TSTP Solution File: SET144+3 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET144+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n002.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 Aug 31 18:19:31 EDT 2022

% Result   : Theorem 0.19s 0.52s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   88 (   4 unt;   0 def)
%            Number of atoms       :  267 (  19 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  292 ( 113   ~; 119   |;  38   &)
%                                         (  15 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   7 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :  117 ( 102   !;  15   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f215,plain,
    $false,
    inference(avatar_sat_refutation,[],[f93,f94,f146,f162,f178,f186,f199,f201,f214]) ).

fof(f214,plain,
    ( spl6_6
    | ~ spl6_8 ),
    inference(avatar_contradiction_clause,[],[f213]) ).

fof(f213,plain,
    ( $false
    | spl6_6
    | ~ spl6_8 ),
    inference(subsumption_resolution,[],[f207,f161]) ).

fof(f161,plain,
    ( ~ member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),sK2)
    | spl6_6 ),
    inference(avatar_component_clause,[],[f159]) ).

fof(f159,plain,
    ( spl6_6
  <=> member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_6])]) ).

fof(f207,plain,
    ( member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),sK2)
    | ~ spl6_8 ),
    inference(resolution,[],[f177,f70]) ).

fof(f70,plain,
    ! [X0] :
      ( ~ member(X0,sK1)
      | member(X0,sK2) ),
    inference(resolution,[],[f50,f54]) ).

fof(f54,plain,
    ! [X2,X0,X1] :
      ( member(X2,X0)
      | ~ subset(X1,X0)
      | ~ member(X2,X1) ),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( member(X2,X0)
            | ~ member(X2,X1) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ( ~ member(sK4(X0,X1),X0)
          & member(sK4(X0,X1),X1) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f31,f32]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ~ member(X3,X0)
          & member(X3,X1) )
     => ( ~ member(sK4(X0,X1),X0)
        & member(sK4(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( member(X2,X0)
            | ~ member(X2,X1) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ? [X3] :
            ( ~ member(X3,X0)
            & member(X3,X1) ) ) ),
    inference(rectify,[],[f30]) ).

fof(f30,plain,
    ! [X1,X0] :
      ( ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0) )
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) ) ),
    inference(nnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) )
    <=> subset(X0,X1) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).

fof(f50,plain,
    subset(sK1,sK2),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ( intersection(union(sK1,sK3),sK2) != union(sK1,intersection(sK3,sK2))
    & subset(sK1,sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f27,f28]) ).

fof(f28,plain,
    ( ? [X0,X1,X2] :
        ( union(X0,intersection(X2,X1)) != intersection(union(X0,X2),X1)
        & subset(X0,X1) )
   => ( intersection(union(sK1,sK3),sK2) != union(sK1,intersection(sK3,sK2))
      & subset(sK1,sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f27,plain,
    ? [X0,X1,X2] :
      ( union(X0,intersection(X2,X1)) != intersection(union(X0,X2),X1)
      & subset(X0,X1) ),
    inference(rectify,[],[f16]) ).

fof(f16,plain,
    ? [X2,X0,X1] :
      ( union(X2,intersection(X1,X0)) != intersection(union(X2,X1),X0)
      & subset(X2,X0) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,plain,
    ~ ! [X2,X0,X1] :
        ( subset(X2,X0)
       => union(X2,intersection(X1,X0)) = intersection(union(X2,X1),X0) ),
    inference(rectify,[],[f10]) ).

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

fof(f9,conjecture,
    ! [X1,X2,X0] :
      ( subset(X0,X1)
     => union(X0,intersection(X2,X1)) = intersection(union(X0,X2),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th44) ).

fof(f177,plain,
    ( member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),sK1)
    | ~ spl6_8 ),
    inference(avatar_component_clause,[],[f175]) ).

fof(f175,plain,
    ( spl6_8
  <=> member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_8])]) ).

fof(f201,plain,
    ( spl6_5
    | ~ spl6_7 ),
    inference(avatar_contradiction_clause,[],[f200]) ).

fof(f200,plain,
    ( $false
    | spl6_5
    | ~ spl6_7 ),
    inference(subsumption_resolution,[],[f193,f180]) ).

fof(f180,plain,
    ( ~ member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),sK3)
    | spl6_5 ),
    inference(resolution,[],[f157,f56]) ).

