TSTP Solution File: SEU360+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU360+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %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 : Sun May  5 09:36:31 EDT 2024

% Result   : Theorem 0.22s 0.42s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   29
%            Number of leaves      :   28
% Syntax   : Number of formulae    :  145 (   8 unt;   0 def)
%            Number of atoms       :  665 (   7 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  863 ( 343   ~; 351   |; 122   &)
%                                         (  21 <=>;  26  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   25 (  23 usr;   7 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   2 con; 0-3 aty)
%            Number of variables   :  255 ( 224   !;  31   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f557,plain,
    $false,
    inference(avatar_sat_refutation,[],[f153,f442,f452,f538,f548,f556]) ).

fof(f556,plain,
    ~ spl18_6,
    inference(avatar_contradiction_clause,[],[f555]) ).

fof(f555,plain,
    ( $false
    | ~ spl18_6 ),
    inference(subsumption_resolution,[],[f554,f96]) ).

fof(f96,plain,
    rel_str(sK4),
    inference(cnf_transformation,[],[f58]) ).

fof(f58,plain,
    ( ( ~ ex_inf_of_relstr_set(sK4,the_carrier(sK4))
      | ~ ex_sup_of_relstr_set(sK4,empty_set) )
    & rel_str(sK4)
    & lower_bounded_relstr(sK4)
    & antisymmetric_relstr(sK4)
    & ~ empty_carrier(sK4) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f32,f57]) ).

fof(f57,plain,
    ( ? [X0] :
        ( ( ~ ex_inf_of_relstr_set(X0,the_carrier(X0))
          | ~ ex_sup_of_relstr_set(X0,empty_set) )
        & rel_str(X0)
        & lower_bounded_relstr(X0)
        & antisymmetric_relstr(X0)
        & ~ empty_carrier(X0) )
   => ( ( ~ ex_inf_of_relstr_set(sK4,the_carrier(sK4))
        | ~ ex_sup_of_relstr_set(sK4,empty_set) )
      & rel_str(sK4)
      & lower_bounded_relstr(sK4)
      & antisymmetric_relstr(sK4)
      & ~ empty_carrier(sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f32,plain,
    ? [X0] :
      ( ( ~ ex_inf_of_relstr_set(X0,the_carrier(X0))
        | ~ ex_sup_of_relstr_set(X0,empty_set) )
      & rel_str(X0)
      & lower_bounded_relstr(X0)
      & antisymmetric_relstr(X0)
      & ~ empty_carrier(X0) ),
    inference(flattening,[],[f31]) ).

fof(f31,plain,
    ? [X0] :
      ( ( ~ ex_inf_of_relstr_set(X0,the_carrier(X0))
        | ~ ex_sup_of_relstr_set(X0,empty_set) )
      & rel_str(X0)
      & lower_bounded_relstr(X0)
      & antisymmetric_relstr(X0)
      & ~ empty_carrier(X0) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,negated_conjecture,
    ~ ! [X0] :
        ( ( rel_str(X0)
          & lower_bounded_relstr(X0)
          & antisymmetric_relstr(X0)
          & ~ empty_carrier(X0) )
       => ( ex_inf_of_relstr_set(X0,the_carrier(X0))
          & ex_sup_of_relstr_set(X0,empty_set) ) ),
    inference(negated_conjecture,[],[f23]) ).

fof(f23,conjecture,
    ! [X0] :
      ( ( rel_str(X0)
        & lower_bounded_relstr(X0)
        & antisymmetric_relstr(X0)
        & ~ empty_carrier(X0) )
     => ( ex_inf_of_relstr_set(X0,the_carrier(X0))
        & ex_sup_of_relstr_set(X0,empty_set) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_yellow_0) ).

fof(f554,plain,
    ( ~ rel_str(sK4)
    | ~ spl18_6 ),
    inference(resolution,[],[f553,f99]) ).

fof(f99,plain,
    ! [X0] :
      ( one_sorted_str(X0)
      | ~ rel_str(X0) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X0] :
      ( one_sorted_str(X0)
      | ~ rel_str(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] :
      ( rel_str(X0)
     => one_sorted_str(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).

fof(f553,plain,
    ( ~ one_sorted_str(sK4)
    | ~ spl18_6 ),
    inference(subsumption_resolution,[],[f550,f93]) ).

fof(f93,plain,
    ~ empty_carrier(sK4),
    inference(cnf_transformation,[],[f58]) ).

fof(f550,plain,
    ( ~ one_sorted_str(sK4)
    | empty_carrier(sK4)
    | ~ spl18_6 ),
    inference(resolution,[],[f537,f110]) ).

fof(f110,plain,
    ! [X0] :
      ( ~ empty(the_carrier(X0))
      | ~ one_sorted_str(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,plain,
    ! [X0] :
      ( ~ empty(the_carrier(X0))
      | ~ one_sorted_str(X0)
      | empty_carrier(X0) ),
    inference(flattening,[],[f39]) ).

fof(f39,plain,
    ! [X0] :
      ( ~ empty(the_carrier(X0))
      | ~ one_sorted_str(X0)
      | empty_carrier(X0) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,axiom,
    ! [X0] :
      ( ( one_sorted_str(X0)
        & ~ empty_carrier(X0) )
     => ~ empty(the_carrier(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).

fof(f537,plain,
    ( empty(the_carrier(sK4))
    | ~ spl18_6 ),
    inference(avatar_component_clause,[],[f535]) ).

fof(f535,plain,
    ( spl18_6
  <=> empty(the_carrier(sK4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_6])]) ).

fof(f548,plain,
    spl18_5,
    inference(avatar_contradiction_clause,[],[f547]) ).

