TSTP Solution File: GEG024_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEG024_1 : TPTP v8.1.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 : Fri Sep 16 14:58:50 EDT 2022
% Result : Theorem 0.13s 0.41s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 30
% Syntax : Number of formulae : 66 ( 23 unt; 9 typ; 0 def)
% Number of atoms : 263 ( 144 equ)
% Maximal formula atoms : 48 ( 4 avg)
% Number of connectives : 268 ( 82 ~; 32 |; 129 &)
% ( 23 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 20 ( 20 fml; 0 var)
% Number arithmetic : 420 ( 105 atm; 57 fun; 258 num; 0 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 10 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 33 ( 9 usr; 29 con; 0-2 aty)
% Number of variables : 97 ( 71 !; 17 ?; 97 :)
% Comments :
%------------------------------------------------------------------------------
tff(d_type,type,
d: ( city * city ) > $int ).
tff(hamburg_type,type,
hamburg: city ).
tff(kiel_type,type,
kiel: city ).
tff(inh_type,type,
inh: city > $int ).
tff(saarbruecken_type,type,
saarbruecken: city ).
tff(frankfurt_type,type,
frankfurt: city ).
tff(cologne_type,type,
cologne: city ).
tff(munich_type,type,
munich: city ).
tff(berlin_type,type,
berlin: city ).
tff(1,plain,
^ [X: city,Y: city] :
refl(
( ( $sum(d(Y,X),$product(-1,d(X,Y))) = 0 )
<=> ( $sum(d(Y,X),$product(-1,d(X,Y))) = 0 ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: city,Y: city] : ( $sum(d(Y,X),$product(-1,d(X,Y))) = 0 )
<=> ! [X: city,Y: city] : ( $sum(d(Y,X),$product(-1,d(X,Y))) = 0 ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: city,Y: city] :
trans(
monotonicity(rewrite($sum(d(X,Y),$product(-1,d(Y,X))) = $sum($product(-1,d(Y,X)),d(X,Y))),
( ( $sum(d(X,Y),$product(-1,d(Y,X))) = 0 )
<=> ( $sum($product(-1,d(Y,X)),d(X,Y)) = 0 ) )),
rewrite(
( ( $sum($product(-1,d(Y,X)),d(X,Y)) = 0 )
<=> ( $sum(d(Y,X),$product(-1,d(X,Y))) = 0 ) )),
( ( $sum(d(X,Y),$product(-1,d(Y,X))) = 0 )
<=> ( $sum(d(Y,X),$product(-1,d(X,Y))) = 0 ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [X: city,Y: city] : ( $sum(d(X,Y),$product(-1,d(Y,X))) = 0 )
<=> ! [X: city,Y: city] : ( $sum(d(Y,X),$product(-1,d(X,Y))) = 0 ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [X: city,Y: city] :
rewrite(
( ( d(X,Y) = d(Y,X) )
<=> ( $sum(d(X,Y),$product(-1,d(Y,X))) = 0 ) )),
inference(bind,[status(th)],]) ).
