%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : GRP172-1 : 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 : n027.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 01:17:30 EDT 2023

% Result   : Unsatisfiable 0.21s 0.42s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : GRP172-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 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 : n027.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 : Tue Aug 29 03:02:53 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.21/0.42  Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.21/0.42  
% 0.21/0.42  % SZS status Unsatisfiable
% 0.21/0.42  
% 0.21/0.42  % SZS output start Proof
% 0.21/0.42  Axiom 1 (left_identity): multiply(identity, X) = X.
% 0.21/0.42  Axiom 2 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
% 0.21/0.42  Axiom 3 (p04b_1): greatest_lower_bound(identity, a) = identity.
% 0.21/0.42  Axiom 4 (p04b_2): greatest_lower_bound(identity, b) = identity.
% 0.21/0.42  Axiom 5 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 0.21/0.42  Axiom 6 (associativity_of_glb): greatest_lower_bound(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(greatest_lower_bound(X, Y), Z).
% 0.21/0.42  Axiom 7 (lub_absorbtion): least_upper_bound(X, greatest_lower_bound(X, Y)) = X.
% 0.21/0.42  Axiom 8 (monotony_glb2): multiply(greatest_lower_bound(X, Y), Z) = greatest_lower_bound(multiply(X, Z), multiply(Y, Z)).
% 0.21/0.42  
% 0.21/0.42  Goal 1 (prove_p04b): greatest_lower_bound(identity, multiply(a, b)) = identity.
% 0.21/0.42  Proof:
% 0.21/0.42    greatest_lower_bound(identity, multiply(a, b))
% 0.21/0.42  = { by axiom 7 (lub_absorbtion) R->L }
% 0.21/0.42    least_upper_bound(greatest_lower_bound(identity, multiply(a, b)), greatest_lower_bound(greatest_lower_bound(identity, multiply(a, b)), b))
% 0.21/0.42  = { by axiom 6 (associativity_of_glb) R->L }
% 0.21/0.42    least_upper_bound(greatest_lower_bound(identity, multiply(a, b)), greatest_lower_bound(identity, greatest_lower_bound(multiply(a, b), b)))
% 0.21/0.42  = { by axiom 2 (symmetry_of_glb) }
% 0.21/0.42    least_upper_bound(greatest_lower_bound(identity, multiply(a, b)), greatest_lower_bound(identity, greatest_lower_bound(b, multiply(a, b))))
% 0.21/0.42  = { by axiom 1 (left_identity) R->L }
% 0.21/0.42    least_upper_bound(greatest_lower_bound(identity, multiply(a, b)), greatest_lower_bound(identity, greatest_lower_bound(multiply(identity, b), multiply(a, b))))
% 0.21/0.42  = { by axiom 8 (monotony_glb2) R->L }
% 0.21/0.42    least_upper_bound(greatest_lower_bound(identity, multiply(a, b)), greatest_lower_bound(identity, multiply(greatest_lower_bound(identity, a), b)))
% 0.21/0.42  = { by axiom 3 (p04b_1) }
% 0.21/0.42    least_upper_bound(greatest_lower_bound(identity, multiply(a, b)), greatest_lower_bound(identity, multiply(identity, b)))
% 0.21/0.42  = { by axiom 1 (left_identity) }
% 0.21/0.42    least_upper_bound(greatest_lower_bound(identity, multiply(a, b)), greatest_lower_bound(identity, b))
% 0.21/0.42  = { by axiom 4 (p04b_2) }
% 0.21/0.42    least_upper_bound(greatest_lower_bound(identity, multiply(a, b)), identity)
% 0.21/0.42  = { by axiom 5 (symmetry_of_lub) }
% 0.21/0.42    least_upper_bound(identity, greatest_lower_bound(identity, multiply(a, b)))
% 0.21/0.42  = { by axiom 7 (lub_absorbtion) }
% 0.21/0.42    identity
% 0.21/0.42  % SZS output end Proof
% 0.21/0.42  
% 0.21/0.42  RESULT: Unsatisfiable (the axioms are contradictory).
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