TSTP Solution File: GRA010+2 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRA010+2 : TPTP v8.1.2. 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 : n015.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 : Tue Aug 22 10:39:25 EDT 2023
% Result : Theorem 5.61s 2.43s
% Output : CNFRefutation 5.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 38
% Syntax : Number of formulae : 52 ( 4 unt; 36 typ; 0 def)
% Number of atoms : 49 ( 11 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 56 ( 23 ~; 22 |; 6 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 64 ( 26 >; 38 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 2 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 9 con; 0-5 aty)
% Number of variables : 41 (; 39 !; 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_13 > #skF_10 > #skF_2 > #skF_7 > #skF_4 > #skF_3 > #skF_9 > #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_13',type,
'#skF_13': ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(vertex,type,
vertex: $i > $o ).
tff(n1,type,
n1: $i ).
tff(length_of,type,
length_of: $i > $i ).
tff(sequential_pairs,type,
sequential_pairs: $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_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('#skF_9',type,
'#skF_9': ( $i * $i * $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_284,negated_conjecture,
~ ( complete
=> ! [P,V1,V2] :
( ( path(V1,V2,P)
& ! [E1,E2] :
( ( on_path(E1,P)
& on_path(E2,P)
& sequential(E1,E2) )
=> ? [E3] : triangle(E1,E2,E3) ) )
=> ( number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complete_means_sequential_pairs_and_triangles) ).
tff(f_254,axiom,
! [P,V1,V2] :
( ( path(V1,V2,P)
& ! [E1,E2] :
( ( on_path(E1,P)
& on_path(E2,P)
& sequential(E1,E2) )
=> ? [E3] : triangle(E1,E2,E3) ) )
=> ( number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).
tff(c_144,plain,
number_of_in(triangles,'#skF_10') != number_of_in(sequential_pairs,'#skF_10'),
inference(cnfTransformation,[status(thm)],[f_284]) ).
tff(c_136,plain,
! [P_84,V1_85,V2_86] :
( on_path('#skF_8'(P_84,V1_85,V2_86),P_84)
| ( number_of_in(triangles,P_84) = number_of_in(sequential_pairs,P_84) )
| ~ path(V1_85,V2_86,P_84) ),
inference(cnfTransformation,[status(thm)],[f_254]) ).
tff(c_138,plain,
! [P_84,V1_85,V2_86] :
( on_path('#skF_7'(P_84,V1_85,V2_86),P_84)
| ( number_of_in(triangles,P_84) = number_of_in(sequential_pairs,P_84) )
| ~ path(V1_85,V2_86,P_84) ),
inference(cnfTransformation,[status(thm)],[f_254]) ).
tff(c_134,plain,
! [P_84,V1_85,V2_86] :
( sequential('#skF_7'(P_84,V1_85,V2_86),'#skF_8'(P_84,V1_85,V2_86))
| ( number_of_in(triangles,P_84) = number_of_in(sequential_pairs,P_84) )
| ~ path(V1_85,V2_86,P_84) ),
inference(cnfTransformation,[status(thm)],[f_254]) ).
tff(c_146,plain,
! [E1_105,E2_106] :
( triangle(E1_105,E2_106,'#skF_13'(E1_105,E2_106))
| ~ sequential(E1_105,E2_106)
| ~ on_path(E2_106,'#skF_10')
| ~ on_path(E1_105,'#skF_10') ),
inference(cnfTransformation,[status(thm)],[f_284]) ).
tff(c_1148,plain,
! [P_374,V1_375,V2_376,E3_377] :
( ~ triangle('#skF_7'(P_374,V1_375,V2_376),'#skF_8'(P_374,V1_375,V2_376),E3_377)
| ( number_of_in(triangles,P_374) = number_of_in(sequential_pairs,P_374) )
| ~ path(V1_375,V2_376,P_374) ),
inference(cnfTransformation,[status(thm)],[f_254]) ).
tff(c_1228,plain,
! [P_389,V1_390,V2_391] :
( ( number_of_in(triangles,P_389) = number_of_in(sequential_pairs,P_389) )
| ~ path(V1_390,V2_391,P_389)
| ~ sequential('#skF_7'(P_389,V1_390,V2_391),'#skF_8'(P_389,V1_390,V2_391))
| ~ on_path('#skF_8'(P_389,V1_390,V2_391),'#skF_10')
| ~ on_path('#skF_7'(P_389,V1_390,V2_391),'#skF_10') ),
inference(resolution,[status(thm)],[c_146,c_1148]) ).
