%------------------------------------------------------------------------------
% File     : Toma---0.4
% Problem  : BOO021-1 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : toma --casc %s

% 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 18:11:01 EDT 2023

% Result   : Unsatisfiable 0.60s 0.79s
% Output   : CNFRefutation 0.60s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : BOO021-1 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.14  % Command    : toma --casc %s
% 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 08:34:38 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.60/0.79  % SZS status Unsatisfiable
% 0.60/0.79  % SZS output start Proof
% 0.60/0.79  original problem:
% 0.60/0.79  axioms:
% 0.60/0.79  multiply(add(X, Y), Y) = Y
% 0.60/0.79  multiply(X, add(Y, Z)) = add(multiply(Y, X), multiply(Z, X))
% 0.60/0.79  add(X, inverse(X)) = n1()
% 0.60/0.79  add(multiply(X, Y), Y) = Y
% 0.60/0.79  add(X, multiply(Y, Z)) = multiply(add(Y, X), add(Z, X))
% 0.60/0.79  multiply(X, inverse(X)) = n0()
% 0.60/0.79  goal:
% 0.60/0.79  multiply(b(), a()) != multiply(a(), b())
% 0.60/0.79  To show the unsatisfiability of the original goal,
% 0.60/0.79  it suffices to show that multiply(b(), a()) = multiply(a(), b()) (skolemized goal) is valid under the axioms.
% 0.60/0.79  Here is an equational proof:
% 0.60/0.79  0: multiply(add(X0, X1), X1) = X1.
% 0.60/0.79  Proof: Axiom.
% 0.60/0.79  
% 0.60/0.79  1: multiply(X0, add(X1, X2)) = add(multiply(X1, X0), multiply(X2, X0)).
% 0.60/0.79  Proof: Axiom.
% 0.60/0.79  
% 0.60/0.79  3: add(multiply(X0, X1), X1) = X1.
% 0.60/0.79  Proof: Axiom.
% 0.60/0.79  
% 0.60/0.79  7: X3 = add(X3, X3).
% 0.60/0.79  Proof: A critical pair between equations 3 and 0.
% 0.60/0.79  
% 0.60/0.79  24: multiply(X0, add(X1, X1)) = multiply(X1, X0).
% 0.60/0.79  Proof: A critical pair between equations 1 and 7.
% 0.60/0.79  
% 0.60/0.79  41: multiply(X0, X1) = multiply(X1, X0).
% 0.60/0.79  Proof: Rewrite equation 24,
% 0.60/0.79                 lhs with equations [7]
% 0.60/0.79                 rhs with equations [].
% 0.60/0.79  
% 0.60/0.79  43: multiply(b(), a()) = multiply(a(), b()).
% 0.60/0.79  Proof: Rewrite lhs with equations []
% 0.60/0.79                 rhs with equations [41].
% 0.60/0.79  
% 0.60/0.79  % SZS output end Proof
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