TSTP Solution File: DAT044_1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : DAT044_1 : TPTP v8.1.2. Released v5.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n020.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 : Sun May  5 05:05:44 EDT 2024

% Result   : Theorem 0.18s 0.38s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   30 (   9 unt;   8 typ;   0 def)
%            Number of atoms       :   46 (   8 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   43 (  19   ~;  10   |;   5   &)
%                                         (   2 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number arithmetic     :   71 (  22 atm;  13 fun;  11 num;  25 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   35 (  31   !;   4   ?;  35   :)

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

tff(func_def_0,type,
    empty: collection ).

tff(func_def_1,type,
    add: ( $int * collection ) > collection ).

tff(func_def_2,type,
    remove: ( $int * collection ) > collection ).

tff(func_def_3,type,
    count: collection > $int ).

tff(func_def_9,type,
    sK0: collection ).

tff(func_def_10,type,
    sK1: $int ).

tff(pred_def_1,type,
    in: ( $int * collection ) > $o ).

tff(f795,plain,
    $false,
    inference(resolution,[],[f788,f106]) ).

tff(f106,plain,
    ! [X0: $int] : $less(X0,$sum(1,X0)),
    inference(superposition,[],[f101,f18]) ).

tff(f18,plain,
    ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
    introduced(theory_axiom_135,[]) ).

tff(f101,plain,
    ! [X0: $int] : $less(X0,$sum(X0,1)),
    inference(resolution,[],[f27,f23]) ).

tff(f23,plain,
    ! [X0: $int] : ~ $less(X0,X0),
    introduced(theory_axiom_142,[]) ).

tff(f27,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X1,$sum(X0,1))
      | $less(X0,X1) ),
    introduced(theory_axiom_147,[]) ).

tff(f788,plain,
    ~ $less(count(sK0),$sum(1,count(sK0))),
    inference(backward_demodulation,[],[f55,f785]) ).

tff(f785,plain,
    count(add(sK1,sK0)) = $sum(1,count(sK0)),
    inference(resolution,[],[f83,f86]) ).

tff(f86,plain,
    ~ in(sK1,sK0),
    inference(resolution,[],[f54,f23]) ).

tff(f54,plain,
    ! [X2: $int] :
      ( $less(X2,sK1)
      | ~ in(X2,sK0) ),
    inference(cnf_transformation,[],[f44]) ).

tff(f44,plain,
    ( ~ $less(count(sK0),count(add(sK1,sK0)))
    & ! [X2: $int] :
        ( $less(X2,sK1)
        | ~ in(X2,sK0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f41,f43]) ).

tff(f43,plain,
    ( ? [X0: collection,X1: $int] :
        ( ~ $less(count(X0),count(add(X1,X0)))
        & ! [X2: $int] :
            ( $less(X2,X1)
            | ~ in(X2,X0) ) )
   => ( ~ $less(count(sK0),count(add(sK1,sK0)))
      & ! [X2: $int] :
          ( $less(X2,sK1)
          | ~ in(X2,sK0) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f41,plain,
    ? [X0: collection,X1: $int] :
      ( ~ $less(count(X0),count(add(X1,X0)))
      & ! [X2: $int] :
          ( $less(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f15]) ).

tff(f15,plain,
    ~ ! [X0: collection,X1: $int] :
        ( ! [X2: $int] :
            ( in(X2,X0)
           => $less(X2,X1) )
       => $less(count(X0),count(add(X1,X0))) ),
    inference(theory_normalization,[],[f14]) ).

tff(f14,negated_conjecture,
    ~ ! [X0: collection,X1: $int] :
        ( ! [X2: $int] :
            ( in(X2,X0)
           => $greater(X1,X2) )
       => $greater(count(add(X1,X0)),count(X0)) ),
    inference(negated_conjecture,[],[f13]) ).

tff(f13,conjecture,
    ! [X0: collection,X1: $int] :
      ( ! [X2: $int] :
          ( in(X2,X0)
         => $greater(X1,X2) )
     => $greater(count(add(X1,X0)),count(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

tff(f83,plain,
    ! [X0: $int,X1: collection] :
      ( in(X0,X1)
      | ( count(add(X0,X1)) = $sum(1,count(X1)) ) ),
    inference(forward_demodulation,[],[f65,f18]) ).

tff(f65,plain,
    ! [X0: $int,X1: collection] :
      ( ( count(add(X0,X1)) = $sum(count(X1),1) )
      | in(X0,X1) ),
    inference(cnf_transformation,[],[f47]) ).

