TSTP Solution File: SEU350+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SEU350+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_uns --cores 0 -t %d %s

% Computer : n007.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 18:29:07 EDT 2022

% Result   : Theorem 0.19s 0.51s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   73 (   7 unt;   0 def)
%            Number of atoms       :  324 (  12 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  401 ( 150   ~; 169   |;  56   &)
%                                         (   8 <=>;  16  =>;   0  <=;   2 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   3 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   82 (  65   !;  17   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f187,plain,
    $false,
    inference(avatar_sat_refutation,[],[f124,f125,f178,f186]) ).

fof(f186,plain,
    ( ~ spl7_1
    | spl7_2 ),
    inference(avatar_contradiction_clause,[],[f185]) ).

fof(f185,plain,
    ( $false
    | ~ spl7_1
    | spl7_2 ),
    inference(subsumption_resolution,[],[f184,f104]) ).

fof(f104,plain,
    lattice(sK1),
    inference(cnf_transformation,[],[f91]) ).

fof(f91,plain,
    ( ~ empty_carrier(sK1)
    & latt_str(sK1)
    & ( ~ relstr_set_smaller(poset_of_lattice(sK1),sK2,sK3)
      | ~ latt_element_smaller(sK1,cast_to_el_of_lattice(sK1,sK3),sK2) )
    & ( relstr_set_smaller(poset_of_lattice(sK1),sK2,sK3)
      | latt_element_smaller(sK1,cast_to_el_of_lattice(sK1,sK3),sK2) )
    & element(sK3,the_carrier(poset_of_lattice(sK1)))
    & lattice(sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f88,f90,f89]) ).

fof(f89,plain,
    ( ? [X0,X1] :
        ( ~ empty_carrier(X0)
        & latt_str(X0)
        & ? [X2] :
            ( ( ~ relstr_set_smaller(poset_of_lattice(X0),X1,X2)
              | ~ latt_element_smaller(X0,cast_to_el_of_lattice(X0,X2),X1) )
            & ( relstr_set_smaller(poset_of_lattice(X0),X1,X2)
              | latt_element_smaller(X0,cast_to_el_of_lattice(X0,X2),X1) )
            & element(X2,the_carrier(poset_of_lattice(X0))) )
        & lattice(X0) )
   => ( ~ empty_carrier(sK1)
      & latt_str(sK1)
      & ? [X2] :
          ( ( ~ relstr_set_smaller(poset_of_lattice(sK1),sK2,X2)
            | ~ latt_element_smaller(sK1,cast_to_el_of_lattice(sK1,X2),sK2) )
          & ( relstr_set_smaller(poset_of_lattice(sK1),sK2,X2)
            | latt_element_smaller(sK1,cast_to_el_of_lattice(sK1,X2),sK2) )
          & element(X2,the_carrier(poset_of_lattice(sK1))) )
      & lattice(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f90,plain,
    ( ? [X2] :
        ( ( ~ relstr_set_smaller(poset_of_lattice(sK1),sK2,X2)
          | ~ latt_element_smaller(sK1,cast_to_el_of_lattice(sK1,X2),sK2) )
        & ( relstr_set_smaller(poset_of_lattice(sK1),sK2,X2)
          | latt_element_smaller(sK1,cast_to_el_of_lattice(sK1,X2),sK2) )
        & element(X2,the_carrier(poset_of_lattice(sK1))) )
   => ( ( ~ relstr_set_smaller(poset_of_lattice(sK1),sK2,sK3)
        | ~ latt_element_smaller(sK1,cast_to_el_of_lattice(sK1,sK3),sK2) )
      & ( relstr_set_smaller(poset_of_lattice(sK1),sK2,sK3)
        | latt_element_smaller(sK1,cast_to_el_of_lattice(sK1,sK3),sK2) )
      & element(sK3,the_carrier(poset_of_lattice(sK1))) ) ),
    introduced(choice_axiom,[]) ).

