↑ Up

Drodi---4.1.1.THM-CRf.s

View TPTP
Problem
Process solution in
SystemOnTSTP
Download .tgz
%------------------------------------------------------------------------------
% File     : Drodi---4.1.1
% Problem  : SET701+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -timeout(300) /export/starexec/sandbox2/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 02:10:29 PM UTC 2026

% Result   : Theorem 1.38s 0.78s
% Output   : CNFRefutation 1.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   15
% Syntax   : Number of formulae    :  102 (   5 unt;  10 def)
%            Number of atoms       :  294 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  315 ( 123   ~; 137   |;  34   &)
%                                         (  17 <=>;   3  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   14 (  13 usr;  11 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :  130 ( 116   !;  14   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [X] :
          ( member(X,A)
         => member(X,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [A,B] :
      ( equal_set(A,B)
    <=> ( subset(B,A)
        & subset(A,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [X,A,B] :
      ( member(X,intersection(A,B))
    <=> ( member(X,B)
        & member(X,A) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [B,A,E] :
      ( member(B,difference(E,A))
    <=> ( ~ member(B,A)
        & member(B,E) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,conjecture,
    ! [A,B,C,E] :
      ( ( subset(B,E)
        & subset(A,E) )
     => ( subset(A,B)
      <=> subset(intersection(A,difference(E,B)),intersection(C,difference(E,C))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f13,negated_conjecture,
    ~ ! [A,B,C,E] :
        ( ( subset(B,E)
          & subset(A,E) )
       => ( subset(A,B)
        <=> subset(intersection(A,difference(E,B)),intersection(C,difference(E,C))) ) ),
    inference(negated_conjecture,[status(cth)],[f12]) ).

fof(f14,plain,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [X] :
          ( member(X,B)
          | ~ member(X,A) ) ),
    inference(pre_NNF_transformation,[status(thm)],[f1]) ).

fof(f15,plain,
    ! [A,B] :
      ( ( ? [X] :
            ( ~ member(X,B)
            & member(X,A) )
        | subset(A,B) )
      & ( ! [X] :
            ( member(X,B)
            | ~ member(X,A) )
        | ~ subset(A,B) ) ),
    inference(NNF_transformation,[status(thm)],[f14]) ).

fof(f16,plain,
    ( ! [A,B] :
        ( ? [X] :
            ( ~ member(X,B)
            & member(X,A) )
        | subset(A,B) )
    & ! [A,B] :
        ( ! [X] :
            ( member(X,B)
            | ~ member(X,A) )
        | ~ subset(A,B) ) ),
    inference(miniscoping,[status(thm)],[f15]) ).

fof(f17,plain,
    ( ! [A,B] :
        ( ( ~ member(sK0_skl(B,A),B)
          & member(sK0_skl(B,A),A) )
        | subset(A,B) )
    & ! [A,B] :
        ( ! [X] :
            ( member(X,B)
            | ~ member(X,A) )
        | ~ subset(A,B) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl(B,A))],[f16]) ).

fof(f18,plain,
    ! [X0,X1,X2] :
      ( member(X2,X1)
      | ~ member(X2,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[status(thm)],[f17]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( member(sK0_skl(X1,X0),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[status(thm)],[f17]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ~ member(sK0_skl(X1,X0),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[status(thm)],[f17]) ).

fof(f21,plain,
    ! [A,B] :
      ( ( ~ subset(B,A)
        | ~ subset(A,B)
        | equal_set(A,B) )
      & ( ( subset(B,A)
          & subset(A,B) )
        | ~ equal_set(A,B) ) ),
    inference(NNF_transformation,[status(thm)],[f2]) ).

fof(f22,plain,
    ( ! [A,B] :
        ( ~ subset(B,A)
        | ~ subset(A,B)
        | equal_set(A,B) )
    & ! [A,B] :
        ( ( subset(B,A)
          & subset(A,B) )
        | ~ equal_set(A,B) ) ),
    inference(miniscoping,[status(thm)],[f21]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ equal_set(X0,X1) ),
    inference(cnf_transformation,[status(thm)],[f22]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
      | ~ equal_set(X0,X1) ),
    inference(cnf_transformation,[status(thm)],[f22]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | ~ subset(X0,X1)
      | equal_set(X0,X1) ),
    inference(cnf_transformation,[status(thm)],[f22]) ).

