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Drodi---4.1.1.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : Drodi---4.1.1
% Problem  : SEU360+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n017.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 24 02:20:17 PM UTC 2026

% Result   : Theorem 0.15s 0.40s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   25
% Syntax   : Number of formulae    :  126 (   9 unt;  16 def)
%            Number of atoms       :  649 (   0 equ)
%            Maximal formula atoms :   14 (   5 avg)
%            Number of connectives :  905 ( 382   ~; 407   |;  74   &)
%                                         (  24 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   30 (  29 usr;  17 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   2 con; 0-3 aty)
%            Number of variables   :  199 ( 181   !;  18   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [A] :
      ( rel_str(A)
     => ( lower_bounded_relstr(A)
      <=> ? [B] :
            ( relstr_element_smaller(A,the_carrier(A),B)
            & element(B,the_carrier(A)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [A] :
      ( rel_str(A)
     => ! [B,C] :
          ( element(C,the_carrier(A))
         => ( relstr_element_smaller(A,B,C)
          <=> ! [D] :
                ( element(D,the_carrier(A))
               => ( in(D,B)
                 => related(A,C,D) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

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

fof(f19,axiom,
    ! [A] :
      ( ( rel_str(A)
        & antisymmetric_relstr(A) )
     => ! [B] :
          ( ex_sup_of_relstr_set(A,B)
        <=> ? [C] :
              ( ! [D] :
                  ( element(D,the_carrier(A))
                 => ( relstr_set_smaller(A,B,D)
                   => related(A,C,D) ) )
              & relstr_set_smaller(A,B,C)
              & element(C,the_carrier(A)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f20,axiom,
    ! [A] :
      ( ( rel_str(A)
        & antisymmetric_relstr(A) )
     => ! [B] :
          ( ex_inf_of_relstr_set(A,B)
        <=> ? [C] :
              ( ! [D] :
                  ( element(D,the_carrier(A))
                 => ( relstr_element_smaller(A,B,D)
                   => related(A,D,C) ) )
              & relstr_element_smaller(A,B,C)
              & element(C,the_carrier(A)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f22,axiom,
    ! [A,B] :
      ( element(A,B)
     => ( in(A,B)
        | empty(B) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

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

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

fof(f33,plain,
    ! [A] :
      ( ( lower_bounded_relstr(A)
      <=> ? [B] :
            ( relstr_element_smaller(A,the_carrier(A),B)
            & element(B,the_carrier(A)) ) )
      | ~ rel_str(A) ),
    inference(pre_NNF_transformation,[status(thm)],[f3]) ).

fof(f34,plain,
    ! [A] :
      ( ( ( ! [B] :
              ( ~ relstr_element_smaller(A,the_carrier(A),B)
              | ~ element(B,the_carrier(A)) )
          | lower_bounded_relstr(A) )
        & ( ? [B] :
              ( relstr_element_smaller(A,the_carrier(A),B)
              & element(B,the_carrier(A)) )
          | ~ lower_bounded_relstr(A) ) )
      | ~ rel_str(A) ),
    inference(NNF_transformation,[status(thm)],[f33]) ).

fof(f35,plain,
    ! [A] :
      ( ( ( ! [B] :
              ( ~ relstr_element_smaller(A,the_carrier(A),B)
              | ~ element(B,the_carrier(A)) )
          | lower_bounded_relstr(A) )
        & ( ( relstr_element_smaller(A,the_carrier(A),sK0_skl(A))
            & element(sK0_skl(A),the_carrier(A)) )
          | ~ lower_bounded_relstr(A) ) )
      | ~ rel_str(A) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(B,sK0_skl(A))],[f34]) ).

fof(f36,plain,
    ! [X0] :
      ( element(sK0_skl(X0),the_carrier(X0))
      | ~ lower_bounded_relstr(X0)
      | ~ rel_str(X0) ),
    inference(cnf_transformation,[status(thm)],[f35]) ).

fof(f37,plain,
    ! [X0] :
      ( relstr_element_smaller(X0,the_carrier(X0),sK0_skl(X0))
      | ~ lower_bounded_relstr(X0)
      | ~ rel_str(X0) ),
    inference(cnf_transformation,[status(thm)],[f35]) ).

fof(f39,plain,
    ! [A] :
      ( ! [B,C] :
          ( ( relstr_element_smaller(A,B,C)
          <=> ! [D] :
                ( related(A,C,D)
                | ~ in(D,B)
                | ~ element(D,the_carrier(A)) ) )
          | ~ element(C,the_carrier(A)) )
      | ~ rel_str(A) ),
    inference(pre_NNF_transformation,[status(thm)],[f4]) ).

fof(f40,plain,
    ! [A] :
      ( ! [B,C] :
          ( ( ( ? [D] :
                  ( ~ related(A,C,D)
                  & in(D,B)
                  & element(D,the_carrier(A)) )
              | relstr_element_smaller(A,B,C) )
            & ( ! [D] :
                  ( related(A,C,D)
                  | ~ in(D,B)
                  | ~ element(D,the_carrier(A)) )
              | ~ relstr_element_smaller(A,B,C) ) )
          | ~ element(C,the_carrier(A)) )
      | ~ rel_str(A) ),
    inference(NNF_transformation,[status(thm)],[f39]) ).

fof(f41,plain,
    ! [A] :
      ( ! [C] :
          ( ( ! [B] :
                ( ? [D] :
                    ( ~ related(A,C,D)
                    & in(D,B)
                    & element(D,the_carrier(A)) )
                | relstr_element_smaller(A,B,C) )
            & ! [B] :
                ( ! [D] :
                    ( related(A,C,D)
                    | ~ in(D,B)
                    | ~ element(D,the_carrier(A)) )
                | ~ relstr_element_smaller(A,B,C) ) )
          | ~ element(C,the_carrier(A)) )
      | ~ rel_str(A) ),
    inference(miniscoping,[status(thm)],[f40]) ).