fof(f88,plain,
    ? [X0,X1] :
      ( ~ empty_carrier(X0)
      & latt_str(X0)
      & ? [X2] :
          ( ( ~ relstr_set_smaller(poset_of_lattice(X0),X1,X2)
            | ~ latt_element_smaller(X0,cast_to_el_of_lattice(X0,X2),X1) )
          & ( relstr_set_smaller(poset_of_lattice(X0),X1,X2)
            | latt_element_smaller(X0,cast_to_el_of_lattice(X0,X2),X1) )
          & element(X2,the_carrier(poset_of_lattice(X0))) )
      & lattice(X0) ),
    inference(flattening,[],[f87]) ).

fof(f87,plain,
    ? [X0,X1] :
      ( ~ empty_carrier(X0)
      & latt_str(X0)
      & ? [X2] :
          ( ( ~ relstr_set_smaller(poset_of_lattice(X0),X1,X2)
            | ~ latt_element_smaller(X0,cast_to_el_of_lattice(X0,X2),X1) )
          & ( relstr_set_smaller(poset_of_lattice(X0),X1,X2)
            | latt_element_smaller(X0,cast_to_el_of_lattice(X0,X2),X1) )
          & element(X2,the_carrier(poset_of_lattice(X0))) )
      & lattice(X0) ),
    inference(nnf_transformation,[],[f80]) ).

fof(f80,plain,
    ? [X0,X1] :
      ( ~ empty_carrier(X0)
      & latt_str(X0)
      & ? [X2] :
          ( ( latt_element_smaller(X0,cast_to_el_of_lattice(X0,X2),X1)
          <~> relstr_set_smaller(poset_of_lattice(X0),X1,X2) )
          & element(X2,the_carrier(poset_of_lattice(X0))) )
      & lattice(X0) ),
    inference(flattening,[],[f79]) ).

fof(f79,plain,
    ? [X1,X0] :
      ( ? [X2] :
          ( ( latt_element_smaller(X0,cast_to_el_of_lattice(X0,X2),X1)
          <~> relstr_set_smaller(poset_of_lattice(X0),X1,X2) )
          & element(X2,the_carrier(poset_of_lattice(X0))) )
      & lattice(X0)
      & ~ empty_carrier(X0)
      & latt_str(X0) ),
    inference(ennf_transformation,[],[f67]) ).

fof(f67,plain,
    ~ ! [X1,X0] :
        ( ( lattice(X0)
          & ~ empty_carrier(X0)
          & latt_str(X0) )
       => ! [X2] :
            ( element(X2,the_carrier(poset_of_lattice(X0)))
           => ( relstr_set_smaller(poset_of_lattice(X0),X1,X2)
            <=> latt_element_smaller(X0,cast_to_el_of_lattice(X0,X2),X1) ) ) ),
    inference(rectify,[],[f60]) ).

fof(f60,negated_conjecture,
    ~ ! [X1,X0] :
        ( ( latt_str(X1)
          & ~ empty_carrier(X1)
          & lattice(X1) )
       => ! [X2] :
            ( element(X2,the_carrier(poset_of_lattice(X1)))
           => ( relstr_set_smaller(poset_of_lattice(X1),X0,X2)
            <=> latt_element_smaller(X1,cast_to_el_of_lattice(X1,X2),X0) ) ) ),
    inference(negated_conjecture,[],[f59]) ).

fof(f59,conjecture,
    ! [X1,X0] :
      ( ( latt_str(X1)
        & ~ empty_carrier(X1)
        & lattice(X1) )
     => ! [X2] :
          ( element(X2,the_carrier(poset_of_lattice(X1)))
         => ( relstr_set_smaller(poset_of_lattice(X1),X0,X2)
          <=> latt_element_smaller(X1,cast_to_el_of_lattice(X1,X2),X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_lattice3) ).

fof(f184,plain,
    ( ~ lattice(sK1)
    | ~ spl7_1
    | spl7_2 ),
    inference(subsumption_resolution,[],[f183,f109]) ).

fof(f109,plain,
    ~ empty_carrier(sK1),
    inference(cnf_transformation,[],[f91]) ).

fof(f183,plain,
    ( empty_carrier(sK1)
    | ~ lattice(sK1)
    | ~ spl7_1
    | spl7_2 ),
    inference(subsumption_resolution,[],[f182,f179]) ).

fof(f179,plain,
    ( ~ latt_element_smaller(sK1,sK3,sK2)
    | spl7_2 ),
    inference(forward_demodulation,[],[f123,f130]) ).

