TSTP Solution File: SEU160+1 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU160+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n028.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Apr 30 15:22:41 EDT 2024

% Result   : Theorem 0.13s 0.37s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   64 (  19 unt;   0 def)
%            Number of atoms       :  156 (  53 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  150 (  58   ~;  60   |;  14   &)
%                                         (  14 <=>;   3  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   15 (  13 usr;  12 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-1 aty)
%            Number of variables   :   39 (  27   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f96,plain,
    $false,
    inference(avatar_sat_refutation,[],[f44,f53,f58,f63,f68,f73,f79,f81,f85,f87,f91,f95]) ).

fof(f95,plain,
    ( spl4_2
    | spl4_4
    | ~ spl4_8
    | ~ spl4_11 ),
    inference(avatar_split_clause,[],[f94,f89,f70,f50,f41]) ).

fof(f41,plain,
    ( spl4_2
  <=> sK0 = singleton(sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).

fof(f50,plain,
    ( spl4_4
  <=> empty_set = sK0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).

fof(f70,plain,
    ( spl4_8
  <=> subset(sK0,singleton(sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).

fof(f89,plain,
    ( spl4_11
  <=> ! [X0,X1] :
        ( singleton(X1) = X0
        | empty_set = X0
        | ~ subset(X0,singleton(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_11])]) ).

fof(f94,plain,
    ( empty_set = sK0
    | sK0 = singleton(sK1)
    | ~ spl4_8
    | ~ spl4_11 ),
    inference(resolution,[],[f90,f72]) ).

fof(f72,plain,
    ( subset(sK0,singleton(sK1))
    | ~ spl4_8 ),
    inference(avatar_component_clause,[],[f70]) ).

fof(f90,plain,
    ( ! [X0,X1] :
        ( ~ subset(X0,singleton(X1))
        | empty_set = X0
        | singleton(X1) = X0 )
    | ~ spl4_11 ),
    inference(avatar_component_clause,[],[f89]) ).

fof(f91,plain,
    spl4_11,
    inference(avatar_split_clause,[],[f27,f89]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( singleton(X1) = X0
      | empty_set = X0
      | ~ subset(X0,singleton(X1)) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( ( subset(X0,singleton(X1))
        | ( singleton(X1) != X0
          & empty_set != X0 ) )
      & ( singleton(X1) = X0
        | empty_set = X0
        | ~ subset(X0,singleton(X1)) ) ),
    inference(flattening,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( ( subset(X0,singleton(X1))
        | ( singleton(X1) != X0
          & empty_set != X0 ) )
      & ( singleton(X1) = X0
        | empty_set = X0
        | ~ subset(X0,singleton(X1)) ) ),
    inference(nnf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( subset(X0,singleton(X1))
    <=> ( singleton(X1) = X0
        | empty_set = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).

fof(f87,plain,
    ( spl4_3
    | ~ spl4_10 ),
    inference(avatar_contradiction_clause,[],[f86]) ).

fof(f86,plain,
    ( $false
    | spl4_3
    | ~ spl4_10 ),
    inference(resolution,[],[f84,f48]) ).

fof(f48,plain,
    ( ~ subset(empty_set,singleton(sK1))
    | spl4_3 ),
    inference(avatar_component_clause,[],[f46]) ).

fof(f46,plain,
    ( spl4_3
  <=> subset(empty_set,singleton(sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).

fof(f84,plain,
    ( ! [X1] : subset(empty_set,singleton(X1))
    | ~ spl4_10 ),
    inference(avatar_component_clause,[],[f83]) ).

fof(f83,plain,
    ( spl4_10
  <=> ! [X1] : subset(empty_set,singleton(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_10])]) ).

fof(f85,plain,
    spl4_10,
    inference(avatar_split_clause,[],[f33,f83]) ).

fof(f33,plain,
    ! [X1] : subset(empty_set,singleton(X1)),
    inference(equality_resolution,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( subset(X0,singleton(X1))
      | empty_set != X0 ),
    inference(cnf_transformation,[],[f17]) ).

fof(f81,plain,
    ( spl4_1
    | ~ spl4_9 ),
    inference(avatar_contradiction_clause,[],[f80]) ).

fof(f80,plain,
    ( $false
    | spl4_1
    | ~ spl4_9 ),
    inference(resolution,[],[f78,f39]) ).

fof(f39,plain,
    ( ~ subset(sK0,sK0)
    | spl4_1 ),
    inference(avatar_component_clause,[],[f37]) ).

fof(f37,plain,
    ( spl4_1
  <=> subset(sK0,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).

fof(f78,plain,
    ( ! [X0] : subset(X0,X0)
    | ~ spl4_9 ),
    inference(avatar_component_clause,[],[f77]) ).

fof(f77,plain,
    ( spl4_9
  <=> ! [X0] : subset(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_9])]) ).

fof(f79,plain,
    spl4_9,
    inference(avatar_split_clause,[],[f26,f77]) ).

fof(f26,plain,
    ! [X0] : subset(X0,X0),
    inference(cnf_transformation,[],[f10]) ).

fof(f10,plain,
    ! [X0] : subset(X0,X0),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] : subset(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

fof(f73,plain,
    ( spl4_8
    | spl4_4
    | spl4_2 ),
    inference(avatar_split_clause,[],[f22,f41,f50,f70]) ).

