TSTP Solution File: SEU148+3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU148+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n009.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 : Sat Sep  2 00:06:50 EDT 2023

% Result   : Theorem 0.21s 0.42s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   30 (   8 unt;   0 def)
%            Number of atoms       :   97 (  60 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  109 (  42   ~;  41   |;  19   &)
%                                         (   3 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   46 (;  39   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f84,plain,
    $false,
    inference(trivial_inequality_removal,[],[f83]) ).

fof(f83,plain,
    sK0 != sK0,
    inference(superposition,[],[f27,f77]) ).

fof(f77,plain,
    sK0 = sK1,
    inference(trivial_inequality_removal,[],[f68]) ).

fof(f68,plain,
    ( empty_set != empty_set
    | sK0 = sK1 ),
    inference(superposition,[],[f29,f63]) ).

fof(f63,plain,
    ( empty_set = singleton(sK0)
    | sK0 = sK1 ),
    inference(resolution,[],[f62,f45]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( ~ in(X0,singleton(X1))
      | X0 = X1 ),
    inference(equality_resolution,[],[f32]) ).

fof(f32,plain,
    ! [X3,X0,X1] :
      ( singleton(X0) != X1
      | ~ in(X3,X1)
      | X0 = X3 ),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ( ( sK2(X0,X1) != X0
            | ~ in(sK2(X0,X1),X1) )
          & ( sK2(X0,X1) = X0
            | in(sK2(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f17,f18]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( X0 != X2
            | ~ in(X2,X1) )
          & ( X0 = X2
            | in(X2,X1) ) )
     => ( ( sK2(X0,X1) != X0
          | ~ in(sK2(X0,X1),X1) )
        & ( sK2(X0,X1) = X0
          | in(sK2(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(rectify,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | X0 != X2 )
            & ( X0 = X2
              | ~ in(X2,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(nnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( singleton(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.OIrIqKtPOU/Vampire---4.8_5871',d1_tarski) ).

fof(f62,plain,
    ( in(sK1,singleton(sK0))
    | empty_set = singleton(sK0) ),
    inference(superposition,[],[f47,f51]) ).

fof(f51,plain,
    ( singleton(sK0) = singleton(sK1)
    | empty_set = singleton(sK0) ),
    inference(resolution,[],[f36,f26]) ).

fof(f26,plain,
    subset(singleton(sK0),singleton(sK1)),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ( sK0 != sK1
    & subset(singleton(sK0),singleton(sK1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f12,f14]) ).

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

fof(f12,plain,
    ? [X0,X1] :
      ( X0 != X1
      & subset(singleton(X0),singleton(X1)) ),
    inference(ennf_transformation,[],[f10]) ).

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

fof(f9,conjecture,
    ! [X0,X1] :
      ( subset(singleton(X0),singleton(X1))
     => X0 = X1 ),
    file('/export/starexec/sandbox2/tmp/tmp.OIrIqKtPOU/Vampire---4.8_5871',t6_zfmisc_1) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ~ subset(X0,singleton(X1))
      | empty_set = X0
      | singleton(X1) = X0 ),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,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,[],[f20]) ).

fof(f20,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,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( subset(X0,singleton(X1))
    <=> ( singleton(X1) = X0
        | empty_set = X0 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.OIrIqKtPOU/Vampire---4.8_5871',l4_zfmisc_1) ).

fof(f47,plain,
    ! [X0] : in(X0,singleton(X0)),
    inference(equality_resolution,[],[f46]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( X0 != X1
      | in(X1,singleton(X0)) ),
    inference(equality_resolution,[],[f33]) ).

fof(f33,plain,
    ! [X3,X0,X1] :
      ( singleton(X0) != X1
      | X0 != X3
      | in(X3,X1) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f29,plain,
    ! [X0] : singleton(X0) != empty_set,
    inference(cnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] : singleton(X0) != empty_set,
    file('/export/starexec/sandbox2/tmp/tmp.OIrIqKtPOU/Vampire---4.8_5871',l1_zfmisc_1) ).

fof(f27,plain,
    sK0 != sK1,
    inference(cnf_transformation,[],[f15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEU148+3 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.35  % Computer : n009.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Wed Aug 30 13:57:50 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.21/0.41  % (5977)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.41  % (5981)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.21/0.41  % (5978)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.21/0.41  % (5979)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.21/0.41  % (5980)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 Vampire---4 for (569ds/0Mi)
% 0.21/0.41  % (5982)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 Vampire---4 for (531ds/0Mi)
% 0.21/0.41  % (5983)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 Vampire---4 for (522ds/0Mi)
% 0.21/0.41  % (5984)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 Vampire---4 for (497ds/0Mi)
% 0.21/0.41  TRYING [1]
% 0.21/0.41  TRYING [2]
% 0.21/0.41  TRYING [3]
% 0.21/0.41  TRYING [4]
% 0.21/0.41  TRYING [1]
% 0.21/0.41  % (5983)First to succeed.
% 0.21/0.41  TRYING [2]
% 0.21/0.42  TRYING [5]
% 0.21/0.42  TRYING [1]
% 0.21/0.42  TRYING [2]
% 0.21/0.42  TRYING [3]
% 0.21/0.42  % (5982)Also succeeded, but the first one will report.
% 0.21/0.42  % (5983)Refutation found. Thanks to Tanya!
% 0.21/0.42  % SZS status Theorem for Vampire---4
% 0.21/0.42  % SZS output start Proof for Vampire---4
% See solution above
% 0.21/0.42  % (5983)------------------------------
% 0.21/0.42  % (5983)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.42  % (5983)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.42  % (5983)Termination reason: Refutation
% 0.21/0.42  
% 0.21/0.42  % (5983)Memory used [KB]: 895
% 0.21/0.42  % (5983)Time elapsed: 0.005 s
% 0.21/0.42  % (5983)------------------------------
% 0.21/0.42  % (5983)------------------------------
% 0.21/0.42  % (5977)Success in time 0.063 s
% 0.21/0.42  % Vampire---4.8 exiting
%------------------------------------------------------------------------------