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Drodi---4.1.1.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : Drodi---4.1.1
% Problem  : KRS167+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n020.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 12:59:51 PM UTC 2026

% Result   : Theorem 0.02s 0.40s
% Output   : CNFRefutation 0.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   88 (   7 unt;   6 def)
%            Number of atoms       :  337 (  26 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  410 ( 161   ~; 179   |;  49   &)
%                                         (  15 <=>;   2  =>;   0  <=;   4 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   15 (  13 usr;   6 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   4 con; 0-1 aty)
%            Number of variables   :  152 ( 123   !;  29   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f9,axiom,
    ! [X] :
      ( ~ cowlNothing(X)
      & cowlThing(X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [X] :
      ( xsd_string(X)
    <=> ~ xsd_integer(X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    ! [X] :
      ( cc1(X)
    <=> ( ! [Y0,Y1] :
            ( ( rp(X,Y1)
              & rp(X,Y0) )
           => Y0 = Y1 )
        & ? [Y0] : rp(X,Y0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    ! [X] :
      ( cc2(X)
    <=> ( ! [Y0,Y1] :
            ( ( rp(X,Y1)
              & rp(X,Y0) )
           => Y0 = Y1 )
        & ? [Y0] : rp(X,Y0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f13,conjecture,
    ( ! [X] :
        ( cc1(X)
      <=> cc2(X) )
    & ! [X] :
        ( xsd_string(X)
      <=> ~ xsd_integer(X) )
    & ! [X] :
        ( ~ cowlNothing(X)
        & cowlThing(X) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f14,negated_conjecture,
    ~ ( ! [X] :
          ( cc1(X)
        <=> cc2(X) )
      & ! [X] :
          ( xsd_string(X)
        <=> ~ xsd_integer(X) )
      & ! [X] :
          ( ~ cowlNothing(X)
          & cowlThing(X) ) ),
    inference(negated_conjecture,[status(cth)],[f13]) ).

fof(f39,plain,
    ( ! [X] : ~ cowlNothing(X)
    & ! [X] : cowlThing(X) ),
    inference(miniscoping,[status(thm)],[f9]) ).

fof(f40,plain,
    ! [X0] : cowlThing(X0),
    inference(cnf_transformation,[status(thm)],[f39]) ).

fof(f41,plain,
    ! [X0] : ~ cowlNothing(X0),
    inference(cnf_transformation,[status(thm)],[f39]) ).

fof(f42,plain,
    ! [X] :
      ( ( xsd_integer(X)
        | xsd_string(X) )
      & ( ~ xsd_integer(X)
        | ~ xsd_string(X) ) ),
    inference(NNF_transformation,[status(thm)],[f10]) ).

fof(f43,plain,
    ( ! [X] :
        ( xsd_integer(X)
        | xsd_string(X) )
    & ! [X] :
        ( ~ xsd_integer(X)
        | ~ xsd_string(X) ) ),
    inference(miniscoping,[status(thm)],[f42]) ).

fof(f44,plain,
    ! [X0] :
      ( ~ xsd_integer(X0)
      | ~ xsd_string(X0) ),
    inference(cnf_transformation,[status(thm)],[f43]) ).

fof(f45,plain,
    ! [X0] :
      ( xsd_integer(X0)
      | xsd_string(X0) ),
    inference(cnf_transformation,[status(thm)],[f43]) ).

fof(f46,plain,
    ! [X] :
      ( cc1(X)
    <=> ( ! [Y0,Y1] :
            ( Y0 = Y1
            | ~ rp(X,Y1)
            | ~ rp(X,Y0) )
        & ? [Y0] : rp(X,Y0) ) ),
    inference(pre_NNF_transformation,[status(thm)],[f11]) ).

fof(f47,plain,
    ! [X] :
      ( ( ? [Y0,Y1] :
            ( Y0 != Y1
            & rp(X,Y1)
            & rp(X,Y0) )
        | ! [Y0] : ~ rp(X,Y0)
        | cc1(X) )
      & ( ( ! [Y0,Y1] :
              ( Y0 = Y1
              | ~ rp(X,Y1)
              | ~ rp(X,Y0) )
          & ? [Y0] : rp(X,Y0) )
        | ~ cc1(X) ) ),
    inference(NNF_transformation,[status(thm)],[f46]) ).

