TSTP Solution File: SET881+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET881+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n022.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 : Wed May  1 03:49:23 EDT 2024

% Result   : Theorem 0.54s 0.76s
% Output   : Refutation 0.54s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   24 (   9 unt;   1 typ;   0 def)
%            Number of atoms       :  187 (  66 equ)
%            Maximal formula atoms :   14 (   8 avg)
%            Number of connectives :  126 (  49   ~;  46   |;  25   &)
%                                         (   4 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :   87 (  87 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   1   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   4 prp; 0-3 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   56 (  47   !;   8   ?;  17   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
tff(pred_def_3,type,
    sQ3_eqProxy: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(f49,plain,
    $false,
    inference(subsumption_resolution,[],[f48,f33]) ).

tff(f33,plain,
    ! [X1: $i,X4: $i] : in(X4,unordered_pair(X4,X1)),
    inference(equality_resolution,[],[f32]) ).

tff(f32,plain,
    ! [X2: $i,X1: $i,X4: $i] :
      ( in(X4,X2)
      | ( unordered_pair(X4,X1) != X2 ) ),
    inference(equality_resolution,[],[f24]) ).

tff(f24,plain,
    ! [X2: $i,X0: $i,X1: $i,X4: $i] :
      ( in(X4,X2)
      | ( X0 != X4 )
      | ( unordered_pair(X0,X1) != X2 ) ),
    inference(cnf_transformation,[],[f19]) ).

tff(f19,plain,
    ! [X0,X1,X2] :
      ( ( ( unordered_pair(X0,X1) = X2 )
        | ( ( ( ( sK2(X0,X1,X2) != X1 )
              & ( sK2(X0,X1,X2) != X0 ) )
            | ~ in(sK2(X0,X1,X2),X2) )
          & ( ( sK2(X0,X1,X2) = X1 )
            | ( sK2(X0,X1,X2) = X0 )
            | in(sK2(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ( ( X1 != X4 )
                & ( X0 != X4 ) ) )
            & ( ( X1 = X4 )
              | ( X0 = X4 )
              | ~ in(X4,X2) ) )
        | ( unordered_pair(X0,X1) != X2 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f17,f18]) ).

tff(f18,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ( ( X1 != X3 )
              & ( X0 != X3 ) )
            | ~ in(X3,X2) )
          & ( ( X1 = X3 )
            | ( X0 = X3 )
            | in(X3,X2) ) )
     => ( ( ( ( sK2(X0,X1,X2) != X1 )
            & ( sK2(X0,X1,X2) != X0 ) )
          | ~ in(sK2(X0,X1,X2),X2) )
        & ( ( sK2(X0,X1,X2) = X1 )
          | ( sK2(X0,X1,X2) = X0 )
          | in(sK2(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f17,plain,
    ! [X0,X1,X2] :
      ( ( ( unordered_pair(X0,X1) = X2 )
        | ? [X3] :
            ( ( ( ( X1 != X3 )
                & ( X0 != X3 ) )
              | ~ in(X3,X2) )
            & ( ( X1 = X3 )
              | ( X0 = X3 )
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ( ( X1 != X4 )
                & ( X0 != X4 ) ) )
            & ( ( X1 = X4 )
              | ( X0 = X4 )
              | ~ in(X4,X2) ) )
        | ( unordered_pair(X0,X1) != X2 ) ) ),
    inference(rectify,[],[f16]) ).

tff(f16,plain,
    ! [X0,X1,X2] :
      ( ( ( unordered_pair(X0,X1) = X2 )
        | ? [X3] :
            ( ( ( ( X1 != X3 )
                & ( X0 != X3 ) )
              | ~ in(X3,X2) )
            & ( ( X1 = X3 )
              | ( X0 = X3 )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ( ( X1 != X3 )
                & ( X0 != X3 ) ) )
            & ( ( X1 = X3 )
              | ( X0 = X3 )
              | ~ in(X3,X2) ) )
        | ( unordered_pair(X0,X1) != X2 ) ) ),
    inference(flattening,[],[f15]) ).

tff(f15,plain,
    ! [X0,X1,X2] :
      ( ( ( unordered_pair(X0,X1) = X2 )
        | ? [X3] :
            ( ( ( ( X1 != X3 )
                & ( X0 != X3 ) )
              | ~ in(X3,X2) )
            & ( ( X1 = X3 )
              | ( X0 = X3 )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ( ( X1 != X3 )
                & ( X0 != X3 ) ) )
            & ( ( X1 = X3 )
              | ( X0 = X3 )
              | ~ in(X3,X2) ) )
        | ( unordered_pair(X0,X1) != X2 ) ) ),
    inference(nnf_transformation,[],[f3]) ).

tff(f3,axiom,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X0,X1) = X2 )
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( ( X1 = X3 )
            | ( X0 = X3 ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.7rHJOkaf0Z/Vampire---4.8_11524',d2_tarski) ).

tff(f48,plain,
    ~ in(sK0,unordered_pair(sK0,sK1)),
    inference(resolution,[],[f37,f36]) ).

tff(f36,plain,
    ~ sQ3_eqProxy($i,empty_set,set_difference(singleton(sK0),unordered_pair(sK0,sK1))),
    inference(equality_proxy_replacement,[],[f20,f35]) ).

tff(f35,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( sQ3_eqProxy(X0,X1,X2)
    <=> ( X1 = X2 ) ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ3_eqProxy])]) ).

