TSTP Solution File: DAT099_1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : DAT099_1 : TPTP v8.1.2. Released v6.1.0.
% 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 : n031.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 02:18:50 EDT 2024

% Result   : Theorem 0.60s 0.78s
% Output   : Refutation 0.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   88 (   9 unt;   9 typ;   0 def)
%            Number of atoms       :  232 (  36 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  258 ( 105   ~;  95   |;  39   &)
%                                         (  13 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number arithmetic     :  225 (  76 atm;   0 fun; 112 num;  37 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :   10 (   6   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :   16 (  11 usr;  11 prp; 0-2 aty)
%            Number of functors    :   12 (   7 usr;   7 con; 0-2 aty)
%            Number of variables   :   60 (  44   !;  16   ?;  60   :)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    list: $tType ).

tff(func_def_0,type,
    nil: list ).

tff(func_def_1,type,
    cons: ( $int * list ) > list ).

tff(func_def_2,type,
    head: list > $int ).

tff(func_def_3,type,
    tail: list > list ).

tff(func_def_11,type,
    sK0: $int ).

tff(func_def_12,type,
    sK1: ( $int * list ) > $int ).

tff(func_def_13,type,
    sK2: ( $int * list ) > list ).

tff(pred_def_1,type,
    inRange: ( $int * list ) > $o ).

tff(f164,plain,
    $false,
    inference(avatar_sat_refutation,[],[f64,f75,f100,f114,f126,f136,f141,f150,f151,f154,f163]) ).

tff(f163,plain,
    ~ spl3_12,
    inference(avatar_contradiction_clause,[],[f162]) ).

tff(f162,plain,
    ( $false
    | ~ spl3_12 ),
    inference(evaluation,[],[f161]) ).

tff(f161,plain,
    ( ~ $less(2,4)
    | ~ spl3_12 ),
    inference(resolution,[],[f113,f44]) ).

tff(f44,plain,
    ! [X0: $int] :
      ( ~ $less(sK0,X0)
      | ~ $less(X0,4) ),
    inference(resolution,[],[f32,f16]) ).

tff(f16,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( $less(X0,X2)
      | ~ $less(X1,X2)
      | ~ $less(X0,X1) ),
    introduced(theory_axiom_143,[]) ).

tff(f32,plain,
    ~ $less(sK0,4),
    inference(cnf_transformation,[],[f26]) ).

tff(f26,plain,
    ( ~ inRange(sK0,cons(1,cons(3,cons(2,nil))))
    & ~ $less(sK0,4) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f24,f25]) ).

tff(f25,plain,
    ( ? [X0: $int] :
        ( ~ inRange(X0,cons(1,cons(3,cons(2,nil))))
        & ~ $less(X0,4) )
   => ( ~ inRange(sK0,cons(1,cons(3,cons(2,nil))))
      & ~ $less(sK0,4) ) ),
    introduced(choice_axiom,[]) ).

tff(f24,plain,
    ? [X0: $int] :
      ( ~ inRange(X0,cons(1,cons(3,cons(2,nil))))
      & ~ $less(X0,4) ),
    inference(ennf_transformation,[],[f22]) ).

tff(f22,plain,
    ~ ! [X0: $int] :
        ( ~ $less(X0,4)
       => inRange(X0,cons(1,cons(3,cons(2,nil)))) ),
    inference(rectify,[],[f9]) ).

tff(f9,plain,
    ~ ! [X2: $int] :
        ( ~ $less(X2,4)
       => inRange(X2,cons(1,cons(3,cons(2,nil)))) ),
    inference(theory_normalization,[],[f7]) ).

tff(f7,negated_conjecture,
    ~ ! [X2: $int] :
        ( $greatereq(X2,4)
       => inRange(X2,cons(1,cons(3,cons(2,nil)))) ),
    inference(negated_conjecture,[],[f6]) ).

