TSTP Solution File: ARI622_1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : ARI622_1 : TPTP v8.1.2. Released v5.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n002.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 02:09:35 EDT 2024

% Result   : Theorem 0.59s 0.76s
% Output   : Refutation 0.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   33 (   2 unt;   3 typ;   0 def)
%            Number of atoms       :  168 (  42 equ)
%            Maximal formula atoms :   13 (   5 avg)
%            Number of connectives :  200 (  62   ~;  86   |;  41   &)
%                                         (   6 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number arithmetic     :  365 (  55 atm;  88 fun; 156 num;  66 var)
%            Number of types       :    2 (   0 usr;   1 ari)
%            Number of type conns  :    4 (   3   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   1 usr;   5 con; 0-2 aty)
%            Number of variables   :   66 (  49   !;  17   ?;  66   :)

% Comments : 
%------------------------------------------------------------------------------
tff(func_def_7,type,
    sK0: $int > $int ).

tff(pred_def_1,type,
    pow2: $int > $o ).

tff(pred_def_4,type,
    sQ1_eqProxy: ( $int * $int ) > $o ).

tff(f135,plain,
    $false,
    inference(evaluation,[],[f132]) ).

tff(f132,plain,
    ( $less($product(8,1),2)
    | $less($sum(2,$product(8,1)),10)
    | $less($product(4,1),2)
    | $less(10,$sum(2,$product(8,1)))
    | $less($product(2,1),2) ),
    inference(resolution,[],[f122,f37]) ).

tff(f37,plain,
    pow2(1),
    inference(equality_resolution,[],[f32]) ).

tff(f32,plain,
    ! [X2: $int] :
      ( pow2(X2)
      | ( 1 != X2 ) ),
    inference(cnf_transformation,[],[f28]) ).

tff(f28,plain,
    ( ! [X0: $int,X1: $int] :
        ( ( $sum(X0,X1) != 10 )
        | ~ pow2(X1)
        | ~ pow2(X0) )
    & ! [X2: $int] :
        ( ( pow2(X2)
          | ( ( ! [X3: $int] :
                  ( ~ pow2(X3)
                  | ( $product(2,X3) != X2 ) )
              | $less(X2,2) )
            & ( 1 != X2 ) ) )
        & ( ( pow2(sK0(X2))
            & ( $product(2,sK0(X2)) = X2 )
            & ~ $less(X2,2) )
          | ( 1 = X2 )
          | ~ pow2(X2) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f26,f27]) ).

tff(f27,plain,
    ! [X2: $int] :
      ( ? [X4: $int] :
          ( pow2(X4)
          & ( $product(2,X4) = X2 ) )
     => ( pow2(sK0(X2))
        & ( $product(2,sK0(X2)) = X2 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f26,plain,
    ( ! [X0: $int,X1: $int] :
        ( ( $sum(X0,X1) != 10 )
        | ~ pow2(X1)
        | ~ pow2(X0) )
    & ! [X2: $int] :
        ( ( pow2(X2)
          | ( ( ! [X3: $int] :
                  ( ~ pow2(X3)
                  | ( $product(2,X3) != X2 ) )
              | $less(X2,2) )
            & ( 1 != X2 ) ) )
        & ( ( ? [X4: $int] :
                ( pow2(X4)
                & ( $product(2,X4) = X2 ) )
            & ~ $less(X2,2) )
          | ( 1 = X2 )
          | ~ pow2(X2) ) ) ),
    inference(rectify,[],[f25]) ).

tff(f25,plain,
    ( ! [X2: $int,X3: $int] :
        ( ( 10 != $sum(X2,X3) )
        | ~ pow2(X3)
        | ~ pow2(X2) )
    & ! [X0: $int] :
        ( ( pow2(X0)
          | ( ( ! [X1: $int] :
                  ( ~ pow2(X1)
                  | ( $product(2,X1) != X0 ) )
              | $less(X0,2) )
            & ( 1 != X0 ) ) )
        & ( ( ? [X1: $int] :
                ( pow2(X1)
                & ( $product(2,X1) = X0 ) )
            & ~ $less(X0,2) )
          | ( 1 = X0 )
          | ~ pow2(X0) ) ) ),
    inference(flattening,[],[f24]) ).

