%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : GRP012-4 : 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 : n007.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 01:16:34 EDT 2023

% Result   : Unsatisfiable 0.14s 0.38s
% Output   : Proof 0.14s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP012-4 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34  % Computer : n007.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Tue Aug 29 02:33:58 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.14/0.38  Command-line arguments: --no-flatten-goal
% 0.14/0.38  
% 0.14/0.38  % SZS status Unsatisfiable
% 0.14/0.38  
% 0.14/0.38  % SZS output start Proof
% 0.14/0.38  Axiom 1 (right_identity): multiply(X, identity) = X.
% 0.14/0.38  Axiom 2 (left_identity): multiply(identity, X) = X.
% 0.14/0.38  Axiom 3 (right_inverse): multiply(X, inverse(X)) = identity.
% 0.14/0.38  Axiom 4 (left_inverse): multiply(inverse(X), X) = identity.
% 0.14/0.38  Axiom 5 (associativity): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 0.14/0.38  
% 0.14/0.38  Lemma 6: multiply(inverse(X), multiply(X, Y)) = Y.
% 0.14/0.38  Proof:
% 0.14/0.38    multiply(inverse(X), multiply(X, Y))
% 0.14/0.38  = { by axiom 5 (associativity) R->L }
% 0.14/0.38    multiply(multiply(inverse(X), X), Y)
% 0.14/0.38  = { by axiom 4 (left_inverse) }
% 0.14/0.38    multiply(identity, Y)
% 0.14/0.38  = { by axiom 2 (left_identity) }
% 0.14/0.38    Y
% 0.14/0.38  
% 0.14/0.38  Goal 1 (prove_inverse_of_product_is_product_of_inverses): inverse(multiply(a, b)) = multiply(inverse(b), inverse(a)).
% 0.14/0.38  Proof:
% 0.14/0.38    inverse(multiply(a, b))
% 0.14/0.38  = { by lemma 6 R->L }
% 0.14/0.38    multiply(inverse(b), multiply(b, inverse(multiply(a, b))))
% 0.14/0.38  = { by lemma 6 R->L }
% 0.14/0.38    multiply(inverse(b), multiply(inverse(a), multiply(a, multiply(b, inverse(multiply(a, b))))))
% 0.14/0.38  = { by axiom 5 (associativity) R->L }
% 0.14/0.38    multiply(inverse(b), multiply(inverse(a), multiply(multiply(a, b), inverse(multiply(a, b)))))
% 0.14/0.38  = { by axiom 3 (right_inverse) }
% 0.14/0.38    multiply(inverse(b), multiply(inverse(a), identity))
% 0.14/0.39  = { by axiom 1 (right_identity) }
% 0.14/0.39    multiply(inverse(b), inverse(a))
% 0.14/0.39  % SZS output end Proof
% 0.14/0.39  
% 0.14/0.39  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------