tff(f20,plain,
    empty_set != set_difference(singleton(sK0),unordered_pair(sK0,sK1)),
    inference(cnf_transformation,[],[f13]) ).

tff(f13,plain,
    empty_set != set_difference(singleton(sK0),unordered_pair(sK0,sK1)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f11,f12]) ).

tff(f12,plain,
    ( ? [X0,X1] : ( empty_set != set_difference(singleton(X0),unordered_pair(X0,X1)) )
   => ( empty_set != set_difference(singleton(sK0),unordered_pair(sK0,sK1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f11,plain,
    ? [X0,X1] : ( empty_set != set_difference(singleton(X0),unordered_pair(X0,X1)) ),
    inference(ennf_transformation,[],[f9]) ).

tff(f9,negated_conjecture,
    ~ ! [X0,X1] : ( empty_set = set_difference(singleton(X0),unordered_pair(X0,X1)) ),
    inference(negated_conjecture,[],[f8]) ).

tff(f8,conjecture,
    ! [X0,X1] : ( empty_set = set_difference(singleton(X0),unordered_pair(X0,X1)) ),
    file('/export/starexec/sandbox2/tmp/tmp.7rHJOkaf0Z/Vampire---4.8_11524',t22_zfmisc_1) ).

tff(f37,plain,
    ! [X0: $i,X1: $i] :
      ( sQ3_eqProxy($i,empty_set,set_difference(singleton(X0),X1))
      | ~ in(X0,X1) ),
    inference(equality_proxy_replacement,[],[f22,f35]) ).

tff(f22,plain,
    ! [X0: $i,X1: $i] :
      ( ( empty_set = set_difference(singleton(X0),X1) )
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f14]) ).

tff(f14,plain,
    ! [X0,X1] :
      ( ( ( empty_set = set_difference(singleton(X0),X1) )
        | ~ in(X0,X1) )
      & ( in(X0,X1)
        | ( empty_set != set_difference(singleton(X0),X1) ) ) ),
    inference(nnf_transformation,[],[f5]) ).

tff(f5,axiom,
    ! [X0,X1] :
      ( ( empty_set = set_difference(singleton(X0),X1) )
    <=> in(X0,X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.7rHJOkaf0Z/Vampire---4.8_11524',l36_zfmisc_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SET881+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.36  % Computer : n022.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Tue Apr 30 17:12:13 EDT 2024
% 0.14/0.37  % CPUTime    : 
% 0.14/0.37  This is a FOF_THM_RFO_SEQ problem
% 0.14/0.37  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.7rHJOkaf0Z/Vampire---4.8_11524
% 0.54/0.75  % (11715)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2996ds/34Mi)
% 0.54/0.76  % (11715)First to succeed.
% 0.54/0.76  % (11719)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2996ds/34Mi)
% 0.54/0.76  % (11721)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2996ds/83Mi)
% 0.54/0.76  % (11717)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.54/0.76  % (11716)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2996ds/51Mi)
% 0.54/0.76  % (11718)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.54/0.76  % (11715)Refutation found. Thanks to Tanya!
% 0.54/0.76  % SZS status Theorem for Vampire---4
% 0.54/0.76  % SZS output start Proof for Vampire---4
% See solution above
% 0.54/0.76  % (11715)------------------------------
% 0.54/0.76  % (11715)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.54/0.76  % (11715)Termination reason: Refutation
% 0.54/0.76  
% 0.54/0.76  % (11715)Memory used [KB]: 978
% 0.54/0.76  % (11715)Time elapsed: 0.003 s
% 0.54/0.76  % (11715)Instructions burned: 3 (million)
% 0.54/0.76  % (11715)------------------------------
% 0.54/0.76  % (11715)------------------------------
% 0.54/0.76  % (11706)Success in time 0.386 s
% 0.54/0.76  terminate called after throwing an instance of 'Lib::SystemFailException'
% 0.54/0.76  11706 Aborted by signal SIGABRT on /export/starexec/sandbox2/tmp/tmp.7rHJOkaf0Z/Vampire---4.8_11524
% 0.54/0.76  % (11706)------------------------------
% 0.54/0.76  % (11706)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.54/0.76  % (11706)Termination reason: Unknown
% 0.54/0.76  % (11706)Termination phase: Unknown
% 0.54/0.76  
% 0.54/0.76  % (11706)Memory used [KB]: 439
% 0.54/0.76  % (11706)Time elapsed: 0.386 s
% 0.54/0.76  % (11706)Instructions burned: 953 (million)
% 0.54/0.76  % (11706)------------------------------
% 0.54/0.76  % (11706)------------------------------
% 0.54/0.76  Version : Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.54/0.76  ???
% 0.54/0.76   ???
% 0.54/0.76    ???
% 0.54/0.76     ???
% 0.54/0.76      ???
% 0.54/0.76       ???
% 0.54/0.76        ???
% 0.54/0.76         ???
% 0.54/0.76          ???
% 0.54/0.76           ???
% 0.54/0.76            ???
% 0.54/0.76             ???
% 0.54/0.76              ???
% 0.54/0.76               ???
% 0.54/0.76                ???
% 0.54/0.76                 ???
% 0.54/0.76                  ???
% 0.54/0.76                   ???
% 0.54/0.76                    ???
% 0.54/0.76                     ???
% 0.54/0.76  % Vampire---4.8 exiting
%------------------------------------------------------------------------------