TSTP Solution File: SEU387+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SEU387+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %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 Aug 31 18:33:33 EDT 2022

% Result   : Theorem 1.88s 0.61s
% Output   : Refutation 1.88s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   55 (  19 unt;   0 def)
%            Number of atoms       :  327 (   6 equ)
%            Maximal formula atoms :   18 (   5 avg)
%            Number of connectives :  410 ( 138   ~; 102   |; 157   &)
%                                         (   3 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   7 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :   27 (  25 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-1 aty)
%            Number of variables   :   58 (  43   !;  15   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f838,plain,
    $false,
    inference(subsumption_resolution,[],[f837,f299]) ).

fof(f299,plain,
    filtered_subset(sK6,boole_POSet(sK5)),
    inference(cnf_transformation,[],[f217]) ).

fof(f217,plain,
    ( ~ empty(sK6)
    & proper_element(sK6,powerset(the_carrier(boole_POSet(sK5))))
    & upper_relstr_subset(sK6,boole_POSet(sK5))
    & filtered_subset(sK6,boole_POSet(sK5))
    & in(sK7,sK6)
    & empty(sK7)
    & element(sK6,powerset(the_carrier(boole_POSet(sK5))))
    & ~ empty(sK5) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f175,f216,f215,f214]) ).

fof(f214,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ~ empty(X1)
            & proper_element(X1,powerset(the_carrier(boole_POSet(X0))))
            & upper_relstr_subset(X1,boole_POSet(X0))
            & filtered_subset(X1,boole_POSet(X0))
            & ? [X2] :
                ( in(X2,X1)
                & empty(X2) )
            & element(X1,powerset(the_carrier(boole_POSet(X0)))) )
        & ~ empty(X0) )
   => ( ? [X1] :
          ( ~ empty(X1)
          & proper_element(X1,powerset(the_carrier(boole_POSet(sK5))))
          & upper_relstr_subset(X1,boole_POSet(sK5))
          & filtered_subset(X1,boole_POSet(sK5))
          & ? [X2] :
              ( in(X2,X1)
              & empty(X2) )
          & element(X1,powerset(the_carrier(boole_POSet(sK5)))) )
      & ~ empty(sK5) ) ),
    introduced(choice_axiom,[]) ).

fof(f215,plain,
    ( ? [X1] :
        ( ~ empty(X1)
        & proper_element(X1,powerset(the_carrier(boole_POSet(sK5))))
        & upper_relstr_subset(X1,boole_POSet(sK5))
        & filtered_subset(X1,boole_POSet(sK5))
        & ? [X2] :
            ( in(X2,X1)
            & empty(X2) )
        & element(X1,powerset(the_carrier(boole_POSet(sK5)))) )
   => ( ~ empty(sK6)
      & proper_element(sK6,powerset(the_carrier(boole_POSet(sK5))))
      & upper_relstr_subset(sK6,boole_POSet(sK5))
      & filtered_subset(sK6,boole_POSet(sK5))
      & ? [X2] :
          ( in(X2,sK6)
          & empty(X2) )
      & element(sK6,powerset(the_carrier(boole_POSet(sK5)))) ) ),
    introduced(choice_axiom,[]) ).

fof(f216,plain,
    ( ? [X2] :
        ( in(X2,sK6)
        & empty(X2) )
   => ( in(sK7,sK6)
      & empty(sK7) ) ),
    introduced(choice_axiom,[]) ).

fof(f175,plain,
    ? [X0] :
      ( ? [X1] :
          ( ~ empty(X1)
          & proper_element(X1,powerset(the_carrier(boole_POSet(X0))))
          & upper_relstr_subset(X1,boole_POSet(X0))
          & filtered_subset(X1,boole_POSet(X0))
          & ? [X2] :
              ( in(X2,X1)
              & empty(X2) )
          & element(X1,powerset(the_carrier(boole_POSet(X0)))) )
      & ~ empty(X0) ),
    inference(flattening,[],[f174]) ).

fof(f174,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( in(X2,X1)
              & empty(X2) )
          & element(X1,powerset(the_carrier(boole_POSet(X0))))
          & filtered_subset(X1,boole_POSet(X0))
          & ~ empty(X1)
          & upper_relstr_subset(X1,boole_POSet(X0))
          & proper_element(X1,powerset(the_carrier(boole_POSet(X0)))) )
      & ~ empty(X0) ),
    inference(ennf_transformation,[],[f79]) ).

