TSTP Solution File: ARI620_1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ARI620_1 : TPTP v8.1.2. Released v5.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n024.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 : Tue Apr 30 10:35:43 EDT 2024

% Result   : Theorem 0.18s 0.52s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   32 (  10 unt;   3 typ;   0 def)
%            Number of atoms       :  108 (  30 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  116 (  37   ~;  37   |;  32   &)
%                                         (   6 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number arithmetic     :  149 (  18 atm;  24 fun;  77 num;  30 var)
%            Number of types       :    2 (   0 usr;   1 ari)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   1 usr;   4 con; 0-2 aty)
%            Number of variables   :   30 (  21   !;   9   ?;  30   :)

% Comments : 
%------------------------------------------------------------------------------
tff(func_def_7,type,
    sK1: $int > $int ).

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

tff(pred_def_4,type,
    sP0: $int > $o ).

tff(f10407,plain,
    $false,
    inference(subsumption_resolution,[],[f10406,f42]) ).

tff(f42,plain,
    ~ sP0(8),
    inference(unit_resulting_resolution,[],[f38,f37]) ).

tff(f37,plain,
    ! [X0: $int] :
      ( ~ sP0(X0)
      | pow2(X0) ),
    inference(cnf_transformation,[],[f30]) ).

tff(f30,plain,
    ( ~ pow2(8)
    & ! [X0: $int] :
        ( ( pow2(X0)
          | ~ sP0(X0) )
        & ( sP0(X0)
          | ~ pow2(X0) ) ) ),
    inference(nnf_transformation,[],[f24]) ).

tff(f24,plain,
    ( ~ pow2(8)
    & ! [X0: $int] :
        ( pow2(X0)
      <=> sP0(X0) ) ),
    inference(definition_folding,[],[f22,f23]) ).

tff(f23,plain,
    ! [X0: $int] :
      ( sP0(X0)
    <=> ( ( ? [X1: $int] :
              ( pow2(X1)
              & ( $product(2,X1) = X0 ) )
          & ~ $less(X0,2) )
        | ( 1 = X0 ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

tff(f22,plain,
    ( ~ pow2(8)
    & ! [X0: $int] :
        ( pow2(X0)
      <=> ( ( ? [X1: $int] :
                ( pow2(X1)
                & ( $product(2,X1) = X0 ) )
            & ~ $less(X0,2) )
          | ( 1 = X0 ) ) ) ),
    inference(ennf_transformation,[],[f3]) ).

tff(f3,plain,
    ~ ( ! [X0: $int] :
          ( pow2(X0)
        <=> ( ( ? [X1: $int] :
                  ( pow2(X1)
                  & ( $product(2,X1) = X0 ) )
              & ~ $less(X0,2) )
            | ( 1 = X0 ) ) )
     => pow2(8) ),
    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 ) ) )
     => pow2(8) ),
    inference(negated_conjecture,[],[f1]) ).

tff(f1,conjecture,
    ( ! [X0: $int] :
        ( pow2(X0)
      <=> ( ( ? [X1: $int] :
                ( pow2(X1)
                & ( $product(2,X1) = X0 ) )
            & $lesseq(2,X0) )
          | ( 1 = X0 ) ) )
   => pow2(8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pow_of_2_8) ).

tff(f38,plain,
    ~ pow2(8),
    inference(cnf_transformation,[],[f30]) ).

tff(f10406,plain,
    sP0(8),
    inference(evaluation,[],[f10404]) ).

tff(f10404,plain,
    ( sP0($product(2,4))
    | $less($product(2,4),2) ),
    inference(resolution,[],[f10396,f40]) ).

tff(f40,plain,
    ! [X1: $int] :
      ( ~ pow2(X1)
      | sP0($product(2,X1))
      | $less($product(2,X1),2) ),
    inference(equality_resolution,[],[f35]) ).

tff(f35,plain,
    ! [X0: $int,X1: $int] :
      ( sP0(X0)
      | ~ pow2(X1)
      | ( $product(2,X1) != X0 )
      | $less(X0,2) ),
    inference(cnf_transformation,[],[f29]) ).

tff(f29,plain,
    ! [X0: $int] :
      ( ( sP0(X0)
        | ( ( ! [X1: $int] :
                ( ~ pow2(X1)
                | ( $product(2,X1) != X0 ) )
            | $less(X0,2) )
          & ( 1 != X0 ) ) )
      & ( ( pow2(sK1(X0))
          & ( $product(2,sK1(X0)) = X0 )
          & ~ $less(X0,2) )
        | ( 1 = X0 )
        | ~ sP0(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f27,f28]) ).

tff(f28,plain,
    ! [X0: $int] :
      ( ? [X2: $int] :
          ( pow2(X2)
          & ( $product(2,X2) = X0 ) )
     => ( pow2(sK1(X0))
        & ( $product(2,sK1(X0)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f27,plain,
    ! [X0: $int] :
      ( ( sP0(X0)
        | ( ( ! [X1: $int] :
                ( ~ pow2(X1)
                | ( $product(2,X1) != X0 ) )
            | $less(X0,2) )
          & ( 1 != X0 ) ) )
      & ( ( ? [X2: $int] :
              ( pow2(X2)
              & ( $product(2,X2) = X0 ) )
          & ~ $less(X0,2) )
        | ( 1 = X0 )
        | ~ sP0(X0) ) ),
    inference(rectify,[],[f26]) ).

