%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET025-3 : TPTP v8.1.0. Released v1.0.0.
% 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 03:31:25 EDT 2022

% Result   : Unsatisfiable 0.77s 0.97s
% Output   : CNFRefutation 0.77s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   15 (  10 unt;   0 nHn;   8 RR)
%            Number of literals    :   22 (  12 equ;   8 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   23 (   5 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(non_ordered_pair4,axiom,
    little_set(non_ordered_pair(X,Y)) ).

cnf(ordered_pair,axiom,
    ordered_pair(X,Y) = non_ordered_pair(singleton_set(X),non_ordered_pair(X,Y)) ).

cnf(prove_ordered_pairs_are_small,negated_conjecture,
    ~ little_set(ordered_pair(a,b)) ).

cnf(refute_0_0,plain,
    little_set(non_ordered_pair(singleton_set(X_119),non_ordered_pair(X_119,X_120))),
    inference(subst,[],[non_ordered_pair4:[bind(X,$fot(singleton_set(X_119))),bind(Y,$fot(non_ordered_pair(X_119,X_120)))]]) ).

cnf(refute_0_1,plain,
    ordered_pair(X_119,X_120) = non_ordered_pair(singleton_set(X_119),non_ordered_pair(X_119,X_120)),
    inference(subst,[],[ordered_pair:[bind(X,$fot(X_119)),bind(Y,$fot(X_120))]]) ).

cnf(refute_0_2,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_3,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_4,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( ordered_pair(X_119,X_120) != non_ordered_pair(singleton_set(X_119),non_ordered_pair(X_119,X_120))
    | non_ordered_pair(singleton_set(X_119),non_ordered_pair(X_119,X_120)) = ordered_pair(X_119,X_120) ),
    inference(subst,[],[refute_0_4:[bind(X0,$fot(ordered_pair(X_119,X_120))),bind(Y0,$fot(non_ordered_pair(singleton_set(X_119),non_ordered_pair(X_119,X_120))))]]) ).

cnf(refute_0_6,plain,
    non_ordered_pair(singleton_set(X_119),non_ordered_pair(X_119,X_120)) = ordered_pair(X_119,X_120),
    inference(resolve,[$cnf( $equal(ordered_pair(X_119,X_120),non_ordered_pair(singleton_set(X_119),non_ordered_pair(X_119,X_120))) )],[refute_0_1,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( non_ordered_pair(singleton_set(X_119),non_ordered_pair(X_119,X_120)) != ordered_pair(X_119,X_120)
    | ~ little_set(non_ordered_pair(singleton_set(X_119),non_ordered_pair(X_119,X_120)))
    | little_set(ordered_pair(X_119,X_120)) ),
    introduced(tautology,[equality,[$cnf( little_set(non_ordered_pair(singleton_set(X_119),non_ordered_pair(X_119,X_120))) ),[0],$fot(ordered_pair(X_119,X_120))]]) ).

cnf(refute_0_8,plain,
    ( ~ little_set(non_ordered_pair(singleton_set(X_119),non_ordered_pair(X_119,X_120)))
    | little_set(ordered_pair(X_119,X_120)) ),
    inference(resolve,[$cnf( $equal(non_ordered_pair(singleton_set(X_119),non_ordered_pair(X_119,X_120)),ordered_pair(X_119,X_120)) )],[refute_0_6,refute_0_7]) ).

cnf(refute_0_9,plain,
    little_set(ordered_pair(X_119,X_120)),
    inference(resolve,[$cnf( little_set(non_ordered_pair(singleton_set(X_119),non_ordered_pair(X_119,X_120))) )],[refute_0_0,refute_0_8]) ).

cnf(refute_0_10,plain,
    little_set(ordered_pair(a,b)),
    inference(subst,[],[refute_0_9:[bind(X_119,$fot(a)),bind(X_120,$fot(b))]]) ).

cnf(refute_0_11,plain,
    $false,
    inference(resolve,[$cnf( little_set(ordered_pair(a,b)) )],[refute_0_10,prove_ordered_pairs_are_small]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SET025-3 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12  % Command  : metis --show proof --show saturation %s
% 0.13/0.33  % Computer : n029.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 : Sun Jul 10 12:52:01 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.77/0.97  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.77/0.97  
% 0.77/0.97  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.77/0.97  
%------------------------------------------------------------------------------