%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : LAT042-1 : 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 : n006.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 06:27:14 EDT 2023

% Result   : Unsatisfiable 0.22s 0.43s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : LAT042-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.14  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35  % Computer : n006.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug 24 04:16:52 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.22/0.43  Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.22/0.43  
% 0.22/0.43  % SZS status Unsatisfiable
% 0.22/0.43  
% 0.22/0.43  % SZS output start Proof
% 0.22/0.43  Axiom 1 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 0.22/0.43  Axiom 2 (commutativity_of_join): join(X, Y) = join(Y, X).
% 0.22/0.43  Axiom 3 (absorption1): meet(X, join(X, Y)) = X.
% 0.22/0.43  Axiom 4 (distributivity): meet(X, join(Y, Z)) = join(meet(X, Y), meet(X, Z)).
% 0.22/0.43  
% 0.22/0.43  Goal 1 (prove_modular_law): join(a, meet(b, join(a, c))) = meet(join(a, b), join(a, c)).
% 0.22/0.43  Proof:
% 0.22/0.43    join(a, meet(b, join(a, c)))
% 0.22/0.43  = { by axiom 2 (commutativity_of_join) R->L }
% 0.22/0.43    join(a, meet(b, join(c, a)))
% 0.22/0.43  = { by axiom 1 (commutativity_of_meet) R->L }
% 0.22/0.43    join(a, meet(join(c, a), b))
% 0.22/0.43  = { by axiom 3 (absorption1) R->L }
% 0.22/0.43    join(meet(a, join(a, c)), meet(join(c, a), b))
% 0.22/0.43  = { by axiom 2 (commutativity_of_join) }
% 0.22/0.43    join(meet(a, join(c, a)), meet(join(c, a), b))
% 0.22/0.43  = { by axiom 1 (commutativity_of_meet) R->L }
% 0.22/0.43    join(meet(join(c, a), a), meet(join(c, a), b))
% 0.22/0.43  = { by axiom 4 (distributivity) R->L }
% 0.22/0.43    meet(join(c, a), join(a, b))
% 0.22/0.43  = { by axiom 1 (commutativity_of_meet) }
% 0.22/0.43    meet(join(a, b), join(c, a))
% 0.22/0.43  = { by axiom 2 (commutativity_of_join) }
% 0.22/0.43    meet(join(b, a), join(c, a))
% 0.22/0.43  = { by axiom 2 (commutativity_of_join) R->L }
% 0.22/0.43    meet(join(b, a), join(a, c))
% 0.22/0.43  = { by axiom 2 (commutativity_of_join) R->L }
% 0.22/0.43    meet(join(a, b), join(a, c))
% 0.22/0.43  % SZS output end Proof
% 0.22/0.43  
% 0.22/0.43  RESULT: Unsatisfiable (the axioms are contradictory).
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