TSTP Solution File: ANA024-2 by Moca---0.1
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%------------------------------------------------------------------------------
% File : Moca---0.1
% Problem : ANA024-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : moca.sh %s
% Computer : n025.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 19:15:40 EDT 2022
% Result : Unsatisfiable 3.17s 3.19s
% Output : Proof 3.17s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ANA024-2 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : moca.sh %s
% 0.12/0.34 % Computer : n025.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 05:09:14 EDT 2022
% 0.12/0.34 % CPUTime :
% 3.17/3.19 % SZS status Unsatisfiable
% 3.17/3.19 % SZS output start Proof
% 3.17/3.19 The input problem is unsatisfiable because
% 3.17/3.19
% 3.17/3.19 [1] the following set of Horn clauses is unsatisfiable:
% 3.17/3.19
% 3.17/3.19 class_OrderedGroup_Oab__group__add(T_a) ==> V_a = c_plus(c_minus(V_a, V_b, T_a), V_b, T_a)
% 3.17/3.19 class_OrderedGroup_Opordered__ab__group__add(T_a) & c_lessequals(c_plus(V_a, V_b, T_a), V_c, T_a) ==> c_lessequals(V_a, c_minus(V_c, V_b, T_a), T_a)
% 3.17/3.19 c_lessequals(v_k(V_U), v_f(V_U), t_b)
% 3.17/3.19 c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b) ==> \bottom
% 3.17/3.19 class_OrderedGroup_Opordered__ab__group__add(T) ==> class_OrderedGroup_Oab__group__add(T)
% 3.17/3.19 class_Ring__and__Field_Oordered__idom(T) ==> class_OrderedGroup_Opordered__ab__group__add(T)
% 3.17/3.19 class_Ring__and__Field_Oordered__idom(t_b)
% 3.17/3.19
% 3.17/3.19 This holds because
% 3.17/3.19
% 3.17/3.19 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 3.17/3.19
% 3.17/3.19 E:
% 3.17/3.19 c_lessequals(v_k(V_U), v_f(V_U), t_b) = true__
% 3.17/3.19 class_Ring__and__Field_Oordered__idom(t_b) = true__
% 3.17/3.19 f1(class_OrderedGroup_Oab__group__add(T_a), V_a, V_b, T_a) = c_plus(c_minus(V_a, V_b, T_a), V_b, T_a)
% 3.17/3.19 f1(true__, V_a, V_b, T_a) = V_a
% 3.17/3.19 f2(true__, V_a, V_c, V_b, T_a) = c_lessequals(V_a, c_minus(V_c, V_b, T_a), T_a)
% 3.17/3.19 f3(c_lessequals(c_plus(V_a, V_b, T_a), V_c, T_a), T_a, V_a, V_c, V_b) = true__
% 3.17/3.19 f3(true__, T_a, V_a, V_c, V_b) = f2(class_OrderedGroup_Opordered__ab__group__add(T_a), V_a, V_c, V_b, T_a)
% 3.17/3.19 f4(c_lessequals(c_minus(v_k(v_x), v_g(v_x), t_b), c_minus(v_f(v_x), v_g(v_x), t_b), t_b)) = true__
% 3.17/3.19 f4(true__) = false__
% 3.17/3.19 f5(class_OrderedGroup_Opordered__ab__group__add(T), T) = true__
% 3.17/3.19 f5(true__, T) = class_OrderedGroup_Oab__group__add(T)
% 3.17/3.19 f6(class_Ring__and__Field_Oordered__idom(T), T) = true__
% 3.17/3.19 f6(true__, T) = class_OrderedGroup_Opordered__ab__group__add(T)
% 3.17/3.19 G:
% 3.17/3.19 true__ = false__
% 3.17/3.19
% 3.17/3.19 This holds because
% 3.17/3.19
% 3.17/3.19 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 3.17/3.19
% 3.17/3.19
% 3.17/3.19 c_lessequals(V_a, c_minus(V_c, V_b, T_a), T_a) -> f2(true__, V_a, V_c, V_b, T_a)
% 3.17/3.19 c_lessequals(v_k(V_U), v_f(V_U), t_b) -> true__
% 3.17/3.19 c_plus(c_minus(V_a, V_b, T_a), V_b, T_a) -> f1(f5(true__, T_a), V_a, V_b, T_a)
% 3.17/3.19 class_OrderedGroup_Oab__group__add(T) -> f5(true__, T)
% 3.17/3.19 class_OrderedGroup_Opordered__ab__group__add(T) -> f6(true__, T)
% 3.17/3.19 class_Ring__and__Field_Oordered__idom(t_b) -> true__
% 3.17/3.19 f1(true__, V_a, V_b, T_a) -> V_a
% 3.17/3.19 f2(true__, c_minus(c_minus(v_k(X0), Y2, t_b), Y3, t_b), c_minus(v_f(X0), Y2, t_b), Y3, t_b) -> true__
% 3.17/3.19 f2(true__, c_minus(v_k(X0), Y2, t_b), v_f(X0), Y2, t_b) -> true__
% 3.17/3.19 f3(c_lessequals(Y1, Y3, t_b), t_b, c_minus(Y1, Y2, t_b), Y3, Y2) -> true__
% 3.17/3.19 f3(c_lessequals(c_plus(V_a, V_b, T_a), V_c, T_a), T_a, V_a, V_c, V_b) -> true__
% 3.17/3.19 f3(c_lessequals(f1(f5(true__, Y2), X0, Y1, Y2), Y3, Y2), Y2, c_minus(X0, Y1, Y2), Y3, Y1) -> true__
% 3.17/3.19 f3(f2(true__, Y0, X1, X2, t_b), t_b, c_minus(Y0, Y2, t_b), c_minus(X1, X2, t_b), Y2) -> true__
% 3.17/3.19 f3(f2(true__, c_plus(Y0, Y1, Y2), X1, X2, Y2), Y2, Y0, c_minus(X1, X2, Y2), Y1) -> true__
% 3.17/3.19 f3(true__, T_a, V_a, V_c, V_b) -> f2(f6(true__, T_a), V_a, V_c, V_b, T_a)
% 3.17/3.19 f4(f2(true__, c_minus(v_k(v_x), v_g(v_x), t_b), v_f(v_x), v_g(v_x), t_b)) -> true__
% 3.17/3.19 f4(true__) -> false__
% 3.17/3.19 f5(f6(true__, Y0), Y0) -> true__
% 3.17/3.19 f5(true__, t_b) -> true__
% 3.17/3.19 f6(class_Ring__and__Field_Oordered__idom(T), T) -> true__
% 3.17/3.19 f6(true__, t_b) -> true__
% 3.17/3.19 false__ -> true__
% 3.17/3.19 with the LPO induced by
% 3.17/3.19 v_g > v_x > f3 > c_lessequals > f2 > class_OrderedGroup_Opordered__ab__group__add > f6 > c_minus > f1 > v_k > class_OrderedGroup_Oab__group__add > f5 > c_plus > v_f > t_b > class_Ring__and__Field_Oordered__idom > f4 > false__ > true__
% 3.17/3.19
% 3.17/3.19 % SZS output end Proof
% 3.17/3.19
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