%------------------------------------------------------------------------------
% File     : Toma---0.4
% Problem  : ROB010-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : toma --casc %s

% Computer : n020.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 14:09:00 EDT 2023

% Result   : Unsatisfiable 0.20s 0.43s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : ROB010-1 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.13  % Command    : toma --casc %s
% 0.12/0.34  % Computer : n020.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 06:53:29 EDT 2023
% 0.12/0.34  % CPUTime    : 
% 0.20/0.43  % SZS status Unsatisfiable
% 0.20/0.43  % SZS output start Proof
% 0.20/0.43  original problem:
% 0.20/0.43  axioms:
% 0.20/0.43  add(X, Y) = add(Y, X)
% 0.20/0.43  add(add(X, Y), Z) = add(X, add(Y, Z))
% 0.20/0.43  negate(add(negate(add(X, Y)), negate(add(X, negate(Y))))) = X
% 0.20/0.43  negate(add(a(), negate(b()))) = c()
% 0.20/0.43  goal:
% 0.20/0.43  negate(add(c(), negate(add(b(), a())))) != a()
% 0.20/0.43  To show the unsatisfiability of the original goal,
% 0.20/0.43  it suffices to show that negate(add(c(), negate(add(b(), a())))) = a() (skolemized goal) is valid under the axioms.
% 0.20/0.43  Here is an equational proof:
% 0.20/0.43  0: add(X0, X1) = add(X1, X0).
% 0.20/0.43  Proof: Axiom.
% 0.20/0.43  
% 0.20/0.43  2: negate(add(negate(add(X0, X1)), negate(add(X0, negate(X1))))) = X0.
% 0.20/0.43  Proof: Axiom.
% 0.20/0.43  
% 0.20/0.43  3: negate(add(a(), negate(b()))) = c().
% 0.20/0.43  Proof: Axiom.
% 0.20/0.43  
% 0.20/0.43  4: negate(add(c(), negate(add(b(), a())))) = a().
% 0.20/0.43  Proof: Rewrite lhs with equations [3,0,0,2]
% 0.20/0.43                 rhs with equations [].
% 0.20/0.43  
% 0.20/0.43  % SZS output end Proof
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