fof(f56,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,X1)
      | member(X0,union(X2,X1)) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f36,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,X1)
        | member(X0,X2)
        | ~ member(X0,union(X2,X1)) )
      & ( member(X0,union(X2,X1))
        | ( ~ member(X0,X1)
          & ~ member(X0,X2) ) ) ),
    inference(rectify,[],[f35]) ).

fof(f35,plain,
    ! [X1,X0,X2] :
      ( ( member(X1,X0)
        | member(X1,X2)
        | ~ member(X1,union(X2,X0)) )
      & ( member(X1,union(X2,X0))
        | ( ~ member(X1,X0)
          & ~ member(X1,X2) ) ) ),
    inference(flattening,[],[f34]) ).

fof(f34,plain,
    ! [X1,X0,X2] :
      ( ( member(X1,X0)
        | member(X1,X2)
        | ~ member(X1,union(X2,X0)) )
      & ( member(X1,union(X2,X0))
        | ( ~ member(X1,X0)
          & ~ member(X1,X2) ) ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X1,X0,X2] :
      ( ( member(X1,X0)
        | member(X1,X2) )
    <=> member(X1,union(X2,X0)) ),
    inference(rectify,[],[f1]) ).

fof(f1,axiom,
    ! [X1,X2,X0] :
      ( member(X2,union(X0,X1))
    <=> ( member(X2,X0)
        | member(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).

fof(f157,plain,
    ( ~ member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),union(sK1,sK3))
    | spl6_5 ),
    inference(avatar_component_clause,[],[f155]) ).

fof(f155,plain,
    ( spl6_5
  <=> member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),union(sK1,sK3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_5])]) ).

fof(f193,plain,
    ( member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),sK3)
    | ~ spl6_7 ),
    inference(resolution,[],[f173,f48]) ).

fof(f48,plain,
    ! [X2,X0,X1] :
      ( member(X2,X0)
      | ~ member(X2,intersection(X0,X1)) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1,X2] :
      ( ( ( member(X2,X0)
          & member(X2,X1) )
        | ~ member(X2,intersection(X0,X1)) )
      & ( member(X2,intersection(X0,X1))
        | ~ member(X2,X0)
        | ~ member(X2,X1) ) ),
    inference(rectify,[],[f25]) ).

fof(f25,plain,
    ! [X2,X1,X0] :
      ( ( ( member(X0,X2)
          & member(X0,X1) )
        | ~ member(X0,intersection(X2,X1)) )
      & ( member(X0,intersection(X2,X1))
        | ~ member(X0,X2)
        | ~ member(X0,X1) ) ),
    inference(flattening,[],[f24]) ).

fof(f24,plain,
    ! [X2,X1,X0] :
      ( ( ( member(X0,X2)
          & member(X0,X1) )
        | ~ member(X0,intersection(X2,X1)) )
      & ( member(X0,intersection(X2,X1))
        | ~ member(X0,X2)
        | ~ member(X0,X1) ) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X2,X1,X0] :
      ( ( member(X0,X2)
        & member(X0,X1) )
    <=> member(X0,intersection(X2,X1)) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X2,X1,X0] :
      ( member(X2,intersection(X0,X1))
    <=> ( member(X2,X0)
        & member(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).

fof(f173,plain,
    ( member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),intersection(sK3,sK2))
    | ~ spl6_7 ),
    inference(avatar_component_clause,[],[f171]) ).

fof(f171,plain,
    ( spl6_7
  <=> member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),intersection(sK3,sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_7])]) ).

fof(f199,plain,
    ( spl6_6
    | ~ spl6_7 ),
    inference(avatar_split_clause,[],[f192,f171,f159]) ).

fof(f192,plain,
    ( member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),sK2)
    | ~ spl6_7 ),
    inference(resolution,[],[f173,f47]) ).

fof(f47,plain,
    ! [X2,X0,X1] :
      ( member(X2,X1)
      | ~ member(X2,intersection(X0,X1)) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f186,plain,
    ( ~ spl6_8
    | spl6_5 ),
    inference(avatar_split_clause,[],[f179,f155,f175]) ).

fof(f179,plain,
    ( ~ member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),sK1)
    | spl6_5 ),
    inference(resolution,[],[f157,f55]) ).