fof(f130,plain,
    sK3 = cast_to_el_of_lattice(sK1,sK3),
    inference(subsumption_resolution,[],[f129,f109]) ).

fof(f129,plain,
    ( empty_carrier(sK1)
    | sK3 = cast_to_el_of_lattice(sK1,sK3) ),
    inference(subsumption_resolution,[],[f128,f108]) ).

fof(f108,plain,
    latt_str(sK1),
    inference(cnf_transformation,[],[f91]) ).

fof(f128,plain,
    ( sK3 = cast_to_el_of_lattice(sK1,sK3)
    | ~ latt_str(sK1)
    | empty_carrier(sK1) ),
    inference(subsumption_resolution,[],[f126,f104]) ).

fof(f126,plain,
    ( ~ lattice(sK1)
    | empty_carrier(sK1)
    | ~ latt_str(sK1)
    | sK3 = cast_to_el_of_lattice(sK1,sK3) ),
    inference(resolution,[],[f115,f105]) ).

fof(f105,plain,
    element(sK3,the_carrier(poset_of_lattice(sK1))),
    inference(cnf_transformation,[],[f91]) ).

fof(f115,plain,
    ! [X0,X1] :
      ( ~ element(X1,the_carrier(poset_of_lattice(X0)))
      | ~ latt_str(X0)
      | cast_to_el_of_lattice(X0,X1) = X1
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f76]) ).

fof(f76,plain,
    ! [X0] :
      ( ~ latt_str(X0)
      | empty_carrier(X0)
      | ! [X1] :
          ( ~ element(X1,the_carrier(poset_of_lattice(X0)))
          | cast_to_el_of_lattice(X0,X1) = X1 )
      | ~ lattice(X0) ),
    inference(flattening,[],[f75]) ).

fof(f75,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ element(X1,the_carrier(poset_of_lattice(X0)))
          | cast_to_el_of_lattice(X0,X1) = X1 )
      | empty_carrier(X0)
      | ~ lattice(X0)
      | ~ latt_str(X0) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0] :
      ( ( ~ empty_carrier(X0)
        & lattice(X0)
        & latt_str(X0) )
     => ! [X1] :
          ( element(X1,the_carrier(poset_of_lattice(X0)))
         => cast_to_el_of_lattice(X0,X1) = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_lattice3) ).

fof(f123,plain,
    ( ~ latt_element_smaller(sK1,cast_to_el_of_lattice(sK1,sK3),sK2)
    | spl7_2 ),
    inference(avatar_component_clause,[],[f121]) ).

fof(f121,plain,
    ( spl7_2
  <=> latt_element_smaller(sK1,cast_to_el_of_lattice(sK1,sK3),sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_2])]) ).

fof(f182,plain,
    ( latt_element_smaller(sK1,sK3,sK2)
    | empty_carrier(sK1)
    | ~ lattice(sK1)
    | ~ spl7_1 ),
    inference(subsumption_resolution,[],[f181,f108]) ).

fof(f181,plain,
    ( ~ latt_str(sK1)
    | empty_carrier(sK1)
    | ~ lattice(sK1)
    | latt_element_smaller(sK1,sK3,sK2)
    | ~ spl7_1 ),
    inference(subsumption_resolution,[],[f180,f145]) ).

fof(f145,plain,
    element(sK3,the_carrier(sK1)),
    inference(subsumption_resolution,[],[f144,f109]) ).

fof(f144,plain,
    ( element(sK3,the_carrier(sK1))
    | empty_carrier(sK1) ),
    inference(subsumption_resolution,[],[f143,f104]) ).

fof(f143,plain,
    ( ~ lattice(sK1)
    | element(sK3,the_carrier(sK1))
    | empty_carrier(sK1) ),
    inference(subsumption_resolution,[],[f142,f105]) ).

fof(f142,plain,
    ( ~ element(sK3,the_carrier(poset_of_lattice(sK1)))
    | empty_carrier(sK1)
    | element(sK3,the_carrier(sK1))
    | ~ lattice(sK1) ),
    inference(subsumption_resolution,[],[f139,f108]) ).