tff(f26,plain,
    ! [X0: $int] :
      ( ( sP0(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 )
        | ~ sP0(X0) ) ),
    inference(flattening,[],[f25]) ).

tff(f25,plain,
    ! [X0: $int] :
      ( ( sP0(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 )
        | ~ sP0(X0) ) ),
    inference(nnf_transformation,[],[f23]) ).

tff(f10396,plain,
    pow2(4),
    inference(unit_resulting_resolution,[],[f10395,f37]) ).

tff(f10395,plain,
    sP0(4),
    inference(evaluation,[],[f10393]) ).

tff(f10393,plain,
    ( sP0($product(2,2))
    | $less($product(2,2),2) ),
    inference(resolution,[],[f10385,f40]) ).

tff(f10385,plain,
    pow2(2),
    inference(unit_resulting_resolution,[],[f10384,f37]) ).

tff(f10384,plain,
    sP0(2),
    inference(evaluation,[],[f10383]) ).

tff(f10383,plain,
    ( sP0($product(2,1))
    | $less($product(2,1),2) ),
    inference(resolution,[],[f40,f43]) ).

tff(f43,plain,
    pow2(1),
    inference(unit_resulting_resolution,[],[f41,f37]) ).

tff(f41,plain,
    sP0(1),
    inference(equality_resolution,[],[f34]) ).

tff(f34,plain,
    ! [X0: $int] :
      ( sP0(X0)
      | ( 1 != X0 ) ),
    inference(cnf_transformation,[],[f29]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem    : ARI620_1 : TPTP v8.1.2. Released v5.1.0.
% 0.11/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34  % Computer : n024.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Apr 30 05:33:06 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.13/0.35  % (14502)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36  % (14505)WARNING: value z3 for option sas not known
% 0.13/0.36  % (14504)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.36  % (14506)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.36  % (14504)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.36  % (14504)Terminated due to inappropriate strategy.
% 0.13/0.36  % (14504)------------------------------
% 0.13/0.36  % (14504)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.36  % (14504)Termination reason: Inappropriate
% 0.13/0.36  
% 0.13/0.36  % (14504)Memory used [KB]: 728
% 0.13/0.36  % (14504)Time elapsed: 0.002 s
% 0.13/0.36  % (14504)Instructions burned: 2 (million)
% 0.13/0.36  % (14504)------------------------------
% 0.13/0.36  % (14504)------------------------------
% 0.13/0.36  % (14509)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.13/0.36  % (14507)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.13/0.36  % (14505)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.36  % (14506)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.36  % (14506)Terminated due to inappropriate strategy.
% 0.13/0.36  % (14506)------------------------------
% 0.13/0.36  % (14506)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.36  % (14506)Termination reason: Inappropriate
% 0.13/0.36  
% 0.13/0.36  % (14506)Memory used [KB]: 728
% 0.13/0.36  % (14506)Time elapsed: 0.002 s
% 0.13/0.36  % (14506)Instructions burned: 2 (million)
% 0.13/0.36  % (14506)------------------------------
% 0.13/0.36  % (14506)------------------------------
% 0.13/0.36  % (14508)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.13/0.36  % (14503)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37  % (14503)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.37  % (14503)Terminated due to inappropriate strategy.
% 0.13/0.37  % (14503)------------------------------
% 0.13/0.37  % (14503)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.37  % (14503)Termination reason: Inappropriate
% 0.13/0.37  
% 0.13/0.37  % (14503)Memory used [KB]: 728
% 0.13/0.37  % (14503)Time elapsed: 0.003 s
% 0.13/0.37  % (14503)Instructions burned: 2 (million)
% 0.13/0.37  % (14503)------------------------------
% 0.13/0.37  % (14503)------------------------------
% 0.13/0.38  % (14510)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.13/0.38  % (14511)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.13/0.38  % (14510)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.38  % (14510)Terminated due to inappropriate strategy.
% 0.13/0.38  % (14510)------------------------------
% 0.13/0.38  % (14510)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.38  % (14510)Termination reason: Inappropriate
% 0.13/0.38  
% 0.13/0.38  % (14510)Memory used [KB]: 727
% 0.13/0.38  % (14510)Time elapsed: 0.002 s
% 0.13/0.38  % (14510)Instructions burned: 2 (million)
% 0.13/0.38  % (14510)------------------------------
% 0.13/0.38  % (14510)------------------------------
% 0.13/0.38  % (14512)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.13/0.39  % (14513)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.18/0.52  % (14511)First to succeed.
% 0.18/0.52  % (14511)Refutation found. Thanks to Tanya!
% 0.18/0.52  % SZS status Theorem for theBenchmark
% 0.18/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.52  % (14511)------------------------------
% 0.18/0.52  % (14511)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.18/0.52  % (14511)Termination reason: Refutation
% 0.18/0.52  
% 0.18/0.52  % (14511)Memory used [KB]: 1751
% 0.18/0.52  % (14511)Time elapsed: 0.141 s
% 0.18/0.52  % (14511)Instructions burned: 324 (million)
% 0.18/0.52  % (14511)------------------------------
% 0.18/0.52  % (14511)------------------------------
% 0.18/0.52  % (14502)Success in time 0.168 s
%------------------------------------------------------------------------------