%------------------------------------------------------------------------------
% File     : Toma---0.4
% Problem  : GRP558-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : toma --casc %s

% Computer : n013.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 01:15:21 EDT 2023

% Result   : Unsatisfiable 1.32s 1.70s
% Output   : CNFRefutation 1.32s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : GRP558-1 : TPTP v8.1.2. Released v2.6.0.
% 0.12/0.13  % Command    : toma --casc %s
% 0.12/0.34  % Computer : n013.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   : Mon Aug 28 22:00:16 EDT 2023
% 0.20/0.35  % CPUTime    : 
% 1.32/1.70  % SZS status Unsatisfiable
% 1.32/1.70  % SZS output start Proof
% 1.32/1.70  original problem:
% 1.32/1.70  axioms:
% 1.32/1.70  divide(A, inverse(divide(divide(B, C), divide(A, C)))) = B
% 1.32/1.70  multiply(A, B) = divide(A, inverse(B))
% 1.32/1.70  goal:
% 1.32/1.70  multiply(multiply(inverse(b2()), b2()), a2()) != a2()
% 1.32/1.70  To show the unsatisfiability of the original goal,
% 1.32/1.70  it suffices to show that multiply(multiply(inverse(b2()), b2()), a2()) = a2() (skolemized goal) is valid under the axioms.
% 1.32/1.70  Here is an equational proof:
% 1.32/1.70  0: divide(X0, inverse(divide(divide(X1, X2), divide(X0, X2)))) = X1.
% 1.32/1.70  Proof: Axiom.
% 1.32/1.70  
% 1.32/1.70  1: multiply(X0, X1) = divide(X0, inverse(X1)).
% 1.32/1.70  Proof: Axiom.
% 1.32/1.70  
% 1.32/1.70  2: X1 = divide(X3, inverse(divide(divide(X1, inverse(divide(divide(X4, X5), divide(X3, X5)))), X4))).
% 1.32/1.70  Proof: A critical pair between equations 0 and 0.
% 1.32/1.70  
% 1.32/1.70  3: X3 = divide(X0, inverse(divide(X4, divide(X0, inverse(divide(divide(X4, X5), divide(X3, X5))))))).
% 1.32/1.70  Proof: A critical pair between equations 0 and 0.
% 1.32/1.70  
% 1.32/1.70  4: X6 = divide(X6, inverse(divide(X7, X7))).
% 1.32/1.70  Proof: A critical pair between equations 3 and 0.
% 1.32/1.70  
% 1.32/1.70  16: X8 = divide(X4, inverse(divide(X8, X4))).
% 1.32/1.70  Proof: A critical pair between equations 2 and 4.
% 1.32/1.70  
% 1.32/1.70  29: X9 = divide(inverse(divide(X10, X10)), inverse(X9)).
% 1.32/1.70  Proof: A critical pair between equations 16 and 4.
% 1.32/1.70  
% 1.32/1.70  43: inverse(divide(X11, X11)) = divide(X7, X7).
% 1.32/1.70  Proof: A critical pair between equations 4 and 29.
% 1.32/1.70  
% 1.32/1.70  52: X6 = divide(X6, divide(X7, X7)).
% 1.32/1.70  Proof: Rewrite equation 4,
% 1.32/1.70                 lhs with equations []
% 1.32/1.70                 rhs with equations [43].
% 1.32/1.70  
% 1.32/1.70  63: X9 = divide(divide(X10, X10), inverse(X9)).
% 1.32/1.70  Proof: A critical pair between equations 16 and 52.
% 1.32/1.70  
% 1.32/1.70  99: multiply(multiply(inverse(b2()), b2()), a2()) = a2().
% 1.32/1.70  Proof: Rewrite lhs with equations [1,1,63]
% 1.32/1.70                 rhs with equations [].
% 1.32/1.70  
% 1.32/1.70  % SZS output end Proof
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