fof(f48,plain,
    ( ! [X] :
        ( ? [Y0,Y1] :
            ( Y0 != Y1
            & rp(X,Y1)
            & rp(X,Y0) )
        | ! [Y0] : ~ rp(X,Y0)
        | cc1(X) )
    & ! [X] :
        ( ( ! [Y0,Y1] :
              ( Y0 = Y1
              | ~ rp(X,Y1)
              | ~ rp(X,Y0) )
          & ? [Y0] : rp(X,Y0) )
        | ~ cc1(X) ) ),
    inference(miniscoping,[status(thm)],[f47]) ).

fof(f49,plain,
    ( ! [X] :
        ( ( sK1_skl(X) != sK2_skl(X)
          & rp(X,sK2_skl(X))
          & rp(X,sK1_skl(X)) )
        | ! [Y0] : ~ rp(X,Y0)
        | cc1(X) )
    & ! [X] :
        ( ( ! [Y0,Y1] :
              ( Y0 = Y1
              | ~ rp(X,Y1)
              | ~ rp(X,Y0) )
          & rp(X,sK0_skl(X)) )
        | ~ cc1(X) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(Y0,sK0_skl(X)),skolemize(Y0,sK1_skl(X)),skolemize(Y1,sK2_skl(X))],[f48]) ).

fof(f50,plain,
    ! [X0] :
      ( rp(X0,sK0_skl(X0))
      | ~ cc1(X0) ),
    inference(cnf_transformation,[status(thm)],[f49]) ).

fof(f51,plain,
    ! [X0,X1,X2] :
      ( X1 = X2
      | ~ rp(X0,X2)
      | ~ rp(X0,X1)
      | ~ cc1(X0) ),
    inference(cnf_transformation,[status(thm)],[f49]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( rp(X0,sK1_skl(X0))
      | ~ rp(X0,X1)
      | cc1(X0) ),
    inference(cnf_transformation,[status(thm)],[f49]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( rp(X0,sK2_skl(X0))
      | ~ rp(X0,X1)
      | cc1(X0) ),
    inference(cnf_transformation,[status(thm)],[f49]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( sK1_skl(X0) != sK2_skl(X0)
      | ~ rp(X0,X1)
      | cc1(X0) ),
    inference(cnf_transformation,[status(thm)],[f49]) ).

fof(f55,plain,
    ! [X] :
      ( cc2(X)
    <=> ( ! [Y0,Y1] :
            ( Y0 = Y1
            | ~ rp(X,Y1)
            | ~ rp(X,Y0) )
        & ? [Y0] : rp(X,Y0) ) ),
    inference(pre_NNF_transformation,[status(thm)],[f12]) ).

fof(f56,plain,
    ! [X] :
      ( ( ? [Y0,Y1] :
            ( Y0 != Y1
            & rp(X,Y1)
            & rp(X,Y0) )
        | ! [Y0] : ~ rp(X,Y0)
        | cc2(X) )
      & ( ( ! [Y0,Y1] :
              ( Y0 = Y1
              | ~ rp(X,Y1)
              | ~ rp(X,Y0) )
          & ? [Y0] : rp(X,Y0) )
        | ~ cc2(X) ) ),
    inference(NNF_transformation,[status(thm)],[f55]) ).

fof(f57,plain,
    ( ! [X] :
        ( ? [Y0,Y1] :
            ( Y0 != Y1
            & rp(X,Y1)
            & rp(X,Y0) )
        | ! [Y0] : ~ rp(X,Y0)
        | cc2(X) )
    & ! [X] :
        ( ( ! [Y0,Y1] :
              ( Y0 = Y1
              | ~ rp(X,Y1)
              | ~ rp(X,Y0) )
          & ? [Y0] : rp(X,Y0) )
        | ~ cc2(X) ) ),
    inference(miniscoping,[status(thm)],[f56]) ).

