TSTP Solution File: GEG021_1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GEG021_1 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n019.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 : Mon May 20 19:57:13 EDT 2024

% Result   : Theorem 0.21s 0.41s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   65 (  30 unt;   9 typ;   0 def)
%            Number of atoms       :  168 ( 112 equ)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives :  130 (  18   ~;   8   |;  86   &)
%                                         (  14 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number arithmetic     :  140 (  17 atm;   6 fun; 117 num;   0 var)
%            Number of types       :    2 (   1 usr;   1 ari)
%            Number of type conns  :    2 (   1   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :   18 (  14 usr;  15 prp; 0-2 aty)
%            Number of functors    :   22 (   8 usr;  20 con; 0-2 aty)
%            Number of variables   :   40 (  40   !;   0   ?;  40   :)

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

tff(func_def_0,type,
    d: ( city * city ) > $int ).

tff(func_def_1,type,
    kiel: city ).

tff(func_def_2,type,
    hamburg: city ).

tff(func_def_3,type,
    berlin: city ).

tff(func_def_4,type,
    cologne: city ).

tff(func_def_5,type,
    frankfurt: city ).

tff(func_def_6,type,
    saarbruecken: city ).

tff(func_def_7,type,
    munich: city ).

tff(f108,plain,
    $false,
    inference(avatar_sat_refutation,[],[f38,f43,f48,f53,f58,f63,f68,f73,f78,f83,f88,f93,f98,f103,f107]) ).

tff(f107,plain,
    ( ~ spl0_3
    | ~ spl0_14 ),
    inference(avatar_contradiction_clause,[],[f106]) ).

tff(f106,plain,
    ( $false
    | ~ spl0_3
    | ~ spl0_14 ),
    inference(evaluation,[],[f105]) ).

tff(f105,plain,
    ( $less(500,480)
    | ~ spl0_3
    | ~ spl0_14 ),
    inference(forward_demodulation,[],[f104,f47]) ).

tff(f47,plain,
    ( ( d(berlin,cologne) = 480 )
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f45]) ).

tff(f45,plain,
    ( spl0_3
  <=> ( d(berlin,cologne) = 480 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

tff(f104,plain,
    ( $less(500,d(berlin,cologne))
    | ~ spl0_14 ),
    inference(forward_demodulation,[],[f102,f19]) ).

tff(f19,plain,
    ! [X4: city,X5: city] : ( d(X4,X5) = d(X5,X4) ),
    inference(cnf_transformation,[],[f18]) ).

tff(f18,plain,
    ( $less(500,d(cologne,berlin))
    & ( 360 = d(munich,saarbruecken) )
    & ( d(munich,frankfurt) = 300 )
    & ( d(hamburg,berlin) = 250 )
    & ( d(hamburg,kiel) = 90 )
    & ( d(cologne,frankfurt) = 150 )
    & ( d(hamburg,frankfurt) = 390 )
    & ( d(hamburg,cologne) = 360 )
    & ( d(saarbruecken,cologne) = 190 )
    & ( d(saarbruecken,frankfurt) = 160 )
    & ( d(berlin,frankfurt) = 420 )
    & ( d(berlin,cologne) = 480 )
    & ( d(berlin,munich) = 510 )
    & ! [X0: city] : ( d(X0,X0) = 0 )
    & ! [X1: city,X2: city,X3: city] : ~ $less($sum(d(X1,X2),d(X2,X3)),d(X1,X3))
    & ! [X4: city,X5: city] : ( d(X4,X5) = d(X5,X4) ) ),
    inference(flattening,[],[f17]) ).