fof(f42,plain,
    ! [A] :
      ( ! [C] :
          ( ( ! [B] :
                ( ( ~ related(A,C,sK1_skl(B,C,A))
                  & in(sK1_skl(B,C,A),B)
                  & element(sK1_skl(B,C,A),the_carrier(A)) )
                | relstr_element_smaller(A,B,C) )
            & ! [B] :
                ( ! [D] :
                    ( related(A,C,D)
                    | ~ in(D,B)
                    | ~ element(D,the_carrier(A)) )
                | ~ relstr_element_smaller(A,B,C) ) )
          | ~ element(C,the_carrier(A)) )
      | ~ rel_str(A) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(B,C,A))],[f41]) ).

fof(f43,plain,
    ! [X0,X1,X2,X3] :
      ( related(X0,X1,X3)
      | ~ in(X3,X2)
      | ~ element(X3,the_carrier(X0))
      | ~ relstr_element_smaller(X0,X2,X1)
      | ~ element(X1,the_carrier(X0))
      | ~ rel_str(X0) ),
    inference(cnf_transformation,[status(thm)],[f42]) ).

fof(f47,plain,
    ! [A] :
      ( one_sorted_str(A)
      | ~ rel_str(A) ),
    inference(pre_NNF_transformation,[status(thm)],[f6]) ).

fof(f48,plain,
    ! [X0] :
      ( one_sorted_str(X0)
      | ~ rel_str(X0) ),
    inference(cnf_transformation,[status(thm)],[f47]) ).

fof(f55,plain,
    ! [A] :
      ( ~ empty(the_carrier(A))
      | ~ one_sorted_str(A)
      | empty_carrier(A) ),
    inference(pre_NNF_transformation,[status(thm)],[f13]) ).

fof(f56,plain,
    ! [X0] :
      ( ~ empty(the_carrier(X0))
      | ~ one_sorted_str(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[status(thm)],[f55]) ).

fof(f68,plain,
    ! [A] :
      ( ! [B] :
          ( ex_sup_of_relstr_set(A,B)
        <=> ? [C] :
              ( ! [D] :
                  ( related(A,C,D)
                  | ~ relstr_set_smaller(A,B,D)
                  | ~ element(D,the_carrier(A)) )
              & relstr_set_smaller(A,B,C)
              & element(C,the_carrier(A)) ) )
      | ~ rel_str(A)
      | ~ antisymmetric_relstr(A) ),
    inference(pre_NNF_transformation,[status(thm)],[f19]) ).

fof(f69,plain,
    ! [A] :
      ( ! [B] :
          ( ( ! [C] :
                ( ? [D] :
                    ( ~ related(A,C,D)
                    & relstr_set_smaller(A,B,D)
                    & element(D,the_carrier(A)) )
                | ~ relstr_set_smaller(A,B,C)
                | ~ element(C,the_carrier(A)) )
            | ex_sup_of_relstr_set(A,B) )
          & ( ? [C] :
                ( ! [D] :
                    ( related(A,C,D)
                    | ~ relstr_set_smaller(A,B,D)
                    | ~ element(D,the_carrier(A)) )
                & relstr_set_smaller(A,B,C)
                & element(C,the_carrier(A)) )
            | ~ ex_sup_of_relstr_set(A,B) ) )
      | ~ rel_str(A)
      | ~ antisymmetric_relstr(A) ),
    inference(NNF_transformation,[status(thm)],[f68]) ).

fof(f70,plain,
    ! [A] :
      ( ( ! [B] :
            ( ! [C] :
                ( ? [D] :
                    ( ~ related(A,C,D)
                    & relstr_set_smaller(A,B,D)
                    & element(D,the_carrier(A)) )
                | ~ relstr_set_smaller(A,B,C)
                | ~ element(C,the_carrier(A)) )
            | ex_sup_of_relstr_set(A,B) )
        & ! [B] :
            ( ? [C] :
                ( ! [D] :
                    ( related(A,C,D)
                    | ~ relstr_set_smaller(A,B,D)
                    | ~ element(D,the_carrier(A)) )
                & relstr_set_smaller(A,B,C)
                & element(C,the_carrier(A)) )
            | ~ ex_sup_of_relstr_set(A,B) ) )
      | ~ rel_str(A)
      | ~ antisymmetric_relstr(A) ),
    inference(miniscoping,[status(thm)],[f69]) ).

fof(f71,plain,
    ! [A] :
      ( ( ! [B] :
            ( ! [C] :
                ( ( ~ related(A,C,sK10_skl(C,B,A))
                  & relstr_set_smaller(A,B,sK10_skl(C,B,A))
                  & element(sK10_skl(C,B,A),the_carrier(A)) )
                | ~ relstr_set_smaller(A,B,C)
                | ~ element(C,the_carrier(A)) )
            | ex_sup_of_relstr_set(A,B) )
        & ! [B] :
            ( ( ! [D] :
                  ( related(A,sK9_skl(B,A),D)
                  | ~ relstr_set_smaller(A,B,D)
                  | ~ element(D,the_carrier(A)) )
              & relstr_set_smaller(A,B,sK9_skl(B,A))
              & element(sK9_skl(B,A),the_carrier(A)) )
            | ~ ex_sup_of_relstr_set(A,B) ) )
      | ~ rel_str(A)
      | ~ antisymmetric_relstr(A) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl]),skolemize(C,sK9_skl(B,A)),skolemize(D,sK10_skl(C,B,A))],[f70]) ).

fof(f75,plain,
    ! [X0,X1,X2] :
      ( element(sK10_skl(X2,X1,X0),the_carrier(X0))
      | ~ relstr_set_smaller(X0,X1,X2)
      | ~ element(X2,the_carrier(X0))
      | ex_sup_of_relstr_set(X0,X1)
      | ~ rel_str(X0)
      | ~ antisymmetric_relstr(X0) ),
    inference(cnf_transformation,[status(thm)],[f71]) ).

