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Drodi---4.1.1.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : Drodi---4.1.1
% Problem  : KRS144+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 : n001.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 12:59:47 PM UTC 2026

% Result   : Theorem 0.14s 0.38s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   87 (   9 unt;  10 def)
%            Number of atoms       :  369 (  83 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  452 ( 170   ~; 185   |;  74   &)
%                                         (  13 <=>;   8  =>;   0  <=;   2 <~>)
%            Maximal formula depth :   15 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   18 (  16 usr;   9 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-1 aty)
%            Number of variables   :  142 ( 109   !;  33   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f8,axiom,
    ! [X] :
      ( ~ cowlNothing(X)
      & cowlThing(X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [X] :
      ( xsd_string(X)
    <=> ~ xsd_integer(X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [X] :
      ( cc(X)
     => ( ! [Y0,Y1,Y2] :
            ( ( rp(X,Y2)
              & rp(X,Y1)
              & rp(X,Y0) )
           => ( Y1 = Y2
              | Y0 = Y2
              | Y0 = Y1 ) )
        & ? [Y0,Y1] :
            ( Y0 != Y1
            & rp(X,Y1)
            & rp(X,Y0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,conjecture,
    ( ! [X] :
        ( cc(X)
       => ? [Y0,Y1] :
            ( Y0 != Y1
            & rp(X,Y1)
            & rp(X,Y0) ) )
    & ! [X] :
        ( cc(X)
       => ! [Y0,Y1,Y2] :
            ( ( rp(X,Y2)
              & rp(X,Y1)
              & rp(X,Y0) )
           => ( Y1 = Y2
              | Y0 = Y2
              | Y0 = Y1 ) ) )
    & ! [X] :
        ( xsd_string(X)
      <=> ~ xsd_integer(X) )
    & ! [X] :
        ( ~ cowlNothing(X)
        & cowlThing(X) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,negated_conjecture,
    ~ ( ! [X] :
          ( cc(X)
         => ? [Y0,Y1] :
              ( Y0 != Y1
              & rp(X,Y1)
              & rp(X,Y0) ) )
      & ! [X] :
          ( cc(X)
         => ! [Y0,Y1,Y2] :
              ( ( rp(X,Y2)
                & rp(X,Y1)
                & rp(X,Y0) )
             => ( Y1 = Y2
                | Y0 = Y2
                | Y0 = Y1 ) ) )
      & ! [X] :
          ( xsd_string(X)
        <=> ~ xsd_integer(X) )
      & ! [X] :
          ( ~ cowlNothing(X)
          & cowlThing(X) ) ),
    inference(negated_conjecture,[status(cth)],[f11]) ).

fof(f34,plain,
    ( ! [X] : ~ cowlNothing(X)
    & ! [X] : cowlThing(X) ),
    inference(miniscoping,[status(thm)],[f8]) ).

fof(f35,plain,
    ! [X0] : cowlThing(X0),
    inference(cnf_transformation,[status(thm)],[f34]) ).

fof(f36,plain,
    ! [X0] : ~ cowlNothing(X0),
    inference(cnf_transformation,[status(thm)],[f34]) ).

fof(f37,plain,
    ! [X] :
      ( ( xsd_integer(X)
        | xsd_string(X) )
      & ( ~ xsd_integer(X)
        | ~ xsd_string(X) ) ),
    inference(NNF_transformation,[status(thm)],[f9]) ).

fof(f38,plain,
    ( ! [X] :
        ( xsd_integer(X)
        | xsd_string(X) )
    & ! [X] :
        ( ~ xsd_integer(X)
        | ~ xsd_string(X) ) ),
    inference(miniscoping,[status(thm)],[f37]) ).

fof(f39,plain,
    ! [X0] :
      ( ~ xsd_integer(X0)
      | ~ xsd_string(X0) ),
    inference(cnf_transformation,[status(thm)],[f38]) ).

fof(f40,plain,
    ! [X0] :
      ( xsd_integer(X0)
      | xsd_string(X0) ),
    inference(cnf_transformation,[status(thm)],[f38]) ).

