TSTP Solution File: SET615+3 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET615+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 : n006.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 : Sun May  5 09:07:36 EDT 2024

% Result   : Theorem 0.57s 0.73s
% Output   : Refutation 0.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   88 (   7 unt;   0 def)
%            Number of atoms       :  240 (  17 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  258 ( 106   ~; 117   |;  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(f125,plain,
    $false,
    inference(avatar_sat_refutation,[],[f51,f52,f74,f78,f79,f84,f85,f90,f93,f103,f108,f112,f115,f122,f123,f124]) ).

fof(f124,plain,
    ( spl5_8
    | ~ spl5_6 ),
    inference(avatar_split_clause,[],[f118,f71,f100]) ).

fof(f100,plain,
    ( spl5_8
  <=> member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_8])]) ).

fof(f71,plain,
    ( spl5_6
  <=> member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),difference(sK0,sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_6])]) ).

fof(f118,plain,
    ( member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),sK0)
    | ~ spl5_6 ),
    inference(resolution,[],[f73,f30]) ).

fof(f30,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,difference(X0,X1))
      | member(X2,X0) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,difference(X0,X1))
        | member(X2,X1)
        | ~ member(X2,X0) )
      & ( ( ~ member(X2,X1)
          & member(X2,X0) )
        | ~ member(X2,difference(X0,X1)) ) ),
    inference(flattening,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,difference(X0,X1))
        | member(X2,X1)
        | ~ member(X2,X0) )
      & ( ( ~ member(X2,X1)
          & member(X2,X0) )
        | ~ member(X2,difference(X0,X1)) ) ),
    inference(nnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1,X2] :
      ( member(X2,difference(X0,X1))
    <=> ( ~ member(X2,X1)
        & member(X2,X0) ) ),
    file('/export/starexec/sandbox/tmp/tmp.bxqWEQmiwQ/Vampire---4.8_13277',difference_defn) ).

fof(f73,plain,
    ( member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),difference(sK0,sK2))
    | ~ spl5_6 ),
    inference(avatar_component_clause,[],[f71]) ).

fof(f123,plain,
    ( ~ spl5_4
    | ~ spl5_6 ),
    inference(avatar_split_clause,[],[f119,f71,f59]) ).

fof(f59,plain,
    ( spl5_4
  <=> member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).

fof(f119,plain,
    ( ~ member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),sK2)
    | ~ spl5_6 ),
    inference(resolution,[],[f73,f31]) ).

fof(f31,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,difference(X0,X1))
      | ~ member(X2,X1) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f122,plain,
    ( ~ spl5_3
    | spl5_4
    | spl5_1 ),
    inference(avatar_split_clause,[],[f116,f44,f59,f55]) ).

fof(f55,plain,
    ( spl5_3
  <=> member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),union(sK0,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).

fof(f44,plain,
    ( spl5_1
  <=> member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),difference(union(sK0,sK1),sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

fof(f116,plain,
    ( member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),sK2)
    | ~ member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),union(sK0,sK1))
    | spl5_1 ),
    inference(resolution,[],[f45,f32]) ).

fof(f32,plain,
    ! [X2,X0,X1] :
      ( member(X2,difference(X0,X1))
      | member(X2,X1)
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f45,plain,
    ( ~ member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),difference(union(sK0,sK1),sK2))
    | spl5_1 ),
    inference(avatar_component_clause,[],[f44]) ).

fof(f115,plain,
    ( ~ spl5_8
    | spl5_3 ),
    inference(avatar_split_clause,[],[f113,f55,f100]) ).

fof(f113,plain,
    ( ~ member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),sK0)
    | spl5_3 ),
    inference(resolution,[],[f57,f28]) ).

fof(f28,plain,
    ! [X2,X0,X1] :
      ( member(X2,union(X0,X1))
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,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,[],[f17]) ).

fof(f17,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.bxqWEQmiwQ/Vampire---4.8_13277',union_defn) ).

fof(f57,plain,
    ( ~ member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),union(sK0,sK1))
    | spl5_3 ),
    inference(avatar_component_clause,[],[f55]) ).

fof(f112,plain,
    ( spl5_4
    | spl5_6
    | ~ spl5_8 ),
    inference(avatar_contradiction_clause,[],[f111]) ).

