TSTP Solution File: SET101-6 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET101-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n013.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 03:32:39 EDT 2022

% Result   : Unsatisfiable 30.21s 30.38s
% Output   : CNFRefutation 30.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   19 (  13 unt;   0 nHn;   7 RR)
%            Number of literals    :   27 (   6 equ;   9 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   26 (   8 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(unordered_pair2,axiom,
    ( ~ member(X,universal_class)
    | member(X,unordered_pair(X,Y)) ) ).

cnf(unordered_pairs_in_universal,axiom,
    member(unordered_pair(X,Y),universal_class) ).

cnf(singleton_set,axiom,
    unordered_pair(X,X) = singleton(X) ).

cnf(ordered_pair,axiom,
    unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ).

cnf(prove_singleton_member_of_ordered_pair_1,negated_conjecture,
    ~ member(singleton(x),ordered_pair(x,y)) ).

cnf(refute_0_0,plain,
    member(unordered_pair(X_14,X_14),universal_class),
    inference(subst,[],[unordered_pairs_in_universal:[bind(X,$fot(X_14)),bind(Y,$fot(X_14))]]) ).

cnf(refute_0_1,plain,
    unordered_pair(X_14,X_14) = singleton(X_14),
    inference(subst,[],[singleton_set:[bind(X,$fot(X_14))]]) ).

cnf(refute_0_2,plain,
    ( unordered_pair(X_14,X_14) != singleton(X_14)
    | ~ member(unordered_pair(X_14,X_14),universal_class)
    | member(singleton(X_14),universal_class) ),
    introduced(tautology,[equality,[$cnf( member(unordered_pair(X_14,X_14),universal_class) ),[0],$fot(singleton(X_14))]]) ).

cnf(refute_0_3,plain,
    ( ~ member(unordered_pair(X_14,X_14),universal_class)
    | member(singleton(X_14),universal_class) ),
    inference(resolve,[$cnf( $equal(unordered_pair(X_14,X_14),singleton(X_14)) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    member(singleton(X_14),universal_class),
    inference(resolve,[$cnf( member(unordered_pair(X_14,X_14),universal_class) )],[refute_0_0,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( ~ member(singleton(X_14),universal_class)
    | member(singleton(X_14),unordered_pair(singleton(X_14),X_270)) ),
    inference(subst,[],[unordered_pair2:[bind(X,$fot(singleton(X_14))),bind(Y,$fot(X_270))]]) ).

cnf(refute_0_6,plain,
    member(singleton(X_14),unordered_pair(singleton(X_14),X_270)),
    inference(resolve,[$cnf( member(singleton(X_14),universal_class) )],[refute_0_4,refute_0_5]) ).

cnf(refute_0_7,plain,
    member(singleton(X_649),unordered_pair(singleton(X_649),unordered_pair(X_649,singleton(Y)))),
    inference(subst,[],[refute_0_6:[bind(X_14,$fot(X_649)),bind(X_270,$fot(unordered_pair(X_649,singleton(Y))))]]) ).

cnf(refute_0_8,plain,
    unordered_pair(singleton(X_649),unordered_pair(X_649,singleton(Y))) = ordered_pair(X_649,Y),
    inference(subst,[],[ordered_pair:[bind(X,$fot(X_649))]]) ).

cnf(refute_0_9,plain,
    ( unordered_pair(singleton(X_649),unordered_pair(X_649,singleton(Y))) != ordered_pair(X_649,Y)
    | ~ member(singleton(X_649),unordered_pair(singleton(X_649),unordered_pair(X_649,singleton(Y))))
    | member(singleton(X_649),ordered_pair(X_649,Y)) ),
    introduced(tautology,[equality,[$cnf( member(singleton(X_649),unordered_pair(singleton(X_649),unordered_pair(X_649,singleton(Y)))) ),[1],$fot(ordered_pair(X_649,Y))]]) ).

cnf(refute_0_10,plain,
    ( ~ member(singleton(X_649),unordered_pair(singleton(X_649),unordered_pair(X_649,singleton(Y))))
    | member(singleton(X_649),ordered_pair(X_649,Y)) ),
    inference(resolve,[$cnf( $equal(unordered_pair(singleton(X_649),unordered_pair(X_649,singleton(Y))),ordered_pair(X_649,Y)) )],[refute_0_8,refute_0_9]) ).

cnf(refute_0_11,plain,
    member(singleton(X_649),ordered_pair(X_649,Y)),
    inference(resolve,[$cnf( member(singleton(X_649),unordered_pair(singleton(X_649),unordered_pair(X_649,singleton(Y)))) )],[refute_0_7,refute_0_10]) ).

cnf(refute_0_12,plain,
    member(singleton(x),ordered_pair(x,y)),
    inference(subst,[],[refute_0_11:[bind(Y,$fot(y)),bind(X_649,$fot(x))]]) ).

cnf(refute_0_13,plain,
    $false,
    inference(resolve,[$cnf( member(singleton(x),ordered_pair(x,y)) )],[refute_0_12,prove_singleton_member_of_ordered_pair_1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET101-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n013.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
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sat Jul  9 18:37:59 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 30.21/30.38  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 30.21/30.38  
% 30.21/30.38  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 30.21/30.38  
%------------------------------------------------------------------------------