tff(f24,plain,
    ( ! [X2: $int,X3: $int] :
        ( ( 10 != $sum(X2,X3) )
        | ~ pow2(X3)
        | ~ pow2(X2) )
    & ! [X0: $int] :
        ( ( pow2(X0)
          | ( ( ! [X1: $int] :
                  ( ~ pow2(X1)
                  | ( $product(2,X1) != X0 ) )
              | $less(X0,2) )
            & ( 1 != X0 ) ) )
        & ( ( ? [X1: $int] :
                ( pow2(X1)
                & ( $product(2,X1) = X0 ) )
            & ~ $less(X0,2) )
          | ( 1 = X0 )
          | ~ pow2(X0) ) ) ),
    inference(nnf_transformation,[],[f23]) ).

tff(f23,plain,
    ( ! [X2: $int,X3: $int] :
        ( ( 10 != $sum(X2,X3) )
        | ~ pow2(X3)
        | ~ pow2(X2) )
    & ! [X0: $int] :
        ( pow2(X0)
      <=> ( ( ? [X1: $int] :
                ( pow2(X1)
                & ( $product(2,X1) = X0 ) )
            & ~ $less(X0,2) )
          | ( 1 = X0 ) ) ) ),
    inference(ennf_transformation,[],[f22]) ).

tff(f22,plain,
    ~ ( ! [X0: $int] :
          ( pow2(X0)
        <=> ( ( ? [X1: $int] :
                  ( pow2(X1)
                  & ( $product(2,X1) = X0 ) )
              & ~ $less(X0,2) )
            | ( 1 = X0 ) ) )
     => ? [X2: $int,X3: $int] :
          ( ( 10 = $sum(X2,X3) )
          & pow2(X3)
          & pow2(X2) ) ),
    inference(rectify,[],[f3]) ).

tff(f3,plain,
    ~ ( ! [X0: $int] :
          ( pow2(X0)
        <=> ( ( ? [X1: $int] :
                  ( pow2(X1)
                  & ( $product(2,X1) = X0 ) )
              & ~ $less(X0,2) )
            | ( 1 = X0 ) ) )
     => ? [X0: $int,X1: $int] :
          ( ( $sum(X0,X1) = 10 )
          & pow2(X1)
          & pow2(X0) ) ),
    inference(theory_normalization,[],[f2]) ).

tff(f2,negated_conjecture,
    ~ ( ! [X0: $int] :
          ( pow2(X0)
        <=> ( ( ? [X1: $int] :
                  ( pow2(X1)
                  & ( $product(2,X1) = X0 ) )
              & $lesseq(2,X0) )
            | ( 1 = X0 ) ) )
     => ? [X0: $int,X1: $int] :
          ( ( $sum(X0,X1) = 10 )
          & pow2(X1)
          & pow2(X0) ) ),
    inference(negated_conjecture,[],[f1]) ).

tff(f1,conjecture,
    ( ! [X0: $int] :
        ( pow2(X0)
      <=> ( ( ? [X1: $int] :
                ( pow2(X1)
                & ( $product(2,X1) = X0 ) )
            & $lesseq(2,X0) )
          | ( 1 = X0 ) ) )
   => ? [X0: $int,X1: $int] :
        ( ( $sum(X0,X1) = 10 )
        & pow2(X1)
        & pow2(X0) ) ),
    file('/export/starexec/sandbox/tmp/tmp.JY6QkCNVOq/Vampire---4.8_11028',sum_of_pows_of_2_eq_10) ).

tff(f122,plain,
    ! [X0: $int] :
      ( ~ pow2(X0)
      | $less($product(8,X0),2)
      | $less($sum(2,$product(8,X0)),10)
      | $less($product(4,X0),2)
      | $less(10,$sum(2,$product(8,X0)))
      | $less($product(2,X0),2) ),
    inference(evaluation,[],[f121]) ).

tff(f121,plain,
    ! [X0: $int] :
      ( $less(10,$sum(2,$product(4,$product(2,X0))))
      | $less($product(4,$product(2,X0)),2)
      | $less($sum(2,$product(4,$product(2,X0))),10)
      | $less($product(2,$product(2,X0)),2)
      | ~ pow2(X0)
      | $less($product(2,X0),2) ),
    inference(resolution,[],[f109,f36]) ).

tff(f36,plain,
    ! [X3: $int] :
      ( pow2($product(2,X3))
      | ~ pow2(X3)
      | $less($product(2,X3),2) ),
    inference(equality_resolution,[],[f33]) ).

tff(f33,plain,
    ! [X2: $int,X3: $int] :
      ( pow2(X2)
      | ~ pow2(X3)
      | ( $product(2,X3) != X2 )
      | $less(X2,2) ),
    inference(cnf_transformation,[],[f28]) ).

tff(f109,plain,
    ! [X0: $int] :
      ( ~ pow2(X0)
      | $less(10,$sum(2,$product(4,X0)))
      | $less($product(4,X0),2)
      | $less($sum(2,$product(4,X0)),10)
      | $less($product(2,X0),2) ),
    inference(evaluation,[],[f108]) ).

