TSTP Solution File: SET016+4 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET016+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n021.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 15:04:20 EDT 2024

% Result   : Theorem 0.22s 0.40s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   56 (  10 unt;   0 def)
%            Number of atoms       :  137 (  40 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  133 (  52   ~;  45   |;  20   &)
%                                         (   9 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   3 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   90 (  79   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f486,plain,
    $false,
    inference(avatar_sat_refutation,[],[f417,f435,f485]) ).

fof(f485,plain,
    ~ spl7_1,
    inference(avatar_contradiction_clause,[],[f484]) ).

fof(f484,plain,
    ( $false
    | ~ spl7_1 ),
    inference(subsumption_resolution,[],[f478,f456]) ).

fof(f456,plain,
    ( sK0 != sK1
    | ~ spl7_1 ),
    inference(superposition,[],[f54,f449]) ).

fof(f449,plain,
    ( sK1 = sK2
    | ~ spl7_1 ),
    inference(resolution,[],[f443,f69]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( ~ member(X0,singleton(X1))
      | X0 = X1 ),
    inference(cnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ( member(X0,singleton(X1))
        | X0 != X1 )
      & ( X0 = X1
        | ~ member(X0,singleton(X1)) ) ),
    inference(nnf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( member(X0,singleton(X1))
    <=> X0 = X1 ),
    inference(rectify,[],[f8]) ).

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

fof(f443,plain,
    ( member(sK1,singleton(sK2))
    | ~ spl7_1 ),
    inference(superposition,[],[f84,f412]) ).

fof(f412,plain,
    ( unordered_pair(sK0,sK1) = singleton(sK2)
    | ~ spl7_1 ),
    inference(avatar_component_clause,[],[f410]) ).

fof(f410,plain,
    ( spl7_1
  <=> unordered_pair(sK0,sK1) = singleton(sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_1])]) ).

fof(f84,plain,
    ! [X2,X1] : member(X2,unordered_pair(X1,X2)),
    inference(equality_resolution,[],[f82]) ).

fof(f82,plain,
    ! [X2,X0,X1] :
      ( member(X0,unordered_pair(X1,X2))
      | X0 != X2 ),
    inference(cnf_transformation,[],[f52]) ).

fof(f52,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,unordered_pair(X1,X2))
        | ( X0 != X2
          & X0 != X1 ) )
      & ( X0 = X2
        | X0 = X1
        | ~ member(X0,unordered_pair(X1,X2)) ) ),
    inference(flattening,[],[f51]) ).

fof(f51,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,unordered_pair(X1,X2))
        | ( X0 != X2
          & X0 != X1 ) )
      & ( X0 = X2
        | X0 = X1
        | ~ member(X0,unordered_pair(X1,X2)) ) ),
    inference(nnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( member(X0,unordered_pair(X1,X2))
    <=> ( X0 = X2
        | X0 = X1 ) ),
    inference(rectify,[],[f9]) ).

fof(f9,axiom,
    ! [X2,X0,X1] :
      ( member(X2,unordered_pair(X0,X1))
    <=> ( X1 = X2
        | X0 = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair) ).

fof(f54,plain,
    sK0 != sK2,
    inference(cnf_transformation,[],[f30]) ).

fof(f30,plain,
    ( sK0 != sK2
    & equal_set(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)),unordered_pair(singleton(sK2),unordered_pair(sK2,sK3))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f25,f29]) ).

fof(f29,plain,
    ( ? [X0,X1,X2,X3] :
        ( X0 != X2
        & equal_set(unordered_pair(singleton(X0),unordered_pair(X0,X1)),unordered_pair(singleton(X2),unordered_pair(X2,X3))) )
   => ( sK0 != sK2
      & equal_set(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)),unordered_pair(singleton(sK2),unordered_pair(sK2,sK3))) ) ),
    introduced(choice_axiom,[]) ).

fof(f25,plain,
    ? [X0,X1,X2,X3] :
      ( X0 != X2
      & equal_set(unordered_pair(singleton(X0),unordered_pair(X0,X1)),unordered_pair(singleton(X2),unordered_pair(X2,X3))) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,plain,
    ~ ! [X0,X1,X2,X3] :
        ( equal_set(unordered_pair(singleton(X0),unordered_pair(X0,X1)),unordered_pair(singleton(X2),unordered_pair(X2,X3)))
       => X0 = X2 ),
    inference(rectify,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ! [X0,X1,X5,X6] :
        ( equal_set(unordered_pair(singleton(X0),unordered_pair(X0,X1)),unordered_pair(singleton(X5),unordered_pair(X5,X6)))
       => X0 = X5 ),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ! [X0,X1,X5,X6] :
      ( equal_set(unordered_pair(singleton(X0),unordered_pair(X0,X1)),unordered_pair(singleton(X5),unordered_pair(X5,X6)))
     => X0 = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI50a) ).

fof(f478,plain,
    ( sK0 = sK1
    | ~ spl7_1 ),
    inference(resolution,[],[f477,f69]) ).

fof(f477,plain,
    ( member(sK0,singleton(sK1))
    | ~ spl7_1 ),
    inference(forward_demodulation,[],[f444,f449]) ).

