%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GEG024_1 : TPTP v9.0.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n004.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 Apr 9 06:13:11 PM UTC 2025
% Result : Theorem 12.80s 4.09s
% Output : CNFRefutation 12.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1
% Syntax : Number of formulae : 10 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 38 ( 24 equ)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 31 ( 3 ~; 5 |; 22 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 51 ( 13 atm; 1 fun; 37 num; 0 var)
% Number of types : 2 ( 1 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 40 ( 18 usr; 37 con; 0-2 aty)
% Number of variables : 12 ( 11 !; 1 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
%$ d > #nlpp > inh > saarbruecken > munich > kiel > hamburg > frankfurt > cologne > berlin
%Foreground sorts:
tff(city,type,
city: $tType ).
%Background operators:
tff('#skE_7',type,
'#skE_7': $int ).
tff('#skE_2',type,
'#skE_2': $int ).
tff('#skE_1',type,
'#skE_1': $int ).
tff('#skE_6',type,
'#skE_6': $int ).
tff('#skE_5',type,
'#skE_5': $int ).
tff('#skE_8',type,
'#skE_8': $int ).
tff('#skE_4',type,
'#skE_4': $int ).
tff('#skE_3',type,
'#skE_3': $int ).
tff('#skE_9',type,
'#skE_9': $int ).
%Foreground operators:
tff(munich,type,
munich: city ).
tff(kiel,type,
kiel: city ).
tff(d,type,
d: ( city * city ) > $int ).
tff(frankfurt,type,
frankfurt: city ).
tff(berlin,type,
berlin: city ).
tff(cologne,type,
cologne: city ).
tff(saarbruecken,type,
saarbruecken: city ).
tff(hamburg,type,
hamburg: city ).
tff(inh,type,
inh: city > $int ).
tff(f_80,negated_conjecture,
~ ( ( ! [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(c_65,plain,
inh(hamburg) = 1774224,
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_60,plain,
d(hamburg,kiel) = 90,
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_49,plain,
! [Y_2: city,X_1: city] : ( d(Y_2,X_1) = d(X_1,Y_2) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_2,plain,
! [X_7: city] :
( ~ $lesseq(1000000,inh(X_7))
| ~ $lesseq(d(kiel,X_7),100) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_1263,plain,
! [X_27: city] :
( $less(inh(X_27),1000000)
| $less(100,d(kiel,X_27)) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_2]) ).
tff(c_13876,plain,
! [Y_1273: city] :
( $less(inh(Y_1273),1000000)
| $less(100,d(Y_1273,kiel)) ),
inference(superposition,[status(thm),theory(equality)],[c_49,c_1263]) ).
tff(c_13896,plain,
( $less(inh(hamburg),1000000)
| $less(100,90) ),
inference(superposition,[status(thm),theory(equality)],[c_60,c_13876]) ).
tff(c_13910,plain,
( $less(1774224,1000000)
| $less(100,90) ),
inference(demodulation,[status(thm),theory(equality)],[c_65,c_13896]) ).
tff(c_13913,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_13910]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEG024_1 : TPTP v9.0.0. Bugfixed v5.2.0.
% 0.12/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Apr 7 19:14:38 EDT 2025
% 0.14/0.35 % CPUTime :
% 12.80/4.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.80/4.09
% 12.80/4.09 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------