fof(f139,plain,
    ( ~ latt_str(sK1)
    | empty_carrier(sK1)
    | element(sK3,the_carrier(sK1))
    | ~ lattice(sK1)
    | ~ element(sK3,the_carrier(poset_of_lattice(sK1))) ),
    inference(superposition,[],[f112,f130]) ).

fof(f112,plain,
    ! [X0,X1] :
      ( element(cast_to_el_of_lattice(X1,X0),the_carrier(X1))
      | empty_carrier(X1)
      | ~ element(X0,the_carrier(poset_of_lattice(X1)))
      | ~ latt_str(X1)
      | ~ lattice(X1) ),
    inference(cnf_transformation,[],[f73]) ).

fof(f73,plain,
    ! [X0,X1] :
      ( element(cast_to_el_of_lattice(X1,X0),the_carrier(X1))
      | ~ lattice(X1)
      | ~ element(X0,the_carrier(poset_of_lattice(X1)))
      | empty_carrier(X1)
      | ~ latt_str(X1) ),
    inference(flattening,[],[f72]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( element(cast_to_el_of_lattice(X1,X0),the_carrier(X1))
      | ~ lattice(X1)
      | ~ latt_str(X1)
      | empty_carrier(X1)
      | ~ element(X0,the_carrier(poset_of_lattice(X1))) ),
    inference(ennf_transformation,[],[f68]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( ( lattice(X1)
        & latt_str(X1)
        & ~ empty_carrier(X1)
        & element(X0,the_carrier(poset_of_lattice(X1))) )
     => element(cast_to_el_of_lattice(X1,X0),the_carrier(X1)) ),
    inference(rectify,[],[f16]) ).

fof(f16,axiom,
    ! [X1,X0] :
      ( ( element(X1,the_carrier(poset_of_lattice(X0)))
        & latt_str(X0)
        & ~ empty_carrier(X0)
        & lattice(X0) )
     => element(cast_to_el_of_lattice(X0,X1),the_carrier(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_lattice3) ).

fof(f180,plain,
    ( ~ element(sK3,the_carrier(sK1))
    | empty_carrier(sK1)
    | latt_element_smaller(sK1,sK3,sK2)
    | ~ lattice(sK1)
    | ~ latt_str(sK1)
    | ~ spl7_1 ),
    inference(resolution,[],[f118,f159]) ).

fof(f159,plain,
    ! [X2,X0,X1] :
      ( ~ relstr_set_smaller(poset_of_lattice(X0),X2,X1)
      | ~ latt_str(X0)
      | latt_element_smaller(X0,X1,X2)
      | empty_carrier(X0)
      | ~ element(X1,the_carrier(X0))
      | ~ lattice(X0) ),
    inference(duplicate_literal_removal,[],[f158]) ).

fof(f158,plain,
    ! [X2,X0,X1] :
      ( empty_carrier(X0)
      | ~ lattice(X0)
      | latt_element_smaller(X0,X1,X2)
      | ~ relstr_set_smaller(poset_of_lattice(X0),X2,X1)
      | empty_carrier(X0)
      | ~ element(X1,the_carrier(X0))
      | ~ lattice(X0)
      | ~ element(X1,the_carrier(X0))
      | ~ latt_str(X0)
      | ~ latt_str(X0) ),
    inference(superposition,[],[f102,f100]) ).

fof(f100,plain,
    ! [X0,X1] :
      ( cast_to_el_of_LattPOSet(X0,X1) = X1
      | ~ element(X1,the_carrier(X0))
      | empty_carrier(X0)
      | ~ lattice(X0)
      | ~ latt_str(X0) ),
    inference(cnf_transformation,[],[f71]) ).

fof(f71,plain,
    ! [X0] :
      ( ~ latt_str(X0)
      | ! [X1] :
          ( ~ element(X1,the_carrier(X0))
          | cast_to_el_of_LattPOSet(X0,X1) = X1 )
      | ~ lattice(X0)
      | empty_carrier(X0) ),
    inference(flattening,[],[f70]) ).

