TSTP Solution File: SET957+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET957+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n015.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 09:19:48 EDT 2024

% Result   : Theorem 0.14s 0.37s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   45 (   6 unt;   0 def)
%            Number of atoms       :  161 (  55 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  165 (  49   ~;  62   |;  42   &)
%                                         (   5 <=>;   6  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   15 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-3 aty)
%            Number of variables   :  104 (  73   !;  31   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1336,plain,
    $false,
    inference(trivial_inequality_removal,[],[f1335]) ).

fof(f1335,plain,
    sK0 != sK0,
    inference(superposition,[],[f34,f1267]) ).

fof(f1267,plain,
    sK0 = sK3,
    inference(duplicate_literal_removal,[],[f1262]) ).

fof(f1262,plain,
    ( sK0 = sK3
    | sK0 = sK3 ),
    inference(resolution,[],[f1261,f1250]) ).

fof(f1250,plain,
    ( in(sK6(sK3,sK0),sK3)
    | sK0 = sK3 ),
    inference(duplicate_literal_removal,[],[f1249]) ).

fof(f1249,plain,
    ( sK0 = sK3
    | sK0 = sK3
    | in(sK6(sK3,sK0),sK3) ),
    inference(resolution,[],[f1248,f40]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( in(sK6(X0,X1),X1)
      | X0 = X1
      | in(sK6(X0,X1),X0) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ( ( ~ in(sK6(X0,X1),X1)
          | ~ in(sK6(X0,X1),X0) )
        & ( in(sK6(X0,X1),X1)
          | in(sK6(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f21,f22]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ in(X2,X1)
            | ~ in(X2,X0) )
          & ( in(X2,X1)
            | in(X2,X0) ) )
     => ( ( ~ in(sK6(X0,X1),X1)
          | ~ in(sK6(X0,X1),X0) )
        & ( in(sK6(X0,X1),X1)
          | in(sK6(X0,X1),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ? [X2] :
          ( ( ~ in(X2,X1)
            | ~ in(X2,X0) )
          & ( in(X2,X1)
            | in(X2,X0) ) ) ),
    inference(nnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ? [X2] :
          ( in(X2,X0)
        <~> in(X2,X1) ) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f11,axiom,
    ! [X0,X1] :
      ( ! [X2] :
          ( in(X2,X0)
        <=> in(X2,X1) )
     => X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).

fof(f1248,plain,
    ( ~ in(sK6(sK3,sK0),sK0)
    | sK0 = sK3 ),
    inference(duplicate_literal_removal,[],[f1244]) ).

fof(f1244,plain,
    ( ~ in(sK6(sK3,sK0),sK0)
    | sK0 = sK3
    | ~ in(sK6(sK3,sK0),sK0)
    | sK0 = sK3 ),
    inference(resolution,[],[f1143,f41]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( ~ in(sK6(X0,X1),X1)
      | ~ in(sK6(X0,X1),X0)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f23]) ).

fof(f1143,plain,
    ( in(sK6(sK3,sK0),sK3)
    | ~ in(sK6(sK3,sK0),sK0)
    | sK0 = sK3 ),
    inference(superposition,[],[f32,f1142]) ).

fof(f1142,plain,
    ( sK6(sK3,sK0) = ordered_pair(sK7(sK1,sK2,sK6(sK3,sK0)),sK8(sK1,sK2,sK6(sK3,sK0)))
    | sK0 = sK3 ),
    inference(duplicate_literal_removal,[],[f1139]) ).

fof(f1139,plain,
    ( sK6(sK3,sK0) = ordered_pair(sK7(sK1,sK2,sK6(sK3,sK0)),sK8(sK1,sK2,sK6(sK3,sK0)))
    | sK0 = sK3
    | sK0 = sK3
    | sK6(sK3,sK0) = ordered_pair(sK7(sK1,sK2,sK6(sK3,sK0)),sK8(sK1,sK2,sK6(sK3,sK0))) ),
    inference(resolution,[],[f1126,f109]) ).

fof(f109,plain,
    ! [X0] :
      ( in(sK6(X0,sK0),X0)
      | sK0 = X0
      | sK6(X0,sK0) = ordered_pair(sK7(sK1,sK2,sK6(X0,sK0)),sK8(sK1,sK2,sK6(X0,sK0))) ),
    inference(resolution,[],[f105,f40]) ).

fof(f105,plain,
    ! [X0] :
      ( ~ in(X0,sK0)
      | ordered_pair(sK7(sK1,sK2,X0),sK8(sK1,sK2,X0)) = X0 ),
    inference(resolution,[],[f44,f30]) ).

fof(f30,plain,
    subset(sK0,cartesian_product2(sK1,sK2)),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ( sK0 != sK3
    & ! [X6,X7] :
        ( ( in(ordered_pair(X6,X7),sK0)
          | ~ in(ordered_pair(X6,X7),sK3) )
        & ( in(ordered_pair(X6,X7),sK3)
          | ~ in(ordered_pair(X6,X7),sK0) ) )
    & subset(sK3,cartesian_product2(sK4,sK5))
    & subset(sK0,cartesian_product2(sK1,sK2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f18,f19]) ).