tff(6,plain,
( ! [X: city,Y: city] : ( d(X,Y) = d(Y,X) )
<=> ! [X: city,Y: city] : ( $sum(d(X,Y),$product(-1,d(Y,X))) = 0 ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [X: city,Y: city] : ( d(X,Y) = d(Y,X) )
<=> ! [X: city,Y: city] : ( d(X,Y) = d(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(8,plain,
( ~ ( ( ! [X: city,Y: city] : ( d(X,Y) = d(Y,X) )
& ! [X: city,Y: city,Z: city] : $lesseq(d(X,Z),$sum(d(X,Y),d(Y,Z)))
& ! [X: city] : ( d(X,X) = 0 )
& ( d(berlin,munich) = 510 )
& ( d(berlin,cologne) = 480 )
& ( d(berlin,frankfurt) = 420 )
& ( d(saarbruecken,frankfurt) = 160 )
& ( d(saarbruecken,cologne) = 190 )
& ( d(hamburg,cologne) = 360 )
& ( d(hamburg,frankfurt) = 390 )
& ( d(cologne,frankfurt) = 150 )
& ( d(hamburg,kiel) = 90 )
& ( d(hamburg,berlin) = 250 )
& ( d(munich,frankfurt) = 300 )
& ( d(munich,saarbruecken) = 360 )
& ( inh(berlin) = 3442675 )
& ( inh(hamburg) = 1774224 )
& ( inh(munich) = 1330440 )
& ( inh(cologne) = 998105 )
& ( inh(frankfurt) = 671927 )
& ( inh(saarbruecken) = 175810 )
& ( inh(kiel) = 238281 ) )
=> ? [X: city] :
( $lesseq(d(kiel,X),100)
& $lesseq(1000000,inh(X)) ) )
<=> ~ ( ~ ( ! [X: city,Y: city] : ( d(X,Y) = d(Y,X) )
& ! [X: city,Y: city,Z: city] : $lesseq(d(X,Z),$sum(d(X,Y),d(Y,Z)))
& ! [X: city] : ( d(X,X) = 0 )
& ( d(berlin,munich) = 510 )
& ( d(berlin,cologne) = 480 )
& ( d(berlin,frankfurt) = 420 )
& ( d(saarbruecken,frankfurt) = 160 )
& ( d(saarbruecken,cologne) = 190 )
& ( d(hamburg,cologne) = 360 )
& ( d(hamburg,frankfurt) = 390 )
& ( d(cologne,frankfurt) = 150 )
& ( d(hamburg,kiel) = 90 )
& ( d(hamburg,berlin) = 250 )
& ( d(munich,frankfurt) = 300 )
& ( d(munich,saarbruecken) = 360 )
& ( inh(berlin) = 3442675 )
& ( inh(hamburg) = 1774224 )
& ( inh(munich) = 1330440 )
& ( inh(cologne) = 998105 )
& ( inh(frankfurt) = 671927 )
& ( inh(saarbruecken) = 175810 )
& ( inh(kiel) = 238281 ) )
| ? [X: city] :
( $lesseq(d(kiel,X),100)
& $lesseq(1000000,inh(X)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
~ ( ( ! [X: city,Y: city] : ( d(X,Y) = d(Y,X) )
& ! [X: city,Y: city,Z: city] : $lesseq(d(X,Z),$sum(d(X,Y),d(Y,Z)))
& ! [X: city] : ( d(X,X) = 0 )
& ( d(berlin,munich) = 510 )
& ( d(berlin,cologne) = 480 )
& ( d(berlin,frankfurt) = 420 )
& ( d(saarbruecken,frankfurt) = 160 )
& ( d(saarbruecken,cologne) = 190 )
& ( d(hamburg,cologne) = 360 )
& ( d(hamburg,frankfurt) = 390 )
& ( d(cologne,frankfurt) = 150 )
& ( d(hamburg,kiel) = 90 )
& ( d(hamburg,berlin) = 250 )
& ( d(munich,frankfurt) = 300 )
& ( d(munich,saarbruecken) = 360 )
& ( inh(berlin) = 3442675 )
& ( inh(hamburg) = 1774224 )
& ( inh(munich) = 1330440 )
& ( inh(cologne) = 998105 )
& ( inh(frankfurt) = 671927 )
& ( inh(saarbruecken) = 175810 )
& ( inh(kiel) = 238281 ) )
=> ? [X: city] :
( $lesseq(d(kiel,X),100)
& $lesseq(1000000,inh(X)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exists_big_city_distance_1) ).
