TSTP Solution File: SET169+3 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET169+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n011.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  1 03:45:32 EDT 2024

% Result   : Theorem 0.57s 0.75s
% Output   : Refutation 0.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   88 (   7 unt;   0 def)
%            Number of atoms       :  244 (  17 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  264 ( 108   ~; 122   |;  20   &)
%                                         (  12 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :   11 (   9 usr;   8 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   75 (  66   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f132,plain,
    $false,
    inference(avatar_sat_refutation,[],[f54,f55,f79,f80,f86,f87,f92,f93,f99,f104,f111,f117,f125,f131]) ).

fof(f131,plain,
    ( spl5_2
    | ~ spl5_5 ),
    inference(avatar_contradiction_clause,[],[f130]) ).

fof(f130,plain,
    ( $false
    | spl5_2
    | ~ spl5_5 ),
    inference(subsumption_resolution,[],[f129,f70]) ).

fof(f70,plain,
    ( member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),intersection(sK0,sK2))
    | ~ spl5_5 ),
    inference(avatar_component_clause,[],[f68]) ).

fof(f68,plain,
    ( spl5_5
  <=> member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),intersection(sK0,sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).

fof(f129,plain,
    ( ~ member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),intersection(sK0,sK2))
    | spl5_2 ),
    inference(resolution,[],[f52,f26]) ).

fof(f26,plain,
    ! [X2,X0,X1] :
      ( member(X2,union(X0,X1))
      | ~ member(X2,X1) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,union(X0,X1))
        | ( ~ member(X2,X1)
          & ~ member(X2,X0) ) )
      & ( member(X2,X1)
        | member(X2,X0)
        | ~ member(X2,union(X0,X1)) ) ),
    inference(flattening,[],[f14]) ).

fof(f14,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,union(X0,X1))
        | ( ~ member(X2,X1)
          & ~ member(X2,X0) ) )
      & ( member(X2,X1)
        | member(X2,X0)
        | ~ member(X2,union(X0,X1)) ) ),
    inference(nnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1,X2] :
      ( member(X2,union(X0,X1))
    <=> ( member(X2,X1)
        | member(X2,X0) ) ),
    file('/export/starexec/sandbox/tmp/tmp.0AVEbEUNqy/Vampire---4.8_18922',union_defn) ).

fof(f52,plain,
    ( ~ member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),union(intersection(sK0,sK1),intersection(sK0,sK2)))
    | spl5_2 ),
    inference(avatar_component_clause,[],[f51]) ).

fof(f51,plain,
    ( spl5_2
  <=> member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),union(intersection(sK0,sK1),intersection(sK0,sK2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

fof(f125,plain,
    ( spl5_4
    | ~ spl5_6 ),
    inference(avatar_contradiction_clause,[],[f124]) ).

fof(f124,plain,
    ( $false
    | spl5_4
    | ~ spl5_6 ),
    inference(subsumption_resolution,[],[f123,f118]) ).

fof(f118,plain,
    ( ~ member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),sK1)
    | spl5_4 ),
    inference(resolution,[],[f64,f25]) ).

fof(f25,plain,
    ! [X2,X0,X1] :
      ( member(X2,union(X0,X1))
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f64,plain,
    ( ~ member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),union(sK1,sK2))
    | spl5_4 ),
    inference(avatar_component_clause,[],[f62]) ).

fof(f62,plain,
    ( spl5_4
  <=> member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),union(sK1,sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).

fof(f123,plain,
    ( member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),sK1)
    | ~ spl5_6 ),
    inference(resolution,[],[f74,f29]) ).