fof(f444,plain,
    ( member(sK0,singleton(sK2))
    | ~ spl7_1 ),
    inference(superposition,[],[f85,f412]) ).

fof(f85,plain,
    ! [X2,X1] : member(X1,unordered_pair(X1,X2)),
    inference(equality_resolution,[],[f81]) ).

fof(f81,plain,
    ! [X2,X0,X1] :
      ( member(X0,unordered_pair(X1,X2))
      | X0 != X1 ),
    inference(cnf_transformation,[],[f52]) ).

fof(f435,plain,
    ~ spl7_2,
    inference(avatar_contradiction_clause,[],[f434]) ).

fof(f434,plain,
    ( $false
    | ~ spl7_2 ),
    inference(subsumption_resolution,[],[f428,f54]) ).

fof(f428,plain,
    ( sK0 = sK2
    | ~ spl7_2 ),
    inference(resolution,[],[f427,f69]) ).

fof(f427,plain,
    ( member(sK2,singleton(sK0))
    | ~ spl7_2 ),
    inference(superposition,[],[f83,f416]) ).

fof(f416,plain,
    ( singleton(sK0) = singleton(sK2)
    | ~ spl7_2 ),
    inference(avatar_component_clause,[],[f414]) ).

fof(f414,plain,
    ( spl7_2
  <=> singleton(sK0) = singleton(sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_2])]) ).

fof(f83,plain,
    ! [X1] : member(X1,singleton(X1)),
    inference(equality_resolution,[],[f70]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( member(X0,singleton(X1))
      | X0 != X1 ),
    inference(cnf_transformation,[],[f44]) ).

fof(f417,plain,
    ( spl7_1
    | spl7_2 ),
    inference(avatar_split_clause,[],[f383,f414,f410]) ).

fof(f383,plain,
    ( singleton(sK0) = singleton(sK2)
    | unordered_pair(sK0,sK1) = singleton(sK2) ),
    inference(resolution,[],[f381,f80]) ).

fof(f80,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,unordered_pair(X1,X2))
      | X0 = X1
      | X0 = X2 ),
    inference(cnf_transformation,[],[f52]) ).

fof(f381,plain,
    member(singleton(sK2),unordered_pair(singleton(sK0),unordered_pair(sK0,sK1))),
    inference(resolution,[],[f179,f105]) ).

fof(f105,plain,
    ! [X2,X0,X1] :
      ( ~ subset(unordered_pair(X0,X2),X1)
      | member(X0,X1) ),
    inference(resolution,[],[f56,f85]) ).

fof(f56,plain,
    ! [X3,X0,X1] :
      ( ~ member(X3,X0)
      | member(X3,X1)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK4(X0,X1),X1)
          & member(sK4(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f32,f33]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK4(X0,X1),X1)
        & member(sK4(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f31]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f1]) ).

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

fof(f179,plain,
    subset(unordered_pair(singleton(sK2),unordered_pair(sK2,sK3)),unordered_pair(singleton(sK0),unordered_pair(sK0,sK1))),
    inference(resolution,[],[f53,f60]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( ~ equal_set(X0,X1)
      | subset(X1,X0) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ( subset(X1,X0)
        & subset(X0,X1) )
      | ~ equal_set(X0,X1) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
     => ( subset(X1,X0)
        & subset(X0,X1) ) ),
    inference(unused_predicate_definition_removal,[],[f2]) ).

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

fof(f53,plain,
    equal_set(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)),unordered_pair(singleton(sK2),unordered_pair(sK2,sK3))),
    inference(cnf_transformation,[],[f30]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SET016+4 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.36  % Computer : n021.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit   : 300
% 0.16/0.36  % WCLimit    : 300
% 0.16/0.36  % DateTime   : Tue Apr 30 01:22:40 EDT 2024
% 0.16/0.37  % CPUTime    : 
% 0.16/0.37  % (4906)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.39  % (4909)WARNING: value z3 for option sas not known
% 0.22/0.39  % (4907)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.39  % (4910)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.39  % (4913)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.22/0.39  % (4912)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.22/0.39  % (4911)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)
% 0.22/0.39  % (4908)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.39  % (4909)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.39  TRYING [1]
% 0.22/0.39  TRYING [2]
% 0.22/0.39  TRYING [3]
% 0.22/0.39  TRYING [1]
% 0.22/0.40  TRYING [2]
% 0.22/0.40  TRYING [4]
% 0.22/0.40  % (4909)First to succeed.
% 0.22/0.40  % (4909)Refutation found. Thanks to Tanya!
% 0.22/0.40  % SZS status Theorem for theBenchmark
% 0.22/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.40  % (4909)------------------------------
% 0.22/0.40  % (4909)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.40  % (4909)Termination reason: Refutation
% 0.22/0.40  
% 0.22/0.40  % (4909)Memory used [KB]: 970
% 0.22/0.40  % (4909)Time elapsed: 0.015 s
% 0.22/0.40  % (4909)Instructions burned: 18 (million)
% 0.22/0.40  % (4909)------------------------------
% 0.22/0.40  % (4909)------------------------------
% 0.22/0.40  % (4906)Success in time 0.031 s
%------------------------------------------------------------------------------