%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : BOO009-2 : 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 : n028.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 : Wed Aug 30 18:11:20 EDT 2023

% Result   : Unsatisfiable 0.19s 0.39s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : BOO009-2 : 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 : n028.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 08:01:53 EDT 2023
% 0.16/0.34  % CPUTime  : 
% 0.19/0.39  Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.39  
% 0.19/0.39  % SZS status Unsatisfiable
% 0.19/0.39  
% 0.19/0.40  % SZS output start Proof
% 0.19/0.40  Axiom 1 (commutativity_of_add): add(X, Y) = add(Y, X).
% 0.19/0.40  Axiom 2 (additive_id1): add(X, additive_identity) = X.
% 0.19/0.40  Axiom 3 (additive_id2): add(additive_identity, X) = X.
% 0.19/0.40  Axiom 4 (commutativity_of_multiply): multiply(X, Y) = multiply(Y, X).
% 0.19/0.40  Axiom 5 (multiplicative_inverse1): multiply(X, inverse(X)) = additive_identity.
% 0.19/0.40  Axiom 6 (distributivity4): multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)).
% 0.19/0.40  Axiom 7 (distributivity2): add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z)).
% 0.19/0.40  
% 0.19/0.40  Goal 1 (prove_operation): multiply(a, add(a, b)) = a.
% 0.19/0.40  Proof:
% 0.19/0.40    multiply(a, add(a, b))
% 0.19/0.40  = { by axiom 2 (additive_id1) R->L }
% 0.19/0.40    multiply(add(a, additive_identity), add(a, b))
% 0.19/0.40  = { by axiom 7 (distributivity2) R->L }
% 0.19/0.40    add(a, multiply(additive_identity, b))
% 0.19/0.40  = { by axiom 4 (commutativity_of_multiply) R->L }
% 0.19/0.40    add(a, multiply(b, additive_identity))
% 0.19/0.40  = { by axiom 3 (additive_id2) R->L }
% 0.19/0.40    add(a, add(additive_identity, multiply(b, additive_identity)))
% 0.19/0.40  = { by axiom 5 (multiplicative_inverse1) R->L }
% 0.19/0.40    add(a, add(multiply(b, inverse(b)), multiply(b, additive_identity)))
% 0.19/0.40  = { by axiom 6 (distributivity4) R->L }
% 0.19/0.40    add(a, multiply(b, add(inverse(b), additive_identity)))
% 0.19/0.40  = { by axiom 1 (commutativity_of_add) }
% 0.19/0.40    add(a, multiply(b, add(additive_identity, inverse(b))))
% 0.19/0.40  = { by axiom 3 (additive_id2) }
% 0.19/0.40    add(a, multiply(b, inverse(b)))
% 0.19/0.40  = { by axiom 5 (multiplicative_inverse1) }
% 0.19/0.40    add(a, additive_identity)
% 0.19/0.40  = { by axiom 2 (additive_id1) }
% 0.19/0.40    a
% 0.19/0.40  % SZS output end Proof
% 0.19/0.40  
% 0.19/0.40  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------