fof(f29,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,intersection(X0,X1))
      | member(X2,X1) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,intersection(X0,X1))
        | ~ member(X2,X1)
        | ~ member(X2,X0) )
      & ( ( member(X2,X1)
          & member(X2,X0) )
        | ~ member(X2,intersection(X0,X1)) ) ),
    inference(flattening,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,intersection(X0,X1))
        | ~ member(X2,X1)
        | ~ member(X2,X0) )
      & ( ( member(X2,X1)
          & member(X2,X0) )
        | ~ member(X2,intersection(X0,X1)) ) ),
    inference(nnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1,X2] :
      ( member(X2,intersection(X0,X1))
    <=> ( member(X2,X1)
        & member(X2,X0) ) ),
    file('/export/starexec/sandbox/tmp/tmp.0AVEbEUNqy/Vampire---4.8_18922',intersection_defn) ).

fof(f74,plain,
    ( member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),intersection(sK0,sK1))
    | ~ spl5_6 ),
    inference(avatar_component_clause,[],[f72]) ).

fof(f72,plain,
    ( spl5_6
  <=> member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),intersection(sK0,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_6])]) ).

fof(f117,plain,
    ( ~ spl5_3
    | ~ spl5_4
    | spl5_6
    | spl5_7 ),
    inference(avatar_contradiction_clause,[],[f116]) ).

fof(f116,plain,
    ( $false
    | ~ spl5_3
    | ~ spl5_4
    | spl5_6
    | spl5_7 ),
    inference(subsumption_resolution,[],[f115,f59]) ).

fof(f59,plain,
    ( member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),sK0)
    | ~ spl5_3 ),
    inference(avatar_component_clause,[],[f58]) ).

fof(f58,plain,
    ( spl5_3
  <=> member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).

fof(f115,plain,
    ( ~ member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),sK0)
    | ~ spl5_4
    | spl5_6
    | spl5_7 ),
    inference(subsumption_resolution,[],[f114,f113]) ).

fof(f113,plain,
    ( member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),sK1)
    | ~ spl5_4
    | spl5_7 ),
    inference(subsumption_resolution,[],[f112,f103]) ).

fof(f103,plain,
    ( ~ member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),sK2)
    | spl5_7 ),
    inference(avatar_component_clause,[],[f101]) ).

fof(f101,plain,
    ( spl5_7
  <=> member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_7])]) ).

fof(f112,plain,
    ( member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),sK1)
    | member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),sK2)
    | ~ spl5_4 ),
    inference(resolution,[],[f63,f24]) ).

fof(f24,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,union(X0,X1))
      | member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f63,plain,
    ( member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),union(sK1,sK2))
    | ~ spl5_4 ),
    inference(avatar_component_clause,[],[f62]) ).

fof(f114,plain,
    ( ~ member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),sK1)
    | ~ member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),sK0)
    | spl5_6 ),
    inference(resolution,[],[f73,f30]) ).

fof(f30,plain,
    ! [X2,X0,X1] :
      ( member(X2,intersection(X0,X1))
      | ~ member(X2,X1)
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f73,plain,
    ( ~ member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),intersection(sK0,sK1))
    | spl5_6 ),
    inference(avatar_component_clause,[],[f72]) ).

fof(f111,plain,
    ( ~ spl5_6
    | spl5_2 ),
    inference(avatar_split_clause,[],[f107,f51,f72]) ).

fof(f107,plain,
    ( ~ member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),intersection(sK0,sK1))
    | spl5_2 ),
    inference(resolution,[],[f52,f25]) ).

fof(f104,plain,
    ( ~ spl5_3
    | ~ spl5_7
    | spl5_5 ),
    inference(avatar_split_clause,[],[f94,f68,f101,f58]) ).

fof(f94,plain,
    ( ~ member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),sK2)
    | ~ member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),sK0)
    | spl5_5 ),
    inference(resolution,[],[f69,f30]) ).

fof(f69,plain,
    ( ~ member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),intersection(sK0,sK2))
    | spl5_5 ),
    inference(avatar_component_clause,[],[f68]) ).

fof(f99,plain,
    ( spl5_3
    | ~ spl5_6 ),
    inference(avatar_split_clause,[],[f95,f72,f58]) ).