fof(f41,plain,
    ! [X] :
      ( ( ! [Y0,Y1,Y2] :
            ( Y1 = Y2
            | Y0 = Y2
            | Y0 = Y1
            | ~ rp(X,Y2)
            | ~ rp(X,Y1)
            | ~ rp(X,Y0) )
        & ? [Y0,Y1] :
            ( Y0 != Y1
            & rp(X,Y1)
            & rp(X,Y0) ) )
      | ~ cc(X) ),
    inference(pre_NNF_transformation,[status(thm)],[f10]) ).

fof(f42,plain,
    ! [X] :
      ( ( ! [Y0,Y1,Y2] :
            ( Y1 = Y2
            | Y0 = Y2
            | Y0 = Y1
            | ~ rp(X,Y2)
            | ~ rp(X,Y1)
            | ~ rp(X,Y0) )
        & sK0_skl(X) != sK1_skl(X)
        & rp(X,sK1_skl(X))
        & rp(X,sK0_skl(X)) )
      | ~ cc(X) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y0,sK0_skl(X)),skolemize(Y1,sK1_skl(X))],[f41]) ).

fof(f43,plain,
    ! [X0] :
      ( rp(X0,sK0_skl(X0))
      | ~ cc(X0) ),
    inference(cnf_transformation,[status(thm)],[f42]) ).

fof(f44,plain,
    ! [X0] :
      ( rp(X0,sK1_skl(X0))
      | ~ cc(X0) ),
    inference(cnf_transformation,[status(thm)],[f42]) ).

fof(f45,plain,
    ! [X0] :
      ( sK0_skl(X0) != sK1_skl(X0)
      | ~ cc(X0) ),
    inference(cnf_transformation,[status(thm)],[f42]) ).

fof(f46,plain,
    ! [X0,X1,X2,X3] :
      ( X2 = X3
      | X1 = X3
      | X1 = X2
      | ~ rp(X0,X3)
      | ~ rp(X0,X2)
      | ~ rp(X0,X1)
      | ~ cc(X0) ),
    inference(cnf_transformation,[status(thm)],[f42]) ).

fof(f47,plain,
    ( ? [X] :
        ( ! [Y0,Y1] :
            ( Y0 = Y1
            | ~ rp(X,Y1)
            | ~ rp(X,Y0) )
        & cc(X) )
    | ? [X] :
        ( ? [Y0,Y1,Y2] :
            ( Y1 != Y2
            & Y0 != Y2
            & Y0 != Y1
            & rp(X,Y2)
            & rp(X,Y1)
            & rp(X,Y0) )
        & cc(X) )
    | ? [X] :
        ( xsd_string(X)
      <~> ~ xsd_integer(X) )
    | ? [X] :
        ( cowlNothing(X)
        | ~ cowlThing(X) ) ),
    inference(pre_NNF_transformation,[status(thm)],[f12]) ).

fof(f48,definition,
    ! [X] :
      ( sP0_prd(X)
    <=> ( xsd_string(X)
      <~> ~ xsd_integer(X) ) ),
    introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).

fof(f49,definition,
    ! [X] :
      ( sP1_prd(X)
    <=> ( ? [Y0,Y1,Y2] :
            ( Y1 != Y2
            & Y0 != Y2
            & Y0 != Y1
            & rp(X,Y2)
            & rp(X,Y1)
            & rp(X,Y0) )
        & cc(X) ) ),
    introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).

fof(f50,plain,
    ( ? [X] :
        ( ! [Y0,Y1] :
            ( Y0 = Y1
            | ~ rp(X,Y1)
            | ~ rp(X,Y0) )
        & cc(X) )
    | ? [X] : sP1_prd(X)
    | ? [X] : sP0_prd(X)
    | ? [X] :
        ( cowlNothing(X)
        | ~ cowlThing(X) ) ),
    inference(formula_renaming,[status(thm)],[f47,f49,f48]) ).

fof(f51,plain,
    ( ? [X] :
        ( ! [Y0,Y1] :
            ( Y0 = Y1
            | ~ rp(X,Y1)
            | ~ rp(X,Y0) )
        & cc(X) )
    | ? [X] : sP1_prd(X)
    | ? [X] : sP0_prd(X)
    | ? [X] : cowlNothing(X)
    | ? [X] : ~ cowlThing(X) ),
    inference(miniscoping,[status(thm)],[f50]) ).

