TSTP Solution File: SET013-1 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET013-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n012.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  : 300s
% DateTime : Tue Apr 30 20:38:37 EDT 2024

% Result   : Unsatisfiable 0.16s 0.50s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   26 (   5 unt;   0 def)
%            Number of atoms       :   53 (   0 equ)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   50 (  23   ~;  27   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   59 (  59   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [Subset,Superset] :
      ( subset(Subset,Superset)
      | member(member_of_1_not_of_2(Subset,Superset),Subset) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [Subset,Superset] :
      ( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
      | subset(Subset,Superset) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [X,Xs,Ys] :
      ( ~ member(X,Xs)
      | ~ member(X,Ys)
      | member(X,intersection(Xs,Ys)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    ! [X,Xs,Ys] :
      ( ~ member(X,intersection(Xs,Ys))
      | member(X,Xs) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    ! [X,Xs,Ys] :
      ( ~ member(X,intersection(Xs,Ys))
      | member(X,Ys) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f15,axiom,
    ! [Set1,Set2] :
      ( ~ subset(Set1,Set2)
      | ~ subset(Set2,Set1)
      | equal_sets(Set2,Set1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f22,negated_conjecture,
    ~ equal_sets(intersection(as,bs),intersection(bs,as)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f26,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(member_of_1_not_of_2(X0,X1),X0) ),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ~ member(member_of_1_not_of_2(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f36,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,X1)
      | ~ member(X0,X2)
      | member(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f37,plain,
    ! [X,Xs] :
      ( ! [Ys] : ~ member(X,intersection(Xs,Ys))
      | member(X,Xs) ),
    inference(miniscoping,[status(esa)],[f11]) ).

fof(f38,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,intersection(X1,X2))
      | member(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f37]) ).

fof(f39,plain,
    ! [X,Ys] :
      ( ! [Xs] : ~ member(X,intersection(Xs,Ys))
      | member(X,Ys) ),
    inference(miniscoping,[status(esa)],[f12]) ).

fof(f40,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,intersection(X1,X2))
      | member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f39]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | ~ subset(X1,X0)
      | equal_sets(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f52,plain,
    ~ equal_sets(intersection(as,bs),intersection(bs,as)),
    inference(cnf_transformation,[status(esa)],[f22]) ).

fof(f59,plain,
    ! [X0,X1,X2] :
      ( subset(intersection(X0,X1),X2)
      | member(member_of_1_not_of_2(intersection(X0,X1),X2),X1) ),
    inference(resolution,[status(thm)],[f26,f40]) ).

fof(f60,plain,
    ! [X0,X1,X2] :
      ( subset(intersection(X0,X1),X2)
      | member(member_of_1_not_of_2(intersection(X0,X1),X2),X0) ),
    inference(resolution,[status(thm)],[f26,f38]) ).

fof(f102,plain,
    ! [X0,X1,X2] :
      ( subset(X0,intersection(X1,X2))
      | ~ member(member_of_1_not_of_2(X0,intersection(X1,X2)),X1)
      | ~ member(member_of_1_not_of_2(X0,intersection(X1,X2)),X2) ),
    inference(resolution,[status(thm)],[f27,f36]) ).

fof(f151,plain,
    ! [X0,X1,X2] :
      ( subset(intersection(X0,X1),intersection(X2,X0))
      | ~ member(member_of_1_not_of_2(intersection(X0,X1),intersection(X2,X0)),X2)
      | subset(intersection(X0,X1),intersection(X2,X0)) ),
    inference(resolution,[status(thm)],[f102,f60]) ).

fof(f152,plain,
    ! [X0,X1,X2] :
      ( subset(intersection(X0,X1),intersection(X2,X0))
      | ~ member(member_of_1_not_of_2(intersection(X0,X1),intersection(X2,X0)),X2) ),
    inference(duplicate_literals_removal,[status(esa)],[f151]) ).

fof(f768,plain,
    ! [X0,X1] :
      ( subset(intersection(X0,X1),intersection(X1,X0))
      | subset(intersection(X0,X1),intersection(X1,X0)) ),
    inference(resolution,[status(thm)],[f152,f59]) ).

fof(f769,plain,
    ! [X0,X1] : subset(intersection(X0,X1),intersection(X1,X0)),
    inference(duplicate_literals_removal,[status(esa)],[f768]) ).

fof(f929,plain,
    ! [X0,X1] :
      ( ~ subset(intersection(X0,X1),intersection(X1,X0))
      | equal_sets(intersection(X1,X0),intersection(X0,X1)) ),
    inference(resolution,[status(thm)],[f769,f43]) ).

fof(f930,plain,
    ! [X0,X1] : equal_sets(intersection(X0,X1),intersection(X1,X0)),
    inference(forward_subsumption_resolution,[status(thm)],[f929,f769]) ).

fof(f990,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f52,f930]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11  % Problem  : SET013-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.09/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32  % Computer : n012.cluster.edu
% 0.10/0.32  % Model    : x86_64 x86_64
% 0.10/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32  % Memory   : 8042.1875MB
% 0.10/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit : 300
% 0.10/0.32  % WCLimit  : 300
% 0.10/0.32  % DateTime : Mon Apr 29 21:28:27 EDT 2024
% 0.10/0.32  % CPUTime  : 
% 0.10/0.33  % Drodi V3.6.0
% 0.16/0.50  % Refutation found
% 0.16/0.50  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/0.50  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.51  % Elapsed time: 0.186732 seconds
% 0.16/0.51  % CPU time: 1.400859 seconds
% 0.16/0.51  % Total memory used: 19.766 MB
% 0.16/0.51  % Net memory used: 18.986 MB
%------------------------------------------------------------------------------