fof(f77,plain,
    ! [X0,X1,X2] :
      ( ~ related(X0,X2,sK10_skl(X2,X1,X0))
      | ~ relstr_set_smaller(X0,X1,X2)
      | ~ element(X2,the_carrier(X0))
      | ex_sup_of_relstr_set(X0,X1)
      | ~ rel_str(X0)
      | ~ antisymmetric_relstr(X0) ),
    inference(cnf_transformation,[status(thm)],[f71]) ).

fof(f78,plain,
    ! [A] :
      ( ! [B] :
          ( ex_inf_of_relstr_set(A,B)
        <=> ? [C] :
              ( ! [D] :
                  ( related(A,D,C)
                  | ~ relstr_element_smaller(A,B,D)
                  | ~ element(D,the_carrier(A)) )
              & relstr_element_smaller(A,B,C)
              & element(C,the_carrier(A)) ) )
      | ~ rel_str(A)
      | ~ antisymmetric_relstr(A) ),
    inference(pre_NNF_transformation,[status(thm)],[f20]) ).

fof(f79,plain,
    ! [A] :
      ( ! [B] :
          ( ( ! [C] :
                ( ? [D] :
                    ( ~ related(A,D,C)
                    & relstr_element_smaller(A,B,D)
                    & element(D,the_carrier(A)) )
                | ~ relstr_element_smaller(A,B,C)
                | ~ element(C,the_carrier(A)) )
            | ex_inf_of_relstr_set(A,B) )
          & ( ? [C] :
                ( ! [D] :
                    ( related(A,D,C)
                    | ~ relstr_element_smaller(A,B,D)
                    | ~ element(D,the_carrier(A)) )
                & relstr_element_smaller(A,B,C)
                & element(C,the_carrier(A)) )
            | ~ ex_inf_of_relstr_set(A,B) ) )
      | ~ rel_str(A)
      | ~ antisymmetric_relstr(A) ),
    inference(NNF_transformation,[status(thm)],[f78]) ).

fof(f80,plain,
    ! [A] :
      ( ( ! [B] :
            ( ! [C] :
                ( ? [D] :
                    ( ~ related(A,D,C)
                    & relstr_element_smaller(A,B,D)
                    & element(D,the_carrier(A)) )
                | ~ relstr_element_smaller(A,B,C)
                | ~ element(C,the_carrier(A)) )
            | ex_inf_of_relstr_set(A,B) )
        & ! [B] :
            ( ? [C] :
                ( ! [D] :
                    ( related(A,D,C)
                    | ~ relstr_element_smaller(A,B,D)
                    | ~ element(D,the_carrier(A)) )
                & relstr_element_smaller(A,B,C)
                & element(C,the_carrier(A)) )
            | ~ ex_inf_of_relstr_set(A,B) ) )
      | ~ rel_str(A)
      | ~ antisymmetric_relstr(A) ),
    inference(miniscoping,[status(thm)],[f79]) ).

fof(f81,plain,
    ! [A] :
      ( ( ! [B] :
            ( ! [C] :
                ( ( ~ related(A,sK12_skl(C,B,A),C)
                  & relstr_element_smaller(A,B,sK12_skl(C,B,A))
                  & element(sK12_skl(C,B,A),the_carrier(A)) )
                | ~ relstr_element_smaller(A,B,C)
                | ~ element(C,the_carrier(A)) )
            | ex_inf_of_relstr_set(A,B) )
        & ! [B] :
            ( ( ! [D] :
                  ( related(A,D,sK11_skl(B,A))
                  | ~ relstr_element_smaller(A,B,D)
                  | ~ element(D,the_carrier(A)) )
              & relstr_element_smaller(A,B,sK11_skl(B,A))
              & element(sK11_skl(B,A),the_carrier(A)) )
            | ~ ex_inf_of_relstr_set(A,B) ) )
      | ~ rel_str(A)
      | ~ antisymmetric_relstr(A) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl]),skolemize(C,sK11_skl(B,A)),skolemize(D,sK12_skl(C,B,A))],[f80]) ).

fof(f85,plain,
    ! [X0,X1,X2] :
      ( element(sK12_skl(X2,X1,X0),the_carrier(X0))
      | ~ relstr_element_smaller(X0,X1,X2)
      | ~ element(X2,the_carrier(X0))
      | ex_inf_of_relstr_set(X0,X1)
      | ~ rel_str(X0)
      | ~ antisymmetric_relstr(X0) ),
    inference(cnf_transformation,[status(thm)],[f81]) ).

fof(f86,plain,
    ! [X0,X1,X2] :
      ( relstr_element_smaller(X0,X1,sK12_skl(X2,X1,X0))
      | ~ relstr_element_smaller(X0,X1,X2)
      | ~ element(X2,the_carrier(X0))
      | ex_inf_of_relstr_set(X0,X1)
      | ~ rel_str(X0)
      | ~ antisymmetric_relstr(X0) ),
    inference(cnf_transformation,[status(thm)],[f81]) ).

fof(f87,plain,
    ! [X0,X1,X2] :
      ( ~ related(X0,sK12_skl(X2,X1,X0),X2)
      | ~ relstr_element_smaller(X0,X1,X2)
      | ~ element(X2,the_carrier(X0))
      | ex_inf_of_relstr_set(X0,X1)
      | ~ rel_str(X0)
      | ~ antisymmetric_relstr(X0) ),
    inference(cnf_transformation,[status(thm)],[f81]) ).

fof(f90,plain,
    ! [A,B] :
      ( in(A,B)
      | empty(B)
      | ~ element(A,B) ),
    inference(pre_NNF_transformation,[status(thm)],[f22]) ).

fof(f91,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(cnf_transformation,[status(thm)],[f90]) ).

fof(f92,plain,
    ? [A] :
      ( ( ~ ex_inf_of_relstr_set(A,the_carrier(A))
        | ~ ex_sup_of_relstr_set(A,empty_set) )
      & rel_str(A)
      & lower_bounded_relstr(A)
      & antisymmetric_relstr(A)
      & ~ empty_carrier(A) ),
    inference(pre_NNF_transformation,[status(thm)],[f24]) ).

