TSTP Solution File: ANA013-2 by Moca---0.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Moca---0.1
% Problem  : ANA013-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : moca.sh %s

% Computer : n003.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 19:15:33 EDT 2022

% Result   : Unsatisfiable 0.77s 0.93s
% Output   : Proof 0.77s
% 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  : ANA013-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command  : moca.sh %s
% 0.14/0.34  % Computer : n003.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Fri Jul  8 06:41:42 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.77/0.93  % SZS status Unsatisfiable
% 0.77/0.93  % SZS output start Proof
% 0.77/0.93  The input problem is unsatisfiable because
% 0.77/0.93  
% 0.77/0.93  [1] the following set of Horn clauses is unsatisfiable:
% 0.77/0.93  
% 0.77/0.93  	c_lessequals(c_times(c_HOL_Oabs(v_c, t_b), c_HOL_Oabs(v_f(v_x(V_U)), t_b), t_b), c_times(V_U, c_HOL_Oabs(v_f(v_x(V_U)), t_b), t_b), t_b) ==> \bottom
% 0.77/0.93  	class_Ring__and__Field_Oordered__idom(t_b)
% 0.77/0.93  	class_Orderings_Oorder(T_a) ==> c_lessequals(V_x, V_x, T_a)
% 0.77/0.93  	class_Ring__and__Field_Oordered__idom(T) ==> class_Orderings_Oorder(T)
% 0.77/0.93  
% 0.77/0.93  This holds because
% 0.77/0.93  
% 0.77/0.93  [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.77/0.93  
% 0.77/0.93  E:
% 0.77/0.93  	class_Ring__and__Field_Oordered__idom(t_b) = true__
% 0.77/0.93  	f1(c_lessequals(c_times(c_HOL_Oabs(v_c, t_b), c_HOL_Oabs(v_f(v_x(V_U)), t_b), t_b), c_times(V_U, c_HOL_Oabs(v_f(v_x(V_U)), t_b), t_b), t_b)) = true__
% 0.77/0.93  	f1(true__) = false__
% 0.77/0.93  	f2(class_Orderings_Oorder(T_a), V_x, T_a) = true__
% 0.77/0.93  	f2(true__, V_x, T_a) = c_lessequals(V_x, V_x, T_a)
% 0.77/0.93  	f3(class_Ring__and__Field_Oordered__idom(T), T) = true__
% 0.77/0.93  	f3(true__, T) = class_Orderings_Oorder(T)
% 0.77/0.93  G:
% 0.77/0.93  	true__ = false__
% 0.77/0.93  
% 0.77/0.93  This holds because
% 0.77/0.93  
% 0.77/0.93  [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.77/0.93  
% 0.77/0.93  
% 0.77/0.93  	c_lessequals(Y1, Y1, t_b) -> true__
% 0.77/0.93  	class_Orderings_Oorder(T) -> f3(true__, T)
% 0.77/0.93  	class_Ring__and__Field_Oordered__idom(t_b) -> true__
% 0.77/0.93  	f1(c_lessequals(c_times(c_HOL_Oabs(v_c, t_b), c_HOL_Oabs(v_f(v_x(V_U)), t_b), t_b), c_times(V_U, c_HOL_Oabs(v_f(v_x(V_U)), t_b), t_b), t_b)) -> true__
% 0.77/0.93  	f1(true__) -> false__
% 0.77/0.93  	f2(f3(true__, Y0), Y1, Y0) -> true__
% 0.77/0.93  	f2(true__, V_x, T_a) -> c_lessequals(V_x, V_x, T_a)
% 0.77/0.93  	f3(class_Ring__and__Field_Oordered__idom(T), T) -> true__
% 0.77/0.93  	f3(true__, t_b) -> true__
% 0.77/0.93  	false__ -> true__
% 0.77/0.93  with the LPO induced by
% 0.77/0.93  	v_x > v_f > v_c > c_HOL_Oabs > c_times > f2 > c_lessequals > class_Orderings_Oorder > f3 > t_b > class_Ring__and__Field_Oordered__idom > f1 > false__ > true__
% 0.77/0.93  
% 0.77/0.93  % SZS output end Proof
% 0.77/0.93  
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