TSTP Solution File: SEU117+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SEU117+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n027.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 0.12s 0.36s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   39 (   9 unt;   0 def)
%            Number of atoms       :  128 (   9 equ)
%            Maximal formula atoms :   15 (   3 avg)
%            Number of connectives :  142 (  53   ~;  51   |;  27   &)
%                                         (   7 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   12 (  10 usr;   3 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   58 (;  54   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ! [A,B] :
      ( element(A,B)
     => ( empty(B)
        | in(A,B) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    ! [A] : preboolean(finite_subsets(A)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f13,axiom,
    ! [A] :
      ( ~ empty(finite_subsets(A))
      & cup_closed(finite_subsets(A))
      & diff_closed(finite_subsets(A))
      & preboolean(finite_subsets(A)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f28,axiom,
    ! [A,B] :
      ( element(A,powerset(B))
    <=> subset(A,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f31,conjecture,
    ! [A,B] :
      ( element(B,finite_subsets(A))
     => element(B,powerset(A)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f32,negated_conjecture,
    ~ ! [A,B] :
        ( element(B,finite_subsets(A))
       => element(B,powerset(A)) ),
    inference(negated_conjecture,[status(cth)],[f31]) ).

fof(f33,axiom,
    ! [A,B] :
      ( preboolean(B)
     => ( B = finite_subsets(A)
      <=> ! [C] :
            ( in(C,B)
          <=> ( subset(C,A)
              & finite(C) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f39,plain,
    ! [A,B] :
      ( ~ element(A,B)
      | empty(B)
      | in(A,B) ),
    inference(pre_NNF_transformation,[status(esa)],[f4]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( ~ element(X0,X1)
      | empty(X1)
      | in(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f39]) ).

fof(f55,plain,
    ! [X0] : preboolean(finite_subsets(X0)),
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f61,plain,
    ( ! [A] : ~ empty(finite_subsets(A))
    & ! [A] : cup_closed(finite_subsets(A))
    & ! [A] : diff_closed(finite_subsets(A))
    & ! [A] : preboolean(finite_subsets(A)) ),
    inference(miniscoping,[status(esa)],[f13]) ).

fof(f62,plain,
    ! [X0] : ~ empty(finite_subsets(X0)),
    inference(cnf_transformation,[status(esa)],[f61]) ).

fof(f118,plain,
    ! [A,B] :
      ( ( ~ element(A,powerset(B))
        | subset(A,B) )
      & ( element(A,powerset(B))
        | ~ subset(A,B) ) ),
    inference(NNF_transformation,[status(esa)],[f28]) ).

fof(f119,plain,
    ( ! [A,B] :
        ( ~ element(A,powerset(B))
        | subset(A,B) )
    & ! [A,B] :
        ( element(A,powerset(B))
        | ~ subset(A,B) ) ),
    inference(miniscoping,[status(esa)],[f118]) ).

fof(f121,plain,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f119]) ).

fof(f128,plain,
    ? [A,B] :
      ( element(B,finite_subsets(A))
      & ~ element(B,powerset(A)) ),
    inference(pre_NNF_transformation,[status(esa)],[f32]) ).

fof(f129,plain,
    ( element(sk0_11,finite_subsets(sk0_10))
    & ~ element(sk0_11,powerset(sk0_10)) ),
    inference(skolemization,[status(esa)],[f128]) ).

fof(f130,plain,
    element(sk0_11,finite_subsets(sk0_10)),
    inference(cnf_transformation,[status(esa)],[f129]) ).

fof(f131,plain,
    ~ element(sk0_11,powerset(sk0_10)),
    inference(cnf_transformation,[status(esa)],[f129]) ).

fof(f132,plain,
    ! [A,B] :
      ( ~ preboolean(B)
      | ( B = finite_subsets(A)
      <=> ! [C] :
            ( in(C,B)
          <=> ( subset(C,A)
              & finite(C) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f33]) ).

fof(f133,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)],[f132]) ).

fof(f134,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)],[f133]) ).

fof(f135,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_12(A,B),B)
                | ~ subset(sk0_12(A,B),A)
                | ~ finite(sk0_12(A,B)) )
              & ( in(sk0_12(A,B),B)
                | ( subset(sk0_12(A,B),A)
                  & finite(sk0_12(A,B)) ) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f134]) ).

fof(f136,plain,
    ! [X0,X1,X2] :
      ( ~ preboolean(X0)
      | X0 != finite_subsets(X1)
      | ~ in(X2,X0)
      | subset(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f135]) ).

fof(f142,plain,
    ! [X0,X1] :
      ( ~ preboolean(finite_subsets(X0))
      | ~ in(X1,finite_subsets(X0))
      | subset(X1,X0) ),
    inference(destructive_equality_resolution,[status(esa)],[f136]) ).

fof(f161,plain,
    ( spl0_2
  <=> empty(finite_subsets(sk0_10)) ),
    introduced(split_symbol_definition) ).

fof(f162,plain,
    ( empty(finite_subsets(sk0_10))
    | ~ spl0_2 ),
    inference(component_clause,[status(thm)],[f161]) ).

fof(f164,plain,
    ( spl0_3
  <=> in(sk0_11,finite_subsets(sk0_10)) ),
    introduced(split_symbol_definition) ).

fof(f165,plain,
    ( in(sk0_11,finite_subsets(sk0_10))
    | ~ spl0_3 ),
    inference(component_clause,[status(thm)],[f164]) ).

fof(f167,plain,
    ( empty(finite_subsets(sk0_10))
    | in(sk0_11,finite_subsets(sk0_10)) ),
    inference(resolution,[status(thm)],[f40,f130]) ).

fof(f168,plain,
    ( spl0_2
    | spl0_3 ),
    inference(split_clause,[status(thm)],[f167,f161,f164]) ).

fof(f169,plain,
    ( $false
    | ~ spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f162,f62]) ).

fof(f170,plain,
    ~ spl0_2,
    inference(contradiction_clause,[status(thm)],[f169]) ).

fof(f241,plain,
    ~ subset(sk0_11,sk0_10),
    inference(resolution,[status(thm)],[f121,f131]) ).

fof(f283,plain,
    ! [X0,X1] :
      ( ~ in(X0,finite_subsets(X1))
      | subset(X0,X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[f142,f55]) ).

fof(f286,plain,
    ( subset(sk0_11,sk0_10)
    | ~ spl0_3 ),
    inference(resolution,[status(thm)],[f283,f165]) ).

fof(f287,plain,
    ( $false
    | ~ spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f286,f241]) ).

fof(f288,plain,
    ~ spl0_3,
    inference(contradiction_clause,[status(thm)],[f287]) ).

fof(f289,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f168,f170,f288]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SEU117+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34  % Computer : n027.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Tue May 30 09:28:47 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  % Drodi V3.5.1
% 0.12/0.36  % Refutation found
% 0.12/0.36  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.36  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/0.58  % Elapsed time: 0.015556 seconds
% 0.24/0.58  % CPU time: 0.047024 seconds
% 0.24/0.58  % Memory used: 12.015 MB
%------------------------------------------------------------------------------