%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : BOO011-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n021.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 : Thu Jul 14 23:44:34 EDT 2022

% Result   : Unsatisfiable 0.12s 0.34s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    9 (   7 unt;   0 nHn;   7 RR)
%            Number of literals    :   12 (  11 equ;   4 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :    2 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(additive_inverse1,axiom,
    add(X,inverse(X)) = multiplicative_identity ).

cnf(additive_id2,axiom,
    add(additive_identity,X) = X ).

cnf(prove_inverse_of_1_is_0,negated_conjecture,
    inverse(additive_identity) != multiplicative_identity ).

cnf(refute_0_0,plain,
    add(additive_identity,inverse(additive_identity)) = multiplicative_identity,
    inference(subst,[],[additive_inverse1:[bind(X,$fot(additive_identity))]]) ).

cnf(refute_0_1,plain,
    add(additive_identity,inverse(additive_identity)) = inverse(additive_identity),
    inference(subst,[],[additive_id2:[bind(X,$fot(inverse(additive_identity)))]]) ).

cnf(refute_0_2,plain,
    ( add(additive_identity,inverse(additive_identity)) != inverse(additive_identity)
    | add(additive_identity,inverse(additive_identity)) != multiplicative_identity
    | inverse(additive_identity) = multiplicative_identity ),
    introduced(tautology,[equality,[$cnf( $equal(add(additive_identity,inverse(additive_identity)),multiplicative_identity) ),[0],$fot(inverse(additive_identity))]]) ).

cnf(refute_0_3,plain,
    ( add(additive_identity,inverse(additive_identity)) != multiplicative_identity
    | inverse(additive_identity) = multiplicative_identity ),
    inference(resolve,[$cnf( $equal(add(additive_identity,inverse(additive_identity)),inverse(additive_identity)) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    inverse(additive_identity) = multiplicative_identity,
    inference(resolve,[$cnf( $equal(add(additive_identity,inverse(additive_identity)),multiplicative_identity) )],[refute_0_0,refute_0_3]) ).

cnf(refute_0_5,plain,
    $false,
    inference(resolve,[$cnf( $equal(inverse(additive_identity),multiplicative_identity) )],[refute_0_4,prove_inverse_of_1_is_0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : BOO011-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n021.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Wed Jun  1 22:34:16 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34  
% 0.12/0.34  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.35  
%------------------------------------------------------------------------------