%------------------------------------------------------------------------------
% File     : Toma---0.4
% Problem  : SWV243-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : toma --casc %s

% Computer : n016.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  : 300s
% DateTime : Thu Aug 31 22:58:57 EDT 2023

% Result   : Unsatisfiable 0.18s 0.52s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SWV243-2 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.12  % Command    : toma --casc %s
% 0.12/0.32  % Computer : n016.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Tue Aug 29 04:54:45 EDT 2023
% 0.12/0.33  % CPUTime    : 
% 0.18/0.52  % SZS status Unsatisfiable
% 0.18/0.52  % SZS output start Proof
% 0.18/0.52  original problem:
% 0.18/0.52  axioms:
% 0.18/0.52  c_Message_Oanalz(c_union(c_Message_Osynth(V_G), V_H, tc_Message_Omsg())) = c_union(c_Message_Oanalz(c_union(V_G, V_H, tc_Message_Omsg())), c_Message_Osynth(V_G), tc_Message_Omsg())
% 0.18/0.52  c_union(V_y, c_emptyset(), T_a) = V_y
% 0.18/0.52  goal:
% 0.18/0.52  c_Message_Oanalz(c_Message_Osynth(v_H())) != c_union(c_Message_Oanalz(v_H()), c_Message_Osynth(v_H()), tc_Message_Omsg())
% 0.18/0.52  To show the unsatisfiability of the original goal,
% 0.18/0.52  it suffices to show that c_Message_Oanalz(c_Message_Osynth(v_H())) = c_union(c_Message_Oanalz(v_H()), c_Message_Osynth(v_H()), tc_Message_Omsg()) (skolemized goal) is valid under the axioms.
% 0.18/0.52  Here is an equational proof:
% 0.18/0.52  0: c_Message_Oanalz(c_union(c_Message_Osynth(X0), X1, tc_Message_Omsg())) = c_union(c_Message_Oanalz(c_union(X0, X1, tc_Message_Omsg())), c_Message_Osynth(X0), tc_Message_Omsg()).
% 0.18/0.52  Proof: Axiom.
% 0.18/0.52  
% 0.18/0.52  1: c_union(X2, c_emptyset(), X3) = X2.
% 0.18/0.52  Proof: Axiom.
% 0.18/0.52  
% 0.18/0.52  2: c_Message_Oanalz(c_union(c_Message_Osynth(X4), c_emptyset(), tc_Message_Omsg())) = c_union(c_Message_Oanalz(X4), c_Message_Osynth(X4), tc_Message_Omsg()).
% 0.18/0.52  Proof: A critical pair between equations 0 and 1.
% 0.18/0.52  
% 0.18/0.52  4: c_Message_Oanalz(c_Message_Osynth(X4)) = c_union(c_Message_Oanalz(X4), c_Message_Osynth(X4), tc_Message_Omsg()).
% 0.18/0.52  Proof: Rewrite equation 2,
% 0.18/0.52                 lhs with equations [1]
% 0.18/0.52                 rhs with equations [].
% 0.18/0.52  
% 0.18/0.52  5: c_Message_Oanalz(c_Message_Osynth(v_H())) = c_union(c_Message_Oanalz(v_H()), c_Message_Osynth(v_H()), tc_Message_Omsg()).
% 0.18/0.52  Proof: Rewrite lhs with equations []
% 0.18/0.52                 rhs with equations [4].
% 0.18/0.52  
% 0.18/0.52  % SZS output end Proof
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