tff(f6,conjecture,
    ! [X2: $int] :
      ( $greatereq(X2,4)
     => inRange(X2,cons(1,cons(3,cons(2,nil)))) ),
    file('/export/starexec/sandbox2/tmp/tmp.lX3K58zaIB/Vampire---4.8_23682',c) ).

tff(f113,plain,
    ( $less(sK0,2)
    | ~ spl3_12 ),
    inference(avatar_component_clause,[],[f111]) ).

tff(f111,plain,
    ( spl3_12
  <=> $less(sK0,2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_12])]) ).

tff(f154,plain,
    ( spl3_10
    | ~ spl3_11 ),
    inference(avatar_contradiction_clause,[],[f153]) ).

tff(f153,plain,
    ( $false
    | spl3_10
    | ~ spl3_11 ),
    inference(evaluation,[],[f152]) ).

tff(f152,plain,
    ( ~ $less(2,3)
    | spl3_10
    | ~ spl3_11 ),
    inference(forward_demodulation,[],[f98,f109]) ).

tff(f109,plain,
    ( ( 2 = sK0 )
    | ~ spl3_11 ),
    inference(avatar_component_clause,[],[f107]) ).

tff(f107,plain,
    ( spl3_11
  <=> ( 2 = sK0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_11])]) ).

tff(f98,plain,
    ( ~ $less(sK0,3)
    | spl3_10 ),
    inference(avatar_component_clause,[],[f97]) ).

tff(f97,plain,
    ( spl3_10
  <=> $less(sK0,3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).

tff(f151,plain,
    ( ~ spl3_7
    | ~ spl3_8
    | spl3_4 ),
    inference(avatar_split_clause,[],[f145,f61,f86,f82]) ).

tff(f82,plain,
    ( spl3_7
  <=> $less(3,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).

tff(f86,plain,
    ( spl3_8
  <=> inRange(sK0,cons(2,nil)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).

tff(f61,plain,
    ( spl3_4
  <=> inRange(sK0,cons(3,cons(2,nil))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

tff(f145,plain,
    ( ~ inRange(sK0,cons(2,nil))
    | ~ $less(3,sK0)
    | spl3_4 ),
    inference(evaluation,[],[f144]) ).

tff(f144,plain,
    ( ~ inRange(sK0,cons(2,nil))
    | ~ $less(3,sK0)
    | $less(3,0)
    | spl3_4 ),
    inference(resolution,[],[f63,f41]) ).

tff(f41,plain,
    ! [X2: $int,X3: list,X0: $int] :
      ( inRange(X0,cons(X2,X3))
      | ~ inRange(X0,X3)
      | ~ $less(X2,X0)
      | $less(X2,0) ),
    inference(equality_resolution,[],[f40]) ).

tff(f40,plain,
    ! [X2: $int,X3: list,X0: $int,X1: list] :
      ( inRange(X0,X1)
      | ~ inRange(X0,X3)
      | ~ $less(X2,X0)
      | $less(X2,0)
      | ( cons(X2,X3) != X1 ) ),
    inference(cnf_transformation,[],[f31]) ).

tff(f31,plain,
    ! [X0: $int,X1: list] :
      ( ( inRange(X0,X1)
        | ( ! [X2: $int,X3: list] :
              ( ~ inRange(X0,X3)
              | ~ $less(X2,X0)
              | $less(X2,0)
              | ( cons(X2,X3) != X1 ) )
          & ( nil != X1 ) ) )
      & ( ( inRange(X0,sK2(X0,X1))
          & $less(sK1(X0,X1),X0)
          & ~ $less(sK1(X0,X1),0)
          & ( cons(sK1(X0,X1),sK2(X0,X1)) = X1 ) )
        | ( nil = X1 )
        | ~ inRange(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f29,f30]) ).

