%------------------------------------------------------------------------------
% File     : Toma---0.4
% Problem  : GRP023-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : toma --casc %s

% Computer : n022.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 01:13:36 EDT 2023

% Result   : Unsatisfiable 0.18s 0.49s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem    : GRP023-2 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.12  % Command    : toma --casc %s
% 0.12/0.32  % Computer : n022.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit   : 300
% 0.12/0.32  % WCLimit    : 300
% 0.12/0.32  % DateTime   : Mon Aug 28 22:20:54 EDT 2023
% 0.12/0.32  % CPUTime    : 
% 0.18/0.49  % SZS status Unsatisfiable
% 0.18/0.49  % SZS output start Proof
% 0.18/0.49  original problem:
% 0.18/0.49  axioms:
% 0.18/0.49  multiply(identity(), X) = X
% 0.18/0.49  multiply(inverse(X), X) = identity()
% 0.18/0.49  multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z))
% 0.18/0.49  multiply(X, identity()) = X
% 0.18/0.49  multiply(X, inverse(X)) = identity()
% 0.18/0.49  goal:
% 0.18/0.49  inverse(identity()) != identity()
% 0.18/0.49  To show the unsatisfiability of the original goal,
% 0.18/0.49  it suffices to show that inverse(identity()) = identity() (skolemized goal) is valid under the axioms.
% 0.18/0.49  Here is an equational proof:
% 0.18/0.49  0: multiply(identity(), X0) = X0.
% 0.18/0.49  Proof: Axiom.
% 0.18/0.49  
% 0.18/0.49  4: multiply(X0, inverse(X0)) = identity().
% 0.18/0.49  Proof: Axiom.
% 0.18/0.49  
% 0.18/0.49  5: inverse(identity()) = identity().
% 0.18/0.49  Proof: A critical pair between equations 0 and 4.
% 0.18/0.49  
% 0.18/0.49  11: inverse(identity()) = identity().
% 0.18/0.49  Proof: Rewrite lhs with equations [5]
% 0.18/0.49                 rhs with equations [].
% 0.18/0.49  
% 0.18/0.49  % SZS output end Proof
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