fof(f93,plain,
    ( ( ~ ex_inf_of_relstr_set(sK13_skl,the_carrier(sK13_skl))
      | ~ ex_sup_of_relstr_set(sK13_skl,empty_set) )
    & rel_str(sK13_skl)
    & lower_bounded_relstr(sK13_skl)
    & antisymmetric_relstr(sK13_skl)
    & ~ empty_carrier(sK13_skl) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl]),skolemize(A,sK13_skl)],[f92]) ).

fof(f94,plain,
    ~ empty_carrier(sK13_skl),
    inference(cnf_transformation,[status(thm)],[f93]) ).

fof(f95,plain,
    antisymmetric_relstr(sK13_skl),
    inference(cnf_transformation,[status(thm)],[f93]) ).

fof(f96,plain,
    lower_bounded_relstr(sK13_skl),
    inference(cnf_transformation,[status(thm)],[f93]) ).

fof(f97,plain,
    rel_str(sK13_skl),
    inference(cnf_transformation,[status(thm)],[f93]) ).

fof(f98,plain,
    ( ~ ex_inf_of_relstr_set(sK13_skl,the_carrier(sK13_skl))
    | ~ ex_sup_of_relstr_set(sK13_skl,empty_set) ),
    inference(cnf_transformation,[status(thm)],[f93]) ).

fof(f101,plain,
    ! [A] :
      ( ! [B] :
          ( ( relstr_element_smaller(A,empty_set,B)
            & relstr_set_smaller(A,empty_set,B) )
          | ~ element(B,the_carrier(A)) )
      | ~ rel_str(A) ),
    inference(pre_NNF_transformation,[status(thm)],[f26]) ).

fof(f102,plain,
    ! [X0,X1] :
      ( relstr_set_smaller(X0,empty_set,X1)
      | ~ element(X1,the_carrier(X0))
      | ~ rel_str(X0) ),
    inference(cnf_transformation,[status(thm)],[f101]) ).

fof(f110,definition,
    ( sQ0_spl
  <=> ex_sup_of_relstr_set(sK13_skl,empty_set) ),
    introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).

fof(f112,plain,
    ( sQ0_spl
    | ~ ex_sup_of_relstr_set(sK13_skl,empty_set) ),
    inference(component_clause,[status(thm)],[f110]) ).

fof(f113,definition,
    ( sQ1_spl
  <=> ex_inf_of_relstr_set(sK13_skl,the_carrier(sK13_skl)) ),
    introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).

fof(f115,plain,
    ( sQ1_spl
    | ~ ex_inf_of_relstr_set(sK13_skl,the_carrier(sK13_skl)) ),
    inference(component_clause,[status(thm)],[f113]) ).

fof(f116,plain,
    ( ~ sQ1_spl
    | ~ sQ0_spl ),
    inference(split_clause,[status(thm)],[f98,f110,f113]) ).

fof(f118,plain,
    ! [X0] :
      ( relstr_set_smaller(X0,empty_set,sK0_skl(X0))
      | ~ rel_str(X0)
      | ~ lower_bounded_relstr(X0)
      | ~ rel_str(X0) ),
    inference(resolution,[status(thm)],[f36,f102]) ).

fof(f119,plain,
    ! [X0] :
      ( relstr_set_smaller(X0,empty_set,sK0_skl(X0))
      | ~ lower_bounded_relstr(X0)
      | ~ rel_str(X0) ),
    inference(duplicate_literals_removal,[status(thm)],[f118]) ).

fof(f130,plain,
    ! [X0,X1,X2,X3] :
      ( related(X2,X3,X0)
      | ~ element(X0,the_carrier(X2))
      | ~ relstr_element_smaller(X2,X1,X3)
      | ~ element(X3,the_carrier(X2))
      | ~ rel_str(X2)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(resolution,[status(thm)],[f91,f43]) ).

fof(f134,plain,
    ! [X0,X1,X2] :
      ( related(sK13_skl,X2,X0)
      | ~ element(X0,the_carrier(sK13_skl))
      | ~ relstr_element_smaller(sK13_skl,X1,X2)
      | ~ element(X2,the_carrier(sK13_skl))
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(resolution,[status(thm)],[f130,f97]) ).

fof(f163,plain,
    ! [X0,X1,X2] :
      ( ~ relstr_element_smaller(sK13_skl,X2,X0)
      | ~ element(X0,the_carrier(sK13_skl))
      | ex_inf_of_relstr_set(sK13_skl,X2)
      | ~ rel_str(sK13_skl)
      | ~ antisymmetric_relstr(sK13_skl)
      | ~ element(X0,the_carrier(sK13_skl))
      | ~ relstr_element_smaller(sK13_skl,X1,sK12_skl(X0,X2,sK13_skl))
      | ~ element(sK12_skl(X0,X2,sK13_skl),the_carrier(sK13_skl))
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(resolution,[status(thm)],[f134,f87]) ).

fof(f164,plain,
    ! [X0,X1,X2] :
      ( ~ relstr_set_smaller(sK13_skl,X1,X0)
      | ~ element(X0,the_carrier(sK13_skl))
      | ex_sup_of_relstr_set(sK13_skl,X1)
      | ~ rel_str(sK13_skl)
      | ~ antisymmetric_relstr(sK13_skl)
      | ~ element(sK10_skl(X0,X1,sK13_skl),the_carrier(sK13_skl))
      | ~ relstr_element_smaller(sK13_skl,X2,X0)
      | ~ element(X0,the_carrier(sK13_skl))
      | empty(X2)
      | ~ element(sK10_skl(X0,X1,sK13_skl),X2) ),
    inference(resolution,[status(thm)],[f134,f77]) ).