fof(f547,plain,
    ( $false
    | spl18_5 ),
    inference(subsumption_resolution,[],[f546,f94]) ).

fof(f94,plain,
    antisymmetric_relstr(sK4),
    inference(cnf_transformation,[],[f58]) ).

fof(f546,plain,
    ( ~ antisymmetric_relstr(sK4)
    | spl18_5 ),
    inference(subsumption_resolution,[],[f545,f96]) ).

fof(f545,plain,
    ( ~ rel_str(sK4)
    | ~ antisymmetric_relstr(sK4)
    | spl18_5 ),
    inference(resolution,[],[f533,f128]) ).

fof(f128,plain,
    ! [X0] :
      ( sP3(X0)
      | ~ rel_str(X0)
      | ~ antisymmetric_relstr(X0) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0] :
      ( sP3(X0)
      | ~ rel_str(X0)
      | ~ antisymmetric_relstr(X0) ),
    inference(definition_folding,[],[f44,f55,f54]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( sP2(X0,X1)
    <=> ? [X2] :
          ( ! [X3] :
              ( related(X0,X3,X2)
              | ~ relstr_element_smaller(X0,X1,X3)
              | ~ element(X3,the_carrier(X0)) )
          & relstr_element_smaller(X0,X1,X2)
          & element(X2,the_carrier(X0)) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f55,plain,
    ! [X0] :
      ( ! [X1] :
          ( ex_inf_of_relstr_set(X0,X1)
        <=> sP2(X0,X1) )
      | ~ sP3(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).

fof(f44,plain,
    ! [X0] :
      ( ! [X1] :
          ( ex_inf_of_relstr_set(X0,X1)
        <=> ? [X2] :
              ( ! [X3] :
                  ( related(X0,X3,X2)
                  | ~ relstr_element_smaller(X0,X1,X3)
                  | ~ element(X3,the_carrier(X0)) )
              & relstr_element_smaller(X0,X1,X2)
              & element(X2,the_carrier(X0)) ) )
      | ~ rel_str(X0)
      | ~ antisymmetric_relstr(X0) ),
    inference(flattening,[],[f43]) ).

fof(f43,plain,
    ! [X0] :
      ( ! [X1] :
          ( ex_inf_of_relstr_set(X0,X1)
        <=> ? [X2] :
              ( ! [X3] :
                  ( related(X0,X3,X2)
                  | ~ relstr_element_smaller(X0,X1,X3)
                  | ~ element(X3,the_carrier(X0)) )
              & relstr_element_smaller(X0,X1,X2)
              & element(X2,the_carrier(X0)) ) )
      | ~ rel_str(X0)
      | ~ antisymmetric_relstr(X0) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,axiom,
    ! [X0] :
      ( ( rel_str(X0)
        & antisymmetric_relstr(X0) )
     => ! [X1] :
          ( ex_inf_of_relstr_set(X0,X1)
        <=> ? [X2] :
              ( ! [X3] :
                  ( element(X3,the_carrier(X0))
                 => ( relstr_element_smaller(X0,X1,X3)
                   => related(X0,X3,X2) ) )
              & relstr_element_smaller(X0,X1,X2)
              & element(X2,the_carrier(X0)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_yellow_0) ).

fof(f533,plain,
    ( ~ sP3(sK4)
    | spl18_5 ),
    inference(avatar_component_clause,[],[f531]) ).

fof(f531,plain,
    ( spl18_5
  <=> sP3(sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_5])]) ).

fof(f538,plain,
    ( ~ spl18_5
    | spl18_6
    | spl18_2 ),
    inference(avatar_split_clause,[],[f529,f150,f535,f531]) ).

fof(f150,plain,
    ( spl18_2
  <=> ex_inf_of_relstr_set(sK4,the_carrier(sK4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_2])]) ).

fof(f529,plain,
    ( empty(the_carrier(sK4))
    | ~ sP3(sK4)
    | spl18_2 ),
    inference(subsumption_resolution,[],[f528,f96]) ).

fof(f528,plain,
    ( empty(the_carrier(sK4))
    | ~ rel_str(sK4)
    | ~ sP3(sK4)
    | spl18_2 ),
    inference(subsumption_resolution,[],[f527,f95]) ).

fof(f95,plain,
    lower_bounded_relstr(sK4),
    inference(cnf_transformation,[],[f58]) ).

fof(f527,plain,
    ( ~ lower_bounded_relstr(sK4)
    | empty(the_carrier(sK4))
    | ~ rel_str(sK4)
    | ~ sP3(sK4)
    | spl18_2 ),
    inference(resolution,[],[f525,f152]) ).

fof(f152,plain,
    ( ~ ex_inf_of_relstr_set(sK4,the_carrier(sK4))
    | spl18_2 ),
    inference(avatar_component_clause,[],[f150]) ).

fof(f525,plain,
    ! [X0] :
      ( ex_inf_of_relstr_set(X0,the_carrier(X0))
      | ~ lower_bounded_relstr(X0)
      | empty(the_carrier(X0))
      | ~ rel_str(X0)
      | ~ sP3(X0) ),
    inference(resolution,[],[f523,f121]) ).

fof(f121,plain,
    ! [X0,X1] :
      ( ~ sP2(X0,X1)
      | ex_inf_of_relstr_set(X0,X1)
      | ~ sP3(X0) ),
    inference(cnf_transformation,[],[f73]) ).

fof(f73,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ex_inf_of_relstr_set(X0,X1)
            | ~ sP2(X0,X1) )
          & ( sP2(X0,X1)
            | ~ ex_inf_of_relstr_set(X0,X1) ) )
      | ~ sP3(X0) ),
    inference(nnf_transformation,[],[f55]) ).

