%------------------------------------------------------------------------------
% File     : Toma---0.4
% Problem  : GRP530-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : toma --casc %s

% Computer : n026.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 01:15:15 EDT 2023

% Result   : Unsatisfiable 0.20s 0.64s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : GRP530-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13  % Command    : toma --casc %s
% 0.12/0.34  % Computer : n026.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 29 00:43:05 EDT 2023
% 0.12/0.34  % CPUTime    : 
% 0.20/0.64  % SZS status Unsatisfiable
% 0.20/0.64  % SZS output start Proof
% 0.20/0.64  original problem:
% 0.20/0.64  axioms:
% 0.20/0.64  divide(divide(A, divide(B, C)), divide(A, B)) = C
% 0.20/0.64  multiply(A, B) = divide(A, divide(divide(C, C), B))
% 0.20/0.64  inverse(A) = divide(divide(B, B), A)
% 0.20/0.64  goal:
% 0.20/0.64  multiply(multiply(inverse(b2()), b2()), a2()) != a2()
% 0.20/0.64  To show the unsatisfiability of the original goal,
% 0.20/0.64  it suffices to show that multiply(multiply(inverse(b2()), b2()), a2()) = a2() (skolemized goal) is valid under the axioms.
% 0.20/0.64  Here is an equational proof:
% 0.20/0.64  0: divide(divide(X0, divide(X1, X2)), divide(X0, X1)) = X2.
% 0.20/0.64  Proof: Axiom.
% 0.20/0.64  
% 0.20/0.64  1: multiply(X0, X1) = divide(X0, divide(divide(X2, X2), X1)).
% 0.20/0.64  Proof: Axiom.
% 0.20/0.64  
% 0.20/0.64  2: inverse(X0) = divide(divide(X1, X1), X0).
% 0.20/0.64  Proof: Axiom.
% 0.20/0.64  
% 0.20/0.64  3: multiply(X0, X1) = divide(X0, inverse(X1)).
% 0.20/0.64  Proof: Rewrite equation 1,
% 0.20/0.64                 lhs with equations []
% 0.20/0.64                 rhs with equations [2].
% 0.20/0.64  
% 0.20/0.64  7: inverse(X0) = divide(inverse(divide(X2, X2)), X0).
% 0.20/0.64  Proof: A critical pair between equations 2 and 2.
% 0.20/0.64  
% 0.20/0.64  13: X2 = divide(inverse(divide(X1, X2)), divide(divide(X3, X3), X1)).
% 0.20/0.64  Proof: A critical pair between equations 0 and 2.
% 0.20/0.64  
% 0.20/0.64  16: X2 = divide(inverse(divide(X1, X2)), inverse(X1)).
% 0.20/0.64  Proof: Rewrite equation 13,
% 0.20/0.64                 lhs with equations []
% 0.20/0.64                 rhs with equations [2].
% 0.20/0.64  
% 0.20/0.64  17: X3 = inverse(inverse(X3)).
% 0.20/0.64  Proof: A critical pair between equations 16 and 7.
% 0.20/0.64  
% 0.20/0.64  32: multiply(multiply(inverse(b2()), b2()), a2()) = a2().
% 0.20/0.64  Proof: Rewrite lhs with equations [3,3,2,17]
% 0.20/0.64                 rhs with equations [].
% 0.20/0.64  
% 0.20/0.64  % SZS output end Proof
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