%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : ANA039-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n019.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 19:15:50 EDT 2022 % Result : Unsatisfiable 15.15s 15.08s % Output : Proof 15.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : ANA039-2 : TPTP v8.1.0. Released v3.2.0. % 0.06/0.13 % Command : moca.sh %s % 0.12/0.34 % Computer : n019.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Fri Jul 8 06:07:53 EDT 2022 % 0.12/0.34 % CPUTime : % 15.15/15.08 % SZS status Unsatisfiable % 15.15/15.08 % SZS output start Proof % 15.15/15.08 The input problem is unsatisfiable because % 15.15/15.08 % 15.15/15.08 [1] the following set of Horn clauses is unsatisfiable: % 15.15/15.08 % 15.15/15.08 c_lessequals(c_HOL_Oabs(v_h(V_U), t_a), c_times(v_c, c_HOL_Oabs(v_f(V_U), t_a), t_a), t_a) % 15.15/15.08 c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a) ==> \bottom % 15.15/15.08 class_Ring__and__Field_Oordered__idom(t_a) % 15.15/15.08 class_OrderedGroup_Olordered__ab__group__abs(T_a) ==> c_lessequals(V_a, c_HOL_Oabs(V_a, T_a), T_a) % 15.15/15.08 class_OrderedGroup_Olordered__ab__group__abs(T_a) ==> c_lessequals(c_0, c_HOL_Oabs(V_a, T_a), T_a) % 15.15/15.08 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) % 15.15/15.08 class_Ring__and__Field_Opordered__semiring(T_a) & c_lessequals(V_a, V_b, T_a) & c_lessequals(c_0, V_c, T_a) ==> c_lessequals(c_times(V_a, V_c, T_a), c_times(V_b, V_c, T_a), T_a) % 15.15/15.08 class_Ring__and__Field_Oordered__idom(T) ==> class_Ring__and__Field_Opordered__semiring(T) % 15.15/15.08 class_Ring__and__Field_Oordered__idom(T) ==> class_Orderings_Oorder(T) % 15.15/15.08 class_Ring__and__Field_Oordered__idom(T) ==> class_OrderedGroup_Olordered__ab__group__abs(T) % 15.15/15.08 % 15.15/15.08 This holds because % 15.15/15.08 % 15.15/15.08 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 15.15/15.08 % 15.15/15.08 E: % 15.15/15.08 c_lessequals(c_HOL_Oabs(v_h(V_U), t_a), c_times(v_c, c_HOL_Oabs(v_f(V_U), t_a), t_a), t_a) = true__ % 15.15/15.08 class_Ring__and__Field_Oordered__idom(t_a) = true__ % 15.15/15.08 f1(c_lessequals(c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a)) = true__ % 15.15/15.08 f1(true__) = false__ % 15.15/15.08 f10(class_Ring__and__Field_Oordered__idom(T), T) = true__ % 15.15/15.08 f10(true__, T) = class_Ring__and__Field_Opordered__semiring(T) % 15.15/15.08 f11(class_Ring__and__Field_Oordered__idom(T), T) = true__ % 15.15/15.08 f11(true__, T) = class_Orderings_Oorder(T) % 15.15/15.08 