TSTP Solution File: SEU230+2 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEU230+2 : TPTP v8.1.2. Released v3.3.0.
% 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 : 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 : Sun May  5 09:21:17 EDT 2024

% Result   : Theorem 0.63s 0.84s
% Output   : Refutation 0.63s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   31 (  14 unt;   0 def)
%            Number of atoms       :  170 (  69 equ)
%            Maximal formula atoms :   14 (   5 avg)
%            Number of connectives :  221 (  82   ~;  84   |;  48   &)
%                                         (   4 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   1 con; 0-3 aty)
%            Number of variables   :   79 (  69   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1666,plain,
    $false,
    inference(subsumption_resolution,[],[f1665,f1368]) ).

fof(f1368,plain,
    ! [X0,X4] : in(X4,unordered_pair(X0,X4)),
    inference(equality_resolution,[],[f1367]) ).

fof(f1367,plain,
    ! [X2,X0,X4] :
      ( in(X4,X2)
      | unordered_pair(X0,X4) != X2 ),
    inference(equality_resolution,[],[f1034]) ).

fof(f1034,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X2)
      | X1 != X4
      | unordered_pair(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f652]) ).

fof(f652,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X0,X1) = X2
        | ( ( ( sK50(X0,X1,X2) != X1
              & sK50(X0,X1,X2) != X0 )
            | ~ in(sK50(X0,X1,X2),X2) )
          & ( sK50(X0,X1,X2) = X1
            | sK50(X0,X1,X2) = X0
            | in(sK50(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,[sK50])],[f650,f651]) ).

fof(f651,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ( X1 != X3
              & X0 != X3 )
            | ~ in(X3,X2) )
          & ( X1 = X3
            | X0 = X3
            | in(X3,X2) ) )
     => ( ( ( sK50(X0,X1,X2) != X1
            & sK50(X0,X1,X2) != X0 )
          | ~ in(sK50(X0,X1,X2),X2) )
        & ( sK50(X0,X1,X2) = X1
          | sK50(X0,X1,X2) = X0
          | in(sK50(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f650,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,[],[f649]) ).

fof(f649,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,[],[f648]) ).

fof(f648,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,[],[f26]) ).

fof(f26,axiom,
    ! [X0,X1,X2] :
      ( unordered_pair(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( X1 = X3
            | X0 = X3 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.8P1OypuAzs/Vampire---4.8_9182',d2_tarski) ).

fof(f1665,plain,
    ~ in(sK2,unordered_pair(sK2,sK2)),
    inference(resolution,[],[f1196,f1340]) ).

fof(f1340,plain,
    ! [X0,X1,X4] :
      ( in(X4,set_union2(X0,X1))
      | ~ in(X4,X1) ),
    inference(equality_resolution,[],[f936]) ).

fof(f936,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X2)
      | ~ in(X4,X1)
      | set_union2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f577]) ).

fof(f577,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ( ( ( ~ in(sK18(X0,X1,X2),X1)
              & ~ in(sK18(X0,X1,X2),X0) )
            | ~ in(sK18(X0,X1,X2),X2) )
          & ( in(sK18(X0,X1,X2),X1)
            | in(sK18(X0,X1,X2),X0)
            | in(sK18(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ( ~ in(X4,X1)
                & ~ in(X4,X0) ) )
            & ( in(X4,X1)
              | in(X4,X0)
              | ~ in(X4,X2) ) )
        | set_union2(X0,X1) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f575,f576]) ).

fof(f576,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ( ~ in(X3,X1)
              & ~ in(X3,X0) )
            | ~ in(X3,X2) )
          & ( in(X3,X1)
            | in(X3,X0)
            | in(X3,X2) ) )
     => ( ( ( ~ in(sK18(X0,X1,X2),X1)
            & ~ in(sK18(X0,X1,X2),X0) )
          | ~ in(sK18(X0,X1,X2),X2) )
        & ( in(sK18(X0,X1,X2),X1)
          | in(sK18(X0,X1,X2),X0)
          | in(sK18(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f575,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ? [X3] :
            ( ( ( ~ in(X3,X1)
                & ~ in(X3,X0) )
              | ~ in(X3,X2) )
            & ( in(X3,X1)
              | in(X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ( ~ in(X4,X1)
                & ~ in(X4,X0) ) )
            & ( in(X4,X1)
              | in(X4,X0)
              | ~ in(X4,X2) ) )
        | set_union2(X0,X1) != X2 ) ),
    inference(rectify,[],[f574]) ).