fof(f30,plain,
    ! [X,A,B] :
      ( ( ~ member(X,B)
        | ~ member(X,A)
        | member(X,intersection(A,B)) )
      & ( ( member(X,B)
          & member(X,A) )
        | ~ member(X,intersection(A,B)) ) ),
    inference(NNF_transformation,[status(thm)],[f4]) ).

fof(f31,plain,
    ( ! [X,A,B] :
        ( ~ member(X,B)
        | ~ member(X,A)
        | member(X,intersection(A,B)) )
    & ! [X,A,B] :
        ( ( member(X,B)
          & member(X,A) )
        | ~ member(X,intersection(A,B)) ) ),
    inference(miniscoping,[status(thm)],[f30]) ).

fof(f32,plain,
    ! [X0,X1,X2] :
      ( member(X0,X1)
      | ~ member(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[status(thm)],[f31]) ).

fof(f33,plain,
    ! [X0,X1,X2] :
      ( member(X0,X2)
      | ~ member(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[status(thm)],[f31]) ).

fof(f34,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,X2)
      | ~ member(X0,X1)
      | member(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[status(thm)],[f31]) ).

fof(f41,plain,
    ! [B,A,E] :
      ( ( member(B,A)
        | ~ member(B,E)
        | member(B,difference(E,A)) )
      & ( ( ~ member(B,A)
          & member(B,E) )
        | ~ member(B,difference(E,A)) ) ),
    inference(NNF_transformation,[status(thm)],[f7]) ).

fof(f42,plain,
    ( ! [B,A,E] :
        ( member(B,A)
        | ~ member(B,E)
        | member(B,difference(E,A)) )
    & ! [B,A,E] :
        ( ( ~ member(B,A)
          & member(B,E) )
        | ~ member(B,difference(E,A)) ) ),
    inference(miniscoping,[status(thm)],[f41]) ).

fof(f44,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,X2)
      | ~ member(X0,difference(X1,X2)) ),
    inference(cnf_transformation,[status(thm)],[f42]) ).

fof(f45,plain,
    ! [X0,X1,X2] :
      ( member(X0,X2)
      | ~ member(X0,X1)
      | member(X0,difference(X1,X2)) ),
    inference(cnf_transformation,[status(thm)],[f42]) ).

fof(f68,plain,
    ? [A,B,C,E] :
      ( ( subset(A,B)
      <~> subset(intersection(A,difference(E,B)),intersection(C,difference(E,C))) )
      & subset(B,E)
      & subset(A,E) ),
    inference(pre_NNF_transformation,[status(thm)],[f13]) ).

fof(f69,plain,
    ? [A,B,C,E] :
      ( ( ~ subset(intersection(A,difference(E,B)),intersection(C,difference(E,C)))
        | ~ subset(A,B) )
      & ( subset(intersection(A,difference(E,B)),intersection(C,difference(E,C)))
        | subset(A,B) )
      & subset(B,E)
      & subset(A,E) ),
    inference(NNF_transformation,[status(thm)],[f68]) ).

fof(f70,plain,
    ? [A,B,E] :
      ( ? [C] :
          ( ( ~ subset(intersection(A,difference(E,B)),intersection(C,difference(E,C)))
            | ~ subset(A,B) )
          & ( subset(intersection(A,difference(E,B)),intersection(C,difference(E,C)))
            | subset(A,B) ) )
      & subset(B,E)
      & subset(A,E) ),
    inference(miniscoping,[status(thm)],[f69]) ).