fof(f166,definition,
    ! [X0,X1,X2] :
      ( sQ7_spl
    <=> ( ~ relstr_element_smaller(sK13_skl,X2,X0)
        | ~ element(X0,the_carrier(sK13_skl))
        | ex_inf_of_relstr_set(sK13_skl,X2)
        | ~ element(X0,the_carrier(sK13_skl))
        | ~ relstr_element_smaller(sK13_skl,X1,sK12_skl(X0,X2,sK13_skl))
        | ~ element(sK12_skl(X0,X2,sK13_skl),the_carrier(sK13_skl))
        | empty(X1)
        | ~ element(X0,X1) ) ),
    introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).

fof(f167,plain,
    ! [X0,X1,X2] :
      ( ~ sQ7_spl
      | ~ relstr_element_smaller(sK13_skl,X2,X0)
      | ~ element(X0,the_carrier(sK13_skl))
      | ex_inf_of_relstr_set(sK13_skl,X2)
      | ~ element(X0,the_carrier(sK13_skl))
      | ~ relstr_element_smaller(sK13_skl,X1,sK12_skl(X0,X2,sK13_skl))
      | ~ element(sK12_skl(X0,X2,sK13_skl),the_carrier(sK13_skl))
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(component_clause,[status(thm)],[f166]) ).

fof(f169,definition,
    ( sQ8_spl
  <=> antisymmetric_relstr(sK13_skl) ),
    introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).

fof(f171,plain,
    ( sQ8_spl
    | ~ antisymmetric_relstr(sK13_skl) ),
    inference(component_clause,[status(thm)],[f169]) ).

fof(f172,definition,
    ( sQ9_spl
  <=> rel_str(sK13_skl) ),
    introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).

fof(f174,plain,
    ( sQ9_spl
    | ~ rel_str(sK13_skl) ),
    inference(component_clause,[status(thm)],[f172]) ).

fof(f175,plain,
    ( ~ sQ9_spl
    | ~ sQ8_spl
    | sQ7_spl ),
    inference(split_clause,[status(thm)],[f163,f166,f169,f172]) ).

fof(f176,definition,
    ! [X0,X1,X2] :
      ( sQ10_spl
    <=> ( ~ relstr_set_smaller(sK13_skl,X1,X0)
        | ~ element(X0,the_carrier(sK13_skl))
        | ex_sup_of_relstr_set(sK13_skl,X1)
        | ~ element(sK10_skl(X0,X1,sK13_skl),the_carrier(sK13_skl))
        | ~ relstr_element_smaller(sK13_skl,X2,X0)
        | ~ element(X0,the_carrier(sK13_skl))
        | empty(X2)
        | ~ element(sK10_skl(X0,X1,sK13_skl),X2) ) ),
    introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).

fof(f177,plain,
    ! [X0,X1,X2] :
      ( ~ sQ10_spl
      | ~ relstr_set_smaller(sK13_skl,X1,X0)
      | ~ element(X0,the_carrier(sK13_skl))
      | ex_sup_of_relstr_set(sK13_skl,X1)
      | ~ element(sK10_skl(X0,X1,sK13_skl),the_carrier(sK13_skl))
      | ~ relstr_element_smaller(sK13_skl,X2,X0)
      | ~ element(X0,the_carrier(sK13_skl))
      | empty(X2)
      | ~ element(sK10_skl(X0,X1,sK13_skl),X2) ),
    inference(component_clause,[status(thm)],[f176]) ).

fof(f179,plain,
    ( ~ sQ9_spl
    | ~ sQ8_spl
    | sQ10_spl ),
    inference(split_clause,[status(thm)],[f164,f176,f169,f172]) ).

fof(f184,plain,
    ( sQ9_spl
    | $false ),
    inference(forward_subsumption_resolution,[status(thm)],[f174,f97]) ).

fof(f185,plain,
    sQ9_spl,
    inference(contradiction_clause,[status(thm)],[f184]) ).

fof(f186,plain,
    ( sQ8_spl
    | $false ),
    inference(forward_subsumption_resolution,[status(thm)],[f171,f95]) ).

fof(f187,plain,
    sQ8_spl,
    inference(contradiction_clause,[status(thm)],[f186]) ).

fof(f189,plain,
    ! [X0,X1,X2] :
      ( ~ sQ7_spl
      | ~ relstr_element_smaller(sK13_skl,X2,X0)
      | ex_inf_of_relstr_set(sK13_skl,X2)
      | ~ element(X0,the_carrier(sK13_skl))
      | ~ relstr_element_smaller(sK13_skl,X1,sK12_skl(X0,X2,sK13_skl))
      | ~ element(sK12_skl(X0,X2,sK13_skl),the_carrier(sK13_skl))
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(duplicate_literals_removal,[status(thm)],[f167]) ).

fof(f190,plain,
    ! [X0,X1,X2] :
      ( ~ sQ10_spl
      | ~ relstr_set_smaller(sK13_skl,X1,X0)
      | ex_sup_of_relstr_set(sK13_skl,X1)
      | ~ element(sK10_skl(X0,X1,sK13_skl),the_carrier(sK13_skl))
      | ~ relstr_element_smaller(sK13_skl,X2,X0)
      | ~ element(X0,the_carrier(sK13_skl))
      | empty(X2)
      | ~ element(sK10_skl(X0,X1,sK13_skl),X2) ),
    inference(duplicate_literals_removal,[status(thm)],[f177]) ).

fof(f191,plain,
    ! [X0,X1,X2] :
      ( ~ sQ7_spl
      | ~ relstr_element_smaller(sK13_skl,X2,X0)
      | ~ element(X0,the_carrier(sK13_skl))
      | ex_inf_of_relstr_set(sK13_skl,X2)
      | ~ rel_str(sK13_skl)
      | ~ antisymmetric_relstr(sK13_skl)
      | ~ relstr_element_smaller(sK13_skl,X2,X0)
      | ex_inf_of_relstr_set(sK13_skl,X2)
      | ~ element(X0,the_carrier(sK13_skl))
      | ~ relstr_element_smaller(sK13_skl,X1,sK12_skl(X0,X2,sK13_skl))
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(resolution,[status(thm)],[f189,f85]) ).