fof(f70,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ element(X1,the_carrier(X0))
          | cast_to_el_of_LattPOSet(X0,X1) = X1 )
      | empty_carrier(X0)
      | ~ latt_str(X0)
      | ~ lattice(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0] :
      ( ( ~ empty_carrier(X0)
        & latt_str(X0)
        & lattice(X0) )
     => ! [X1] :
          ( element(X1,the_carrier(X0))
         => cast_to_el_of_LattPOSet(X0,X1) = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_lattice3) ).

fof(f102,plain,
    ! [X2,X0,X1] :
      ( ~ relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
      | ~ latt_str(X1)
      | latt_element_smaller(X1,X2,X0)
      | empty_carrier(X1)
      | ~ element(X2,the_carrier(X1))
      | ~ lattice(X1) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
              | ~ latt_element_smaller(X1,X2,X0) )
            & ( latt_element_smaller(X1,X2,X0)
              | ~ relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2)) ) )
          | ~ element(X2,the_carrier(X1)) )
      | ~ latt_str(X1)
      | ~ lattice(X1)
      | empty_carrier(X1) ),
    inference(nnf_transformation,[],[f78]) ).

fof(f78,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
          <=> latt_element_smaller(X1,X2,X0) )
          | ~ element(X2,the_carrier(X1)) )
      | ~ latt_str(X1)
      | ~ lattice(X1)
      | empty_carrier(X1) ),
    inference(flattening,[],[f77]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
          <=> latt_element_smaller(X1,X2,X0) )
          | ~ element(X2,the_carrier(X1)) )
      | ~ latt_str(X1)
      | ~ lattice(X1)
      | empty_carrier(X1) ),
    inference(ennf_transformation,[],[f58]) ).

fof(f58,axiom,
    ! [X0,X1] :
      ( ( latt_str(X1)
        & lattice(X1)
        & ~ empty_carrier(X1) )
     => ! [X2] :
          ( element(X2,the_carrier(X1))
         => ( relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
          <=> latt_element_smaller(X1,X2,X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_lattice3) ).

fof(f118,plain,
    ( relstr_set_smaller(poset_of_lattice(sK1),sK2,sK3)
    | ~ spl7_1 ),
    inference(avatar_component_clause,[],[f117]) ).

fof(f117,plain,
    ( spl7_1
  <=> relstr_set_smaller(poset_of_lattice(sK1),sK2,sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_1])]) ).

fof(f178,plain,
    ( spl7_1
    | ~ spl7_2 ),
    inference(avatar_contradiction_clause,[],[f177]) ).

fof(f177,plain,
    ( $false
    | spl7_1
    | ~ spl7_2 ),
    inference(subsumption_resolution,[],[f176,f104]) ).

fof(f176,plain,
    ( ~ lattice(sK1)
    | spl7_1
    | ~ spl7_2 ),
    inference(subsumption_resolution,[],[f175,f109]) ).

fof(f175,plain,
    ( empty_carrier(sK1)
    | ~ lattice(sK1)
    | spl7_1
    | ~ spl7_2 ),
    inference(subsumption_resolution,[],[f174,f145]) ).

fof(f174,plain,
    ( ~ element(sK3,the_carrier(sK1))
    | empty_carrier(sK1)
    | ~ lattice(sK1)
    | spl7_1
    | ~ spl7_2 ),
    inference(subsumption_resolution,[],[f173,f131]) ).

fof(f131,plain,
    ( latt_element_smaller(sK1,sK3,sK2)
    | ~ spl7_2 ),
    inference(backward_demodulation,[],[f122,f130]) ).

fof(f122,plain,
    ( latt_element_smaller(sK1,cast_to_el_of_lattice(sK1,sK3),sK2)
    | ~ spl7_2 ),
    inference(avatar_component_clause,[],[f121]) ).

fof(f173,plain,
    ( ~ latt_element_smaller(sK1,sK3,sK2)
    | ~ element(sK3,the_carrier(sK1))
    | empty_carrier(sK1)
    | ~ lattice(sK1)
    | spl7_1 ),
    inference(subsumption_resolution,[],[f167,f108]) ).

fof(f167,plain,
    ( ~ latt_str(sK1)
    | empty_carrier(sK1)
    | ~ lattice(sK1)
    | ~ latt_element_smaller(sK1,sK3,sK2)
    | ~ element(sK3,the_carrier(sK1))
    | spl7_1 ),
    inference(resolution,[],[f165,f119]) ).

