TSTP Solution File: SET095+4 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET095+4 : TPTP v8.1.2. Released v2.2.0.
% 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 20:39:06 EDT 2024

% Result   : Theorem 0.13s 0.38s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   22 (   4 unt;   0 def)
%            Number of atoms       :   59 (   7 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   60 (  23   ~;  21   |;  10   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   47 (  43   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [X] :
          ( member(X,A)
         => member(X,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [X,A] :
      ( member(X,singleton(A))
    <=> X = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,conjecture,
    ! [A,X] :
      ( member(X,A)
     => subset(singleton(X),A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f13,negated_conjecture,
    ~ ! [A,X] :
        ( member(X,A)
       => subset(singleton(X),A) ),
    inference(negated_conjecture,[status(cth)],[f12]) ).

fof(f14,plain,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [X] :
          ( ~ member(X,A)
          | member(X,B) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f1]) ).

fof(f15,plain,
    ! [A,B] :
      ( ( ~ subset(A,B)
        | ! [X] :
            ( ~ member(X,A)
            | member(X,B) ) )
      & ( subset(A,B)
        | ? [X] :
            ( member(X,A)
            & ~ member(X,B) ) ) ),
    inference(NNF_transformation,[status(esa)],[f14]) ).

fof(f16,plain,
    ( ! [A,B] :
        ( ~ subset(A,B)
        | ! [X] :
            ( ~ member(X,A)
            | member(X,B) ) )
    & ! [A,B] :
        ( subset(A,B)
        | ? [X] :
            ( member(X,A)
            & ~ member(X,B) ) ) ),
    inference(miniscoping,[status(esa)],[f15]) ).

fof(f17,plain,
    ( ! [A,B] :
        ( ~ subset(A,B)
        | ! [X] :
            ( ~ member(X,A)
            | member(X,B) ) )
    & ! [A,B] :
        ( subset(A,B)
        | ( member(sk0_0(B,A),A)
          & ~ member(sk0_0(B,A),B) ) ) ),
    inference(skolemization,[status(esa)],[f16]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sk0_0(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sk0_0(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f46,plain,
    ! [X,A] :
      ( ( ~ member(X,singleton(A))
        | X = A )
      & ( member(X,singleton(A))
        | X != A ) ),
    inference(NNF_transformation,[status(esa)],[f8]) ).

fof(f47,plain,
    ( ! [X,A] :
        ( ~ member(X,singleton(A))
        | X = A )
    & ! [X,A] :
        ( member(X,singleton(A))
        | X != A ) ),
    inference(miniscoping,[status(esa)],[f46]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( ~ member(X0,singleton(X1))
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f47]) ).

fof(f68,plain,
    ? [A,X] :
      ( member(X,A)
      & ~ subset(singleton(X),A) ),
    inference(pre_NNF_transformation,[status(esa)],[f13]) ).

fof(f69,plain,
    ( member(sk0_4,sk0_3)
    & ~ subset(singleton(sk0_4),sk0_3) ),
    inference(skolemization,[status(esa)],[f68]) ).

fof(f70,plain,
    member(sk0_4,sk0_3),
    inference(cnf_transformation,[status(esa)],[f69]) ).

fof(f71,plain,
    ~ subset(singleton(sk0_4),sk0_3),
    inference(cnf_transformation,[status(esa)],[f69]) ).

fof(f81,plain,
    ! [X0,X1] :
      ( subset(singleton(X0),X1)
      | sk0_0(X1,singleton(X0)) = X0 ),
    inference(resolution,[status(thm)],[f19,f48]) ).

fof(f93,plain,
    ! [X0,X1] :
      ( subset(singleton(X0),X1)
      | ~ member(X0,X1)
      | subset(singleton(X0),X1) ),
    inference(paramodulation,[status(thm)],[f81,f20]) ).

fof(f94,plain,
    ! [X0,X1] :
      ( subset(singleton(X0),X1)
      | ~ member(X0,X1) ),
    inference(duplicate_literals_removal,[status(esa)],[f93]) ).

fof(f104,plain,
    ~ member(sk0_4,sk0_3),
    inference(resolution,[status(thm)],[f94,f71]) ).

fof(f105,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f104,f70]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SET095+4 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n012.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  : 300
% 0.13/0.34  % DateTime : Mon Apr 29 21:37:57 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  % Drodi V3.6.0
% 0.13/0.38  % Refutation found
% 0.13/0.38  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40  % Elapsed time: 0.032832 seconds
% 0.13/0.40  % CPU time: 0.078946 seconds
% 0.13/0.40  % Total memory used: 14.683 MB
% 0.13/0.40  % Net memory used: 14.635 MB
%------------------------------------------------------------------------------