fof(f523,plain,
    ! [X0] :
      ( sP2(X0,the_carrier(X0))
      | ~ rel_str(X0)
      | ~ lower_bounded_relstr(X0)
      | empty(the_carrier(X0)) ),
    inference(duplicate_literal_removal,[],[f522]) ).

fof(f522,plain,
    ! [X0] :
      ( ~ rel_str(X0)
      | sP2(X0,the_carrier(X0))
      | ~ lower_bounded_relstr(X0)
      | ~ rel_str(X0)
      | empty(the_carrier(X0))
      | ~ lower_bounded_relstr(X0) ),
    inference(resolution,[],[f509,f161]) ).

fof(f161,plain,
    ! [X0] :
      ( in(sK5(X0),the_carrier(X0))
      | ~ rel_str(X0)
      | empty(the_carrier(X0))
      | ~ lower_bounded_relstr(X0) ),
    inference(resolution,[],[f100,f132]) ).

fof(f132,plain,
    ! [X0,X1] :
      ( ~ element(X0,X1)
      | empty(X1)
      | in(X0,X1) ),
    inference(cnf_transformation,[],[f48]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(flattening,[],[f47]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,axiom,
    ! [X0,X1] :
      ( element(X0,X1)
     => ( in(X0,X1)
        | empty(X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).

fof(f100,plain,
    ! [X0] :
      ( element(sK5(X0),the_carrier(X0))
      | ~ lower_bounded_relstr(X0)
      | ~ rel_str(X0) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,plain,
    ! [X0] :
      ( ( ( lower_bounded_relstr(X0)
          | ! [X1] :
              ( ~ relstr_element_smaller(X0,the_carrier(X0),X1)
              | ~ element(X1,the_carrier(X0)) ) )
        & ( ( relstr_element_smaller(X0,the_carrier(X0),sK5(X0))
            & element(sK5(X0),the_carrier(X0)) )
          | ~ lower_bounded_relstr(X0) ) )
      | ~ rel_str(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f60,f61]) ).

fof(f61,plain,
    ! [X0] :
      ( ? [X2] :
          ( relstr_element_smaller(X0,the_carrier(X0),X2)
          & element(X2,the_carrier(X0)) )
     => ( relstr_element_smaller(X0,the_carrier(X0),sK5(X0))
        & element(sK5(X0),the_carrier(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f60,plain,
    ! [X0] :
      ( ( ( lower_bounded_relstr(X0)
          | ! [X1] :
              ( ~ relstr_element_smaller(X0,the_carrier(X0),X1)
              | ~ element(X1,the_carrier(X0)) ) )
        & ( ? [X2] :
              ( relstr_element_smaller(X0,the_carrier(X0),X2)
              & element(X2,the_carrier(X0)) )
          | ~ lower_bounded_relstr(X0) ) )
      | ~ rel_str(X0) ),
    inference(rectify,[],[f59]) ).

fof(f59,plain,
    ! [X0] :
      ( ( ( lower_bounded_relstr(X0)
          | ! [X1] :
              ( ~ relstr_element_smaller(X0,the_carrier(X0),X1)
              | ~ element(X1,the_carrier(X0)) ) )
        & ( ? [X1] :
              ( relstr_element_smaller(X0,the_carrier(X0),X1)
              & element(X1,the_carrier(X0)) )
          | ~ lower_bounded_relstr(X0) ) )
      | ~ rel_str(X0) ),
    inference(nnf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X0] :
      ( ( lower_bounded_relstr(X0)
      <=> ? [X1] :
            ( relstr_element_smaller(X0,the_carrier(X0),X1)
            & element(X1,the_carrier(X0)) ) )
      | ~ rel_str(X0) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] :
      ( rel_str(X0)
     => ( lower_bounded_relstr(X0)
      <=> ? [X1] :
            ( relstr_element_smaller(X0,the_carrier(X0),X1)
            & element(X1,the_carrier(X0)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_yellow_0) ).

fof(f509,plain,
    ! [X0] :
      ( ~ in(sK5(X0),the_carrier(X0))
      | ~ rel_str(X0)
      | sP2(X0,the_carrier(X0))
      | ~ lower_bounded_relstr(X0) ),
    inference(subsumption_resolution,[],[f495,f131]) ).

fof(f131,plain,
    ! [X0,X1] :
      ( element(X0,X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f46]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( element(X0,X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,axiom,
    ! [X0,X1] :
      ( in(X0,X1)
     => element(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).

fof(f495,plain,
    ! [X0] :
      ( ~ in(sK5(X0),the_carrier(X0))
      | ~ rel_str(X0)
      | sP2(X0,the_carrier(X0))
      | ~ element(sK5(X0),the_carrier(X0))
      | ~ lower_bounded_relstr(X0) ),
    inference(duplicate_literal_removal,[],[f478]) ).

fof(f478,plain,
    ! [X0] :
      ( ~ in(sK5(X0),the_carrier(X0))
      | ~ rel_str(X0)
      | sP2(X0,the_carrier(X0))
      | ~ element(sK5(X0),the_carrier(X0))
      | ~ lower_bounded_relstr(X0)
      | ~ rel_str(X0) ),
    inference(resolution,[],[f463,f101]) ).

fof(f101,plain,
    ! [X0] :
      ( relstr_element_smaller(X0,the_carrier(X0),sK5(X0))
      | ~ lower_bounded_relstr(X0)
      | ~ rel_str(X0) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f463,plain,
    ! [X2,X0,X1] :
      ( ~ relstr_element_smaller(X1,X2,X0)
      | ~ in(X0,X2)
      | ~ rel_str(X1)
      | sP2(X1,X2)
      | ~ element(X0,the_carrier(X1)) ),
    inference(duplicate_literal_removal,[],[f459]) ).

