%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : RNG007-4 : 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 : n005.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 13:58:45 EDT 2023

% Result   : Unsatisfiable 0.13s 0.39s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : RNG007-4 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34  % Computer : n005.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sun Aug 27 01:25:53 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.39  Command-line arguments: --no-flatten-goal
% 0.13/0.39  
% 0.13/0.39  % SZS status Unsatisfiable
% 0.13/0.39  
% 0.13/0.39  % SZS output start Proof
% 0.13/0.39  Axiom 1 (additive_inverse_additive_inverse): additive_inverse(additive_inverse(X)) = X.
% 0.13/0.39  Axiom 2 (commutative_addition): add(X, Y) = add(Y, X).
% 0.13/0.39  Axiom 3 (boolean_ring): multiply(X, X) = X.
% 0.13/0.39  Axiom 4 (left_additive_inverse): add(additive_inverse(X), X) = additive_identity.
% 0.13/0.39  Axiom 5 (multiply_additive_inverse1): multiply(X, additive_inverse(Y)) = additive_inverse(multiply(X, Y)).
% 0.13/0.39  Axiom 6 (multiply_additive_inverse2): multiply(additive_inverse(X), Y) = additive_inverse(multiply(X, Y)).
% 0.13/0.39  
% 0.13/0.39  Goal 1 (prove_inverse): add(a, a) = additive_identity.
% 0.13/0.39  Proof:
% 0.13/0.39    add(a, a)
% 0.13/0.39  = { by axiom 3 (boolean_ring) R->L }
% 0.13/0.39    add(a, multiply(a, a))
% 0.13/0.39  = { by axiom 1 (additive_inverse_additive_inverse) R->L }
% 0.13/0.39    add(a, additive_inverse(additive_inverse(multiply(a, a))))
% 0.13/0.39  = { by axiom 5 (multiply_additive_inverse1) R->L }
% 0.13/0.39    add(a, additive_inverse(multiply(a, additive_inverse(a))))
% 0.13/0.39  = { by axiom 6 (multiply_additive_inverse2) R->L }
% 0.13/0.39    add(a, multiply(additive_inverse(a), additive_inverse(a)))
% 0.13/0.39  = { by axiom 3 (boolean_ring) }
% 0.13/0.39    add(a, additive_inverse(a))
% 0.13/0.39  = { by axiom 2 (commutative_addition) R->L }
% 0.13/0.39    add(additive_inverse(a), a)
% 0.13/0.39  = { by axiom 4 (left_additive_inverse) }
% 0.13/0.39    additive_identity
% 0.13/0.39  % SZS output end Proof
% 0.13/0.39  
% 0.13/0.39  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------