TSTP Solution File: SET355+4 by Drodi---3.5.1

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%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET355+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n011.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 : Wed May 31 12:34:27 EDT 2023

% Result   : Theorem 0.13s 0.36s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   23 (   4 unt;   0 def)
%            Number of atoms       :   72 (   0 equ)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :   80 (  31   ~;  28   |;  15   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   59 (;  52   !;   7   ?)

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

fof(f10,axiom,
    ! [X,A] :
      ( member(X,sum(A))
    <=> ? [Y] :
          ( member(Y,A)
          & member(X,Y) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f13,negated_conjecture,
    ~ ! [A,X] :
        ( member(X,A)
       => subset(X,sum(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(f55,plain,
    ! [X,A] :
      ( ( ~ member(X,sum(A))
        | ? [Y] :
            ( member(Y,A)
            & member(X,Y) ) )
      & ( member(X,sum(A))
        | ! [Y] :
            ( ~ member(Y,A)
            | ~ member(X,Y) ) ) ),
    inference(NNF_transformation,[status(esa)],[f10]) ).

fof(f56,plain,
    ( ! [X,A] :
        ( ~ member(X,sum(A))
        | ? [Y] :
            ( member(Y,A)
            & member(X,Y) ) )
    & ! [X,A] :
        ( member(X,sum(A))
        | ! [Y] :
            ( ~ member(Y,A)
            | ~ member(X,Y) ) ) ),
    inference(miniscoping,[status(esa)],[f55]) ).

fof(f57,plain,
    ( ! [X,A] :
        ( ~ member(X,sum(A))
        | ( member(sk0_1(A,X),A)
          & member(X,sk0_1(A,X)) ) )
    & ! [X,A] :
        ( member(X,sum(A))
        | ! [Y] :
            ( ~ member(Y,A)
            | ~ member(X,Y) ) ) ),
    inference(skolemization,[status(esa)],[f56]) ).

fof(f60,plain,
    ! [X0,X1,X2] :
      ( member(X0,sum(X1))
      | ~ member(X2,X1)
      | ~ member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f57]) ).

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

fof(f69,plain,
    ( member(sk0_4,sk0_3)
    & ~ subset(sk0_4,sum(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(sk0_4,sum(sk0_3)),
    inference(cnf_transformation,[status(esa)],[f69]) ).

fof(f93,plain,
    ! [X0,X1,X2] :
      ( subset(X0,sum(X1))
      | ~ member(X2,X1)
      | ~ member(sk0_0(sum(X1),X0),X2) ),
    inference(resolution,[status(thm)],[f20,f60]) ).

fof(f140,plain,
    ! [X0,X1] :
      ( subset(X0,sum(X1))
      | ~ member(X0,X1)
      | subset(X0,sum(X1)) ),
    inference(resolution,[status(thm)],[f93,f19]) ).

fof(f141,plain,
    ! [X0,X1] :
      ( subset(X0,sum(X1))
      | ~ member(X0,X1) ),
    inference(duplicate_literals_removal,[status(esa)],[f140]) ).

fof(f160,plain,
    ~ member(sk0_4,sk0_3),
    inference(resolution,[status(thm)],[f141,f71]) ).

fof(f161,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f160,f70]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SET355+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 : n011.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 : Tue May 30 10:13:27 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.5.1
% 0.13/0.36  % Refutation found
% 0.13/0.36  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.36  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.37  % Elapsed time: 0.023374 seconds
% 0.13/0.37  % CPU time: 0.043643 seconds
% 0.13/0.37  % Memory used: 11.661 MB
%------------------------------------------------------------------------------