%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRA002+3 : 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 8.94s 3.11s
% Output : CNFRefutation 9.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 107 ( 17 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 114 ( 48 ~; 45 |; 10 &)
% ( 1 <=>; 9 =>; 1 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 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 : 24 ( 24 usr; 9 con; 0-5 aty)
% Number of variables : 95 ( 92 !; 3 ?; 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_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_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_272,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/sandbox2/benchmark/theBenchmark.p',maximal_path_length) ).
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_238,axiom,
! [V1,V2,P] :
( path(V1,V2,P)
=> ( number_of_in(sequential_pairs,P) = minus(length_of(P),n1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',path_length_sequential_pairs) ).
tff(f_252,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(f_173,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_defn) ).
tff(f_265,lemma,
( complete
=> ! [V1,V2,E1,E2,P] :
( ( shortest_path(V1,V2,P)
& precedes(E1,E2,P)
& sequential(E1,E2) )
=> ? [E3] : triangle(E1,E2,E3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sequential_is_triangle) ).
tff(f_254,axiom,
! [Things,InThese] : less_or_equal(number_of_in(Things,InThese),number_of_in(Things,graph)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',graph_has_them_all) ).
tff(c_146,plain,
shortest_path('#skF_11','#skF_12','#skF_10'),
inference(cnfTransformation,[status(thm)],[f_272]) ).
tff(c_180,plain,
! [V1_139,V2_140,SP_141] :
( path(V1_139,V2_140,SP_141)
| ~ shortest_path(V1_139,V2_140,SP_141) ),
inference(cnfTransformation,[status(thm)],[f_201]) ).
tff(c_184,plain,
path('#skF_11','#skF_12','#skF_10'),
inference(resolution,[status(thm)],[c_146,c_180]) ).
tff(c_229,plain,
! [P_161,V1_162,V2_163] :
( ( minus(length_of(P_161),n1) = number_of_in(sequential_pairs,P_161) )
| ~ path(V1_162,V2_163,P_161) ),
inference(cnfTransformation,[status(thm)],[f_238]) ).
tff(c_232,plain,
minus(length_of('#skF_10'),n1) = number_of_in(sequential_pairs,'#skF_10'),
inference(resolution,[status(thm)],[c_184,c_229]) ).
tff(c_144,plain,
~ less_or_equal(minus(length_of('#skF_10'),n1),number_of_in(triangles,graph)),
inference(cnfTransformation,[status(thm)],[f_272]) ).
tff(c_233,plain,
~ less_or_equal(number_of_in(sequential_pairs,'#skF_10'),number_of_in(triangles,graph)),
inference(demodulation,[status(thm),theory(equality)],[c_232,c_144]) ).
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_252]) ).
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_252]) ).
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_252]) ).
tff(c_584,plain,
! [P_239,V1_237,E2_240,V2_236,E1_238] :
( ~ sequential(E1_238,E2_240)
| precedes(E1_238,E2_240,P_239)
| ~ on_path(E2_240,P_239)
| ~ on_path(E1_238,P_239)
| ~ path(V1_237,V2_236,P_239) ),
inference(cnfTransformation,[status(thm)],[f_173]) ).
tff(c_590,plain,
! [E1_238,E2_240] :
( ~ sequential(E1_238,E2_240)
| precedes(E1_238,E2_240,'#skF_10')
| ~ on_path(E2_240,'#skF_10')
| ~ on_path(E1_238,'#skF_10') ),
inference(resolution,[status(thm)],[c_184,c_584]) ).
tff(c_148,plain,
complete,
inference(cnfTransformation,[status(thm)],[f_272]) ).
tff(c_142,plain,
! [E2_98,V1_95,P_99,V2_96,E1_97] :
( triangle(E1_97,E2_98,'#skF_9'(E2_98,E1_97,P_99,V1_95,V2_96))
| ~ sequential(E1_97,E2_98)
| ~ precedes(E1_97,E2_98,P_99)
| ~ shortest_path(V1_95,V2_96,P_99)
| ~ complete ),
inference(cnfTransformation,[status(thm)],[f_265]) ).
tff(c_951,plain,
! [E1_342,E2_341,V2_345,V1_344,P_343] :
( triangle(E1_342,E2_341,'#skF_9'(E2_341,E1_342,P_343,V1_344,V2_345))
| ~ sequential(E1_342,E2_341)
| ~ precedes(E1_342,E2_341,P_343)
| ~ shortest_path(V1_344,V2_345,P_343) ),
inference(demodulation,[status(thm),theory(equality)],[c_148,c_142]) ).
tff(c_132,plain,
! [P_84,V1_85,V2_86,E3_92] :
( ~ triangle('#skF_7'(P_84,V1_85,V2_86),'#skF_8'(P_84,V1_85,V2_86),E3_92)
| ( 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_252]) ).
