%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : GRP175-4 : 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 : n010.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 01:17:32 EDT 2023

% Result   : Unsatisfiable 0.21s 0.41s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GRP175-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.13  % 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 : n010.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 19:39:19 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.41  Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.41  
% 0.21/0.41  % SZS status Unsatisfiable
% 0.21/0.41  
% 0.21/0.41  % SZS output start Proof
% 0.21/0.41  Axiom 1 (symmetry_of_glb): greatest_lower_bound(X, Y) = greatest_lower_bound(Y, X).
% 0.21/0.41  Axiom 2 (p06d_1): greatest_lower_bound(identity, b) = identity.
% 0.21/0.41  Axiom 3 (symmetry_of_lub): least_upper_bound(X, Y) = least_upper_bound(Y, X).
% 0.21/0.41  Axiom 4 (left_identity): multiply(identity, X) = X.
% 0.21/0.41  Axiom 5 (left_inverse): multiply(inverse(X), X) = identity.
% 0.21/0.41  Axiom 6 (lub_absorbtion): least_upper_bound(X, greatest_lower_bound(X, Y)) = X.
% 0.21/0.41  Axiom 7 (monotony_lub1): multiply(X, least_upper_bound(Y, Z)) = least_upper_bound(multiply(X, Y), multiply(X, Z)).
% 0.21/0.41  Axiom 8 (monotony_lub2): multiply(least_upper_bound(X, Y), Z) = least_upper_bound(multiply(X, Z), multiply(Y, Z)).
% 0.21/0.41  
% 0.21/0.41  Goal 1 (prove_p06d): least_upper_bound(identity, multiply(inverse(a), multiply(b, a))) = multiply(inverse(a), multiply(b, a)).
% 0.21/0.41  Proof:
% 0.21/0.41    least_upper_bound(identity, multiply(inverse(a), multiply(b, a)))
% 0.21/0.41  = { by axiom 5 (left_inverse) R->L }
% 0.21/0.41    least_upper_bound(multiply(inverse(a), a), multiply(inverse(a), multiply(b, a)))
% 0.21/0.41  = { by axiom 7 (monotony_lub1) R->L }
% 0.21/0.41    multiply(inverse(a), least_upper_bound(a, multiply(b, a)))
% 0.21/0.41  = { by axiom 4 (left_identity) R->L }
% 0.21/0.41    multiply(inverse(a), least_upper_bound(multiply(identity, a), multiply(b, a)))
% 0.21/0.41  = { by axiom 8 (monotony_lub2) R->L }
% 0.21/0.41    multiply(inverse(a), multiply(least_upper_bound(identity, b), a))
% 0.21/0.41  = { by axiom 3 (symmetry_of_lub) }
% 0.21/0.41    multiply(inverse(a), multiply(least_upper_bound(b, identity), a))
% 0.21/0.41  = { by axiom 2 (p06d_1) R->L }
% 0.21/0.41    multiply(inverse(a), multiply(least_upper_bound(b, greatest_lower_bound(identity, b)), a))
% 0.21/0.41  = { by axiom 1 (symmetry_of_glb) }
% 0.21/0.41    multiply(inverse(a), multiply(least_upper_bound(b, greatest_lower_bound(b, identity)), a))
% 0.21/0.41  = { by axiom 6 (lub_absorbtion) }
% 0.21/0.41    multiply(inverse(a), multiply(b, a))
% 0.21/0.41  % SZS output end Proof
% 0.21/0.41  
% 0.21/0.41  RESULT: Unsatisfiable (the axioms are contradictory).
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