%------------------------------------------------------------------------------
% File     : Toma---0.4
% Problem  : LAT033-1 : TPTP v8.1.2. Bugfixed v2.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : toma --casc %s

% Computer : n015.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 06:25:29 EDT 2023

% Result   : Unsatisfiable 0.20s 0.58s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : LAT033-1 : TPTP v8.1.2. Bugfixed v2.5.0.
% 0.00/0.13  % Command    : toma --casc %s
% 0.13/0.34  % Computer : n015.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 06:27:05 EDT 2023
% 0.13/0.34  % CPUTime    : 
% 0.20/0.58  % SZS status Unsatisfiable
% 0.20/0.58  % SZS output start Proof
% 0.20/0.58  original problem:
% 0.20/0.58  axioms:
% 0.20/0.58  meet(X, join(X, Y)) = X
% 0.20/0.58  join(X, meet(X, Y)) = X
% 0.20/0.58  meet(X, Y) = meet(Y, X)
% 0.20/0.58  join(X, Y) = join(Y, X)
% 0.20/0.58  meet(meet(X, Y), Z) = meet(X, meet(Y, Z))
% 0.20/0.58  join(join(X, Y), Z) = join(X, join(Y, Z))
% 0.20/0.58  goal:
% 0.20/0.58  join(xx(), xx()) != xx()
% 0.20/0.58  To show the unsatisfiability of the original goal,
% 0.20/0.58  it suffices to show that join(xx(), xx()) = xx() (skolemized goal) is valid under the axioms.
% 0.20/0.58  Here is an equational proof:
% 0.20/0.58  0: meet(X0, join(X0, X1)) = X0.
% 0.20/0.58  Proof: Axiom.
% 0.20/0.58  
% 0.20/0.58  1: join(X0, meet(X0, X1)) = X0.
% 0.20/0.58  Proof: Axiom.
% 0.20/0.58  
% 0.20/0.58  7: X2 = join(X2, X2).
% 0.20/0.58  Proof: A critical pair between equations 1 and 0.
% 0.20/0.58  
% 0.20/0.58  20: join(xx(), xx()) = xx().
% 0.20/0.58  Proof: Rewrite lhs with equations [7]
% 0.20/0.58                 rhs with equations [].
% 0.20/0.58  
% 0.20/0.58  % SZS output end Proof
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