TSTP Solution File: SWW600_2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWW600_2 : TPTP v8.2.0. Released v6.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n022.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 May 21 07:27:29 EDT 2024

% Result   : Theorem 0.13s 0.41s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   41
% Syntax   : Number of formulae    :   50 (   3 unt;  38 typ;   0 def)
%            Number of atoms       :   98 (  46 equ)
%            Maximal formula atoms :   18 (   8 avg)
%            Number of connectives :  140 (  54   ~;   0   |;  72   &)
%                                         (   0 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (  12 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number arithmetic     :  299 (  51 atm; 105 fun;  51 num;  92 var)
%            Number of types       :    6 (   4 usr;   1 ari)
%            Number of type conns  :   33 (  18   >;  15   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   32 (  29 usr;  17 con; 0-4 aty)
%            Number of variables   :   92 (  48   !;  44   ?;  92   :)

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

tff(type_def_6,type,
    ty: $tType ).

tff(type_def_7,type,
    bool: $tType ).

tff(type_def_8,type,
    tuple0: $tType ).

tff(func_def_0,type,
    witness: ty > uni ).

tff(func_def_1,type,
    int: ty ).

tff(func_def_2,type,
    real: ty ).

tff(func_def_3,type,
    bool1: ty ).

tff(func_def_4,type,
    true: bool ).

tff(func_def_5,type,
    false: bool ).

tff(func_def_6,type,
    match_bool: ( ty * bool * uni * uni ) > uni ).

tff(func_def_7,type,
    tuple01: ty ).

tff(func_def_8,type,
    tuple02: tuple0 ).

tff(func_def_9,type,
    qtmark: ty ).

tff(func_def_12,type,
    abs: $int > $int ).

tff(func_def_14,type,
    div: ( $int * $int ) > $int ).

tff(func_def_15,type,
    mod: ( $int * $int ) > $int ).

tff(func_def_22,type,
    gcd: ( $int * $int ) > $int ).

tff(func_def_23,type,
    ref: ty > ty ).

tff(func_def_24,type,
    mk_ref: ( ty * uni ) > uni ).

tff(func_def_25,type,
    contents: ( ty * uni ) > uni ).

tff(func_def_27,type,
    sK1: $int ).

tff(func_def_28,type,
    sK2: $int ).

tff(func_def_29,type,
    sK3: $int ).

tff(func_def_30,type,
    sK4: $int ).

tff(func_def_31,type,
    sK5: $int ).

tff(func_def_32,type,
    sK6: $int ).

tff(func_def_33,type,
    sK7: $int ).

tff(func_def_34,type,
    sK8: $int ).

tff(func_def_35,type,
    sK9: $int > $int ).

tff(func_def_36,type,
    sK10: $int > $int ).

tff(func_def_37,type,
    sK11: ( $int * $int ) > $int ).

tff(func_def_38,type,
    sK12: ( $int * $int * $int ) > $int ).

tff(pred_def_1,type,
    sort: ( ty * uni ) > $o ).

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

tff(pred_def_5,type,
    even: $int > $o ).

tff(pred_def_6,type,
    odd: $int > $o ).

tff(pred_def_7,type,
    sP0: ( $int * $int * $int ) > $o ).

tff(f415,plain,
    $false,
    inference(subsumption_resolution,[],[f309,f312]) ).

tff(f312,plain,
    ! [X8: $int,X9: $int] : ( $sum($product(X8,sK1),$product(X9,sK2)) != sK8 ),
    inference(cnf_transformation,[],[f283]) ).

tff(f283,plain,
    ( ! [X8: $int,X9: $int] : ( $sum($product(X8,sK1),$product(X9,sK2)) != sK8 )
    & ~ $less(0,sK7)
    & ( sK7 = $sum($product(sK4,sK1),$product(sK3,sK2)) )
    & ( sK8 = $sum($product(sK6,sK1),$product(sK5,sK2)) )
    & ( gcd(sK1,sK2) = gcd(sK8,sK7) )
    & ~ $less(sK7,0)
    & ~ $less(sK8,0)
    & ~ $less(sK2,0)
    & ~ $less(sK1,0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8])],[f205,f282,f281]) ).

tff(f281,plain,
    ( ? [X0: $int,X1: $int] :
        ( ? [X2: $int,X3: $int,X4: $int,X5: $int,X6: $int,X7: $int] :
            ( ! [X8: $int,X9: $int] : ( $sum($product(X8,X0),$product(X9,X1)) != X7 )
            & ~ $less(0,X6)
            & ( $sum($product(X3,X0),$product(X2,X1)) = X6 )
            & ( $sum($product(X5,X0),$product(X4,X1)) = X7 )
            & ( gcd(X0,X1) = gcd(X7,X6) )
            & ~ $less(X6,0)
            & ~ $less(X7,0) )
        & ~ $less(X1,0)
        & ~ $less(X0,0) )
   => ( ? [X7: $int,X6: $int,X5: $int,X4: $int,X3: $int,X2: $int] :
          ( ! [X9: $int,X8: $int] : ( $sum($product(X8,sK1),$product(X9,sK2)) != X7 )
          & ~ $less(0,X6)
          & ( $sum($product(X3,sK1),$product(X2,sK2)) = X6 )
          & ( $sum($product(X5,sK1),$product(X4,sK2)) = X7 )
          & ( gcd(X7,X6) = gcd(sK1,sK2) )
          & ~ $less(X6,0)
          & ~ $less(X7,0) )
      & ~ $less(sK2,0)
      & ~ $less(sK1,0) ) ),
    introduced(choice_axiom,[]) ).