tff(10,plain,
~ ( ~ ( ! [X: city,Y: city] : ( d(X,Y) = d(Y,X) )
& ! [X: city,Y: city,Z: city] : $lesseq(d(X,Z),$sum(d(X,Y),d(Y,Z)))
& ! [X: city] : ( d(X,X) = 0 )
& ( d(berlin,munich) = 510 )
& ( d(berlin,cologne) = 480 )
& ( d(berlin,frankfurt) = 420 )
& ( d(saarbruecken,frankfurt) = 160 )
& ( d(saarbruecken,cologne) = 190 )
& ( d(hamburg,cologne) = 360 )
& ( d(hamburg,frankfurt) = 390 )
& ( d(cologne,frankfurt) = 150 )
& ( d(hamburg,kiel) = 90 )
& ( d(hamburg,berlin) = 250 )
& ( d(munich,frankfurt) = 300 )
& ( d(munich,saarbruecken) = 360 )
& ( inh(berlin) = 3442675 )
& ( inh(hamburg) = 1774224 )
& ( inh(munich) = 1330440 )
& ( inh(cologne) = 998105 )
& ( inh(frankfurt) = 671927 )
& ( inh(saarbruecken) = 175810 )
& ( inh(kiel) = 238281 ) )
| ? [X: city] :
( $lesseq(d(kiel,X),100)
& $lesseq(1000000,inh(X)) ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( ! [X: city,Y: city] : ( d(X,Y) = d(Y,X) )
& ! [X: city,Y: city,Z: city] : $lesseq(d(X,Z),$sum(d(X,Y),d(Y,Z)))
& ! [X: city] : ( d(X,X) = 0 )
& ( d(berlin,munich) = 510 )
& ( d(berlin,cologne) = 480 )
& ( d(berlin,frankfurt) = 420 )
& ( d(saarbruecken,frankfurt) = 160 )
& ( d(saarbruecken,cologne) = 190 )
& ( d(hamburg,cologne) = 360 )
& ( d(hamburg,frankfurt) = 390 )
& ( d(cologne,frankfurt) = 150 )
& ( d(hamburg,kiel) = 90 )
& ( d(hamburg,berlin) = 250 )
& ( d(munich,frankfurt) = 300 )
& ( d(munich,saarbruecken) = 360 )
& ( inh(berlin) = 3442675 )
& ( inh(hamburg) = 1774224 )
& ( inh(munich) = 1330440 )
& ( inh(cologne) = 998105 )
& ( inh(frankfurt) = 671927 )
& ( inh(saarbruecken) = 175810 )
& ( inh(kiel) = 238281 ) ),
inference(or_elim,[status(thm)],[10]) ).
tff(12,plain,
! [X: city,Y: city] : ( d(X,Y) = d(Y,X) ),
inference(and_elim,[status(thm)],[11]) ).
tff(13,plain,
! [X: city,Y: city] : ( d(X,Y) = d(Y,X) ),
inference(modus_ponens,[status(thm)],[12,7]) ).
tff(14,plain,
! [X: city,Y: city] : ( $sum(d(X,Y),$product(-1,d(Y,X))) = 0 ),
inference(modus_ponens,[status(thm)],[13,6]) ).
tff(15,plain,
! [X: city,Y: city] : ( $sum(d(Y,X),$product(-1,d(X,Y))) = 0 ),
inference(modus_ponens,[status(thm)],[14,4]) ).
tff(16,plain,
! [X: city,Y: city] : ( $sum(d(Y,X),$product(-1,d(X,Y))) = 0 ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [X: city,Y: city] : ( $sum(d(Y,X),$product(-1,d(X,Y))) = 0 ),
inference(modus_ponens,[status(thm)],[16,2]) ).
tff(18,plain,
( ~ ! [X: city,Y: city] : ( $sum(d(Y,X),$product(-1,d(X,Y))) = 0 )
| ( $sum(d(hamburg,kiel),$product(-1,d(kiel,hamburg))) = 0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
$sum(d(hamburg,kiel),$product(-1,d(kiel,hamburg))) = 0,
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
( ( $sum(d(hamburg,kiel),$product(-1,d(kiel,hamburg))) != 0 )
| $greatereq($sum(d(hamburg,kiel),$product(-1,d(kiel,hamburg))),0) ),
inference(theory_lemma,[status(thm)],]) ).
