%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : FLD006-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %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  : 600s
% DateTime : Sat Jul 16 02:19:20 EDT 2022

% Result   : Unsatisfiable 1.07s 1.28s
% Output   : CNFRefutation 1.07s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    9 (   5 unt;   0 nHn;   9 RR)
%            Number of literals    :   13 (   0 equ;   5 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    2 (   2 usr;   1 con; 0-1 aty)
%            Number of variables   :    4 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(existence_of_inverse_addition,axiom,
    ( sum(additive_inverse(X),X,additive_identity)
    | ~ defined(X) ) ).

cnf(commutativity_addition,axiom,
    ( sum(Y,X,Z)
    | ~ sum(X,Y,Z) ) ).

cnf(well_definedness_of_additive_identity,axiom,
    defined(additive_identity) ).

cnf(not_sum_1,negated_conjecture,
    ~ sum(additive_identity,additive_inverse(additive_identity),additive_identity) ).

cnf(refute_0_0,plain,
    ( ~ defined(additive_identity)
    | sum(additive_inverse(additive_identity),additive_identity,additive_identity) ),
    inference(subst,[],[existence_of_inverse_addition:[bind(X,$fot(additive_identity))]]) ).

cnf(refute_0_1,plain,
    sum(additive_inverse(additive_identity),additive_identity,additive_identity),
    inference(resolve,[$cnf( defined(additive_identity) )],[well_definedness_of_additive_identity,refute_0_0]) ).

cnf(refute_0_2,plain,
    ( ~ sum(additive_inverse(additive_identity),additive_identity,additive_identity)
    | sum(additive_identity,additive_inverse(additive_identity),additive_identity) ),
    inference(subst,[],[commutativity_addition:[bind(X,$fot(additive_inverse(additive_identity))),bind(Y,$fot(additive_identity)),bind(Z,$fot(additive_identity))]]) ).

cnf(refute_0_3,plain,
    sum(additive_identity,additive_inverse(additive_identity),additive_identity),
    inference(resolve,[$cnf( sum(additive_inverse(additive_identity),additive_identity,additive_identity) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    $false,
    inference(resolve,[$cnf( sum(additive_identity,additive_inverse(additive_identity),additive_identity) )],[refute_0_3,not_sum_1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09  % Problem  : FLD006-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.05/0.09  % Command  : metis --show proof --show saturation %s
% 0.08/0.28  % Computer : n032.cluster.edu
% 0.08/0.28  % Model    : x86_64 x86_64
% 0.08/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28  % Memory   : 8042.1875MB
% 0.08/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28  % CPULimit : 300
% 0.08/0.28  % WCLimit  : 600
% 0.08/0.28  % DateTime : Mon Jun  6 21:16:35 EDT 2022
% 0.08/0.28  % CPUTime  : 
% 0.08/0.28  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.07/1.28  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.07/1.28  
% 1.07/1.28  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.07/1.29  
%------------------------------------------------------------------------------