TSTP Solution File: SET171+3 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET171+3 : TPTP v8.2.0. 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 : n018.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 : Tue May 21 03:09:25 EDT 2024

% Result   : Theorem 0.55s 0.73s
% Output   : Refutation 0.55s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   92 (   7 unt;   0 def)
%            Number of atoms       :  252 (  17 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  267 ( 107   ~; 125   |;  20   &)
%                                         (  13 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :   12 (  10 usr;   9 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   75 (  66   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f285,plain,
    $false,
    inference(avatar_sat_refutation,[],[f74,f75,f122,f136,f152,f168,f177,f178,f198,f213,f214,f240,f282,f283,f284]) ).

fof(f284,plain,
    ( ~ spl6_7
    | spl6_1 ),
    inference(avatar_split_clause,[],[f247,f67,f145]) ).

fof(f145,plain,
    ( spl6_7
  <=> member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_7])]) ).

fof(f67,plain,
    ( spl6_1
  <=> member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),union(sK2,intersection(sK3,sK4))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).

fof(f247,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),sK2)
    | spl6_1 ),
    inference(resolution,[],[f68,f30]) ).

fof(f30,plain,
    ! [X2,X0,X1] :
      ( member(X2,union(X0,X1))
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[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(flattening,[],[f13]) ).

fof(f13,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/benchmark/theBenchmark.p',union_defn) ).

fof(f68,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),union(sK2,intersection(sK3,sK4)))
    | spl6_1 ),
    inference(avatar_component_clause,[],[f67]) ).

fof(f283,plain,
    ( spl6_10
    | ~ spl6_2 ),
    inference(avatar_split_clause,[],[f262,f71,f165]) ).

fof(f165,plain,
    ( spl6_10
  <=> member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),union(sK2,sK4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_10])]) ).

fof(f71,plain,
    ( spl6_2
  <=> member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),intersection(union(sK2,sK3),union(sK2,sK4))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).

fof(f262,plain,
    ( member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),union(sK2,sK4))
    | ~ spl6_2 ),
    inference(resolution,[],[f73,f33]) ).

fof(f33,plain,
    ! [X2,X0,X1] :
      ( member(X2,X1)
      | ~ member(X2,intersection(X0,X1)) ),
    inference(cnf_transformation,[],[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(flattening,[],[f15]) ).

fof(f15,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/benchmark/theBenchmark.p',intersection_defn) ).

fof(f73,plain,
    ( member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),intersection(union(sK2,sK3),union(sK2,sK4)))
    | ~ spl6_2 ),
    inference(avatar_component_clause,[],[f71]) ).

fof(f282,plain,
    ( spl6_6
    | spl6_7
    | ~ spl6_10 ),
    inference(avatar_contradiction_clause,[],[f281]) ).

fof(f281,plain,
    ( $false
    | spl6_6
    | spl6_7
    | ~ spl6_10 ),
    inference(subsumption_resolution,[],[f280,f146]) ).

fof(f146,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),sK2)
    | spl6_7 ),
    inference(avatar_component_clause,[],[f145]) ).

fof(f280,plain,
    ( member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),sK2)
    | spl6_6
    | ~ spl6_10 ),
    inference(subsumption_resolution,[],[f274,f121]) ).

fof(f121,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),sK4)
    | spl6_6 ),
    inference(avatar_component_clause,[],[f119]) ).

fof(f119,plain,
    ( spl6_6
  <=> member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_6])]) ).

fof(f274,plain,
    ( member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),sK4)
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),sK2)
    | ~ spl6_10 ),
    inference(resolution,[],[f166,f29]) ).

fof(f29,plain,
    ! [X2,X0,X1] :
      ( member(X2,X1)
      | member(X2,X0)
      | ~ member(X2,union(X0,X1)) ),
    inference(cnf_transformation,[],[f14]) ).

fof(f166,plain,
    ( member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),union(sK2,sK4))
    | ~ spl6_10 ),
    inference(avatar_component_clause,[],[f165]) ).

fof(f240,plain,
    ( ~ spl6_5
    | spl6_9 ),
    inference(avatar_contradiction_clause,[],[f239]) ).

fof(f239,plain,
    ( $false
    | ~ spl6_5
    | spl6_9 ),
    inference(subsumption_resolution,[],[f233,f116]) ).

fof(f116,plain,
    ( member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),sK3)
    | ~ spl6_5 ),
    inference(avatar_component_clause,[],[f115]) ).

fof(f115,plain,
    ( spl6_5
  <=> member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_5])]) ).

