TSTP Solution File: GRA002+4 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : GRA002+4 : 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/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 : n020.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 10:39:24 EDT 2023
% Result : Theorem 4.05s 2.07s
% Output : CNFRefutation 4.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 39
% Syntax : Number of formulae : 53 ( 11 unt; 34 typ; 0 def)
% Number of atoms : 33 ( 8 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 23 ( 9 ~; 5 |; 2 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 57 ( 24 >; 33 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 2 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 9 con; 0-5 aty)
% Number of variables : 29 (; 29 !; 0 ?; 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_2 > #skF_9 > #skF_7 > #skF_4 > #skF_3 > #skF_8 > #skF_1
%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(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_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(path,type,
path: ( $i * $i * $i ) > $o ).
tff(minus,type,
minus: ( $i * $i ) > $i ).
tff(f_267,negated_conjecture,
~ ( complete
=> ! [P,V1,V2] :
( shortest_path(V1,V2,P)
=> less_or_equal(minus(length_of(P),n1),number_of_in(triangles,graph)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maximal_path_length) ).
tff(f_260,lemma,
( complete
=> ! [P,V1,V2] :
( shortest_path(V1,V2,P)
=> ( number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',triangles_and_sequential_pairs) ).
tff(f_254,axiom,
! [Things,InThese] : less_or_equal(number_of_in(Things,InThese),number_of_in(Things,graph)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',graph_has_them_all) ).
tff(f_201,axiom,
! [V1,V2,SP] :
( shortest_path(V1,V2,SP)
<=> ( path(V1,V2,SP)
& ( V1 != V2 )
& ! [P] :
( path(V1,V2,P)
=> less_or_equal(length_of(SP),length_of(P)) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',shortest_path_defn) ).
tff(f_238,axiom,
! [V1,V2,P] :
( path(V1,V2,P)
=> ( number_of_in(sequential_pairs,P) = minus(length_of(P),n1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',path_length_sequential_pairs) ).
tff(c_146,plain,
shortest_path('#skF_10','#skF_11','#skF_9'),
inference(cnfTransformation,[status(thm)],[f_267]) ).
tff(c_148,plain,
complete,
inference(cnfTransformation,[status(thm)],[f_267]) ).
tff(c_142,plain,
! [P_95,V1_96,V2_97] :
( ( number_of_in(triangles,P_95) = number_of_in(sequential_pairs,P_95) )
| ~ shortest_path(V1_96,V2_97,P_95)
| ~ complete ),
inference(cnfTransformation,[status(thm)],[f_260]) ).
tff(c_217,plain,
! [P_155,V1_156,V2_157] :
( ( number_of_in(triangles,P_155) = number_of_in(sequential_pairs,P_155) )
| ~ shortest_path(V1_156,V2_157,P_155) ),
inference(demodulation,[status(thm),theory(equality)],[c_148,c_142]) ).
tff(c_221,plain,
number_of_in(triangles,'#skF_9') = number_of_in(sequential_pairs,'#skF_9'),
inference(resolution,[status(thm)],[c_146,c_217]) ).
tff(c_140,plain,
! [Things_93,InThese_94] : less_or_equal(number_of_in(Things_93,InThese_94),number_of_in(Things_93,graph)),
inference(cnfTransformation,[status(thm)],[f_254]) ).
tff(c_225,plain,
less_or_equal(number_of_in(sequential_pairs,'#skF_9'),number_of_in(triangles,graph)),
inference(superposition,[status(thm),theory(equality)],[c_221,c_140]) ).
tff(c_180,plain,
! [V1_136,V2_137,SP_138] :
( path(V1_136,V2_137,SP_138)
| ~ shortest_path(V1_136,V2_137,SP_138) ),
inference(cnfTransformation,[status(thm)],[f_201]) ).
tff(c_184,plain,
path('#skF_10','#skF_11','#skF_9'),
inference(resolution,[status(thm)],[c_146,c_180]) ).
tff(c_262,plain,
! [P_175,V1_176,V2_177] :
( ( minus(length_of(P_175),n1) = number_of_in(sequential_pairs,P_175) )
| ~ path(V1_176,V2_177,P_175) ),
inference(cnfTransformation,[status(thm)],[f_238]) ).
tff(c_265,plain,
minus(length_of('#skF_9'),n1) = number_of_in(sequential_pairs,'#skF_9'),
inference(resolution,[status(thm)],[c_184,c_262]) ).
tff(c_144,plain,
~ less_or_equal(minus(length_of('#skF_9'),n1),number_of_in(triangles,graph)),
inference(cnfTransformation,[status(thm)],[f_267]) ).
tff(c_266,plain,
~ less_or_equal(number_of_in(sequential_pairs,'#skF_9'),number_of_in(triangles,graph)),
inference(demodulation,[status(thm),theory(equality)],[c_265,c_144]) ).
tff(c_269,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_225,c_266]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRA002+4 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.00/0.13 % 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
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 18:06:37 EDT 2023
% 0.13/0.35 % CPUTime :
% 4.05/2.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.05/2.07
% 4.05/2.08 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.39/2.10
% 4.39/2.10 Inference rules
% 4.39/2.10 ----------------------
% 4.39/2.10 #Ref : 0
% 4.39/2.10 #Sup : 21
% 4.39/2.10 #Fact : 0
% 4.39/2.10 #Define : 0
% 4.39/2.10 #Split : 1
% 4.39/2.10 #Chain : 0
% 4.39/2.10 #Close : 0
% 4.39/2.10
% 4.39/2.10 Ordering : KBO
% 4.39/2.10
% 4.39/2.10 Simplification rules
% 4.39/2.10 ----------------------
% 4.39/2.10 #Subsume : 2
% 4.39/2.10 #Demod : 9
% 4.39/2.10 #Tautology : 13
% 4.39/2.10 #SimpNegUnit : 1
% 4.39/2.10 #BackRed : 2
% 4.39/2.10
% 4.39/2.10 #Partial instantiations: 0
% 4.39/2.10 #Strategies tried : 1
% 4.39/2.10
% 4.39/2.10 Timing (in seconds)
% 4.39/2.10 ----------------------
% 4.39/2.11 Preprocessing : 0.64
% 4.39/2.11 Parsing : 0.30
% 4.39/2.11 CNF conversion : 0.05
% 4.39/2.11 Main loop : 0.31
% 4.39/2.11 Inferencing : 0.09
% 4.39/2.11 Reduction : 0.09
% 4.39/2.11 Demodulation : 0.06
% 4.39/2.11 BG Simplification : 0.03
% 4.39/2.11 Subsumption : 0.08
% 4.39/2.11 Abstraction : 0.02
% 4.39/2.11 MUC search : 0.00
% 4.39/2.11 Cooper : 0.00
% 4.39/2.11 Total : 1.00
% 4.39/2.11 Index Insertion : 0.00
% 4.39/2.11 Index Deletion : 0.00
% 4.39/2.11 Index Matching : 0.00
% 4.39/2.11 BG Taut test : 0.00
%------------------------------------------------------------------------------