fof(f79,negated_conjecture,
    ~ ! [X0] :
        ( ~ empty(X0)
       => ! [X1] :
            ( ( element(X1,powerset(the_carrier(boole_POSet(X0))))
              & filtered_subset(X1,boole_POSet(X0))
              & ~ empty(X1)
              & upper_relstr_subset(X1,boole_POSet(X0))
              & proper_element(X1,powerset(the_carrier(boole_POSet(X0)))) )
           => ! [X2] :
                ~ ( in(X2,X1)
                  & empty(X2) ) ) ),
    inference(negated_conjecture,[],[f78]) ).

fof(f78,conjecture,
    ! [X0] :
      ( ~ empty(X0)
     => ! [X1] :
          ( ( element(X1,powerset(the_carrier(boole_POSet(X0))))
            & filtered_subset(X1,boole_POSet(X0))
            & ~ empty(X1)
            & upper_relstr_subset(X1,boole_POSet(X0))
            & proper_element(X1,powerset(the_carrier(boole_POSet(X0)))) )
         => ! [X2] :
              ~ ( in(X2,X1)
                & empty(X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_yellow19) ).

fof(f837,plain,
    ~ filtered_subset(sK6,boole_POSet(sK5)),
    inference(subsumption_resolution,[],[f836,f503]) ).

fof(f503,plain,
    ! [X0] : rel_str(boole_POSet(X0)),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,axiom,
    ! [X0] :
      ( strict_rel_str(boole_POSet(X0))
      & rel_str(boole_POSet(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_yellow_1) ).

fof(f836,plain,
    ( ~ rel_str(boole_POSet(sK5))
    | ~ filtered_subset(sK6,boole_POSet(sK5)) ),
    inference(subsumption_resolution,[],[f835,f547]) ).

fof(f547,plain,
    ! [X0] : in(bottom_of_relstr(boole_POSet(X0)),sK6),
    inference(superposition,[],[f544,f329]) ).

fof(f329,plain,
    ! [X0] : empty_set = bottom_of_relstr(boole_POSet(X0)),
    inference(cnf_transformation,[],[f75]) ).

fof(f75,axiom,
    ! [X0] : empty_set = bottom_of_relstr(boole_POSet(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_yellow_1) ).

fof(f544,plain,
    in(empty_set,sK6),
    inference(backward_demodulation,[],[f298,f542]) ).

fof(f542,plain,
    empty_set = sK7,
    inference(resolution,[],[f288,f297]) ).

fof(f297,plain,
    empty(sK7),
    inference(cnf_transformation,[],[f217]) ).

fof(f288,plain,
    ! [X0] :
      ( ~ empty(X0)
      | empty_set = X0 ),
    inference(cnf_transformation,[],[f180]) ).

fof(f180,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f83]) ).

fof(f83,axiom,
    ! [X0] :
      ( empty(X0)
     => empty_set = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

fof(f298,plain,
    in(sK7,sK6),
    inference(cnf_transformation,[],[f217]) ).

fof(f835,plain,
    ( ~ in(bottom_of_relstr(boole_POSet(sK5)),sK6)
    | ~ rel_str(boole_POSet(sK5))
    | ~ filtered_subset(sK6,boole_POSet(sK5)) ),
    inference(subsumption_resolution,[],[f834,f416]) ).

fof(f416,plain,
    ! [X0] : transitive_relstr(boole_POSet(X0)),
    inference(cnf_transformation,[],[f116]) ).

fof(f116,plain,
    ! [X0] :
      ( up_complete_relstr(boole_POSet(X0))
      & antisymmetric_relstr(boole_POSet(X0))
      & upper_bounded_relstr(boole_POSet(X0))
      & with_infima_relstr(boole_POSet(X0))
      & strict_rel_str(boole_POSet(X0))
      & transitive_relstr(boole_POSet(X0))
      & bounded_relstr(boole_POSet(X0))
      & complete_relstr(boole_POSet(X0))
      & join_complete_relstr(boole_POSet(X0))
      & ~ empty_carrier(boole_POSet(X0))
      & with_suprema_relstr(boole_POSet(X0))
      & reflexive_relstr(boole_POSet(X0))
      & lower_bounded_relstr(boole_POSet(X0)) ),
    inference(pure_predicate_removal,[],[f112]) ).

