%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : ANA009-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n011.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 1.35s 1.50s % Output : Proof 1.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ANA009-2 : TPTP v8.1.0. Released v3.2.0. % 0.12/0.12 % Command : moca.sh %s % 0.12/0.33 % Computer : n011.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Fri Jul 8 04:13:09 EDT 2022 % 0.19/0.33 % CPUTime : % 1.35/1.50 % SZS status Unsatisfiable % 1.35/1.50 % SZS output start Proof % 1.35/1.50 The input problem is unsatisfiable because % 1.35/1.50 % 1.35/1.50 [1] the following set of Horn clauses is unsatisfiable: % 1.35/1.50 % 1.35/1.50 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a) & c_lessequals(V_a, V_b, T_a) ==> c_lessequals(c_plus(V_a, V_c, T_a), c_plus(V_b, V_c, T_a), T_a) % 1.35/1.50 class_OrderedGroup_Oab__group__add(T_a) ==> c_plus(V_a, c_uminus(V_a, T_a), T_a) = c_0 % 1.35/1.50 c_lessequals(v_lb(V_U), v_f(V_U), t_b) % 1.35/1.50 c_lessequals(c_0, c_plus(v_f(v_x), c_uminus(v_lb(v_x), t_b), t_b), t_b) ==> \bottom % 1.35/1.50 class_Ring__and__Field_Oordered__idom(T) ==> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T) % 1.35/1.50 class_Ring__and__Field_Oordered__idom(T) ==> class_OrderedGroup_Oab__group__add(T) % 1.35/1.50 class_Ring__and__Field_Oordered__idom(t_b) % 1.35/1.50 % 1.35/1.50 This holds because % 1.35/1.50 % 1.35/1.50 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 1.35/1.50 % 1.35/1.50 E: % 1.35/1.50 c_lessequals(v_lb(V_U), v_f(V_U), t_b) = true__ % 1.35/1.50 class_Ring__and__Field_Oordered__idom(t_b) = true__ % 1.35/1.50 f1(true__, V_a, V_c, T_a, V_b) = c_lessequals(c_plus(V_a, V_c, T_a), c_plus(V_b, V_c, T_a), T_a) % 1.35/1.50 f2(c_lessequals(V_a, V_b, T_a), T_a, V_a, V_c, V_b) = true__ % 1.35/1.50 f2(true__, T_a, V_a, V_c, V_b) = f1(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a), V_a, V_c, T_a, V_b) % 1.35/1.50 f3(class_OrderedGroup_Oab__group__add(T_a), V_a, T_a) = c_0 % 1.35/1.50 f3(true__, V_a, T_a) = c_plus(V_a, c_uminus(V_a, T_a), T_a) % 1.35/1.50 f4(c_lessequals(c_0, c_plus(v_f(v_x), c_uminus(v_lb(v_x), t_b), t_b), t_b)) = true__ % 1.35/1.50 f4(true__) = false__ % 1.35/1.50 f5(class_Ring__and__Field_Oordered__idom(T), T) = true__ % 1.35/1.50 f5(true__, T) = class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T) % 1.35/1.50 f6(class_Ring__and__Field_Oordered__idom(T), T) = true__ % 1.35/1.50 f6(true__, T) = class_OrderedGroup_Oab__group__add(T) % 1.35/1.50 G: % 1.35/1.50 true__ = false__ % 1.35/1.50 % 1.35/1.50 This holds because % 1.35/1.50 % 1.35/1.50 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 1.35/1.50 % 1.35/1.50 % 1.35/1.50 c_lessequals(c_0, c_plus(Y2, c_uminus(Y0, t_b), t_b), t_b) -> f1(true__, Y0, c_uminus(Y0, t_b), t_b, Y2) % 1.35/1.50 c_lessequals(c_plus(V_a, V_c, T_a), c_plus(V_b, V_c, T_a), T_a) -> f1(true__, V_a, V_c, T_a, V_b) % 1.35/1.50 c_lessequals(c_plus(Y0, c_uminus(Y1, t_b), t_b), c_0, t_b) -> f1(true__, Y0, c_uminus(Y1, t_b), t_b, Y1) % 1.35/1.50 c_lessequals(c_plus(Y0, c_uminus(Y3, Y2), Y2), f3(true__, Y3, Y2), Y2) -> f1(true__, Y0, c_uminus(Y3, Y2), Y2, Y3) % 1.35/1.50 c_lessequals(f3(true__, Y0, Y2), c_plus(Y3, c_uminus(Y0, Y2), Y2), Y2) -> f1(true__, Y0, c_uminus(Y0, Y2), Y2, Y3) % 1.35/1.50 c_lessequals(v_lb(V_U), v_f(V_U), t_b) -> true__ % 1.35/1.50 c_plus(V_a, c_uminus(V_a, T_a), T_a) -> f3(true__, V_a, T_a) % 1.35/1.50 class_OrderedGroup_Oab__group__add(T) -> f6(true__, T) % 1.35/1.50 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T) -> f5(true__, T) % 1.35/1.50 class_Ring__and__Field_Oordered__idom(t_b) -> true__ % 1.35/1.50 f1(f5(true__, t_b), v_lb(X0), Y3, t_b, v_f(X0)) -> true__ % 1.35/1.50 f1(true__, Y0, c_uminus(Y0, Y1), Y1, Y0) -> c_lessequals(f3(true__, Y0, Y1), f3(true__, Y0, Y1), Y1) % 1.35/1.50 f1(true__, c_0, Y2, t_b, c_plus(c_0, c_uminus(c_plus(v_lb(X0), c_uminus(v_f(X0), t_b), t_b), t_b), t_b)) -> true__ % 1.35/1.50 f1(true__, c_0, Y2, t_b, c_plus(c_plus(v_f(X1), c_uminus(v_lb(X1), t_b), t_b), c_uminus(c_0, t_b), t_b)) -> true__ % 1.35/1.50 f1(true__, c_0, Y3, t_b, c_plus(v_f(X0), c_uminus(v_lb(X0), t_b), t_b)) -> true__ % 1.35/1.50 f1(true__, c_plus(c_0, Y1, t_b), Y4, t_b, c_plus(c_plus(v_f(X1), c_uminus(v_lb(X1), t_b), t_b), Y1, t_b)) -> true__ % 1.35/1.50 f1(true__, c_plus(c_0, c_uminus(c_plus(v_f(X1), c_uminus(v_lb(X1), t_b), t_b), t_b), t_b), Y2, t_b, c_0) -> true__ % 1.35/1.50 f1(true__, c_plus(c_plus(v_lb(X0), X1, t_b), Y1, t_b), Y4, t_b, c_plus(c_plus(v_f(X0), X1, t_b), Y1, t_b)) -> true__ % 1.35/1.50 f1(true__, c_plus(c_plus(v_lb(X0), c_uminus(v_f(X0), t_b), t_b), Y1, t_b), Y4, t_b, c_plus(c_0, Y1, t_b)) -> true__ % 1.35/1.50 f1(true__, c_plus(v_lb(X0), Y1, t_b), Y4, t_b, c_plus(v_f(X0), Y1, t_b)) -> true__ % 1.35/1.50 f1(true__, c_plus(v_lb(X0), c_uminus(v_f(X0), t_b), t_b), Y3, t_b, c_0) -> true__ % 1.35/1.50 f1(true__, v_lb(Y0), Y1, t_b, v_f(Y0)) -> true__ % 1.35/1.50 f2(c_lessequals(V_a, V_b, T_a), T_a, V_a, V_c, V_b) -> true__ % 1.35/1.50 f2(f1(true__, X0, X1, Y2, X3), Y2, c_plus(X0, X1, Y2), Y3, c_plus(X3, X1, Y2)) -> true__ % 1.35/1.50 f2(f1(true__, Y0, c_uminus(Y0, Y2), Y2, Y3), Y2, f3(true__, Y0, Y2), Y4, c_plus(Y3, c_uminus(Y0, Y2), Y2)) -> true__ % 1.35/1.50 f2(f1(true__, Y0, c_uminus(Y0, t_b), t_b, Y2), t_b, c_0, Y3, c_plus(Y2, c_uminus(Y0, t_b), t_b)) -> true__ % 1.35/1.50 f2(f1(true__, Y0, c_uminus(Y1, t_b), t_b, Y1), t_b, c_plus(Y0, c_uminus(Y1, t_b), t_b), Y3, c_0) -> true__ % 1.35/1.50 f2(f1(true__, Y0, c_uminus(Y3, Y2), Y2, Y3), Y2, c_plus(Y0, c_uminus(Y3, Y2), Y2), Y4, f3(true__, Y3, Y2)) -> true__ % 1.35/1.50 f2(true__, T_a, V_a, V_c, V_b) -> f1(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a), V_a, V_c, T_a, V_b) % 1.35/1.50 f3(class_OrderedGroup_Oab__group__add(T_a), V_a, T_a) -> c_0 % 1.35/1.50 f3(f6(true__, Y0), Y1, Y0) -> c_0 % 1.35/1.50 f3(true__, Y1, t_b) -> c_0 % 1.35/1.50 f4(c_lessequals(c_0, c_plus(v_f(v_x), c_uminus(v_lb(v_x), t_b), t_b), t_b)) -> true__ % 1.35/1.50 f4(true__) -> false__ % 1.35/1.50 f5(class_Ring__and__Field_Oordered__idom(T), T) -> true__ % 1.35/1.50 f5(true__, t_b) -> true__ % 1.35/1.50 f6(class_Ring__and__Field_Oordered__idom(T), T) -> true__ % 1.35/1.50 f6(true__, t_b) -> true__ % 1.35/1.50 false__ -> true__ % 1.35/1.50 with the LPO induced by % 1.35/1.50 c_uminus > f3 > c_0 > v_lb > f2 > c_lessequals > f1 > class_OrderedGroup_Opordered__ab__semigroup__add__imp__le > f5 > class_OrderedGroup_Oab__group__add > f6 > class_Ring__and__Field_Oordered__idom > v_x > f4 > t_b > v_f > c_plus > false__ > true__ % 1.35/1.50 % 1.35/1.50 % SZS output end Proof % 1.35/1.50 %------------------------------------------------------------------------------