TSTP Solution File: NUM386+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM386+1 : TPTP v8.1.2. Released 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 : n009.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 10:51:34 EDT 2023
% Result : Theorem 9.37s 3.28s
% Output : CNFRefutation 9.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 35
% Syntax : Number of formulae : 107 ( 45 unt; 31 typ; 0 def)
% Number of atoms : 118 ( 24 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 83 ( 41 ~; 37 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 25 ( 16 >; 9 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 15 con; 0-3 aty)
% Number of variables : 54 (; 54 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > element > relation_non_empty > relation_empty_yielding > relation > one_to_one > function > empty > set_union2 > #nlpp > succ > singleton > empty_set > #skF_5 > #skF_18 > #skF_17 > #skF_11 > #skF_15 > #skF_19 > #skF_4 > #skF_7 > #skF_10 > #skF_16 > #skF_14 > #skF_6 > #skF_13 > #skF_9 > #skF_8 > #skF_3 > #skF_2 > #skF_1 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff(relation,type,
relation: $i > $o ).
tff('#skF_18',type,
'#skF_18': $i ).
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_17',type,
'#skF_17': $i ).
tff('#skF_11',type,
'#skF_11': $i ).
tff(relation_non_empty,type,
relation_non_empty: $i > $o ).
tff('#skF_15',type,
'#skF_15': $i ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(one_to_one,type,
one_to_one: $i > $o ).
tff(function,type,
function: $i > $o ).
tff('#skF_19',type,
'#skF_19': $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff(relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
tff('#skF_10',type,
'#skF_10': $i ).
tff('#skF_16',type,
'#skF_16': $i ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_14',type,
'#skF_14': $i ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_13',type,
'#skF_13': $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_9',type,
'#skF_9': $i ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(set_union2,type,
set_union2: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(succ,type,
succ: $i > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_62,axiom,
! [A,B] :
( ( B = singleton(A) )
<=> ! [C] :
( in(C,B)
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
tff(f_55,axiom,
! [A] : ( succ(A) = set_union2(A,singleton(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).
tff(f_71,axiom,
! [A,B,C] :
( ( C = set_union2(A,B) )
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
tff(f_159,negated_conjecture,
~ ! [A,B] :
( in(A,succ(B))
<=> ( in(A,B)
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_ordinal1) ).
tff(c_20,plain,
! [C_13] : in(C_13,singleton(C_13)),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_16,plain,
! [A_8] : ( set_union2(A_8,singleton(A_8)) = succ(A_8) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_10023,plain,
! [D_792,B_793,A_794] :
( ~ in(D_792,B_793)
| in(D_792,set_union2(A_794,B_793)) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_11076,plain,
! [D_874,A_875] :
( ~ in(D_874,singleton(A_875))
| in(D_874,succ(A_875)) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_10023]) ).
tff(c_7589,plain,
! [D_598,B_599,A_600] :
( ~ in(D_598,B_599)
| in(D_598,set_union2(A_600,B_599)) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_8690,plain,
! [D_681,A_682] :
( ~ in(D_681,singleton(A_682))
| in(D_681,succ(A_682)) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_7589]) ).
tff(c_118,plain,
( ( '#skF_17' = '#skF_16' )
| in('#skF_16','#skF_17')
| ( '#skF_18' != '#skF_19' ) ),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_143,plain,
'#skF_18' != '#skF_19',
inference(splitLeft,[status(thm)],[c_118]) ).
tff(c_120,plain,
( ~ in('#skF_16',succ('#skF_17'))
| ~ in('#skF_18','#skF_19') ),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_144,plain,
~ in('#skF_18','#skF_19'),
inference(splitLeft,[status(thm)],[c_120]) ).
tff(c_2303,plain,
! [D_204,B_205,A_206] :
( ~ in(D_204,B_205)
| in(D_204,set_union2(A_206,B_205)) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_3520,plain,
! [D_293,A_294] :
( ~ in(D_293,singleton(A_294))
| in(D_293,succ(A_294)) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_2303]) ).
tff(c_126,plain,
( ( '#skF_17' = '#skF_16' )
| in('#skF_16','#skF_17')
| in('#skF_18',succ('#skF_19')) ),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_381,plain,
in('#skF_18',succ('#skF_19')),
inference(splitLeft,[status(thm)],[c_126]) ).
tff(c_747,plain,
! [D_95,B_96,A_97] :
( in(D_95,B_96)
| in(D_95,A_97)
| ~ in(D_95,set_union2(A_97,B_96)) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_2076,plain,
! [D_187,A_188] :
( in(D_187,singleton(A_188))
| in(D_187,A_188)
| ~ in(D_187,succ(A_188)) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_747]) ).
tff(c_2116,plain,
( in('#skF_18',singleton('#skF_19'))
| in('#skF_18','#skF_19') ),
inference(resolution,[status(thm)],[c_381,c_2076]) ).
