%------------------------------------------------------------------------------
% File     : Toma---0.4
% Problem  : GRP533-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : toma --casc %s

% Computer : n031.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 01:15:16 EDT 2023

% Result   : Unsatisfiable 0.21s 0.53s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : GRP533-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.14  % Command    : toma --casc %s
% 0.14/0.35  % Computer : n031.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   : Tue Aug 29 01:01:40 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.21/0.53  % SZS status Unsatisfiable
% 0.21/0.53  % SZS output start Proof
% 0.21/0.53  original problem:
% 0.21/0.53  axioms:
% 0.21/0.53  divide(divide(A, divide(divide(A, B), C)), B) = C
% 0.21/0.53  multiply(A, B) = divide(A, divide(divide(C, C), B))
% 0.21/0.53  inverse(A) = divide(divide(B, B), A)
% 0.21/0.53  identity() = divide(A, A)
% 0.21/0.53  goal:
% 0.21/0.53  multiply(inverse(a1()), a1()) != multiply(inverse(b1()), b1())
% 0.21/0.53  To show the unsatisfiability of the original goal,
% 0.21/0.53  it suffices to show that multiply(inverse(a1()), a1()) = multiply(inverse(b1()), b1()) (skolemized goal) is valid under the axioms.
% 0.21/0.53  Here is an equational proof:
% 0.21/0.53  1: multiply(X0, X1) = divide(X0, divide(divide(X2, X2), X1)).
% 0.21/0.53  Proof: Axiom.
% 0.21/0.53  
% 0.21/0.53  2: inverse(X0) = divide(divide(X1, X1), X0).
% 0.21/0.53  Proof: Axiom.
% 0.21/0.53  
% 0.21/0.53  3: identity() = divide(X0, X0).
% 0.21/0.53  Proof: Axiom.
% 0.21/0.53  
% 0.21/0.53  4: multiply(X0, X1) = divide(X0, divide(identity(), X1)).
% 0.21/0.53  Proof: Rewrite equation 1,
% 0.21/0.53                 lhs with equations []
% 0.21/0.53                 rhs with equations [3].
% 0.21/0.53  
% 0.21/0.53  5: inverse(X0) = divide(identity(), X0).
% 0.21/0.53  Proof: Rewrite equation 2,
% 0.21/0.53                 lhs with equations []
% 0.21/0.53                 rhs with equations [3].
% 0.21/0.53  
% 0.21/0.53  18: multiply(inverse(a1()), a1()) = multiply(inverse(b1()), b1()).
% 0.21/0.53  Proof: Rewrite lhs with equations [5,4,3]
% 0.21/0.53                 rhs with equations [5,4,3].
% 0.21/0.53  
% 0.21/0.53  % SZS output end Proof
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