TSTP Solution File: ANA007-2 by Moca---0.1
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% File : Moca---0.1
% Problem : ANA007-2 : 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 19:15:28 EDT 2022
% Result : Unsatisfiable 0.95s 1.16s
% Output : Proof 0.95s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ANA007-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : moca.sh %s
% 0.13/0.34 % Computer : n011.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 06:47:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.95/1.16 % SZS status Unsatisfiable
% 0.95/1.16 % SZS output start Proof
% 0.95/1.16 The input problem is unsatisfiable because
% 0.95/1.16
% 0.95/1.16 [1] the following set of Horn clauses is unsatisfiable:
% 0.95/1.16
% 0.95/1.16 c_lessequals(c_HOL_Oabs(v_f(v_x(V_U)), t_b), c_times(V_U, c_HOL_Oabs(v_f(v_x(V_U)), t_b), t_b), t_b) ==> \bottom
% 0.95/1.16 class_Ring__and__Field_Oordered__idom(t_b)
% 0.95/1.16 class_Orderings_Oorder(T_a) ==> c_lessequals(V_x, V_x, T_a)
% 0.95/1.16 class_Ring__and__Field_Oordered__idom(T_a) ==> V_c = c_times(c_1, V_c, T_a)
% 0.95/1.16 class_Ring__and__Field_Oordered__idom(T) ==> class_Orderings_Oorder(T)
% 0.95/1.16
% 0.95/1.16 This holds because
% 0.95/1.16
% 0.95/1.16 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.95/1.16
% 0.95/1.16 E:
% 0.95/1.16 class_Ring__and__Field_Oordered__idom(t_b) = true__
% 0.95/1.16 f1(c_lessequals(c_HOL_Oabs(v_f(v_x(V_U)), t_b), c_times(V_U, c_HOL_Oabs(v_f(v_x(V_U)), t_b), t_b), t_b)) = true__
% 0.95/1.16 f1(true__) = false__
% 0.95/1.16 f2(class_Orderings_Oorder(T_a), V_x, T_a) = true__
% 0.95/1.16 f2(true__, V_x, T_a) = c_lessequals(V_x, V_x, T_a)
% 0.95/1.16 f3(class_Ring__and__Field_Oordered__idom(T_a), V_c, T_a) = c_times(c_1, V_c, T_a)
% 0.95/1.16 f3(true__, V_c, T_a) = V_c
% 0.95/1.16 f4(class_Ring__and__Field_Oordered__idom(T), T) = true__
% 0.95/1.16 f4(true__, T) = class_Orderings_Oorder(T)
% 0.95/1.16 G:
% 0.95/1.16 true__ = false__
% 0.95/1.16
% 0.95/1.16 This holds because
% 0.95/1.16
% 0.95/1.16 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.95/1.16
% 0.95/1.16
% 0.95/1.16 c_lessequals(V_x, V_x, T_a) -> f2(true__, V_x, T_a)
% 0.95/1.16 c_times(c_1, Y1, t_b) -> Y1
% 0.95/1.16 class_Orderings_Oorder(T) -> f4(true__, T)
% 0.95/1.16 class_Ring__and__Field_Oordered__idom(t_b) -> true__
% 0.95/1.16 f1(c_lessequals(c_HOL_Oabs(v_f(v_x(V_U)), t_b), c_times(V_U, c_HOL_Oabs(v_f(v_x(V_U)), t_b), t_b), t_b)) -> true__
% 0.95/1.16 f1(f2(true__, c_HOL_Oabs(v_f(v_x(c_1)), t_b), t_b)) -> true__
% 0.95/1.16 f1(true__) -> false__
% 0.95/1.16 f2(class_Orderings_Oorder(T_a), V_x, T_a) -> true__
% 0.95/1.16 f2(f4(true__, Y0), Y1, Y0) -> true__
% 0.95/1.16 f2(true__, Y1, t_b) -> true__
% 0.95/1.16 f3(class_Ring__and__Field_Oordered__idom(T_a), V_c, T_a) -> c_times(c_1, V_c, T_a)
% 0.95/1.16 f3(true__, V_c, T_a) -> V_c
% 0.95/1.16 f4(class_Ring__and__Field_Oordered__idom(T), T) -> true__
% 0.95/1.16 f4(true__, t_b) -> true__
% 0.95/1.16 false__ -> true__
% 0.95/1.16 with the LPO induced by
% 0.95/1.16 class_Orderings_Oorder > f4 > class_Ring__and__Field_Oordered__idom > c_1 > f3 > c_lessequals > f2 > c_times > t_b > v_x > v_f > c_HOL_Oabs > f1 > false__ > true__
% 0.95/1.16
% 0.95/1.16 % SZS output end Proof
% 0.95/1.16
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