%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : RNG013-6 : 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 : n015.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 13:58:48 EDT 2023

% Result   : Unsatisfiable 0.16s 0.40s
% Output   : Proof 0.16s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : RNG013-6 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.16/0.34  % Computer : n015.cluster.edu
% 0.16/0.34  % Model    : x86_64 x86_64
% 0.16/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34  % Memory   : 8042.1875MB
% 0.16/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34  % CPULimit : 300
% 0.16/0.34  % WCLimit  : 300
% 0.16/0.34  % DateTime : Sun Aug 27 02:28:53 EDT 2023
% 0.16/0.34  % CPUTime  : 
% 0.16/0.40  Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.16/0.40  
% 0.16/0.40  % SZS status Unsatisfiable
% 0.16/0.40  
% 0.16/0.41  % SZS output start Proof
% 0.16/0.41  Axiom 1 (left_multiplicative_zero): multiply(additive_identity, X) = additive_identity.
% 0.16/0.41  Axiom 2 (commutativity_for_addition): add(X, Y) = add(Y, X).
% 0.16/0.41  Axiom 3 (right_additive_identity): add(X, additive_identity) = X.
% 0.16/0.41  Axiom 4 (left_additive_identity): add(additive_identity, X) = X.
% 0.16/0.41  Axiom 5 (additive_inverse_additive_inverse): additive_inverse(additive_inverse(X)) = X.
% 0.16/0.41  Axiom 6 (right_additive_inverse): add(X, additive_inverse(X)) = additive_identity.
% 0.16/0.41  Axiom 7 (associativity_for_addition): add(X, add(Y, Z)) = add(add(X, Y), Z).
% 0.16/0.41  Axiom 8 (distribute2): multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)).
% 0.16/0.41  
% 0.16/0.41  Goal 1 (prove_equation): multiply(additive_inverse(a), b) = additive_inverse(multiply(a, b)).
% 0.16/0.41  Proof:
% 0.16/0.41    multiply(additive_inverse(a), b)
% 0.16/0.41  = { by axiom 4 (left_additive_identity) R->L }
% 0.16/0.41    add(additive_identity, multiply(additive_inverse(a), b))
% 0.16/0.41  = { by axiom 6 (right_additive_inverse) R->L }
% 0.16/0.41    add(add(additive_inverse(multiply(a, b)), additive_inverse(additive_inverse(multiply(a, b)))), multiply(additive_inverse(a), b))
% 0.16/0.41  = { by axiom 7 (associativity_for_addition) R->L }
% 0.16/0.41    add(additive_inverse(multiply(a, b)), add(additive_inverse(additive_inverse(multiply(a, b))), multiply(additive_inverse(a), b)))
% 0.16/0.41  = { by axiom 2 (commutativity_for_addition) }
% 0.16/0.41    add(additive_inverse(multiply(a, b)), add(multiply(additive_inverse(a), b), additive_inverse(additive_inverse(multiply(a, b)))))
% 0.16/0.41  = { by axiom 5 (additive_inverse_additive_inverse) }
% 0.16/0.41    add(additive_inverse(multiply(a, b)), add(multiply(additive_inverse(a), b), multiply(a, b)))
% 0.16/0.41  = { by axiom 8 (distribute2) R->L }
% 0.16/0.41    add(additive_inverse(multiply(a, b)), multiply(add(additive_inverse(a), a), b))
% 0.16/0.41  = { by axiom 2 (commutativity_for_addition) }
% 0.16/0.41    add(additive_inverse(multiply(a, b)), multiply(add(a, additive_inverse(a)), b))
% 0.16/0.41  = { by axiom 6 (right_additive_inverse) }
% 0.16/0.41    add(additive_inverse(multiply(a, b)), multiply(additive_identity, b))
% 0.16/0.41  = { by axiom 1 (left_multiplicative_zero) }
% 0.16/0.41    add(additive_inverse(multiply(a, b)), additive_identity)
% 0.16/0.41  = { by axiom 3 (right_additive_identity) }
% 0.16/0.41    additive_inverse(multiply(a, b))
% 0.16/0.41  % SZS output end Proof
% 0.16/0.41  
% 0.16/0.41  RESULT: Unsatisfiable (the axioms are contradictory).
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