%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : GRP168-2 : 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 : n017.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 01:17:28 EDT 2023

% Result   : Unsatisfiable 0.20s 0.40s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : GRP168-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.07/0.14  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35  % Computer : n017.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Mon Aug 28 21:59:13 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.20/0.40  Command-line arguments: --no-flatten-goal
% 0.20/0.40  
% 0.20/0.40  % SZS status Unsatisfiable
% 0.20/0.40  
% 0.20/0.40  % SZS output start Proof
% 0.20/0.40  Axiom 1 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
% 0.20/0.40  Axiom 2 (p01b_1): greatest_lower_bound(a, b) = a.
% 0.20/0.40  Axiom 3 (monotony_glb1): multiply(X, greatest_lower_bound(Y, Z)) = greatest_lower_bound(multiply(X, Y), multiply(X, Z)).
% 0.20/0.40  Axiom 4 (monotony_glb2): multiply(greatest_lower_bound(X, Y), Z) = greatest_lower_bound(multiply(X, Z), multiply(Y, Z)).
% 0.20/0.40  
% 0.20/0.40  Goal 1 (prove_p01b): greatest_lower_bound(multiply(inverse(c), multiply(a, c)), multiply(inverse(c), multiply(b, c))) = multiply(inverse(c), multiply(a, c)).
% 0.20/0.40  Proof:
% 0.20/0.40    greatest_lower_bound(multiply(inverse(c), multiply(a, c)), multiply(inverse(c), multiply(b, c)))
% 0.20/0.40  = { by axiom 1 (symmetry_of_glb) }
% 0.20/0.40    greatest_lower_bound(multiply(inverse(c), multiply(b, c)), multiply(inverse(c), multiply(a, c)))
% 0.20/0.40  = { by axiom 3 (monotony_glb1) R->L }
% 0.20/0.40    multiply(inverse(c), greatest_lower_bound(multiply(b, c), multiply(a, c)))
% 0.20/0.40  = { by axiom 4 (monotony_glb2) R->L }
% 0.20/0.40    multiply(inverse(c), multiply(greatest_lower_bound(b, a), c))
% 0.20/0.40  = { by axiom 1 (symmetry_of_glb) R->L }
% 0.20/0.40    multiply(inverse(c), multiply(greatest_lower_bound(a, b), c))
% 0.20/0.40  = { by axiom 2 (p01b_1) }
% 0.20/0.40    multiply(inverse(c), multiply(a, c))
% 0.20/0.40  % SZS output end Proof
% 0.20/0.40  
% 0.20/0.40  RESULT: Unsatisfiable (the axioms are contradictory).
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