fof(f22,plain,
    ( sK0 = singleton(sK1)
    | empty_set = sK0
    | subset(sK0,singleton(sK1)) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ( ( ( sK0 != singleton(sK1)
        & empty_set != sK0 )
      | ~ subset(sK0,singleton(sK1)) )
    & ( sK0 = singleton(sK1)
      | empty_set = sK0
      | subset(sK0,singleton(sK1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f14]) ).

fof(f14,plain,
    ( ? [X0,X1] :
        ( ( ( singleton(X1) != X0
            & empty_set != X0 )
          | ~ subset(X0,singleton(X1)) )
        & ( singleton(X1) = X0
          | empty_set = X0
          | subset(X0,singleton(X1)) ) )
   => ( ( ( sK0 != singleton(sK1)
          & empty_set != sK0 )
        | ~ subset(sK0,singleton(sK1)) )
      & ( sK0 = singleton(sK1)
        | empty_set = sK0
        | subset(sK0,singleton(sK1)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f13,plain,
    ? [X0,X1] :
      ( ( ( singleton(X1) != X0
          & empty_set != X0 )
        | ~ subset(X0,singleton(X1)) )
      & ( singleton(X1) = X0
        | empty_set = X0
        | subset(X0,singleton(X1)) ) ),
    inference(flattening,[],[f12]) ).

fof(f12,plain,
    ? [X0,X1] :
      ( ( ( singleton(X1) != X0
          & empty_set != X0 )
        | ~ subset(X0,singleton(X1)) )
      & ( singleton(X1) = X0
        | empty_set = X0
        | subset(X0,singleton(X1)) ) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f11,plain,
    ? [X0,X1] :
      ( subset(X0,singleton(X1))
    <~> ( singleton(X1) = X0
        | empty_set = X0 ) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,negated_conjecture,
    ~ ! [X0,X1] :
        ( subset(X0,singleton(X1))
      <=> ( singleton(X1) = X0
          | empty_set = X0 ) ),
    inference(negated_conjecture,[],[f7]) ).

fof(f7,conjecture,
    ! [X0,X1] :
      ( subset(X0,singleton(X1))
    <=> ( singleton(X1) = X0
        | empty_set = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).

fof(f68,plain,
    spl4_7,
    inference(avatar_split_clause,[],[f31,f65]) ).

fof(f65,plain,
    ( spl4_7
  <=> empty(sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).

fof(f31,plain,
    empty(sK3),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    empty(sK3),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f1,f20]) ).

fof(f20,plain,
    ( ? [X0] : empty(X0)
   => empty(sK3) ),
    introduced(choice_axiom,[]) ).

fof(f1,axiom,
    ? [X0] : empty(X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).

fof(f63,plain,
    ~ spl4_6,
    inference(avatar_split_clause,[],[f30,f60]) ).

fof(f60,plain,
    ( spl4_6
  <=> empty(sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_6])]) ).

fof(f30,plain,
    ~ empty(sK2),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ~ empty(sK2),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f2,f18]) ).

fof(f18,plain,
    ( ? [X0] : ~ empty(X0)
   => ~ empty(sK2) ),
    introduced(choice_axiom,[]) ).

fof(f2,axiom,
    ? [X0] : ~ empty(X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).

fof(f58,plain,
    spl4_5,
    inference(avatar_split_clause,[],[f25,f55]) ).

fof(f55,plain,
    ( spl4_5
  <=> empty(empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).

fof(f25,plain,
    empty(empty_set),
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    empty(empty_set),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).

fof(f53,plain,
    ( ~ spl4_3
    | ~ spl4_4 ),
    inference(avatar_split_clause,[],[f35,f50,f46]) ).

fof(f35,plain,
    ( empty_set != sK0
    | ~ subset(empty_set,singleton(sK1)) ),
    inference(inner_rewriting,[],[f23]) ).

fof(f23,plain,
    ( empty_set != sK0
    | ~ subset(sK0,singleton(sK1)) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f44,plain,
    ( ~ spl4_1
    | ~ spl4_2 ),
    inference(avatar_split_clause,[],[f34,f41,f37]) ).

fof(f34,plain,
    ( sK0 != singleton(sK1)
    | ~ subset(sK0,sK0) ),
    inference(inner_rewriting,[],[f24]) ).

fof(f24,plain,
    ( sK0 != singleton(sK1)
    | ~ subset(sK0,singleton(sK1)) ),
    inference(cnf_transformation,[],[f15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEU160+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34  % Computer : n028.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   : Mon Apr 29 21:12:44 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  % (19662)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37  % (19667)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.13/0.37  % (19667)First to succeed.
% 0.13/0.37  % (19667)Refutation found. Thanks to Tanya!
% 0.13/0.37  % SZS status Theorem for theBenchmark
% 0.13/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.37  % (19667)------------------------------
% 0.13/0.37  % (19667)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.37  % (19667)Termination reason: Refutation
% 0.13/0.37  
% 0.13/0.37  % (19667)Memory used [KB]: 763
% 0.13/0.37  % (19667)Time elapsed: 0.004 s
% 0.13/0.37  % (19667)Instructions burned: 4 (million)
% 0.13/0.37  % (19667)------------------------------
% 0.13/0.37  % (19667)------------------------------
% 0.13/0.37  % (19662)Success in time 0.019 s
%------------------------------------------------------------------------------