fof(f58,plain,
    ( ! [X] :
        ( ( sK4_skl(X) != sK5_skl(X)
          & rp(X,sK5_skl(X))
          & rp(X,sK4_skl(X)) )
        | ! [Y0] : ~ rp(X,Y0)
        | cc2(X) )
    & ! [X] :
        ( ( ! [Y0,Y1] :
              ( Y0 = Y1
              | ~ rp(X,Y1)
              | ~ rp(X,Y0) )
          & rp(X,sK3_skl(X)) )
        | ~ cc2(X) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl]),skolemize(Y0,sK3_skl(X)),skolemize(Y0,sK4_skl(X)),skolemize(Y1,sK5_skl(X))],[f57]) ).

fof(f59,plain,
    ! [X0] :
      ( rp(X0,sK3_skl(X0))
      | ~ cc2(X0) ),
    inference(cnf_transformation,[status(thm)],[f58]) ).

fof(f60,plain,
    ! [X0,X1,X2] :
      ( X1 = X2
      | ~ rp(X0,X2)
      | ~ rp(X0,X1)
      | ~ cc2(X0) ),
    inference(cnf_transformation,[status(thm)],[f58]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( rp(X0,sK4_skl(X0))
      | ~ rp(X0,X1)
      | cc2(X0) ),
    inference(cnf_transformation,[status(thm)],[f58]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( rp(X0,sK5_skl(X0))
      | ~ rp(X0,X1)
      | cc2(X0) ),
    inference(cnf_transformation,[status(thm)],[f58]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( sK4_skl(X0) != sK5_skl(X0)
      | ~ rp(X0,X1)
      | cc2(X0) ),
    inference(cnf_transformation,[status(thm)],[f58]) ).

fof(f64,plain,
    ( ? [X] :
        ( cc1(X)
      <~> cc2(X) )
    | ? [X] :
        ( xsd_string(X)
      <~> ~ xsd_integer(X) )
    | ? [X] :
        ( cowlNothing(X)
        | ~ cowlThing(X) ) ),
    inference(pre_NNF_transformation,[status(thm)],[f14]) ).

fof(f65,definition,
    ! [X] :
      ( sP0_prd(X)
    <=> ( xsd_string(X)
      <~> ~ xsd_integer(X) ) ),
    introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).

fof(f66,plain,
    ( ? [X] :
        ( cc1(X)
      <~> cc2(X) )
    | ? [X] : sP0_prd(X)
    | ? [X] :
        ( cowlNothing(X)
        | ~ cowlThing(X) ) ),
    inference(formula_renaming,[status(thm)],[f64,f65]) ).

fof(f67,plain,
    ( ? [X] :
        ( ( ~ cc2(X)
          | ~ cc1(X) )
        & ( cc2(X)
          | cc1(X) ) )
    | ? [X] : sP0_prd(X)
    | ? [X] :
        ( cowlNothing(X)
        | ~ cowlThing(X) ) ),
    inference(NNF_transformation,[status(thm)],[f66]) ).

fof(f68,plain,
    ( ? [X] :
        ( ( ~ cc2(X)
          | ~ cc1(X) )
        & ( cc2(X)
          | cc1(X) ) )
    | ? [X] : sP0_prd(X)
    | ? [X] : cowlNothing(X)
    | ? [X] : ~ cowlThing(X) ),
    inference(miniscoping,[status(thm)],[f67]) ).

fof(f69,plain,
    ( ( ( ~ cc2(sK9_skl)
        | ~ cc1(sK9_skl) )
      & ( cc2(sK9_skl)
        | cc1(sK9_skl) ) )
    | sP0_prd(sK8_skl)
    | cowlNothing(sK7_skl)
    | ~ cowlThing(sK6_skl) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl,sK8_skl,sK9_skl]),skolemize(X,sK6_skl),skolemize(X,sK7_skl),skolemize(X,sK8_skl),skolemize(X,sK9_skl)],[f68]) ).

