%------------------------------------------------------------------------------
% File     : Toma---0.4
% Problem  : LAT039-2 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : toma --casc %s

% Computer : n007.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 06:25:30 EDT 2023

% Result   : Unsatisfiable 0.20s 0.45s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : LAT039-2 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.13  % Command    : toma --casc %s
% 0.13/0.34  % Computer : n007.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Thu Aug 24 09:54:10 EDT 2023
% 0.13/0.34  % CPUTime    : 
% 0.20/0.45  % SZS status Unsatisfiable
% 0.20/0.45  % SZS output start Proof
% 0.20/0.45  original problem:
% 0.20/0.45  axioms:
% 0.20/0.45  meet(X, X) = X
% 0.20/0.45  join(X, X) = X
% 0.20/0.45  meet(X, join(X, Y)) = X
% 0.20/0.45  join(X, meet(X, Y)) = X
% 0.20/0.45  meet(X, Y) = meet(Y, X)
% 0.20/0.45  join(X, Y) = join(Y, X)
% 0.20/0.45  meet(meet(X, Y), Z) = meet(X, meet(Y, Z))
% 0.20/0.45  join(join(X, Y), Z) = join(X, join(Y, Z))
% 0.20/0.45  join(X, meet(Y, Z)) = meet(join(X, Y), join(X, Z))
% 0.20/0.45  meet(X, join(Y, Z)) = join(meet(X, Y), meet(X, Z))
% 0.20/0.45  join(xx(), yy()) = yy()
% 0.20/0.45  goal:
% 0.20/0.45  join(xx(), meet(yy(), zz())) != meet(join(xx(), yy()), join(xx(), zz()))
% 0.20/0.45  To show the unsatisfiability of the original goal,
% 0.20/0.45  it suffices to show that join(xx(), meet(yy(), zz())) = meet(join(xx(), yy()), join(xx(), zz())) (skolemized goal) is valid under the axioms.
% 0.20/0.45  Here is an equational proof:
% 0.20/0.45  8: join(X0, meet(X1, X2)) = meet(join(X0, X1), join(X0, X2)).
% 0.20/0.45  Proof: Axiom.
% 0.20/0.45  
% 0.20/0.45  10: join(xx(), yy()) = yy().
% 0.20/0.45  Proof: Axiom.
% 0.20/0.45  
% 0.20/0.45  12: join(xx(), meet(yy(), zz())) = meet(join(xx(), yy()), join(xx(), zz())).
% 0.20/0.45  Proof: Rewrite lhs with equations [8,10]
% 0.20/0.45                 rhs with equations [10].
% 0.20/0.45  
% 0.20/0.45  % SZS output end Proof
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