fof(f233,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),sK3)
    | spl6_9 ),
    inference(resolution,[],[f163,f31]) ).

fof(f31,plain,
    ! [X2,X0,X1] :
      ( member(X2,union(X0,X1))
      | ~ member(X2,X1) ),
    inference(cnf_transformation,[],[f14]) ).

fof(f163,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),union(sK2,sK3))
    | spl6_9 ),
    inference(avatar_component_clause,[],[f161]) ).

fof(f161,plain,
    ( spl6_9
  <=> member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),union(sK2,sK3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_9])]) ).

fof(f214,plain,
    ( ~ spl6_6
    | spl6_10 ),
    inference(avatar_split_clause,[],[f206,f165,f119]) ).

fof(f206,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),sK4)
    | spl6_10 ),
    inference(resolution,[],[f167,f31]) ).

fof(f167,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),union(sK2,sK4))
    | spl6_10 ),
    inference(avatar_component_clause,[],[f165]) ).

fof(f213,plain,
    ( ~ spl6_7
    | spl6_10 ),
    inference(avatar_contradiction_clause,[],[f212]) ).

fof(f212,plain,
    ( $false
    | ~ spl6_7
    | spl6_10 ),
    inference(subsumption_resolution,[],[f205,f147]) ).

fof(f147,plain,
    ( member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),sK2)
    | ~ spl6_7 ),
    inference(avatar_component_clause,[],[f145]) ).

fof(f205,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),sK2)
    | spl6_10 ),
    inference(resolution,[],[f167,f30]) ).

fof(f198,plain,
    ( ~ spl6_7
    | spl6_9 ),
    inference(avatar_contradiction_clause,[],[f197]) ).

fof(f197,plain,
    ( $false
    | ~ spl6_7
    | spl6_9 ),
    inference(subsumption_resolution,[],[f190,f147]) ).

fof(f190,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),sK2)
    | spl6_9 ),
    inference(resolution,[],[f163,f30]) ).

fof(f178,plain,
    ( spl6_6
    | ~ spl6_8 ),
    inference(avatar_split_clause,[],[f170,f149,f119]) ).

fof(f149,plain,
    ( spl6_8
  <=> member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),intersection(sK3,sK4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_8])]) ).

fof(f170,plain,
    ( member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),sK4)
    | ~ spl6_8 ),
    inference(resolution,[],[f151,f33]) ).

fof(f151,plain,
    ( member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),intersection(sK3,sK4))
    | ~ spl6_8 ),
    inference(avatar_component_clause,[],[f149]) ).

fof(f177,plain,
    ( spl6_5
    | ~ spl6_8 ),
    inference(avatar_contradiction_clause,[],[f176]) ).

fof(f176,plain,
    ( $false
    | spl6_5
    | ~ spl6_8 ),
    inference(subsumption_resolution,[],[f169,f117]) ).

fof(f117,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),sK3)
    | spl6_5 ),
    inference(avatar_component_clause,[],[f115]) ).

fof(f169,plain,
    ( member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),sK3)
    | ~ spl6_8 ),
    inference(resolution,[],[f151,f32]) ).

fof(f32,plain,
    ! [X2,X0,X1] :
      ( member(X2,X0)
      | ~ member(X2,intersection(X0,X1)) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f168,plain,
    ( ~ spl6_9
    | ~ spl6_10
    | spl6_2 ),
    inference(avatar_split_clause,[],[f154,f71,f165,f161]) ).

fof(f154,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),union(sK2,sK4))
    | ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),union(sK2,sK3))
    | spl6_2 ),
    inference(resolution,[],[f72,f34]) ).

fof(f34,plain,
    ! [X2,X0,X1] :
      ( member(X2,intersection(X0,X1))
      | ~ member(X2,X1)
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f72,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),intersection(union(sK2,sK3),union(sK2,sK4)))
    | spl6_2 ),
    inference(avatar_component_clause,[],[f71]) ).

fof(f152,plain,
    ( spl6_7
    | spl6_8
    | ~ spl6_1 ),
    inference(avatar_split_clause,[],[f138,f67,f149,f145]) ).

fof(f138,plain,
    ( member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),intersection(sK3,sK4))
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),sK2)
    | ~ spl6_1 ),
    inference(resolution,[],[f69,f29]) ).

fof(f69,plain,
    ( member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),union(sK2,intersection(sK3,sK4)))
    | ~ spl6_1 ),
    inference(avatar_component_clause,[],[f67]) ).

