%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : ANA035-2 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n007.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 19:15:48 EDT 2022 % Result : Unsatisfiable 61.75s 61.73s % Output : Proof 61.75s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : ANA035-2 : TPTP v8.1.0. Released v3.2.0. % 0.08/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n007.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Fri Jul 8 05:16:45 EDT 2022 % 0.13/0.34 % CPUTime : % 61.75/61.73 % SZS status Unsatisfiable % 61.75/61.73 % SZS output start Proof % 61.75/61.73 The input problem is unsatisfiable because % 61.75/61.73 % 61.75/61.73 [1] the following set of Horn clauses is unsatisfiable: % 61.75/61.73 % 61.75/61.73 c_times(c_times(v_c, v_ca, t_b), c_HOL_Oabs(c_times(v_f(v_x), v_g(v_x), t_b), t_b), t_b) = c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b) ==> \bottom % 61.75/61.73 class_Ring__and__Field_Oordered__idom(t_b) % 61.75/61.73 class_OrderedGroup_Oab__semigroup__mult(T_a) ==> c_times(V_a, V_b, T_a) = c_times(V_b, V_a, T_a) % 61.75/61.73 class_OrderedGroup_Oab__semigroup__mult(T_a) ==> c_times(V_a, c_times(V_b, V_c, T_a), T_a) = c_times(V_b, c_times(V_a, V_c, T_a), T_a) % 61.75/61.73 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) % 61.75/61.73 class_Ring__and__Field_Oordered__idom(T) ==> class_OrderedGroup_Oab__semigroup__mult(T) % 61.75/61.73 % 61.75/61.73 This holds because % 61.75/61.73 % 61.75/61.73 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 61.75/61.73 % 61.75/61.73 E: % 61.75/61.73 class_Ring__and__Field_Oordered__idom(t_b) = true__ % 61.75/61.73 f1(c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b)) = false__ % 61.75/61.73 f1(c_times(c_times(v_c, v_ca, t_b), c_HOL_Oabs(c_times(v_f(v_x), v_g(v_x), t_b), t_b), t_b)) = true__ % 61.75/61.73 f2(class_OrderedGroup_Oab__semigroup__mult(T_a), V_a, V_b, T_a) = c_times(V_b, V_a, T_a) % 61.75/61.73 f2(true__, V_a, V_b, T_a) = c_times(V_a, V_b, T_a) % 61.75/61.73 f3(class_OrderedGroup_Oab__semigroup__mult(T_a), V_a, V_b, V_c, T_a) = c_times(V_b, c_times(V_a, V_c, T_a), T_a) % 61.75/61.73 f3(true__, V_a, V_b, V_c, T_a) = c_times(V_a, c_times(V_b, V_c, T_a), T_a) % 61.75/61.73 f4(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) % 61.75/61.73 f4(true__, V_a, V_b, T_a) = c_HOL_Oabs(c_times(V_a, V_b, T_a), T_a) % 61.75/61.73 f5(class_Ring__and__Field_Oordered__idom(T), T) = true__ % 61.75/61.73 f5(true__, T) = class_OrderedGroup_Oab__semigroup__mult(T) % 61.75/61.73 G: % 61.75/61.73 true__ = false__ % 61.75/61.73 % 61.75/61.73 This holds because % 61.75/61.73 % 61.75/61.73 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 61.75/61.73 % 61.75/61.73 c_times(Y1, Y2, t_b) = c_times(Y2, Y1, t_b) % 61.75/61.73 c_times(Y1, c_times(Y2, Y3, t_b), t_b) = c_times(Y2, c_times(Y1, Y3, t_b), t_b) % 61.75/61.73 c_times(Y2, c_times(Y0, Y1, t_b), t_b) = c_times(Y1, c_times(Y0, Y2, t_b), t_b) % 61.75/61.73 c_times(Y2, c_times(Y1, Y0, t_b), t_b) = c_times(Y1, c_times(Y0, Y2, t_b), t_b) % 61.75/61.73 c_times(Y2, c_times(Y1, Y0, t_b), t_b) = c_times(Y2, c_times(Y0, Y1, t_b), t_b) % 61.75/61.73 c_times(c_HOL_Oabs(X1, t_b), c_times(c_HOL_Oabs(X2, t_b), c_HOL_Oabs(Y0, t_b), t_b), t_b) = c_times(c_HOL_Oabs(Y0, t_b), c_times(c_HOL_Oabs(X1, t_b), c_HOL_Oabs(X2, t_b), t_b), t_b) % 61.75/61.73 