%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : GRP166-3 : 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 : n021.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 0.11s 0.37s
% Output   : Proof 0.11s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : GRP166-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.06/0.11  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.32  % Computer : n021.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Tue Aug 29 00:05:13 EDT 2023
% 0.11/0.32  % CPUTime  : 
% 0.11/0.37  Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.11/0.37  
% 0.11/0.37  % SZS status Unsatisfiable
% 0.11/0.37  
% 0.11/0.37  % SZS output start Proof
% 0.11/0.37  Axiom 1 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 0.11/0.37  Axiom 2 (lat3a_2): least_upper_bound(b, identity) = b.
% 0.11/0.37  Axiom 3 (left_identity): multiply(identity, X) = X.
% 0.11/0.37  Axiom 4 (monotony_lub2): multiply(least_upper_bound(X, Y), Z) = least_upper_bound(multiply(X, Z), multiply(Y, Z)).
% 0.11/0.37  
% 0.11/0.37  Goal 1 (prove_lat3a): least_upper_bound(a, multiply(b, a)) = multiply(b, a).
% 0.11/0.37  Proof:
% 0.11/0.37    least_upper_bound(a, multiply(b, a))
% 0.11/0.37  = { by axiom 3 (left_identity) R->L }
% 0.11/0.37    least_upper_bound(multiply(identity, a), multiply(b, a))
% 0.11/0.37  = { by axiom 4 (monotony_lub2) R->L }
% 0.11/0.37    multiply(least_upper_bound(identity, b), a)
% 0.11/0.37  = { by axiom 1 (symmetry_of_lub) R->L }
% 0.11/0.37    multiply(least_upper_bound(b, identity), a)
% 0.11/0.37  = { by axiom 2 (lat3a_2) }
% 0.11/0.37    multiply(b, a)
% 0.11/0.37  % SZS output end Proof
% 0.11/0.37  
% 0.11/0.37  RESULT: Unsatisfiable (the axioms are contradictory).
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