TSTP Solution File: SEU317+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SEU317+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n020.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 12:36:41 EDT 2023

% Result   : Theorem 0.19s 0.44s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   46 (   7 unt;   0 def)
%            Number of atoms       :  172 (   0 equ)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives :  213 (  87   ~;  88   |;  21   &)
%                                         (   7 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   7 usr;   3 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   2 con; 0-3 aty)
%            Number of variables   :   92 (;  87   !;   5   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f17,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( in(C,A)
         => in(C,B) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f36,axiom,
    ! [A,B] :
      ( element(A,powerset(B))
    <=> subset(A,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f37,axiom,
    ! [A] :
      ( top_str(A)
     => ! [B] :
          ( element(B,powerset(the_carrier(A)))
         => ! [C] :
              ( in(C,the_carrier(A))
             => ( in(C,topstr_closure(A,B))
              <=> ! [D] :
                    ( element(D,powerset(the_carrier(A)))
                   => ( ( closed_subset(D,A)
                        & subset(B,D) )
                     => in(C,D) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f38,conjecture,
    ! [A] :
      ( top_str(A)
     => ! [B] :
          ( element(B,powerset(the_carrier(A)))
         => subset(B,topstr_closure(A,B)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f39,negated_conjecture,
    ~ ! [A] :
        ( top_str(A)
       => ! [B] :
            ( element(B,powerset(the_carrier(A)))
           => subset(B,topstr_closure(A,B)) ) ),
    inference(negated_conjecture,[status(cth)],[f38]) ).

fof(f101,plain,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( ~ in(C,A)
          | in(C,B) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f17]) ).

fof(f102,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)],[f101]) ).

fof(f103,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)],[f102]) ).

fof(f104,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)],[f103]) ).

fof(f105,plain,
    ! [X0,X1,X2] :
      ( ~ subset(X0,X1)
      | ~ in(X2,X0)
      | in(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f104]) ).

fof(f106,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sk0_0(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f104]) ).

fof(f107,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sk0_0(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f104]) ).

fof(f145,plain,
    ! [A,B] :
      ( ( ~ element(A,powerset(B))
        | subset(A,B) )
      & ( element(A,powerset(B))
        | ~ subset(A,B) ) ),
    inference(NNF_transformation,[status(esa)],[f36]) ).

fof(f146,plain,
    ( ! [A,B] :
        ( ~ element(A,powerset(B))
        | subset(A,B) )
    & ! [A,B] :
        ( element(A,powerset(B))
        | ~ subset(A,B) ) ),
    inference(miniscoping,[status(esa)],[f145]) ).

fof(f147,plain,
    ! [X0,X1] :
      ( ~ element(X0,powerset(X1))
      | subset(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f146]) ).

fof(f148,plain,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f146]) ).

fof(f149,plain,
    ! [A] :
      ( ~ top_str(A)
      | ! [B] :
          ( ~ element(B,powerset(the_carrier(A)))
          | ! [C] :
              ( ~ in(C,the_carrier(A))
              | ( in(C,topstr_closure(A,B))
              <=> ! [D] :
                    ( ~ element(D,powerset(the_carrier(A)))
                    | ~ closed_subset(D,A)
                    | ~ subset(B,D)
                    | in(C,D) ) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f37]) ).

fof(f150,plain,
    ! [A] :
      ( ~ top_str(A)
      | ! [B] :
          ( ~ element(B,powerset(the_carrier(A)))
          | ! [C] :
              ( ~ in(C,the_carrier(A))
              | ( ( ~ in(C,topstr_closure(A,B))
                  | ! [D] :
                      ( ~ element(D,powerset(the_carrier(A)))
                      | ~ closed_subset(D,A)
                      | ~ subset(B,D)
                      | in(C,D) ) )
                & ( in(C,topstr_closure(A,B))
                  | ? [D] :
                      ( element(D,powerset(the_carrier(A)))
                      & closed_subset(D,A)
                      & subset(B,D)
                      & ~ in(C,D) ) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f149]) ).

fof(f151,plain,
    ! [A] :
      ( ~ top_str(A)
      | ! [B] :
          ( ~ element(B,powerset(the_carrier(A)))
          | ! [C] :
              ( ~ in(C,the_carrier(A))
              | ( ( ~ in(C,topstr_closure(A,B))
                  | ! [D] :
                      ( ~ element(D,powerset(the_carrier(A)))
                      | ~ closed_subset(D,A)
                      | ~ subset(B,D)
                      | in(C,D) ) )
                & ( in(C,topstr_closure(A,B))
                  | ( element(sk0_7(C,B,A),powerset(the_carrier(A)))
                    & closed_subset(sk0_7(C,B,A),A)
                    & subset(B,sk0_7(C,B,A))
                    & ~ in(C,sk0_7(C,B,A)) ) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f150]) ).

fof(f155,plain,
    ! [X0,X1,X2] :
      ( ~ top_str(X0)
      | ~ element(X1,powerset(the_carrier(X0)))
      | ~ in(X2,the_carrier(X0))
      | in(X2,topstr_closure(X0,X1))
      | subset(X1,sk0_7(X2,X1,X0)) ),
    inference(cnf_transformation,[status(esa)],[f151]) ).

fof(f156,plain,
    ! [X0,X1,X2] :
      ( ~ top_str(X0)
      | ~ element(X1,powerset(the_carrier(X0)))
      | ~ in(X2,the_carrier(X0))
      | in(X2,topstr_closure(X0,X1))
      | ~ in(X2,sk0_7(X2,X1,X0)) ),
    inference(cnf_transformation,[status(esa)],[f151]) ).

