%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET115-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n004.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 03:32:49 EDT 2022

% Result   : Unsatisfiable 1.25s 1.44s
% Output   : CNFRefutation 1.25s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   10 (   5 unt;   3 nHn;   9 RR)
%            Number of literals    :   17 (  16 equ;   6 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;   1 con; 0-2 aty)
%            Number of variables   :    1 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(existence_of_1st_and_2nd_4,axiom,
    ( ordered_pair(first(X),second(X)) = X
    | first(X) = X ) ).

cnf(prove_unique_1st_and_2nd_in_pair_of_non_sets3_1,negated_conjecture,
    ordered_pair(first(x),second(x)) != x ).

cnf(prove_unique_1st_in_pair_of_non_sets,negated_conjecture,
    first(x) != x ).

cnf(refute_0_0,plain,
    ( first(x) = x
    | ordered_pair(first(x),second(x)) = x ),
    inference(subst,[],[existence_of_1st_and_2nd_4:[bind(X,$fot(x))]]) ).

cnf(refute_0_1,plain,
    ( ordered_pair(first(x),second(x)) != x
    | x != x
    | ordered_pair(first(x),second(x)) = x ),
    introduced(tautology,[equality,[$cnf( ~ $equal(ordered_pair(first(x),second(x)),x) ),[0],$fot(x)]]) ).

cnf(refute_0_2,plain,
    ( x != x
    | first(x) = x
    | ordered_pair(first(x),second(x)) = x ),
    inference(resolve,[$cnf( $equal(ordered_pair(first(x),second(x)),x) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    ( x != x
    | first(x) = x ),
    inference(resolve,[$cnf( $equal(ordered_pair(first(x),second(x)),x) )],[refute_0_2,prove_unique_1st_and_2nd_in_pair_of_non_sets3_1]) ).

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

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

cnf(refute_0_6,plain,
    $false,
    inference(resolve,[$cnf( $equal(first(x),x) )],[refute_0_5,prove_unique_1st_in_pair_of_non_sets]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : SET115-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% 0.11/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n004.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 : Sun Jul 10 07:35:22 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.25/1.44  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.25/1.44  
% 1.25/1.44  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.25/1.45  
%------------------------------------------------------------------------------