fof(f19,plain,
    ( ? [X0,X1,X2,X3,X4,X5] :
        ( X0 != X3
        & ! [X6,X7] :
            ( ( in(ordered_pair(X6,X7),X0)
              | ~ in(ordered_pair(X6,X7),X3) )
            & ( in(ordered_pair(X6,X7),X3)
              | ~ in(ordered_pair(X6,X7),X0) ) )
        & subset(X3,cartesian_product2(X4,X5))
        & subset(X0,cartesian_product2(X1,X2)) )
   => ( sK0 != sK3
      & ! [X7,X6] :
          ( ( in(ordered_pair(X6,X7),sK0)
            | ~ in(ordered_pair(X6,X7),sK3) )
          & ( in(ordered_pair(X6,X7),sK3)
            | ~ in(ordered_pair(X6,X7),sK0) ) )
      & subset(sK3,cartesian_product2(sK4,sK5))
      & subset(sK0,cartesian_product2(sK1,sK2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ? [X0,X1,X2,X3,X4,X5] :
      ( X0 != X3
      & ! [X6,X7] :
          ( ( in(ordered_pair(X6,X7),X0)
            | ~ in(ordered_pair(X6,X7),X3) )
          & ( in(ordered_pair(X6,X7),X3)
            | ~ in(ordered_pair(X6,X7),X0) ) )
      & subset(X3,cartesian_product2(X4,X5))
      & subset(X0,cartesian_product2(X1,X2)) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f14,plain,
    ? [X0,X1,X2,X3,X4,X5] :
      ( X0 != X3
      & ! [X6,X7] :
          ( in(ordered_pair(X6,X7),X0)
        <=> in(ordered_pair(X6,X7),X3) )
      & subset(X3,cartesian_product2(X4,X5))
      & subset(X0,cartesian_product2(X1,X2)) ),
    inference(flattening,[],[f13]) ).

fof(f13,plain,
    ? [X0,X1,X2,X3,X4,X5] :
      ( X0 != X3
      & ! [X6,X7] :
          ( in(ordered_pair(X6,X7),X0)
        <=> in(ordered_pair(X6,X7),X3) )
      & subset(X3,cartesian_product2(X4,X5))
      & subset(X0,cartesian_product2(X1,X2)) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,negated_conjecture,
    ~ ! [X0,X1,X2,X3,X4,X5] :
        ( ( ! [X6,X7] :
              ( in(ordered_pair(X6,X7),X0)
            <=> in(ordered_pair(X6,X7),X3) )
          & subset(X3,cartesian_product2(X4,X5))
          & subset(X0,cartesian_product2(X1,X2)) )
       => X0 = X3 ),
    inference(negated_conjecture,[],[f9]) ).

fof(f9,conjecture,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ( ! [X6,X7] :
            ( in(ordered_pair(X6,X7),X0)
          <=> in(ordered_pair(X6,X7),X3) )
        & subset(X3,cartesian_product2(X4,X5))
        & subset(X0,cartesian_product2(X1,X2)) )
     => X0 = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t110_zfmisc_1) ).

fof(f44,plain,
    ! [X2,X3,X0,X1] :
      ( ~ subset(X0,cartesian_product2(X1,X2))
      | ~ in(X3,X0)
      | ordered_pair(sK7(X1,X2,X3),sK8(X1,X2,X3)) = X3 ),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1,X2,X3] :
      ( ( ordered_pair(sK7(X1,X2,X3),sK8(X1,X2,X3)) = X3
        & in(sK8(X1,X2,X3),X2)
        & in(sK7(X1,X2,X3),X1) )
      | ~ in(X3,X0)
      | ~ subset(X0,cartesian_product2(X1,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f17,f24]) ).

fof(f24,plain,
    ! [X1,X2,X3] :
      ( ? [X4,X5] :
          ( ordered_pair(X4,X5) = X3
          & in(X5,X2)
          & in(X4,X1) )
     => ( ordered_pair(sK7(X1,X2,X3),sK8(X1,X2,X3)) = X3
        & in(sK8(X1,X2,X3),X2)
        & in(sK7(X1,X2,X3),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f17,plain,
    ! [X0,X1,X2,X3] :
      ( ? [X4,X5] :
          ( ordered_pair(X4,X5) = X3
          & in(X5,X2)
          & in(X4,X1) )
      | ~ in(X3,X0)
      | ~ subset(X0,cartesian_product2(X1,X2)) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0,X1,X2,X3] :
      ~ ( ! [X4,X5] :
            ~ ( ordered_pair(X4,X5) = X3
              & in(X5,X2)
              & in(X4,X1) )
        & in(X3,X0)
        & subset(X0,cartesian_product2(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t103_zfmisc_1) ).

