TSTP Solution File: SET734+4 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET734+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 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 : n023.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 03:48:46 EDT 2024

% Result   : Theorem 0.55s 0.74s
% Output   : Refutation 0.55s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   43 (   6 unt;   0 def)
%            Number of atoms       :  170 (   0 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  192 (  65   ~;  52   |;  51   &)
%                                         (   8 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   8 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-5 aty)
%            Number of variables   :  160 ( 136   !;  24   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f90,plain,
    $false,
    inference(subsumption_resolution,[],[f89,f78]) ).

fof(f78,plain,
    member(sK6(sK1,sK2,sK3),sK3),
    inference(resolution,[],[f60,f69]) ).

fof(f69,plain,
    ! [X2,X0,X1] :
      ( surjective(X0,X1,X2)
      | member(sK6(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0,X1,X2] :
      ( surjective(X0,X1,X2)
      | ( ! [X4] :
            ( ~ apply(X0,X4,sK6(X0,X1,X2))
            | ~ member(X4,X1) )
        & member(sK6(X0,X1,X2),X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f46,f55]) ).

fof(f55,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ! [X4] :
              ( ~ apply(X0,X4,X3)
              | ~ member(X4,X1) )
          & member(X3,X2) )
     => ( ! [X4] :
            ( ~ apply(X0,X4,sK6(X0,X1,X2))
            | ~ member(X4,X1) )
        & member(sK6(X0,X1,X2),X2) ) ),
    introduced(choice_axiom,[]) ).

fof(f46,plain,
    ! [X0,X1,X2] :
      ( surjective(X0,X1,X2)
      | ? [X3] :
          ( ! [X4] :
              ( ~ apply(X0,X4,X3)
              | ~ member(X4,X1) )
          & member(X3,X2) ) ),
    inference(ennf_transformation,[],[f36]) ).

fof(f36,plain,
    ! [X0,X1,X2] :
      ( ! [X3] :
          ( member(X3,X2)
         => ? [X4] :
              ( apply(X0,X4,X3)
              & member(X4,X1) ) )
     => surjective(X0,X1,X2) ),
    inference(unused_predicate_definition_removal,[],[f35]) ).

fof(f35,plain,
    ! [X0,X1,X2] :
      ( surjective(X0,X1,X2)
    <=> ! [X3] :
          ( member(X3,X2)
         => ? [X4] :
              ( apply(X0,X4,X3)
              & member(X4,X1) ) ) ),
    inference(rectify,[],[f18]) ).

fof(f18,axiom,
    ! [X5,X0,X1] :
      ( surjective(X5,X0,X1)
    <=> ! [X4] :
          ( member(X4,X1)
         => ? [X3] :
              ( apply(X5,X3,X4)
              & member(X3,X0) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.jbVUDc0wyq/Vampire---4.8_8016',surjective) ).

fof(f60,plain,
    ~ surjective(sK1,sK2,sK3),
    inference(cnf_transformation,[],[f48]) ).

fof(f48,plain,
    ( ~ surjective(sK1,sK2,sK3)
    & identity(compose_function(sK1,sK0,sK3,sK2,sK3),sK3)
    & maps(sK0,sK3,sK2)
    & maps(sK1,sK2,sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f40,f47]) ).

fof(f47,plain,
    ( ? [X0,X1,X2,X3] :
        ( ~ surjective(X1,X2,X3)
        & identity(compose_function(X1,X0,X3,X2,X3),X3)
        & maps(X0,X3,X2)
        & maps(X1,X2,X3) )
   => ( ~ surjective(sK1,sK2,sK3)
      & identity(compose_function(sK1,sK0,sK3,sK2,sK3),sK3)
      & maps(sK0,sK3,sK2)
      & maps(sK1,sK2,sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f40,plain,
    ? [X0,X1,X2,X3] :
      ( ~ surjective(X1,X2,X3)
      & identity(compose_function(X1,X0,X3,X2,X3),X3)
      & maps(X0,X3,X2)
      & maps(X1,X2,X3) ),
    inference(flattening,[],[f39]) ).

fof(f39,plain,
    ? [X0,X1,X2,X3] :
      ( ~ surjective(X1,X2,X3)
      & identity(compose_function(X1,X0,X3,X2,X3),X3)
      & maps(X0,X3,X2)
      & maps(X1,X2,X3) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f31,plain,
    ~ ! [X0,X1,X2,X3] :
        ( ( identity(compose_function(X1,X0,X3,X2,X3),X3)
          & maps(X0,X3,X2)
          & maps(X1,X2,X3) )
       => surjective(X1,X2,X3) ),
    inference(rectify,[],[f30]) ).