fof(f95,plain,
    ( member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),sK0)
    | ~ spl5_6 ),
    inference(resolution,[],[f74,f28]) ).

fof(f28,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,intersection(X0,X1))
      | member(X2,X0) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f93,plain,
    ( spl5_5
    | spl5_6
    | ~ spl5_2 ),
    inference(avatar_split_clause,[],[f88,f51,f72,f68]) ).

fof(f88,plain,
    ( member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),intersection(sK0,sK1))
    | member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),intersection(sK0,sK2))
    | ~ spl5_2 ),
    inference(resolution,[],[f53,f24]) ).

fof(f53,plain,
    ( member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),union(intersection(sK0,sK1),intersection(sK0,sK2)))
    | ~ spl5_2 ),
    inference(avatar_component_clause,[],[f51]) ).

fof(f92,plain,
    ( spl5_4
    | ~ spl5_5 ),
    inference(avatar_contradiction_clause,[],[f91]) ).

fof(f91,plain,
    ( $false
    | spl5_4
    | ~ spl5_5 ),
    inference(subsumption_resolution,[],[f90,f83]) ).

fof(f83,plain,
    ( member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),sK2)
    | ~ spl5_5 ),
    inference(resolution,[],[f70,f29]) ).

fof(f90,plain,
    ( ~ member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),sK2)
    | spl5_4 ),
    inference(resolution,[],[f64,f26]) ).

fof(f87,plain,
    ( ~ spl5_3
    | ~ spl5_4
    | spl5_1 ),
    inference(avatar_split_clause,[],[f81,f47,f62,f58]) ).

fof(f47,plain,
    ( spl5_1
  <=> member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),intersection(sK0,union(sK1,sK2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

fof(f81,plain,
    ( ~ member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),union(sK1,sK2))
    | ~ member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),sK0)
    | spl5_1 ),
    inference(resolution,[],[f48,f30]) ).

fof(f48,plain,
    ( ~ member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),intersection(sK0,union(sK1,sK2)))
    | spl5_1 ),
    inference(avatar_component_clause,[],[f47]) ).

fof(f86,plain,
    ( spl5_3
    | ~ spl5_5 ),
    inference(avatar_split_clause,[],[f82,f68,f58]) ).

fof(f82,plain,
    ( member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),sK0)
    | ~ spl5_5 ),
    inference(resolution,[],[f70,f28]) ).

fof(f80,plain,
    ( spl5_4
    | ~ spl5_1 ),
    inference(avatar_split_clause,[],[f77,f47,f62]) ).

fof(f77,plain,
    ( member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),union(sK1,sK2))
    | ~ spl5_1 ),
    inference(resolution,[],[f49,f29]) ).

fof(f49,plain,
    ( member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),intersection(sK0,union(sK1,sK2)))
    | ~ spl5_1 ),
    inference(avatar_component_clause,[],[f47]) ).

fof(f79,plain,
    ( ~ spl5_1
    | spl5_3 ),
    inference(avatar_contradiction_clause,[],[f78]) ).

fof(f78,plain,
    ( $false
    | ~ spl5_1
    | spl5_3 ),
    inference(subsumption_resolution,[],[f76,f60]) ).

fof(f60,plain,
    ( ~ member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),sK0)
    | spl5_3 ),
    inference(avatar_component_clause,[],[f58]) ).

fof(f76,plain,
    ( member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),sK0)
    | ~ spl5_1 ),
    inference(resolution,[],[f49,f28]) ).

fof(f55,plain,
    ( ~ spl5_1
    | ~ spl5_2 ),
    inference(avatar_split_clause,[],[f45,f51,f47]) ).