tff(f30,plain,
    ! [X0: $int,X1: list] :
      ( ? [X4: $int,X5: list] :
          ( inRange(X0,X5)
          & $less(X4,X0)
          & ~ $less(X4,0)
          & ( cons(X4,X5) = X1 ) )
     => ( inRange(X0,sK2(X0,X1))
        & $less(sK1(X0,X1),X0)
        & ~ $less(sK1(X0,X1),0)
        & ( cons(sK1(X0,X1),sK2(X0,X1)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f29,plain,
    ! [X0: $int,X1: list] :
      ( ( inRange(X0,X1)
        | ( ! [X2: $int,X3: list] :
              ( ~ inRange(X0,X3)
              | ~ $less(X2,X0)
              | $less(X2,0)
              | ( cons(X2,X3) != X1 ) )
          & ( nil != X1 ) ) )
      & ( ? [X4: $int,X5: list] :
            ( inRange(X0,X5)
            & $less(X4,X0)
            & ~ $less(X4,0)
            & ( cons(X4,X5) = X1 ) )
        | ( nil = X1 )
        | ~ inRange(X0,X1) ) ),
    inference(rectify,[],[f28]) ).

tff(f28,plain,
    ! [X0: $int,X1: list] :
      ( ( inRange(X0,X1)
        | ( ! [X2: $int,X3: list] :
              ( ~ inRange(X0,X3)
              | ~ $less(X2,X0)
              | $less(X2,0)
              | ( cons(X2,X3) != X1 ) )
          & ( nil != X1 ) ) )
      & ( ? [X2: $int,X3: list] :
            ( inRange(X0,X3)
            & $less(X2,X0)
            & ~ $less(X2,0)
            & ( cons(X2,X3) = X1 ) )
        | ( nil = X1 )
        | ~ inRange(X0,X1) ) ),
    inference(flattening,[],[f27]) ).

tff(f27,plain,
    ! [X0: $int,X1: list] :
      ( ( inRange(X0,X1)
        | ( ! [X2: $int,X3: list] :
              ( ~ inRange(X0,X3)
              | ~ $less(X2,X0)
              | $less(X2,0)
              | ( cons(X2,X3) != X1 ) )
          & ( nil != X1 ) ) )
      & ( ? [X2: $int,X3: list] :
            ( inRange(X0,X3)
            & $less(X2,X0)
            & ~ $less(X2,0)
            & ( cons(X2,X3) = X1 ) )
        | ( nil = X1 )
        | ~ inRange(X0,X1) ) ),
    inference(nnf_transformation,[],[f23]) ).

tff(f23,plain,
    ! [X0: $int,X1: list] :
      ( inRange(X0,X1)
    <=> ( ? [X2: $int,X3: list] :
            ( inRange(X0,X3)
            & $less(X2,X0)
            & ~ $less(X2,0)
            & ( cons(X2,X3) = X1 ) )
        | ( nil = X1 ) ) ),
    inference(rectify,[],[f8]) ).

tff(f8,plain,
    ! [X2: $int,X1: list] :
      ( inRange(X2,X1)
    <=> ( ? [X0: $int,X3: list] :
            ( inRange(X2,X3)
            & $less(X0,X2)
            & ~ $less(X0,0)
            & ( cons(X0,X3) = X1 ) )
        | ( nil = X1 ) ) ),
    inference(theory_normalization,[],[f5]) ).

tff(f5,axiom,
    ! [X2: $int,X1: list] :
      ( inRange(X2,X1)
    <=> ( ? [X0: $int,X3: list] :
            ( inRange(X2,X3)
            & $less(X0,X2)
            & $lesseq(0,X0)
            & ( cons(X0,X3) = X1 ) )
        | ( nil = X1 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.lX3K58zaIB/Vampire---4.8_23682',inRange) ).

tff(f63,plain,
    ( ~ inRange(sK0,cons(3,cons(2,nil)))
    | spl3_4 ),
    inference(avatar_component_clause,[],[f61]) ).