fof(f55,plain,
    ! [X2,X0,X1] :
      ( member(X0,union(X2,X1))
      | ~ member(X0,X2) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f178,plain,
    ( spl6_7
    | spl6_8
    | ~ spl6_4 ),
    inference(avatar_split_clause,[],[f164,f90,f175,f171]) ).

fof(f90,plain,
    ( spl6_4
  <=> member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),union(sK1,intersection(sK3,sK2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_4])]) ).

fof(f164,plain,
    ( member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),sK1)
    | member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),intersection(sK3,sK2))
    | ~ spl6_4 ),
    inference(resolution,[],[f91,f57]) ).

fof(f57,plain,
    ! [X2,X0,X1] :
      ( member(X0,X1)
      | member(X0,X2)
      | ~ member(X0,union(X2,X1)) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f91,plain,
    ( member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),union(sK1,intersection(sK3,sK2)))
    | ~ spl6_4 ),
    inference(avatar_component_clause,[],[f90]) ).

fof(f162,plain,
    ( ~ spl6_5
    | ~ spl6_6
    | spl6_3 ),
    inference(avatar_split_clause,[],[f148,f86,f159,f155]) ).

fof(f86,plain,
    ( spl6_3
  <=> member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),intersection(union(sK1,sK3),sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_3])]) ).

fof(f148,plain,
    ( ~ member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),sK2)
    | ~ member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),union(sK1,sK3))
    | spl6_3 ),
    inference(resolution,[],[f88,f46]) ).

fof(f46,plain,
    ! [X2,X0,X1] :
      ( member(X2,intersection(X0,X1))
      | ~ member(X2,X1)
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f88,plain,
    ( ~ member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),intersection(union(sK1,sK3),sK2))
    | spl6_3 ),
    inference(avatar_component_clause,[],[f86]) ).

fof(f146,plain,
    ( ~ spl6_3
    | spl6_4 ),
    inference(avatar_contradiction_clause,[],[f145]) ).

fof(f145,plain,
    ( $false
    | ~ spl6_3
    | spl6_4 ),
    inference(subsumption_resolution,[],[f144,f106]) ).

fof(f106,plain,
    ( member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),sK2)
    | ~ spl6_3 ),
    inference(resolution,[],[f87,f47]) ).

fof(f87,plain,
    ( member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),intersection(union(sK1,sK3),sK2))
    | ~ spl6_3 ),
    inference(avatar_component_clause,[],[f86]) ).

fof(f144,plain,
    ( ~ member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),sK2)
    | ~ spl6_3
    | spl6_4 ),
    inference(subsumption_resolution,[],[f138,f137]) ).

fof(f137,plain,
    ( member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),sK3)
    | ~ spl6_3
    | spl6_4 ),
    inference(subsumption_resolution,[],[f131,f114]) ).

fof(f114,plain,
    ( ~ member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),sK1)
    | spl6_4 ),
    inference(resolution,[],[f92,f55]) ).

fof(f92,plain,
    ( ~ member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),union(sK1,intersection(sK3,sK2)))
    | spl6_4 ),
    inference(avatar_component_clause,[],[f90]) ).

fof(f131,plain,
    ( member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),sK3)
    | member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),sK1)
    | ~ spl6_3 ),
    inference(resolution,[],[f107,f57]) ).

fof(f107,plain,
    ( member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),union(sK1,sK3))
    | ~ spl6_3 ),
    inference(resolution,[],[f87,f48]) ).

fof(f138,plain,
    ( ~ member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),sK3)
    | ~ member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),sK2)
    | spl6_4 ),
    inference(resolution,[],[f115,f46]) ).

fof(f115,plain,
    ( ~ member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),intersection(sK3,sK2))
    | spl6_4 ),
    inference(resolution,[],[f92,f56]) ).

fof(f94,plain,
    ( spl6_3
    | spl6_4 ),
    inference(avatar_split_clause,[],[f75,f90,f86]) ).

fof(f75,plain,
    ( member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),union(sK1,intersection(sK3,sK2)))
    | member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),intersection(union(sK1,sK3),sK2)) ),
    inference(resolution,[],[f68,f66]) ).

