TSTP Solution File: SET169+3 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET169+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n028.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed May 31 12:34:11 EDT 2023

% Result   : Theorem 150.37s 19.26s
% Output   : CNFRefutation 150.91s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   24
% Syntax   : Number of formulae    :  130 (  21 unt;   0 def)
%            Number of atoms       :  332 (  27 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  324 ( 122   ~; 148   |;  29   &)
%                                         (  24 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   21 (  19 usr;  18 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :  153 (; 146   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [B,C,D] :
      ( member(D,union(B,C))
    <=> ( member(D,B)
        | member(D,C) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [B,C,D] :
      ( member(D,intersection(B,C))
    <=> ( member(D,B)
        & member(D,C) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [B,C] :
      ( B = C
    <=> ( subset(B,C)
        & subset(C,B) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [B,C] : intersection(B,C) = intersection(C,B),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [B,C] :
      ( subset(B,C)
    <=> ! [D] :
          ( member(D,B)
         => member(D,C) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [B,C] :
      ( B = C
    <=> ! [D] :
          ( member(D,B)
        <=> member(D,C) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,conjecture,
    ! [B,C,D] : intersection(B,union(C,D)) = union(intersection(B,C),intersection(B,D)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,negated_conjecture,
    ~ ! [B,C,D] : intersection(B,union(C,D)) = union(intersection(B,C),intersection(B,D)),
    inference(negated_conjecture,[status(cth)],[f9]) ).

fof(f11,plain,
    ! [B,C,D] :
      ( ( ~ member(D,union(B,C))
        | member(D,B)
        | member(D,C) )
      & ( member(D,union(B,C))
        | ( ~ member(D,B)
          & ~ member(D,C) ) ) ),
    inference(NNF_transformation,[status(esa)],[f1]) ).

fof(f12,plain,
    ( ! [B,C,D] :
        ( ~ member(D,union(B,C))
        | member(D,B)
        | member(D,C) )
    & ! [B,C,D] :
        ( member(D,union(B,C))
        | ( ~ member(D,B)
          & ~ member(D,C) ) ) ),
    inference(miniscoping,[status(esa)],[f11]) ).

fof(f13,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,union(X1,X2))
      | member(X0,X1)
      | member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f14,plain,
    ! [X0,X1,X2] :
      ( member(X0,union(X1,X2))
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f15,plain,
    ! [X0,X1,X2] :
      ( member(X0,union(X1,X2))
      | ~ member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f16,plain,
    ! [B,C,D] :
      ( ( ~ member(D,intersection(B,C))
        | ( member(D,B)
          & member(D,C) ) )
      & ( member(D,intersection(B,C))
        | ~ member(D,B)
        | ~ member(D,C) ) ),
    inference(NNF_transformation,[status(esa)],[f2]) ).

fof(f17,plain,
    ( ! [B,C,D] :
        ( ~ member(D,intersection(B,C))
        | ( member(D,B)
          & member(D,C) ) )
    & ! [B,C,D] :
        ( member(D,intersection(B,C))
        | ~ member(D,B)
        | ~ member(D,C) ) ),
    inference(miniscoping,[status(esa)],[f16]) ).

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

fof(f19,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,intersection(X1,X2))
      | member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f20,plain,
    ! [X0,X1,X2] :
      ( member(X0,intersection(X1,X2))
      | ~ member(X0,X1)
      | ~ member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f21,plain,
    ! [B,C] :
      ( ( B != C
        | ( subset(B,C)
          & subset(C,B) ) )
      & ( B = C
        | ~ subset(B,C)
        | ~ subset(C,B) ) ),
    inference(NNF_transformation,[status(esa)],[f3]) ).

fof(f22,plain,
    ( ! [B,C] :
        ( B != C
        | ( subset(B,C)
          & subset(C,B) ) )
    & ! [B,C] :
        ( B = C
        | ~ subset(B,C)
        | ~ subset(C,B) ) ),
    inference(miniscoping,[status(esa)],[f21]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( X0 != X1
      | subset(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f22]) ).

fof(f27,plain,
    ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f28,plain,
    ! [B,C] :
      ( subset(B,C)
    <=> ! [D] :
          ( ~ member(D,B)
          | member(D,C) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f6]) ).