fof(f192,definition,
    ! [X0,X1,X2] :
      ( sQ12_spl
    <=> ( ~ relstr_element_smaller(sK13_skl,X2,X0)
        | ~ element(X0,the_carrier(sK13_skl))
        | ex_inf_of_relstr_set(sK13_skl,X2)
        | ~ relstr_element_smaller(sK13_skl,X2,X0)
        | ex_inf_of_relstr_set(sK13_skl,X2)
        | ~ element(X0,the_carrier(sK13_skl))
        | ~ relstr_element_smaller(sK13_skl,X1,sK12_skl(X0,X2,sK13_skl))
        | empty(X1)
        | ~ element(X0,X1) ) ),
    introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).

fof(f193,plain,
    ! [X0,X1,X2] :
      ( ~ sQ12_spl
      | ~ relstr_element_smaller(sK13_skl,X2,X0)
      | ~ element(X0,the_carrier(sK13_skl))
      | ex_inf_of_relstr_set(sK13_skl,X2)
      | ~ relstr_element_smaller(sK13_skl,X2,X0)
      | ex_inf_of_relstr_set(sK13_skl,X2)
      | ~ element(X0,the_carrier(sK13_skl))
      | ~ relstr_element_smaller(sK13_skl,X1,sK12_skl(X0,X2,sK13_skl))
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(component_clause,[status(thm)],[f192]) ).

fof(f195,plain,
    ( ~ sQ7_spl
    | ~ sQ9_spl
    | ~ sQ8_spl
    | sQ12_spl ),
    inference(split_clause,[status(thm)],[f191,f192,f169,f172,f166]) ).

fof(f196,plain,
    ! [X0,X1,X2] :
      ( ~ sQ12_spl
      | ~ relstr_element_smaller(sK13_skl,X2,X0)
      | ex_inf_of_relstr_set(sK13_skl,X2)
      | ~ element(X0,the_carrier(sK13_skl))
      | ~ relstr_element_smaller(sK13_skl,X1,sK12_skl(X0,X2,sK13_skl))
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(duplicate_literals_removal,[status(thm)],[f193]) ).

fof(f212,plain,
    ! [X0,X1,X2] :
      ( ~ sQ10_spl
      | ~ relstr_set_smaller(sK13_skl,X1,X0)
      | ~ element(X0,the_carrier(sK13_skl))
      | ex_sup_of_relstr_set(sK13_skl,X1)
      | ~ rel_str(sK13_skl)
      | ~ antisymmetric_relstr(sK13_skl)
      | ~ relstr_set_smaller(sK13_skl,X1,X0)
      | ex_sup_of_relstr_set(sK13_skl,X1)
      | ~ relstr_element_smaller(sK13_skl,X2,X0)
      | ~ element(X0,the_carrier(sK13_skl))
      | empty(X2)
      | ~ element(sK10_skl(X0,X1,sK13_skl),X2) ),
    inference(resolution,[status(thm)],[f190,f75]) ).

fof(f213,definition,
    ! [X0,X1,X2] :
      ( sQ16_spl
    <=> ( ~ relstr_set_smaller(sK13_skl,X1,X0)
        | ~ element(X0,the_carrier(sK13_skl))
        | ex_sup_of_relstr_set(sK13_skl,X1)
        | ~ relstr_set_smaller(sK13_skl,X1,X0)
        | ex_sup_of_relstr_set(sK13_skl,X1)
        | ~ relstr_element_smaller(sK13_skl,X2,X0)
        | ~ element(X0,the_carrier(sK13_skl))
        | empty(X2)
        | ~ element(sK10_skl(X0,X1,sK13_skl),X2) ) ),
    introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).

fof(f214,plain,
    ! [X0,X1,X2] :
      ( ~ sQ16_spl
      | ~ relstr_set_smaller(sK13_skl,X1,X0)
      | ~ element(X0,the_carrier(sK13_skl))
      | ex_sup_of_relstr_set(sK13_skl,X1)
      | ~ relstr_set_smaller(sK13_skl,X1,X0)
      | ex_sup_of_relstr_set(sK13_skl,X1)
      | ~ relstr_element_smaller(sK13_skl,X2,X0)
      | ~ element(X0,the_carrier(sK13_skl))
      | empty(X2)
      | ~ element(sK10_skl(X0,X1,sK13_skl),X2) ),
    inference(component_clause,[status(thm)],[f213]) ).

fof(f216,plain,
    ( ~ sQ10_spl
    | ~ sQ9_spl
    | ~ sQ8_spl
    | sQ16_spl ),
    inference(split_clause,[status(thm)],[f212,f213,f169,f172,f176]) ).

fof(f217,plain,
    ! [X0,X1,X2] :
      ( ~ sQ16_spl
      | ~ relstr_set_smaller(sK13_skl,X1,X0)
      | ex_sup_of_relstr_set(sK13_skl,X1)
      | ~ relstr_element_smaller(sK13_skl,X2,X0)
      | ~ element(X0,the_carrier(sK13_skl))
      | empty(X2)
      | ~ element(sK10_skl(X0,X1,sK13_skl),X2) ),
    inference(duplicate_literals_removal,[status(thm)],[f214]) ).

fof(f218,plain,
    ! [X0,X1] :
      ( ~ sQ16_spl
      | ~ relstr_set_smaller(sK13_skl,X1,X0)
      | ~ element(X0,the_carrier(sK13_skl))
      | ex_sup_of_relstr_set(sK13_skl,X1)
      | ~ rel_str(sK13_skl)
      | ~ antisymmetric_relstr(sK13_skl)
      | ~ relstr_set_smaller(sK13_skl,X1,X0)
      | ex_sup_of_relstr_set(sK13_skl,X1)
      | ~ relstr_element_smaller(sK13_skl,the_carrier(sK13_skl),X0)
      | ~ element(X0,the_carrier(sK13_skl))
      | empty(the_carrier(sK13_skl)) ),
    inference(resolution,[status(thm)],[f217,f75]) ).