fof(f136,plain,
    ( spl6_1
    | ~ spl6_2
    | spl6_5 ),
    inference(avatar_contradiction_clause,[],[f135]) ).

fof(f135,plain,
    ( $false
    | spl6_1
    | ~ spl6_2
    | spl6_5 ),
    inference(subsumption_resolution,[],[f134,f88]) ).

fof(f88,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),sK2)
    | spl6_1 ),
    inference(resolution,[],[f68,f30]) ).

fof(f134,plain,
    ( member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),sK2)
    | ~ spl6_2
    | spl6_5 ),
    inference(subsumption_resolution,[],[f128,f117]) ).

fof(f128,plain,
    ( member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),sK3)
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),sK2)
    | ~ spl6_2 ),
    inference(resolution,[],[f96,f29]) ).

fof(f96,plain,
    ( member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),union(sK2,sK3))
    | ~ spl6_2 ),
    inference(resolution,[],[f73,f32]) ).

fof(f122,plain,
    ( ~ spl6_5
    | ~ spl6_6
    | spl6_1 ),
    inference(avatar_split_clause,[],[f108,f67,f119,f115]) ).

fof(f108,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),sK4)
    | ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),sK3)
    | spl6_1 ),
    inference(resolution,[],[f89,f34]) ).

fof(f89,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),intersection(sK3,sK4))
    | spl6_1 ),
    inference(resolution,[],[f68,f31]) ).

fof(f75,plain,
    ( ~ spl6_1
    | ~ spl6_2 ),
    inference(avatar_split_clause,[],[f63,f71,f67]) ).

fof(f63,plain,
    ( ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),intersection(union(sK2,sK3),union(sK2,sK4)))
    | ~ member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),union(sK2,intersection(sK3,sK4))) ),
    inference(resolution,[],[f59,f57]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( sQ5_eqProxy(X0,X1)
      | ~ member(sK1(X0,X1),X1)
      | ~ member(sK1(X0,X1),X0) ),
    inference(equality_proxy_replacement,[],[f47,f53]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( sQ5_eqProxy(X0,X1)
    <=> X0 = X1 ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ5_eqProxy])]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ member(sK1(X0,X1),X1)
      | ~ member(sK1(X0,X1),X0) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ( ( ~ member(sK1(X0,X1),X1)
            | ~ member(sK1(X0,X1),X0) )
          & ( member(sK1(X0,X1),X1)
            | member(sK1(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,[sK1])],[f24,f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ member(X2,X1)
            | ~ member(X2,X0) )
          & ( member(X2,X1)
            | member(X2,X0) ) )
     => ( ( ~ member(sK1(X0,X1),X1)
          | ~ member(sK1(X0,X1),X0) )
        & ( member(sK1(X0,X1),X1)
          | member(sK1(X0,X1),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f24,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,[],[f23]) ).

fof(f23,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/benchmark/theBenchmark.p',equal_member_defn) ).

fof(f59,plain,
    ~ sQ5_eqProxy(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),
    inference(equality_proxy_replacement,[],[f48,f53]) ).

fof(f48,plain,
    union(sK2,intersection(sK3,sK4)) != intersection(union(sK2,sK3),union(sK2,sK4)),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    union(sK2,intersection(sK3,sK4)) != intersection(union(sK2,sK3),union(sK2,sK4)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f12,f27]) ).

fof(f27,plain,
    ( ? [X0,X1,X2] : union(X0,intersection(X1,X2)) != intersection(union(X0,X1),union(X0,X2))
   => union(sK2,intersection(sK3,sK4)) != intersection(union(sK2,sK3),union(sK2,sK4)) ),
    introduced(choice_axiom,[]) ).

fof(f12,plain,
    ? [X0,X1,X2] : union(X0,intersection(X1,X2)) != intersection(union(X0,X1),union(X0,X2)),
    inference(ennf_transformation,[],[f10]) ).

