TSTP Solution File: SET947+1 by Drodi---3.5.1

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%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET947+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n024.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 12:35:35 EDT 2023

% Result   : Theorem 0.16s 0.54s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   26 (   7 unt;   0 def)
%            Number of atoms       :   85 (   8 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :   96 (  37   ~;  38   |;  15   &)
%                                         (   4 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   1 con; 0-2 aty)
%            Number of variables   :   65 (;  60   !;   5   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [A,B] :
      ( B = powerset(A)
    <=> ! [C] :
          ( in(C,B)
        <=> subset(C,A) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( in(C,A)
         => in(C,B) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [A,B] :
      ( in(A,B)
     => subset(A,union(B)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,conjecture,
    ! [A] : subset(A,powerset(union(A))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,negated_conjecture,
    ~ ! [A] : subset(A,powerset(union(A))),
    inference(negated_conjecture,[status(cth)],[f8]) ).

fof(f12,plain,
    ! [A,B] :
      ( ( B != powerset(A)
        | ! [C] :
            ( ( ~ in(C,B)
              | subset(C,A) )
            & ( in(C,B)
              | ~ subset(C,A) ) ) )
      & ( B = powerset(A)
        | ? [C] :
            ( ( ~ in(C,B)
              | ~ subset(C,A) )
            & ( in(C,B)
              | subset(C,A) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f2]) ).

fof(f13,plain,
    ( ! [A,B] :
        ( B != powerset(A)
        | ( ! [C] :
              ( ~ in(C,B)
              | subset(C,A) )
          & ! [C] :
              ( in(C,B)
              | ~ subset(C,A) ) ) )
    & ! [A,B] :
        ( B = powerset(A)
        | ? [C] :
            ( ( ~ in(C,B)
              | ~ subset(C,A) )
            & ( in(C,B)
              | subset(C,A) ) ) ) ),
    inference(miniscoping,[status(esa)],[f12]) ).

fof(f14,plain,
    ( ! [A,B] :
        ( B != powerset(A)
        | ( ! [C] :
              ( ~ in(C,B)
              | subset(C,A) )
          & ! [C] :
              ( in(C,B)
              | ~ subset(C,A) ) ) )
    & ! [A,B] :
        ( B = powerset(A)
        | ( ( ~ in(sk0_0(B,A),B)
            | ~ subset(sk0_0(B,A),A) )
          & ( in(sk0_0(B,A),B)
            | subset(sk0_0(B,A),A) ) ) ) ),
    inference(skolemization,[status(esa)],[f13]) ).

fof(f16,plain,
    ! [X0,X1,X2] :
      ( X0 != powerset(X1)
      | in(X2,X0)
      | ~ subset(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f19,plain,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( ~ in(C,A)
          | in(C,B) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f3]) ).

fof(f20,plain,
    ! [A,B] :
      ( ( ~ subset(A,B)
        | ! [C] :
            ( ~ in(C,A)
            | in(C,B) ) )
      & ( subset(A,B)
        | ? [C] :
            ( in(C,A)
            & ~ in(C,B) ) ) ),
    inference(NNF_transformation,[status(esa)],[f19]) ).

fof(f21,plain,
    ( ! [A,B] :
        ( ~ subset(A,B)
        | ! [C] :
            ( ~ in(C,A)
            | in(C,B) ) )
    & ! [A,B] :
        ( subset(A,B)
        | ? [C] :
            ( in(C,A)
            & ~ in(C,B) ) ) ),
    inference(miniscoping,[status(esa)],[f20]) ).

fof(f22,plain,
    ( ! [A,B] :
        ( ~ subset(A,B)
        | ! [C] :
            ( ~ in(C,A)
            | in(C,B) ) )
    & ! [A,B] :
        ( subset(A,B)
        | ( in(sk0_1(B,A),A)
          & ~ in(sk0_1(B,A),B) ) ) ),
    inference(skolemization,[status(esa)],[f21]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sk0_1(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f22]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sk0_1(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f22]) ).

fof(f26,plain,
    ! [A,B] :
      ( ~ in(A,B)
      | subset(A,union(B)) ),
    inference(pre_NNF_transformation,[status(esa)],[f4]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | subset(X0,union(X1)) ),
    inference(cnf_transformation,[status(esa)],[f26]) ).

fof(f34,plain,
    ? [A] : ~ subset(A,powerset(union(A))),
    inference(pre_NNF_transformation,[status(esa)],[f9]) ).

fof(f35,plain,
    ~ subset(sk0_4,powerset(union(sk0_4))),
    inference(skolemization,[status(esa)],[f34]) ).

fof(f36,plain,
    ~ subset(sk0_4,powerset(union(sk0_4))),
    inference(cnf_transformation,[status(esa)],[f35]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( in(X0,powerset(X1))
      | ~ subset(X0,X1) ),
    inference(destructive_equality_resolution,[status(esa)],[f16]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( subset(X0,powerset(X1))
      | ~ subset(sk0_1(powerset(X1),X0),X1) ),
    inference(resolution,[status(thm)],[f25,f38]) ).

fof(f81,plain,
    ! [X0,X1] :
      ( subset(X0,powerset(union(X1)))
      | ~ in(sk0_1(powerset(union(X1)),X0),X1) ),
    inference(resolution,[status(thm)],[f64,f27]) ).

fof(f189,plain,
    ! [X0] :
      ( subset(X0,powerset(union(X0)))
      | subset(X0,powerset(union(X0))) ),
    inference(resolution,[status(thm)],[f81,f24]) ).

fof(f190,plain,
    ! [X0] : subset(X0,powerset(union(X0))),
    inference(duplicate_literals_removal,[status(esa)],[f189]) ).

fof(f200,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f36,f190]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem  : SET947+1 : TPTP v8.1.2. Released v3.2.0.
% 0.05/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.31  % Computer : n024.cluster.edu
% 0.09/0.31  % Model    : x86_64 x86_64
% 0.09/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31  % Memory   : 8042.1875MB
% 0.09/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31  % CPULimit : 300
% 0.09/0.31  % WCLimit  : 300
% 0.09/0.31  % DateTime : Tue May 30 10:18:48 EDT 2023
% 0.09/0.31  % CPUTime  : 
% 0.15/0.32  % Drodi V3.5.1
% 0.16/0.54  % Refutation found
% 0.16/0.54  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.54  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.54  % Elapsed time: 0.017583 seconds
% 0.16/0.54  % CPU time: 0.025168 seconds
% 0.16/0.54  % Memory used: 3.018 MB
%------------------------------------------------------------------------------