TSTP Solution File: GEG022_1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : GEG022_1 : TPTP v8.1.0. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n018.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 Aug 31 16:07:18 EDT 2022

% Result   : Theorem 0.20s 0.52s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   27 (  10 unt;   9 typ;   0 def)
%            Number of atoms       :  125 ( 102 equ)
%            Maximal formula atoms :   16 (   6 avg)
%            Number of connectives :  123 (  16   ~;   2   |; 101   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   8 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number arithmetic     :  144 (  22 atm;  11 fun; 108 num;   3 var)
%            Number of types       :    2 (   1 usr;   1 ari)
%            Number of type conns  :    2 (   1   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   22 (   8 usr;  20 con; 0-2 aty)
%            Number of variables   :   51 (  51   !;   0   ?;  51   :)

% 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(f189,plain,
    $false,
    inference(evaluation,[],[f188]) ).

tff(f188,plain,
    ~ $less($sum(390,300),700),
    inference(forward_demodulation,[],[f173,f55]) ).

tff(f55,plain,
    300 = d(frankfurt,munich),
    inference(superposition,[],[f29,f34]) ).

tff(f34,plain,
    ! [X3: city,X4: city] : ( d(X3,X4) = d(X4,X3) ),
    inference(cnf_transformation,[],[f19]) ).

tff(f19,plain,
    ( ! [X0: city,X1: city,X2: city] : ~ $less($sum(d(X0,X2),d(X2,X1)),d(X0,X1))
    & ! [X3: city,X4: city] : ( d(X3,X4) = d(X4,X3) )
    & ( d(saarbruecken,cologne) = 190 )
    & ( d(hamburg,berlin) = 250 )
    & $less(700,d(hamburg,munich))
    & ( d(berlin,frankfurt) = 420 )
    & ( d(munich,frankfurt) = 300 )
    & ( d(hamburg,kiel) = 90 )
    & ( d(saarbruecken,frankfurt) = 160 )
    & ( d(hamburg,frankfurt) = 390 )
    & ( d(berlin,munich) = 510 )
    & ( d(hamburg,cologne) = 360 )
    & ( d(berlin,cologne) = 480 )
    & ( 360 = d(munich,saarbruecken) )
    & ( d(cologne,frankfurt) = 150 )
    & ! [X5: city] : ( 0 = d(X5,X5) ) ),
    inference(rectify,[],[f18]) ).

tff(f18,plain,
    ( ! [X3: city,X4: city,X5: city] : ~ $less($sum(d(X3,X5),d(X5,X4)),d(X3,X4))
    & ! [X1: city,X0: city] : ( d(X0,X1) = d(X1,X0) )
    & ( d(saarbruecken,cologne) = 190 )
    & ( d(hamburg,berlin) = 250 )
    & $less(700,d(hamburg,munich))
    & ( d(berlin,frankfurt) = 420 )
    & ( d(munich,frankfurt) = 300 )
    & ( d(hamburg,kiel) = 90 )
    & ( d(saarbruecken,frankfurt) = 160 )
    & ( d(hamburg,frankfurt) = 390 )
    & ( d(berlin,munich) = 510 )
    & ( d(hamburg,cologne) = 360 )
    & ( d(berlin,cologne) = 480 )
    & ( 360 = d(munich,saarbruecken) )
    & ( d(cologne,frankfurt) = 150 )
    & ! [X2: city] : ( 0 = d(X2,X2) ) ),
    inference(flattening,[],[f17]) ).

tff(f17,plain,
    ( $less(700,d(hamburg,munich))
    & ( d(munich,frankfurt) = 300 )
    & ( d(saarbruecken,frankfurt) = 160 )
    & ( d(berlin,munich) = 510 )
    & ( d(hamburg,frankfurt) = 390 )
    & ( d(cologne,frankfurt) = 150 )
    & ! [X3: city,X4: city,X5: city] : ~ $less($sum(d(X3,X5),d(X5,X4)),d(X3,X4))
    & ( d(berlin,cologne) = 480 )
    & ( d(hamburg,cologne) = 360 )
    & ! [X1: city,X0: city] : ( d(X0,X1) = d(X1,X0) )
    & ! [X2: city] : ( 0 = d(X2,X2) )
    & ( d(hamburg,berlin) = 250 )
    & ( d(saarbruecken,cologne) = 190 )
    & ( 360 = d(munich,saarbruecken) )
    & ( d(berlin,frankfurt) = 420 )
    & ( d(hamburg,kiel) = 90 ) ),
    inference(ennf_transformation,[],[f16]) ).