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

fof(f9,conjecture,
    ! [X0,X1,X2] : union(X0,intersection(X1,X2)) = intersection(union(X0,X1),union(X0,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_union_distributes_over_intersection) ).

fof(f74,plain,
    ( spl6_1
    | spl6_2 ),
    inference(avatar_split_clause,[],[f62,f71,f67]) ).

fof(f62,plain,
    ( member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),intersection(union(sK2,sK3),union(sK2,sK4)))
    | member(sK1(union(sK2,intersection(sK3,sK4)),intersection(union(sK2,sK3),union(sK2,sK4))),union(sK2,intersection(sK3,sK4))) ),
    inference(resolution,[],[f59,f58]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( sQ5_eqProxy(X0,X1)
      | member(sK1(X0,X1),X1)
      | member(sK1(X0,X1),X0) ),
    inference(equality_proxy_replacement,[],[f46,f53]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( X0 = X1
      | member(sK1(X0,X1),X1)
      | member(sK1(X0,X1),X0) ),
    inference(cnf_transformation,[],[f26]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET171+3 : TPTP v8.2.0. Released v2.2.0.
% 0.12/0.14  % 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
% 0.14/0.35  % Computer : n018.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon May 20 12:54:23 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  This is a FOF_THM_RFO_SEQ problem
% 0.14/0.35  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/benchmark/theBenchmark.p
% 0.55/0.72  % (30222)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 theBenchmark for (2996ds/83Mi)
% 0.55/0.73  % (30216)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 theBenchmark for (2996ds/34Mi)
% 0.55/0.73  % (30218)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on theBenchmark for (2996ds/78Mi)
% 0.55/0.73  % (30217)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 theBenchmark for (2996ds/51Mi)
% 0.55/0.73  % (30222)Refutation not found, incomplete strategy% (30222)------------------------------
% 0.55/0.73  % (30222)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.73  % (30222)Termination reason: Refutation not found, incomplete strategy
% 0.55/0.73  
% 0.55/0.73  % (30222)Memory used [KB]: 956
% 0.55/0.73  % (30222)Time elapsed: 0.002 s
% 0.55/0.73  % (30222)Instructions burned: 3 (million)
% 0.55/0.73  % (30219)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on theBenchmark for (2996ds/33Mi)
% 0.55/0.73  % (30221)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on theBenchmark for (2996ds/45Mi)
% 0.55/0.73  % (30220)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 theBenchmark for (2996ds/34Mi)
% 0.55/0.73  % (30222)------------------------------
% 0.55/0.73  % (30222)------------------------------
% 0.55/0.73  % (30221)Refutation not found, incomplete strategy% (30221)------------------------------
% 0.55/0.73  % (30221)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.73  % (30221)Termination reason: Refutation not found, incomplete strategy
% 0.55/0.73  
% 0.55/0.73  % (30221)Memory used [KB]: 955
% 0.55/0.73  % (30221)Time elapsed: 0.003 s
% 0.55/0.73  % (30219)Refutation not found, incomplete strategy% (30219)------------------------------
% 0.55/0.73  % (30219)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.73  % (30219)Termination reason: Refutation not found, incomplete strategy
% 0.55/0.73  
% 0.55/0.73  % (30219)Memory used [KB]: 969
% 0.55/0.73  % (30219)Time elapsed: 0.003 s
% 0.55/0.73  % (30219)Instructions burned: 2 (million)
% 0.55/0.73  % (30221)Instructions burned: 2 (million)
% 0.55/0.73  % (30219)------------------------------
% 0.55/0.73  % (30219)------------------------------
% 0.55/0.73  % (30221)------------------------------
% 0.55/0.73  % (30221)------------------------------
% 0.55/0.73  % (30223)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on theBenchmark for (2996ds/56Mi)
% 0.55/0.73  % (30220)First to succeed.
% 0.55/0.73  % (30223)Also succeeded, but the first one will report.
% 0.55/0.73  % (30220)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-30215"
% 0.55/0.73  % (30226)lrs+1010_1:2_sil=4000:tgt=ground:nwc=10.0:st=2.0:i=208:sd=1:bd=off:ss=axioms_0 on theBenchmark for (2996ds/208Mi)
% 0.55/0.73  % (30216)Also succeeded, but the first one will report.
% 0.55/0.73  % (30224)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on theBenchmark for (2996ds/55Mi)
% 0.55/0.73  % (30220)Refutation found. Thanks to Tanya!
% 0.55/0.73  % SZS status Theorem for theBenchmark
% 0.55/0.73  % SZS output start Proof for theBenchmark
% See solution above
% 0.55/0.73  % (30220)------------------------------
% 0.55/0.73  % (30220)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.73  % (30220)Termination reason: Refutation
% 0.55/0.73  
% 0.55/0.73  % (30220)Memory used [KB]: 1072
% 0.55/0.73  % (30220)Time elapsed: 0.006 s
% 0.55/0.73  % (30220)Instructions burned: 8 (million)
% 0.55/0.73  % (30215)Success in time 0.373 s
% 0.55/0.73  % Vampire---4.8 exiting
%------------------------------------------------------------------------------