tff(f108,plain,
    ! [X0: $int] :
      ( $less($sum(2,$product(2,$product(2,X0))),10)
      | $less(10,$sum(2,$product(2,$product(2,X0))))
      | $less($product(2,$product(2,X0)),2)
      | ~ pow2(X0)
      | $less($product(2,X0),2) ),
    inference(resolution,[],[f104,f36]) ).

tff(f104,plain,
    ! [X0: $int] :
      ( ~ pow2(X0)
      | $less($sum(2,$product(2,X0)),10)
      | $less(10,$sum(2,$product(2,X0)))
      | $less($product(2,X0),2) ),
    inference(resolution,[],[f102,f36]) ).

tff(f102,plain,
    ! [X0: $int] :
      ( ~ pow2(X0)
      | $less(10,$sum(2,X0))
      | $less($sum(2,X0),10) ),
    inference(evaluation,[],[f99]) ).

tff(f99,plain,
    ! [X0: $int] :
      ( $less($sum($product(2,1),X0),10)
      | $less(10,$sum($product(2,1),X0))
      | ~ pow2(X0)
      | $less($product(2,1),2) ),
    inference(resolution,[],[f89,f37]) ).

tff(f89,plain,
    ! [X0: $int,X1: $int] :
      ( ~ pow2(X1)
      | $less($sum($product(2,X1),X0),10)
      | $less(10,$sum($product(2,X1),X0))
      | ~ pow2(X0)
      | $less($product(2,X1),2) ),
    inference(resolution,[],[f63,f36]) ).

tff(f63,plain,
    ! [X0: $int,X1: $int] :
      ( ~ pow2(X1)
      | ~ pow2(X0)
      | $less($sum(X1,X0),10)
      | $less(10,$sum(X1,X0)) ),
    inference(resolution,[],[f52,f46]) ).

tff(f46,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X0,X1)
      | $less(X1,X0)
      | sQ1_eqProxy(X0,X1) ),
    inference(equality_proxy_replacement,[],[f11,f38]) ).

tff(f38,plain,
    ! [X0: $int,X1: $int] :
      ( sQ1_eqProxy(X0,X1)
    <=> ( X0 = X1 ) ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ1_eqProxy])]) ).

tff(f11,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X0,X1)
      | $less(X1,X0)
      | ( X0 = X1 ) ),
    introduced(theory_axiom_144,[]) ).

tff(f52,plain,
    ! [X0: $int,X1: $int] :
      ( ~ sQ1_eqProxy($sum(X0,X1),10)
      | ~ pow2(X1)
      | ~ pow2(X0) ),
    inference(equality_proxy_replacement,[],[f34,f38]) ).

tff(f34,plain,
    ! [X0: $int,X1: $int] :
      ( ( $sum(X0,X1) != 10 )
      | ~ pow2(X1)
      | ~ pow2(X0) ),
    inference(cnf_transformation,[],[f28]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : ARI622_1 : TPTP v8.1.2. Released v5.1.0.
% 0.15/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.36  % Computer : n002.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Tue Apr 30 19:11:10 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  This is a TF0_THM_EQU_ARI problem
% 0.22/0.37  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.JY6QkCNVOq/Vampire---4.8_11028
% 0.59/0.75  % (11288)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)
% 0.59/0.75  % (11282)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)
% 0.59/0.75  % (11284)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.59/0.75  % (11283)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)
% 0.59/0.75  % (11286)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)
% 0.59/0.75  % (11285)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)
% 0.59/0.75  % (11287)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)
% 0.59/0.76  % (11286)First to succeed.
% 0.59/0.76  % (11286)Refutation found. Thanks to Tanya!
% 0.59/0.76  % SZS status Theorem for Vampire---4
% 0.59/0.76  % SZS output start Proof for Vampire---4
% See solution above
% 0.59/0.76  % (11286)------------------------------
% 0.59/0.76  % (11286)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.59/0.76  % (11286)Termination reason: Refutation
% 0.59/0.76  
% 0.59/0.76  % (11286)Memory used [KB]: 1077
% 0.59/0.76  % (11286)Time elapsed: 0.006 s
% 0.59/0.76  % (11286)Instructions burned: 8 (million)
% 0.59/0.76  % (11286)------------------------------
% 0.59/0.76  % (11286)------------------------------
% 0.59/0.76  % (11278)Success in time 0.378 s
% 0.59/0.76  % Vampire---4.8 exiting
%------------------------------------------------------------------------------