fof(f574,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ? [X3] :
            ( ( ( ~ in(X3,X1)
                & ~ in(X3,X0) )
              | ~ in(X3,X2) )
            & ( in(X3,X1)
              | in(X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ( ~ in(X3,X1)
                & ~ in(X3,X0) ) )
            & ( in(X3,X1)
              | in(X3,X0)
              | ~ in(X3,X2) ) )
        | set_union2(X0,X1) != X2 ) ),
    inference(flattening,[],[f573]) ).

fof(f573,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ? [X3] :
            ( ( ( ~ in(X3,X1)
                & ~ in(X3,X0) )
              | ~ in(X3,X2) )
            & ( in(X3,X1)
              | in(X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ( ~ in(X3,X1)
                & ~ in(X3,X0) ) )
            & ( in(X3,X1)
              | in(X3,X0)
              | ~ in(X3,X2) ) )
        | set_union2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f27]) ).

fof(f27,axiom,
    ! [X0,X1,X2] :
      ( set_union2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            | in(X3,X0) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.8P1OypuAzs/Vampire---4.8_9182',d2_xboole_0) ).

fof(f1196,plain,
    ~ in(sK2,set_union2(sK2,unordered_pair(sK2,sK2))),
    inference(definition_unfolding,[],[f756,f1179]) ).

fof(f1179,plain,
    ! [X0] : succ(X0) = set_union2(X0,unordered_pair(X0,X0)),
    inference(definition_unfolding,[],[f1029,f886]) ).

fof(f886,plain,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    inference(cnf_transformation,[],[f233]) ).

fof(f233,axiom,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    file('/export/starexec/sandbox2/tmp/tmp.8P1OypuAzs/Vampire---4.8_9182',t69_enumset1) ).

fof(f1029,plain,
    ! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,axiom,
    ! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
    file('/export/starexec/sandbox2/tmp/tmp.8P1OypuAzs/Vampire---4.8_9182',d1_ordinal1) ).

fof(f756,plain,
    ~ in(sK2,succ(sK2)),
    inference(cnf_transformation,[],[f504]) ).

fof(f504,plain,
    ~ in(sK2,succ(sK2)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f278,f503]) ).

fof(f503,plain,
    ( ? [X0] : ~ in(X0,succ(X0))
   => ~ in(sK2,succ(sK2)) ),
    introduced(choice_axiom,[]) ).

fof(f278,plain,
    ? [X0] : ~ in(X0,succ(X0)),
    inference(ennf_transformation,[],[f144]) ).

fof(f144,negated_conjecture,
    ~ ! [X0] : in(X0,succ(X0)),
    inference(negated_conjecture,[],[f143]) ).

fof(f143,conjecture,
    ! [X0] : in(X0,succ(X0)),
    file('/export/starexec/sandbox2/tmp/tmp.8P1OypuAzs/Vampire---4.8_9182',t10_ordinal1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SEU230+2 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.15  % 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 : n021.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   : Fri May  3 11:51:28 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.14/0.36  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.8P1OypuAzs/Vampire---4.8_9182
% 0.63/0.82  % (9585)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2995ds/56Mi)
% 0.63/0.83  % (9577)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 (2995ds/34Mi)
% 0.63/0.83  % (9579)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2995ds/78Mi)
% 0.63/0.83  % (9581)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 (2995ds/34Mi)
% 0.63/0.83  % (9578)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 (2995ds/51Mi)
% 0.63/0.83  % (9580)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2995ds/33Mi)
% 0.63/0.83  % (9582)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/45Mi)
% 0.63/0.83  % (9583)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 (2995ds/83Mi)
% 0.63/0.84  % (9585)First to succeed.
% 0.63/0.84  % (9585)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-9399"
% 0.63/0.84  % (9585)Refutation found. Thanks to Tanya!
% 0.63/0.84  % SZS status Theorem for Vampire---4
% 0.63/0.84  % SZS output start Proof for Vampire---4
% See solution above
% 0.63/0.84  % (9585)------------------------------
% 0.63/0.84  % (9585)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.63/0.84  % (9585)Termination reason: Refutation
% 0.63/0.84  
% 0.63/0.84  % (9585)Memory used [KB]: 1874
% 0.63/0.84  % (9585)Time elapsed: 0.014 s
% 0.63/0.84  % (9585)Instructions burned: 41 (million)
% 0.63/0.84  % (9399)Success in time 0.455 s
% 0.63/0.84  % Vampire---4.8 exiting
%------------------------------------------------------------------------------