fof(f112,plain,
    ! [X0] :
      ( with_suprema_relstr(boole_POSet(X0))
      & join_complete_relstr(boole_POSet(X0))
      & lower_bounded_relstr(boole_POSet(X0))
      & with_infima_relstr(boole_POSet(X0))
      & reflexive_relstr(boole_POSet(X0))
      & upper_bounded_relstr(boole_POSet(X0))
      & antisymmetric_relstr(boole_POSet(X0))
      & ~ v1_yellow_3(boole_POSet(X0))
      & ~ empty_carrier(boole_POSet(X0))
      & bounded_relstr(boole_POSet(X0))
      & strict_rel_str(boole_POSet(X0))
      & transitive_relstr(boole_POSet(X0))
      & complete_relstr(boole_POSet(X0))
      & up_complete_relstr(boole_POSet(X0)) ),
    inference(pure_predicate_removal,[],[f109]) ).

fof(f109,plain,
    ! [X0] :
      ( with_suprema_relstr(boole_POSet(X0))
      & join_complete_relstr(boole_POSet(X0))
      & lower_bounded_relstr(boole_POSet(X0))
      & with_infima_relstr(boole_POSet(X0))
      & reflexive_relstr(boole_POSet(X0))
      & upper_bounded_relstr(boole_POSet(X0))
      & antisymmetric_relstr(boole_POSet(X0))
      & ~ v1_yellow_3(boole_POSet(X0))
      & ~ empty_carrier(boole_POSet(X0))
      & bounded_relstr(boole_POSet(X0))
      & strict_rel_str(boole_POSet(X0))
      & transitive_relstr(boole_POSet(X0))
      & complete_relstr(boole_POSet(X0))
      & distributive_relstr(boole_POSet(X0))
      & up_complete_relstr(boole_POSet(X0)) ),
    inference(pure_predicate_removal,[],[f106]) ).

fof(f106,plain,
    ! [X0] :
      ( with_suprema_relstr(boole_POSet(X0))
      & join_complete_relstr(boole_POSet(X0))
      & lower_bounded_relstr(boole_POSet(X0))
      & with_infima_relstr(boole_POSet(X0))
      & reflexive_relstr(boole_POSet(X0))
      & upper_bounded_relstr(boole_POSet(X0))
      & antisymmetric_relstr(boole_POSet(X0))
      & heyting_relstr(boole_POSet(X0))
      & ~ v1_yellow_3(boole_POSet(X0))
      & ~ empty_carrier(boole_POSet(X0))
      & bounded_relstr(boole_POSet(X0))
      & strict_rel_str(boole_POSet(X0))
      & transitive_relstr(boole_POSet(X0))
      & complete_relstr(boole_POSet(X0))
      & distributive_relstr(boole_POSet(X0))
      & up_complete_relstr(boole_POSet(X0)) ),
    inference(pure_predicate_removal,[],[f103]) ).

fof(f103,plain,
    ! [X0] :
      ( with_suprema_relstr(boole_POSet(X0))
      & join_complete_relstr(boole_POSet(X0))
      & lower_bounded_relstr(boole_POSet(X0))
      & complemented_relstr(boole_POSet(X0))
      & with_infima_relstr(boole_POSet(X0))
      & reflexive_relstr(boole_POSet(X0))
      & upper_bounded_relstr(boole_POSet(X0))
      & antisymmetric_relstr(boole_POSet(X0))
      & heyting_relstr(boole_POSet(X0))
      & ~ v1_yellow_3(boole_POSet(X0))
      & ~ empty_carrier(boole_POSet(X0))
      & bounded_relstr(boole_POSet(X0))
      & strict_rel_str(boole_POSet(X0))
      & transitive_relstr(boole_POSet(X0))
      & complete_relstr(boole_POSet(X0))
      & distributive_relstr(boole_POSet(X0))
      & up_complete_relstr(boole_POSet(X0)) ),
    inference(pure_predicate_removal,[],[f43]) ).

fof(f43,axiom,
    ! [X0] :
      ( with_suprema_relstr(boole_POSet(X0))
      & join_complete_relstr(boole_POSet(X0))
      & lower_bounded_relstr(boole_POSet(X0))
      & complemented_relstr(boole_POSet(X0))
      & with_infima_relstr(boole_POSet(X0))
      & reflexive_relstr(boole_POSet(X0))
      & upper_bounded_relstr(boole_POSet(X0))
      & antisymmetric_relstr(boole_POSet(X0))
      & heyting_relstr(boole_POSet(X0))
      & ~ v1_yellow_3(boole_POSet(X0))
      & ~ empty_carrier(boole_POSet(X0))
      & bounded_relstr(boole_POSet(X0))
      & boolean_relstr(boole_POSet(X0))
      & strict_rel_str(boole_POSet(X0))
      & transitive_relstr(boole_POSet(X0))
      & complete_relstr(boole_POSet(X0))
      & distributive_relstr(boole_POSet(X0))
      & up_complete_relstr(boole_POSet(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_waybel_7) ).