fof(f29,plain,
    ! [B,C] :
      ( ( ~ subset(B,C)
        | ! [D] :
            ( ~ member(D,B)
            | member(D,C) ) )
      & ( subset(B,C)
        | ? [D] :
            ( member(D,B)
            & ~ member(D,C) ) ) ),
    inference(NNF_transformation,[status(esa)],[f28]) ).

fof(f30,plain,
    ( ! [B,C] :
        ( ~ subset(B,C)
        | ! [D] :
            ( ~ member(D,B)
            | member(D,C) ) )
    & ! [B,C] :
        ( subset(B,C)
        | ? [D] :
            ( member(D,B)
            & ~ member(D,C) ) ) ),
    inference(miniscoping,[status(esa)],[f29]) ).

fof(f31,plain,
    ( ! [B,C] :
        ( ~ subset(B,C)
        | ! [D] :
            ( ~ member(D,B)
            | member(D,C) ) )
    & ! [B,C] :
        ( subset(B,C)
        | ( member(sk0_0(C,B),B)
          & ~ member(sk0_0(C,B),C) ) ) ),
    inference(skolemization,[status(esa)],[f30]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sk0_0(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sk0_0(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f36,plain,
    ! [B,C] :
      ( ( B != C
        | ! [D] :
            ( ( ~ member(D,B)
              | member(D,C) )
            & ( member(D,B)
              | ~ member(D,C) ) ) )
      & ( B = C
        | ? [D] :
            ( ( ~ member(D,B)
              | ~ member(D,C) )
            & ( member(D,B)
              | member(D,C) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f8]) ).

fof(f37,plain,
    ( ! [B,C] :
        ( B != C
        | ( ! [D] :
              ( ~ member(D,B)
              | member(D,C) )
          & ! [D] :
              ( member(D,B)
              | ~ member(D,C) ) ) )
    & ! [B,C] :
        ( B = C
        | ? [D] :
            ( ( ~ member(D,B)
              | ~ member(D,C) )
            & ( member(D,B)
              | member(D,C) ) ) ) ),
    inference(miniscoping,[status(esa)],[f36]) ).

fof(f38,plain,
    ( ! [B,C] :
        ( B != C
        | ( ! [D] :
              ( ~ member(D,B)
              | member(D,C) )
          & ! [D] :
              ( member(D,B)
              | ~ member(D,C) ) ) )
    & ! [B,C] :
        ( B = C
        | ( ( ~ member(sk0_1(C,B),B)
            | ~ member(sk0_1(C,B),C) )
          & ( member(sk0_1(C,B),B)
            | member(sk0_1(C,B),C) ) ) ) ),
    inference(skolemization,[status(esa)],[f37]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ member(sk0_1(X1,X0),X0)
      | ~ member(sk0_1(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f38]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( X0 = X1
      | member(sk0_1(X1,X0),X0)
      | member(sk0_1(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f38]) ).

fof(f43,plain,
    ? [B,C,D] : intersection(B,union(C,D)) != union(intersection(B,C),intersection(B,D)),
    inference(pre_NNF_transformation,[status(esa)],[f10]) ).

fof(f44,plain,
    intersection(sk0_2,union(sk0_3,sk0_4)) != union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4)),
    inference(skolemization,[status(esa)],[f43]) ).

fof(f45,plain,
    intersection(sk0_2,union(sk0_3,sk0_4)) != union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4)),
    inference(cnf_transformation,[status(esa)],[f44]) ).

fof(f46,plain,
    ! [X0] : subset(X0,X0),
    inference(destructive_equality_resolution,[status(esa)],[f23]) ).

fof(f77,plain,
    ! [X0,X1,X2,X3] :
      ( member(X0,X1)
      | ~ member(X0,union(intersection(X1,X2),X3))
      | member(X0,X3) ),
    inference(resolution,[status(thm)],[f18,f13]) ).

fof(f87,plain,
    ! [X0,X1,X2,X3] :
      ( member(X0,X1)
      | ~ member(X0,union(X2,intersection(X3,X1)))
      | member(X0,X2) ),
    inference(resolution,[status(thm)],[f19,f13]) ).

fof(f92,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(X0,intersection(X1,union(X2,X3)))
      | member(X0,X2)
      | member(X0,X3) ),
    inference(resolution,[status(thm)],[f19,f13]) ).