fof(f45,plain,
    ( ~ member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),union(intersection(sK0,sK1),intersection(sK0,sK2)))
    | ~ member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),intersection(sK0,union(sK1,sK2))) ),
    inference(resolution,[],[f38,f41]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( sQ4_eqProxy(X0,X1)
      | ~ member(sK3(X0,X1),X1)
      | ~ member(sK3(X0,X1),X0) ),
    inference(equality_proxy_replacement,[],[f34,f37]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( sQ4_eqProxy(X0,X1)
    <=> X0 = X1 ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ4_eqProxy])]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ member(sK3(X0,X1),X1)
      | ~ member(sK3(X0,X1),X0) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ( ( ~ member(sK3(X0,X1),X1)
            | ~ member(sK3(X0,X1),X0) )
          & ( member(sK3(X0,X1),X1)
            | member(sK3(X0,X1),X0) ) ) )
      & ( ! [X3] :
            ( ( member(X3,X0)
              | ~ member(X3,X1) )
            & ( member(X3,X1)
              | ~ member(X3,X0) ) )
        | X0 != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f19,f20]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ member(X2,X1)
            | ~ member(X2,X0) )
          & ( member(X2,X1)
            | member(X2,X0) ) )
     => ( ( ~ member(sK3(X0,X1),X1)
          | ~ member(sK3(X0,X1),X0) )
        & ( member(sK3(X0,X1),X1)
          | member(sK3(X0,X1),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ? [X2] :
            ( ( ~ member(X2,X1)
              | ~ member(X2,X0) )
            & ( member(X2,X1)
              | member(X2,X0) ) ) )
      & ( ! [X3] :
            ( ( member(X3,X0)
              | ~ member(X3,X1) )
            & ( member(X3,X1)
              | ~ member(X3,X0) ) )
        | X0 != X1 ) ),
    inference(rectify,[],[f18]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ? [X2] :
            ( ( ~ member(X2,X1)
              | ~ member(X2,X0) )
            & ( member(X2,X1)
              | member(X2,X0) ) ) )
      & ( ! [X2] :
            ( ( member(X2,X0)
              | ~ member(X2,X1) )
            & ( member(X2,X1)
              | ~ member(X2,X0) ) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0,X1] :
      ( X0 = X1
    <=> ! [X2] :
          ( member(X2,X0)
        <=> member(X2,X1) ) ),
    file('/export/starexec/sandbox/tmp/tmp.0AVEbEUNqy/Vampire---4.8_18922',equal_member_defn) ).

fof(f38,plain,
    ~ sQ4_eqProxy(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),
    inference(equality_proxy_replacement,[],[f22,f37]) ).

fof(f22,plain,
    intersection(sK0,union(sK1,sK2)) != union(intersection(sK0,sK1),intersection(sK0,sK2)),
    inference(cnf_transformation,[],[f13]) ).

fof(f13,plain,
    intersection(sK0,union(sK1,sK2)) != union(intersection(sK0,sK1),intersection(sK0,sK2)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f11,f12]) ).

fof(f12,plain,
    ( ? [X0,X1,X2] : intersection(X0,union(X1,X2)) != union(intersection(X0,X1),intersection(X0,X2))
   => intersection(sK0,union(sK1,sK2)) != union(intersection(sK0,sK1),intersection(sK0,sK2)) ),
    introduced(choice_axiom,[]) ).

fof(f11,plain,
    ? [X0,X1,X2] : intersection(X0,union(X1,X2)) != union(intersection(X0,X1),intersection(X0,X2)),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,negated_conjecture,
    ~ ! [X0,X1,X2] : intersection(X0,union(X1,X2)) = union(intersection(X0,X1),intersection(X0,X2)),
    inference(negated_conjecture,[],[f9]) ).

fof(f9,conjecture,
    ! [X0,X1,X2] : intersection(X0,union(X1,X2)) = union(intersection(X0,X1),intersection(X0,X2)),
    file('/export/starexec/sandbox/tmp/tmp.0AVEbEUNqy/Vampire---4.8_18922',prove_intersection_distributes_over_union) ).