tff(f150,plain,
    ~ spl3_10,
    inference(avatar_contradiction_clause,[],[f149]) ).

tff(f149,plain,
    ( $false
    | ~ spl3_10 ),
    inference(evaluation,[],[f148]) ).

tff(f148,plain,
    ( ~ $less(3,4)
    | ~ spl3_10 ),
    inference(resolution,[],[f99,f44]) ).

tff(f99,plain,
    ( $less(sK0,3)
    | ~ spl3_10 ),
    inference(avatar_component_clause,[],[f97]) ).

tff(f141,plain,
    ~ spl3_6,
    inference(avatar_contradiction_clause,[],[f140]) ).

tff(f140,plain,
    ( $false
    | ~ spl3_6 ),
    inference(evaluation,[],[f139]) ).

tff(f139,plain,
    ( ~ $less(1,4)
    | ~ spl3_6 ),
    inference(resolution,[],[f74,f44]) ).

tff(f74,plain,
    ( $less(sK0,1)
    | ~ spl3_6 ),
    inference(avatar_component_clause,[],[f72]) ).

tff(f72,plain,
    ( spl3_6
  <=> $less(sK0,1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).

tff(f136,plain,
    ~ spl3_5,
    inference(avatar_contradiction_clause,[],[f135]) ).

tff(f135,plain,
    ( $false
    | ~ spl3_5 ),
    inference(evaluation,[],[f129]) ).

tff(f129,plain,
    ( ~ $less(1,4)
    | ~ spl3_5 ),
    inference(superposition,[],[f32,f70]) ).

tff(f70,plain,
    ( ( 1 = sK0 )
    | ~ spl3_5 ),
    inference(avatar_component_clause,[],[f68]) ).

tff(f68,plain,
    ( spl3_5
  <=> ( 1 = sK0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).

tff(f126,plain,
    ~ spl3_9,
    inference(avatar_contradiction_clause,[],[f125]) ).

tff(f125,plain,
    ( $false
    | ~ spl3_9 ),
    inference(evaluation,[],[f117]) ).

tff(f117,plain,
    ( ~ $less(3,4)
    | ~ spl3_9 ),
    inference(superposition,[],[f32,f95]) ).

tff(f95,plain,
    ( ( 3 = sK0 )
    | ~ spl3_9 ),
    inference(avatar_component_clause,[],[f93]) ).

tff(f93,plain,
    ( spl3_9
  <=> ( 3 = sK0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).

tff(f114,plain,
    ( spl3_11
    | spl3_12
    | spl3_8 ),
    inference(avatar_split_clause,[],[f104,f86,f111,f107]) ).

tff(f104,plain,
    ( $less(sK0,2)
    | ( 2 = sK0 )
    | spl3_8 ),
    inference(resolution,[],[f103,f17]) ).

tff(f17,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X1,X0)
      | $less(X0,X1)
      | ( X0 = X1 ) ),
    introduced(theory_axiom_144,[]) ).

tff(f103,plain,
    ( ~ $less(2,sK0)
    | spl3_8 ),
    inference(subsumption_resolution,[],[f102,f42]) ).

tff(f42,plain,
    ! [X0: $int] : inRange(X0,nil),
    inference(equality_resolution,[],[f39]) ).

tff(f39,plain,
    ! [X0: $int,X1: list] :
      ( inRange(X0,X1)
      | ( nil != X1 ) ),
    inference(cnf_transformation,[],[f31]) ).

tff(f102,plain,
    ( ~ inRange(sK0,nil)
    | ~ $less(2,sK0)
    | spl3_8 ),
    inference(evaluation,[],[f101]) ).

tff(f101,plain,
    ( ~ inRange(sK0,nil)
    | ~ $less(2,sK0)
    | $less(2,0)
    | spl3_8 ),
    inference(resolution,[],[f88,f41]) ).

