%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : BOO003-4 : TPTP v8.1.2. Released v1.1.0.
% 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 : n003.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 18:11:15 EDT 2023

% Result   : Unsatisfiable 0.21s 0.38s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : BOO003-4 : TPTP v8.1.2. Released v1.1.0.
% 0.12/0.13  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34  % Computer : n003.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Sun Aug 27 08:08:54 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.21/0.38  Command-line arguments: --no-flatten-goal
% 0.21/0.38  
% 0.21/0.38  % SZS status Unsatisfiable
% 0.21/0.38  
% 0.21/0.38  % SZS output start Proof
% 0.21/0.38  Axiom 1 (commutativity_of_add): add(X, Y) = add(Y, X).
% 0.21/0.38  Axiom 2 (additive_id1): add(X, additive_identity) = X.
% 0.21/0.38  Axiom 3 (multiplicative_id1): multiply(X, multiplicative_identity) = X.
% 0.21/0.38  Axiom 4 (distributivity2): multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)).
% 0.21/0.38  Axiom 5 (distributivity1): add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z)).
% 0.21/0.38  
% 0.21/0.38  Lemma 6: add(additive_identity, X) = X.
% 0.21/0.38  Proof:
% 0.21/0.38    add(additive_identity, X)
% 0.21/0.38  = { by axiom 1 (commutativity_of_add) R->L }
% 0.21/0.38    add(X, additive_identity)
% 0.21/0.38  = { by axiom 2 (additive_id1) }
% 0.21/0.38    X
% 0.21/0.38  
% 0.21/0.38  Goal 1 (prove_a_times_a_is_a): multiply(a, a) = a.
% 0.21/0.38  Proof:
% 0.21/0.38    multiply(a, a)
% 0.21/0.38  = { by axiom 2 (additive_id1) R->L }
% 0.21/0.38    multiply(a, add(a, additive_identity))
% 0.21/0.38  = { by axiom 2 (additive_id1) R->L }
% 0.21/0.38    multiply(add(a, additive_identity), add(a, additive_identity))
% 0.21/0.38  = { by axiom 5 (distributivity1) R->L }
% 0.21/0.38    add(a, multiply(additive_identity, additive_identity))
% 0.21/0.38  = { by lemma 6 R->L }
% 0.21/0.38    add(a, add(additive_identity, multiply(additive_identity, additive_identity)))
% 0.21/0.38  = { by axiom 3 (multiplicative_id1) R->L }
% 0.21/0.38    add(a, add(multiply(additive_identity, multiplicative_identity), multiply(additive_identity, additive_identity)))
% 0.21/0.38  = { by axiom 4 (distributivity2) R->L }
% 0.21/0.38    add(a, multiply(additive_identity, add(multiplicative_identity, additive_identity)))
% 0.21/0.38  = { by axiom 1 (commutativity_of_add) }
% 0.21/0.38    add(a, multiply(additive_identity, add(additive_identity, multiplicative_identity)))
% 0.21/0.38  = { by lemma 6 }
% 0.21/0.38    add(a, multiply(additive_identity, multiplicative_identity))
% 0.21/0.38  = { by axiom 3 (multiplicative_id1) }
% 0.21/0.38    add(a, additive_identity)
% 0.21/0.38  = { by axiom 2 (additive_id1) }
% 0.21/0.38    a
% 0.21/0.38  % SZS output end Proof
% 0.21/0.38  
% 0.21/0.38  RESULT: Unsatisfiable (the axioms are contradictory).
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