TSTP Solution File: SEU114+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SEU114+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n028.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 12:35:51 EDT 2023

% Result   : Theorem 1.99s 0.61s
% Output   : CNFRefutation 2.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   51 (   8 unt;   0 def)
%            Number of atoms       :  180 (  22 equ)
%            Maximal formula atoms :   15 (   3 avg)
%            Number of connectives :  207 (  78   ~;  82   |;  32   &)
%                                         (   8 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   1 con; 0-2 aty)
%            Number of variables   :  106 (; 101   !;   5   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ! [A] :
      ( finite(A)
     => ! [B] :
          ( element(B,powerset(A))
         => finite(B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [A,B] :
      ( A = B
    <=> ( subset(A,B)
        & subset(B,A) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( in(C,A)
         => in(C,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [A,B] :
      ( preboolean(B)
     => ( B = finite_subsets(A)
      <=> ! [C] :
            ( in(C,B)
          <=> ( subset(C,A)
              & finite(C) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [A] : preboolean(finite_subsets(A)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f27,axiom,
    ! [A,B] :
      ( in(A,B)
     => element(A,B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f28,axiom,
    ! [A] : subset(finite_subsets(A),powerset(A)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f29,conjecture,
    ! [A] :
      ( finite(A)
     => finite_subsets(A) = powerset(A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f30,negated_conjecture,
    ~ ! [A] :
        ( finite(A)
       => finite_subsets(A) = powerset(A) ),
    inference(negated_conjecture,[status(cth)],[f29]) ).

fof(f32,axiom,
    ! [A,B] :
      ( element(A,powerset(B))
    <=> subset(A,B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f45,plain,
    ! [A] :
      ( ~ finite(A)
      | ! [B] :
          ( ~ element(B,powerset(A))
          | finite(B) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f4]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( ~ finite(X0)
      | ~ element(X1,powerset(X0))
      | finite(X1) ),
    inference(cnf_transformation,[status(esa)],[f45]) ).

fof(f52,plain,
    ! [A,B] :
      ( ( A != B
        | ( subset(A,B)
          & subset(B,A) ) )
      & ( A = B
        | ~ subset(A,B)
        | ~ subset(B,A) ) ),
    inference(NNF_transformation,[status(esa)],[f7]) ).

fof(f53,plain,
    ( ! [A,B] :
        ( A != B
        | ( subset(A,B)
          & subset(B,A) ) )
    & ! [A,B] :
        ( A = B
        | ~ subset(A,B)
        | ~ subset(B,A) ) ),
    inference(miniscoping,[status(esa)],[f52]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ subset(X0,X1)
      | ~ subset(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f53]) ).

fof(f57,plain,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( ~ in(C,A)
          | in(C,B) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f8]) ).

fof(f58,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)],[f57]) ).

fof(f59,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)],[f58]) ).

fof(f60,plain,
    ( ! [A,B] :
        ( ~ subset(A,B)
        | ! [C] :
            ( ~ in(C,A)
            | in(C,B) ) )
    & ! [A,B] :
        ( subset(A,B)
        | ( in(sk0_0(B,A),A)
          & ~ in(sk0_0(B,A),B) ) ) ),
    inference(skolemization,[status(esa)],[f59]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sk0_0(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f60]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sk0_0(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f60]) ).

fof(f64,plain,
    ! [A,B] :
      ( ~ preboolean(B)
      | ( B = finite_subsets(A)
      <=> ! [C] :
            ( in(C,B)
          <=> ( subset(C,A)
              & finite(C) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f9]) ).

fof(f65,plain,
    ! [A,B] :
      ( ~ preboolean(B)
      | ( ( B != finite_subsets(A)
          | ! [C] :
              ( ( ~ in(C,B)
                | ( subset(C,A)
                  & finite(C) ) )
              & ( in(C,B)
                | ~ subset(C,A)
                | ~ finite(C) ) ) )
        & ( B = finite_subsets(A)
          | ? [C] :
              ( ( ~ in(C,B)
                | ~ subset(C,A)
                | ~ finite(C) )
              & ( in(C,B)
                | ( subset(C,A)
                  & finite(C) ) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f64]) ).