tff(f17,plain,
    ( $less(500,d(cologne,berlin))
    & ( 360 = d(munich,saarbruecken) )
    & ( d(munich,frankfurt) = 300 )
    & ( d(hamburg,berlin) = 250 )
    & ( d(hamburg,kiel) = 90 )
    & ( d(cologne,frankfurt) = 150 )
    & ( d(hamburg,frankfurt) = 390 )
    & ( d(hamburg,cologne) = 360 )
    & ( d(saarbruecken,cologne) = 190 )
    & ( d(saarbruecken,frankfurt) = 160 )
    & ( d(berlin,frankfurt) = 420 )
    & ( d(berlin,cologne) = 480 )
    & ( d(berlin,munich) = 510 )
    & ! [X0: city] : ( d(X0,X0) = 0 )
    & ! [X1: city,X2: city,X3: city] : ~ $less($sum(d(X1,X2),d(X2,X3)),d(X1,X3))
    & ! [X4: city,X5: city] : ( d(X4,X5) = d(X5,X4) ) ),
    inference(ennf_transformation,[],[f16]) ).

tff(f16,plain,
    ~ ( ( ( 360 = d(munich,saarbruecken) )
        & ( d(munich,frankfurt) = 300 )
        & ( d(hamburg,berlin) = 250 )
        & ( d(hamburg,kiel) = 90 )
        & ( d(cologne,frankfurt) = 150 )
        & ( d(hamburg,frankfurt) = 390 )
        & ( d(hamburg,cologne) = 360 )
        & ( d(saarbruecken,cologne) = 190 )
        & ( d(saarbruecken,frankfurt) = 160 )
        & ( d(berlin,frankfurt) = 420 )
        & ( d(berlin,cologne) = 480 )
        & ( d(berlin,munich) = 510 )
        & ! [X0: city] : ( d(X0,X0) = 0 )
        & ! [X1: city,X2: city,X3: city] : ~ $less($sum(d(X1,X2),d(X2,X3)),d(X1,X3))
        & ! [X4: city,X5: city] : ( d(X4,X5) = d(X5,X4) ) )
     => ~ $less(500,d(cologne,berlin)) ),
    inference(rectify,[],[f3]) ).

tff(f3,plain,
    ~ ( ( ( 360 = d(munich,saarbruecken) )
        & ( d(munich,frankfurt) = 300 )
        & ( d(hamburg,berlin) = 250 )
        & ( d(hamburg,kiel) = 90 )
        & ( d(cologne,frankfurt) = 150 )
        & ( d(hamburg,frankfurt) = 390 )
        & ( d(hamburg,cologne) = 360 )
        & ( d(saarbruecken,cologne) = 190 )
        & ( d(saarbruecken,frankfurt) = 160 )
        & ( d(berlin,frankfurt) = 420 )
        & ( d(berlin,cologne) = 480 )
        & ( d(berlin,munich) = 510 )
        & ! [X0: city] : ( d(X0,X0) = 0 )
        & ! [X0: city,X1: city,X2: city] : ~ $less($sum(d(X0,X1),d(X1,X2)),d(X0,X2))
        & ! [X0: city,X1: city] : ( d(X0,X1) = d(X1,X0) ) )
     => ~ $less(500,d(cologne,berlin)) ),
    inference(theory_normalization,[],[f2]) ).

tff(f2,negated_conjecture,
    ~ ( ( ( 360 = d(munich,saarbruecken) )
        & ( d(munich,frankfurt) = 300 )
        & ( d(hamburg,berlin) = 250 )
        & ( d(hamburg,kiel) = 90 )
        & ( d(cologne,frankfurt) = 150 )
        & ( d(hamburg,frankfurt) = 390 )
        & ( d(hamburg,cologne) = 360 )
        & ( d(saarbruecken,cologne) = 190 )
        & ( d(saarbruecken,frankfurt) = 160 )
        & ( d(berlin,frankfurt) = 420 )
        & ( d(berlin,cologne) = 480 )
        & ( d(berlin,munich) = 510 )
        & ! [X0: city] : ( d(X0,X0) = 0 )
        & ! [X0: city,X1: city,X2: city] : $lesseq(d(X0,X2),$sum(d(X0,X1),d(X1,X2)))
        & ! [X0: city,X1: city] : ( d(X0,X1) = d(X1,X0) ) )
     => $lesseq(d(cologne,berlin),500) ),
    inference(negated_conjecture,[],[f1]) ).

