%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : BOO013-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 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 : Wed Aug 30 18:11:23 EDT 2023

% Result   : Unsatisfiable 0.14s 0.40s
% Output   : Proof 0.14s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : BOO013-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.08/0.14  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35  % Computer : n005.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Sun Aug 27 07:40:23 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.14/0.40  Command-line arguments: --no-flatten-goal
% 0.14/0.40  
% 0.14/0.40  % SZS status Unsatisfiable
% 0.14/0.40  
% 0.14/0.40  % SZS output start Proof
% 0.14/0.40  Axiom 1 (b_and_multiplicative_identity): add(a, b) = multiplicative_identity.
% 0.14/0.40  Axiom 2 (c_and_multiplicative_identity): add(a, c) = multiplicative_identity.
% 0.14/0.40  Axiom 3 (additive_id2): add(additive_identity, X) = X.
% 0.14/0.40  Axiom 4 (commutativity_of_multiply): multiply(X, Y) = multiply(Y, X).
% 0.14/0.40  Axiom 5 (multiplicative_id1): multiply(X, multiplicative_identity) = X.
% 0.14/0.40  Axiom 6 (b_a_additive_identity): multiply(a, b) = additive_identity.
% 0.14/0.40  Axiom 7 (c_a_additive_identity): multiply(a, c) = additive_identity.
% 0.14/0.40  Axiom 8 (distributivity4): multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)).
% 0.14/0.40  
% 0.14/0.40  Goal 1 (prove_b_is_a): b = c.
% 0.14/0.40  Proof:
% 0.14/0.40    b
% 0.14/0.40  = { by axiom 5 (multiplicative_id1) R->L }
% 0.14/0.40    multiply(b, multiplicative_identity)
% 0.14/0.40  = { by axiom 2 (c_and_multiplicative_identity) R->L }
% 0.14/0.40    multiply(b, add(a, c))
% 0.14/0.40  = { by axiom 8 (distributivity4) }
% 0.14/0.40    add(multiply(b, a), multiply(b, c))
% 0.14/0.40  = { by axiom 4 (commutativity_of_multiply) R->L }
% 0.14/0.40    add(multiply(a, b), multiply(b, c))
% 0.14/0.40  = { by axiom 6 (b_a_additive_identity) }
% 0.14/0.40    add(additive_identity, multiply(b, c))
% 0.14/0.40  = { by axiom 3 (additive_id2) }
% 0.14/0.40    multiply(b, c)
% 0.14/0.40  = { by axiom 4 (commutativity_of_multiply) R->L }
% 0.14/0.40    multiply(c, b)
% 0.14/0.40  = { by axiom 3 (additive_id2) R->L }
% 0.14/0.40    add(additive_identity, multiply(c, b))
% 0.14/0.40  = { by axiom 7 (c_a_additive_identity) R->L }
% 0.14/0.40    add(multiply(a, c), multiply(c, b))
% 0.14/0.40  = { by axiom 4 (commutativity_of_multiply) }
% 0.14/0.40    add(multiply(c, a), multiply(c, b))
% 0.14/0.40  = { by axiom 8 (distributivity4) R->L }
% 0.14/0.40    multiply(c, add(a, b))
% 0.14/0.40  = { by axiom 1 (b_and_multiplicative_identity) }
% 0.14/0.40    multiply(c, multiplicative_identity)
% 0.14/0.40  = { by axiom 5 (multiplicative_id1) }
% 0.14/0.40    c
% 0.14/0.40  % SZS output end Proof
% 0.14/0.40  
% 0.14/0.40  RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------