%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET296-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n028.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 : Tue Jul 19 03:34:03 EDT 2022

% Result   : Unsatisfiable 0.20s 0.45s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    8 (   6 unt;   0 nHn;   7 RR)
%            Number of literals    :   11 (  10 equ;   5 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;   1 con; 0-1 aty)
%            Number of variables   :    1 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(range_of,axiom,
    domain_of(inverse(Z)) = range_of(Z) ).

cnf(prove_domain_of_inverse_1,negated_conjecture,
    domain_of(inverse(x)) != range_of(x) ).

cnf(refute_0_0,plain,
    domain_of(inverse(x)) = range_of(x),
    inference(subst,[],[range_of:[bind(Z,$fot(x))]]) ).

cnf(refute_0_1,plain,
    ( domain_of(inverse(x)) != range_of(x)
    | range_of(x) != range_of(x)
    | domain_of(inverse(x)) = range_of(x) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(domain_of(inverse(x)),range_of(x)) ),[0],$fot(range_of(x))]]) ).

cnf(refute_0_2,plain,
    ( range_of(x) != range_of(x)
    | domain_of(inverse(x)) = range_of(x) ),
    inference(resolve,[$cnf( $equal(domain_of(inverse(x)),range_of(x)) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    range_of(x) != range_of(x),
    inference(resolve,[$cnf( $equal(domain_of(inverse(x)),range_of(x)) )],[refute_0_2,prove_domain_of_inverse_1]) ).

cnf(refute_0_4,plain,
    range_of(x) = range_of(x),
    introduced(tautology,[refl,[$fot(range_of(x))]]) ).

cnf(refute_0_5,plain,
    $false,
    inference(resolve,[$cnf( $equal(range_of(x),range_of(x)) )],[refute_0_4,refute_0_3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET296-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.34  % Computer : n028.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  : 600
% 0.12/0.34  % DateTime : Sun Jul 10 03:04:56 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.45  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.45  
% 0.20/0.45  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.45  
%------------------------------------------------------------------------------