tff(f1,conjecture,
    ( ( ( 360 = d(munich,saarbruecken) )
      & ( d(munich,frankfurt) = 300 )
      & ( d(hamburg,berlin) = 250 )
      & ( d(hamburg,kiel) = 90 )
      & ( d(cologne,frankfurt) = 150 )
      & ( d(hamburg,frankfurt) = 390 )
      & ( d(hamburg,cologne) = 360 )
      & ( d(saarbruecken,cologne) = 190 )
      & ( d(saarbruecken,frankfurt) = 160 )
      & ( d(berlin,frankfurt) = 420 )
      & ( d(berlin,cologne) = 480 )
      & ( d(berlin,munich) = 510 )
      & ! [X0: city] : ( d(X0,X0) = 0 )
      & ! [X0: city,X1: city,X2: city] : $lesseq(d(X0,X2),$sum(d(X0,X1),d(X1,X2)))
      & ! [X0: city,X1: city] : ( d(X0,X1) = d(X1,X0) ) )
   => $lesseq(d(cologne,berlin),500) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',city_distance_1) ).

tff(f102,plain,
    ( $less(500,d(cologne,berlin))
    | ~ spl0_14 ),
    inference(avatar_component_clause,[],[f100]) ).

tff(f100,plain,
    ( spl0_14
  <=> $less(500,d(cologne,berlin)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

tff(f103,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f34,f100]) ).

tff(f34,plain,
    $less(500,d(cologne,berlin)),
    inference(cnf_transformation,[],[f18]) ).

tff(f98,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f33,f95]) ).

tff(f95,plain,
    ( spl0_13
  <=> ( 360 = d(munich,saarbruecken) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

tff(f33,plain,
    360 = d(munich,saarbruecken),
    inference(cnf_transformation,[],[f18]) ).

tff(f93,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f32,f90]) ).

tff(f90,plain,
    ( spl0_12
  <=> ( d(munich,frankfurt) = 300 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

tff(f32,plain,
    d(munich,frankfurt) = 300,
    inference(cnf_transformation,[],[f18]) ).

tff(f88,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f31,f85]) ).

tff(f85,plain,
    ( spl0_11
  <=> ( d(hamburg,berlin) = 250 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

tff(f31,plain,
    d(hamburg,berlin) = 250,
    inference(cnf_transformation,[],[f18]) ).

tff(f83,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f30,f80]) ).

tff(f80,plain,
    ( spl0_10
  <=> ( d(hamburg,kiel) = 90 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

tff(f30,plain,
    d(hamburg,kiel) = 90,
    inference(cnf_transformation,[],[f18]) ).

tff(f78,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f29,f75]) ).

tff(f75,plain,
    ( spl0_9
  <=> ( d(cologne,frankfurt) = 150 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

tff(f29,plain,
    d(cologne,frankfurt) = 150,
    inference(cnf_transformation,[],[f18]) ).

tff(f73,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f28,f70]) ).

tff(f70,plain,
    ( spl0_8
  <=> ( d(hamburg,frankfurt) = 390 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

tff(f28,plain,
    d(hamburg,frankfurt) = 390,
    inference(cnf_transformation,[],[f18]) ).

tff(f68,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f27,f65]) ).

tff(f65,plain,
    ( spl0_7
  <=> ( d(hamburg,cologne) = 360 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

tff(f27,plain,
    d(hamburg,cologne) = 360,
    inference(cnf_transformation,[],[f18]) ).

tff(f63,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f26,f60]) ).

tff(f60,plain,
    ( spl0_6
  <=> ( d(saarbruecken,cologne) = 190 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

tff(f26,plain,
    d(saarbruecken,cologne) = 190,
    inference(cnf_transformation,[],[f18]) ).

tff(f58,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f25,f55]) ).

tff(f55,plain,
    ( spl0_5
  <=> ( d(saarbruecken,frankfurt) = 160 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

tff(f25,plain,
    d(saarbruecken,frankfurt) = 160,
    inference(cnf_transformation,[],[f18]) ).

tff(f53,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f24,f50]) ).

tff(f50,plain,
    ( spl0_4
  <=> ( d(berlin,frankfurt) = 420 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

tff(f24,plain,
    d(berlin,frankfurt) = 420,
    inference(cnf_transformation,[],[f18]) ).