f12(class_Ring__and__Field_Oordered__idom(T), T) = true__ % 15.15/15.08 f12(true__, T) = class_OrderedGroup_Olordered__ab__group__abs(T) % 15.15/15.08 f2(class_OrderedGroup_Olordered__ab__group__abs(T_a), V_a, T_a) = true__ % 15.15/15.08 f2(true__, V_a, T_a) = c_lessequals(V_a, c_HOL_Oabs(V_a, T_a), T_a) % 15.15/15.08 f3(class_OrderedGroup_Olordered__ab__group__abs(T_a), V_a, T_a) = true__ % 15.15/15.08 f3(true__, V_a, T_a) = c_lessequals(c_0, c_HOL_Oabs(V_a, T_a), T_a) % 15.15/15.08 f4(true__, V_x, V_z, T_a) = c_lessequals(V_x, V_z, T_a) % 15.15/15.08 f5(true__, T_a, V_x, V_z) = f4(class_Orderings_Oorder(T_a), V_x, V_z, T_a) % 15.15/15.08 f6(c_lessequals(V_x, V_y, T_a), V_y, V_z, T_a, V_x) = true__ % 15.15/15.08 f6(true__, V_y, V_z, T_a, V_x) = f5(c_lessequals(V_y, V_z, T_a), T_a, V_x, V_z) % 15.15/15.08 f7(true__, V_a, V_c, T_a, V_b) = c_lessequals(c_times(V_a, V_c, T_a), c_times(V_b, V_c, T_a), T_a) % 15.15/15.08 f8(true__, T_a, V_a, V_c, V_b) = f7(class_Ring__and__Field_Opordered__semiring(T_a), V_a, V_c, T_a, V_b) % 15.15/15.08 f9(c_lessequals(c_0, V_c, T_a), V_a, V_b, T_a, V_c) = true__ % 15.15/15.08 f9(true__, V_a, V_b, T_a, V_c) = f8(c_lessequals(V_a, V_b, T_a), T_a, V_a, V_c, V_b) % 15.15/15.08 G: % 15.15/15.08 true__ = false__ % 15.15/15.08 % 15.15/15.08 This holds because % 15.15/15.08 % 15.15/15.08 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 15.15/15.08 % 15.15/15.08 % 15.15/15.08 c_lessequals(V_x, V_z, T_a) -> f4(true__, V_x, V_z, T_a) % 15.15/15.08 class_OrderedGroup_Olordered__ab__group__abs(T) -> f12(true__, T) % 15.15/15.08 class_Orderings_Oorder(T) -> f11(true__, T) % 15.15/15.08 class_Ring__and__Field_Oordered__idom(t_a) -> true__ % 15.15/15.08 class_Ring__and__Field_Opordered__semiring(T) -> f10(true__, T) % 15.15/15.08 f1(f4(true__, c_HOL_Oabs(v_h(v_x), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(v_x), t_a), t_a), t_a)) -> true__ % 15.15/15.08 f1(true__) -> false__ % 15.15/15.08 f10(class_Ring__and__Field_Oordered__idom(T), T) -> true__ % 15.15/15.08 f10(true__, t_a) -> true__ % 15.15/15.08 f11(class_Ring__and__Field_Oordered__idom(T), T) -> true__ % 15.15/15.08 f11(true__, t_a) -> true__ % 15.15/15.08 f12(class_Ring__and__Field_Oordered__idom(T), T) -> true__ % 15.15/15.08 f12(true__, t_a) -> true__ % 15.15/15.08 f2(f12(true__, Y0), Y1, Y0) -> true__ % 15.15/15.08 f2(true__, V_a, T_a) -> f4(true__, V_a, c_HOL_Oabs(V_a, T_a), T_a) % 15.15/15.08 f3(f12(true__, Y0), Y1, Y0) -> true__ % 15.15/15.08 f3(true__, V_a, T_a) -> f4(true__, c_0, c_HOL_Oabs(V_a, T_a), T_a) % 15.15/15.08 