%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRA005+1 : TPTP v9.0.0. Bugfixed v3.2.0.
% 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 : n008.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 06:23:19 PM UTC 2025
% Result : Theorem 5.19s 2.27s
% Output : CNFRefutation 5.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 2
% Syntax : Number of formulae : 11 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 26 ( 11 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 30 ( 15 ~; 7 |; 6 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 2 prp; 0-3 aty)
% Number of functors : 26 ( 26 usr; 12 con; 0-5 aty)
% Number of variables : 27 ( 25 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ triangle > shortest_path > precedes > path > sequential > on_path > less_or_equal > in_path > vertex > edge > path_cons > number_of_in > minus > #nlpp > tail_of > length_of > head_of > triangles > sequential_pairs > n1 > graph > empty > edges > complete > #skF_11 > #skF_6 > #skF_5 > #skF_10 > #skF_14 > #skF_13 > #skF_2 > #skF_9 > #skF_7 > #skF_4 > #skF_3 > #skF_8 > #skF_1 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(head_of,type,
head_of: $i > $i ).
tff(less_or_equal,type,
less_or_equal: ( $i * $i ) > $o ).
tff(triangle,type,
triangle: ( $i * $i * $i ) > $o ).
tff(triangles,type,
triangles: $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff(number_of_in,type,
number_of_in: ( $i * $i ) > $i ).
tff(on_path,type,
on_path: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i * $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(vertex,type,
vertex: $i > $o ).
tff(n1,type,
n1: $i ).
tff('#skF_14',type,
'#skF_14': $i ).
tff(length_of,type,
length_of: $i > $i ).
tff(sequential_pairs,type,
sequential_pairs: $i ).
tff('#skF_13',type,
'#skF_13': $i ).
tff(edge,type,
edge: $i > $o ).
tff('#skF_2',type,
'#skF_2': ( $i * $i * $i ) > $i ).
tff(precedes,type,
precedes: ( $i * $i * $i ) > $o ).
tff(graph,type,
graph: $i ).
tff('#skF_9',type,
'#skF_9': $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i * $i ) > $i ).
tff(in_path,type,
in_path: ( $i * $i ) > $o ).
tff(sequential,type,
sequential: ( $i * $i ) > $o ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i ) > $i ).
tff(tail_of,type,
tail_of: $i > $i ).
tff(edges,type,
edges: $i ).
tff(complete,type,
complete: $o ).
tff(path_cons,type,
path_cons: ( $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i * $i ) > $i ).
tff(empty,type,
empty: $i ).
tff(shortest_path,type,
shortest_path: ( $i * $i * $i ) > $o ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(path,type,
path: ( $i * $i * $i ) > $o ).
tff(minus,type,
minus: ( $i * $i ) > $i ).
tff(f_267,negated_conjecture,
~ ! [V1,V2,E1,E2,P] :
( ( shortest_path(V1,V2,P)
& precedes(E1,E2,P) )
=> ~ ? [E3] :
( edge(E3)
& ( tail_of(E3) = tail_of(E1) )
& ( head_of(E3) = head_of(E2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_short_cut_edge) ).
tff(f_214,axiom,
! [V1,V2,E1,E2,P] :
( ( shortest_path(V1,V2,P)
& precedes(E1,E2,P) )
=> ( ~ ? [E3] :
( ( tail_of(E3) = tail_of(E1) )
& ( head_of(E3) = head_of(E2) ) )
& ~ precedes(E2,E1,P) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',shortest_path_properties) ).
tff(c_144,plain,
tail_of('#skF_11') = tail_of('#skF_14'),
inference(cnfTransformation,[status(thm)],[f_267]) ).
tff(c_148,plain,
precedes('#skF_11','#skF_12','#skF_13'),
inference(cnfTransformation,[status(thm)],[f_267]) ).
tff(c_142,plain,
head_of('#skF_14') = head_of('#skF_12'),
inference(cnfTransformation,[status(thm)],[f_267]) ).
tff(c_629,plain,
! [V1_295,E1_298,E2_296,V2_297,P_294,E3_299] :
( ( head_of(E3_299) != head_of(E2_296) )
| ( tail_of(E3_299) != tail_of(E1_298) )
| ~ precedes(E1_298,E2_296,P_294)
| ~ shortest_path(V1_295,V2_297,P_294) ),
inference(cnfTransformation,[status(thm)],[f_214]) ).
tff(c_742,plain,
! [V2_315,P_316,E2_313,E1_312,V1_314] :
( ( head_of(E2_313) != head_of('#skF_12') )
| ( tail_of(E1_312) != tail_of('#skF_14') )
| ~ precedes(E1_312,E2_313,P_316)
| ~ shortest_path(V1_314,V2_315,P_316) ),
inference(superposition,[status(thm),theory(equality)],[c_142,c_629]) ).
tff(c_744,plain,
! [V1_314,V2_315] :
( ( tail_of('#skF_11') != tail_of('#skF_14') )
| ~ shortest_path(V1_314,V2_315,'#skF_13') ),
inference(resolution,[status(thm)],[c_148,c_742]) ).
tff(c_747,plain,
! [V1_314,V2_315] : ~ shortest_path(V1_314,V2_315,'#skF_13'),
inference(demodulation,[status(thm),theory(equality)],[c_144,c_744]) ).
tff(c_150,plain,
shortest_path('#skF_9','#skF_10','#skF_13'),
inference(cnfTransformation,[status(thm)],[f_267]) ).
tff(c_749,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_747,c_150]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRA005+1 : TPTP v9.0.0. Bugfixed v3.2.0.
% 0.07/0.13 % 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
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Apr 7 20:49:47 EDT 2025
% 0.14/0.34 % CPUTime :
% 5.19/2.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.19/2.27
% 5.19/2.27 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------