fof(f66,plain,
    ! [X0,X1] :
      ( member(sK0(X0,X1),X1)
      | member(sK0(X0,X1),X0)
      | sQ5_eqProxy(X0,X1) ),
    inference(equality_proxy_replacement,[],[f43,f62]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( sQ5_eqProxy(X0,X1)
    <=> X0 = X1 ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ5_eqProxy])]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( X0 = X1
      | member(sK0(X0,X1),X0)
      | member(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ( ( ~ member(sK0(X0,X1),X0)
            | ~ member(sK0(X0,X1),X1) )
          & ( member(sK0(X0,X1),X0)
            | member(sK0(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( member(X3,X1)
              | ~ member(X3,X0) )
            & ( member(X3,X0)
              | ~ member(X3,X1) ) )
        | X0 != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f21,f22]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ member(X2,X0)
            | ~ member(X2,X1) )
          & ( member(X2,X0)
            | member(X2,X1) ) )
     => ( ( ~ member(sK0(X0,X1),X0)
          | ~ member(sK0(X0,X1),X1) )
        & ( member(sK0(X0,X1),X0)
          | member(sK0(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ? [X2] :
            ( ( ~ member(X2,X0)
              | ~ member(X2,X1) )
            & ( member(X2,X0)
              | member(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( member(X3,X1)
              | ~ member(X3,X0) )
            & ( member(X3,X0)
              | ~ member(X3,X1) ) )
        | X0 != X1 ) ),
    inference(rectify,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ? [X2] :
            ( ( ~ member(X2,X0)
              | ~ member(X2,X1) )
            & ( member(X2,X0)
              | member(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( member(X2,X1)
              | ~ member(X2,X0) )
            & ( member(X2,X0)
              | ~ member(X2,X1) ) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0,X1] :
      ( X0 = X1
    <=> ! [X2] :
          ( member(X2,X1)
        <=> member(X2,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).

fof(f68,plain,
    ~ sQ5_eqProxy(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),
    inference(equality_proxy_replacement,[],[f51,f62]) ).

fof(f51,plain,
    intersection(union(sK1,sK3),sK2) != union(sK1,intersection(sK3,sK2)),
    inference(cnf_transformation,[],[f29]) ).

fof(f93,plain,
    ( ~ spl6_3
    | ~ spl6_4 ),
    inference(avatar_split_clause,[],[f73,f90,f86]) ).

fof(f73,plain,
    ( ~ member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),union(sK1,intersection(sK3,sK2)))
    | ~ member(sK0(intersection(union(sK1,sK3),sK2),union(sK1,intersection(sK3,sK2))),intersection(union(sK1,sK3),sK2)) ),
    inference(resolution,[],[f68,f65]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( ~ member(sK0(X0,X1),X1)
      | ~ member(sK0(X0,X1),X0)
      | sQ5_eqProxy(X0,X1) ),
    inference(equality_proxy_replacement,[],[f44,f62]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ member(sK0(X0,X1),X0)
      | ~ member(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f23]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : SET144+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34  % Computer : n002.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 13:34:44 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.19/0.50  % (22401)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.19/0.51  % (22394)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.51  % (22395)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.51  % (22404)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.52  % (22401)First to succeed.
% 0.19/0.52  % (22410)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 0.19/0.52  % (22393)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.52  % (22393)Refutation not found, incomplete strategy% (22393)------------------------------
% 0.19/0.52  % (22393)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (22393)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (22393)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.52  
% 0.19/0.52  % (22393)Memory used [KB]: 6012
% 0.19/0.52  % (22393)Time elapsed: 0.114 s
% 0.19/0.52  % (22393)Instructions burned: 2 (million)
% 0.19/0.52  % (22393)------------------------------
% 0.19/0.52  % (22393)------------------------------
% 0.19/0.52  % (22391)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.52  % (22401)Refutation found. Thanks to Tanya!
% 0.19/0.52  % SZS status Theorem for theBenchmark
% 0.19/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.52  % (22401)------------------------------
% 0.19/0.52  % (22401)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (22401)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (22401)Termination reason: Refutation
% 0.19/0.52  
% 0.19/0.52  % (22401)Memory used [KB]: 6012
% 0.19/0.52  % (22401)Time elapsed: 0.095 s
% 0.19/0.52  % (22401)Instructions burned: 3 (million)
% 0.19/0.52  % (22401)------------------------------
% 0.19/0.52  % (22401)------------------------------
% 0.19/0.52  % (22390)Success in time 0.168 s
%------------------------------------------------------------------------------