%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP023-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %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  : 600s
% DateTime : Sat Jul 16 10:32:19 EDT 2022

% Result   : Unsatisfiable 0.18s 0.34s
% Output   : CNFRefutation 0.18s
% 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    :    3 (   3 usr;   1 con; 0-2 aty)
%            Number of variables   :    2 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
    multiply(identity,X) = X ).

cnf(right_inverse,axiom,
    multiply(X,inverse(X)) = identity ).

cnf(prove_inverse_of_id_is_id,negated_conjecture,
    inverse(identity) != identity ).

cnf(refute_0_0,plain,
    multiply(identity,inverse(identity)) = identity,
    inference(subst,[],[right_inverse:[bind(X,$fot(identity))]]) ).

cnf(refute_0_1,plain,
    multiply(identity,inverse(identity)) = inverse(identity),
    inference(subst,[],[left_identity:[bind(X,$fot(inverse(identity)))]]) ).

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

cnf(refute_0_3,plain,
    ( multiply(identity,inverse(identity)) != identity
    | inverse(identity) = identity ),
    inference(resolve,[$cnf( $equal(multiply(identity,inverse(identity)),inverse(identity)) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    inverse(identity) = identity,
    inference(resolve,[$cnf( $equal(multiply(identity,inverse(identity)),identity) )],[refute_0_0,refute_0_3]) ).

cnf(refute_0_5,plain,
    $false,
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[refute_0_4,prove_inverse_of_id_is_id]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : GRP023-2 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n013.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 : Mon Jun 13 17:54:58 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.34  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.34  
% 0.18/0.34  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.34  
%------------------------------------------------------------------------------