fof(f219,definition,
    ( sQ17_spl
  <=> empty(the_carrier(sK13_skl)) ),
    introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).

fof(f220,plain,
    ( ~ sQ17_spl
    | empty(the_carrier(sK13_skl)) ),
    inference(component_clause,[status(thm)],[f219]) ).

fof(f222,definition,
    ! [X0,X1] :
      ( sQ18_spl
    <=> ( ~ relstr_set_smaller(sK13_skl,X1,X0)
        | ~ element(X0,the_carrier(sK13_skl))
        | ex_sup_of_relstr_set(sK13_skl,X1)
        | ~ relstr_set_smaller(sK13_skl,X1,X0)
        | ex_sup_of_relstr_set(sK13_skl,X1)
        | ~ relstr_element_smaller(sK13_skl,the_carrier(sK13_skl),X0)
        | ~ element(X0,the_carrier(sK13_skl)) ) ),
    introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).

fof(f223,plain,
    ! [X0,X1] :
      ( ~ sQ18_spl
      | ~ relstr_set_smaller(sK13_skl,X1,X0)
      | ~ element(X0,the_carrier(sK13_skl))
      | ex_sup_of_relstr_set(sK13_skl,X1)
      | ~ relstr_set_smaller(sK13_skl,X1,X0)
      | ex_sup_of_relstr_set(sK13_skl,X1)
      | ~ relstr_element_smaller(sK13_skl,the_carrier(sK13_skl),X0)
      | ~ element(X0,the_carrier(sK13_skl)) ),
    inference(component_clause,[status(thm)],[f222]) ).

fof(f225,plain,
    ( ~ sQ16_spl
    | ~ sQ9_spl
    | ~ sQ8_spl
    | sQ18_spl
    | sQ17_spl ),
    inference(split_clause,[status(thm)],[f218,f219,f222,f169,f172,f213]) ).

fof(f241,plain,
    ( ~ sQ17_spl
    | ~ one_sorted_str(sK13_skl)
    | empty_carrier(sK13_skl) ),
    inference(resolution,[status(thm)],[f220,f56]) ).

fof(f244,definition,
    ( sQ22_spl
  <=> empty_carrier(sK13_skl) ),
    introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).

fof(f245,plain,
    ( ~ sQ22_spl
    | empty_carrier(sK13_skl) ),
    inference(component_clause,[status(thm)],[f244]) ).

fof(f247,definition,
    ( sQ23_spl
  <=> one_sorted_str(sK13_skl) ),
    introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).

fof(f249,plain,
    ( sQ23_spl
    | ~ one_sorted_str(sK13_skl) ),
    inference(component_clause,[status(thm)],[f247]) ).

fof(f250,plain,
    ( ~ sQ17_spl
    | ~ sQ23_spl
    | sQ22_spl ),
    inference(split_clause,[status(thm)],[f241,f244,f247,f219]) ).

fof(f251,plain,
    ( ~ sQ22_spl
    | $false ),
    inference(forward_subsumption_resolution,[status(thm)],[f245,f94]) ).

fof(f252,plain,
    ~ sQ22_spl,
    inference(contradiction_clause,[status(thm)],[f251]) ).

fof(f253,plain,
    ( sQ23_spl
    | ~ rel_str(sK13_skl) ),
    inference(resolution,[status(thm)],[f249,f48]) ).

fof(f254,plain,
    ( sQ23_spl
    | ~ sQ9_spl ),
    inference(split_clause,[status(thm)],[f253,f172,f247]) ).

fof(f255,plain,
    ! [X0,X1] :
      ( ~ sQ18_spl
      | ~ relstr_set_smaller(sK13_skl,X1,X0)
      | ex_sup_of_relstr_set(sK13_skl,X1)
      | ~ relstr_element_smaller(sK13_skl,the_carrier(sK13_skl),X0)
      | ~ element(X0,the_carrier(sK13_skl)) ),
    inference(duplicate_literals_removal,[status(thm)],[f223]) ).

fof(f256,plain,
    ! [X0] :
      ( sQ0_spl
      | ~ sQ18_spl
      | ~ relstr_set_smaller(sK13_skl,empty_set,X0)
      | ~ relstr_element_smaller(sK13_skl,the_carrier(sK13_skl),X0)
      | ~ element(X0,the_carrier(sK13_skl)) ),
    inference(resolution,[status(thm)],[f255,f112]) ).

fof(f276,plain,
    ( sQ0_spl
    | ~ sQ18_spl
    | ~ lower_bounded_relstr(sK13_skl)
    | ~ rel_str(sK13_skl)
    | ~ relstr_set_smaller(sK13_skl,empty_set,sK0_skl(sK13_skl))
    | ~ element(sK0_skl(sK13_skl),the_carrier(sK13_skl)) ),
    inference(resolution,[status(thm)],[f256,f37]) ).

fof(f290,definition,
    ( sQ30_spl
  <=> element(sK0_skl(sK13_skl),the_carrier(sK13_skl)) ),
    introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).

fof(f292,plain,
    ( sQ30_spl
    | ~ element(sK0_skl(sK13_skl),the_carrier(sK13_skl)) ),
    inference(component_clause,[status(thm)],[f290]) ).

fof(f293,definition,
    ( sQ31_spl
  <=> relstr_set_smaller(sK13_skl,empty_set,sK0_skl(sK13_skl)) ),
    introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).

fof(f295,plain,
    ( sQ31_spl
    | ~ relstr_set_smaller(sK13_skl,empty_set,sK0_skl(sK13_skl)) ),
    inference(component_clause,[status(thm)],[f293]) ).

fof(f296,definition,
    ( sQ32_spl
  <=> lower_bounded_relstr(sK13_skl) ),
    introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).

fof(f298,plain,
    ( sQ32_spl
    | ~ lower_bounded_relstr(sK13_skl) ),
    inference(component_clause,[status(thm)],[f296]) ).

