TSTP Solution File: SWV277-2 by Moca---0.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Moca---0.1
% Problem  : SWV277-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : moca.sh %s

% Computer : n023.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 : Wed Jul 20 20:42:38 EDT 2022

% Result   : Unsatisfiable 0.58s 0.73s
% Output   : Proof 0.58s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.06  % Problem  : SWV277-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.07  % Command  : moca.sh %s
% 0.06/0.25  % Computer : n023.cluster.edu
% 0.06/0.25  % Model    : x86_64 x86_64
% 0.06/0.25  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25  % Memory   : 8042.1875MB
% 0.06/0.25  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25  % CPULimit : 300
% 0.06/0.25  % WCLimit  : 600
% 0.06/0.25  % DateTime : Tue Jun 14 23:59:05 EDT 2022
% 0.06/0.25  % CPUTime  : 
% 0.58/0.73  % SZS status Unsatisfiable
% 0.58/0.73  % SZS output start Proof
% 0.58/0.73  The input problem is unsatisfiable because
% 0.58/0.73  
% 0.58/0.73  [1] the following set of Horn clauses is unsatisfiable:
% 0.58/0.73  
% 0.58/0.73  	c_lessequals(c_Message_Oanalz(V_H), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg))
% 0.58/0.73  	c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg)) ==> c_lessequals(c_Message_OkeysFor(V_G), c_Message_OkeysFor(V_H), tc_set(tc_nat))
% 0.58/0.73  	c_in(V_c, V_A, T_a) & c_lessequals(V_A, V_B, tc_set(T_a)) ==> c_in(V_c, V_B, T_a)
% 0.58/0.73  	c_in(v_K, c_Message_OkeysFor(c_Message_Oparts(v_H)), tc_nat) ==> \bottom
% 0.58/0.73  	c_in(v_K, c_Message_OkeysFor(c_Message_Oanalz(v_H)), tc_nat)
% 0.58/0.73  
% 0.58/0.73  This holds because
% 0.58/0.73  
% 0.58/0.73  [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)):
% 0.58/0.73  
% 0.58/0.73  E:
% 0.58/0.73  	c_in(v_K, c_Message_OkeysFor(c_Message_Oanalz(v_H)), tc_nat) = true__
% 0.58/0.73  	c_lessequals(c_Message_Oanalz(V_H), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)) = true__
% 0.58/0.73  	f1(c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg)), V_G, V_H) = true__
% 0.58/0.73  	f1(true__, V_G, V_H) = c_lessequals(c_Message_OkeysFor(V_G), c_Message_OkeysFor(V_H), tc_set(tc_nat))
% 0.58/0.73  	f2(true__, V_c, V_B, T_a) = c_in(V_c, V_B, T_a)
% 0.58/0.73  	f3(c_lessequals(V_A, V_B, tc_set(T_a)), V_c, V_A, T_a, V_B) = true__
% 0.58/0.73  	f3(true__, V_c, V_A, T_a, V_B) = f2(c_in(V_c, V_A, T_a), V_c, V_B, T_a)
% 0.58/0.73  	f4(c_in(v_K, c_Message_OkeysFor(c_Message_Oparts(v_H)), tc_nat)) = true__
% 0.58/0.73  	f4(true__) = false__
% 0.58/0.73  G:
% 0.58/0.73  	true__ = false__
% 0.58/0.73  
% 0.58/0.73  This holds because
% 0.58/0.73  
% 0.58/0.73  [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS:
% 0.58/0.73  
% 0.58/0.73  
% 0.58/0.73  	c_in(V_c, V_B, T_a) -> f2(true__, V_c, V_B, T_a)
% 0.58/0.73  	c_in(v_K, c_Message_OkeysFor(c_Message_Oanalz(v_H)), tc_nat) -> true__
% 0.58/0.73  	c_lessequals(c_Message_Oanalz(V_H), c_Message_Oparts(V_H), tc_set(tc_Message_Omsg)) -> true__
% 0.58/0.73  	c_lessequals(c_Message_OkeysFor(V_G), c_Message_OkeysFor(V_H), tc_set(tc_nat)) -> f1(true__, V_G, V_H)
% 0.58/0.73  	f1(c_lessequals(V_G, V_H, tc_set(tc_Message_Omsg)), V_G, V_H) -> true__
% 0.58/0.73  	f1(true__, c_Message_Oanalz(X0), c_Message_Oparts(X0)) -> true__
% 0.58/0.73  	f2(f2(true__, Y2, c_Message_OkeysFor(c_Message_Oanalz(X0)), tc_nat), Y2, c_Message_OkeysFor(c_Message_Oparts(X0)), tc_nat) -> true__
% 0.58/0.73  	f2(f2(true__, Y3, c_Message_Oanalz(X0), tc_Message_Omsg), Y3, c_Message_Oparts(X0), tc_Message_Omsg) -> true__
% 0.58/0.73  	f2(true__, v_K, c_Message_OkeysFor(c_Message_Oanalz(v_H)), tc_nat) -> true__
% 0.58/0.73  	f2(true__, v_K, c_Message_OkeysFor(c_Message_Oparts(v_H)), tc_nat) -> true__
% 0.58/0.73  	f3(c_lessequals(V_A, V_B, tc_set(T_a)), V_c, V_A, T_a, V_B) -> true__
% 0.58/0.73  	f3(f1(true__, X0, X1), Y3, c_Message_OkeysFor(X0), tc_nat, c_Message_OkeysFor(X1)) -> true__
% 0.58/0.73  	f3(true__, V_c, V_A, T_a, V_B) -> f2(c_in(V_c, V_A, T_a), V_c, V_B, T_a)
% 0.58/0.73  	f4(c_in(v_K, c_Message_OkeysFor(c_Message_Oparts(v_H)), tc_nat)) -> true__
% 0.58/0.73  	f4(f2(true__, v_K, c_Message_OkeysFor(c_Message_Oparts(v_H)), tc_nat)) -> true__
% 0.58/0.73  	f4(true__) -> false__
% 0.58/0.73  	false__ -> true__
% 0.58/0.73  with the LPO induced by
% 0.58/0.73  	v_H > v_K > f4 > f3 > c_in > f2 > c_Message_Oanalz > c_lessequals > f1 > tc_nat > c_Message_OkeysFor > tc_Message_Omsg > tc_set > c_Message_Oparts > false__ > true__
% 0.58/0.73  
% 0.58/0.73  % SZS output end Proof
% 0.58/0.73  
%------------------------------------------------------------------------------