fof(f52,plain,
    ( ( ! [Y0,Y1] :
          ( Y0 = Y1
          | ~ rp(sK6_skl,Y1)
          | ~ rp(sK6_skl,Y0) )
      & cc(sK6_skl) )
    | sP1_prd(sK5_skl)
    | sP0_prd(sK4_skl)
    | cowlNothing(sK3_skl)
    | ~ cowlThing(sK2_skl) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl,sK5_skl,sK6_skl]),skolemize(X,sK2_skl),skolemize(X,sK3_skl),skolemize(X,sK4_skl),skolemize(X,sK5_skl),skolemize(X,sK6_skl)],[f51]) ).

fof(f53,plain,
    ( cc(sK6_skl)
    | sP1_prd(sK5_skl)
    | sP0_prd(sK4_skl)
    | cowlNothing(sK3_skl)
    | ~ cowlThing(sK2_skl) ),
    inference(cnf_transformation,[status(thm)],[f52]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ rp(sK6_skl,X1)
      | ~ rp(sK6_skl,X0)
      | sP1_prd(sK5_skl)
      | sP0_prd(sK4_skl)
      | cowlNothing(sK3_skl)
      | ~ cowlThing(sK2_skl) ),
    inference(cnf_transformation,[status(thm)],[f52]) ).

fof(f55,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)],[f48]) ).

fof(f56,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)],[f55]) ).

fof(f57,plain,
    ! [X0] :
      ( ~ xsd_integer(X0)
      | xsd_string(X0)
      | ~ sP0_prd(X0) ),
    inference(cnf_transformation,[status(thm)],[f56]) ).

fof(f58,plain,
    ! [X0] :
      ( xsd_integer(X0)
      | ~ xsd_string(X0)
      | ~ sP0_prd(X0) ),
    inference(cnf_transformation,[status(thm)],[f56]) ).

fof(f61,plain,
    ! [X] :
      ( ( ! [Y0,Y1,Y2] :
            ( Y1 = Y2
            | Y0 = Y2
            | Y0 = Y1
            | ~ rp(X,Y2)
            | ~ rp(X,Y1)
            | ~ rp(X,Y0) )
        | ~ cc(X)
        | sP1_prd(X) )
      & ( ( ? [Y0,Y1,Y2] :
              ( Y1 != Y2
              & Y0 != Y2
              & Y0 != Y1
              & rp(X,Y2)
              & rp(X,Y1)
              & rp(X,Y0) )
          & cc(X) )
        | ~ sP1_prd(X) ) ),
    inference(NNF_transformation,[status(thm)],[f49]) ).

fof(f62,plain,
    ( ! [X] :
        ( ! [Y0,Y1,Y2] :
            ( Y1 = Y2
            | Y0 = Y2
            | Y0 = Y1
            | ~ rp(X,Y2)
            | ~ rp(X,Y1)
            | ~ rp(X,Y0) )
        | ~ cc(X)
        | sP1_prd(X) )
    & ! [X] :
        ( ( ? [Y0,Y1,Y2] :
              ( Y1 != Y2
              & Y0 != Y2
              & Y0 != Y1
              & rp(X,Y2)
              & rp(X,Y1)
              & rp(X,Y0) )
          & cc(X) )
        | ~ sP1_prd(X) ) ),
    inference(miniscoping,[status(thm)],[f61]) ).

fof(f63,plain,
    ( ! [X] :
        ( ! [Y0,Y1,Y2] :
            ( Y1 = Y2
            | Y0 = Y2
            | Y0 = Y1
            | ~ rp(X,Y2)
            | ~ rp(X,Y1)
            | ~ rp(X,Y0) )
        | ~ cc(X)
        | sP1_prd(X) )
    & ! [X] :
        ( ( sK8_skl(X) != sK9_skl(X)
          & sK7_skl(X) != sK9_skl(X)
          & sK7_skl(X) != sK8_skl(X)
          & rp(X,sK9_skl(X))
          & rp(X,sK8_skl(X))
          & rp(X,sK7_skl(X))
          & cc(X) )
        | ~ sP1_prd(X) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl,sK9_skl]),skolemize(Y0,sK7_skl(X)),skolemize(Y1,sK8_skl(X)),skolemize(Y2,sK9_skl(X))],[f62]) ).

