b) % 4.67/4.66 f2(true__, v_h(Y0), t_b) -> v_h(Y0) % 4.67/4.66 f2(true__, v_l(Y0, Y1), t_b) -> v_l(Y0, Y1) % 4.67/4.66 f3(c_lessequals(c_0, V_y, T_a), T_a, V_y) -> V_y % 4.67/4.66 f3(true__, T_a, V_y) -> f2(f8(true__, T_a), V_y, T_a) % 4.67/4.66 f4(true__, V_a, V_b, T_a) -> c_lessequals(c_0, c_times(V_a, V_b, T_a), T_a) % 4.67/4.66 f5(c_lessequals(c_0, Y2, t_b), t_b, c_times(v_h(X0), v_h(X1), t_b), Y2) -> true__ % 4.67/4.66 f5(c_lessequals(c_0, Y2, t_b), t_b, c_times(v_h(X0), v_l(X1, X2), t_b), Y2) -> true__ % 4.67/4.66 f5(c_lessequals(c_0, Y2, t_b), t_b, c_times(v_l(X0, X1), v_h(X2), t_b), Y2) -> true__ % 4.67/4.66 f5(c_lessequals(c_0, Y2, t_b), t_b, c_times(v_l(X0, X1), v_l(X2, X3), t_b), Y2) -> true__ % 4.67/4.66 f5(c_lessequals(c_0, Y2, t_b), t_b, v_h(X0), Y2) -> true__ % 4.67/4.66 f5(c_lessequals(c_0, Y2, t_b), t_b, v_l(X0, X1), Y2) -> true__ % 4.67/4.66 f5(true__, T_a, V_a, V_b) -> f4(f7(true__, T_a), V_a, V_b, T_a) % 4.67/4.66 f6(c_lessequals(c_0, V_a, T_a), V_b, T_a, V_a) -> true__ % 4.67/4.66 f6(true__, V_b, T_a, V_a) -> f5(c_lessequals(c_0, V_b, T_a), T_a, V_a, V_b) % 4.67/4.66 f6(true__, Y2, t_b, c_times(v_h(X0), v_h(X1), t_b)) -> true__ % 4.67/4.66 f6(true__, Y2, t_b, c_times(v_h(X0), v_l(X1, X2), t_b)) -> true__ % 4.67/4.66 f6(true__, Y2, t_b, c_times(v_l(X0, X1), v_h(X2), t_b)) -> true__ % 4.67/4.66 f6(true__, Y2, t_b, v_h(X0)) -> true__ % 4.67/4.66 f6(true__, Y2, t_b, v_l(X0, X1)) -> true__ % 4.67/4.66 f7(class_Ring__and__Field_Oordered__idom(T), T) -> true__ % 4.67/4.66 f7(true__, t_b) -> true__ % 4.67/4.66 f8(class_Ring__and__Field_Oordered__idom(T), T) -> true__ % 4.67/4.66 f8(true__, t_b) -> true__ % 4.67/4.66 false__ -> true__ % 4.67/4.66 with the LPO induced by % 4.67/4.66 v_h > f6 > f5 > class_Ring__and__Field_Opordered__cancel__semiring > f7 > f4 > c_lessequals > c_times > v_k > v_xa > v_x > f1 > f3 > c_HOL_Oabs > f2 > class_OrderedGroup_Olordered__ab__group__abs > f8 > v_l > c_0 > t_b > class_Ring__and__Field_Oordered__idom > false__ > true__ % 4.67/4.66 % 4.67/4.66 % SZS output end Proof % 4.67/4.66 %------------------------------------------------------------------------------