tff(f48,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f23,f45]) ).

tff(f23,plain,
    d(berlin,cologne) = 480,
    inference(cnf_transformation,[],[f18]) ).

tff(f43,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f22,f40]) ).

tff(f40,plain,
    ( spl0_2
  <=> ( d(berlin,munich) = 510 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

tff(f22,plain,
    d(berlin,munich) = 510,
    inference(cnf_transformation,[],[f18]) ).

tff(f38,plain,
    spl0_1,
    inference(avatar_split_clause,[],[f21,f36]) ).

tff(f36,plain,
    ( spl0_1
  <=> ! [X0: city] : ( d(X0,X0) = 0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

tff(f21,plain,
    ! [X0: city] : ( d(X0,X0) = 0 ),
    inference(cnf_transformation,[],[f18]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : GEG021_1 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36  % Computer : n019.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Sat May 18 21:56:38 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.37  % (29535)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.39  % (29538)WARNING: value z3 for option sas not known
% 0.21/0.40  % (29538)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)
% 0.21/0.40  % (29539)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.40  % (29537)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.40  % (29536)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.40  % (29540)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)
% 0.21/0.40  % (29542)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)
% 0.21/0.40  % (29541)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)
% 0.21/0.40  % (29536)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.21/0.40  % (29537)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.21/0.40  % (29537)Terminated due to inappropriate strategy.
% 0.21/0.40  % (29537)------------------------------
% 0.21/0.40  % (29537)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.40  % (29537)Termination reason: Inappropriate
% 0.21/0.40  
% 0.21/0.40  % (29537)Memory used [KB]: 727
% 0.21/0.40  % (29537)Time elapsed: 0.003 s
% 0.21/0.40  % (29537)Instructions burned: 2 (million)
% 0.21/0.40  % (29539)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.21/0.40  % (29539)Terminated due to inappropriate strategy.
% 0.21/0.40  % (29539)------------------------------
% 0.21/0.40  % (29539)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.40  % (29539)Termination reason: Inappropriate
% 0.21/0.40  
% 0.21/0.40  % (29539)Memory used [KB]: 727
% 0.21/0.40  % (29539)Time elapsed: 0.003 s
% 0.21/0.40  % (29539)Instructions burned: 2 (million)
% 0.21/0.40  % (29536)Terminated due to inappropriate strategy.
% 0.21/0.40  % (29536)------------------------------
% 0.21/0.40  % (29536)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.40  % (29536)Termination reason: Inappropriate
% 0.21/0.40  
% 0.21/0.40  % (29536)Memory used [KB]: 727
% 0.21/0.40  % (29536)Time elapsed: 0.004 s
% 0.21/0.40  % (29536)Instructions burned: 2 (million)
% 0.21/0.40  % (29537)------------------------------
% 0.21/0.40  % (29537)------------------------------
% 0.21/0.40  % (29539)------------------------------
% 0.21/0.40  % (29539)------------------------------
% 0.21/0.40  % (29536)------------------------------
% 0.21/0.40  % (29536)------------------------------
% 0.21/0.40  % (29540)First to succeed.
% 0.21/0.40  % (29538)Also succeeded, but the first one will report.
% 0.21/0.40  % (29542)Also succeeded, but the first one will report.
% 0.21/0.40  % (29541)Also succeeded, but the first one will report.
% 0.21/0.41  % (29540)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-29535"
% 0.21/0.41  % (29540)Refutation found. Thanks to Tanya!
% 0.21/0.41  % SZS status Theorem for theBenchmark
% 0.21/0.41  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.41  % (29540)------------------------------
% 0.21/0.41  % (29540)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.41  % (29540)Termination reason: Refutation
% 0.21/0.41  
% 0.21/0.41  % (29540)Memory used [KB]: 768
% 0.21/0.41  % (29540)Time elapsed: 0.009 s
% 0.21/0.41  % (29540)Instructions burned: 6 (million)
% 0.21/0.41  % (29535)Success in time 0.035 s
%------------------------------------------------------------------------------