fof(f119,plain,
    ( ~ relstr_set_smaller(poset_of_lattice(sK1),sK2,sK3)
    | spl7_1 ),
    inference(avatar_component_clause,[],[f117]) ).

fof(f165,plain,
    ! [X2,X0,X1] :
      ( relstr_set_smaller(poset_of_lattice(X0),X2,X1)
      | ~ lattice(X0)
      | empty_carrier(X0)
      | ~ element(X1,the_carrier(X0))
      | ~ latt_element_smaller(X0,X1,X2)
      | ~ latt_str(X0) ),
    inference(duplicate_literal_removal,[],[f162]) ).

fof(f162,plain,
    ! [X2,X0,X1] :
      ( ~ lattice(X0)
      | empty_carrier(X0)
      | ~ latt_element_smaller(X0,X1,X2)
      | ~ latt_str(X0)
      | empty_carrier(X0)
      | ~ latt_str(X0)
      | ~ element(X1,the_carrier(X0))
      | relstr_set_smaller(poset_of_lattice(X0),X2,X1)
      | ~ element(X1,the_carrier(X0))
      | ~ lattice(X0) ),
    inference(superposition,[],[f103,f100]) ).

fof(f103,plain,
    ! [X2,X0,X1] :
      ( relstr_set_smaller(poset_of_lattice(X1),X0,cast_to_el_of_LattPOSet(X1,X2))
      | ~ latt_str(X1)
      | empty_carrier(X1)
      | ~ element(X2,the_carrier(X1))
      | ~ lattice(X1)
      | ~ latt_element_smaller(X1,X2,X0) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f125,plain,
    ( spl7_2
    | spl7_1 ),
    inference(avatar_split_clause,[],[f106,f117,f121]) ).

fof(f106,plain,
    ( relstr_set_smaller(poset_of_lattice(sK1),sK2,sK3)
    | latt_element_smaller(sK1,cast_to_el_of_lattice(sK1,sK3),sK2) ),
    inference(cnf_transformation,[],[f91]) ).

fof(f124,plain,
    ( ~ spl7_1
    | ~ spl7_2 ),
    inference(avatar_split_clause,[],[f107,f121,f117]) ).

fof(f107,plain,
    ( ~ latt_element_smaller(sK1,cast_to_el_of_lattice(sK1,sK3),sK2)
    | ~ relstr_set_smaller(poset_of_lattice(sK1),sK2,sK3) ),
    inference(cnf_transformation,[],[f91]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : SEU350+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.34  % Computer : n007.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 Aug 30 15:01:46 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.49  % (28506)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.19/0.50  % (28498)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.50  % (28498)Instruction limit reached!
% 0.19/0.50  % (28498)------------------------------
% 0.19/0.50  % (28498)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50  % (28498)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50  % (28498)Termination reason: Unknown
% 0.19/0.50  % (28498)Termination phase: Property scanning
% 0.19/0.50  
% 0.19/0.50  % (28498)Memory used [KB]: 1535
% 0.19/0.50  % (28498)Time elapsed: 0.005 s
% 0.19/0.50  % (28498)Instructions burned: 3 (million)
% 0.19/0.50  % (28498)------------------------------
% 0.19/0.50  % (28498)------------------------------
% 0.19/0.50  % (28490)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.51  % (28495)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.51  % (28496)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.19/0.51  % (28490)First to succeed.
% 0.19/0.51  % (28490)Refutation found. Thanks to Tanya!
% 0.19/0.51  % SZS status Theorem for theBenchmark
% 0.19/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.51  % (28490)------------------------------
% 0.19/0.51  % (28490)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (28490)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (28490)Termination reason: Refutation
% 0.19/0.51  
% 0.19/0.51  % (28490)Memory used [KB]: 6012
% 0.19/0.51  % (28490)Time elapsed: 0.067 s
% 0.19/0.51  % (28490)Instructions burned: 5 (million)
% 0.19/0.51  % (28490)------------------------------
% 0.19/0.51  % (28490)------------------------------
% 0.19/0.51  % (28483)Success in time 0.166 s
%------------------------------------------------------------------------------