tff(21,plain,
$greatereq($sum(d(hamburg,kiel),$product(-1,d(kiel,hamburg))),0),
inference(unit_resolution,[status(thm)],[20,19]) ).
tff(22,plain,
( ( inh(hamburg) = 1774224 )
<=> ( inh(hamburg) = 1774224 ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
inh(hamburg) = 1774224,
inference(and_elim,[status(thm)],[11]) ).
tff(24,plain,
inh(hamburg) = 1774224,
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
( ( inh(hamburg) != 1774224 )
| $greatereq(inh(hamburg),1774224) ),
inference(theory_lemma,[status(thm)],]) ).
tff(26,plain,
$greatereq(inh(hamburg),1774224),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
( ~ $greatereq(inh(hamburg),1774224)
| $greatereq(inh(hamburg),1000000) ),
inference(theory_lemma,[status(thm)],]) ).
tff(28,plain,
$greatereq(inh(hamburg),1000000),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
^ [X: city] :
refl(
( ( ~ $lesseq(d(kiel,X),100)
| ~ $greatereq(inh(X),1000000) )
<=> ( ~ $lesseq(d(kiel,X),100)
| ~ $greatereq(inh(X),1000000) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [X: city] :
( ~ $lesseq(d(kiel,X),100)
| ~ $greatereq(inh(X),1000000) )
<=> ! [X: city] :
( ~ $lesseq(d(kiel,X),100)
| ~ $greatereq(inh(X),1000000) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
^ [X: city] :
trans(
monotonicity(
rewrite(
( ( $lesseq(d(kiel,X),100)
& $greatereq(inh(X),1000000) )
<=> ~ ( ~ $lesseq(d(kiel,X),100)
| ~ $greatereq(inh(X),1000000) ) )),
( ~ ( $lesseq(d(kiel,X),100)
& $greatereq(inh(X),1000000) )
<=> ~ ~ ( ~ $lesseq(d(kiel,X),100)
| ~ $greatereq(inh(X),1000000) ) )),
rewrite(
( ~ ~ ( ~ $lesseq(d(kiel,X),100)
| ~ $greatereq(inh(X),1000000) )
<=> ( ~ $lesseq(d(kiel,X),100)
| ~ $greatereq(inh(X),1000000) ) )),
( ~ ( $lesseq(d(kiel,X),100)
& $greatereq(inh(X),1000000) )
<=> ( ~ $lesseq(d(kiel,X),100)
| ~ $greatereq(inh(X),1000000) ) )),
inference(bind,[status(th)],]) ).
tff(32,plain,
( ! [X: city] :
~ ( $lesseq(d(kiel,X),100)
& $greatereq(inh(X),1000000) )
<=> ! [X: city] :
( ~ $lesseq(d(kiel,X),100)
| ~ $greatereq(inh(X),1000000) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ~ ? [X: city] :
( $lesseq(d(kiel,X),100)
& $greatereq(inh(X),1000000) )
<=> ~ ? [X: city] :
( $lesseq(d(kiel,X),100)
& $greatereq(inh(X),1000000) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
( ~ ? [X: city] :
( $lesseq(d(kiel,X),100)
& $lesseq(1000000,inh(X)) )
<=> ~ ? [X: city] :
( $lesseq(d(kiel,X),100)
& $greatereq(inh(X),1000000) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ~ ? [X: city] :
( $lesseq(d(kiel,X),100)
& $lesseq(1000000,inh(X)) )
<=> ~ ? [X: city] :
( $lesseq(d(kiel,X),100)
& $lesseq(1000000,inh(X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
~ ? [X: city] :
( $lesseq(d(kiel,X),100)
& $lesseq(1000000,inh(X)) ),
inference(or_elim,[status(thm)],[10]) ).
tff(37,plain,
~ ? [X: city] :
( $lesseq(d(kiel,X),100)
& $lesseq(1000000,inh(X)) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
~ ? [X: city] :
( $lesseq(d(kiel,X),100)
& $lesseq(1000000,inh(X)) ),
inference(modus_ponens,[status(thm)],[37,35]) ).