fof(f161,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(X0,X1)
      | ~ member(X0,X2)
      | member(X0,union(X3,intersection(X1,X2))) ),
    inference(resolution,[status(thm)],[f20,f15]) ).

fof(f162,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(X0,X1)
      | ~ member(X0,X2)
      | member(X0,union(intersection(X1,X2),X3)) ),
    inference(resolution,[status(thm)],[f20,f14]) ).

fof(f187,plain,
    ! [X0,X1,X2,X3] :
      ( member(X0,intersection(X1,union(X2,X3)))
      | ~ member(X0,X1)
      | ~ member(X0,X3) ),
    inference(resolution,[status(thm)],[f20,f15]) ).

fof(f188,plain,
    ! [X0,X1,X2,X3] :
      ( member(X0,intersection(X1,union(X2,X3)))
      | ~ member(X0,X1)
      | ~ member(X0,X2) ),
    inference(resolution,[status(thm)],[f20,f14]) ).

fof(f231,plain,
    ! [X0,X1,X2] :
      ( subset(X0,X1)
      | ~ member(sk0_0(X1,X0),intersection(X2,X1)) ),
    inference(resolution,[status(thm)],[f34,f19]) ).

fof(f239,plain,
    ! [X0,X1] :
      ( subset(intersection(X0,X1),X1)
      | subset(intersection(X0,X1),X1) ),
    inference(resolution,[status(thm)],[f231,f33]) ).

fof(f240,plain,
    ! [X0,X1] : subset(intersection(X0,X1),X1),
    inference(duplicate_literals_removal,[status(esa)],[f239]) ).

fof(f252,plain,
    ! [X0,X1] : subset(intersection(X0,X1),X0),
    inference(paramodulation,[status(thm)],[f27,f240]) ).

fof(f321,plain,
    ( spl0_4
  <=> member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))) ),
    introduced(split_symbol_definition) ).

fof(f322,plain,
    ( member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4)))
    | ~ spl0_4 ),
    inference(component_clause,[status(thm)],[f321]) ).

fof(f323,plain,
    ( ~ member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4)))
    | spl0_4 ),
    inference(component_clause,[status(thm)],[f321]) ).

fof(f324,plain,
    ( spl0_5
  <=> member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),intersection(sk0_2,union(sk0_3,sk0_4))) ),
    introduced(split_symbol_definition) ).

fof(f325,plain,
    ( member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),intersection(sk0_2,union(sk0_3,sk0_4)))
    | ~ spl0_5 ),
    inference(component_clause,[status(thm)],[f324]) ).

fof(f326,plain,
    ( ~ member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),intersection(sk0_2,union(sk0_3,sk0_4)))
    | spl0_5 ),
    inference(component_clause,[status(thm)],[f324]) ).

fof(f327,plain,
    ( ~ member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4)))
    | ~ member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),intersection(sk0_2,union(sk0_3,sk0_4))) ),
    inference(resolution,[status(thm)],[f41,f45]) ).

fof(f328,plain,
    ( ~ spl0_4
    | ~ spl0_5 ),
    inference(split_clause,[status(thm)],[f327,f321,f324]) ).

fof(f355,plain,
    ( member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4)))
    | member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),intersection(sk0_2,union(sk0_3,sk0_4))) ),
    inference(resolution,[status(thm)],[f42,f45]) ).

fof(f356,plain,
    ( spl0_4
    | spl0_5 ),
    inference(split_clause,[status(thm)],[f355,f321,f324]) ).

fof(f412,plain,
    ( spl0_6
  <=> union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4)) = intersection(sk0_2,union(sk0_3,sk0_4)) ),
    introduced(split_symbol_definition) ).

fof(f413,plain,
    ( union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4)) = intersection(sk0_2,union(sk0_3,sk0_4))
    | ~ spl0_6 ),
    inference(component_clause,[status(thm)],[f412]) ).

fof(f417,plain,
    ( spl0_7
  <=> member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_2) ),
    introduced(split_symbol_definition) ).

fof(f419,plain,
    ( ~ member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_2)
    | spl0_7 ),
    inference(component_clause,[status(thm)],[f417]) ).