fof(f70,plain,
    ( cc2(sK9_skl)
    | cc1(sK9_skl)
    | sP0_prd(sK8_skl)
    | cowlNothing(sK7_skl)
    | ~ cowlThing(sK6_skl) ),
    inference(cnf_transformation,[status(thm)],[f69]) ).

fof(f71,plain,
    ( ~ cc2(sK9_skl)
    | ~ cc1(sK9_skl)
    | sP0_prd(sK8_skl)
    | cowlNothing(sK7_skl)
    | ~ cowlThing(sK6_skl) ),
    inference(cnf_transformation,[status(thm)],[f69]) ).

fof(f72,plain,
    ! [X] :
      ( ( ( ( xsd_integer(X)
            | xsd_string(X) )
          & ( ~ xsd_integer(X)
            | ~ xsd_string(X) ) )
        | sP0_prd(X) )
      & ( ( ( xsd_integer(X)
            | ~ xsd_string(X) )
          & ( ~ xsd_integer(X)
            | xsd_string(X) ) )
        | ~ sP0_prd(X) ) ),
    inference(NNF_transformation,[status(thm)],[f65]) ).

fof(f73,plain,
    ( ! [X] :
        ( ( ( xsd_integer(X)
            | xsd_string(X) )
          & ( ~ xsd_integer(X)
            | ~ xsd_string(X) ) )
        | sP0_prd(X) )
    & ! [X] :
        ( ( ( xsd_integer(X)
            | ~ xsd_string(X) )
          & ( ~ xsd_integer(X)
            | xsd_string(X) ) )
        | ~ sP0_prd(X) ) ),
    inference(miniscoping,[status(thm)],[f72]) ).

fof(f74,plain,
    ! [X0] :
      ( ~ xsd_integer(X0)
      | xsd_string(X0)
      | ~ sP0_prd(X0) ),
    inference(cnf_transformation,[status(thm)],[f73]) ).

fof(f75,plain,
    ! [X0] :
      ( xsd_integer(X0)
      | ~ xsd_string(X0)
      | ~ sP0_prd(X0) ),
    inference(cnf_transformation,[status(thm)],[f73]) ).

fof(f78,definition,
    ( sQ0_spl
  <=> cowlThing(sK6_skl) ),
    introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).

fof(f80,plain,
    ( sQ0_spl
    | ~ cowlThing(sK6_skl) ),
    inference(component_clause,[status(thm)],[f78]) ).

fof(f81,definition,
    ( sQ1_spl
  <=> cowlNothing(sK7_skl) ),
    introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).

fof(f82,plain,
    ( ~ sQ1_spl
    | cowlNothing(sK7_skl) ),
    inference(component_clause,[status(thm)],[f81]) ).

fof(f84,definition,
    ( sQ2_spl
  <=> sP0_prd(sK8_skl) ),
    introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).

fof(f85,plain,
    ( ~ sQ2_spl
    | sP0_prd(sK8_skl) ),
    inference(component_clause,[status(thm)],[f84]) ).

fof(f87,definition,
    ( sQ3_spl
  <=> cc1(sK9_skl) ),
    introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).

fof(f88,plain,
    ( ~ sQ3_spl
    | cc1(sK9_skl) ),
    inference(component_clause,[status(thm)],[f87]) ).

fof(f90,definition,
    ( sQ4_spl
  <=> cc2(sK9_skl) ),
    introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).

fof(f91,plain,
    ( ~ sQ4_spl
    | cc2(sK9_skl) ),
    inference(component_clause,[status(thm)],[f90]) ).

fof(f92,plain,
    ( sQ4_spl
    | ~ cc2(sK9_skl) ),
    inference(component_clause,[status(thm)],[f90]) ).

fof(f93,plain,
    ( sQ4_spl
    | sQ3_spl
    | sQ2_spl
    | sQ1_spl
    | ~ sQ0_spl ),
    inference(split_clause,[status(thm)],[f70,f78,f81,f84,f87,f90]) ).