tff(39,plain,
~ ? [X: city] :
( $lesseq(d(kiel,X),100)
& $lesseq(1000000,inh(X)) ),
inference(modus_ponens,[status(thm)],[38,35]) ).
tff(40,plain,
~ ? [X: city] :
( $lesseq(d(kiel,X),100)
& $greatereq(inh(X),1000000) ),
inference(modus_ponens,[status(thm)],[39,34]) ).
tff(41,plain,
~ ? [X: city] :
( $lesseq(d(kiel,X),100)
& $greatereq(inh(X),1000000) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
~ ? [X: city] :
( $lesseq(d(kiel,X),100)
& $greatereq(inh(X),1000000) ),
inference(modus_ponens,[status(thm)],[41,33]) ).
tff(43,plain,
^ [X: city] :
refl(
$oeq(
~ ( $lesseq(d(kiel,X),100)
& $greatereq(inh(X),1000000) ),
~ ( $lesseq(d(kiel,X),100)
& $greatereq(inh(X),1000000) ))),
inference(bind,[status(th)],]) ).
tff(44,plain,
! [X: city] :
~ ( $lesseq(d(kiel,X),100)
& $greatereq(inh(X),1000000) ),
inference(nnf-neg,[status(sab)],[42,43]) ).
tff(45,plain,
! [X: city] :
( ~ $lesseq(d(kiel,X),100)
| ~ $greatereq(inh(X),1000000) ),
inference(modus_ponens,[status(thm)],[44,32]) ).
tff(46,plain,
! [X: city] :
( ~ $lesseq(d(kiel,X),100)
| ~ $greatereq(inh(X),1000000) ),
inference(modus_ponens,[status(thm)],[45,30]) ).
tff(47,plain,
( ( ~ ! [X: city] :
( ~ $lesseq(d(kiel,X),100)
| ~ $greatereq(inh(X),1000000) )
| ~ $lesseq(d(kiel,hamburg),100)
| ~ $greatereq(inh(hamburg),1000000) )
<=> ( ~ ! [X: city] :
( ~ $lesseq(d(kiel,X),100)
| ~ $greatereq(inh(X),1000000) )
| ~ $lesseq(d(kiel,hamburg),100)
| ~ $greatereq(inh(hamburg),1000000) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,plain,
( ~ ! [X: city] :
( ~ $lesseq(d(kiel,X),100)
| ~ $greatereq(inh(X),1000000) )
| ~ $lesseq(d(kiel,hamburg),100)
| ~ $greatereq(inh(hamburg),1000000) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
( ~ ! [X: city] :
( ~ $lesseq(d(kiel,X),100)
| ~ $greatereq(inh(X),1000000) )
| ~ $lesseq(d(kiel,hamburg),100)
| ~ $greatereq(inh(hamburg),1000000) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
( ~ $lesseq(d(kiel,hamburg),100)
| ~ $greatereq(inh(hamburg),1000000) ),
inference(unit_resolution,[status(thm)],[49,46]) ).
tff(51,plain,
~ $lesseq(d(kiel,hamburg),100),
inference(unit_resolution,[status(thm)],[50,28]) ).
tff(52,plain,
( ( d(hamburg,kiel) = 90 )
<=> ( d(hamburg,kiel) = 90 ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
d(hamburg,kiel) = 90,
inference(and_elim,[status(thm)],[11]) ).
tff(54,plain,
d(hamburg,kiel) = 90,
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
( ( d(hamburg,kiel) != 90 )
| $lesseq(d(hamburg,kiel),90) ),
inference(theory_lemma,[status(thm)],]) ).
tff(56,plain,
$lesseq(d(hamburg,kiel),90),
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
$false,
inference(theory_lemma,[status(thm)],[56,51,21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GEG024_1 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.13/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n003.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 : Wed Aug 31 04:26:23 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.13/0.41 % SZS status Theorem
% 0.13/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------