fof(f71,plain,
    ( ( ~ subset(intersection(sK3_skl,difference(sK5_skl,sK4_skl)),intersection(sK6_skl,difference(sK5_skl,sK6_skl)))
      | ~ subset(sK3_skl,sK4_skl) )
    & ( subset(intersection(sK3_skl,difference(sK5_skl,sK4_skl)),intersection(sK6_skl,difference(sK5_skl,sK6_skl)))
      | subset(sK3_skl,sK4_skl) )
    & subset(sK4_skl,sK5_skl)
    & subset(sK3_skl,sK5_skl) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl,sK6_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl),skolemize(E,sK5_skl),skolemize(C,sK6_skl)],[f70]) ).

fof(f72,plain,
    subset(sK3_skl,sK5_skl),
    inference(cnf_transformation,[status(thm)],[f71]) ).

fof(f73,plain,
    subset(sK4_skl,sK5_skl),
    inference(cnf_transformation,[status(thm)],[f71]) ).

fof(f74,plain,
    ( subset(intersection(sK3_skl,difference(sK5_skl,sK4_skl)),intersection(sK6_skl,difference(sK5_skl,sK6_skl)))
    | subset(sK3_skl,sK4_skl) ),
    inference(cnf_transformation,[status(thm)],[f71]) ).

fof(f75,plain,
    ( ~ subset(intersection(sK3_skl,difference(sK5_skl,sK4_skl)),intersection(sK6_skl,difference(sK5_skl,sK6_skl)))
    | ~ subset(sK3_skl,sK4_skl) ),
    inference(cnf_transformation,[status(thm)],[f71]) ).

fof(f76,definition,
    ( sQ0_spl
  <=> subset(sK3_skl,sK4_skl) ),
    introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).

fof(f77,plain,
    ( ~ sQ0_spl
    | subset(sK3_skl,sK4_skl) ),
    inference(component_clause,[status(thm)],[f76]) ).

fof(f79,definition,
    ( sQ1_spl
  <=> subset(intersection(sK3_skl,difference(sK5_skl,sK4_skl)),intersection(sK6_skl,difference(sK5_skl,sK6_skl))) ),
    introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).

fof(f80,plain,
    ( ~ sQ1_spl
    | subset(intersection(sK3_skl,difference(sK5_skl,sK4_skl)),intersection(sK6_skl,difference(sK5_skl,sK6_skl))) ),
    inference(component_clause,[status(thm)],[f79]) ).

fof(f81,plain,
    ( sQ1_spl
    | ~ subset(intersection(sK3_skl,difference(sK5_skl,sK4_skl)),intersection(sK6_skl,difference(sK5_skl,sK6_skl))) ),
    inference(component_clause,[status(thm)],[f79]) ).

fof(f82,plain,
    ( sQ1_spl
    | sQ0_spl ),
    inference(split_clause,[status(thm)],[f74,f76,f79]) ).

fof(f83,plain,
    ( ~ sQ1_spl
    | ~ sQ0_spl ),
    inference(split_clause,[status(thm)],[f75,f76,f79]) ).

fof(f87,plain,
    ! [X0] :
      ( ~ sQ1_spl
      | member(X0,intersection(sK6_skl,difference(sK5_skl,sK6_skl)))
      | ~ member(X0,intersection(sK3_skl,difference(sK5_skl,sK4_skl))) ),
    inference(resolution,[status(thm)],[f18,f80]) ).

fof(f89,plain,
    ! [X0] :
      ( member(X0,sK5_skl)
      | ~ member(X0,sK3_skl) ),
    inference(resolution,[status(thm)],[f18,f72]) ).

fof(f94,plain,
    ! [X0] :
      ( ~ sQ1_spl
      | ~ member(X0,difference(sK5_skl,sK4_skl))
      | ~ member(X0,sK3_skl)
      | member(X0,intersection(sK6_skl,difference(sK5_skl,sK6_skl))) ),
    inference(resolution,[status(thm)],[f87,f34]) ).

fof(f95,plain,
    ! [X0] :
      ( ~ sQ1_spl
      | member(X0,difference(sK5_skl,sK6_skl))
      | ~ member(X0,difference(sK5_skl,sK4_skl))
      | ~ member(X0,sK3_skl) ),
    inference(resolution,[status(thm)],[f94,f33]) ).

