%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRA003+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 : 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 : Wed Apr 9 06:23:18 PM UTC 2025
% Result : Theorem 4.50s 2.03s
% Output : CNFRefutation 4.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 56 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 128 ( 23 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 122 ( 50 ~; 38 |; 24 &)
% ( 1 <=>; 7 =>; 0 <=; 2 <~>)
% Maximal formula depth : 15 ( 4 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 : 25 ( 25 usr; 11 con; 0-5 aty)
% Number of variables : 83 ( 79 !; 4 ?; 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_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(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_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/sandbox2/benchmark/Axioms/GRA001+0.ax',shortest_path_defn) ).
tff(f_275,negated_conjecture,
~ ! [V1,V2,E1,E2,P] :
( ( shortest_path(V1,V2,P)
& precedes(E1,E2,P) )
=> ( vertex(V1)
& vertex(V2)
& ( V1 != V2 )
& edge(E1)
& edge(E2)
& ( E1 != E2 )
& path(V1,V2,P) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vertices_and_edges) ).
tff(f_123,axiom,
! [V1,V2,P] :
( path(V1,V2,P)
=> ( vertex(V1)
& vertex(V2)
& ? [E] :
( edge(E)
& ( V1 = tail_of(E) )
& ( ( ( V2 = head_of(E) )
& ( P = path_cons(E,empty) ) )
<~> ? [TP] :
( path(head_of(E),V2,TP)
& ( P = path_cons(E,TP) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',path_properties) ).
tff(f_189,axiom,
! [P,V1,V2] :
( path(V1,V2,P)
=> ! [E1,E2] :
( precedes(E1,E2,P)
=> ( on_path(E1,P)
& on_path(E2,P)
& ( sequential(E1,E2)
<~> ? [E3] :
( sequential(E1,E3)
& precedes(E3,E2,P) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',precedes_properties) ).
tff(f_133,axiom,
! [V1,V2,P,E] :
( ( path(V1,V2,P)
& on_path(E,P) )
=> ( edge(E)
& in_path(head_of(E),P)
& in_path(tail_of(E),P) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',on_path_properties) ).
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_102,plain,
! [V2_63,SP_64] : ~ shortest_path(V2_63,V2_63,SP_64),
inference(cnfTransformation,[status(thm)],[f_201]) ).
tff(c_142,plain,
( ~ path('#skF_9','#skF_10','#skF_13')
| ( '#skF_11' = '#skF_12' )
| ~ edge('#skF_12')
| ~ edge('#skF_11')
| ( '#skF_10' = '#skF_9' )
| ~ vertex('#skF_10')
| ~ vertex('#skF_9') ),
inference(cnfTransformation,[status(thm)],[f_275]) ).
tff(c_154,plain,
~ vertex('#skF_9'),
inference(splitLeft,[status(thm)],[c_142]) ).
tff(c_146,plain,
shortest_path('#skF_9','#skF_10','#skF_13'),
inference(cnfTransformation,[status(thm)],[f_275]) ).
tff(c_165,plain,
! [V1_133,V2_134,SP_135] :
( path(V1_133,V2_134,SP_135)
| ~ shortest_path(V1_133,V2_134,SP_135) ),
inference(cnfTransformation,[status(thm)],[f_201]) ).
tff(c_169,plain,
path('#skF_9','#skF_10','#skF_13'),
inference(resolution,[status(thm)],[c_146,c_165]) ).
tff(c_38,plain,
! [V1_15,V2_16,P_17] :
( vertex(V1_15)
| ~ path(V1_15,V2_16,P_17) ),
inference(cnfTransformation,[status(thm)],[f_123]) ).
tff(c_172,plain,
vertex('#skF_9'),
inference(resolution,[status(thm)],[c_169,c_38]) ).
tff(c_179,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_154,c_172]) ).
tff(c_180,plain,
( ~ vertex('#skF_10')
| ~ edge('#skF_11')
| ~ edge('#skF_12')
| ~ path('#skF_9','#skF_10','#skF_13')
| ( '#skF_10' = '#skF_9' )
| ( '#skF_11' = '#skF_12' ) ),
inference(splitRight,[status(thm)],[c_142]) ).
tff(c_187,plain,
~ path('#skF_9','#skF_10','#skF_13'),
inference(splitLeft,[status(thm)],[c_180]) ).
tff(c_193,plain,
! [V1_162,V2_163,SP_164] :
( path(V1_162,V2_163,SP_164)
| ~ shortest_path(V1_162,V2_163,SP_164) ),
inference(cnfTransformation,[status(thm)],[f_201]) ).
tff(c_196,plain,
path('#skF_9','#skF_10','#skF_13'),
inference(resolution,[status(thm)],[c_146,c_193]) ).
tff(c_200,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_187,c_196]) ).
tff(c_202,plain,
path('#skF_9','#skF_10','#skF_13'),
inference(splitRight,[status(thm)],[c_180]) ).
tff(c_36,plain,
! [V2_16,V1_15,P_17] :
( vertex(V2_16)
| ~ path(V1_15,V2_16,P_17) ),
inference(cnfTransformation,[status(thm)],[f_123]) ).
tff(c_211,plain,
vertex('#skF_10'),
inference(resolution,[status(thm)],[c_202,c_36]) ).
tff(c_201,plain,
( ~ edge('#skF_12')
| ~ edge('#skF_11')
| ~ vertex('#skF_10')
| ( '#skF_11' = '#skF_12' )
| ( '#skF_10' = '#skF_9' ) ),
inference(splitRight,[status(thm)],[c_180]) ).
tff(c_213,plain,
( ~ edge('#skF_12')
| ~ edge('#skF_11')
| ( '#skF_11' = '#skF_12' )
| ( '#skF_10' = '#skF_9' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_211,c_201]) ).