fof(f66,plain,
    ! [B] :
      ( ~ preboolean(B)
      | ( ! [A] :
            ( B != finite_subsets(A)
            | ( ! [C] :
                  ( ~ in(C,B)
                  | ( subset(C,A)
                    & finite(C) ) )
              & ! [C] :
                  ( in(C,B)
                  | ~ subset(C,A)
                  | ~ finite(C) ) ) )
        & ! [A] :
            ( B = finite_subsets(A)
            | ? [C] :
                ( ( ~ in(C,B)
                  | ~ subset(C,A)
                  | ~ finite(C) )
                & ( in(C,B)
                  | ( subset(C,A)
                    & finite(C) ) ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f65]) ).

fof(f67,plain,
    ! [B] :
      ( ~ preboolean(B)
      | ( ! [A] :
            ( B != finite_subsets(A)
            | ( ! [C] :
                  ( ~ in(C,B)
                  | ( subset(C,A)
                    & finite(C) ) )
              & ! [C] :
                  ( in(C,B)
                  | ~ subset(C,A)
                  | ~ finite(C) ) ) )
        & ! [A] :
            ( B = finite_subsets(A)
            | ( ( ~ in(sk0_1(A,B),B)
                | ~ subset(sk0_1(A,B),A)
                | ~ finite(sk0_1(A,B)) )
              & ( in(sk0_1(A,B),B)
                | ( subset(sk0_1(A,B),A)
                  & finite(sk0_1(A,B)) ) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f66]) ).

fof(f70,plain,
    ! [X0,X1,X2] :
      ( ~ preboolean(X0)
      | X0 != finite_subsets(X1)
      | in(X2,X0)
      | ~ subset(X2,X1)
      | ~ finite(X2) ),
    inference(cnf_transformation,[status(esa)],[f67]) ).

fof(f74,plain,
    ! [X0] : preboolean(finite_subsets(X0)),
    inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f135,plain,
    ! [A,B] :
      ( ~ in(A,B)
      | element(A,B) ),
    inference(pre_NNF_transformation,[status(esa)],[f27]) ).

fof(f136,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | element(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f135]) ).

fof(f137,plain,
    ! [X0] : subset(finite_subsets(X0),powerset(X0)),
    inference(cnf_transformation,[status(esa)],[f28]) ).

fof(f138,plain,
    ? [A] :
      ( finite(A)
      & finite_subsets(A) != powerset(A) ),
    inference(pre_NNF_transformation,[status(esa)],[f30]) ).

fof(f139,plain,
    ( finite(sk0_12)
    & finite_subsets(sk0_12) != powerset(sk0_12) ),
    inference(skolemization,[status(esa)],[f138]) ).

fof(f140,plain,
    finite(sk0_12),
    inference(cnf_transformation,[status(esa)],[f139]) ).

fof(f141,plain,
    finite_subsets(sk0_12) != powerset(sk0_12),
    inference(cnf_transformation,[status(esa)],[f139]) ).

fof(f144,plain,
    ! [A,B] :
      ( ( ~ element(A,powerset(B))
        | subset(A,B) )
      & ( element(A,powerset(B))
        | ~ subset(A,B) ) ),
    inference(NNF_transformation,[status(esa)],[f32]) ).

fof(f145,plain,
    ( ! [A,B] :
        ( ~ element(A,powerset(B))
        | subset(A,B) )
    & ! [A,B] :
        ( element(A,powerset(B))
        | ~ subset(A,B) ) ),
    inference(miniscoping,[status(esa)],[f144]) ).

fof(f146,plain,
    ! [X0,X1] :
      ( ~ element(X0,powerset(X1))
      | subset(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f145]) ).

