TSTP Solution File: NUM009-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM009-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 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 : n027.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 10:50:50 EDT 2023
% Result : Unsatisfiable 7.97s 2.79s
% Output : CNFRefutation 7.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 115
% Syntax : Number of formulae : 124 ( 7 unt; 110 typ; 0 def)
% Number of atoms : 23 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 9 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 183 ( 98 >; 85 *; 0 +; 0 <<)
% Number of predicates : 20 ( 19 usr; 1 prp; 0-5 aty)
% Number of functors : 91 ( 91 usr; 12 con; 0-5 aty)
% Number of variables : 8 (; 8 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ homomorphism > inverse > maps > identity > subset > proper_subset > member > group > disjoint > commutes > closed > associative > single_valued_set > relation > ordered_pair_predicate > one_to_one_function > little_set > function > finite > f33 > f32 > f38 > f37 > f31 > f30 > f29 > f28 > f22 > apply_to_two_arguments > union > restrict > ordered_pair > non_ordered_pair > intersection > image > f9 > f8 > f7 > f6 > f53 > f52 > f51 > f50 > f5 > f48 > f47 > f46 > f45 > f43 > f42 > f41 > f40 > f4 > f39 > f36 > f35 > f34 > f27 > f23 > f17 > f16 > f14 > f13 > f12 > f11 > f10 > f1 > cross_product > compose > apply > #nlpp > successor > singleton_set > sigma > second > rotate_right > range_of > powerset > flip_range_of > first > f59 > f58 > f57 > f56 > f55 > f54 > f49 > f44 > f3 > f26 > f24 > f21 > f20 > f2 > f19 > f18 > domain_of > converse > complement > universal_set > twin_prime_numbers > times > prime_numbers > plus > natural_numbers > infinity > identity_relation > f25 > even_numbers > estin > empty_set
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(f3,type,
f3: $i > $i ).
tff(f11,type,
f11: ( $i * $i ) > $i ).
tff(f5,type,
f5: ( $i * $i ) > $i ).
tff(f54,type,
f54: $i > $i ).
tff(flip_range_of,type,
flip_range_of: $i > $i ).
tff(f59,type,
f59: $i > $i ).
tff(f45,type,
f45: ( $i * $i ) > $i ).
tff(relation,type,
relation: $i > $o ).
tff(f18,type,
f18: $i > $i ).
tff(plus,type,
plus: $i ).
tff(f36,type,
f36: ( $i * $i ) > $i ).
tff(f52,type,
f52: ( $i * $i ) > $i ).
tff(f39,type,
f39: ( $i * $i ) > $i ).
tff(f12,type,
f12: ( $i * $i ) > $i ).
tff(even_numbers,type,
even_numbers: $i ).
tff(natural_numbers,type,
natural_numbers: $i ).
tff(estin,type,
estin: $i ).
tff(ordered_pair_predicate,type,
ordered_pair_predicate: $i > $o ).
tff(maps,type,
maps: ( $i * $i * $i ) > $o ).
tff(identity,type,
identity: ( $i * $i * $i ) > $o ).
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff(f13,type,
f13: ( $i * $i ) > $i ).
tff(times,type,
times: $i ).
tff(f9,type,
f9: ( $i * $i ) > $i ).
tff(associative,type,
associative: ( $i * $i ) > $o ).
tff(one_to_one_function,type,
one_to_one_function: $i > $o ).
tff(f14,type,
f14: ( $i * $i ) > $i ).
tff(finite,type,
finite: $i > $o ).
tff(f55,type,
f55: $i > $i ).
tff(apply_to_two_arguments,type,
apply_to_two_arguments: ( $i * $i * $i ) > $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff(f58,type,
f58: $i > $i ).
tff(f25,type,
f25: $i ).
tff(intersection,type,
intersection: ( $i * $i ) > $i ).
tff(second,type,
second: $i > $i ).
tff(union,type,
union: ( $i * $i ) > $i ).
tff(function,type,
function: $i > $o ).
tff(f30,type,
f30: ( $i * $i * $i ) > $i ).
tff(f20,type,
f20: $i > $i ).
tff(f32,type,
f32: ( $i * $i * $i * $i * $i ) > $i ).
tff(f56,type,
f56: $i > $i ).
tff(f17,type,
f17: ( $i * $i ) > $i ).