fof(f96,plain,
    ! [X0] :
      ( ~ sQ1_spl
      | member(X0,sK6_skl)
      | ~ member(X0,difference(sK5_skl,sK4_skl))
      | ~ member(X0,sK3_skl) ),
    inference(resolution,[status(thm)],[f94,f32]) ).

fof(f97,plain,
    ! [X0] :
      ( ~ sQ1_spl
      | member(X0,sK4_skl)
      | ~ member(X0,sK5_skl)
      | member(X0,sK6_skl)
      | ~ member(X0,sK3_skl) ),
    inference(resolution,[status(thm)],[f96,f45]) ).

fof(f98,plain,
    ! [X0] :
      ( ~ sQ1_spl
      | member(X0,sK4_skl)
      | member(X0,sK6_skl)
      | ~ member(X0,sK3_skl) ),
    inference(forward_subsumption_resolution,[status(thm)],[f97,f89]) ).

fof(f99,plain,
    ! [X0] :
      ( ~ sQ1_spl
      | member(X0,sK4_skl)
      | ~ member(X0,sK5_skl)
      | member(X0,difference(sK5_skl,sK6_skl))
      | ~ member(X0,sK3_skl) ),
    inference(resolution,[status(thm)],[f95,f45]) ).

fof(f100,plain,
    ! [X0] :
      ( ~ sQ1_spl
      | member(X0,sK4_skl)
      | member(X0,difference(sK5_skl,sK6_skl))
      | ~ member(X0,sK3_skl) ),
    inference(forward_subsumption_resolution,[status(thm)],[f99,f89]) ).

fof(f101,plain,
    ! [X0] :
      ( ~ sQ1_spl
      | ~ member(X0,sK6_skl)
      | member(X0,sK4_skl)
      | ~ member(X0,sK3_skl) ),
    inference(resolution,[status(thm)],[f100,f44]) ).

fof(f103,plain,
    ! [X0] :
      ( ~ sQ1_spl
      | member(X0,sK4_skl)
      | ~ member(X0,sK3_skl) ),
    inference(forward_subsumption_resolution,[status(thm)],[f101,f98]) ).

fof(f108,plain,
    ! [X0] :
      ( ~ sQ1_spl
      | member(sK0_skl(X0,sK3_skl),sK4_skl)
      | subset(sK3_skl,X0) ),
    inference(resolution,[status(thm)],[f19,f103]) ).

fof(f112,plain,
    ! [X0,X1,X2] :
      ( member(sK0_skl(X2,intersection(X0,X1)),X1)
      | subset(intersection(X0,X1),X2) ),
    inference(resolution,[status(thm)],[f19,f33]) ).

fof(f113,plain,
    ! [X0,X1,X2] :
      ( member(sK0_skl(X2,intersection(X0,X1)),X0)
      | subset(intersection(X0,X1),X2) ),
    inference(resolution,[status(thm)],[f19,f32]) ).

fof(f134,plain,
    ( ~ subset(sK5_skl,sK4_skl)
    | equal_set(sK5_skl,sK4_skl) ),
    inference(resolution,[status(thm)],[f25,f73]) ).

fof(f135,plain,
    ( ~ subset(sK5_skl,sK3_skl)
    | equal_set(sK5_skl,sK3_skl) ),
    inference(resolution,[status(thm)],[f25,f72]) ).

fof(f144,definition,
    ( sQ4_spl
  <=> equal_set(sK5_skl,sK4_skl) ),
    introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).

fof(f145,plain,
    ( ~ sQ4_spl
    | equal_set(sK5_skl,sK4_skl) ),
    inference(component_clause,[status(thm)],[f144]) ).

fof(f147,definition,
    ( sQ5_spl
  <=> subset(sK5_skl,sK4_skl) ),
    introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).

fof(f149,plain,
    ( sQ5_spl
    | ~ subset(sK5_skl,sK4_skl) ),
    inference(component_clause,[status(thm)],[f147]) ).

