%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET024-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n007.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 03:31:24 EDT 2022

% Result   : Unsatisfiable 5.67s 5.84s
% Output   : CNFRefutation 5.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   20 (  11 unt;   0 nHn;  12 RR)
%            Number of literals    :   33 (  15 equ;  14 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-2 aty)
%            Number of variables   :   16 (   5 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(non_ordered_pair3,axiom,
    ( member(U,non_ordered_pair(X,Y))
    | ~ little_set(U)
    | U != Y ) ).

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

cnf(a_little_set,hypothesis,
    little_set(a) ).

cnf(prove_membership_of_singleton_set,negated_conjecture,
    ~ member(a,singleton_set(a)) ).

cnf(refute_0_0,plain,
    ( Y != Y
    | ~ little_set(Y)
    | member(Y,non_ordered_pair(X,Y)) ),
    inference(subst,[],[non_ordered_pair3:[bind(U,$fot(Y))]]) ).

cnf(refute_0_1,plain,
    Y = Y,
    introduced(tautology,[refl,[$fot(Y)]]) ).

cnf(refute_0_2,plain,
    ( ~ little_set(Y)
    | member(Y,non_ordered_pair(X,Y)) ),
    inference(resolve,[$cnf( $equal(Y,Y) )],[refute_0_1,refute_0_0]) ).

cnf(refute_0_3,plain,
    ( ~ little_set(a)
    | member(a,non_ordered_pair(X_197,a)) ),
    inference(subst,[],[refute_0_2:[bind(X,$fot(X_197)),bind(Y,$fot(a))]]) ).

cnf(refute_0_4,plain,
    member(a,non_ordered_pair(X_197,a)),
    inference(resolve,[$cnf( little_set(a) )],[a_little_set,refute_0_3]) ).

cnf(refute_0_5,plain,
    member(a,non_ordered_pair(a,a)),
    inference(subst,[],[refute_0_4:[bind(X_197,$fot(a))]]) ).

cnf(refute_0_6,plain,
    singleton_set(a) = non_ordered_pair(a,a),
    inference(subst,[],[singleton_set:[bind(X,$fot(a))]]) ).

cnf(refute_0_7,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_8,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_9,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_7,refute_0_8]) ).

cnf(refute_0_10,plain,
    ( singleton_set(a) != non_ordered_pair(a,a)
    | non_ordered_pair(a,a) = singleton_set(a) ),
    inference(subst,[],[refute_0_9:[bind(X0,$fot(singleton_set(a))),bind(Y0,$fot(non_ordered_pair(a,a)))]]) ).

cnf(refute_0_11,plain,
    non_ordered_pair(a,a) = singleton_set(a),
    inference(resolve,[$cnf( $equal(singleton_set(a),non_ordered_pair(a,a)) )],[refute_0_6,refute_0_10]) ).

cnf(refute_0_12,plain,
    ( non_ordered_pair(a,a) != singleton_set(a)
    | ~ member(a,non_ordered_pair(a,a))
    | member(a,singleton_set(a)) ),
    introduced(tautology,[equality,[$cnf( member(a,non_ordered_pair(a,a)) ),[1],$fot(singleton_set(a))]]) ).

cnf(refute_0_13,plain,
    ( ~ member(a,non_ordered_pair(a,a))
    | member(a,singleton_set(a)) ),
    inference(resolve,[$cnf( $equal(non_ordered_pair(a,a),singleton_set(a)) )],[refute_0_11,refute_0_12]) ).

cnf(refute_0_14,plain,
    member(a,singleton_set(a)),
    inference(resolve,[$cnf( member(a,non_ordered_pair(a,a)) )],[refute_0_5,refute_0_13]) ).

cnf(refute_0_15,plain,
    $false,
    inference(resolve,[$cnf( member(a,singleton_set(a)) )],[refute_0_14,prove_membership_of_singleton_set]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET024-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.34  % Computer : n007.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 20:06:47 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 5.67/5.84  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.67/5.84  
% 5.67/5.84  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.67/5.84  
%------------------------------------------------------------------------------