fof(f166,plain,
    ! [X0,X1] :
      ( ~ preboolean(finite_subsets(X0))
      | in(X1,finite_subsets(X0))
      | ~ subset(X1,X0)
      | ~ finite(X1) ),
    inference(destructive_equality_resolution,[status(esa)],[f70]) ).

fof(f177,plain,
    ! [X0] :
      ( powerset(X0) = finite_subsets(X0)
      | ~ subset(powerset(X0),finite_subsets(X0)) ),
    inference(resolution,[status(thm)],[f56,f137]) ).

fof(f319,plain,
    ! [X0,X1] :
      ( in(X0,finite_subsets(X1))
      | ~ subset(X0,X1)
      | ~ finite(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f166,f74]) ).

fof(f320,plain,
    ! [X0,X1] :
      ( ~ subset(sk0_0(finite_subsets(X0),X1),X0)
      | ~ finite(sk0_0(finite_subsets(X0),X1))
      | subset(X1,finite_subsets(X0)) ),
    inference(resolution,[status(thm)],[f319,f63]) ).

fof(f378,plain,
    ! [X0,X1] :
      ( element(sk0_0(X0,X1),X1)
      | subset(X1,X0) ),
    inference(resolution,[status(thm)],[f136,f62]) ).

fof(f1496,plain,
    ! [X0,X1] :
      ( subset(powerset(X0),X1)
      | ~ finite(X0)
      | finite(sk0_0(X1,powerset(X0))) ),
    inference(resolution,[status(thm)],[f378,f46]) ).

fof(f1498,plain,
    ! [X0,X1] :
      ( subset(powerset(X0),X1)
      | subset(sk0_0(X1,powerset(X0)),X0) ),
    inference(resolution,[status(thm)],[f378,f146]) ).

fof(f1860,plain,
    ! [X0] :
      ( subset(powerset(X0),finite_subsets(X0))
      | ~ finite(sk0_0(finite_subsets(X0),powerset(X0)))
      | subset(powerset(X0),finite_subsets(X0)) ),
    inference(resolution,[status(thm)],[f1498,f320]) ).

fof(f1861,plain,
    ! [X0] :
      ( subset(powerset(X0),finite_subsets(X0))
      | ~ finite(sk0_0(finite_subsets(X0),powerset(X0))) ),
    inference(duplicate_literals_removal,[status(esa)],[f1860]) ).

fof(f1875,plain,
    ! [X0] :
      ( subset(powerset(X0),finite_subsets(X0))
      | subset(powerset(X0),finite_subsets(X0))
      | ~ finite(X0) ),
    inference(resolution,[status(thm)],[f1861,f1496]) ).

fof(f1876,plain,
    ! [X0] :
      ( subset(powerset(X0),finite_subsets(X0))
      | ~ finite(X0) ),
    inference(duplicate_literals_removal,[status(esa)],[f1875]) ).

fof(f1879,plain,
    ! [X0] :
      ( ~ finite(X0)
      | powerset(X0) = finite_subsets(X0) ),
    inference(resolution,[status(thm)],[f1876,f177]) ).

fof(f1890,plain,
    ~ finite(sk0_12),
    inference(resolution,[status(thm)],[f1879,f141]) ).

fof(f1891,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f1890,f140]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SEU114+1 : TPTP v8.1.2. Released v3.2.0.
% 0.10/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33  % Computer : n028.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Tue May 30 09:31:17 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  % Drodi V3.5.1
% 1.99/0.61  % Refutation found
% 1.99/0.61  % SZS status Theorem for theBenchmark: Theorem is valid
% 1.99/0.61  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.20/0.63  % Elapsed time: 0.293075 seconds
% 2.20/0.63  % CPU time: 2.197899 seconds
% 2.20/0.63  % Memory used: 72.415 MB
%------------------------------------------------------------------------------