tff(f16,plain,
    ~ ( ( ( d(munich,frankfurt) = 300 )
        & ( d(saarbruecken,frankfurt) = 160 )
        & ( d(berlin,munich) = 510 )
        & ( d(hamburg,frankfurt) = 390 )
        & ( d(cologne,frankfurt) = 150 )
        & ! [X3: city,X4: city,X5: city] : ~ $less($sum(d(X3,X5),d(X5,X4)),d(X3,X4))
        & ( d(berlin,cologne) = 480 )
        & ( d(hamburg,cologne) = 360 )
        & ! [X1: city,X0: city] : ( d(X0,X1) = d(X1,X0) )
        & ! [X2: city] : ( 0 = d(X2,X2) )
        & ( d(hamburg,berlin) = 250 )
        & ( d(saarbruecken,cologne) = 190 )
        & ( 360 = d(munich,saarbruecken) )
        & ( d(berlin,frankfurt) = 420 )
        & ( d(hamburg,kiel) = 90 ) )
     => ~ $less(700,d(hamburg,munich)) ),
    inference(rectify,[],[f3]) ).

tff(f3,plain,
    ~ ( ( ( d(berlin,frankfurt) = 420 )
        & ! [X1: city,X0: city] : ( d(X0,X1) = d(X1,X0) )
        & ( d(munich,frankfurt) = 300 )
        & ( d(hamburg,kiel) = 90 )
        & ( 360 = d(munich,saarbruecken) )
        & ( d(hamburg,frankfurt) = 390 )
        & ( d(cologne,frankfurt) = 150 )
        & ( d(hamburg,cologne) = 360 )
        & ! [X0: city] : ( d(X0,X0) = 0 )
        & ( d(saarbruecken,frankfurt) = 160 )
        & ( d(hamburg,berlin) = 250 )
        & ! [X0: city,X2: city,X1: city] : ~ $less($sum(d(X0,X1),d(X1,X2)),d(X0,X2))
        & ( d(berlin,munich) = 510 )
        & ( d(saarbruecken,cologne) = 190 )
        & ( d(berlin,cologne) = 480 ) )
     => ~ $less(700,d(hamburg,munich)) ),
    inference(theory_normalization,[],[f2]) ).

tff(f2,negated_conjecture,
    ~ ( ( ( d(berlin,frankfurt) = 420 )
        & ! [X1: city,X0: city] : ( d(X0,X1) = d(X1,X0) )
        & ( d(munich,frankfurt) = 300 )
        & ( d(hamburg,kiel) = 90 )
        & ( 360 = d(munich,saarbruecken) )
        & ( d(hamburg,frankfurt) = 390 )
        & ( d(cologne,frankfurt) = 150 )
        & ( d(hamburg,cologne) = 360 )
        & ! [X0: city] : ( d(X0,X0) = 0 )
        & ( d(saarbruecken,frankfurt) = 160 )
        & ( d(hamburg,berlin) = 250 )
        & ! [X0: city,X2: city,X1: city] : $lesseq(d(X0,X2),$sum(d(X0,X1),d(X1,X2)))
        & ( d(berlin,munich) = 510 )
        & ( d(saarbruecken,cologne) = 190 )
        & ( d(berlin,cologne) = 480 ) )
     => $lesseq(d(hamburg,munich),700) ),
    inference(negated_conjecture,[],[f1]) ).

