TSTP Solution File: SEU263+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU263+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 : n019.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 15:25:41 EDT 2024

% Result   : Theorem 0.22s 0.43s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   57 (  10 unt;   0 def)
%            Number of atoms       :  131 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  125 (  51   ~;  42   |;  16   &)
%                                         (   5 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    9 (   8 usr;   4 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :  106 (  94   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1046,plain,
    $false,
    inference(avatar_sat_refutation,[],[f1035,f1037,f1041,f1045]) ).

fof(f1045,plain,
    spl7_11,
    inference(avatar_contradiction_clause,[],[f1042]) ).

fof(f1042,plain,
    ( $false
    | spl7_11 ),
    inference(resolution,[],[f1034,f45]) ).

fof(f45,plain,
    subset(relation_rng(sK3),sK1),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,plain,
    ( ~ relation_of2_as_subset(sK3,sK2,sK1)
    & subset(relation_rng(sK3),sK1)
    & relation_of2_as_subset(sK3,sK2,sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f24,f33]) ).

fof(f33,plain,
    ( ? [X0,X1,X2,X3] :
        ( ~ relation_of2_as_subset(X3,X2,X1)
        & subset(relation_rng(X3),X1)
        & relation_of2_as_subset(X3,X2,X0) )
   => ( ~ relation_of2_as_subset(sK3,sK2,sK1)
      & subset(relation_rng(sK3),sK1)
      & relation_of2_as_subset(sK3,sK2,sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f24,plain,
    ? [X0,X1,X2,X3] :
      ( ~ relation_of2_as_subset(X3,X2,X1)
      & subset(relation_rng(X3),X1)
      & relation_of2_as_subset(X3,X2,X0) ),
    inference(flattening,[],[f23]) ).

fof(f23,plain,
    ? [X0,X1,X2,X3] :
      ( ~ relation_of2_as_subset(X3,X2,X1)
      & subset(relation_rng(X3),X1)
      & relation_of2_as_subset(X3,X2,X0) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,negated_conjecture,
    ~ ! [X0,X1,X2,X3] :
        ( relation_of2_as_subset(X3,X2,X0)
       => ( subset(relation_rng(X3),X1)
         => relation_of2_as_subset(X3,X2,X1) ) ),
    inference(negated_conjecture,[],[f17]) ).

fof(f17,conjecture,
    ! [X0,X1,X2,X3] :
      ( relation_of2_as_subset(X3,X2,X0)
     => ( subset(relation_rng(X3),X1)
       => relation_of2_as_subset(X3,X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_relset_1) ).

fof(f1034,plain,
    ( ~ subset(relation_rng(sK3),sK1)
    | spl7_11 ),
    inference(avatar_component_clause,[],[f1032]) ).

fof(f1032,plain,
    ( spl7_11
  <=> subset(relation_rng(sK3),sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_11])]) ).

fof(f1041,plain,
    spl7_10,
    inference(avatar_contradiction_clause,[],[f1038]) ).

fof(f1038,plain,
    ( $false
    | spl7_10 ),
    inference(resolution,[],[f1030,f66]) ).

fof(f66,plain,
    subset(relation_dom(sK3),sK2),
    inference(resolution,[],[f55,f44]) ).

fof(f44,plain,
    relation_of2_as_subset(sK3,sK2,sK0),
    inference(cnf_transformation,[],[f34]) ).

fof(f55,plain,
    ! [X2,X0,X1] :
      ( ~ relation_of2_as_subset(X2,X0,X1)
      | subset(relation_dom(X2),X0) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( ( subset(relation_rng(X2),X1)
        & subset(relation_dom(X2),X0) )
      | ~ relation_of2_as_subset(X2,X0,X1) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X0,X1,X2] :
      ( relation_of2_as_subset(X2,X0,X1)
     => ( subset(relation_rng(X2),X1)
        & subset(relation_dom(X2),X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_relset_1) ).

fof(f1030,plain,
    ( ~ subset(relation_dom(sK3),sK2)
    | spl7_10 ),
    inference(avatar_component_clause,[],[f1028]) ).

