%------------------------------------------------------------------------------
% File     : Toma---0.4
% Problem  : GRP518-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : toma --casc %s

% Computer : n032.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 01:15:13 EDT 2023

% Result   : Unsatisfiable 1.69s 1.96s
% Output   : CNFRefutation 1.69s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem    : GRP518-1 : TPTP v8.1.2. Released v2.6.0.
% 0.10/0.11  % Command    : toma --casc %s
% 0.10/0.30  % Computer : n032.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit   : 300
% 0.10/0.30  % WCLimit    : 300
% 0.10/0.30  % DateTime   : Tue Aug 29 02:28:46 EDT 2023
% 0.10/0.30  % CPUTime    : 
% 1.69/1.96  % SZS status Unsatisfiable
% 1.69/1.96  % SZS output start Proof
% 1.69/1.96  original problem:
% 1.69/1.96  axioms:
% 1.69/1.96  multiply(A, multiply(multiply(inverse(multiply(A, B)), C), B)) = C
% 1.69/1.96  goal:
% 1.69/1.96  multiply(multiply(inverse(b2()), b2()), a2()) != a2()
% 1.69/1.96  To show the unsatisfiability of the original goal,
% 1.69/1.96  it suffices to show that multiply(multiply(inverse(b2()), b2()), a2()) = a2() (skolemized goal) is valid under the axioms.
% 1.69/1.96  Here is an equational proof:
% 1.69/1.96  0: multiply(X0, multiply(multiply(inverse(multiply(X0, X1)), X2), X1)) = X2.
% 1.69/1.96  Proof: Axiom.
% 1.69/1.96  
% 1.69/1.96  1: X2 = multiply(X3, multiply(multiply(inverse(X5), X2), multiply(multiply(inverse(multiply(X3, X4)), X5), X4))).
% 1.69/1.96  Proof: A critical pair between equations 0 and 0.
% 1.69/1.96  
% 1.69/1.96  3: X2 = multiply(multiply(inverse(X8), X2), X8).
% 1.69/1.96  Proof: A critical pair between equations 1 and 0.
% 1.69/1.96  
% 1.69/1.96  8: X2 = multiply(X6, multiply(multiply(inverse(X5), X2), multiply(multiply(inverse(X8), X5), multiply(multiply(inverse(multiply(X6, X7)), X8), X7)))).
% 1.69/1.96  Proof: A critical pair between equations 1 and 0.
% 1.69/1.96  
% 1.69/1.96  22: X2 = multiply(multiply(inverse(X11), X5), multiply(multiply(inverse(X5), X2), X11)).
% 1.69/1.96  Proof: A critical pair between equations 8 and 0.
% 1.69/1.96  
% 1.69/1.96  42: X13 = multiply(multiply(inverse(X12), X12), X13).
% 1.69/1.96  Proof: A critical pair between equations 22 and 3.
% 1.69/1.96  
% 1.69/1.96  62: multiply(multiply(inverse(b2()), b2()), a2()) = a2().
% 1.69/1.96  Proof: Rewrite lhs with equations [42]
% 1.69/1.96                 rhs with equations [].
% 1.69/1.96  
% 1.69/1.96  % SZS output end Proof
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