fof(f150,plain,
    ( ~ sQ5_spl
    | sQ4_spl ),
    inference(split_clause,[status(thm)],[f134,f144,f147]) ).

fof(f151,definition,
    ( sQ6_spl
  <=> equal_set(sK5_skl,sK3_skl) ),
    introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).

fof(f152,plain,
    ( ~ sQ6_spl
    | equal_set(sK5_skl,sK3_skl) ),
    inference(component_clause,[status(thm)],[f151]) ).

fof(f154,definition,
    ( sQ7_spl
  <=> subset(sK5_skl,sK3_skl) ),
    introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).

fof(f156,plain,
    ( sQ7_spl
    | ~ subset(sK5_skl,sK3_skl) ),
    inference(component_clause,[status(thm)],[f154]) ).

fof(f157,plain,
    ( ~ sQ7_spl
    | sQ6_spl ),
    inference(split_clause,[status(thm)],[f135,f151,f154]) ).

fof(f162,plain,
    ( ~ sQ6_spl
    | subset(sK5_skl,sK3_skl) ),
    inference(resolution,[status(thm)],[f152,f23]) ).

fof(f182,plain,
    ( ~ sQ4_spl
    | subset(sK5_skl,sK4_skl) ),
    inference(resolution,[status(thm)],[f145,f23]) ).

fof(f183,plain,
    ( ~ sQ6_spl
    | ~ subset(sK3_skl,sK5_skl)
    | equal_set(sK3_skl,sK5_skl) ),
    inference(resolution,[status(thm)],[f162,f25]) ).

fof(f185,definition,
    ( sQ8_spl
  <=> equal_set(sK3_skl,sK5_skl) ),
    introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).

fof(f186,plain,
    ( ~ sQ8_spl
    | equal_set(sK3_skl,sK5_skl) ),
    inference(component_clause,[status(thm)],[f185]) ).

fof(f188,definition,
    ( sQ9_spl
  <=> subset(sK3_skl,sK5_skl) ),
    introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).

fof(f190,plain,
    ( sQ9_spl
    | ~ subset(sK3_skl,sK5_skl) ),
    inference(component_clause,[status(thm)],[f188]) ).

fof(f191,plain,
    ( ~ sQ6_spl
    | ~ sQ9_spl
    | sQ8_spl ),
    inference(split_clause,[status(thm)],[f183,f185,f188,f151]) ).

fof(f192,plain,
    ( sQ9_spl
    | $false ),
    inference(forward_subsumption_resolution,[status(thm)],[f190,f72]) ).

fof(f193,plain,
    sQ9_spl,
    inference(contradiction_clause,[status(thm)],[f192]) ).

fof(f194,plain,
    ( ~ sQ4_spl
    | ~ subset(sK4_skl,sK5_skl)
    | equal_set(sK4_skl,sK5_skl) ),
    inference(resolution,[status(thm)],[f182,f25]) ).

fof(f196,definition,
    ( sQ10_spl
  <=> equal_set(sK4_skl,sK5_skl) ),
    introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).

fof(f197,plain,
    ( ~ sQ10_spl
    | equal_set(sK4_skl,sK5_skl) ),
    inference(component_clause,[status(thm)],[f196]) ).

fof(f199,definition,
    ( sQ11_spl
  <=> subset(sK4_skl,sK5_skl) ),
    introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).

fof(f201,plain,
    ( sQ11_spl
    | ~ subset(sK4_skl,sK5_skl) ),
    inference(component_clause,[status(thm)],[f199]) ).

fof(f202,plain,
    ( ~ sQ4_spl
    | ~ sQ11_spl
    | sQ10_spl ),
    inference(split_clause,[status(thm)],[f194,f196,f199,f144]) ).

fof(f203,plain,
    ( sQ11_spl
    | $false ),
    inference(forward_subsumption_resolution,[status(thm)],[f201,f73]) ).

fof(f204,plain,
    sQ11_spl,
    inference(contradiction_clause,[status(thm)],[f203]) ).