fof(f64,plain,
    ! [X0] :
      ( cc(X0)
      | ~ sP1_prd(X0) ),
    inference(cnf_transformation,[status(thm)],[f63]) ).

fof(f65,plain,
    ! [X0] :
      ( rp(X0,sK7_skl(X0))
      | ~ sP1_prd(X0) ),
    inference(cnf_transformation,[status(thm)],[f63]) ).

fof(f66,plain,
    ! [X0] :
      ( rp(X0,sK8_skl(X0))
      | ~ sP1_prd(X0) ),
    inference(cnf_transformation,[status(thm)],[f63]) ).

fof(f67,plain,
    ! [X0] :
      ( rp(X0,sK9_skl(X0))
      | ~ sP1_prd(X0) ),
    inference(cnf_transformation,[status(thm)],[f63]) ).

fof(f68,plain,
    ! [X0] :
      ( sK7_skl(X0) != sK8_skl(X0)
      | ~ sP1_prd(X0) ),
    inference(cnf_transformation,[status(thm)],[f63]) ).

fof(f69,plain,
    ! [X0] :
      ( sK7_skl(X0) != sK9_skl(X0)
      | ~ sP1_prd(X0) ),
    inference(cnf_transformation,[status(thm)],[f63]) ).

fof(f70,plain,
    ! [X0] :
      ( sK8_skl(X0) != sK9_skl(X0)
      | ~ sP1_prd(X0) ),
    inference(cnf_transformation,[status(thm)],[f63]) ).

fof(f72,definition,
    ( sQ0_spl
  <=> cowlThing(sK2_skl) ),
    introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).

fof(f74,plain,
    ( sQ0_spl
    | ~ cowlThing(sK2_skl) ),
    inference(component_clause,[status(thm)],[f72]) ).

fof(f75,definition,
    ( sQ1_spl
  <=> cowlNothing(sK3_skl) ),
    introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).

fof(f76,plain,
    ( ~ sQ1_spl
    | cowlNothing(sK3_skl) ),
    inference(component_clause,[status(thm)],[f75]) ).

fof(f78,definition,
    ( sQ2_spl
  <=> sP0_prd(sK4_skl) ),
    introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).

fof(f79,plain,
    ( ~ sQ2_spl
    | sP0_prd(sK4_skl) ),
    inference(component_clause,[status(thm)],[f78]) ).

fof(f81,definition,
    ( sQ3_spl
  <=> sP1_prd(sK5_skl) ),
    introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).

fof(f82,plain,
    ( ~ sQ3_spl
    | sP1_prd(sK5_skl) ),
    inference(component_clause,[status(thm)],[f81]) ).

fof(f84,definition,
    ( sQ4_spl
  <=> cc(sK6_skl) ),
    introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).

fof(f85,plain,
    ( ~ sQ4_spl
    | cc(sK6_skl) ),
    inference(component_clause,[status(thm)],[f84]) ).

fof(f87,plain,
    ( sQ4_spl
    | sQ3_spl
    | sQ2_spl
    | sQ1_spl
    | ~ sQ0_spl ),
    inference(split_clause,[status(thm)],[f53,f72,f75,f78,f81,f84]) ).

fof(f88,definition,
    ! [X0,X1] :
      ( sQ5_spl
    <=> ( X0 = X1
        | ~ rp(sK6_skl,X1)
        | ~ rp(sK6_skl,X0) ) ),
    introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).

fof(f89,plain,
    ! [X0,X1] :
      ( ~ sQ5_spl
      | X0 = X1
      | ~ rp(sK6_skl,X1)
      | ~ rp(sK6_skl,X0) ),
    inference(component_clause,[status(thm)],[f88]) ).