tff(f88,plain,
    ( ~ inRange(sK0,cons(2,nil))
    | spl3_8 ),
    inference(avatar_component_clause,[],[f86]) ).

tff(f100,plain,
    ( spl3_9
    | spl3_10
    | spl3_7 ),
    inference(avatar_split_clause,[],[f90,f82,f97,f93]) ).

tff(f90,plain,
    ( $less(sK0,3)
    | ( 3 = sK0 )
    | spl3_7 ),
    inference(resolution,[],[f84,f17]) ).

tff(f84,plain,
    ( ~ $less(3,sK0)
    | spl3_7 ),
    inference(avatar_component_clause,[],[f82]) ).

tff(f75,plain,
    ( spl3_5
    | spl3_6
    | spl3_3 ),
    inference(avatar_split_clause,[],[f65,f57,f72,f68]) ).

tff(f57,plain,
    ( spl3_3
  <=> $less(1,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

tff(f65,plain,
    ( $less(sK0,1)
    | ( 1 = sK0 )
    | spl3_3 ),
    inference(resolution,[],[f59,f17]) ).

tff(f59,plain,
    ( ~ $less(1,sK0)
    | spl3_3 ),
    inference(avatar_component_clause,[],[f57]) ).

tff(f64,plain,
    ( ~ spl3_3
    | ~ spl3_4 ),
    inference(avatar_split_clause,[],[f55,f61,f57]) ).

tff(f55,plain,
    ( ~ inRange(sK0,cons(3,cons(2,nil)))
    | ~ $less(1,sK0) ),
    inference(evaluation,[],[f54]) ).

tff(f54,plain,
    ( ~ inRange(sK0,cons(3,cons(2,nil)))
    | ~ $less(1,sK0)
    | $less(1,0) ),
    inference(resolution,[],[f33,f41]) ).

tff(f33,plain,
    ~ inRange(sK0,cons(1,cons(3,cons(2,nil)))),
    inference(cnf_transformation,[],[f26]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem    : DAT099_1 : TPTP v8.1.2. Released v6.1.0.
% 0.09/0.10  % 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
% 0.10/0.30  % Computer : n031.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit   : 300
% 0.10/0.30  % WCLimit    : 300
% 0.10/0.30  % DateTime   : Tue Apr 30 17:06:14 EDT 2024
% 0.10/0.30  % CPUTime    : 
% 0.10/0.30  This is a TF0_THM_EQU_ARI problem
% 0.10/0.30  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.lX3K58zaIB/Vampire---4.8_23682
% 0.60/0.77  % (23795)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)
% 0.60/0.77  % (23793)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2995ds/78Mi)
% 0.60/0.77  % (23792)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)
% 0.60/0.77  % (23794)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)
% 0.60/0.77  % (23791)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)
% 0.60/0.77  % (23796)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)
% 0.60/0.77  % (23797)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)
% 0.60/0.77  % (23798)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)
% 0.60/0.77  % (23796)First to succeed.
% 0.60/0.78  % (23797)Also succeeded, but the first one will report.
% 0.60/0.78  % (23796)Refutation found. Thanks to Tanya!
% 0.60/0.78  % SZS status Theorem for Vampire---4
% 0.60/0.78  % SZS output start Proof for Vampire---4
% See solution above
% 0.60/0.78  % (23796)------------------------------
% 0.60/0.78  % (23796)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.60/0.78  % (23796)Termination reason: Refutation
% 0.60/0.78  
% 0.60/0.78  % (23796)Memory used [KB]: 1075
% 0.60/0.78  % (23796)Time elapsed: 0.007 s
% 0.60/0.78  % (23796)Instructions burned: 8 (million)
% 0.60/0.78  % (23796)------------------------------
% 0.60/0.78  % (23796)------------------------------
% 0.60/0.78  % (23790)Success in time 0.469 s
% 0.60/0.78  % Vampire---4.8 exiting
%------------------------------------------------------------------------------