fof(f834,plain,
    ( ~ transitive_relstr(boole_POSet(sK5))
    | ~ rel_str(boole_POSet(sK5))
    | ~ in(bottom_of_relstr(boole_POSet(sK5)),sK6)
    | ~ filtered_subset(sK6,boole_POSet(sK5)) ),
    inference(subsumption_resolution,[],[f833,f412]) ).

fof(f412,plain,
    ! [X0] : ~ empty_carrier(boole_POSet(X0)),
    inference(cnf_transformation,[],[f116]) ).

fof(f833,plain,
    ( empty_carrier(boole_POSet(sK5))
    | ~ rel_str(boole_POSet(sK5))
    | ~ transitive_relstr(boole_POSet(sK5))
    | ~ in(bottom_of_relstr(boole_POSet(sK5)),sK6)
    | ~ filtered_subset(sK6,boole_POSet(sK5)) ),
    inference(subsumption_resolution,[],[f832,f300]) ).

fof(f300,plain,
    upper_relstr_subset(sK6,boole_POSet(sK5)),
    inference(cnf_transformation,[],[f217]) ).

fof(f832,plain,
    ( ~ upper_relstr_subset(sK6,boole_POSet(sK5))
    | empty_carrier(boole_POSet(sK5))
    | ~ transitive_relstr(boole_POSet(sK5))
    | ~ in(bottom_of_relstr(boole_POSet(sK5)),sK6)
    | ~ rel_str(boole_POSet(sK5))
    | ~ filtered_subset(sK6,boole_POSet(sK5)) ),
    inference(subsumption_resolution,[],[f831,f420]) ).

fof(f420,plain,
    ! [X0] : antisymmetric_relstr(boole_POSet(X0)),
    inference(cnf_transformation,[],[f116]) ).

fof(f831,plain,
    ( ~ antisymmetric_relstr(boole_POSet(sK5))
    | ~ filtered_subset(sK6,boole_POSet(sK5))
    | ~ transitive_relstr(boole_POSet(sK5))
    | ~ rel_str(boole_POSet(sK5))
    | ~ upper_relstr_subset(sK6,boole_POSet(sK5))
    | empty_carrier(boole_POSet(sK5))
    | ~ in(bottom_of_relstr(boole_POSet(sK5)),sK6) ),
    inference(subsumption_resolution,[],[f830,f409]) ).

fof(f409,plain,
    ! [X0] : lower_bounded_relstr(boole_POSet(X0)),
    inference(cnf_transformation,[],[f116]) ).

fof(f830,plain,
    ( ~ lower_bounded_relstr(boole_POSet(sK5))
    | ~ in(bottom_of_relstr(boole_POSet(sK5)),sK6)
    | ~ antisymmetric_relstr(boole_POSet(sK5))
    | ~ transitive_relstr(boole_POSet(sK5))
    | empty_carrier(boole_POSet(sK5))
    | ~ rel_str(boole_POSet(sK5))
    | ~ upper_relstr_subset(sK6,boole_POSet(sK5))
    | ~ filtered_subset(sK6,boole_POSet(sK5)) ),
    inference(subsumption_resolution,[],[f829,f410]) ).

fof(f410,plain,
    ! [X0] : reflexive_relstr(boole_POSet(X0)),
    inference(cnf_transformation,[],[f116]) ).

fof(f829,plain,
    ( ~ reflexive_relstr(boole_POSet(sK5))
    | ~ filtered_subset(sK6,boole_POSet(sK5))
    | ~ lower_bounded_relstr(boole_POSet(sK5))
    | ~ transitive_relstr(boole_POSet(sK5))
    | ~ antisymmetric_relstr(boole_POSet(sK5))
    | empty_carrier(boole_POSet(sK5))
    | ~ upper_relstr_subset(sK6,boole_POSet(sK5))
    | ~ rel_str(boole_POSet(sK5))
    | ~ in(bottom_of_relstr(boole_POSet(sK5)),sK6) ),
    inference(subsumption_resolution,[],[f823,f296]) ).