fof(f91,plain,
    ( sQ5_spl
    | sQ3_spl
    | sQ2_spl
    | sQ1_spl
    | ~ sQ0_spl ),
    inference(split_clause,[status(thm)],[f54,f72,f75,f78,f81,f88]) ).

fof(f96,plain,
    ! [X0] :
      ( ~ xsd_integer(X0)
      | ~ sP0_prd(X0) ),
    inference(backward_subsumption_resolution,[status(thm)],[f57,f39]) ).

fof(f97,plain,
    ! [X0] :
      ( ~ xsd_string(X0)
      | ~ sP0_prd(X0) ),
    inference(backward_subsumption_resolution,[status(thm)],[f58,f39]) ).

fof(f100,plain,
    ! [X0] :
      ( xsd_integer(X0)
      | ~ sP0_prd(X0) ),
    inference(resolution,[status(thm)],[f97,f40]) ).

fof(f101,plain,
    ! [X0] : ~ sP0_prd(X0),
    inference(forward_subsumption_resolution,[status(thm)],[f100,f96]) ).

fof(f103,plain,
    ! [X0,X1,X2] :
      ( ~ sP1_prd(X0)
      | sK9_skl(X0) = X2
      | X1 = X2
      | X1 = sK9_skl(X0)
      | ~ rp(X0,X2)
      | ~ rp(X0,X1)
      | ~ cc(X0) ),
    inference(resolution,[status(thm)],[f46,f67]) ).

fof(f112,plain,
    ! [X0,X1,X2] :
      ( ~ sP1_prd(X0)
      | sK9_skl(X0) = X2
      | X1 = X2
      | X1 = sK9_skl(X0)
      | ~ rp(X0,X2)
      | ~ rp(X0,X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[f103,f64]) ).

fof(f133,plain,
    ! [X0,X1] :
      ( ~ sP1_prd(X0)
      | ~ sP1_prd(X0)
      | sK9_skl(X0) = sK8_skl(X0)
      | X1 = sK8_skl(X0)
      | X1 = sK9_skl(X0)
      | ~ rp(X0,X1) ),
    inference(resolution,[status(thm)],[f112,f66]) ).

fof(f137,plain,
    ! [X0,X1] :
      ( ~ sP1_prd(X0)
      | sK9_skl(X0) = sK8_skl(X0)
      | X1 = sK8_skl(X0)
      | X1 = sK9_skl(X0)
      | ~ rp(X0,X1) ),
    inference(duplicate_literals_removal,[status(thm)],[f133]) ).

fof(f138,plain,
    ! [X0,X1] :
      ( ~ sP1_prd(X0)
      | X1 = sK8_skl(X0)
      | X1 = sK9_skl(X0)
      | ~ rp(X0,X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[f137,f70]) ).

fof(f145,plain,
    ! [X0] :
      ( ~ sP1_prd(X0)
      | ~ sP1_prd(X0)
      | sK7_skl(X0) = sK8_skl(X0)
      | sK7_skl(X0) = sK9_skl(X0) ),
    inference(resolution,[status(thm)],[f138,f65]) ).

fof(f148,plain,
    ! [X0] :
      ( ~ sP1_prd(X0)
      | sK7_skl(X0) = sK8_skl(X0)
      | sK7_skl(X0) = sK9_skl(X0) ),
    inference(duplicate_literals_removal,[status(thm)],[f145]) ).

fof(f149,plain,
    ! [X0] :
      ( ~ sP1_prd(X0)
      | sK7_skl(X0) = sK8_skl(X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f148,f69]) ).

fof(f150,plain,
    ( ~ sQ3_spl
    | $false ),
    inference(backward_subsumption_resolution,[status(thm)],[f82,f151]) ).

fof(f151,plain,
    ! [X0] : ~ sP1_prd(X0),
    inference(forward_subsumption_resolution,[status(thm)],[f149,f68]) ).

fof(f152,plain,
    ~ sQ3_spl,
    inference(contradiction_clause,[status(thm)],[f150]) ).

fof(f153,plain,
    ( ~ sQ2_spl
    | $false ),
    inference(forward_subsumption_resolution,[status(thm)],[f79,f101]) ).