fof(f111,plain,
    ( $false
    | spl5_4
    | spl5_6
    | ~ spl5_8 ),
    inference(subsumption_resolution,[],[f110,f102]) ).

fof(f102,plain,
    ( member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),sK0)
    | ~ spl5_8 ),
    inference(avatar_component_clause,[],[f100]) ).

fof(f110,plain,
    ( ~ member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),sK0)
    | spl5_4
    | spl5_6 ),
    inference(subsumption_resolution,[],[f109,f60]) ).

fof(f60,plain,
    ( ~ member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),sK2)
    | spl5_4 ),
    inference(avatar_component_clause,[],[f59]) ).

fof(f109,plain,
    ( member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),sK2)
    | ~ member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),sK0)
    | spl5_6 ),
    inference(resolution,[],[f72,f32]) ).

fof(f72,plain,
    ( ~ member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),difference(sK0,sK2))
    | spl5_6 ),
    inference(avatar_component_clause,[],[f71]) ).

fof(f108,plain,
    ( ~ spl5_7
    | spl5_4
    | spl5_5 ),
    inference(avatar_split_clause,[],[f105,f67,f59,f96]) ).

fof(f96,plain,
    ( spl5_7
  <=> member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_7])]) ).

fof(f67,plain,
    ( spl5_5
  <=> member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),difference(sK1,sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).

fof(f105,plain,
    ( ~ member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),sK1)
    | spl5_4
    | spl5_5 ),
    inference(subsumption_resolution,[],[f104,f60]) ).

fof(f104,plain,
    ( member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),sK2)
    | ~ member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),sK1)
    | spl5_5 ),
    inference(resolution,[],[f68,f32]) ).

fof(f68,plain,
    ( ~ member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),difference(sK1,sK2))
    | spl5_5 ),
    inference(avatar_component_clause,[],[f67]) ).

fof(f103,plain,
    ( spl5_7
    | spl5_8
    | ~ spl5_3 ),
    inference(avatar_split_clause,[],[f94,f55,f100,f96]) ).

fof(f94,plain,
    ( member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),sK0)
    | member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),sK1)
    | ~ spl5_3 ),
    inference(resolution,[],[f56,f27]) ).

fof(f27,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,union(X0,X1))
      | member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f56,plain,
    ( member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),union(sK0,sK1))
    | ~ spl5_3 ),
    inference(avatar_component_clause,[],[f55]) ).

fof(f93,plain,
    ( ~ spl5_5
    | spl5_2 ),
    inference(avatar_split_clause,[],[f89,f48,f67]) ).

fof(f48,plain,
    ( spl5_2
  <=> member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),union(difference(sK0,sK2),difference(sK1,sK2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

fof(f89,plain,
    ( ~ member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),difference(sK1,sK2))
    | spl5_2 ),
    inference(resolution,[],[f49,f29]) ).

fof(f29,plain,
    ! [X2,X0,X1] :
      ( member(X2,union(X0,X1))
      | ~ member(X2,X1) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f49,plain,
    ( ~ member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),union(difference(sK0,sK2),difference(sK1,sK2)))
    | spl5_2 ),
    inference(avatar_component_clause,[],[f48]) ).

fof(f90,plain,
    ( ~ spl5_6
    | spl5_2 ),
    inference(avatar_split_clause,[],[f88,f48,f71]) ).

fof(f88,plain,
    ( ~ member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),difference(sK0,sK2))
    | spl5_2 ),
    inference(resolution,[],[f49,f28]) ).

fof(f85,plain,
    ( ~ spl5_4
    | ~ spl5_5 ),
    inference(avatar_split_clause,[],[f82,f67,f59]) ).

fof(f82,plain,
    ( ~ member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),sK2)
    | ~ spl5_5 ),
    inference(resolution,[],[f69,f31]) ).

fof(f69,plain,
    ( member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),difference(sK1,sK2))
    | ~ spl5_5 ),
    inference(avatar_component_clause,[],[f67]) ).

fof(f84,plain,
    ( spl5_3
    | ~ spl5_5 ),
    inference(avatar_contradiction_clause,[],[f83]) ).

