%------------------------------------------------------------------------------
% File     : Toma---0.4
% Problem  : RNG023-6 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : toma --casc %s

% Computer : n014.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 13:58:10 EDT 2023

% Result   : Unsatisfiable 0.21s 0.47s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : RNG023-6 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14  % Command    : toma --casc %s
% 0.15/0.36  % Computer : n014.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Sun Aug 27 02:08:46 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.21/0.47  % SZS status Unsatisfiable
% 0.21/0.47  % SZS output start Proof
% 0.21/0.47  original problem:
% 0.21/0.47  axioms:
% 0.21/0.47  add(additive_identity(), X) = X
% 0.21/0.47  add(X, additive_identity()) = X
% 0.21/0.47  multiply(additive_identity(), X) = additive_identity()
% 0.21/0.47  multiply(X, additive_identity()) = additive_identity()
% 0.21/0.47  add(additive_inverse(X), X) = additive_identity()
% 0.21/0.47  add(X, additive_inverse(X)) = additive_identity()
% 0.21/0.47  additive_inverse(additive_inverse(X)) = X
% 0.21/0.47  multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z))
% 0.21/0.47  multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z))
% 0.21/0.47  add(X, Y) = add(Y, X)
% 0.21/0.47  add(X, add(Y, Z)) = add(add(X, Y), Z)
% 0.21/0.47  multiply(multiply(X, Y), Y) = multiply(X, multiply(Y, Y))
% 0.21/0.47  multiply(multiply(X, X), Y) = multiply(X, multiply(X, Y))
% 0.21/0.47  associator(X, Y, Z) = add(multiply(multiply(X, Y), Z), additive_inverse(multiply(X, multiply(Y, Z))))
% 0.21/0.47  commutator(X, Y) = add(multiply(Y, X), additive_inverse(multiply(X, Y)))
% 0.21/0.47  goal:
% 0.21/0.47  associator(x(), x(), y()) != additive_identity()
% 0.21/0.47  To show the unsatisfiability of the original goal,
% 0.21/0.47  it suffices to show that associator(x(), x(), y()) = additive_identity() (skolemized goal) is valid under the axioms.
% 0.21/0.47  Here is an equational proof:
% 0.21/0.47  5: add(X0, additive_inverse(X0)) = additive_identity().
% 0.21/0.47  Proof: Axiom.
% 0.21/0.47  
% 0.21/0.47  12: multiply(multiply(X0, X0), X1) = multiply(X0, multiply(X0, X1)).
% 0.21/0.47  Proof: Axiom.
% 0.21/0.47  
% 0.21/0.47  13: associator(X0, X1, X2) = add(multiply(multiply(X0, X1), X2), additive_inverse(multiply(X0, multiply(X1, X2)))).
% 0.21/0.47  Proof: Axiom.
% 0.21/0.47  
% 0.21/0.47  15: associator(x(), x(), y()) = additive_identity().
% 0.21/0.47  Proof: Rewrite lhs with equations [13,12,5]
% 0.21/0.47                 rhs with equations [].
% 0.21/0.47  
% 0.21/0.47  % SZS output end Proof
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