tff(c_2131,plain,
in('#skF_18',singleton('#skF_19')),
inference(negUnitSimplification,[status(thm)],[c_144,c_2116]) ).
tff(c_18,plain,
! [C_13,A_9] :
( ( C_13 = A_9 )
| ~ in(C_13,singleton(A_9)) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_2140,plain,
'#skF_18' = '#skF_19',
inference(resolution,[status(thm)],[c_2131,c_18]) ).
tff(c_2155,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_143,c_2140]) ).
tff(c_2156,plain,
( in('#skF_16','#skF_17')
| ( '#skF_17' = '#skF_16' ) ),
inference(splitRight,[status(thm)],[c_126]) ).
tff(c_2159,plain,
'#skF_17' = '#skF_16',
inference(splitLeft,[status(thm)],[c_2156]) ).
tff(c_124,plain,
( ~ in('#skF_16',succ('#skF_17'))
| in('#skF_18',succ('#skF_19')) ),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_191,plain,
~ in('#skF_16',succ('#skF_17')),
inference(splitLeft,[status(thm)],[c_124]) ).
tff(c_2160,plain,
~ in('#skF_16',succ('#skF_16')),
inference(demodulation,[status(thm),theory(equality)],[c_2159,c_191]) ).
tff(c_3593,plain,
~ in('#skF_16',singleton('#skF_16')),
inference(resolution,[status(thm)],[c_3520,c_2160]) ).
tff(c_3631,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_20,c_3593]) ).
tff(c_3632,plain,
in('#skF_16','#skF_17'),
inference(splitRight,[status(thm)],[c_2156]) ).
tff(c_3690,plain,
! [D_301,A_302,B_303] :
( ~ in(D_301,A_302)
| in(D_301,set_union2(A_302,B_303)) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_3876,plain,
! [D_322,A_323] :
( ~ in(D_322,A_323)
| in(D_322,succ(A_323)) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_3690]) ).
tff(c_3906,plain,
~ in('#skF_16','#skF_17'),
inference(resolution,[status(thm)],[c_3876,c_191]) ).
tff(c_3921,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3632,c_3906]) ).
tff(c_3922,plain,
in('#skF_18',succ('#skF_19')),
inference(splitRight,[status(thm)],[c_124]) ).
tff(c_4485,plain,
! [D_372,B_373,A_374] :
( in(D_372,B_373)
| in(D_372,A_374)
| ~ in(D_372,set_union2(A_374,B_373)) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_6281,plain,
! [D_488,A_489] :
( in(D_488,singleton(A_489))
| in(D_488,A_489)
| ~ in(D_488,succ(A_489)) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_4485]) ).
tff(c_6321,plain,
( in('#skF_18',singleton('#skF_19'))
| in('#skF_18','#skF_19') ),
inference(resolution,[status(thm)],[c_3922,c_6281]) ).
tff(c_6339,plain,
in('#skF_18',singleton('#skF_19')),
inference(negUnitSimplification,[status(thm)],[c_144,c_6321]) ).
tff(c_6351,plain,
'#skF_18' = '#skF_19',
inference(resolution,[status(thm)],[c_6339,c_18]) ).
tff(c_6365,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_143,c_6351]) ).
tff(c_6367,plain,
in('#skF_18','#skF_19'),
inference(splitRight,[status(thm)],[c_120]) ).
tff(c_122,plain,
( ( '#skF_17' = '#skF_16' )
| in('#skF_16','#skF_17')
| ~ in('#skF_18','#skF_19') ),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_6370,plain,
( ( '#skF_17' = '#skF_16' )
| in('#skF_16','#skF_17') ),
inference(demodulation,[status(thm),theory(equality)],[c_6367,c_122]) ).
tff(c_6371,plain,
in('#skF_16','#skF_17'),
inference(splitLeft,[status(thm)],[c_6370]) ).
tff(c_6719,plain,
! [D_523,A_524,B_525] :
( ~ in(D_523,A_524)
| in(D_523,set_union2(A_524,B_525)) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_7116,plain,
! [D_561,A_562] :
( ~ in(D_561,A_562)
| in(D_561,succ(A_562)) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_6719]) ).
tff(c_6433,plain,
~ in('#skF_16',succ('#skF_17')),
inference(splitLeft,[status(thm)],[c_124]) ).
tff(c_7143,plain,
~ in('#skF_16','#skF_17'),
inference(resolution,[status(thm)],[c_7116,c_6433]) ).
tff(c_7157,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6371,c_7143]) ).
tff(c_7159,plain,
in('#skF_16',succ('#skF_17')),
inference(splitRight,[status(thm)],[c_124]) ).
tff(c_6366,plain,
~ in('#skF_16',succ('#skF_17')),
inference(splitRight,[status(thm)],[c_120]) ).
tff(c_7190,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_7159,c_6366]) ).