fof(f470,plain,
    ! [X0] :
      ( ~ member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),intersection(sk0_2,X0))
      | spl0_7 ),
    inference(resolution,[status(thm)],[f419,f18]) ).

fof(f547,plain,
    ( union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4)) = intersection(sk0_2,union(sk0_3,sk0_4))
    | member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4)))
    | spl0_7 ),
    inference(resolution,[status(thm)],[f470,f42]) ).

fof(f548,plain,
    ( spl0_6
    | spl0_4
    | spl0_7 ),
    inference(split_clause,[status(thm)],[f547,f412,f321,f417]) ).

fof(f590,plain,
    ( $false
    | ~ spl0_6 ),
    inference(forward_subsumption_resolution,[status(thm)],[f413,f45]) ).

fof(f591,plain,
    ~ spl0_6,
    inference(contradiction_clause,[status(thm)],[f590]) ).

fof(f756,plain,
    ( spl0_12
  <=> member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_4) ),
    introduced(split_symbol_definition) ).

fof(f956,plain,
    ( spl0_13
  <=> member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),intersection(sk0_2,sk0_3)) ),
    introduced(split_symbol_definition) ).

fof(f957,plain,
    ( member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),intersection(sk0_2,sk0_3))
    | ~ spl0_13 ),
    inference(component_clause,[status(thm)],[f956]) ).

fof(f959,plain,
    ( spl0_14
  <=> member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),intersection(sk0_2,sk0_4)) ),
    introduced(split_symbol_definition) ).

fof(f960,plain,
    ( member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),intersection(sk0_2,sk0_4))
    | ~ spl0_14 ),
    inference(component_clause,[status(thm)],[f959]) ).

fof(f3401,plain,
    ( spl0_31
  <=> intersection(sk0_2,union(sk0_3,sk0_4)) = intersection(sk0_2,union(sk0_3,sk0_4)) ),
    introduced(split_symbol_definition) ).

fof(f3403,plain,
    ( intersection(sk0_2,union(sk0_3,sk0_4)) != intersection(sk0_2,union(sk0_3,sk0_4))
    | spl0_31 ),
    inference(component_clause,[status(thm)],[f3401]) ).

fof(f5527,plain,
    ( spl0_107
  <=> subset(sk0_2,sk0_2) ),
    introduced(split_symbol_definition) ).

fof(f5529,plain,
    ( ~ subset(sk0_2,sk0_2)
    | spl0_107 ),
    inference(component_clause,[status(thm)],[f5527]) ).

fof(f5551,plain,
    ( $false
    | spl0_107 ),
    inference(forward_subsumption_resolution,[status(thm)],[f5529,f46]) ).

fof(f5552,plain,
    spl0_107,
    inference(contradiction_clause,[status(thm)],[f5551]) ).

fof(f6059,plain,
    ( spl0_127
  <=> subset(intersection(union(sk0_3,sk0_4),sk0_2),sk0_2) ),
    introduced(split_symbol_definition) ).

fof(f6061,plain,
    ( ~ subset(intersection(union(sk0_3,sk0_4),sk0_2),sk0_2)
    | spl0_127 ),
    inference(component_clause,[status(thm)],[f6059]) ).

fof(f6098,plain,
    ( ~ subset(intersection(sk0_2,union(sk0_3,sk0_4)),sk0_2)
    | spl0_127 ),
    inference(forward_demodulation,[status(thm)],[f27,f6061]) ).

fof(f6099,plain,
    ( $false
    | spl0_127 ),
    inference(forward_subsumption_resolution,[status(thm)],[f6098,f252]) ).

fof(f6100,plain,
    spl0_127,
    inference(contradiction_clause,[status(thm)],[f6099]) ).

fof(f7533,plain,
    ( spl0_155
  <=> subset(intersection(sk0_2,union(sk0_3,sk0_4)),sk0_2) ),
    introduced(split_symbol_definition) ).

fof(f7535,plain,
    ( ~ subset(intersection(sk0_2,union(sk0_3,sk0_4)),sk0_2)
    | spl0_155 ),
    inference(component_clause,[status(thm)],[f7533]) ).

fof(f7560,plain,
    ( $false
    | spl0_155 ),
    inference(forward_subsumption_resolution,[status(thm)],[f7535,f252]) ).

