%------------------------------------------------------------------------------
% File     : Toma---0.4
% Problem  : SWV262-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : toma --casc %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  : 300s
% DateTime : Thu Aug 31 22:59:02 EDT 2023

% Result   : Unsatisfiable 0.20s 0.43s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SWV262-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command    : toma --casc %s
% 0.11/0.34  % Computer : n025.cluster.edu
% 0.11/0.34  % Model    : x86_64 x86_64
% 0.11/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34  % Memory   : 8042.1875MB
% 0.11/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34  % CPULimit   : 300
% 0.11/0.34  % WCLimit    : 300
% 0.11/0.34  % DateTime   : Tue Aug 29 10:03:40 EDT 2023
% 0.11/0.34  % CPUTime    : 
% 0.20/0.43  % SZS status Unsatisfiable
% 0.20/0.43  % SZS output start Proof
% 0.20/0.43  original problem:
% 0.20/0.43  axioms:
% 0.20/0.43  c_Message_Oparts(c_union(V_G, V_H, tc_Message_Omsg())) = c_union(c_Message_Oparts(V_G), c_Message_Oparts(V_H), tc_Message_Omsg())
% 0.20/0.43  c_union(c_emptyset(), V_y, T_a) = V_y
% 0.20/0.43  c_union(c_insert(V_a, V_B, T_a), V_C, T_a) = c_insert(V_a, c_union(V_B, V_C, T_a), T_a)
% 0.20/0.43  goal:
% 0.20/0.43  c_Message_Oparts(c_insert(v_X(), c_insert(v_Y(), v_H(), tc_Message_Omsg()), tc_Message_Omsg())) != c_union(c_union(c_Message_Oparts(c_insert(v_X(), c_emptyset(), tc_Message_Omsg())), c_Message_Oparts(c_insert(v_Y(), c_emptyset(), tc_Message_Omsg())), tc_Message_Omsg()), c_Message_Oparts(v_H()), tc_Message_Omsg())
% 0.20/0.43  To show the unsatisfiability of the original goal,
% 0.20/0.43  it suffices to show that c_Message_Oparts(c_insert(v_X(), c_insert(v_Y(), v_H(), tc_Message_Omsg()), tc_Message_Omsg())) = c_union(c_union(c_Message_Oparts(c_insert(v_X(), c_emptyset(), tc_Message_Omsg())), c_Message_Oparts(c_insert(v_Y(), c_emptyset(), tc_Message_Omsg())), tc_Message_Omsg()), c_Message_Oparts(v_H()), tc_Message_Omsg()) (skolemized goal) is valid under the axioms.
% 0.20/0.43  Here is an equational proof:
% 0.20/0.43  0: c_Message_Oparts(c_union(X0, X1, tc_Message_Omsg())) = c_union(c_Message_Oparts(X0), c_Message_Oparts(X1), tc_Message_Omsg()).
% 0.20/0.43  Proof: Axiom.
% 0.20/0.43  
% 0.20/0.43  1: c_union(c_emptyset(), X2, X3) = X2.
% 0.20/0.43  Proof: Axiom.
% 0.20/0.43  
% 0.20/0.43  2: c_union(c_insert(X4, X5, X3), X6, X3) = c_insert(X4, c_union(X5, X6, X3), X3).
% 0.20/0.43  Proof: Axiom.
% 0.20/0.43  
% 0.20/0.43  3: c_Message_Oparts(c_insert(v_X(), c_insert(v_Y(), v_H(), tc_Message_Omsg()), tc_Message_Omsg())) = c_union(c_union(c_Message_Oparts(c_insert(v_X(), c_emptyset(), tc_Message_Omsg())), c_Message_Oparts(c_insert(v_Y(), c_emptyset(), tc_Message_Omsg())), tc_Message_Omsg()), c_Message_Oparts(v_H()), tc_Message_Omsg()).
% 0.20/0.43  Proof: Rewrite lhs with equations []
% 0.20/0.43                 rhs with equations [0,2,1,0,2,2,1].
% 0.20/0.43  
% 0.20/0.43  % SZS output end Proof
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