tff(c_3390,plain,
! [P_1032,V2_1034,V1_1036,V2_1033,P_1037,V1_1035] :
( ( number_of_in(triangles,P_1032) = number_of_in(sequential_pairs,P_1032) )
| ~ path(V1_1035,V2_1033,P_1032)
| ~ sequential('#skF_7'(P_1032,V1_1035,V2_1033),'#skF_8'(P_1032,V1_1035,V2_1033))
| ~ precedes('#skF_7'(P_1032,V1_1035,V2_1033),'#skF_8'(P_1032,V1_1035,V2_1033),P_1037)
| ~ shortest_path(V1_1036,V2_1034,P_1037) ),
inference(resolution,[status(thm)],[c_951,c_132]) ).
tff(c_3410,plain,
! [P_1032,V2_1034,V1_1036,V2_1033,V1_1035] :
( ( number_of_in(triangles,P_1032) = number_of_in(sequential_pairs,P_1032) )
| ~ path(V1_1035,V2_1033,P_1032)
| ~ shortest_path(V1_1036,V2_1034,'#skF_10')
| ~ sequential('#skF_7'(P_1032,V1_1035,V2_1033),'#skF_8'(P_1032,V1_1035,V2_1033))
| ~ on_path('#skF_8'(P_1032,V1_1035,V2_1033),'#skF_10')
| ~ on_path('#skF_7'(P_1032,V1_1035,V2_1033),'#skF_10') ),
inference(resolution,[status(thm)],[c_590,c_3390]) ).
tff(c_3692,plain,
! [V1_1036,V2_1034] : ~ shortest_path(V1_1036,V2_1034,'#skF_10'),
inference(splitLeft,[status(thm)],[c_3410]) ).
tff(c_3694,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3692,c_146]) ).
tff(c_3696,plain,
! [P_1126,V1_1127,V2_1128] :
( ( number_of_in(triangles,P_1126) = number_of_in(sequential_pairs,P_1126) )
| ~ path(V1_1127,V2_1128,P_1126)
| ~ sequential('#skF_7'(P_1126,V1_1127,V2_1128),'#skF_8'(P_1126,V1_1127,V2_1128))
| ~ on_path('#skF_8'(P_1126,V1_1127,V2_1128),'#skF_10')
| ~ on_path('#skF_7'(P_1126,V1_1127,V2_1128),'#skF_10') ),
inference(splitRight,[status(thm)],[c_3410]) ).
tff(c_3705,plain,
! [P_1129,V1_1130,V2_1131] :
( ~ on_path('#skF_8'(P_1129,V1_1130,V2_1131),'#skF_10')
| ~ on_path('#skF_7'(P_1129,V1_1130,V2_1131),'#skF_10')
| ( number_of_in(triangles,P_1129) = number_of_in(sequential_pairs,P_1129) )
| ~ path(V1_1130,V2_1131,P_1129) ),
inference(resolution,[status(thm)],[c_134,c_3696]) ).
tff(c_3710,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_3705]) ).
tff(c_3712,plain,
! [V1_1132,V2_1133] :
( ~ on_path('#skF_8'('#skF_10',V1_1132,V2_1133),'#skF_10')
| ~ path(V1_1132,V2_1133,'#skF_10') ),
inference(splitLeft,[status(thm)],[c_3710]) ).
tff(c_3717,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_3712]) ).
tff(c_3742,plain,
! [V1_85,V2_86] : ~ path(V1_85,V2_86,'#skF_10'),
inference(splitLeft,[status(thm)],[c_3717]) ).
tff(c_3744,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3742,c_184]) ).
tff(c_3745,plain,
number_of_in(triangles,'#skF_10') = number_of_in(sequential_pairs,'#skF_10'),
inference(splitRight,[status(thm)],[c_3717]) ).
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_3749,plain,
less_or_equal(number_of_in(sequential_pairs,'#skF_10'),number_of_in(triangles,graph)),
inference(superposition,[status(thm),theory(equality)],[c_3745,c_140]) ).
tff(c_3753,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_233,c_3749]) ).
tff(c_3754,plain,
number_of_in(triangles,'#skF_10') = number_of_in(sequential_pairs,'#skF_10'),
inference(splitRight,[status(thm)],[c_3710]) ).
tff(c_3767,plain,
less_or_equal(number_of_in(sequential_pairs,'#skF_10'),number_of_in(triangles,graph)),
inference(superposition,[status(thm),theory(equality)],[c_3754,c_140]) ).
tff(c_3771,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_233,c_3767]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRA002+3 : TPTP v9.0.0. Bugfixed v3.2.0.
% 0.03/0.13 % 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
% 0.12/0.33 % 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 20:49:49 EDT 2025
% 0.12/0.34 % CPUTime :
% 8.94/3.11 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.94/3.11
% 8.94/3.11 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------