tff(f1,conjecture,
    ( ( ( d(berlin,frankfurt) = 420 )
      & ! [X1: city,X0: city] : ( d(X0,X1) = d(X1,X0) )
      & ( d(munich,frankfurt) = 300 )
      & ( d(hamburg,kiel) = 90 )
      & ( 360 = d(munich,saarbruecken) )
      & ( d(hamburg,frankfurt) = 390 )
      & ( d(cologne,frankfurt) = 150 )
      & ( d(hamburg,cologne) = 360 )
      & ! [X0: city] : ( d(X0,X0) = 0 )
      & ( d(saarbruecken,frankfurt) = 160 )
      & ( d(hamburg,berlin) = 250 )
      & ! [X0: city,X2: city,X1: city] : $lesseq(d(X0,X2),$sum(d(X0,X1),d(X1,X2)))
      & ( d(berlin,munich) = 510 )
      & ( d(saarbruecken,cologne) = 190 )
      & ( d(berlin,cologne) = 480 ) )
   => $lesseq(d(hamburg,munich),700) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',city_distance_2) ).

tff(f29,plain,
    d(munich,frankfurt) = 300,
    inference(cnf_transformation,[],[f19]) ).

tff(f173,plain,
    ~ $less($sum(390,d(frankfurt,munich)),700),
    inference(superposition,[],[f61,f26]) ).

tff(f26,plain,
    d(hamburg,frankfurt) = 390,
    inference(cnf_transformation,[],[f19]) ).

tff(f61,plain,
    ! [X0: city] : ~ $less($sum(d(hamburg,X0),d(X0,munich)),700),
    inference(unit_resulting_resolution,[],[f31,f35,f10]) ).

tff(f10,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X1,X2)
      | $less(X0,X2)
      | ~ $less(X0,X1) ),
    introduced(theory_axiom_148,[]) ).

tff(f35,plain,
    ! [X2: city,X0: city,X1: city] : ~ $less($sum(d(X0,X2),d(X2,X1)),d(X0,X1)),
    inference(cnf_transformation,[],[f19]) ).

tff(f31,plain,
    $less(700,d(hamburg,munich)),
    inference(cnf_transformation,[],[f19]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : GEG022=1 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.03/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.35  % Computer : n018.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   : Mon Aug 29 21:03:54 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.50  % (28629)ott+1011_1:2_br=off:bs=unit_only:bsr=unit_only:nwc=5.0:s2a=on:s2agt=32:urr=on:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.20/0.50  % (28638)lrs+10_1:1_ep=R:gve=force:plsq=on:plsqr=32,1:uwa=one_side_interpreted:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.50  % (28639)dis+10_1:64_nwc=1.4:tha=off:i=21:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 0.20/0.50  % (28636)dis+32_1:1_bd=off:nm=4:sos=on:ss=included:i=4:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.20/0.50  % (28638)Instruction limit reached!
% 0.20/0.50  % (28638)------------------------------
% 0.20/0.50  % (28638)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50  % (28638)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50  % (28638)Termination reason: Unknown
% 0.20/0.50  % (28638)Termination phase: Saturation
% 0.20/0.50  
% 0.20/0.50  % (28638)Memory used [KB]: 5500
% 0.20/0.50  % (28638)Time elapsed: 0.109 s
% 0.20/0.50  % (28638)Instructions burned: 3 (million)
% 0.20/0.50  % (28638)------------------------------
% 0.20/0.50  % (28638)------------------------------
% 0.20/0.51  % (28631)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=32:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/32Mi)
% 0.20/0.51  % (28628)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.51  % (28630)lrs+10_1:32_s2a=on:s2agt=10:sgt=8:ss=axioms:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.20/0.51  % (28631)First to succeed.
% 0.20/0.51  % (28643)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.20/0.52  % (28631)Refutation found. Thanks to Tanya!
% 0.20/0.52  % SZS status Theorem for theBenchmark
% 0.20/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.52  % (28631)------------------------------
% 0.20/0.52  % (28631)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52  % (28631)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52  % (28631)Termination reason: Refutation
% 0.20/0.52  
% 0.20/0.52  % (28631)Memory used [KB]: 5756
% 0.20/0.52  % (28631)Time elapsed: 0.110 s
% 0.20/0.52  % (28631)Instructions burned: 10 (million)
% 0.20/0.52  % (28631)------------------------------
% 0.20/0.52  % (28631)------------------------------
% 0.20/0.52  % (28622)Success in time 0.16 s
%------------------------------------------------------------------------------