tff(c_1373,plain,
! [P_425,V1_426,V2_427] :
( ~ on_path('#skF_8'(P_425,V1_426,V2_427),'#skF_10')
| ~ on_path('#skF_7'(P_425,V1_426,V2_427),'#skF_10')
| ( number_of_in(triangles,P_425) = number_of_in(sequential_pairs,P_425) )
| ~ path(V1_426,V2_427,P_425) ),
inference(resolution,[status(thm)],[c_134,c_1228]) ).
tff(c_1377,plain,
! [V1_85,V2_86] :
( ~ on_path('#skF_8'('#skF_10',V1_85,V2_86),'#skF_10')
| ( number_of_in(triangles,'#skF_10') = number_of_in(sequential_pairs,'#skF_10') )
| ~ path(V1_85,V2_86,'#skF_10') ),
inference(resolution,[status(thm)],[c_138,c_1373]) ).
tff(c_1381,plain,
! [V1_428,V2_429] :
( ~ on_path('#skF_8'('#skF_10',V1_428,V2_429),'#skF_10')
| ~ path(V1_428,V2_429,'#skF_10') ),
inference(negUnitSimplification,[status(thm)],[c_144,c_144,c_1377]) ).
tff(c_1385,plain,
! [V1_85,V2_86] :
( ( number_of_in(triangles,'#skF_10') = number_of_in(sequential_pairs,'#skF_10') )
| ~ path(V1_85,V2_86,'#skF_10') ),
inference(resolution,[status(thm)],[c_136,c_1381]) ).
tff(c_1388,plain,
! [V1_85,V2_86] : ~ path(V1_85,V2_86,'#skF_10'),
inference(negUnitSimplification,[status(thm)],[c_144,c_1385]) ).
tff(c_148,plain,
path('#skF_11','#skF_12','#skF_10'),
inference(cnfTransformation,[status(thm)],[f_284]) ).
tff(c_1390,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1388,c_148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRA010+2 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.00/0.14 % 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
% 0.15/0.36 % Computer : n015.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 3 18:22:29 EDT 2023
% 0.15/0.36 % CPUTime :
% 5.61/2.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.61/2.43
% 5.61/2.43 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.61/2.46
% 5.61/2.46 Inference rules
% 5.61/2.46 ----------------------
% 5.61/2.46 #Ref : 2
% 5.61/2.46 #Sup : 316
% 5.61/2.46 #Fact : 4
% 5.61/2.46 #Define : 0
% 5.61/2.46 #Split : 4
% 5.61/2.46 #Chain : 0
% 5.61/2.46 #Close : 0
% 5.61/2.46
% 5.61/2.46 Ordering : KBO
% 5.61/2.46
% 5.61/2.46 Simplification rules
% 5.61/2.46 ----------------------
% 5.61/2.46 #Subsume : 60
% 5.61/2.46 #Demod : 7
% 5.61/2.46 #Tautology : 75
% 5.61/2.46 #SimpNegUnit : 5
% 5.61/2.46 #BackRed : 3
% 5.61/2.46
% 5.61/2.46 #Partial instantiations: 0
% 5.61/2.46 #Strategies tried : 1
% 5.61/2.46
% 5.61/2.46 Timing (in seconds)
% 5.61/2.46 ----------------------
% 5.61/2.46 Preprocessing : 0.64
% 5.61/2.46 Parsing : 0.29
% 5.61/2.46 CNF conversion : 0.05
% 5.61/2.46 Main loop : 0.67
% 5.61/2.46 Inferencing : 0.25
% 5.61/2.46 Reduction : 0.16
% 5.61/2.46 Demodulation : 0.10
% 5.61/2.46 BG Simplification : 0.05
% 5.61/2.46 Subsumption : 0.17
% 5.61/2.46 Abstraction : 0.03
% 5.61/2.46 MUC search : 0.00
% 5.61/2.46 Cooper : 0.00
% 5.61/2.46 Total : 1.36
% 5.61/2.46 Index Insertion : 0.00
% 5.61/2.46 Index Deletion : 0.00
% 5.61/2.46 Index Matching : 0.00
% 5.61/2.46 BG Taut test : 0.00
%------------------------------------------------------------------------------