fof(f205,plain,
    ( ~ sQ8_spl
    | subset(sK5_skl,sK3_skl) ),
    inference(resolution,[status(thm)],[f186,f24]) ).

fof(f207,plain,
    ( ~ sQ8_spl
    | sQ7_spl
    | $false ),
    inference(forward_subsumption_resolution,[status(thm)],[f205,f156]) ).

fof(f208,plain,
    ( ~ sQ8_spl
    | sQ7_spl ),
    inference(contradiction_clause,[status(thm)],[f207]) ).

fof(f211,plain,
    ( ~ sQ10_spl
    | subset(sK5_skl,sK4_skl) ),
    inference(resolution,[status(thm)],[f197,f24]) ).

fof(f213,plain,
    ( ~ sQ10_spl
    | sQ5_spl
    | $false ),
    inference(forward_subsumption_resolution,[status(thm)],[f211,f149]) ).

fof(f214,plain,
    ( ~ sQ10_spl
    | sQ5_spl ),
    inference(contradiction_clause,[status(thm)],[f213]) ).

fof(f329,plain,
    ( ~ sQ1_spl
    | subset(sK3_skl,sK4_skl)
    | subset(sK3_skl,sK4_skl) ),
    inference(resolution,[status(thm)],[f108,f20]) ).

fof(f331,plain,
    ( ~ sQ1_spl
    | sQ0_spl ),
    inference(split_clause,[status(thm)],[f329,f76,f79]) ).

fof(f333,plain,
    ! [X0] :
      ( ~ sQ0_spl
      | member(X0,sK4_skl)
      | ~ member(X0,sK3_skl) ),
    inference(resolution,[status(thm)],[f77,f18]) ).

fof(f398,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(sK0_skl(X3,intersection(X0,difference(X1,X2))),X2)
      | subset(intersection(X0,difference(X1,X2)),X3) ),
    inference(resolution,[status(thm)],[f112,f44]) ).

fof(f423,plain,
    ! [X0,X1] :
      ( ~ sQ0_spl
      | member(sK0_skl(X1,intersection(sK3_skl,X0)),sK4_skl)
      | subset(intersection(sK3_skl,X0),X1) ),
    inference(resolution,[status(thm)],[f113,f333]) ).

fof(f4155,plain,
    ! [X0,X1] :
      ( ~ sQ0_spl
      | subset(intersection(sK3_skl,difference(X0,sK4_skl)),X1)
      | subset(intersection(sK3_skl,difference(X0,sK4_skl)),X1) ),
    inference(resolution,[status(thm)],[f398,f423]) ).

fof(f4194,plain,
    ! [X0,X1] :
      ( ~ sQ0_spl
      | subset(intersection(sK3_skl,difference(X0,sK4_skl)),X1) ),
    inference(duplicate_literals_removal,[status(thm)],[f4155]) ).

fof(f4339,plain,
    ( sQ1_spl
    | ~ sQ0_spl
    | $false ),
    inference(backward_subsumption_resolution,[status(thm)],[f81,f4194]) ).

fof(f4345,plain,
    ( sQ1_spl
    | ~ sQ0_spl ),
    inference(contradiction_clause,[status(thm)],[f4339]) ).

fof(f4346,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f82,f83,f150,f157,f191,f193,f202,f204,f208,f214,f331,f4345]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : SET701+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04  % Command  : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35  % Computer : n001.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 : Mon Sep 21 05:38:28 UTC 2026
% 0.08/0.35  % CPUTime  : 
% 0.12/0.36  % Drodi V4.1.1
% 1.38/0.78  % Refutation found
% 1.38/0.78  % SZS status Theorem for theBenchmark: Theorem is valid
% 1.38/0.78  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.80  % Elapsed time: 0.428233 seconds
% 0.21/0.80  % CPU time: 3.102688 seconds
% 0.21/0.80  % Total memory used: 124.106 MB
% 0.21/0.80  % Net memory used: 117.067 MB
%------------------------------------------------------------------------------