tff(f282,plain,
    ( ? [X7: $int,X6: $int,X5: $int,X4: $int,X3: $int,X2: $int] :
        ( ! [X9: $int,X8: $int] : ( $sum($product(X8,sK1),$product(X9,sK2)) != X7 )
        & ~ $less(0,X6)
        & ( $sum($product(X3,sK1),$product(X2,sK2)) = X6 )
        & ( $sum($product(X5,sK1),$product(X4,sK2)) = X7 )
        & ( gcd(X7,X6) = gcd(sK1,sK2) )
        & ~ $less(X6,0)
        & ~ $less(X7,0) )
   => ( ! [X9: $int,X8: $int] : ( $sum($product(X8,sK1),$product(X9,sK2)) != sK8 )
      & ~ $less(0,sK7)
      & ( sK7 = $sum($product(sK4,sK1),$product(sK3,sK2)) )
      & ( sK8 = $sum($product(sK6,sK1),$product(sK5,sK2)) )
      & ( gcd(sK1,sK2) = gcd(sK8,sK7) )
      & ~ $less(sK7,0)
      & ~ $less(sK8,0) ) ),
    introduced(choice_axiom,[]) ).

tff(f205,plain,
    ? [X0: $int,X1: $int] :
      ( ? [X2: $int,X3: $int,X4: $int,X5: $int,X6: $int,X7: $int] :
          ( ! [X8: $int,X9: $int] : ( $sum($product(X8,X0),$product(X9,X1)) != X7 )
          & ~ $less(0,X6)
          & ( $sum($product(X3,X0),$product(X2,X1)) = X6 )
          & ( $sum($product(X5,X0),$product(X4,X1)) = X7 )
          & ( gcd(X0,X1) = gcd(X7,X6) )
          & ~ $less(X6,0)
          & ~ $less(X7,0) )
      & ~ $less(X1,0)
      & ~ $less(X0,0) ),
    inference(flattening,[],[f204]) ).

tff(f204,plain,
    ? [X0: $int,X1: $int] :
      ( ? [X2: $int,X3: $int,X4: $int,X5: $int,X6: $int,X7: $int] :
          ( ! [X8: $int,X9: $int] : ( $sum($product(X8,X0),$product(X9,X1)) != X7 )
          & ~ $less(0,X6)
          & ( $sum($product(X3,X0),$product(X2,X1)) = X6 )
          & ( $sum($product(X5,X0),$product(X4,X1)) = X7 )
          & ( gcd(X0,X1) = gcd(X7,X6) )
          & ~ $less(X6,0)
          & ~ $less(X7,0) )
      & ~ $less(X1,0)
      & ~ $less(X0,0) ),
    inference(ennf_transformation,[],[f130]) ).

tff(f130,plain,
    ~ ! [X0: $int,X1: $int] :
        ( ( ~ $less(X1,0)
          & ~ $less(X0,0) )
       => ! [X2: $int,X3: $int,X4: $int,X5: $int,X6: $int,X7: $int] :
            ( ( ( $sum($product(X3,X0),$product(X2,X1)) = X6 )
              & ( $sum($product(X5,X0),$product(X4,X1)) = X7 )
              & ( gcd(X0,X1) = gcd(X7,X6) )
              & ~ $less(X6,0)
              & ~ $less(X7,0) )
           => ( ~ $less(0,X6)
             => ? [X8: $int,X9: $int] : ( $sum($product(X8,X0),$product(X9,X1)) = X7 ) ) ) ),
    inference(rectify,[],[f85]) ).

tff(f85,plain,
    ~ ! [X1: $int,X7: $int] :
        ( ( ~ $less(X7,0)
          & ~ $less(X1,0) )
       => ! [X8: $int,X12: $int,X11: $int,X0: $int,X14: $int,X2: $int] :
            ( ( ( $sum($product(X12,X1),$product(X8,X7)) = X14 )
              & ( $sum($product(X0,X1),$product(X11,X7)) = X2 )
              & ( gcd(X1,X7) = gcd(X2,X14) )
              & ~ $less(X14,0)
              & ~ $less(X2,0) )
           => ( ~ $less(0,X14)
             => ? [X15: $int,X16: $int] : ( $sum($product(X15,X1),$product(X16,X7)) = X2 ) ) ) ),
    inference(theory_normalization,[],[f84]) ).