fof(f7561,plain,
    spl0_155,
    inference(contradiction_clause,[status(thm)],[f7560]) ).

fof(f7737,plain,
    ( spl0_158
  <=> subset(union(sk0_3,sk0_4),union(sk0_3,sk0_4)) ),
    introduced(split_symbol_definition) ).

fof(f7739,plain,
    ( ~ subset(union(sk0_3,sk0_4),union(sk0_3,sk0_4))
    | spl0_158 ),
    inference(component_clause,[status(thm)],[f7737]) ).

fof(f7765,plain,
    ( $false
    | spl0_158 ),
    inference(forward_subsumption_resolution,[status(thm)],[f7739,f46]) ).

fof(f7766,plain,
    spl0_158,
    inference(contradiction_clause,[status(thm)],[f7765]) ).

fof(f7838,plain,
    ( spl0_162
  <=> subset(intersection(union(sk0_3,sk0_4),sk0_2),union(sk0_3,sk0_4)) ),
    introduced(split_symbol_definition) ).

fof(f7840,plain,
    ( ~ subset(intersection(union(sk0_3,sk0_4),sk0_2),union(sk0_3,sk0_4))
    | spl0_162 ),
    inference(component_clause,[status(thm)],[f7838]) ).

fof(f7877,plain,
    ( ~ subset(intersection(sk0_2,union(sk0_3,sk0_4)),union(sk0_3,sk0_4))
    | spl0_162 ),
    inference(forward_demodulation,[status(thm)],[f27,f7840]) ).

fof(f7878,plain,
    ( $false
    | spl0_162 ),
    inference(forward_subsumption_resolution,[status(thm)],[f7877,f240]) ).

fof(f7879,plain,
    spl0_162,
    inference(contradiction_clause,[status(thm)],[f7878]) ).

fof(f8612,plain,
    ( spl0_175
  <=> subset(intersection(sk0_2,sk0_2),sk0_2) ),
    introduced(split_symbol_definition) ).

fof(f8614,plain,
    ( ~ subset(intersection(sk0_2,sk0_2),sk0_2)
    | spl0_175 ),
    inference(component_clause,[status(thm)],[f8612]) ).

fof(f8635,plain,
    ( $false
    | spl0_175 ),
    inference(forward_subsumption_resolution,[status(thm)],[f8614,f252]) ).

fof(f8636,plain,
    spl0_175,
    inference(contradiction_clause,[status(thm)],[f8635]) ).

fof(f11162,plain,
    ( member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_2)
    | member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),intersection(sk0_2,sk0_4))
    | ~ spl0_4 ),
    inference(resolution,[status(thm)],[f322,f77]) ).

fof(f11163,plain,
    ( spl0_7
    | spl0_14
    | ~ spl0_4 ),
    inference(split_clause,[status(thm)],[f11162,f417,f959,f321]) ).

fof(f13048,plain,
    ( spl0_209
  <=> subset(intersection(sk0_2,union(sk0_3,sk0_4)),intersection(sk0_2,union(sk0_3,sk0_4))) ),
    introduced(split_symbol_definition) ).

fof(f13050,plain,
    ( ~ subset(intersection(sk0_2,union(sk0_3,sk0_4)),intersection(sk0_2,union(sk0_3,sk0_4)))
    | spl0_209 ),
    inference(component_clause,[status(thm)],[f13048]) ).

fof(f13165,plain,
    ( $false
    | spl0_209 ),
    inference(forward_subsumption_resolution,[status(thm)],[f13050,f46]) ).

fof(f13166,plain,
    spl0_209,
    inference(contradiction_clause,[status(thm)],[f13165]) ).

fof(f13922,plain,
    ( member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_4)
    | member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),intersection(sk0_2,sk0_3))
    | ~ spl0_4 ),
    inference(resolution,[status(thm)],[f87,f322]) ).

fof(f13923,plain,
    ( spl0_12
    | spl0_13
    | ~ spl0_4 ),
    inference(split_clause,[status(thm)],[f13922,f756,f956,f321]) ).

fof(f14449,plain,
    ( spl0_227
  <=> member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_3) ),
    introduced(split_symbol_definition) ).