f4(true__, Y0, c_HOL_Oabs(c_HOL_Oabs(Y0, t_a), t_a), t_a) -> true__ % 15.15/15.08 f4(true__, Y0, c_HOL_Oabs(c_HOL_Oabs(c_HOL_Oabs(Y0, t_a), t_a), t_a), t_a) -> true__ % 15.15/15.08 f4(true__, Y0, c_HOL_Oabs(c_HOL_Oabs(c_HOL_Oabs(c_HOL_Oabs(Y0, t_a), t_a), t_a), t_a), t_a) -> true__ % 15.15/15.08 f4(true__, Y0, c_HOL_Oabs(c_HOL_Oabs(c_HOL_Oabs(c_HOL_Oabs(c_HOL_Oabs(Y0, t_a), t_a), t_a), t_a), t_a), t_a) -> true__ % 15.15/15.08 f4(true__, Y0, c_HOL_Oabs(c_HOL_Oabs(c_HOL_Oabs(c_HOL_Oabs(c_HOL_Oabs(c_HOL_Oabs(Y0, t_a), t_a), t_a), t_a), t_a), t_a), t_a) -> true__ % 15.15/15.08 f4(true__, Y1, c_HOL_Oabs(Y1, t_a), t_a) -> true__ % 15.15/15.08 f4(true__, c_0, c_HOL_Oabs(Y1, t_a), t_a) -> true__ % 15.15/15.08 f4(true__, c_0, c_times(c_HOL_Oabs(c_HOL_Oabs(v_c, t_a), t_a), c_HOL_Oabs(v_f(Y0), t_a), t_a), t_a) -> true__ % 15.15/15.08 f4(true__, c_0, c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(Y0), t_a), t_a), t_a) -> true__ % 15.15/15.08 f4(true__, c_0, c_times(v_c, c_HOL_Oabs(v_f(X0), t_a), t_a), t_a) -> true__ % 15.15/15.08 f4(true__, c_HOL_Oabs(v_h(Y0), t_a), c_HOL_Oabs(c_HOL_Oabs(c_times(v_c, c_HOL_Oabs(v_f(Y0), t_a), t_a), t_a), t_a), t_a) -> true__ % 15.15/15.08 f4(true__, c_HOL_Oabs(v_h(Y0), t_a), c_HOL_Oabs(c_times(v_c, c_HOL_Oabs(v_f(Y0), t_a), t_a), t_a), t_a) -> true__ % 15.15/15.08 f4(true__, c_HOL_Oabs(v_h(Y0), t_a), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(Y0), t_a), t_a), t_a) -> true__ % 15.15/15.08 f4(true__, c_HOL_Oabs(v_h(Y0), t_a), c_times(v_c, c_HOL_Oabs(v_f(Y0), t_a), t_a), t_a) -> true__ % 15.15/15.08 f4(true__, c_times(Y0, c_HOL_Oabs(Y2, t_a), t_a), c_times(c_HOL_Oabs(Y0, t_a), c_HOL_Oabs(Y2, t_a), t_a), t_a) -> true__ % 15.15/15.08 f4(true__, c_times(c_0, c_HOL_Oabs(Y2, t_a), t_a), c_times(c_HOL_Oabs(X0, t_a), c_HOL_Oabs(Y2, t_a), t_a), t_a) -> true__ % 15.15/15.08 f4(true__, v_h(X0), c_HOL_Oabs(c_times(v_c, c_HOL_Oabs(v_f(X0), t_a), t_a), t_a), t_a) -> true__ % 15.15/15.08 f4(true__, v_h(X0), c_times(v_c, c_HOL_Oabs(v_f(X0), t_a), t_a), t_a) -> true__ % 15.15/15.08 f4(true__, v_h(Y0), c_HOL_Oabs(c_HOL_Oabs(c_HOL_Oabs(c_times(v_c, c_HOL_Oabs(v_f(Y0), t_a), t_a), t_a), t_a), t_a), t_a) -> true__ % 15.15/15.08 f4(true__, v_h(Y0), c_HOL_Oabs(c_HOL_Oabs(c_times(v_c, c_HOL_Oabs(v_f(Y0), t_a), t_a), t_a), t_a), t_a) -> true__ % 15.15/15.08 f4(true__, v_h(Y0), c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(Y0), t_a), t_a), t_a) -> true__ % 15.15/15.08 f5(f4(true__, c_HOL_Oabs(X0, t_a), Y3, t_a), t_a, c_0, Y3) -> true__ % 15.15/15.08 f5(f4(true__, c_HOL_Oabs(Y0, t_a), Y3, t_a), t_a, Y0, Y3) -> true__ % 15.15/15.08 f5(f4(true__, c_HOL_Oabs(c_HOL_Oabs(Y0, t_a), t_a), Y3, t_a), t_a, Y0, Y3) -> true__ % 15.15/15.08 f5(f4(true__, c_HOL_Oabs(c_HOL_Oabs(c_HOL_Oabs(Y0, t_a), t_a), t_a), Y3, t_a), t_a, Y0, Y3) -> true__ % 15.15/15.08 f5(f4(true__, c_HOL_Oabs(c_HOL_Oabs(c_HOL_Oabs(c_HOL_Oabs(Y0, t_a), t_a), t_a), t_a), Y3, t_a), t_a, Y0, Y3) -> true__ % 15.15/15.08 f5(f4(true__, c_HOL_Oabs(c_times(v_c, c_HOL_Oabs(v_f(X0), t_a), t_a), t_a), Y3, t_a), t_a, v_h(X0), Y3) -> true__ % 15.15/15.08 f5(f4(true__, c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(X0), t_a), t_a), Y3, t_a), t_a, c_0, Y3) -> true__ % 15.15/15.08 f5(f4(true__, c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(X0), t_a), t_a), Y3, t_a), t_a, v_h(X0), Y3) -> true__ % 15.15/15.08 f5(f4(true__, c_times(v_c, c_HOL_Oabs(v_f(X0), t_a), t_a), Y3, t_a), t_a, c_0, Y3) -> true__ % 15.15/15.08 f5(f4(true__, c_times(v_c, c_HOL_Oabs(v_f(X0), t_a), t_a), Y3, t_a), t_a, c_HOL_Oabs(v_h(X0), t_a), Y3) -> true__ % 15.15/15.08 f5(f4(true__, c_times(v_c, c_HOL_Oabs(v_f(X0), t_a), t_a), Y3, t_a), t_a, v_h(X0), Y3) -> true__ % 15.15/15.08 f5(true__, T_a, V_x, V_z) -> f4(f11(true__, T_a), V_x, V_z, T_a) % 15.15/15.08 f6(f4(true__, Y0, Y1, Y2), Y1, Y3, Y2, Y0) -> true__ % 15.15/15.08 f6(true__, V_y, V_z, T_a, V_x) -> f5(f4(true__, V_y, V_z, T_a), T_a, V_x, V_z) % 15.15/15.08 f7(true__, V_a, V_c, T_a, V_b) -> f4(true__, c_times(V_a, V_c, T_a), c_times(V_b, V_c, T_a), T_a) % 15.15/15.08 f8(f4(true__, Y2, Y3, t_a), t_a, Y2, c_HOL_Oabs(X0, t_a), Y3) -> true__ % 15.15/15.08 f8(f4(true__, Y2, Y3, t_a), t_a, Y2, c_times(c_HOL_Oabs(v_c, t_a), c_HOL_Oabs(v_f(X0), t_a), t_a), Y3) -> true__ % 15.15/15.08 f8(f4(true__, Y2, Y3, t_a), t_a, Y2, c_times(v_c, c_HOL_Oabs(v_f(X0), t_a), t_a), Y3) -> true__ % 15.15/15.08 f8(true__, T_a, V_a, V_c, V_b) -> f7(f10(true__, T_a), V_a, V_c, T_a, V_b) % 15.15/15.08 f9(f4(true__, c_0, Y0, Y1), Y2, Y3, Y1, Y0) -> true__ % 15.15/15.08 f9(true__, V_a, V_b, T_a, V_c) -> f8(f4(true__, V_a, V_b, T_a), T_a, V_a, V_c, V_b) % 15.15/15.08 false__ -> true__ % 15.15/15.08 with the LPO induced by % 15.15/15.08 v_x > v_h > class_OrderedGroup_Olordered__ab__group__abs > f12 > t_a > f3 > c_0 > f9 > f6 > f5 > f2 > f8 > f7 > c_lessequals > class_Orderings_Oorder > class_Ring__and__Field_Opordered__semiring > f10 > f11 > c_times > f1 > f4 > v_f > v_c > class_Ring__and__Field_Oordered__idom > c_HOL_Oabs > false__ > true__ % 15.15/15.08 % 15.15/15.08 % SZS output end Proof % 15.15/15.08 %------------------------------------------------------------------------------