tff(c_7191,plain,
'#skF_17' = '#skF_16',
inference(splitRight,[status(thm)],[c_6370]) ).
tff(c_7286,plain,
~ in('#skF_16',succ('#skF_16')),
inference(demodulation,[status(thm),theory(equality)],[c_7191,c_6366]) ).
tff(c_8764,plain,
~ in('#skF_16',singleton('#skF_16')),
inference(resolution,[status(thm)],[c_8690,c_7286]) ).
tff(c_8791,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_20,c_8764]) ).
tff(c_8793,plain,
'#skF_18' = '#skF_19',
inference(splitRight,[status(thm)],[c_118]) ).
tff(c_116,plain,
( ~ in('#skF_16',succ('#skF_17'))
| ( '#skF_18' != '#skF_19' ) ),
inference(cnfTransformation,[status(thm)],[f_159]) ).
tff(c_142,plain,
'#skF_18' != '#skF_19',
inference(splitLeft,[status(thm)],[c_116]) ).
tff(c_8800,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8793,c_142]) ).
tff(c_8802,plain,
'#skF_18' = '#skF_19',
inference(splitRight,[status(thm)],[c_116]) ).
tff(c_8809,plain,
( ( '#skF_17' = '#skF_16' )
| in('#skF_16','#skF_17') ),
inference(demodulation,[status(thm),theory(equality)],[c_8802,c_118]) ).
tff(c_8810,plain,
in('#skF_16','#skF_17'),
inference(splitLeft,[status(thm)],[c_8809]) ).
tff(c_9219,plain,
! [D_718,A_719,B_720] :
( ~ in(D_718,A_719)
| in(D_718,set_union2(A_719,B_720)) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_9516,plain,
! [D_750,A_751] :
( ~ in(D_750,A_751)
| in(D_750,succ(A_751)) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_9219]) ).
tff(c_8801,plain,
~ in('#skF_16',succ('#skF_17')),
inference(splitRight,[status(thm)],[c_116]) ).
tff(c_9543,plain,
~ in('#skF_16','#skF_17'),
inference(resolution,[status(thm)],[c_9516,c_8801]) ).
tff(c_9557,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8810,c_9543]) ).
tff(c_9558,plain,
'#skF_17' = '#skF_16',
inference(splitRight,[status(thm)],[c_8809]) ).
tff(c_9581,plain,
~ in('#skF_16',succ('#skF_16')),
inference(demodulation,[status(thm),theory(equality)],[c_9558,c_8801]) ).
tff(c_11150,plain,
~ in('#skF_16',singleton('#skF_16')),
inference(resolution,[status(thm)],[c_11076,c_9581]) ).
tff(c_11177,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_20,c_11150]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM386+1 : TPTP v8.1.2. Released 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
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 3 15:03:23 EDT 2023
% 0.14/0.35 % CPUTime :
% 9.37/3.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.37/3.29
% 9.37/3.29 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.78/3.32
% 9.78/3.32 Inference rules
% 9.78/3.32 ----------------------
% 9.78/3.32 #Ref : 0
% 9.78/3.32 #Sup : 2598
% 9.78/3.32 #Fact : 10
% 9.78/3.32 #Define : 0
% 9.78/3.32 #Split : 62
% 9.78/3.32 #Chain : 0
% 9.78/3.32 #Close : 0
% 9.78/3.32
% 9.78/3.32 Ordering : KBO
% 9.78/3.32
% 9.78/3.32 Simplification rules
% 9.78/3.32 ----------------------
% 9.78/3.32 #Subsume : 739
% 9.78/3.32 #Demod : 398
% 9.78/3.32 #Tautology : 635
% 9.78/3.32 #SimpNegUnit : 75
% 9.78/3.32 #BackRed : 72
% 9.78/3.32
% 9.78/3.32 #Partial instantiations: 0
% 9.78/3.32 #Strategies tried : 1
% 9.78/3.32
% 9.78/3.32 Timing (in seconds)
% 9.78/3.32 ----------------------
% 9.78/3.32 Preprocessing : 0.58
% 9.78/3.32 Parsing : 0.28
% 9.78/3.32 CNF conversion : 0.05
% 9.78/3.32 Main loop : 1.63
% 9.78/3.33 Inferencing : 0.58
% 9.78/3.33 Reduction : 0.51
% 9.78/3.33 Demodulation : 0.35
% 9.78/3.33 BG Simplification : 0.06
% 9.78/3.33 Subsumption : 0.35
% 9.78/3.33 Abstraction : 0.06
% 9.78/3.33 MUC search : 0.00
% 9.78/3.33 Cooper : 0.00
% 9.78/3.33 Total : 2.27
% 9.78/3.33 Index Insertion : 0.00
% 9.78/3.33 Index Deletion : 0.00
% 9.78/3.33 Index Matching : 0.00
% 9.78/3.33 BG Taut test : 0.00
%------------------------------------------------------------------------------