%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : LAT045-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof

% Computer : n002.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 06:27:15 EDT 2023

% Result   : Unsatisfiable 0.22s 0.49s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : LAT045-1 : TPTP v8.1.2. Released v2.5.0.
% 0.08/0.15  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.37  % Computer : n002.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Thu Aug 24 08:04:31 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 0.22/0.49  Command-line arguments: --no-flatten-goal
% 0.22/0.49  
% 0.22/0.49  % SZS status Unsatisfiable
% 0.22/0.49  
% 0.22/0.49  % SZS output start Proof
% 0.22/0.49  Axiom 1 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 0.22/0.49  Axiom 2 (commutativity_of_join): join(X, Y) = join(Y, X).
% 0.22/0.50  Axiom 3 (invertability1): join(complement(X), X) = n1.
% 0.22/0.50  Axiom 4 (absorption1): meet(X, join(X, Y)) = X.
% 0.22/0.50  Axiom 5 (modular_law): join(X, meet(Y, join(X, Z))) = meet(join(X, Y), join(X, Z)).
% 0.22/0.50  
% 0.22/0.50  Lemma 6: join(X, complement(X)) = n1.
% 0.22/0.50  Proof:
% 0.22/0.50    join(X, complement(X))
% 0.22/0.50  = { by axiom 2 (commutativity_of_join) R->L }
% 0.22/0.50    join(complement(X), X)
% 0.22/0.50  = { by axiom 3 (invertability1) }
% 0.22/0.50    n1
% 0.22/0.50  
% 0.22/0.50  Goal 1 (prove_orthomodular_law): join(a, meet(complement(a), join(a, b))) = join(a, b).
% 0.22/0.50  Proof:
% 0.22/0.50    join(a, meet(complement(a), join(a, b)))
% 0.22/0.50  = { by axiom 5 (modular_law) }
% 0.22/0.50    meet(join(a, complement(a)), join(a, b))
% 0.22/0.50  = { by lemma 6 }
% 0.22/0.50    meet(n1, join(a, b))
% 0.22/0.50  = { by axiom 1 (commutativity_of_meet) R->L }
% 0.22/0.50    meet(join(a, b), n1)
% 0.22/0.50  = { by lemma 6 R->L }
% 0.22/0.50    meet(join(a, b), join(join(a, b), complement(join(a, b))))
% 0.22/0.50  = { by axiom 4 (absorption1) }
% 0.22/0.50    join(a, b)
% 0.22/0.50  % SZS output end Proof
% 0.22/0.50  
% 0.22/0.51  RESULT: Unsatisfiable (the axioms are contradictory).
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