%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GEG021_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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n032.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 06:13:10 PM UTC 2025
% Result : Theorem 2.31s 1.56s
% Output : CNFRefutation 2.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 1
% Syntax : Number of formulae : 7 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 22 ( 16 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 17 ( 2 ~; 0 |; 14 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 25 ( 5 atm; 1 fun; 19 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 : 22 ( 8 usr; 20 con; 0-2 aty)
% Number of variables : 8 ( 8 !; 0 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
%$ d > #nlpp > saarbruecken > munich > kiel > hamburg > frankfurt > cologne > berlin
%Foreground sorts:
tff(city,type,
city: $tType ).
%Background operators:
%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(f_63,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 ) )
=> $lesseq(d(cologne,berlin),500) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',city_distance_1) ).
tff(c_39,plain,
d(berlin,cologne) = 480,
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_35,plain,
! [Y_2: city,X_1: city] : ( d(Y_2,X_1) = d(X_1,Y_2) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_2,plain,
~ $lesseq(d(cologne,berlin),500),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_50,plain,
$less(500,d(cologne,berlin)),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_2]) ).
tff(c_51,plain,
$less(500,480),
inference(demodulation,[status(thm),theory(equality)],[c_39,c_35,c_50]) ).
tff(c_53,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : GEG021_1 : TPTP v9.0.0. Bugfixed v5.2.0.
% 0.00/0.09 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Mon Apr 7 19:14:30 EDT 2025
% 0.09/0.28 % CPUTime :
% 2.31/1.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.31/1.56
% 2.31/1.56 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------