fof(f14877,plain,
    ( spl0_231
  <=> subset(intersection(sk0_2,union(sk0_3,sk0_4)),union(sk0_3,sk0_4)) ),
    introduced(split_symbol_definition) ).

fof(f14879,plain,
    ( ~ subset(intersection(sk0_2,union(sk0_3,sk0_4)),union(sk0_3,sk0_4))
    | spl0_231 ),
    inference(component_clause,[status(thm)],[f14877]) ).

fof(f14904,plain,
    ( $false
    | spl0_231 ),
    inference(forward_subsumption_resolution,[status(thm)],[f14879,f240]) ).

fof(f14905,plain,
    spl0_231,
    inference(contradiction_clause,[status(thm)],[f14904]) ).

fof(f21730,plain,
    ( $false
    | spl0_31 ),
    inference(trivial_equality_resolution,[status(esa)],[f3403]) ).

fof(f21731,plain,
    spl0_31,
    inference(contradiction_clause,[status(thm)],[f21730]) ).

fof(f24046,plain,
    ( member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_3)
    | member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_4)
    | ~ spl0_5 ),
    inference(resolution,[status(thm)],[f325,f92]) ).

fof(f24047,plain,
    ( spl0_227
    | spl0_12
    | ~ spl0_5 ),
    inference(split_clause,[status(thm)],[f24046,f14449,f756,f324]) ).

fof(f24419,plain,
    ( ~ member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_2)
    | ~ member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_3)
    | spl0_4 ),
    inference(resolution,[status(thm)],[f323,f162]) ).

fof(f24420,plain,
    ( ~ spl0_7
    | ~ spl0_227
    | spl0_4 ),
    inference(split_clause,[status(thm)],[f24419,f417,f14449,f321]) ).

fof(f24421,plain,
    ( ~ member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_2)
    | ~ member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_4)
    | spl0_4 ),
    inference(resolution,[status(thm)],[f323,f161]) ).

fof(f24422,plain,
    ( ~ spl0_7
    | ~ spl0_12
    | spl0_4 ),
    inference(split_clause,[status(thm)],[f24421,f417,f756,f321]) ).

fof(f40469,plain,
    ( ~ member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_2)
    | ~ member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_4)
    | spl0_5 ),
    inference(resolution,[status(thm)],[f187,f326]) ).

fof(f40470,plain,
    ( ~ spl0_7
    | ~ spl0_12
    | spl0_5 ),
    inference(split_clause,[status(thm)],[f40469,f417,f756,f324]) ).

fof(f46299,plain,
    ( ~ member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_2)
    | ~ member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_3)
    | spl0_5 ),
    inference(resolution,[status(thm)],[f188,f326]) ).

fof(f46300,plain,
    ( ~ spl0_7
    | ~ spl0_227
    | spl0_5 ),
    inference(split_clause,[status(thm)],[f46299,f417,f14449,f324]) ).

fof(f51485,plain,
    ( member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_2)
    | ~ spl0_14 ),
    inference(resolution,[status(thm)],[f960,f18]) ).

fof(f51486,plain,
    ( spl0_7
    | ~ spl0_14 ),
    inference(split_clause,[status(thm)],[f51485,f417,f959]) ).

fof(f51609,plain,
    ( member(sk0_1(intersection(sk0_2,union(sk0_3,sk0_4)),union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4))),sk0_3)
    | ~ spl0_13 ),
    inference(resolution,[status(thm)],[f957,f19]) ).

fof(f51610,plain,
    ( spl0_227
    | ~ spl0_13 ),
    inference(split_clause,[status(thm)],[f51609,f14449,f956]) ).

fof(f51718,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f328,f356,f548,f591,f5552,f6100,f7561,f7766,f7879,f8636,f11163,f13166,f13923,f14905,f21731,f24047,f24420,f24422,f40470,f46300,f51486,f51610]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SET169+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33  % Computer : n028.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Tue May 30 10:26:47 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  % Drodi V3.5.1
% 150.37/19.26  % Refutation found
% 150.37/19.26  % SZS status Theorem for theBenchmark: Theorem is valid
% 150.37/19.26  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 152.38/19.60  % Elapsed time: 19.210346 seconds
% 152.38/19.60  % CPU time: 151.767248 seconds
% 152.38/19.60  % Memory used: 1.217 GB
%------------------------------------------------------------------------------