%------------------------------------------------------------------------------
% File     : Toma---0.4
% Problem  : LAT014-1 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : toma --casc %s

% Computer : n001.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 06:25:26 EDT 2023

% Result   : Unsatisfiable 0.19s 0.48s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : LAT014-1 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13  % Command    : toma --casc %s
% 0.12/0.34  % Computer : n001.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Thu Aug 24 07:36:55 EDT 2023
% 0.12/0.34  % CPUTime    : 
% 0.19/0.48  % SZS status Unsatisfiable
% 0.19/0.48  % SZS output start Proof
% 0.19/0.48  original problem:
% 0.19/0.48  axioms:
% 0.19/0.48  join(X, meet(Y, meet(X, Z))) = X
% 0.19/0.48  meet(X, join(Y, join(X, Z))) = X
% 0.19/0.48  join(join(meet(X, Y), meet(Y, Z)), Y) = Y
% 0.19/0.48  meet(meet(join(X, Y), join(Y, Z)), Y) = Y
% 0.19/0.48  goal:
% 0.19/0.48  meet(a(), join(a(), b())) != a()
% 0.19/0.48  To show the unsatisfiability of the original goal,
% 0.19/0.48  it suffices to show that meet(a(), join(a(), b())) = a() (skolemized goal) is valid under the axioms.
% 0.19/0.48  Here is an equational proof:
% 0.19/0.48  1: meet(X0, join(X1, join(X0, X2))) = X0.
% 0.19/0.48  Proof: Axiom.
% 0.19/0.48  
% 0.19/0.48  2: join(join(meet(X0, X1), meet(X1, X2)), X1) = X1.
% 0.19/0.48  Proof: Axiom.
% 0.19/0.48  
% 0.19/0.48  7: X0 = meet(X0, join(X0, X2)).
% 0.19/0.48  Proof: A critical pair between equations 1 and 2.
% 0.19/0.48  
% 0.19/0.48  18: meet(a(), join(a(), b())) = a().
% 0.19/0.48  Proof: Rewrite lhs with equations [7]
% 0.19/0.48                 rhs with equations [].
% 0.19/0.48  
% 0.19/0.48  % SZS output end Proof
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