fof(f83,plain,
    ( $false
    | spl5_3
    | ~ spl5_5 ),
    inference(subsumption_resolution,[],[f81,f64]) ).

fof(f64,plain,
    ( ~ member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),sK1)
    | spl5_3 ),
    inference(resolution,[],[f57,f29]) ).

fof(f81,plain,
    ( member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),sK1)
    | ~ spl5_5 ),
    inference(resolution,[],[f69,f30]) ).

fof(f79,plain,
    ( ~ spl5_4
    | ~ spl5_1 ),
    inference(avatar_split_clause,[],[f76,f44,f59]) ).

fof(f76,plain,
    ( ~ member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),sK2)
    | ~ spl5_1 ),
    inference(resolution,[],[f46,f31]) ).

fof(f46,plain,
    ( member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),difference(union(sK0,sK1),sK2))
    | ~ spl5_1 ),
    inference(avatar_component_clause,[],[f44]) ).

fof(f78,plain,
    ( ~ spl5_1
    | spl5_3 ),
    inference(avatar_contradiction_clause,[],[f77]) ).

fof(f77,plain,
    ( $false
    | ~ spl5_1
    | spl5_3 ),
    inference(subsumption_resolution,[],[f75,f57]) ).

fof(f75,plain,
    ( member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),union(sK0,sK1))
    | ~ spl5_1 ),
    inference(resolution,[],[f46,f30]) ).

fof(f74,plain,
    ( spl5_5
    | spl5_6
    | ~ spl5_2 ),
    inference(avatar_split_clause,[],[f65,f48,f71,f67]) ).

fof(f65,plain,
    ( member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),difference(sK0,sK2))
    | member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),difference(sK1,sK2))
    | ~ spl5_2 ),
    inference(resolution,[],[f50,f27]) ).

fof(f50,plain,
    ( member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),union(difference(sK0,sK2),difference(sK1,sK2)))
    | ~ spl5_2 ),
    inference(avatar_component_clause,[],[f48]) ).

fof(f52,plain,
    ( ~ spl5_1
    | ~ spl5_2 ),
    inference(avatar_split_clause,[],[f42,f48,f44]) ).

fof(f42,plain,
    ( ~ member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),union(difference(sK0,sK2),difference(sK1,sK2)))
    | ~ member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),difference(union(sK0,sK1),sK2)) ),
    inference(resolution,[],[f36,f37]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( sQ4_eqProxy(X0,X1)
      | ~ member(sK3(X0,X1),X1)
      | ~ member(sK3(X0,X1),X0) ),
    inference(equality_proxy_replacement,[],[f25,f35]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( sQ4_eqProxy(X0,X1)
    <=> X0 = X1 ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ4_eqProxy])]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ member(sK3(X0,X1),X1)
      | ~ member(sK3(X0,X1),X0) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,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])],[f14,f15]) ).

fof(f15,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(f14,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,[],[f13]) ).

fof(f13,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,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( X0 = X1
    <=> ! [X2] :
          ( member(X2,X0)
        <=> member(X2,X1) ) ),
    file('/export/starexec/sandbox/tmp/tmp.bxqWEQmiwQ/Vampire---4.8_13277',equal_member_defn) ).

fof(f36,plain,
    ~ sQ4_eqProxy(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),
    inference(equality_proxy_replacement,[],[f21,f35]) ).

fof(f21,plain,
    difference(union(sK0,sK1),sK2) != union(difference(sK0,sK2),difference(sK1,sK2)),
    inference(cnf_transformation,[],[f12]) ).

fof(f12,plain,
    difference(union(sK0,sK1),sK2) != union(difference(sK0,sK2),difference(sK1,sK2)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f10,f11]) ).

fof(f11,plain,
    ( ? [X0,X1,X2] : difference(union(X0,X1),X2) != union(difference(X0,X2),difference(X1,X2))
   => difference(union(sK0,sK1),sK2) != union(difference(sK0,sK2),difference(sK1,sK2)) ),
    introduced(choice_axiom,[]) ).

fof(f10,plain,
    ? [X0,X1,X2] : difference(union(X0,X1),X2) != union(difference(X0,X2),difference(X1,X2)),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,negated_conjecture,
    ~ ! [X0,X1,X2] : difference(union(X0,X1),X2) = union(difference(X0,X2),difference(X1,X2)),
    inference(negated_conjecture,[],[f8]) ).