fof(f296,plain,
    element(sK6,powerset(the_carrier(boole_POSet(sK5)))),
    inference(cnf_transformation,[],[f217]) ).

fof(f823,plain,
    ( ~ element(sK6,powerset(the_carrier(boole_POSet(sK5))))
    | ~ transitive_relstr(boole_POSet(sK5))
    | ~ lower_bounded_relstr(boole_POSet(sK5))
    | empty_carrier(boole_POSet(sK5))
    | ~ rel_str(boole_POSet(sK5))
    | ~ upper_relstr_subset(sK6,boole_POSet(sK5))
    | ~ reflexive_relstr(boole_POSet(sK5))
    | ~ filtered_subset(sK6,boole_POSet(sK5))
    | ~ in(bottom_of_relstr(boole_POSet(sK5)),sK6)
    | ~ antisymmetric_relstr(boole_POSet(sK5)) ),
    inference(resolution,[],[f818,f301]) ).

fof(f301,plain,
    proper_element(sK6,powerset(the_carrier(boole_POSet(sK5)))),
    inference(cnf_transformation,[],[f217]) ).

fof(f818,plain,
    ! [X0,X1] :
      ( ~ proper_element(X1,powerset(the_carrier(X0)))
      | ~ upper_relstr_subset(X1,X0)
      | ~ in(bottom_of_relstr(X0),X1)
      | ~ filtered_subset(X1,X0)
      | ~ reflexive_relstr(X0)
      | ~ lower_bounded_relstr(X0)
      | empty_carrier(X0)
      | ~ antisymmetric_relstr(X0)
      | ~ element(X1,powerset(the_carrier(X0)))
      | ~ transitive_relstr(X0)
      | ~ rel_str(X0) ),
    inference(subsumption_resolution,[],[f511,f480]) ).

fof(f480,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | ~ empty(X1) ),
    inference(cnf_transformation,[],[f185]) ).

fof(f185,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f84]) ).

fof(f84,axiom,
    ! [X1,X0] :
      ~ ( in(X0,X1)
        & empty(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).

fof(f511,plain,
    ! [X0,X1] :
      ( ~ reflexive_relstr(X0)
      | ~ upper_relstr_subset(X1,X0)
      | ~ antisymmetric_relstr(X0)
      | ~ lower_bounded_relstr(X0)
      | empty_carrier(X0)
      | ~ rel_str(X0)
      | ~ element(X1,powerset(the_carrier(X0)))
      | ~ in(bottom_of_relstr(X0),X1)
      | empty(X1)
      | ~ proper_element(X1,powerset(the_carrier(X0)))
      | ~ filtered_subset(X1,X0)
      | ~ transitive_relstr(X0) ),
    inference(cnf_transformation,[],[f268]) ).

fof(f268,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ upper_relstr_subset(X1,X0)
          | ~ element(X1,powerset(the_carrier(X0)))
          | empty(X1)
          | ( ( proper_element(X1,powerset(the_carrier(X0)))
              | in(bottom_of_relstr(X0),X1) )
            & ( ~ in(bottom_of_relstr(X0),X1)
              | ~ proper_element(X1,powerset(the_carrier(X0))) ) )
          | ~ filtered_subset(X1,X0) )
      | ~ antisymmetric_relstr(X0)
      | ~ reflexive_relstr(X0)
      | ~ lower_bounded_relstr(X0)
      | ~ transitive_relstr(X0)
      | empty_carrier(X0)
      | ~ rel_str(X0) ),
    inference(nnf_transformation,[],[f134]) ).

fof(f134,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ upper_relstr_subset(X1,X0)
          | ~ element(X1,powerset(the_carrier(X0)))
          | empty(X1)
          | ( proper_element(X1,powerset(the_carrier(X0)))
          <=> ~ in(bottom_of_relstr(X0),X1) )
          | ~ filtered_subset(X1,X0) )
      | ~ antisymmetric_relstr(X0)
      | ~ reflexive_relstr(X0)
      | ~ lower_bounded_relstr(X0)
      | ~ transitive_relstr(X0)
      | empty_carrier(X0)
      | ~ rel_str(X0) ),
    inference(flattening,[],[f133]) ).