fof(f1028,plain,
    ( spl7_10
  <=> subset(relation_dom(sK3),sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_10])]) ).

fof(f1037,plain,
    spl7_9,
    inference(avatar_contradiction_clause,[],[f1036]) ).

fof(f1036,plain,
    ( $false
    | spl7_9 ),
    inference(resolution,[],[f1026,f95]) ).

fof(f95,plain,
    relation(sK3),
    inference(resolution,[],[f93,f44]) ).

fof(f93,plain,
    ! [X2,X0,X1] :
      ( ~ relation_of2_as_subset(X0,X1,X2)
      | relation(X0) ),
    inference(resolution,[],[f54,f57]) ).

fof(f57,plain,
    ! [X2,X0,X1] :
      ( ~ element(X2,powerset(cartesian_product2(X0,X1)))
      | relation(X2) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1,X2] :
      ( relation(X2)
      | ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1,X2] :
      ( element(X2,powerset(cartesian_product2(X0,X1)))
     => relation(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).

fof(f54,plain,
    ! [X2,X0,X1] :
      ( element(X2,powerset(cartesian_product2(X0,X1)))
      | ~ relation_of2_as_subset(X2,X0,X1) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1,X2] :
      ( element(X2,powerset(cartesian_product2(X0,X1)))
      | ~ relation_of2_as_subset(X2,X0,X1) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1,X2] :
      ( relation_of2_as_subset(X2,X0,X1)
     => element(X2,powerset(cartesian_product2(X0,X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).

fof(f1026,plain,
    ( ~ relation(sK3)
    | spl7_9 ),
    inference(avatar_component_clause,[],[f1024]) ).

fof(f1024,plain,
    ( spl7_9
  <=> relation(sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_9])]) ).

fof(f1035,plain,
    ( ~ spl7_9
    | ~ spl7_10
    | ~ spl7_11 ),
    inference(avatar_split_clause,[],[f442,f1032,f1028,f1024]) ).

fof(f442,plain,
    ( ~ subset(relation_rng(sK3),sK1)
    | ~ subset(relation_dom(sK3),sK2)
    | ~ relation(sK3) ),
    inference(resolution,[],[f114,f47]) ).

fof(f47,plain,
    ! [X0] :
      ( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0] :
      ( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,axiom,
    ! [X0] :
      ( relation(X0)
     => subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relat_1) ).

fof(f114,plain,
    ! [X0,X1] :
      ( ~ subset(sK3,cartesian_product2(X0,X1))
      | ~ subset(X1,sK1)
      | ~ subset(X0,sK2) ),
    inference(resolution,[],[f108,f63]) ).

fof(f63,plain,
    ! [X2,X3,X0,X1] :
      ( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
      | ~ subset(X2,X3)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X0,X1,X2,X3] :
      ( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
      | ~ subset(X2,X3)
      | ~ subset(X0,X1) ),
    inference(flattening,[],[f31]) ).

fof(f31,plain,
    ! [X0,X1,X2,X3] :
      ( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
      | ~ subset(X2,X3)
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0,X1,X2,X3] :
      ( ( subset(X2,X3)
        & subset(X0,X1) )
     => subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).

fof(f108,plain,
    ! [X0] :
      ( ~ subset(X0,cartesian_product2(sK2,sK1))
      | ~ subset(sK3,X0) ),
    inference(resolution,[],[f88,f72]) ).

fof(f72,plain,
    ~ relation_of2(sK3,sK2,sK1),
    inference(resolution,[],[f62,f46]) ).

fof(f46,plain,
    ~ relation_of2_as_subset(sK3,sK2,sK1),
    inference(cnf_transformation,[],[f34]) ).

fof(f62,plain,
    ! [X2,X0,X1] :
      ( relation_of2_as_subset(X2,X0,X1)
      | ~ relation_of2(X2,X0,X1) ),
    inference(cnf_transformation,[],[f43]) ).

fof(f43,plain,
    ! [X0,X1,X2] :
      ( ( relation_of2_as_subset(X2,X0,X1)
        | ~ relation_of2(X2,X0,X1) )
      & ( relation_of2(X2,X0,X1)
        | ~ relation_of2_as_subset(X2,X0,X1) ) ),
    inference(nnf_transformation,[],[f13]) ).