fof(f30,negated_conjecture,
    ~ ! [X5,X9,X0,X1] :
        ( ( identity(compose_function(X9,X5,X1,X0,X1),X1)
          & maps(X5,X1,X0)
          & maps(X9,X0,X1) )
       => surjective(X9,X0,X1) ),
    inference(negated_conjecture,[],[f29]) ).

fof(f29,conjecture,
    ! [X5,X9,X0,X1] :
      ( ( identity(compose_function(X9,X5,X1,X0,X1),X1)
        & maps(X5,X1,X0)
        & maps(X9,X0,X1) )
     => surjective(X9,X0,X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.jbVUDc0wyq/Vampire---4.8_8016',thII25) ).

fof(f89,plain,
    ~ member(sK6(sK1,sK2,sK3),sK3),
    inference(resolution,[],[f88,f86]) ).

fof(f86,plain,
    ! [X0] :
      ( member(sK5(sK1,sK0,sK2,X0,X0),sK2)
      | ~ member(X0,sK3) ),
    inference(duplicate_literal_removal,[],[f81]) ).

fof(f81,plain,
    ! [X0] :
      ( ~ member(X0,sK3)
      | member(sK5(sK1,sK0,sK2,X0,X0),sK2)
      | ~ member(X0,sK3)
      | ~ member(X0,sK3) ),
    inference(resolution,[],[f80,f65]) ).

fof(f65,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
      | member(sK5(X0,X1,X3,X5,X6),X3)
      | ~ member(X6,X4)
      | ~ member(X5,X2) ),
    inference(cnf_transformation,[],[f54]) ).

fof(f54,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
          | ! [X7] :
              ( ~ apply(X0,X7,X6)
              | ~ apply(X1,X5,X7)
              | ~ member(X7,X3) ) )
        & ( ( apply(X0,sK5(X0,X1,X3,X5,X6),X6)
            & apply(X1,X5,sK5(X0,X1,X3,X5,X6))
            & member(sK5(X0,X1,X3,X5,X6),X3) )
          | ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) )
      | ~ member(X6,X4)
      | ~ member(X5,X2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f52,f53]) ).

fof(f53,plain,
    ! [X0,X1,X3,X5,X6] :
      ( ? [X8] :
          ( apply(X0,X8,X6)
          & apply(X1,X5,X8)
          & member(X8,X3) )
     => ( apply(X0,sK5(X0,X1,X3,X5,X6),X6)
        & apply(X1,X5,sK5(X0,X1,X3,X5,X6))
        & member(sK5(X0,X1,X3,X5,X6),X3) ) ),
    introduced(choice_axiom,[]) ).

fof(f52,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
          | ! [X7] :
              ( ~ apply(X0,X7,X6)
              | ~ apply(X1,X5,X7)
              | ~ member(X7,X3) ) )
        & ( ? [X8] :
              ( apply(X0,X8,X6)
              & apply(X1,X5,X8)
              & member(X8,X3) )
          | ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) )
      | ~ member(X6,X4)
      | ~ member(X5,X2) ),
    inference(rectify,[],[f51]) ).

fof(f51,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
          | ! [X7] :
              ( ~ apply(X0,X7,X6)
              | ~ apply(X1,X5,X7)
              | ~ member(X7,X3) ) )
        & ( ? [X7] :
              ( apply(X0,X7,X6)
              & apply(X1,X5,X7)
              & member(X7,X3) )
          | ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6) ) )
      | ~ member(X6,X4)
      | ~ member(X5,X2) ),
    inference(nnf_transformation,[],[f45]) ).

fof(f45,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
      <=> ? [X7] :
            ( apply(X0,X7,X6)
            & apply(X1,X5,X7)
            & member(X7,X3) ) )
      | ~ member(X6,X4)
      | ~ member(X5,X2) ),
    inference(flattening,[],[f44]) ).

fof(f44,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
      <=> ? [X7] :
            ( apply(X0,X7,X6)
            & apply(X1,X5,X7)
            & member(X7,X3) ) )
      | ~ member(X6,X4)
      | ~ member(X5,X2) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ( member(X6,X4)
        & member(X5,X2) )
     => ( apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
      <=> ? [X7] :
            ( apply(X0,X7,X6)
            & apply(X1,X5,X7)
            & member(X7,X3) ) ) ),
    inference(rectify,[],[f14]) ).

fof(f14,axiom,
    ! [X9,X5,X0,X1,X10,X2,X11] :
      ( ( member(X11,X10)
        & member(X2,X0) )
     => ( apply(compose_function(X9,X5,X0,X1,X10),X2,X11)
      <=> ? [X4] :
            ( apply(X9,X4,X11)
            & apply(X5,X2,X4)
            & member(X4,X1) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.jbVUDc0wyq/Vampire---4.8_8016',compose_function) ).