fof(f94,plain,
    ( ~ sQ4_spl
    | ~ sQ3_spl
    | sQ2_spl
    | sQ1_spl
    | ~ sQ0_spl ),
    inference(split_clause,[status(thm)],[f71,f78,f81,f84,f87,f90]) ).

fof(f98,plain,
    ! [X0] :
      ( ~ xsd_integer(X0)
      | ~ sP0_prd(X0) ),
    inference(backward_subsumption_resolution,[status(thm)],[f74,f44]) ).

fof(f99,plain,
    ! [X0] :
      ( ~ xsd_string(X0)
      | ~ sP0_prd(X0) ),
    inference(backward_subsumption_resolution,[status(thm)],[f75,f44]) ).

fof(f102,plain,
    ! [X0] :
      ( xsd_integer(X0)
      | ~ sP0_prd(X0) ),
    inference(resolution,[status(thm)],[f99,f45]) ).

fof(f103,plain,
    ! [X0] : ~ sP0_prd(X0),
    inference(forward_subsumption_resolution,[status(thm)],[f102,f98]) ).

fof(f104,plain,
    ( ~ sQ2_spl
    | $false ),
    inference(backward_subsumption_resolution,[status(thm)],[f85,f103]) ).

fof(f105,plain,
    ~ sQ2_spl,
    inference(contradiction_clause,[status(thm)],[f104]) ).

fof(f106,plain,
    ( ~ sQ1_spl
    | $false ),
    inference(forward_subsumption_resolution,[status(thm)],[f82,f41]) ).

fof(f107,plain,
    ~ sQ1_spl,
    inference(contradiction_clause,[status(thm)],[f106]) ).

fof(f108,plain,
    ( sQ0_spl
    | $false ),
    inference(forward_subsumption_resolution,[status(thm)],[f80,f40]) ).

fof(f109,plain,
    sQ0_spl,
    inference(contradiction_clause,[status(thm)],[f108]) ).

fof(f131,plain,
    ! [X0,X1,X2] :
      ( X2 = sK2_skl(X0)
      | ~ rp(X0,X2)
      | ~ cc2(X0)
      | ~ rp(X0,X1)
      | cc1(X0) ),
    inference(resolution,[status(thm)],[f53,f60]) ).

fof(f138,plain,
    ! [X0,X1,X2] :
      ( X2 = sK4_skl(X0)
      | ~ rp(X0,X2)
      | ~ cc1(X0)
      | ~ rp(X0,X1)
      | cc2(X0) ),
    inference(resolution,[status(thm)],[f61,f51]) ).

fof(f148,plain,
    ! [X0,X1,X2] :
      ( ~ rp(X0,X2)
      | cc1(X0)
      | sK1_skl(X0) = sK2_skl(X0)
      | ~ cc2(X0)
      | ~ rp(X0,X1)
      | cc1(X0) ),
    inference(resolution,[status(thm)],[f131,f52]) ).

fof(f151,plain,
    ! [X0,X1,X2] :
      ( ~ rp(X0,X2)
      | sK1_skl(X0) = sK2_skl(X0)
      | ~ cc2(X0)
      | ~ rp(X0,X1)
      | cc1(X0) ),
    inference(duplicate_literals_removal,[status(thm)],[f148]) ).

fof(f152,plain,
    ! [X0,X1,X2] :
      ( ~ rp(X0,X2)
      | ~ cc2(X0)
      | ~ rp(X0,X1)
      | cc1(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f151,f54]) ).

fof(f156,plain,
    ! [X0,X1] :
      ( ~ cc2(X0)
      | ~ cc2(X0)
      | ~ rp(X0,X1)
      | cc1(X0) ),
    inference(resolution,[status(thm)],[f152,f59]) ).

fof(f160,plain,
    ! [X0,X1] :
      ( ~ cc2(X0)
      | ~ rp(X0,X1)
      | cc1(X0) ),
    inference(duplicate_literals_removal,[status(thm)],[f156]) ).

