%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : GRP166-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% 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 : n031.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 01:17:27 EDT 2023

% Result   : Unsatisfiable 0.19s 0.39s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GRP166-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.12/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34  % Computer : n031.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Mon Aug 28 20:03:55 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.39  Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.19/0.39  
% 0.19/0.39  % SZS status Unsatisfiable
% 0.19/0.39  
% 0.19/0.39  % SZS output start Proof
% 0.19/0.39  Axiom 1 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
% 0.19/0.39  Axiom 2 (lat3b_2): greatest_lower_bound(b, identity) = identity.
% 0.19/0.39  Axiom 3 (left_identity): multiply(identity, X) = X.
% 0.19/0.39  Axiom 4 (monotony_glb2): multiply(greatest_lower_bound(X, Y), Z) = greatest_lower_bound(multiply(X, Z), multiply(Y, Z)).
% 0.19/0.39  
% 0.19/0.39  Goal 1 (prove_lat3b): greatest_lower_bound(a, multiply(b, a)) = a.
% 0.19/0.39  Proof:
% 0.19/0.39    greatest_lower_bound(a, multiply(b, a))
% 0.19/0.39  = { by axiom 3 (left_identity) R->L }
% 0.19/0.39    greatest_lower_bound(multiply(identity, a), multiply(b, a))
% 0.19/0.39  = { by axiom 4 (monotony_glb2) R->L }
% 0.19/0.39    multiply(greatest_lower_bound(identity, b), a)
% 0.19/0.39  = { by axiom 1 (symmetry_of_glb) }
% 0.19/0.39    multiply(greatest_lower_bound(b, identity), a)
% 0.19/0.39  = { by axiom 2 (lat3b_2) }
% 0.19/0.39    multiply(identity, a)
% 0.19/0.39  = { by axiom 3 (left_identity) }
% 0.19/0.39    a
% 0.19/0.39  % SZS output end Proof
% 0.19/0.39  
% 0.19/0.39  RESULT: Unsatisfiable (the axioms are contradictory).
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