fof(f299,plain,
    ( sQ0_spl
    | ~ sQ18_spl
    | ~ sQ32_spl
    | ~ sQ9_spl
    | ~ sQ31_spl
    | ~ sQ30_spl ),
    inference(split_clause,[status(thm)],[f276,f290,f293,f172,f296,f222,f110]) ).

fof(f322,plain,
    ! [X0,X1] :
      ( ~ sQ12_spl
      | sQ1_spl
      | ~ relstr_element_smaller(sK13_skl,the_carrier(sK13_skl),X0)
      | ~ element(X0,the_carrier(sK13_skl))
      | ~ relstr_element_smaller(sK13_skl,X1,sK12_skl(X0,the_carrier(sK13_skl),sK13_skl))
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(resolution,[status(thm)],[f115,f196]) ).

fof(f374,plain,
    ! [X0] :
      ( ~ sQ12_spl
      | sQ1_spl
      | ~ relstr_element_smaller(sK13_skl,the_carrier(sK13_skl),X0)
      | ~ element(X0,the_carrier(sK13_skl))
      | ex_inf_of_relstr_set(sK13_skl,the_carrier(sK13_skl))
      | ~ rel_str(sK13_skl)
      | ~ antisymmetric_relstr(sK13_skl)
      | ~ relstr_element_smaller(sK13_skl,the_carrier(sK13_skl),X0)
      | ~ element(X0,the_carrier(sK13_skl))
      | empty(the_carrier(sK13_skl))
      | ~ element(X0,the_carrier(sK13_skl)) ),
    inference(resolution,[status(thm)],[f322,f86]) ).

fof(f384,definition,
    ! [X0] :
      ( sQ49_spl
    <=> ( ~ relstr_element_smaller(sK13_skl,the_carrier(sK13_skl),X0)
        | ~ element(X0,the_carrier(sK13_skl))
        | ~ relstr_element_smaller(sK13_skl,the_carrier(sK13_skl),X0)
        | ~ element(X0,the_carrier(sK13_skl))
        | ~ element(X0,the_carrier(sK13_skl)) ) ),
    introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).

fof(f385,plain,
    ! [X0] :
      ( ~ sQ49_spl
      | ~ relstr_element_smaller(sK13_skl,the_carrier(sK13_skl),X0)
      | ~ element(X0,the_carrier(sK13_skl))
      | ~ relstr_element_smaller(sK13_skl,the_carrier(sK13_skl),X0)
      | ~ element(X0,the_carrier(sK13_skl))
      | ~ element(X0,the_carrier(sK13_skl)) ),
    inference(component_clause,[status(thm)],[f384]) ).

fof(f387,plain,
    ( ~ sQ12_spl
    | sQ1_spl
    | ~ sQ9_spl
    | ~ sQ8_spl
    | sQ17_spl
    | sQ49_spl ),
    inference(split_clause,[status(thm)],[f374,f384,f219,f169,f172,f113,f192]) ).

fof(f396,plain,
    ! [X0] :
      ( ~ sQ49_spl
      | ~ relstr_element_smaller(sK13_skl,the_carrier(sK13_skl),X0)
      | ~ element(X0,the_carrier(sK13_skl)) ),
    inference(duplicate_literals_removal,[status(thm)],[f385]) ).

fof(f398,plain,
    ( ~ sQ49_spl
    | ~ lower_bounded_relstr(sK13_skl)
    | ~ rel_str(sK13_skl)
    | ~ element(sK0_skl(sK13_skl),the_carrier(sK13_skl)) ),
    inference(resolution,[status(thm)],[f396,f37]) ).

fof(f403,plain,
    ( ~ sQ49_spl
    | ~ sQ32_spl
    | ~ sQ9_spl
    | ~ sQ30_spl ),
    inference(split_clause,[status(thm)],[f398,f290,f172,f296,f384]) ).

fof(f418,plain,
    ( sQ30_spl
    | ~ lower_bounded_relstr(sK13_skl)
    | ~ rel_str(sK13_skl) ),
    inference(resolution,[status(thm)],[f292,f36]) ).

fof(f419,plain,
    ( sQ30_spl
    | ~ sQ32_spl
    | ~ sQ9_spl ),
    inference(split_clause,[status(thm)],[f418,f172,f296,f290]) ).

fof(f420,plain,
    ( sQ32_spl
    | $false ),
    inference(forward_subsumption_resolution,[status(thm)],[f298,f96]) ).

fof(f421,plain,
    sQ32_spl,
    inference(contradiction_clause,[status(thm)],[f420]) ).

fof(f441,plain,
    ( sQ31_spl
    | ~ lower_bounded_relstr(sK13_skl)
    | ~ rel_str(sK13_skl) ),
    inference(resolution,[status(thm)],[f295,f119]) ).

fof(f442,plain,
    ( sQ31_spl
    | ~ sQ32_spl
    | ~ sQ9_spl ),
    inference(split_clause,[status(thm)],[f441,f172,f296,f293]) ).

fof(f443,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f116,f175,f179,f185,f187,f195,f216,f225,f250,f252,f254,f299,f387,f403,f419,f421,f442]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SEU360+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04  % Command  : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36  % Computer : n017.cluster.edu
% 0.09/0.36  % Model    : x86_64 x86_64
% 0.09/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36  % Memory   : 8046.5625MB
% 0.09/0.36  % OS       : Linux 6.8.0-71-generic
% 0.09/0.36  % CPULimit : 300
% 0.09/0.36  % WCLimit  : 300
% 0.09/0.36  % DateTime : Mon Sep 21 06:10:26 UTC 2026
% 0.09/0.36  % CPUTime  : 
% 0.09/0.38  % Drodi V4.1.1
% 0.15/0.40  % Refutation found
% 0.15/0.40  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.40  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.43  % Elapsed time: 0.058025 seconds
% 0.15/0.43  % CPU time: 0.171565 seconds
% 0.15/0.43  % Total memory used: 82.828 MB
% 0.15/0.43  % Net memory used: 82.661 MB
%------------------------------------------------------------------------------