tff(f49,type,
f49: $i > $i ).
tff(f48,type,
f48: ( $i * $i ) > $i ).
tff(single_valued_set,type,
single_valued_set: $i > $o ).
tff(f44,type,
f44: $i > $i ).
tff(converse,type,
converse: $i > $i ).
tff(f38,type,
f38: ( $i * $i * $i * $i ) > $i ).
tff(proper_subset,type,
proper_subset: ( $i * $i ) > $o ).
tff(cross_product,type,
cross_product: ( $i * $i ) > $i ).
tff(group,type,
group: ( $i * $i ) > $o ).
tff(f24,type,
f24: $i > $i ).
tff(f7,type,
f7: ( $i * $i ) > $i ).
tff(f26,type,
f26: $i > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(singleton_set,type,
singleton_set: $i > $i ).
tff(f22,type,
f22: ( $i * $i * $i ) > $i ).
tff(f2,type,
f2: $i > $i ).
tff(f31,type,
f31: ( $i * $i * $i ) > $i ).
tff(complement,type,
complement: $i > $i ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff(f51,type,
f51: ( $i * $i ) > $i ).
tff(commutes,type,
commutes: ( $i * $i ) > $o ).
tff(f28,type,
f28: ( $i * $i * $i ) > $i ).
tff(f35,type,
f35: ( $i * $i ) > $i ).
tff(disjoint,type,
disjoint: ( $i * $i ) > $o ).
tff(restrict,type,
restrict: ( $i * $i ) > $i ).
tff(first,type,
first: $i > $i ).
tff(sigma,type,
sigma: $i > $i ).
tff(f46,type,
f46: ( $i * $i ) > $i ).
tff(f42,type,
f42: ( $i * $i ) > $i ).
tff(little_set,type,
little_set: $i > $o ).
tff(f33,type,
f33: ( $i * $i * $i * $i * $i ) > $i ).
tff(f8,type,
f8: ( $i * $i ) > $i ).
tff(empty_set,type,
empty_set: $i ).
tff(f47,type,
f47: ( $i * $i ) > $i ).
tff(f21,type,
f21: $i > $i ).
tff(image,type,
image: ( $i * $i ) > $i ).
tff(range_of,type,
range_of: $i > $i ).
tff(f57,type,
f57: $i > $i ).
tff(f4,type,
f4: ( $i * $i ) > $i ).
tff(f23,type,
f23: ( $i * $i ) > $i ).
tff(non_ordered_pair,type,
non_ordered_pair: ( $i * $i ) > $i ).
tff(f29,type,
f29: ( $i * $i * $i ) > $i ).
tff(compose,type,
compose: ( $i * $i ) > $i ).
tff(f43,type,
f43: ( $i * $i ) > $i ).
tff(f40,type,
f40: ( $i * $i ) > $i ).
tff(f16,type,
f16: ( $i * $i ) > $i ).
tff(f53,type,
f53: ( $i * $i ) > $i ).
tff(domain_of,type,
domain_of: $i > $i ).
tff(f10,type,
f10: ( $i * $i ) > $i ).
tff(f27,type,
f27: ( $i * $i ) > $i ).
tff(closed,type,
closed: ( $i * $i ) > $o ).
tff(twin_prime_numbers,type,
twin_prime_numbers: $i ).
tff(prime_numbers,type,
prime_numbers: $i ).
tff(f50,type,
f50: ( $i * $i ) > $i ).
tff(infinity,type,
infinity: $i ).
tff(homomorphism,type,
homomorphism: ( $i * $i * $i * $i * $i ) > $o ).
tff(powerset,type,
powerset: $i > $i ).
tff(f37,type,
f37: ( $i * $i * $i ) > $i ).
tff(f19,type,
f19: $i > $i ).
tff(inverse,type,
inverse: ( $i * $i * $i * $i ) > $o ).
tff(universal_set,type,
universal_set: $i ).
tff(successor,type,
successor: $i > $i ).
tff(f41,type,
f41: ( $i * $i ) > $i ).
tff(f34,type,
f34: ( $i * $i ) > $i ).
tff(rotate_right,type,
rotate_right: $i > $i ).
tff(identity_relation,type,
identity_relation: $i ).
tff(f1,type,
f1: ( $i * $i ) > $i ).