fof(f157,plain,
    ? [A] :
      ( top_str(A)
      & ? [B] :
          ( element(B,powerset(the_carrier(A)))
          & ~ subset(B,topstr_closure(A,B)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f39]) ).

fof(f158,plain,
    ( top_str(sk0_8)
    & element(sk0_9,powerset(the_carrier(sk0_8)))
    & ~ subset(sk0_9,topstr_closure(sk0_8,sk0_9)) ),
    inference(skolemization,[status(esa)],[f157]) ).

fof(f159,plain,
    top_str(sk0_8),
    inference(cnf_transformation,[status(esa)],[f158]) ).

fof(f160,plain,
    element(sk0_9,powerset(the_carrier(sk0_8))),
    inference(cnf_transformation,[status(esa)],[f158]) ).

fof(f161,plain,
    ~ subset(sk0_9,topstr_closure(sk0_8,sk0_9)),
    inference(cnf_transformation,[status(esa)],[f158]) ).

fof(f176,plain,
    subset(sk0_9,the_carrier(sk0_8)),
    inference(resolution,[status(thm)],[f147,f160]) ).

fof(f182,plain,
    ( spl0_0
  <=> top_str(sk0_8) ),
    introduced(split_symbol_definition) ).

fof(f184,plain,
    ( ~ top_str(sk0_8)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f182]) ).

fof(f191,plain,
    ( $false
    | spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f184,f159]) ).

fof(f192,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f191]) ).

fof(f536,plain,
    ! [X0,X1,X2,X3] :
      ( ~ top_str(X0)
      | ~ element(X1,powerset(the_carrier(X0)))
      | ~ in(X2,the_carrier(X0))
      | in(X2,topstr_closure(X0,X1))
      | ~ in(X3,X1)
      | in(X3,sk0_7(X2,X1,X0)) ),
    inference(resolution,[status(thm)],[f155,f105]) ).

fof(f539,plain,
    ! [X0,X1,X2] :
      ( ~ top_str(X0)
      | ~ element(X1,powerset(the_carrier(X0)))
      | ~ in(X2,the_carrier(X0))
      | in(X2,topstr_closure(X0,X1))
      | ~ in(X2,X1)
      | ~ top_str(X0)
      | ~ element(X1,powerset(the_carrier(X0)))
      | ~ in(X2,the_carrier(X0))
      | in(X2,topstr_closure(X0,X1)) ),
    inference(resolution,[status(thm)],[f536,f156]) ).

fof(f540,plain,
    ! [X0,X1,X2] :
      ( ~ top_str(X0)
      | ~ element(X1,powerset(the_carrier(X0)))
      | ~ in(X2,the_carrier(X0))
      | in(X2,topstr_closure(X0,X1))
      | ~ in(X2,X1) ),
    inference(duplicate_literals_removal,[status(esa)],[f539]) ).

fof(f559,plain,
    ! [X0,X1,X2] :
      ( ~ top_str(X0)
      | ~ in(X1,the_carrier(X0))
      | in(X1,topstr_closure(X0,X2))
      | ~ in(X1,X2)
      | ~ subset(X2,the_carrier(X0)) ),
    inference(resolution,[status(thm)],[f540,f148]) ).

fof(f560,plain,
    ! [X0,X1,X2] :
      ( ~ top_str(X0)
      | in(X1,topstr_closure(X0,X2))
      | ~ in(X1,X2)
      | ~ subset(X2,the_carrier(X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[f559,f105]) ).

fof(f572,plain,
    ( spl0_26
  <=> subset(sk0_9,the_carrier(sk0_8)) ),
    introduced(split_symbol_definition) ).

fof(f574,plain,
    ( ~ subset(sk0_9,the_carrier(sk0_8))
    | spl0_26 ),
    inference(component_clause,[status(thm)],[f572]) ).

fof(f584,plain,
    ( $false
    | spl0_26 ),
    inference(forward_subsumption_resolution,[status(thm)],[f574,f176]) ).

fof(f585,plain,
    spl0_26,
    inference(contradiction_clause,[status(thm)],[f584]) ).

fof(f586,plain,
    ! [X0,X1,X2] :
      ( ~ top_str(X0)
      | ~ in(sk0_0(topstr_closure(X0,X1),X2),X1)
      | ~ subset(X1,the_carrier(X0))
      | subset(X2,topstr_closure(X0,X1)) ),
    inference(resolution,[status(thm)],[f560,f107]) ).

fof(f640,plain,
    ! [X0,X1] :
      ( ~ top_str(X0)
      | ~ subset(X1,the_carrier(X0))
      | subset(X1,topstr_closure(X0,X1))
      | subset(X1,topstr_closure(X0,X1)) ),
    inference(resolution,[status(thm)],[f586,f106]) ).

fof(f641,plain,
    ! [X0,X1] :
      ( ~ top_str(X0)
      | ~ subset(X1,the_carrier(X0))
      | subset(X1,topstr_closure(X0,X1)) ),
    inference(duplicate_literals_removal,[status(esa)],[f640]) ).

fof(f646,plain,
    ( ~ top_str(sk0_8)
    | ~ subset(sk0_9,the_carrier(sk0_8)) ),
    inference(resolution,[status(thm)],[f641,f161]) ).

fof(f647,plain,
    ( ~ spl0_0
    | ~ spl0_26 ),
    inference(split_clause,[status(thm)],[f646,f182,f572]) ).

fof(f650,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f192,f585,f647]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU317+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n020.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 09:07:28 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.5.1
% 0.19/0.44  % Refutation found
% 0.19/0.44  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.44  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.45  % Elapsed time: 0.103894 seconds
% 0.19/0.45  % CPU time: 0.695932 seconds
% 0.19/0.45  % Memory used: 54.028 MB
%------------------------------------------------------------------------------