fof(f8,conjecture,
    ! [X0,X1,X2] : difference(union(X0,X1),X2) = union(difference(X0,X2),difference(X1,X2)),
    file('/export/starexec/sandbox/tmp/tmp.bxqWEQmiwQ/Vampire---4.8_13277',prove_difference_distributes_over_union) ).

fof(f51,plain,
    ( spl5_1
    | spl5_2 ),
    inference(avatar_split_clause,[],[f41,f48,f44]) ).

fof(f41,plain,
    ( member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),union(difference(sK0,sK2),difference(sK1,sK2)))
    | member(sK3(difference(union(sK0,sK1),sK2),union(difference(sK0,sK2),difference(sK1,sK2))),difference(union(sK0,sK1),sK2)) ),
    inference(resolution,[],[f36,f38]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( sQ4_eqProxy(X0,X1)
      | member(sK3(X0,X1),X1)
      | member(sK3(X0,X1),X0) ),
    inference(equality_proxy_replacement,[],[f24,f35]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( X0 = X1
      | member(sK3(X0,X1),X1)
      | member(sK3(X0,X1),X0) ),
    inference(cnf_transformation,[],[f16]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SET615+3 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.14  % 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
% 0.14/0.34  % Computer : n006.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Fri May  3 17:02:52 EDT 2024
% 0.14/0.34  % 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/tmp/tmp.bxqWEQmiwQ/Vampire---4.8_13277
% 0.50/0.73  % (13393)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)
% 0.50/0.73  % (13386)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)
% 0.50/0.73  % (13388)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.50/0.73  % (13390)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)
% 0.50/0.73  % (13387)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)
% 0.50/0.73  % (13389)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)
% 0.50/0.73  % (13391)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)
% 0.50/0.73  % (13392)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)
% 0.50/0.73  % (13393)First to succeed.
% 0.50/0.73  % (13391)Refutation not found, incomplete strategy% (13391)------------------------------
% 0.50/0.73  % (13391)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.50/0.73  % (13391)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.73  
% 0.57/0.73  % (13391)Memory used [KB]: 955
% 0.57/0.73  % (13393)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-13385"
% 0.57/0.73  % (13391)Time elapsed: 0.003 s
% 0.57/0.73  % (13391)Instructions burned: 2 (million)
% 0.57/0.73  % (13389)Refutation not found, incomplete strategy% (13389)------------------------------
% 0.57/0.73  % (13389)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.73  % (13389)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.73  
% 0.57/0.73  % (13389)Memory used [KB]: 971
% 0.57/0.73  % (13389)Time elapsed: 0.003 s
% 0.57/0.73  % (13389)Instructions burned: 3 (million)
% 0.57/0.73  % (13392)Refutation not found, incomplete strategy% (13392)------------------------------
% 0.57/0.73  % (13392)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.73  % (13392)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.73  % (13391)------------------------------
% 0.57/0.73  % (13391)------------------------------
% 0.57/0.73  
% 0.57/0.73  % (13392)Memory used [KB]: 955
% 0.57/0.73  % (13392)Time elapsed: 0.003 s
% 0.57/0.73  % (13392)Instructions burned: 3 (million)
% 0.57/0.73  % (13389)------------------------------
% 0.57/0.73  % (13389)------------------------------
% 0.57/0.73  % (13393)Refutation found. Thanks to Tanya!
% 0.57/0.73  % SZS status Theorem for Vampire---4
% 0.57/0.73  % SZS output start Proof for Vampire---4
% See solution above
% 0.57/0.73  % (13393)------------------------------
% 0.57/0.73  % (13393)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.57/0.73  % (13393)Termination reason: Refutation
% 0.57/0.73  
% 0.57/0.73  % (13393)Memory used [KB]: 1000
% 0.57/0.73  % (13393)Time elapsed: 0.004 s
% 0.57/0.73  % (13393)Instructions burned: 7 (million)
% 0.57/0.73  % (13385)Success in time 0.376 s
% 0.57/0.73  % Vampire---4.8 exiting
%------------------------------------------------------------------------------