%------------------------------------------------------------------------------
% File     : Toma---0.4
% Problem  : BOO011-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : toma --casc %s

% Computer : n002.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 18:10:57 EDT 2023

% Result   : Unsatisfiable 0.62s 0.91s
% Output   : CNFRefutation 0.62s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : BOO011-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.12/0.14  % Command    : toma --casc %s
% 0.13/0.35  % Computer : n002.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Sun Aug 27 08:30:48 EDT 2023
% 0.13/0.35  % CPUTime    : 
% 0.62/0.91  % SZS status Unsatisfiable
% 0.62/0.91  % SZS output start Proof
% 0.62/0.91  original problem:
% 0.62/0.91  axioms:
% 0.62/0.91  add(X, Y) = add(Y, X)
% 0.62/0.91  multiply(X, Y) = multiply(Y, X)
% 0.62/0.91  add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z))
% 0.62/0.91  multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z))
% 0.62/0.91  add(X, additive_identity()) = X
% 0.62/0.91  multiply(X, multiplicative_identity()) = X
% 0.62/0.91  add(X, inverse(X)) = multiplicative_identity()
% 0.62/0.91  multiply(X, inverse(X)) = additive_identity()
% 0.62/0.91  goal:
% 0.62/0.91  inverse(additive_identity()) != multiplicative_identity()
% 0.62/0.91  To show the unsatisfiability of the original goal,
% 0.62/0.91  it suffices to show that inverse(additive_identity()) = multiplicative_identity() (skolemized goal) is valid under the axioms.
% 0.62/0.91  Here is an equational proof:
% 0.62/0.91  0: add(X0, X1) = add(X1, X0).
% 0.62/0.91  Proof: Axiom.
% 0.62/0.91  
% 0.62/0.91  4: add(X0, additive_identity()) = X0.
% 0.62/0.91  Proof: Axiom.
% 0.62/0.91  
% 0.62/0.91  6: add(X0, inverse(X0)) = multiplicative_identity().
% 0.62/0.91  Proof: Axiom.
% 0.62/0.91  
% 0.62/0.91  9: add(additive_identity(), X2) = X2.
% 0.62/0.91  Proof: A critical pair between equations 0 and 4.
% 0.62/0.91  
% 0.62/0.91  31: inverse(additive_identity()) = multiplicative_identity().
% 0.62/0.91  Proof: A critical pair between equations 9 and 6.
% 0.62/0.91  
% 0.62/0.91  63: inverse(additive_identity()) = multiplicative_identity().
% 0.62/0.91  Proof: Rewrite lhs with equations []
% 0.62/0.91                 rhs with equations [31].
% 0.62/0.91  
% 0.62/0.91  % SZS output end Proof
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