%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : GRP022-2 : TPTP v8.1.2. Released v1.0.0.
% 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 : n012.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 01:16:37 EDT 2023

% Result   : Unsatisfiable 0.14s 0.39s
% Output   : Proof 0.14s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : GRP022-2 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36  % Computer : n012.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Tue Aug 29 02:37:54 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.14/0.39  Command-line arguments: --no-flatten-goal
% 0.14/0.39  
% 0.14/0.39  % SZS status Unsatisfiable
% 0.14/0.39  
% 0.14/0.40  % SZS output start Proof
% 0.14/0.40  Axiom 1 (right_identity): multiply(X, identity) = X.
% 0.14/0.40  Axiom 2 (left_identity): multiply(identity, X) = X.
% 0.14/0.40  Axiom 3 (right_inverse): multiply(X, inverse(X)) = identity.
% 0.14/0.40  Axiom 4 (associativity): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 0.14/0.40  
% 0.14/0.40  Goal 1 (prove_inverse_of_inverse_is_original): inverse(inverse(a)) = a.
% 0.14/0.40  Proof:
% 0.14/0.40    inverse(inverse(a))
% 0.14/0.40  = { by axiom 2 (left_identity) R->L }
% 0.14/0.40    multiply(identity, inverse(inverse(a)))
% 0.14/0.40  = { by axiom 3 (right_inverse) R->L }
% 0.14/0.40    multiply(multiply(a, inverse(a)), inverse(inverse(a)))
% 0.14/0.40  = { by axiom 4 (associativity) }
% 0.14/0.40    multiply(a, multiply(inverse(a), inverse(inverse(a))))
% 0.14/0.40  = { by axiom 3 (right_inverse) }
% 0.14/0.40    multiply(a, identity)
% 0.14/0.40  = { by axiom 1 (right_identity) }
% 0.14/0.40    a
% 0.14/0.40  % SZS output end Proof
% 0.14/0.40  
% 0.14/0.40  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------