tff(f6,type,
f6: ( $i * $i ) > $i ).
tff(f_1770,axiom,
~ member(empty_set,natural_numbers),
file(unknown,unknown) ).
tff(f_450,axiom,
member(empty_set,infinity),
file(unknown,unknown) ).
tff(f_54,axiom,
! [X,Y] :
( ~ member(X,Y)
| little_set(X) ),
file(unknown,unknown) ).
tff(f_1255,axiom,
! [Z] :
( member(Z,natural_numbers)
| ~ little_set(Z)
| member(empty_set,f44(Z)) ),
file(unknown,unknown) ).
tff(f_1270,axiom,
! [Z] :
( member(Z,natural_numbers)
| ~ member(Z,f44(Z)) ),
file(unknown,unknown) ).
tff(c_440,plain,
~ member(empty_set,natural_numbers),
inference(cnfTransformation,[status(thm)],[f_1770]) ).
tff(c_122,plain,
member(empty_set,infinity),
inference(cnfTransformation,[status(thm)],[f_450]) ).
tff(c_454,plain,
! [X_495,Y_496] :
( little_set(X_495)
| ~ member(X_495,Y_496) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_458,plain,
little_set(empty_set),
inference(resolution,[status(thm)],[c_122,c_454]) ).
tff(c_2493,plain,
! [Z_681] :
( member(empty_set,f44(Z_681))
| ~ little_set(Z_681)
| member(Z_681,natural_numbers) ),
inference(cnfTransformation,[status(thm)],[f_1255]) ).
tff(c_342,plain,
! [Z_403] :
( ~ member(Z_403,f44(Z_403))
| member(Z_403,natural_numbers) ),
inference(cnfTransformation,[status(thm)],[f_1270]) ).
tff(c_2497,plain,
( ~ little_set(empty_set)
| member(empty_set,natural_numbers) ),
inference(resolution,[status(thm)],[c_2493,c_342]) ).
tff(c_2506,plain,
member(empty_set,natural_numbers),
inference(demodulation,[status(thm),theory(equality)],[c_458,c_2497]) ).
tff(c_2508,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_440,c_2506]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM009-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 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
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 3 15:35:23 EDT 2023
% 0.13/0.35 % CPUTime :
% 7.97/2.79 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.97/2.80
% 7.97/2.80 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.97/2.83
% 7.97/2.83 Inference rules
% 7.97/2.83 ----------------------
% 7.97/2.83 #Ref : 0
% 7.97/2.83 #Sup : 404
% 7.97/2.83 #Fact : 0
% 7.97/2.83 #Define : 0
% 7.97/2.83 #Split : 13
% 7.97/2.83 #Chain : 0
% 7.97/2.83 #Close : 0
% 7.97/2.83
% 7.97/2.83 Ordering : KBO
% 7.97/2.83
% 7.97/2.83 Simplification rules
% 7.97/2.83 ----------------------
% 7.97/2.83 #Subsume : 25
% 7.97/2.83 #Demod : 49
% 7.97/2.83 #Tautology : 61
% 7.97/2.83 #SimpNegUnit : 3
% 7.97/2.83 #BackRed : 13
% 7.97/2.83
% 7.97/2.83 #Partial instantiations: 0
% 7.97/2.83 #Strategies tried : 1
% 7.97/2.83
% 7.97/2.83 Timing (in seconds)
% 7.97/2.83 ----------------------
% 7.97/2.83 Preprocessing : 0.97
% 7.97/2.83 Parsing : 0.52
% 7.97/2.83 CNF conversion : 0.09
% 7.97/2.83 Main loop : 0.80
% 7.97/2.83 Inferencing : 0.25
% 7.97/2.83 Reduction : 0.25
% 7.97/2.83 Demodulation : 0.16
% 7.97/2.83 BG Simplification : 0.07
% 7.97/2.83 Subsumption : 0.17
% 7.97/2.83 Abstraction : 0.03
% 7.97/2.83 MUC search : 0.00
% 7.97/2.83 Cooper : 0.00
% 7.97/2.83 Total : 1.82
% 7.97/2.83 Index Insertion : 0.00
% 7.97/2.83 Index Deletion : 0.00
% 7.97/2.83 Index Matching : 0.00
% 7.97/2.83 BG Taut test : 0.00
%------------------------------------------------------------------------------