%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET113-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n029.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 03:32:48 EDT 2022

% Result   : Unsatisfiable 1.26s 1.44s
% Output   : CNFRefutation 1.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    3
% Syntax   : Number of clauses     :    6 (   4 unt;   2 nHn;   5 RR)
%            Number of literals    :    8 (   4 equ;   2 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :    1 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(existence_of_1st_and_2nd_2,axiom,
    ( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
    | first(X) = X ) ).

cnf(prove_unique_1st_and_2nd_in_pair_of_non_sets1_1,negated_conjecture,
    ~ member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class)) ).

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

cnf(refute_0_0,plain,
    ( first(x) = x
    | member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class)) ),
    inference(subst,[],[existence_of_1st_and_2nd_2:[bind(X,$fot(x))]]) ).

cnf(refute_0_1,plain,
    first(x) = x,
    inference(resolve,[$cnf( member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class)) )],[refute_0_0,prove_unique_1st_and_2nd_in_pair_of_non_sets1_1]) ).

cnf(refute_0_2,plain,
    $false,
    inference(resolve,[$cnf( $equal(first(x),x) )],[refute_0_1,prove_unique_1st_in_pair_of_non_sets]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SET113-7 : TPTP v8.1.0. Bugfixed v7.3.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n029.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Mon Jul 11 07:55:17 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.26/1.44  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.26/1.44  
% 1.26/1.44  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.26/1.44  
%------------------------------------------------------------------------------