c_times(c_HOL_Oabs(X1, t_b), c_times(c_HOL_Oabs(Y0, t_b), c_HOL_Oabs(X2, t_b), t_b), t_b) = c_times(c_HOL_Oabs(Y0, t_b), c_times(c_HOL_Oabs(X1, t_b), c_HOL_Oabs(X2, t_b), t_b), t_b) % 61.75/61.73 c_times(c_HOL_Oabs(X2, t_b), c_times(c_HOL_Oabs(X1, t_b), c_HOL_Oabs(Y0, t_b), t_b), t_b) = c_times(c_HOL_Oabs(Y0, t_b), c_times(c_HOL_Oabs(X1, t_b), c_HOL_Oabs(X2, t_b), t_b), t_b) % 61.75/61.73 c_times(c_HOL_Oabs(Y1, t_b), c_HOL_Oabs(Y0, t_b), t_b) = c_times(c_HOL_Oabs(Y0, t_b), c_HOL_Oabs(Y1, t_b), t_b) % 61.75/61.73 c_HOL_Oabs(c_times(Y1, Y2, t_b), t_b) -> c_times(c_HOL_Oabs(Y1, t_b), c_HOL_Oabs(Y2, t_b), t_b) % 61.75/61.73 c_times(c_times(Y1, Y2, t_b), Y0, t_b) -> c_times(Y2, c_times(Y1, Y0, t_b), t_b) % 61.75/61.73 class_OrderedGroup_Oab__semigroup__mult(T) -> f5(true__, T) % 61.75/61.73 class_Ring__and__Field_Oordered__idom(t_b) -> true__ % 61.75/61.73 f1(c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_times(v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b)) -> false__ % 61.75/61.73 f1(c_times(c_times(v_c, v_ca, t_b), c_HOL_Oabs(c_times(v_f(v_x), v_g(v_x), t_b), t_b), t_b)) -> true__ % 61.75/61.73 f1(c_times(c_times(v_ca, v_c, t_b), c_HOL_Oabs(c_times(v_f(v_x), v_g(v_x), t_b), t_b), t_b)) -> true__ % 61.75/61.73 f1(c_times(c_times(v_ca, v_c, t_b), c_times(c_HOL_Oabs(v_f(v_x), t_b), c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b)) -> true__ % 61.75/61.73 f1(c_times(v_c, c_times(v_ca, c_times(c_HOL_Oabs(v_f(v_x), t_b), c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b)) -> false__ % 61.75/61.73 f1(c_times(v_c, c_times(v_ca, c_times(c_HOL_Oabs(v_f(v_x), t_b), c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b), t_b)) -> true__ % 61.75/61.73 f1(c_times(v_ca, c_times(c_times(v_c, c_HOL_Oabs(v_f(v_x), t_b), t_b), c_HOL_Oabs(v_g(v_x), t_b), t_b), t_b)) -> false__ % 61.75/61.73 f1(f2(true__, f2(true__, v_c, v_ca, t_b), c_HOL_Oabs(f2(true__, v_f(v_x), v_g(v_x), t_b), t_b), t_b)) -> true__ % 61.75/61.73 f1(f2(true__, v_c, f2(true__, v_ca, c_HOL_Oabs(f2(true__, v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b)) -> false__ % 61.75/61.73 f1(f2(true__, v_c, f2(true__, v_ca, c_HOL_Oabs(f2(true__, v_f(v_x), v_g(v_x), t_b), t_b), t_b), t_b)) -> true__ % 61.75/61.73 f1(f3(true__, f2(true__, c_HOL_Oabs(v_f(v_x), t_b), v_c, t_b), v_ca, c_HOL_Oabs(v_g(v_x), t_b), t_b)) -> false__ % 61.75/61.73 f2(f5(true__, Y0), Y1, Y2, Y0) -> c_times(Y2, Y1, Y0) % 61.75/61.73 f2(true__, V_a, V_b, T_a) -> c_times(V_a, V_b, T_a) % 61.75/61.73 f2(true__, f2(true__, Y1, Y2, t_b), Y0, t_b) -> c_times(Y1, c_times(Y0, Y2, t_b), t_b) % 61.75/61.73 f2(true__, f2(true__, Y1, Y2, t_b), Y0, t_b) -> c_times(Y1, c_times(Y2, Y0, t_b), t_b) % 61.75/61.73 f3(f5(true__, Y3), Y1, Y0, Y2, Y3) -> c_times(Y0, c_times(Y1, Y2, Y3), Y3) % 61.75/61.73 f3(true__, V_a, V_b, V_c, T_a) -> c_times(V_a, c_times(V_b, V_c, T_a), T_a) % 61.75/61.73 f4(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) % 61.75/61.73 f4(true__, V_a, V_b, T_a) -> c_HOL_Oabs(c_times(V_a, V_b, T_a), T_a) % 61.75/61.73 f5(class_Ring__and__Field_Oordered__idom(T), T) -> true__ % 61.75/61.73 f5(true__, t_b) -> true__ % 61.75/61.73 false__ -> true__ % 61.75/61.73 with the LPO induced by % 61.75/61.73 v_x > f2 > f3 > f1 > class_Ring__and__Field_Oordered__idom > f4 > c_HOL_Oabs > c_times > v_g > v_f > v_ca > v_c > class_OrderedGroup_Oab__semigroup__mult > t_b > f5 > false__ > true__ % 61.75/61.73 % 61.75/61.73 % SZS output end Proof % 61.75/61.73 %------------------------------------------------------------------------------