fof(f165,plain,
    ! [X0] :
      ( ~ cc2(X0)
      | ~ cc2(X0)
      | cc1(X0) ),
    inference(resolution,[status(thm)],[f160,f59]) ).

fof(f169,plain,
    ! [X0] :
      ( ~ cc2(X0)
      | cc1(X0) ),
    inference(duplicate_literals_removal,[status(thm)],[f165]) ).

fof(f171,plain,
    ! [X0,X1,X2] :
      ( ~ rp(X0,X2)
      | cc2(X0)
      | sK5_skl(X0) = sK4_skl(X0)
      | ~ cc1(X0)
      | ~ rp(X0,X1)
      | cc2(X0) ),
    inference(resolution,[status(thm)],[f138,f62]) ).

fof(f177,plain,
    ! [X0,X1,X2] :
      ( ~ rp(X0,X2)
      | sK5_skl(X0) = sK4_skl(X0)
      | ~ cc1(X0)
      | ~ rp(X0,X1)
      | cc2(X0) ),
    inference(duplicate_literals_removal,[status(thm)],[f171]) ).

fof(f178,plain,
    ! [X0,X1,X2] :
      ( ~ rp(X0,X2)
      | ~ cc1(X0)
      | ~ rp(X0,X1)
      | cc2(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f177,f63]) ).

fof(f195,plain,
    ! [X0,X1] :
      ( ~ cc1(X0)
      | ~ cc1(X0)
      | ~ rp(X0,X1)
      | cc2(X0) ),
    inference(resolution,[status(thm)],[f178,f50]) ).

fof(f198,plain,
    ! [X0,X1] :
      ( ~ cc1(X0)
      | ~ rp(X0,X1)
      | cc2(X0) ),
    inference(duplicate_literals_removal,[status(thm)],[f195]) ).

fof(f204,plain,
    ! [X0] :
      ( ~ cc1(X0)
      | ~ cc1(X0)
      | cc2(X0) ),
    inference(resolution,[status(thm)],[f198,f50]) ).

fof(f207,plain,
    ! [X0] :
      ( ~ cc1(X0)
      | cc2(X0) ),
    inference(duplicate_literals_removal,[status(thm)],[f204]) ).

fof(f208,plain,
    ( ~ sQ3_spl
    | cc2(sK9_skl) ),
    inference(resolution,[status(thm)],[f207,f88]) ).

fof(f209,plain,
    ( ~ sQ3_spl
    | sQ4_spl
    | $false ),
    inference(forward_subsumption_resolution,[status(thm)],[f208,f92]) ).

fof(f210,plain,
    ( ~ sQ3_spl
    | sQ4_spl ),
    inference(contradiction_clause,[status(thm)],[f209]) ).

fof(f211,plain,
    ( ~ sQ4_spl
    | cc1(sK9_skl) ),
    inference(resolution,[status(thm)],[f91,f169]) ).

fof(f212,plain,
    ( ~ sQ4_spl
    | sQ3_spl ),
    inference(split_clause,[status(thm)],[f211,f87,f90]) ).

fof(f213,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f93,f94,f105,f107,f109,f210,f212]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : KRS167+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04  % Command  : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35  % Computer : n020.cluster.edu
% 0.08/0.35  % Model    : x86_64 x86_64
% 0.08/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35  % Memory   : 8046.5625MB
% 0.08/0.35  % OS       : Linux 6.8.0-71-generic
% 0.08/0.35  % CPULimit : 300
% 0.08/0.35  % WCLimit  : 300
% 0.08/0.35  % DateTime : Sun Sep 20 22:55:49 UTC 2026
% 0.02/0.36  % CPUTime  : 
% 0.02/0.37  % Drodi V4.1.1
% 0.02/0.40  % Refutation found
% 0.02/0.40  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.02/0.40  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.02/0.44  % Elapsed time: 0.062688 seconds
% 0.02/0.44  % CPU time: 0.157102 seconds
% 0.02/0.44  % Total memory used: 80.784 MB
% 0.02/0.44  % Net memory used: 80.530 MB
%------------------------------------------------------------------------------