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% File     : Toma---0.4
% Problem  : LAT088-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : toma --casc %s

% Computer : n012.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 06:25:37 EDT 2023

% Result   : Unsatisfiable 0.72s 1.07s
% Output   : CNFRefutation 0.72s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : LAT088-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.14  % Command    : toma --casc %s
% 0.15/0.36  % Computer : n012.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Thu Aug 24 08:05:12 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.72/1.07  % SZS status Unsatisfiable
% 0.72/1.07  % SZS output start Proof
% 0.72/1.07  original problem:
% 0.72/1.07  axioms:
% 0.72/1.07  join(meet(A, B), meet(A, join(A, B))) = A
% 0.72/1.07  join(meet(A, A), meet(B, join(A, A))) = A
% 0.72/1.07  join(meet(A, B), meet(B, join(A, B))) = B
% 0.72/1.07  meet(meet(join(A, B), join(C, A)), A) = A
% 0.72/1.07  join(join(meet(A, B), meet(C, A)), A) = A
% 0.72/1.07  goal:
% 0.72/1.07  meet(a(), a()) != a()
% 0.72/1.07  To show the unsatisfiability of the original goal,
% 0.72/1.07  it suffices to show that meet(a(), a()) = a() (skolemized goal) is valid under the axioms.
% 0.72/1.07  Here is an equational proof:
% 0.72/1.07  0: join(meet(X0, X1), meet(X0, join(X0, X1))) = X0.
% 0.72/1.07  Proof: Axiom.
% 0.72/1.07  
% 0.72/1.07  2: join(meet(X0, X1), meet(X1, join(X0, X1))) = X1.
% 0.72/1.07  Proof: Axiom.
% 0.72/1.07  
% 0.72/1.07  3: meet(meet(join(X0, X1), join(X2, X0)), X0) = X0.
% 0.72/1.07  Proof: Axiom.
% 0.72/1.07  
% 0.72/1.07  4: join(join(meet(X0, X1), meet(X2, X0)), X0) = X0.
% 0.72/1.07  Proof: Axiom.
% 0.72/1.07  
% 0.72/1.07  6: X3 = meet(meet(join(X3, X1), X3), X3).
% 0.72/1.07  Proof: A critical pair between equations 3 and 4.
% 0.72/1.07  
% 0.72/1.07  8: X3 = join(X3, meet(X3, join(meet(join(X3, X4), join(X5, X3)), X3))).
% 0.72/1.07  Proof: A critical pair between equations 2 and 3.
% 0.72/1.07  
% 0.72/1.07  17: X6 = meet(meet(X6, X6), X6).
% 0.72/1.07  Proof: A critical pair between equations 6 and 8.
% 0.72/1.07  
% 0.72/1.07  39: meet(X7, X7) = join(X7, meet(meet(X7, X7), join(meet(X7, X7), X7))).
% 0.72/1.07  Proof: A critical pair between equations 0 and 17.
% 0.72/1.07  
% 0.72/1.07  44: X8 = meet(meet(meet(X8, X8), X8), X8).
% 0.72/1.07  Proof: A critical pair between equations 6 and 39.
% 0.72/1.07  
% 0.72/1.07  57: X8 = meet(X8, X8).
% 0.72/1.07  Proof: Rewrite equation 44,
% 0.72/1.07                 lhs with equations []
% 0.72/1.07                 rhs with equations [17].
% 0.72/1.07  
% 0.72/1.07  65: meet(a(), a()) = a().
% 0.72/1.07  Proof: Rewrite lhs with equations [57]
% 0.72/1.07                 rhs with equations [].
% 0.72/1.07  
% 0.72/1.07  % SZS output end Proof
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