fof(f459,plain,
    ! [X2,X0,X1] :
      ( ~ element(X0,the_carrier(X1))
      | ~ in(X0,X2)
      | ~ rel_str(X1)
      | sP2(X1,X2)
      | ~ relstr_element_smaller(X1,X2,X0)
      | ~ element(X0,the_carrier(X1))
      | sP2(X1,X2)
      | ~ relstr_element_smaller(X1,X2,X0)
      | ~ element(X0,the_carrier(X1)) ),
    inference(resolution,[],[f287,f127]) ).

fof(f127,plain,
    ! [X2,X0,X1] :
      ( ~ related(X0,sK9(X0,X1,X2),X2)
      | sP2(X0,X1)
      | ~ relstr_element_smaller(X0,X1,X2)
      | ~ element(X2,the_carrier(X0)) ),
    inference(cnf_transformation,[],[f78]) ).

fof(f78,plain,
    ! [X0,X1] :
      ( ( sP2(X0,X1)
        | ! [X2] :
            ( ( ~ related(X0,sK9(X0,X1,X2),X2)
              & relstr_element_smaller(X0,X1,sK9(X0,X1,X2))
              & element(sK9(X0,X1,X2),the_carrier(X0)) )
            | ~ relstr_element_smaller(X0,X1,X2)
            | ~ element(X2,the_carrier(X0)) ) )
      & ( ( ! [X5] :
              ( related(X0,X5,sK10(X0,X1))
              | ~ relstr_element_smaller(X0,X1,X5)
              | ~ element(X5,the_carrier(X0)) )
          & relstr_element_smaller(X0,X1,sK10(X0,X1))
          & element(sK10(X0,X1),the_carrier(X0)) )
        | ~ sP2(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f75,f77,f76]) ).

fof(f76,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ~ related(X0,X3,X2)
          & relstr_element_smaller(X0,X1,X3)
          & element(X3,the_carrier(X0)) )
     => ( ~ related(X0,sK9(X0,X1,X2),X2)
        & relstr_element_smaller(X0,X1,sK9(X0,X1,X2))
        & element(sK9(X0,X1,X2),the_carrier(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ! [X5] :
              ( related(X0,X5,X4)
              | ~ relstr_element_smaller(X0,X1,X5)
              | ~ element(X5,the_carrier(X0)) )
          & relstr_element_smaller(X0,X1,X4)
          & element(X4,the_carrier(X0)) )
     => ( ! [X5] :
            ( related(X0,X5,sK10(X0,X1))
            | ~ relstr_element_smaller(X0,X1,X5)
            | ~ element(X5,the_carrier(X0)) )
        & relstr_element_smaller(X0,X1,sK10(X0,X1))
        & element(sK10(X0,X1),the_carrier(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( ( sP2(X0,X1)
        | ! [X2] :
            ( ? [X3] :
                ( ~ related(X0,X3,X2)
                & relstr_element_smaller(X0,X1,X3)
                & element(X3,the_carrier(X0)) )
            | ~ relstr_element_smaller(X0,X1,X2)
            | ~ element(X2,the_carrier(X0)) ) )
      & ( ? [X4] :
            ( ! [X5] :
                ( related(X0,X5,X4)
                | ~ relstr_element_smaller(X0,X1,X5)
                | ~ element(X5,the_carrier(X0)) )
            & relstr_element_smaller(X0,X1,X4)
            & element(X4,the_carrier(X0)) )
        | ~ sP2(X0,X1) ) ),
    inference(rectify,[],[f74]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( ( sP2(X0,X1)
        | ! [X2] :
            ( ? [X3] :
                ( ~ related(X0,X3,X2)
                & relstr_element_smaller(X0,X1,X3)
                & element(X3,the_carrier(X0)) )
            | ~ relstr_element_smaller(X0,X1,X2)
            | ~ element(X2,the_carrier(X0)) ) )
      & ( ? [X2] :
            ( ! [X3] :
                ( related(X0,X3,X2)
                | ~ relstr_element_smaller(X0,X1,X3)
                | ~ element(X3,the_carrier(X0)) )
            & relstr_element_smaller(X0,X1,X2)
            & element(X2,the_carrier(X0)) )
        | ~ sP2(X0,X1) ) ),
    inference(nnf_transformation,[],[f54]) ).

fof(f287,plain,
    ! [X2,X3,X0,X1] :
      ( related(X2,sK9(X2,X1,X3),X0)
      | ~ element(X0,the_carrier(X2))
      | ~ in(X0,X1)
      | ~ rel_str(X2)
      | sP2(X2,X1)
      | ~ relstr_element_smaller(X2,X1,X3)
      | ~ element(X3,the_carrier(X2)) ),
    inference(subsumption_resolution,[],[f264,f125]) ).

fof(f125,plain,
    ! [X2,X0,X1] :
      ( element(sK9(X0,X1,X2),the_carrier(X0))
      | sP2(X0,X1)
      | ~ relstr_element_smaller(X0,X1,X2)
      | ~ element(X2,the_carrier(X0)) ),
    inference(cnf_transformation,[],[f78]) ).

fof(f264,plain,
    ! [X2,X3,X0,X1] :
      ( ~ in(X0,X1)
      | ~ element(X0,the_carrier(X2))
      | related(X2,sK9(X2,X1,X3),X0)
      | ~ element(sK9(X2,X1,X3),the_carrier(X2))
      | ~ rel_str(X2)
      | sP2(X2,X1)
      | ~ relstr_element_smaller(X2,X1,X3)
      | ~ element(X3,the_carrier(X2)) ),
    inference(resolution,[],[f105,f126]) ).