fof(f13,axiom,
    ! [X0,X1,X2] :
      ( relation_of2_as_subset(X2,X0,X1)
    <=> relation_of2(X2,X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).

fof(f88,plain,
    ! [X2,X3,X0,X1] :
      ( relation_of2(X0,X1,X2)
      | ~ subset(X3,cartesian_product2(X1,X2))
      | ~ subset(X0,X3) ),
    inference(resolution,[],[f60,f58]) ).

fof(f58,plain,
    ! [X2,X0,X1] :
      ( subset(X0,X2)
      | ~ subset(X1,X2)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,plain,
    ! [X0,X1,X2] :
      ( subset(X0,X2)
      | ~ subset(X1,X2)
      | ~ subset(X0,X1) ),
    inference(flattening,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( subset(X0,X2)
      | ~ subset(X1,X2)
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,axiom,
    ! [X0,X1,X2] :
      ( ( subset(X1,X2)
        & subset(X0,X1) )
     => subset(X0,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).

fof(f60,plain,
    ! [X2,X0,X1] :
      ( ~ subset(X2,cartesian_product2(X0,X1))
      | relation_of2(X2,X0,X1) ),
    inference(cnf_transformation,[],[f42]) ).

fof(f42,plain,
    ! [X0,X1,X2] :
      ( ( relation_of2(X2,X0,X1)
        | ~ subset(X2,cartesian_product2(X0,X1)) )
      & ( subset(X2,cartesian_product2(X0,X1))
        | ~ relation_of2(X2,X0,X1) ) ),
    inference(nnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1,X2] :
      ( relation_of2(X2,X0,X1)
    <=> subset(X2,cartesian_product2(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relset_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : SEU263+1 : TPTP v8.1.2. Released v3.3.0.
% 0.04/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n019.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Mon Apr 29 20:43:44 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.37  % (15687)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.39  % (15688)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.22/0.39  TRYING [1]
% 0.22/0.39  TRYING [2]
% 0.22/0.40  TRYING [3]
% 0.22/0.40  % (15694)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.22/0.40  % (15691)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.22/0.40  % (15693)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.22/0.40  % (15689)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.40  % (15692)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.22/0.40  % (15690)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.22/0.40  TRYING [1]
% 0.22/0.40  TRYING [1,1]
% 0.22/0.40  TRYING [2]
% 0.22/0.40  TRYING [1,1]
% 0.22/0.40  TRYING [2,1]
% 0.22/0.40  TRYING [2,1]
% 0.22/0.40  TRYING [4]
% 0.22/0.40  TRYING [3]
% 0.22/0.40  TRYING [3,1]
% 0.22/0.40  TRYING [3,1]
% 0.22/0.41  TRYING [2,2]
% 0.22/0.41  TRYING [2,2]
% 0.22/0.41  TRYING [3,2]
% 0.22/0.41  TRYING [3,2]
% 0.22/0.41  TRYING [4]
% 0.22/0.42  TRYING [4,1]
% 0.22/0.42  TRYING [4,1]
% 0.22/0.43  % (15690)First to succeed.
% 0.22/0.43  TRYING [4,2]
% 0.22/0.43  TRYING [4,2]
% 0.22/0.43  % (15690)Refutation found. Thanks to Tanya!
% 0.22/0.43  % SZS status Theorem for theBenchmark
% 0.22/0.43  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.43  % (15690)------------------------------
% 0.22/0.43  % (15690)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.43  % (15690)Termination reason: Refutation
% 0.22/0.43  
% 0.22/0.43  % (15690)Memory used [KB]: 1074
% 0.22/0.43  % (15690)Time elapsed: 0.037 s
% 0.22/0.43  % (15690)Instructions burned: 32 (million)
% 0.22/0.43  % (15690)------------------------------
% 0.22/0.43  % (15690)------------------------------
% 0.22/0.43  % (15687)Success in time 0.066 s
%------------------------------------------------------------------------------