TSTP Solution File: GEG021_1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEG021_1 : TPTP v8.1.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of formulae : 38 ( 17 unt; 8 typ; 0 def)
% Number of atoms : 128 ( 104 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 102 ( 13 ~; 5 |; 70 &)
% ( 12 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number arithmetic : 204 ( 17 atm; 57 fun; 130 num; 0 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 9 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 24 ( 8 usr; 21 con; 0-2 aty)
% Number of variables : 66 ( 60 !; 0 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
tff(d_type,type,
d: ( city * city ) > $int ).
tff(cologne_type,type,
cologne: city ).
tff(berlin_type,type,
berlin: city ).
tff(saarbruecken_type,type,
saarbruecken: city ).
tff(munich_type,type,
munich: city ).
tff(frankfurt_type,type,
frankfurt: city ).
tff(hamburg_type,type,
hamburg: city ).
tff(kiel_type,type,
kiel: city ).
tff(1,plain,
( ( d(berlin,cologne) = 480 )
<=> ( d(berlin,cologne) = 480 ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,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 ) )
=> $lesseq(d(cologne,berlin),500) )
<=> ~ ( ~ ( ! [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 ) )
| $lesseq(d(cologne,berlin),500) ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,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 ) )
=> $lesseq(d(cologne,berlin),500) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',city_distance_1) ).
tff(4,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 ) )
| $lesseq(d(cologne,berlin),500) ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,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 ) ),
inference(or_elim,[status(thm)],[4]) ).
tff(6,plain,
d(berlin,cologne) = 480,
inference(and_elim,[status(thm)],[5]) ).
tff(7,plain,
d(berlin,cologne) = 480,
inference(modus_ponens,[status(thm)],[6,1]) ).
tff(8,plain,
( ( d(berlin,cologne) != 480 )
| $lesseq(d(berlin,cologne),480) ),
inference(theory_lemma,[status(thm)],]) ).
tff(9,plain,
$lesseq(d(berlin,cologne),480),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,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(11,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)],[10]) ).
tff(12,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(13,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)],[12]) ).
tff(14,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(15,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)],[14]) ).
tff(16,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(17,plain,
! [X: city,Y: city] : ( d(X,Y) = d(Y,X) ),
inference(and_elim,[status(thm)],[5]) ).
tff(18,plain,
! [X: city,Y: city] : ( d(X,Y) = d(Y,X) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
! [X: city,Y: city] : ( $sum(d(X,Y),$product(-1,d(Y,X))) = 0 ),
inference(modus_ponens,[status(thm)],[18,15]) ).
tff(20,plain,
! [X: city,Y: city] : ( $sum(d(Y,X),$product(-1,d(X,Y))) = 0 ),
inference(modus_ponens,[status(thm)],[19,13]) ).
tff(21,plain,
! [X: city,Y: city] : ( $sum(d(Y,X),$product(-1,d(X,Y))) = 0 ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [X: city,Y: city] : ( $sum(d(Y,X),$product(-1,d(X,Y))) = 0 ),
inference(modus_ponens,[status(thm)],[21,11]) ).
tff(23,plain,
( ~ ! [X: city,Y: city] : ( $sum(d(Y,X),$product(-1,d(X,Y))) = 0 )
| ( $sum(d(berlin,cologne),$product(-1,d(cologne,berlin))) = 0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
$sum(d(berlin,cologne),$product(-1,d(cologne,berlin))) = 0,
inference(unit_resolution,[status(thm)],[23,22]) ).
tff(25,plain,
( ( $sum(d(berlin,cologne),$product(-1,d(cologne,berlin))) != 0 )
| $greatereq($sum(d(berlin,cologne),$product(-1,d(cologne,berlin))),0) ),
inference(theory_lemma,[status(thm)],]) ).
tff(26,plain,
$greatereq($sum(d(berlin,cologne),$product(-1,d(cologne,berlin))),0),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
( ~ $lesseq(d(cologne,berlin),500)
<=> ~ $lesseq(d(cologne,berlin),500) ),
inference(rewrite,[status(thm)],]) ).
tff(28,plain,
~ $lesseq(d(cologne,berlin),500),
inference(or_elim,[status(thm)],[4]) ).
tff(29,plain,
~ $lesseq(d(cologne,berlin),500),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
$false,
inference(theory_lemma,[status(thm)],[29,26,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEG021_1 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Aug 31 04:39:36 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.33 Usage: tptp [options] [-file:]file
% 0.13/0.33 -h, -? prints this message.
% 0.13/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.33 -m, -model generate model.
% 0.13/0.33 -p, -proof generate proof.
% 0.13/0.33 -c, -core generate unsat core of named formulas.
% 0.13/0.33 -st, -statistics display statistics.
% 0.13/0.33 -t:timeout set timeout (in second).
% 0.13/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.33 -<param>:<value> configuration parameter and value.
% 0.13/0.33 -o:<output-file> file to place output in.
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------