fof(f126,plain,
    ! [X2,X0,X1] :
      ( relstr_element_smaller(X0,X1,sK9(X0,X1,X2))
      | sP2(X0,X1)
      | ~ relstr_element_smaller(X0,X1,X2)
      | ~ element(X2,the_carrier(X0)) ),
    inference(cnf_transformation,[],[f78]) ).

fof(f105,plain,
    ! [X2,X0,X1,X4] :
      ( ~ relstr_element_smaller(X0,X1,X2)
      | ~ in(X4,X1)
      | ~ element(X4,the_carrier(X0))
      | related(X0,X2,X4)
      | ~ element(X2,the_carrier(X0))
      | ~ rel_str(X0) ),
    inference(cnf_transformation,[],[f66]) ).

fof(f66,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( ( relstr_element_smaller(X0,X1,X2)
              | ( ~ related(X0,X2,sK6(X0,X1,X2))
                & in(sK6(X0,X1,X2),X1)
                & element(sK6(X0,X1,X2),the_carrier(X0)) ) )
            & ( ! [X4] :
                  ( related(X0,X2,X4)
                  | ~ in(X4,X1)
                  | ~ element(X4,the_carrier(X0)) )
              | ~ relstr_element_smaller(X0,X1,X2) ) )
          | ~ element(X2,the_carrier(X0)) )
      | ~ rel_str(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f64,f65]) ).

fof(f65,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ~ related(X0,X2,X3)
          & in(X3,X1)
          & element(X3,the_carrier(X0)) )
     => ( ~ related(X0,X2,sK6(X0,X1,X2))
        & in(sK6(X0,X1,X2),X1)
        & element(sK6(X0,X1,X2),the_carrier(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f64,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( ( relstr_element_smaller(X0,X1,X2)
              | ? [X3] :
                  ( ~ related(X0,X2,X3)
                  & in(X3,X1)
                  & element(X3,the_carrier(X0)) ) )
            & ( ! [X4] :
                  ( related(X0,X2,X4)
                  | ~ in(X4,X1)
                  | ~ element(X4,the_carrier(X0)) )
              | ~ relstr_element_smaller(X0,X1,X2) ) )
          | ~ element(X2,the_carrier(X0)) )
      | ~ rel_str(X0) ),
    inference(rectify,[],[f63]) ).

fof(f63,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( ( relstr_element_smaller(X0,X1,X2)
              | ? [X3] :
                  ( ~ related(X0,X2,X3)
                  & in(X3,X1)
                  & element(X3,the_carrier(X0)) ) )
            & ( ! [X3] :
                  ( related(X0,X2,X3)
                  | ~ in(X3,X1)
                  | ~ element(X3,the_carrier(X0)) )
              | ~ relstr_element_smaller(X0,X1,X2) ) )
          | ~ element(X2,the_carrier(X0)) )
      | ~ rel_str(X0) ),
    inference(nnf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( relstr_element_smaller(X0,X1,X2)
          <=> ! [X3] :
                ( related(X0,X2,X3)
                | ~ in(X3,X1)
                | ~ element(X3,the_carrier(X0)) ) )
          | ~ element(X2,the_carrier(X0)) )
      | ~ rel_str(X0) ),
    inference(flattening,[],[f36]) ).

fof(f36,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( relstr_element_smaller(X0,X1,X2)
          <=> ! [X3] :
                ( related(X0,X2,X3)
                | ~ in(X3,X1)
                | ~ element(X3,the_carrier(X0)) ) )
          | ~ element(X2,the_carrier(X0)) )
      | ~ rel_str(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] :
      ( rel_str(X0)
     => ! [X1,X2] :
          ( element(X2,the_carrier(X0))
         => ( relstr_element_smaller(X0,X1,X2)
          <=> ! [X3] :
                ( element(X3,the_carrier(X0))
               => ( in(X3,X1)
                 => related(X0,X2,X3) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_lattice3) ).

fof(f452,plain,
    ( spl18_3
    | spl18_4 ),
    inference(avatar_split_clause,[],[f444,f449,f446]) ).

fof(f446,plain,
    ( spl18_3
  <=> ! [X0] :
        ( the_carrier(sK4) = X0
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_3])]) ).

fof(f449,plain,
    ( spl18_4
  <=> sP0(sK4,empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_4])]) ).

fof(f444,plain,
    ! [X0] :
      ( sP0(sK4,empty_set)
      | the_carrier(sK4) = X0
      | ~ empty(X0) ),
    inference(subsumption_resolution,[],[f443,f96]) ).

fof(f443,plain,
    ! [X0] :
      ( ~ rel_str(sK4)
      | sP0(sK4,empty_set)
      | the_carrier(sK4) = X0
      | ~ empty(X0) ),
    inference(resolution,[],[f418,f95]) ).

fof(f418,plain,
    ! [X0,X1] :
      ( ~ lower_bounded_relstr(X0)
      | ~ rel_str(X0)
      | sP0(X0,empty_set)
      | the_carrier(X0) = X1
      | ~ empty(X1) ),
    inference(resolution,[],[f415,f133]) ).

fof(f133,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | X0 = X1
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | X0 = X1
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f28,axiom,
    ! [X0,X1] :
      ~ ( empty(X1)
        & X0 != X1
        & empty(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).

fof(f415,plain,
    ! [X0] :
      ( empty(the_carrier(X0))
      | sP0(X0,empty_set)
      | ~ rel_str(X0)
      | ~ lower_bounded_relstr(X0) ),
    inference(duplicate_literal_removal,[],[f414]) ).