tff(f84,negated_conjecture,
    ~ ! [X1: $int,X7: $int] :
        ( ( $lesseq(0,X7)
          & $lesseq(0,X1) )
       => ! [X8: $int,X12: $int,X11: $int,X0: $int,X14: $int,X2: $int] :
            ( ( ( $sum($product(X12,X1),$product(X8,X7)) = X14 )
              & ( $sum($product(X0,X1),$product(X11,X7)) = X2 )
              & ( gcd(X1,X7) = gcd(X2,X14) )
              & $lesseq(0,X14)
              & $lesseq(0,X2) )
           => ( ~ $less(0,X14)
             => ? [X15: $int,X16: $int] : ( $sum($product(X15,X1),$product(X16,X7)) = X2 ) ) ) ),
    inference(negated_conjecture,[],[f83]) ).

tff(f83,conjecture,
    ! [X1: $int,X7: $int] :
      ( ( $lesseq(0,X7)
        & $lesseq(0,X1) )
     => ! [X8: $int,X12: $int,X11: $int,X0: $int,X14: $int,X2: $int] :
          ( ( ( $sum($product(X12,X1),$product(X8,X7)) = X14 )
            & ( $sum($product(X0,X1),$product(X11,X7)) = X2 )
            & ( gcd(X1,X7) = gcd(X2,X14) )
            & $lesseq(0,X14)
            & $lesseq(0,X2) )
         => ( ~ $less(0,X14)
           => ? [X15: $int,X16: $int] : ( $sum($product(X15,X1),$product(X16,X7)) = X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',wP_parameter_gcd) ).

tff(f309,plain,
    sK8 = $sum($product(sK6,sK1),$product(sK5,sK2)),
    inference(cnf_transformation,[],[f283]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : SWW600_2 : TPTP v8.2.0. Released v6.1.0.
% 0.12/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35  % Computer : n022.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Sat May 18 20:23:23 EDT 2024
% 0.13/0.36  % CPUTime    : 
% 0.13/0.36  % (10988)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.39  % (10990)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.39  % (10990)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.39  % (10990)Terminated due to inappropriate strategy.
% 0.13/0.39  % (10990)------------------------------
% 0.13/0.39  % (10990)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.39  % (10990)Termination reason: Inappropriate
% 0.13/0.39  
% 0.13/0.39  % (10990)Memory used [KB]: 921
% 0.13/0.39  % (10990)Time elapsed: 0.006 s
% 0.13/0.39  % (10990)Instructions burned: 8 (million)
% 0.13/0.39  % (10991)WARNING: value z3 for option sas not known
% 0.13/0.39  % (10990)------------------------------
% 0.13/0.39  % (10990)------------------------------
% 0.13/0.39  % (10989)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.39  % (10991)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)
% 0.13/0.39  % (10992)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.39  % (10993)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)
% 0.13/0.39  % (10994)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)
% 0.13/0.39  % (10995)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)
% 0.13/0.40  % (10989)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.40  % (10989)Terminated due to inappropriate strategy.
% 0.13/0.40  % (10989)------------------------------
% 0.13/0.40  % (10989)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.40  % (10989)Termination reason: Inappropriate
% 0.13/0.40  
% 0.13/0.40  % (10989)Memory used [KB]: 921
% 0.13/0.40  % (10989)Time elapsed: 0.009 s
% 0.13/0.40  % (10989)Instructions burned: 8 (million)
% 0.13/0.40  % (10992)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.40  % (10992)Terminated due to inappropriate strategy.
% 0.13/0.40  % (10992)------------------------------
% 0.13/0.40  % (10992)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.40  % (10989)------------------------------
% 0.13/0.40  % (10989)------------------------------
% 0.13/0.40  % (10992)Termination reason: Inappropriate
% 0.13/0.40  
% 0.13/0.40  % (10992)Memory used [KB]: 921
% 0.13/0.40  % (10992)Time elapsed: 0.009 s
% 0.13/0.40  % (10992)Instructions burned: 8 (million)
% 0.13/0.40  % (10992)------------------------------
% 0.13/0.40  % (10992)------------------------------
% 0.13/0.40  % (10995)First to succeed.
% 0.13/0.40  % (10995)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-10988"
% 0.13/0.41  % (10995)Refutation found. Thanks to Tanya!
% 0.13/0.41  % SZS status Theorem for theBenchmark
% 0.13/0.41  % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.41  % (10995)------------------------------
% 0.13/0.41  % (10995)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.41  % (10995)Termination reason: Refutation
% 0.13/0.41  
% 0.13/0.41  % (10995)Memory used [KB]: 949
% 0.13/0.41  % (10995)Time elapsed: 0.013 s
% 0.13/0.41  % (10995)Instructions burned: 11 (million)
% 0.13/0.41  % (10988)Success in time 0.043 s
%------------------------------------------------------------------------------