%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : GRP518-1 : TPTP v8.1.2. Released v2.6.0.
% 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 : n031.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 01:18:44 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
% 0.11/0.11  % Problem  : GRP518-1 : TPTP v8.1.2. Released v2.6.0.
% 0.11/0.12  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.33  % Computer : n031.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Tue Aug 29 02:50:55 EDT 2023
% 0.11/0.33  % CPUTime  : 
% 0.11/0.37  Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 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 (single_axiom): multiply(X, multiply(multiply(inverse(multiply(X, Y)), Z), Y)) = Z.
% 0.11/0.37  
% 0.11/0.37  Lemma 2: multiply(multiply(inverse(X), Y), X) = Y.
% 0.11/0.37  Proof:
% 0.11/0.37    multiply(multiply(inverse(X), Y), X)
% 0.11/0.37  = { by axiom 1 (single_axiom) R->L }
% 0.11/0.37    multiply(multiply(inverse(X), Y), multiply(multiply(inverse(X), Y), multiply(multiply(inverse(multiply(multiply(inverse(X), Y), Z)), X), Z)))
% 0.11/0.37  = { by axiom 1 (single_axiom) R->L }
% 0.11/0.37    multiply(multiply(inverse(X), Y), multiply(multiply(inverse(multiply(multiply(inverse(X), Y), multiply(multiply(inverse(multiply(multiply(inverse(X), Y), Z)), X), Z))), Y), multiply(multiply(inverse(multiply(multiply(inverse(X), Y), Z)), X), Z)))
% 0.11/0.37  = { by axiom 1 (single_axiom) }
% 0.11/0.37    Y
% 0.11/0.37  
% 0.11/0.37  Goal 1 (prove_these_axioms_2): multiply(multiply(inverse(b2), b2), a2) = a2.
% 0.11/0.37  Proof:
% 0.11/0.37    multiply(multiply(inverse(b2), b2), a2)
% 0.11/0.37  = { by lemma 2 R->L }
% 0.11/0.37    multiply(multiply(inverse(b2), b2), multiply(multiply(inverse(b2), a2), b2))
% 0.11/0.37  = { by lemma 2 R->L }
% 0.11/0.37    multiply(multiply(inverse(b2), b2), multiply(multiply(inverse(multiply(multiply(inverse(b2), b2), b2)), a2), b2))
% 0.11/0.37  = { by axiom 1 (single_axiom) }
% 0.11/0.37    a2
% 0.11/0.37  % SZS output end Proof
% 0.11/0.37  
% 0.11/0.37  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------