fof(f414,plain,
    ! [X0] :
      ( empty(the_carrier(X0))
      | sP0(X0,empty_set)
      | ~ rel_str(X0)
      | ~ lower_bounded_relstr(X0)
      | ~ rel_str(X0)
      | ~ lower_bounded_relstr(X0) ),
    inference(resolution,[],[f411,f169]) ).

fof(f169,plain,
    ! [X0] :
      ( relstr_set_smaller(X0,empty_set,sK5(X0))
      | ~ rel_str(X0)
      | ~ lower_bounded_relstr(X0) ),
    inference(duplicate_literal_removal,[],[f165]) ).

fof(f165,plain,
    ! [X0] :
      ( relstr_set_smaller(X0,empty_set,sK5(X0))
      | ~ rel_str(X0)
      | ~ lower_bounded_relstr(X0)
      | ~ rel_str(X0) ),
    inference(resolution,[],[f103,f100]) ).

fof(f103,plain,
    ! [X0,X1] :
      ( ~ element(X1,the_carrier(X0))
      | relstr_set_smaller(X0,empty_set,X1)
      | ~ rel_str(X0) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relstr_element_smaller(X0,empty_set,X1)
            & relstr_set_smaller(X0,empty_set,X1) )
          | ~ element(X1,the_carrier(X0)) )
      | ~ rel_str(X0) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f26,axiom,
    ! [X0] :
      ( rel_str(X0)
     => ! [X1] :
          ( element(X1,the_carrier(X0))
         => ( relstr_element_smaller(X0,empty_set,X1)
            & relstr_set_smaller(X0,empty_set,X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_yellow_0) ).

fof(f411,plain,
    ! [X0,X1] :
      ( ~ relstr_set_smaller(X0,X1,sK5(X0))
      | empty(the_carrier(X0))
      | sP0(X0,X1)
      | ~ rel_str(X0)
      | ~ lower_bounded_relstr(X0) ),
    inference(subsumption_resolution,[],[f410,f100]) ).

fof(f410,plain,
    ! [X0,X1] :
      ( ~ relstr_set_smaller(X0,X1,sK5(X0))
      | ~ element(sK5(X0),the_carrier(X0))
      | empty(the_carrier(X0))
      | sP0(X0,X1)
      | ~ rel_str(X0)
      | ~ lower_bounded_relstr(X0) ),
    inference(duplicate_literal_removal,[],[f403]) ).

fof(f403,plain,
    ! [X0,X1] :
      ( ~ relstr_set_smaller(X0,X1,sK5(X0))
      | ~ element(sK5(X0),the_carrier(X0))
      | empty(the_carrier(X0))
      | sP0(X0,X1)
      | ~ rel_str(X0)
      | ~ lower_bounded_relstr(X0)
      | sP0(X0,X1)
      | ~ relstr_set_smaller(X0,X1,sK5(X0)) ),
    inference(resolution,[],[f234,f300]) ).

fof(f300,plain,
    ! [X0,X1] :
      ( ~ in(sK7(X0,X1,sK5(X0)),the_carrier(X0))
      | ~ rel_str(X0)
      | ~ lower_bounded_relstr(X0)
      | sP0(X0,X1)
      | ~ relstr_set_smaller(X0,X1,sK5(X0)) ),
    inference(subsumption_resolution,[],[f297,f100]) ).

fof(f297,plain,
    ! [X0,X1] :
      ( ~ in(sK7(X0,X1,sK5(X0)),the_carrier(X0))
      | ~ rel_str(X0)
      | ~ lower_bounded_relstr(X0)
      | sP0(X0,X1)
      | ~ relstr_set_smaller(X0,X1,sK5(X0))
      | ~ element(sK5(X0),the_carrier(X0)) ),
    inference(resolution,[],[f290,f118]) ).

fof(f118,plain,
    ! [X2,X0,X1] :
      ( ~ related(X0,X2,sK7(X0,X1,X2))
      | sP0(X0,X1)
      | ~ relstr_set_smaller(X0,X1,X2)
      | ~ element(X2,the_carrier(X0)) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ! [X2] :
            ( ( ~ related(X0,X2,sK7(X0,X1,X2))
              & relstr_set_smaller(X0,X1,sK7(X0,X1,X2))
              & element(sK7(X0,X1,X2),the_carrier(X0)) )
            | ~ relstr_set_smaller(X0,X1,X2)
            | ~ element(X2,the_carrier(X0)) ) )
      & ( ( ! [X5] :
              ( related(X0,sK8(X0,X1),X5)
              | ~ relstr_set_smaller(X0,X1,X5)
              | ~ element(X5,the_carrier(X0)) )
          & relstr_set_smaller(X0,X1,sK8(X0,X1))
          & element(sK8(X0,X1),the_carrier(X0)) )
        | ~ sP0(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f69,f71,f70]) ).