fof(f133,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( proper_element(X1,powerset(the_carrier(X0)))
          <=> ~ in(bottom_of_relstr(X0),X1) )
          | ~ upper_relstr_subset(X1,X0)
          | empty(X1)
          | ~ element(X1,powerset(the_carrier(X0)))
          | ~ filtered_subset(X1,X0) )
      | ~ transitive_relstr(X0)
      | ~ lower_bounded_relstr(X0)
      | empty_carrier(X0)
      | ~ reflexive_relstr(X0)
      | ~ rel_str(X0)
      | ~ antisymmetric_relstr(X0) ),
    inference(ennf_transformation,[],[f86]) ).

fof(f86,axiom,
    ! [X0] :
      ( ( transitive_relstr(X0)
        & lower_bounded_relstr(X0)
        & ~ empty_carrier(X0)
        & reflexive_relstr(X0)
        & rel_str(X0)
        & antisymmetric_relstr(X0) )
     => ! [X1] :
          ( ( upper_relstr_subset(X1,X0)
            & ~ empty(X1)
            & element(X1,powerset(the_carrier(X0)))
            & filtered_subset(X1,X0) )
         => ( proper_element(X1,powerset(the_carrier(X0)))
          <=> ~ in(bottom_of_relstr(X0),X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_waybel_7) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : SEU387+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n028.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 Aug 30 15:31:48 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.20/0.55  % (16890)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.56  % (16891)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.56  % (16898)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.56  % (16906)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.20/0.56  % (16899)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.20/0.57  TRYING [1]
% 0.20/0.57  % (16891)Instruction limit reached!
% 0.20/0.57  % (16891)------------------------------
% 0.20/0.57  % (16891)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.57  % (16907)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.20/0.58  % (16891)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.58  % (16891)Termination reason: Unknown
% 0.20/0.58  % (16891)Termination phase: Saturation
% 0.20/0.58  
% 0.20/0.58  % (16891)Memory used [KB]: 5628
% 0.20/0.58  % (16891)Time elapsed: 0.116 s
% 0.20/0.58  % (16891)Instructions burned: 8 (million)
% 0.20/0.58  % (16891)------------------------------
% 0.20/0.58  % (16891)------------------------------
% 1.71/0.58  % (16885)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.71/0.58  % (16889)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 1.71/0.58  % (16887)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.71/0.59  TRYING [2]
% 1.71/0.59  % (16893)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.71/0.59  % (16892)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.71/0.59  % (16886)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 1.71/0.59  TRYING [3]
% 1.71/0.59  % (16892)Instruction limit reached!
% 1.71/0.59  % (16892)------------------------------
% 1.71/0.59  % (16892)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.71/0.59  % (16892)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.71/0.59  % (16892)Termination reason: Unknown
% 1.71/0.59  % (16892)Termination phase: Preprocessing 3
% 1.71/0.59  
% 1.71/0.59  % (16892)Memory used [KB]: 1023
% 1.71/0.59  % (16892)Time elapsed: 0.003 s
% 1.71/0.59  % (16892)Instructions burned: 3 (million)
% 1.71/0.59  % (16892)------------------------------
% 1.71/0.59  % (16892)------------------------------
% 1.71/0.59  % (16895)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.71/0.59  % (16900)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.71/0.59  % (16909)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 1.71/0.59  % (16904)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 1.71/0.60  % (16910)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 1.88/0.60  % (16908)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 1.88/0.60  % (16912)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 1.88/0.60  % (16911)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 1.88/0.60  % (16888)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.88/0.60  % (16897)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.88/0.60  % (16894)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.88/0.60  % (16902)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.88/0.60  % (16896)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 1.88/0.60  % (16884)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 1.88/0.60  % (16901)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 1.88/0.61  % (16906)First to succeed.
% 1.88/0.61  % (16903)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.88/0.61  % (16906)Refutation found. Thanks to Tanya!
% 1.88/0.61  % SZS status Theorem for theBenchmark
% 1.88/0.61  % SZS output start Proof for theBenchmark
% See solution above
% 1.88/0.61  % (16906)------------------------------
% 1.88/0.61  % (16906)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.88/0.61  % (16906)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.88/0.61  % (16906)Termination reason: Refutation
% 1.88/0.61  
% 1.88/0.61  % (16906)Memory used [KB]: 1407
% 1.88/0.61  % (16906)Time elapsed: 0.161 s
% 1.88/0.61  % (16906)Instructions burned: 20 (million)
% 1.88/0.61  % (16906)------------------------------
% 1.88/0.61  % (16906)------------------------------
% 1.88/0.61  % (16883)Success in time 0.254 s
%------------------------------------------------------------------------------