%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : GRP162-1 : 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 : n022.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 01:17:25 EDT 2023

% Result   : Unsatisfiable 0.12s 0.39s
% Output   : Proof 0.12s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : GRP162-1 : 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 : n022.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 19:48:24 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.12/0.39  Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.12/0.39  
% 0.12/0.39  % SZS status Unsatisfiable
% 0.12/0.39  
% 0.12/0.39  % SZS output start Proof
% 0.12/0.39  Axiom 1 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 0.12/0.39  Axiom 2 (ax_transa_1): least_upper_bound(a, b) = b.
% 0.12/0.39  Axiom 3 (ax_transa_2): least_upper_bound(b, c) = c.
% 0.12/0.39  Axiom 4 (associativity_of_lub): least_upper_bound(X, least_upper_bound(Y, Z)) = least_upper_bound(least_upper_bound(X, Y), Z).
% 0.12/0.39  
% 0.12/0.39  Lemma 5: least_upper_bound(c, b) = c.
% 0.12/0.39  Proof:
% 0.12/0.39    least_upper_bound(c, b)
% 0.12/0.39  = { by axiom 1 (symmetry_of_lub) R->L }
% 0.12/0.39    least_upper_bound(b, c)
% 0.12/0.39  = { by axiom 3 (ax_transa_2) }
% 0.12/0.39    c
% 0.12/0.39  
% 0.12/0.39  Goal 1 (prove_ax_transa): least_upper_bound(a, c) = c.
% 0.12/0.39  Proof:
% 0.12/0.39    least_upper_bound(a, c)
% 0.12/0.39  = { by lemma 5 R->L }
% 0.12/0.39    least_upper_bound(a, least_upper_bound(c, b))
% 0.12/0.39  = { by axiom 1 (symmetry_of_lub) R->L }
% 0.12/0.39    least_upper_bound(a, least_upper_bound(b, c))
% 0.12/0.39  = { by axiom 4 (associativity_of_lub) }
% 0.12/0.39    least_upper_bound(least_upper_bound(a, b), c)
% 0.12/0.39  = { by axiom 2 (ax_transa_1) }
% 0.12/0.39    least_upper_bound(b, c)
% 0.12/0.39  = { by axiom 1 (symmetry_of_lub) }
% 0.12/0.39    least_upper_bound(c, b)
% 0.12/0.39  = { by lemma 5 }
% 0.12/0.39    c
% 0.12/0.39  % SZS output end Proof
% 0.12/0.39  
% 0.12/0.39  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------