fof(f154,plain,
    ~ sQ2_spl,
    inference(contradiction_clause,[status(thm)],[f153]) ).

fof(f155,plain,
    ( ~ sQ1_spl
    | $false ),
    inference(forward_subsumption_resolution,[status(thm)],[f76,f36]) ).

fof(f156,plain,
    ~ sQ1_spl,
    inference(contradiction_clause,[status(thm)],[f155]) ).

fof(f157,plain,
    ( sQ0_spl
    | $false ),
    inference(forward_subsumption_resolution,[status(thm)],[f74,f35]) ).

fof(f158,plain,
    sQ0_spl,
    inference(contradiction_clause,[status(thm)],[f157]) ).

fof(f159,plain,
    ! [X0] :
      ( ~ sQ5_spl
      | ~ cc(sK6_skl)
      | X0 = sK1_skl(sK6_skl)
      | ~ rp(sK6_skl,X0) ),
    inference(resolution,[status(thm)],[f89,f44]) ).

fof(f161,definition,
    ! [X0] :
      ( sQ6_spl
    <=> ( X0 = sK1_skl(sK6_skl)
        | ~ rp(sK6_skl,X0) ) ),
    introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).

fof(f162,plain,
    ! [X0] :
      ( ~ sQ6_spl
      | X0 = sK1_skl(sK6_skl)
      | ~ rp(sK6_skl,X0) ),
    inference(component_clause,[status(thm)],[f161]) ).

fof(f164,plain,
    ( ~ sQ5_spl
    | ~ sQ4_spl
    | sQ6_spl ),
    inference(split_clause,[status(thm)],[f159,f161,f84,f88]) ).

fof(f170,plain,
    ( ~ sQ6_spl
    | ~ cc(sK6_skl)
    | sK0_skl(sK6_skl) = sK1_skl(sK6_skl) ),
    inference(resolution,[status(thm)],[f162,f43]) ).

fof(f175,definition,
    ( sQ9_spl
  <=> sK0_skl(sK6_skl) = sK1_skl(sK6_skl) ),
    introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).

fof(f176,plain,
    ( ~ sQ9_spl
    | sK0_skl(sK6_skl) = sK1_skl(sK6_skl) ),
    inference(component_clause,[status(thm)],[f175]) ).

fof(f178,plain,
    ( ~ sQ6_spl
    | ~ sQ4_spl
    | sQ9_spl ),
    inference(split_clause,[status(thm)],[f170,f175,f84,f161]) ).

fof(f180,plain,
    ( ~ sQ9_spl
    | ~ cc(sK6_skl) ),
    inference(resolution,[status(thm)],[f176,f45]) ).

fof(f183,plain,
    ( ~ sQ9_spl
    | ~ sQ4_spl
    | $false ),
    inference(forward_subsumption_resolution,[status(thm)],[f180,f85]) ).

fof(f184,plain,
    ( ~ sQ9_spl
    | ~ sQ4_spl ),
    inference(contradiction_clause,[status(thm)],[f183]) ).

fof(f185,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f87,f91,f152,f154,f156,f158,f164,f178,f184]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : KRS144+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04  % Command  : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36  % Computer : n001.cluster.edu
% 0.10/0.36  % Model    : x86_64 x86_64
% 0.10/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36  % Memory   : 8046.5625MB
% 0.10/0.36  % OS       : Linux 6.8.0-71-generic
% 0.10/0.36  % CPULimit : 300
% 0.10/0.36  % WCLimit  : 300
% 0.10/0.36  % DateTime : Sun Sep 20 23:00:14 UTC 2026
% 0.10/0.36  % CPUTime  : 
% 0.10/0.37  % Drodi V4.1.1
% 0.14/0.38  % Refutation found
% 0.14/0.38  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.38  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41  % Elapsed time: 0.041828 seconds
% 0.14/0.41  % CPU time: 0.119066 seconds
% 0.14/0.41  % Total memory used: 45.520 MB
% 0.14/0.41  % Net memory used: 45.399 MB
%------------------------------------------------------------------------------