fof(f70,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ~ related(X0,X2,X3)
          & relstr_set_smaller(X0,X1,X3)
          & element(X3,the_carrier(X0)) )
     => ( ~ related(X0,X2,sK7(X0,X1,X2))
        & relstr_set_smaller(X0,X1,sK7(X0,X1,X2))
        & element(sK7(X0,X1,X2),the_carrier(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ! [X5] :
              ( related(X0,X4,X5)
              | ~ relstr_set_smaller(X0,X1,X5)
              | ~ element(X5,the_carrier(X0)) )
          & relstr_set_smaller(X0,X1,X4)
          & element(X4,the_carrier(X0)) )
     => ( ! [X5] :
            ( related(X0,sK8(X0,X1),X5)
            | ~ relstr_set_smaller(X0,X1,X5)
            | ~ element(X5,the_carrier(X0)) )
        & relstr_set_smaller(X0,X1,sK8(X0,X1))
        & element(sK8(X0,X1),the_carrier(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ! [X2] :
            ( ? [X3] :
                ( ~ related(X0,X2,X3)
                & relstr_set_smaller(X0,X1,X3)
                & element(X3,the_carrier(X0)) )
            | ~ relstr_set_smaller(X0,X1,X2)
            | ~ element(X2,the_carrier(X0)) ) )
      & ( ? [X4] :
            ( ! [X5] :
                ( related(X0,X4,X5)
                | ~ relstr_set_smaller(X0,X1,X5)
                | ~ element(X5,the_carrier(X0)) )
            & relstr_set_smaller(X0,X1,X4)
            & element(X4,the_carrier(X0)) )
        | ~ sP0(X0,X1) ) ),
    inference(rectify,[],[f68]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ! [X2] :
            ( ? [X3] :
                ( ~ related(X0,X2,X3)
                & relstr_set_smaller(X0,X1,X3)
                & element(X3,the_carrier(X0)) )
            | ~ relstr_set_smaller(X0,X1,X2)
            | ~ element(X2,the_carrier(X0)) ) )
      & ( ? [X2] :
            ( ! [X3] :
                ( related(X0,X2,X3)
                | ~ relstr_set_smaller(X0,X1,X3)
                | ~ element(X3,the_carrier(X0)) )
            & relstr_set_smaller(X0,X1,X2)
            & element(X2,the_carrier(X0)) )
        | ~ sP0(X0,X1) ) ),
    inference(nnf_transformation,[],[f51]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
    <=> ? [X2] :
          ( ! [X3] :
              ( related(X0,X2,X3)
              | ~ relstr_set_smaller(X0,X1,X3)
              | ~ element(X3,the_carrier(X0)) )
          & relstr_set_smaller(X0,X1,X2)
          & element(X2,the_carrier(X0)) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f290,plain,
    ! [X0,X1] :
      ( related(X1,sK5(X1),X0)
      | ~ in(X0,the_carrier(X1))
      | ~ rel_str(X1)
      | ~ lower_bounded_relstr(X1) ),
    inference(subsumption_resolution,[],[f289,f100]) ).

fof(f289,plain,
    ! [X0,X1] :
      ( ~ in(X0,the_carrier(X1))
      | related(X1,sK5(X1),X0)
      | ~ element(sK5(X1),the_carrier(X1))
      | ~ rel_str(X1)
      | ~ lower_bounded_relstr(X1) ),
    inference(subsumption_resolution,[],[f279,f131]) ).

fof(f279,plain,
    ! [X0,X1] :
      ( ~ in(X0,the_carrier(X1))
      | ~ element(X0,the_carrier(X1))
      | related(X1,sK5(X1),X0)
      | ~ element(sK5(X1),the_carrier(X1))
      | ~ rel_str(X1)
      | ~ lower_bounded_relstr(X1) ),
    inference(duplicate_literal_removal,[],[f268]) ).

fof(f268,plain,
    ! [X0,X1] :
      ( ~ in(X0,the_carrier(X1))
      | ~ element(X0,the_carrier(X1))
      | related(X1,sK5(X1),X0)
      | ~ element(sK5(X1),the_carrier(X1))
      | ~ rel_str(X1)
      | ~ lower_bounded_relstr(X1)
      | ~ rel_str(X1) ),
    inference(resolution,[],[f105,f101]) ).

fof(f234,plain,
    ! [X2,X0,X1] :
      ( in(sK7(X0,X1,X2),the_carrier(X0))
      | ~ relstr_set_smaller(X0,X1,X2)
      | ~ element(X2,the_carrier(X0))
      | empty(the_carrier(X0))
      | sP0(X0,X1) ),
    inference(resolution,[],[f116,f132]) ).

fof(f116,plain,
    ! [X2,X0,X1] :
      ( element(sK7(X0,X1,X2),the_carrier(X0))
      | sP0(X0,X1)
      | ~ relstr_set_smaller(X0,X1,X2)
      | ~ element(X2,the_carrier(X0)) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f442,plain,
    spl18_1,
    inference(avatar_contradiction_clause,[],[f441]) ).

fof(f441,plain,
    ( $false
    | spl18_1 ),
    inference(subsumption_resolution,[],[f440,f94]) ).

fof(f440,plain,
    ( ~ antisymmetric_relstr(sK4)
    | spl18_1 ),
    inference(subsumption_resolution,[],[f439,f96]) ).

fof(f439,plain,
    ( ~ rel_str(sK4)
    | ~ antisymmetric_relstr(sK4)
    | spl18_1 ),
    inference(resolution,[],[f438,f119]) ).

fof(f119,plain,
    ! [X0] :
      ( sP1(X0)
      | ~ rel_str(X0)
      | ~ antisymmetric_relstr(X0) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f53,plain,
    ! [X0] :
      ( sP1(X0)
      | ~ rel_str(X0)
      | ~ antisymmetric_relstr(X0) ),
    inference(definition_folding,[],[f42,f52,f51]) ).

fof(f52,plain,
    ! [X0] :
      ( ! [X1] :
          ( ex_sup_of_relstr_set(X0,X1)
        <=> sP0(X0,X1) )
      | ~ sP1(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f42,plain,
    ! [X0] :
      ( ! [X1] :
          ( ex_sup_of_relstr_set(X0,X1)
        <=> ? [X2] :
              ( ! [X3] :
                  ( related(X0,X2,X3)
                  | ~ relstr_set_smaller(X0,X1,X3)
                  | ~ element(X3,the_carrier(X0)) )
              & relstr_set_smaller(X0,X1,X2)
              & element(X2,the_carrier(X0)) ) )
      | ~ rel_str(X0)
      | ~ antisymmetric_relstr(X0) ),
    inference(flattening,[],[f41]) ).