fof(f80,plain,
    ! [X0] :
      ( apply(compose_function(sK1,sK0,sK3,sK2,sK3),X0,X0)
      | ~ member(X0,sK3) ),
    inference(resolution,[],[f59,f64]) ).

fof(f64,plain,
    ! [X2,X0,X1] :
      ( ~ identity(X0,X1)
      | ~ member(X2,X1)
      | apply(X0,X2,X2) ),
    inference(cnf_transformation,[],[f43]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( apply(X0,X2,X2)
          | ~ member(X2,X1) )
      | ~ identity(X0,X1) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( identity(X0,X1)
     => ! [X2] :
          ( member(X2,X1)
         => apply(X0,X2,X2) ) ),
    inference(unused_predicate_definition_removal,[],[f33]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( identity(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
         => apply(X0,X2,X2) ) ),
    inference(rectify,[],[f16]) ).

fof(f16,axiom,
    ! [X5,X0] :
      ( identity(X5,X0)
    <=> ! [X2] :
          ( member(X2,X0)
         => apply(X5,X2,X2) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.jbVUDc0wyq/Vampire---4.8_8016',identity) ).

fof(f59,plain,
    identity(compose_function(sK1,sK0,sK3,sK2,sK3),sK3),
    inference(cnf_transformation,[],[f48]) ).

fof(f88,plain,
    ~ member(sK5(sK1,sK0,sK2,sK6(sK1,sK2,sK3),sK6(sK1,sK2,sK3)),sK2),
    inference(subsumption_resolution,[],[f87,f78]) ).

fof(f87,plain,
    ( ~ member(sK6(sK1,sK2,sK3),sK3)
    | ~ member(sK5(sK1,sK0,sK2,sK6(sK1,sK2,sK3),sK6(sK1,sK2,sK3)),sK2) ),
    inference(resolution,[],[f84,f79]) ).

fof(f79,plain,
    ! [X0] :
      ( ~ apply(sK1,X0,sK6(sK1,sK2,sK3))
      | ~ member(X0,sK2) ),
    inference(resolution,[],[f60,f70]) ).

fof(f70,plain,
    ! [X2,X0,X1,X4] :
      ( surjective(X0,X1,X2)
      | ~ apply(X0,X4,sK6(X0,X1,X2))
      | ~ member(X4,X1) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f84,plain,
    ! [X0] :
      ( apply(sK1,sK5(sK1,sK0,sK2,X0,X0),X0)
      | ~ member(X0,sK3) ),
    inference(duplicate_literal_removal,[],[f83]) ).

fof(f83,plain,
    ! [X0] :
      ( ~ member(X0,sK3)
      | apply(sK1,sK5(sK1,sK0,sK2,X0,X0),X0)
      | ~ member(X0,sK3)
      | ~ member(X0,sK3) ),
    inference(resolution,[],[f80,f67]) ).

fof(f67,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ apply(compose_function(X0,X1,X2,X3,X4),X5,X6)
      | apply(X0,sK5(X0,X1,X3,X5,X6),X6)
      | ~ member(X6,X4)
      | ~ member(X5,X2) ),
    inference(cnf_transformation,[],[f54]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : SET734+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.12/0.14  % 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
% 0.15/0.35  % Computer : n023.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Tue Apr 30 17:27:40 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.15/0.35  This is a FOF_THM_RFO_SEQ problem
% 0.15/0.35  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.jbVUDc0wyq/Vampire---4.8_8016
% 0.55/0.73  % (8214)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)
% 0.55/0.73  % (8215)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 (2996ds/56Mi)
% 0.55/0.73  % (8215)First to succeed.
% 0.55/0.73  % (8210)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.55/0.73  % (8208)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)
% 0.55/0.73  % (8209)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)
% 0.55/0.73  % (8211)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)
% 0.55/0.73  % (8212)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)
% 0.55/0.73  % (8213)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.55/0.74  % (8215)Refutation found. Thanks to Tanya!
% 0.55/0.74  % SZS status Theorem for Vampire---4
% 0.55/0.74  % SZS output start Proof for Vampire---4
% See solution above
% 0.55/0.74  % (8215)------------------------------
% 0.55/0.74  % (8215)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.55/0.74  % (8215)Termination reason: Refutation
% 0.55/0.74  
% 0.55/0.74  % (8215)Memory used [KB]: 1073
% 0.55/0.74  % (8215)Time elapsed: 0.002 s
% 0.55/0.74  % (8215)Instructions burned: 5 (million)
% 0.55/0.74  % (8215)------------------------------
% 0.55/0.74  % (8215)------------------------------
% 0.55/0.74  % (8176)Success in time 0.374 s
% 0.55/0.74  % Vampire---4.8 exiting
%------------------------------------------------------------------------------