%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : BOO018-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %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  : 600s
% DateTime : Thu Jul 14 23:44:42 EDT 2022

% Result   : Unsatisfiable 0.13s 0.35s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   14 (  10 unt;   0 nHn;   9 RR)
%            Number of literals    :   20 (  19 equ;   7 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 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   :    8 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(commutativity_of_multiply,axiom,
    multiply(X,Y) = multiply(Y,X) ).

cnf(multiplicative_id1,axiom,
    multiply(X,multiplicative_identity) = X ).

cnf(multiplicative_inverse1,axiom,
    multiply(X,inverse(X)) = additive_identity ).

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

cnf(refute_0_0,plain,
    multiply(multiplicative_identity,inverse(multiplicative_identity)) = additive_identity,
    inference(subst,[],[multiplicative_inverse1:[bind(X,$fot(multiplicative_identity))]]) ).

cnf(refute_0_1,plain,
    multiply(X,multiplicative_identity) = multiply(multiplicative_identity,X),
    inference(subst,[],[commutativity_of_multiply:[bind(Y,$fot(multiplicative_identity))]]) ).

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

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

cnf(refute_0_4,plain,
    multiply(multiplicative_identity,X) = X,
    inference(resolve,[$cnf( $equal(multiply(X,multiplicative_identity),X) )],[multiplicative_id1,refute_0_3]) ).

cnf(refute_0_5,plain,
    multiply(multiplicative_identity,inverse(multiplicative_identity)) = inverse(multiplicative_identity),
    inference(subst,[],[refute_0_4:[bind(X,$fot(inverse(multiplicative_identity)))]]) ).

cnf(refute_0_6,plain,
    ( multiply(multiplicative_identity,inverse(multiplicative_identity)) != additive_identity
    | multiply(multiplicative_identity,inverse(multiplicative_identity)) != inverse(multiplicative_identity)
    | inverse(multiplicative_identity) = additive_identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(multiplicative_identity,inverse(multiplicative_identity)),additive_identity) ),[0],$fot(inverse(multiplicative_identity))]]) ).

cnf(refute_0_7,plain,
    ( multiply(multiplicative_identity,inverse(multiplicative_identity)) != additive_identity
    | inverse(multiplicative_identity) = additive_identity ),
    inference(resolve,[$cnf( $equal(multiply(multiplicative_identity,inverse(multiplicative_identity)),inverse(multiplicative_identity)) )],[refute_0_5,refute_0_6]) ).

cnf(refute_0_8,plain,
    inverse(multiplicative_identity) = additive_identity,
    inference(resolve,[$cnf( $equal(multiply(multiplicative_identity,inverse(multiplicative_identity)),additive_identity) )],[refute_0_0,refute_0_7]) ).

cnf(refute_0_9,plain,
    $false,
    inference(resolve,[$cnf( $equal(inverse(multiplicative_identity),additive_identity) )],[refute_0_8,prove_inverse_of_1_is_0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : BOO018-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.12  % Command  : metis --show proof --show saturation %s
% 0.13/0.33  % Computer : n020.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Wed Jun  1 21:40:38 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35  
% 0.13/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.35  
%------------------------------------------------------------------------------