tff(c_214,plain,
~ edge('#skF_11'),
inference(splitLeft,[status(thm)],[c_213]) ).
tff(c_144,plain,
precedes('#skF_11','#skF_12','#skF_13'),
inference(cnfTransformation,[status(thm)],[f_275]) ).
tff(c_261,plain,
! [P_205,E1_203,E2_204,V2_206,V1_207] :
( on_path(E1_203,P_205)
| ~ precedes(E1_203,E2_204,P_205)
| ~ path(V1_207,V2_206,P_205) ),
inference(cnfTransformation,[status(thm)],[f_189]) ).
tff(c_264,plain,
! [V1_207,V2_206] :
( on_path('#skF_11','#skF_13')
| ~ path(V1_207,V2_206,'#skF_13') ),
inference(resolution,[status(thm)],[c_144,c_261]) ).
tff(c_272,plain,
! [V1_207,V2_206] : ~ path(V1_207,V2_206,'#skF_13'),
inference(splitLeft,[status(thm)],[c_264]) ).
tff(c_274,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_272,c_202]) ).
tff(c_275,plain,
on_path('#skF_11','#skF_13'),
inference(splitRight,[status(thm)],[c_264]) ).
tff(c_62,plain,
! [E_29,P_28,V1_26,V2_27] :
( edge(E_29)
| ~ on_path(E_29,P_28)
| ~ path(V1_26,V2_27,P_28) ),
inference(cnfTransformation,[status(thm)],[f_133]) ).
tff(c_277,plain,
! [V1_26,V2_27] :
( edge('#skF_11')
| ~ path(V1_26,V2_27,'#skF_13') ),
inference(resolution,[status(thm)],[c_275,c_62]) ).
tff(c_280,plain,
! [V1_26,V2_27] : ~ path(V1_26,V2_27,'#skF_13'),
inference(negUnitSimplification,[status(thm)],[c_214,c_277]) ).
tff(c_282,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_280,c_202]) ).
tff(c_283,plain,
( ~ edge('#skF_12')
| ( '#skF_10' = '#skF_9' )
| ( '#skF_11' = '#skF_12' ) ),
inference(splitRight,[status(thm)],[c_213]) ).
tff(c_290,plain,
~ edge('#skF_12'),
inference(splitLeft,[status(thm)],[c_283]) ).
tff(c_372,plain,
! [V2_258,P_257,V1_259,E2_256,E1_255] :
( on_path(E2_256,P_257)
| ~ precedes(E1_255,E2_256,P_257)
| ~ path(V1_259,V2_258,P_257) ),
inference(cnfTransformation,[status(thm)],[f_189]) ).
tff(c_375,plain,
! [V1_259,V2_258] :
( on_path('#skF_12','#skF_13')
| ~ path(V1_259,V2_258,'#skF_13') ),
inference(resolution,[status(thm)],[c_144,c_372]) ).
tff(c_376,plain,
! [V1_259,V2_258] : ~ path(V1_259,V2_258,'#skF_13'),
inference(splitLeft,[status(thm)],[c_375]) ).
tff(c_382,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_376,c_202]) ).
tff(c_383,plain,
on_path('#skF_12','#skF_13'),
inference(splitRight,[status(thm)],[c_375]) ).
tff(c_385,plain,
! [V1_26,V2_27] :
( edge('#skF_12')
| ~ path(V1_26,V2_27,'#skF_13') ),
inference(resolution,[status(thm)],[c_383,c_62]) ).
tff(c_388,plain,
! [V1_26,V2_27] : ~ path(V1_26,V2_27,'#skF_13'),
inference(negUnitSimplification,[status(thm)],[c_290,c_385]) ).
tff(c_390,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_388,c_202]) ).
tff(c_391,plain,
( ( '#skF_11' = '#skF_12' )
| ( '#skF_10' = '#skF_9' ) ),
inference(splitRight,[status(thm)],[c_283]) ).
tff(c_397,plain,
'#skF_10' = '#skF_9',
inference(splitLeft,[status(thm)],[c_391]) ).
tff(c_400,plain,
shortest_path('#skF_9','#skF_9','#skF_13'),
inference(demodulation,[status(thm),theory(equality)],[c_397,c_146]) ).
tff(c_403,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_102,c_400]) ).
tff(c_404,plain,
'#skF_11' = '#skF_12',
inference(splitRight,[status(thm)],[c_391]) ).
tff(c_408,plain,
precedes('#skF_12','#skF_12','#skF_13'),
inference(demodulation,[status(thm),theory(equality)],[c_404,c_144]) ).
tff(c_518,plain,
! [V1_327,E2_328,P_326,V2_329,E1_330] :
( ~ precedes(E2_328,E1_330,P_326)
| ~ precedes(E1_330,E2_328,P_326)
| ~ shortest_path(V1_327,V2_329,P_326) ),
inference(cnfTransformation,[status(thm)],[f_214]) ).
tff(c_520,plain,
! [V1_327,V2_329] :
( ~ precedes('#skF_12','#skF_12','#skF_13')
| ~ shortest_path(V1_327,V2_329,'#skF_13') ),
inference(resolution,[status(thm)],[c_408,c_518]) ).
tff(c_523,plain,
! [V1_327,V2_329] : ~ shortest_path(V1_327,V2_329,'#skF_13'),
inference(demodulation,[status(thm),theory(equality)],[c_408,c_520]) ).
tff(c_525,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_523,c_146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GRA003+1 : TPTP v9.0.0. Bugfixed v3.2.0.
% 0.07/0.12 % 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
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Apr 7 20:49:34 EDT 2025
% 0.12/0.33 % CPUTime :
% 4.50/2.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.68/2.04
% 4.68/2.04 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------