tff(f47,plain,
    ! [X0: $int,X1: collection] :
      ( ( ~ in(X0,X1)
        | ( count(add(X0,X1)) != $sum(count(X1),1) ) )
      & ( ( count(add(X0,X1)) = $sum(count(X1),1) )
        | in(X0,X1) ) ),
    inference(nnf_transformation,[],[f36]) ).

tff(f36,plain,
    ! [X0: $int,X1: collection] :
      ( ~ in(X0,X1)
    <=> ( count(add(X0,X1)) = $sum(count(X1),1) ) ),
    inference(rectify,[],[f8]) ).

tff(f8,axiom,
    ! [X13: $int,X14: collection] :
      ( ~ in(X13,X14)
    <=> ( count(add(X13,X14)) = $sum(count(X14),1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).

tff(f55,plain,
    ~ $less(count(sK0),count(add(sK1,sK0))),
    inference(cnf_transformation,[],[f44]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : DAT044_1 : TPTP v8.1.2. Released v5.0.0.
% 0.03/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.32  % Computer : n020.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit   : 300
% 0.12/0.32  % WCLimit    : 300
% 0.12/0.32  % DateTime   : Fri May  3 12:56:31 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 0.12/0.33  % (15377)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.34  % (15382)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)
% 0.12/0.34  % (15384)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)
% 0.12/0.34  % (15383)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)
% 0.12/0.34  % (15380)WARNING: value z3 for option sas not known
% 0.12/0.34  % (15378)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.35  % (15378)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.12/0.35  % (15378)Terminated due to inappropriate strategy.
% 0.12/0.35  % (15378)------------------------------
% 0.12/0.35  % (15378)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.35  % (15378)Termination reason: Inappropriate
% 0.12/0.35  
% 0.12/0.35  % (15378)Memory used [KB]: 766
% 0.12/0.35  % (15378)Time elapsed: 0.003 s
% 0.12/0.35  % (15378)Instructions burned: 3 (million)
% 0.12/0.35  % (15381)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.35  % (15379)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.35  % (15380)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)
% 0.12/0.35  % (15378)------------------------------
% 0.12/0.35  % (15378)------------------------------
% 0.12/0.35  % (15379)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.12/0.35  % (15381)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.12/0.35  % (15379)Terminated due to inappropriate strategy.
% 0.12/0.35  % (15379)------------------------------
% 0.12/0.35  % (15379)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.35  % (15379)Termination reason: Inappropriate
% 0.12/0.35  
% 0.12/0.35  % (15379)Memory used [KB]: 767
% 0.12/0.35  % (15379)Time elapsed: 0.003 s
% 0.12/0.35  % (15379)Instructions burned: 3 (million)
% 0.12/0.35  % (15381)Terminated due to inappropriate strategy.
% 0.12/0.35  % (15381)------------------------------
% 0.12/0.35  % (15381)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.35  % (15381)Termination reason: Inappropriate
% 0.12/0.35  
% 0.12/0.35  % (15381)Memory used [KB]: 766
% 0.12/0.35  % (15381)Time elapsed: 0.003 s
% 0.12/0.35  % (15381)Instructions burned: 3 (million)
% 0.12/0.35  % (15379)------------------------------
% 0.12/0.35  % (15379)------------------------------
% 0.12/0.35  % (15381)------------------------------
% 0.12/0.35  % (15381)------------------------------
% 0.12/0.36  % (15385)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.18/0.36  % (15385)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.18/0.36  % (15385)Terminated due to inappropriate strategy.
% 0.18/0.36  % (15385)------------------------------
% 0.18/0.36  % (15385)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.18/0.36  % (15385)Termination reason: Inappropriate
% 0.18/0.36  
% 0.18/0.36  % (15385)Memory used [KB]: 766
% 0.18/0.36  % (15385)Time elapsed: 0.002 s
% 0.18/0.36  % (15385)Instructions burned: 3 (million)
% 0.18/0.36  % (15385)------------------------------
% 0.18/0.36  % (15385)------------------------------
% 0.18/0.36  % (15386)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)
% 0.18/0.36  % (15387)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)
% 0.18/0.38  % (15383)First to succeed.
% 0.18/0.38  % (15383)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-15377"
% 0.18/0.38  % (15383)Refutation found. Thanks to Tanya!
% 0.18/0.38  % SZS status Theorem for theBenchmark
% 0.18/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.38  % (15383)------------------------------
% 0.18/0.38  % (15383)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.18/0.38  % (15383)Termination reason: Refutation
% 0.18/0.38  
% 0.18/0.38  % (15383)Memory used [KB]: 1280
% 0.18/0.38  % (15383)Time elapsed: 0.034 s
% 0.18/0.38  % (15383)Instructions burned: 59 (million)
% 0.18/0.38  % (15377)Success in time 0.036 s
%------------------------------------------------------------------------------