fof(f41,plain,
    ! [X0] :
      ( ! [X1] :
          ( ex_sup_of_relstr_set(X0,X1)
        <=> ? [X2] :
              ( ! [X3] :
                  ( related(X0,X2,X3)
                  | ~ relstr_set_smaller(X0,X1,X3)
                  | ~ element(X3,the_carrier(X0)) )
              & relstr_set_smaller(X0,X1,X2)
              & element(X2,the_carrier(X0)) ) )
      | ~ rel_str(X0)
      | ~ antisymmetric_relstr(X0) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,axiom,
    ! [X0] :
      ( ( rel_str(X0)
        & antisymmetric_relstr(X0) )
     => ! [X1] :
          ( ex_sup_of_relstr_set(X0,X1)
        <=> ? [X2] :
              ( ! [X3] :
                  ( element(X3,the_carrier(X0))
                 => ( relstr_set_smaller(X0,X1,X3)
                   => related(X0,X2,X3) ) )
              & relstr_set_smaller(X0,X1,X2)
              & element(X2,the_carrier(X0)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_yellow_0) ).

fof(f438,plain,
    ( ~ sP1(sK4)
    | spl18_1 ),
    inference(subsumption_resolution,[],[f437,f96]) ).

fof(f437,plain,
    ( ~ rel_str(sK4)
    | ~ sP1(sK4)
    | spl18_1 ),
    inference(subsumption_resolution,[],[f436,f93]) ).

fof(f436,plain,
    ( empty_carrier(sK4)
    | ~ rel_str(sK4)
    | ~ sP1(sK4)
    | spl18_1 ),
    inference(subsumption_resolution,[],[f435,f95]) ).

fof(f435,plain,
    ( ~ lower_bounded_relstr(sK4)
    | empty_carrier(sK4)
    | ~ rel_str(sK4)
    | ~ sP1(sK4)
    | spl18_1 ),
    inference(resolution,[],[f423,f148]) ).

fof(f148,plain,
    ( ~ ex_sup_of_relstr_set(sK4,empty_set)
    | spl18_1 ),
    inference(avatar_component_clause,[],[f146]) ).

fof(f146,plain,
    ( spl18_1
  <=> ex_sup_of_relstr_set(sK4,empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_1])]) ).

fof(f423,plain,
    ! [X0] :
      ( ex_sup_of_relstr_set(X0,empty_set)
      | ~ lower_bounded_relstr(X0)
      | empty_carrier(X0)
      | ~ rel_str(X0)
      | ~ sP1(X0) ),
    inference(resolution,[],[f421,f112]) ).

fof(f112,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | ex_sup_of_relstr_set(X0,X1)
      | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f67,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ex_sup_of_relstr_set(X0,X1)
            | ~ sP0(X0,X1) )
          & ( sP0(X0,X1)
            | ~ ex_sup_of_relstr_set(X0,X1) ) )
      | ~ sP1(X0) ),
    inference(nnf_transformation,[],[f52]) ).

fof(f421,plain,
    ! [X0] :
      ( sP0(X0,empty_set)
      | ~ rel_str(X0)
      | ~ lower_bounded_relstr(X0)
      | empty_carrier(X0) ),
    inference(subsumption_resolution,[],[f417,f99]) ).

fof(f417,plain,
    ! [X0] :
      ( sP0(X0,empty_set)
      | ~ rel_str(X0)
      | ~ lower_bounded_relstr(X0)
      | ~ one_sorted_str(X0)
      | empty_carrier(X0) ),
    inference(resolution,[],[f415,f110]) ).

fof(f153,plain,
    ( ~ spl18_1
    | ~ spl18_2 ),
    inference(avatar_split_clause,[],[f97,f150,f146]) ).

fof(f97,plain,
    ( ~ ex_inf_of_relstr_set(sK4,the_carrier(sK4))
    | ~ ex_sup_of_relstr_set(sK4,empty_set) ),
    inference(cnf_transformation,[],[f58]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SEU360+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36  % Computer : n020.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Fri May  3 11:46:16 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  % (7626)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38  % (7627)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.39  % (7631)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.22/0.39  % (7629)WARNING: value z3 for option sas not known
% 0.22/0.39  % (7630)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.39  % (7628)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.39  % (7629)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.39  % (7632)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.22/0.39  % (7633)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.22/0.40  TRYING [1]
% 0.22/0.40  TRYING [1]
% 0.22/0.40  TRYING [2]
% 0.22/0.40  TRYING [2]
% 0.22/0.40  TRYING [3]
% 0.22/0.41  TRYING [1]
% 0.22/0.42  TRYING [2]
% 0.22/0.42  TRYING [4]
% 0.22/0.42  TRYING [3]
% 0.22/0.42  % (7629)First to succeed.
% 0.22/0.42  % (7629)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-7626"
% 0.22/0.42  % (7629)Refutation found. Thanks to Tanya!
% 0.22/0.42  % SZS status Theorem for theBenchmark
% 0.22/0.42  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.43  % (7629)------------------------------
% 0.22/0.43  % (7629)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.43  % (7629)Termination reason: Refutation
% 0.22/0.43  
% 0.22/0.43  % (7629)Memory used [KB]: 1076
% 0.22/0.43  % (7629)Time elapsed: 0.034 s
% 0.22/0.43  % (7629)Instructions burned: 34 (million)
% 0.22/0.43  % (7626)Success in time 0.061 s
%------------------------------------------------------------------------------