fof(f1126,plain,
    ( ~ in(sK6(sK3,sK0),sK3)
    | sK6(sK3,sK0) = ordered_pair(sK7(sK1,sK2,sK6(sK3,sK0)),sK8(sK1,sK2,sK6(sK3,sK0)))
    | sK0 = sK3 ),
    inference(duplicate_literal_removal,[],[f1116]) ).

fof(f1116,plain,
    ( ~ in(sK6(sK3,sK0),sK3)
    | sK6(sK3,sK0) = ordered_pair(sK7(sK1,sK2,sK6(sK3,sK0)),sK8(sK1,sK2,sK6(sK3,sK0)))
    | sK6(sK3,sK0) = ordered_pair(sK7(sK1,sK2,sK6(sK3,sK0)),sK8(sK1,sK2,sK6(sK3,sK0)))
    | sK0 = sK3 ),
    inference(superposition,[],[f108,f233]) ).

fof(f233,plain,
    ( sK6(sK3,sK0) = ordered_pair(sK7(sK4,sK5,sK6(sK3,sK0)),sK8(sK4,sK5,sK6(sK3,sK0)))
    | sK6(sK3,sK0) = ordered_pair(sK7(sK1,sK2,sK6(sK3,sK0)),sK8(sK1,sK2,sK6(sK3,sK0)))
    | sK0 = sK3 ),
    inference(resolution,[],[f109,f106]) ).

fof(f106,plain,
    ! [X0] :
      ( ~ in(X0,sK3)
      | ordered_pair(sK7(sK4,sK5,X0),sK8(sK4,sK5,X0)) = X0 ),
    inference(resolution,[],[f44,f31]) ).

fof(f31,plain,
    subset(sK3,cartesian_product2(sK4,sK5)),
    inference(cnf_transformation,[],[f20]) ).

fof(f108,plain,
    ! [X0,X1] :
      ( ~ in(ordered_pair(X0,X1),sK3)
      | ordered_pair(X0,X1) = ordered_pair(sK7(sK1,sK2,ordered_pair(X0,X1)),sK8(sK1,sK2,ordered_pair(X0,X1))) ),
    inference(resolution,[],[f105,f33]) ).

fof(f33,plain,
    ! [X6,X7] :
      ( in(ordered_pair(X6,X7),sK0)
      | ~ in(ordered_pair(X6,X7),sK3) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f32,plain,
    ! [X6,X7] :
      ( in(ordered_pair(X6,X7),sK3)
      | ~ in(ordered_pair(X6,X7),sK0) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f1261,plain,
    ( ~ in(sK6(sK3,sK0),sK3)
    | sK0 = sK3 ),
    inference(duplicate_literal_removal,[],[f1256]) ).

fof(f1256,plain,
    ( ~ in(sK6(sK3,sK0),sK3)
    | sK0 = sK3
    | sK0 = sK3 ),
    inference(resolution,[],[f1144,f1248]) ).

fof(f1144,plain,
    ( in(sK6(sK3,sK0),sK0)
    | ~ in(sK6(sK3,sK0),sK3)
    | sK0 = sK3 ),
    inference(superposition,[],[f33,f1142]) ).

fof(f34,plain,
    sK0 != sK3,
    inference(cnf_transformation,[],[f20]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08  % Problem    : SET957+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.00/0.10  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.09/0.29  % Computer : n015.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit   : 300
% 0.09/0.29  % WCLimit    : 300
% 0.09/0.29  % DateTime   : Fri May  3 16:35:23 EDT 2024
% 0.09/0.29  % CPUTime    : 
% 0.09/0.29  % (23583)Running in auto input_syntax mode. Trying TPTP
% 0.09/0.31  % (23589)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)
% 0.09/0.31  % (23588)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)
% 0.09/0.31  % (23586)WARNING: value z3 for option sas not known
% 0.14/0.31  % (23587)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.31  % (23585)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.31  % (23584)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.31  % (23586)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)
% 0.14/0.31  % (23590)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)
% 0.14/0.31  TRYING [1]
% 0.14/0.31  TRYING [2]
% 0.14/0.31  TRYING [1]
% 0.14/0.31  TRYING [3]
% 0.14/0.31  TRYING [2]
% 0.14/0.32  TRYING [3]
% 0.14/0.36  TRYING [4]
% 0.14/0.37  % (23589)First to succeed.
% 0.14/0.37  % (23589)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-23583"
% 0.14/0.37  % (23589)Refutation found. Thanks to Tanya!
% 0.14/0.37  % SZS status Theorem for theBenchmark
% 0.14/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.37  % (23589)------------------------------
% 0.14/0.37  % (23589)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.37  % (23589)Termination reason: Refutation
% 0.14/0.37  
% 0.14/0.37  % (23589)Memory used [KB]: 1753
% 0.14/0.37  % (23589)Time elapsed: 0.061 s
% 0.14/0.37  % (23589)Instructions burned: 151 (million)
% 0.14/0.37  % (23583)Success in time 0.076 s
%------------------------------------------------------------------------------