fof(f54,plain,
    ( spl5_1
    | spl5_2 ),
    inference(avatar_split_clause,[],[f44,f51,f47]) ).

fof(f44,plain,
    ( member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),union(intersection(sK0,sK1),intersection(sK0,sK2)))
    | member(sK3(intersection(sK0,union(sK1,sK2)),union(intersection(sK0,sK1),intersection(sK0,sK2))),intersection(sK0,union(sK1,sK2))) ),
    inference(resolution,[],[f38,f42]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( sQ4_eqProxy(X0,X1)
      | member(sK3(X0,X1),X1)
      | member(sK3(X0,X1),X0) ),
    inference(equality_proxy_replacement,[],[f33,f37]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( X0 = X1
      | member(sK3(X0,X1),X1)
      | member(sK3(X0,X1),X0) ),
    inference(cnf_transformation,[],[f21]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SET169+3 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.36  % Computer : n011.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Tue Apr 30 17:17:46 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.0AVEbEUNqy/Vampire---4.8_18922
% 0.57/0.74  % (19179)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2996ds/56Mi)
% 0.57/0.74  % (19178)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2996ds/83Mi)
% 0.57/0.74  % (19172)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2996ds/34Mi)
% 0.57/0.74  % (19174)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.57/0.74  % (19175)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.57/0.74  % (19173)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2996ds/51Mi)
% 0.57/0.74  % (19176)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2996ds/34Mi)
% 0.57/0.75  % (19177)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.57/0.75  % (19179)First to succeed.
% 0.57/0.75  % (19178)Refutation not found, incomplete strategy% (19178)------------------------------
% 0.57/0.75  % (19178)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.57/0.75  % (19178)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.75  
% 0.57/0.75  % (19178)Memory used [KB]: 955
% 0.57/0.75  % (19178)Time elapsed: 0.003 s
% 0.57/0.75  % (19177)Refutation not found, incomplete strategy% (19177)------------------------------
% 0.57/0.75  % (19177)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.57/0.75  % (19178)Instructions burned: 3 (million)
% 0.57/0.75  % (19178)------------------------------
% 0.57/0.75  % (19178)------------------------------
% 0.57/0.75  % (19177)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.75  
% 0.57/0.75  % (19177)Memory used [KB]: 954
% 0.57/0.75  % (19177)Time elapsed: 0.003 s
% 0.57/0.75  % (19177)Instructions burned: 2 (million)
% 0.57/0.75  % (19175)Refutation not found, incomplete strategy% (19175)------------------------------
% 0.57/0.75  % (19175)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.57/0.75  % (19175)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.75  
% 0.57/0.75  % (19175)Memory used [KB]: 968
% 0.57/0.75  % (19175)Time elapsed: 0.003 s
% 0.57/0.75  % (19175)Instructions burned: 2 (million)
% 0.57/0.75  % (19175)------------------------------
% 0.57/0.75  % (19175)------------------------------
% 0.57/0.75  % (19177)------------------------------
% 0.57/0.75  % (19177)------------------------------
% 0.57/0.75  % (19179)Refutation found. Thanks to Tanya!
% 0.57/0.75  % SZS status Theorem for Vampire---4
% 0.57/0.75  % SZS output start Proof for Vampire---4
% See solution above
% 0.57/0.75  % (19179)------------------------------
% 0.57/0.75  % (19179)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.57/0.75  % (19179)Termination reason: Refutation
% 0.57/0.75  
% 0.57/0.75  % (19179)Memory used [KB]: 1000
% 0.57/0.75  % (19179)Time elapsed: 0.004 s
% 0.57/0.75  % (19179)Instructions burned: 7 (million)
% 0.57/0.75  % (19179)------------------------------
% 0.57/0.75  % (19179)------------------------------
% 0.57/0.75  % (19168)Success in time 0.384 s
% 0.57/0.75  % Vampire---4.8 exiting
%------------------------------------------------------------------------------