TSTP Solution File: NUM409+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM409+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/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 : n028.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 10:51:36 EDT 2023
% Result : Theorem 5.71s 2.23s
% Output : CNFRefutation 5.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 52
% Syntax : Number of formulae : 83 ( 21 unt; 43 typ; 0 def)
% Number of atoms : 81 ( 12 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 67 ( 26 ~; 22 |; 12 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 38 ( 27 >; 11 *; 0 +; 0 <<)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 16 con; 0-3 aty)
% Number of variables : 26 (; 24 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ transfinite_sequence_of > subset > in > element > with_non_empty_elements > transfinite_sequence > relation_non_empty > relation_empty_yielding > relation > ordinal > one_to_one > function > epsilon_transitive > epsilon_connected > empty > unordered_pair > ordered_pair > #nlpp > singleton > relation_rng > relation_dom > powerset > empty_set > #skF_5 > #skF_20 > #skF_18 > #skF_17 > #skF_11 > #skF_15 > #skF_19 > #skF_4 > #skF_7 > #skF_3 > #skF_10 > #skF_16 > #skF_14 > #skF_13 > #skF_21 > #skF_9 > #skF_8 > #skF_2 > #skF_1 > #skF_6 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(with_non_empty_elements,type,
with_non_empty_elements: $i > $o ).
tff(epsilon_connected,type,
epsilon_connected: $i > $o ).
tff('#skF_5',type,
'#skF_5': $i > $i ).
tff(relation,type,
relation: $i > $o ).
tff('#skF_20',type,
'#skF_20': $i ).
tff(transfinite_sequence_of,type,
transfinite_sequence_of: ( $i * $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(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(epsilon_transitive,type,
epsilon_transitive: $i > $o ).
tff(element,type,
element: ( $i * $i ) > $o ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
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_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff('#skF_16',type,
'#skF_16': $i ).
tff(ordinal,type,
ordinal: $i > $o ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_14',type,
'#skF_14': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_13',type,
'#skF_13': $i ).
tff(empty,type,
empty: $i > $o ).
tff('#skF_21',type,
'#skF_21': $i ).
tff('#skF_9',type,
'#skF_9': $i ).
tff(empty_set,type,
empty_set: $i ).
tff(relation_dom,type,
relation_dom: $i > $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(powerset,type,
powerset: $i > $i ).
tff(relation_rng,type,
relation_rng: $i > $i ).
tff(transfinite_sequence,type,
transfinite_sequence: $i > $o ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_6',type,
'#skF_6': $i > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_217,axiom,
? [A] :
( relation(A)
& function(A)
& one_to_one(A)
& empty(A)
& epsilon_transitive(A)
& epsilon_connected(A)
& ordinal(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_ordinal1) ).
tff(f_175,axiom,
! [A] :
( empty(A)
=> ( empty(relation_dom(A))
& relation(relation_dom(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
tff(f_306,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
tff(f_195,axiom,
? [A] :
( empty(A)
& relation(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
tff(f_94,axiom,
! [A] :
( ( relation(A)
& function(A) )
=> ( transfinite_sequence(A)
<=> ordinal(relation_dom(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_ordinal1) ).
tff(f_276,axiom,
! [A] : subset(empty_set,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
tff(f_181,axiom,
! [A] :
( empty(A)
=> ( empty(relation_rng(A))
& relation(relation_rng(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
tff(f_104,axiom,
! [A,B] :
( ( relation(B)
& function(B)
& transfinite_sequence(B) )
=> ( transfinite_sequence_of(B,A)
<=> subset(relation_rng(B),A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_ordinal1) ).
tff(f_283,negated_conjecture,
~ ! [A] : transfinite_sequence_of(empty_set,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_ordinal1) ).
tff(c_138,plain,
relation('#skF_12'),
inference(cnfTransformation,[status(thm)],[f_217]) ).
tff(c_136,plain,
function('#skF_12'),
inference(cnfTransformation,[status(thm)],[f_217]) ).
tff(c_126,plain,
ordinal('#skF_12'),
inference(cnfTransformation,[status(thm)],[f_217]) ).
tff(c_132,plain,
empty('#skF_12'),
inference(cnfTransformation,[status(thm)],[f_217]) ).
tff(c_376,plain,
! [A_119] :
( empty(relation_dom(A_119))
| ~ empty(A_119) ),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_218,plain,
! [A_93] :
( ( empty_set = A_93 )
| ~ empty(A_93) ),
inference(cnfTransformation,[status(thm)],[f_306]) ).
tff(c_237,plain,
empty_set = '#skF_12',
inference(resolution,[status(thm)],[c_132,c_218]) ).
tff(c_116,plain,
empty('#skF_9'),
inference(cnfTransformation,[status(thm)],[f_195]) ).
tff(c_236,plain,
empty_set = '#skF_9',
inference(resolution,[status(thm)],[c_116,c_218]) ).
tff(c_257,plain,
'#skF_9' = '#skF_12',
inference(demodulation,[status(thm),theory(equality)],[c_237,c_236]) ).
tff(c_204,plain,
! [A_85] :
( ( empty_set = A_85 )
| ~ empty(A_85) ),
inference(cnfTransformation,[status(thm)],[f_306]) ).
tff(c_240,plain,
! [A_85] :
( ( A_85 = '#skF_9' )
| ~ empty(A_85) ),
inference(demodulation,[status(thm),theory(equality)],[c_236,c_204]) ).
tff(c_344,plain,
! [A_85] :
( ( A_85 = '#skF_12' )
| ~ empty(A_85) ),
inference(demodulation,[status(thm),theory(equality)],[c_257,c_240]) ).
tff(c_418,plain,
! [A_123] :
( ( relation_dom(A_123) = '#skF_12' )
| ~ empty(A_123) ),
inference(resolution,[status(thm)],[c_376,c_344]) ).
tff(c_430,plain,
relation_dom('#skF_12') = '#skF_12',
inference(resolution,[status(thm)],[c_132,c_418]) ).
tff(c_889,plain,
! [A_154] :
( transfinite_sequence(A_154)
| ~ ordinal(relation_dom(A_154))
| ~ function(A_154)
| ~ relation(A_154) ),
inference(cnfTransformation,[status(thm)],[f_94]) ).
tff(c_898,plain,
( transfinite_sequence('#skF_12')
| ~ ordinal('#skF_12')
| ~ function('#skF_12')
| ~ relation('#skF_12') ),
inference(superposition,[status(thm),theory(equality)],[c_430,c_889]) ).
tff(c_910,plain,
transfinite_sequence('#skF_12'),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_136,c_126,c_898]) ).
tff(c_188,plain,
! [A_75] : subset(empty_set,A_75),
inference(cnfTransformation,[status(thm)],[f_276]) ).
tff(c_241,plain,
! [A_75] : subset('#skF_9',A_75),
inference(demodulation,[status(thm),theory(equality)],[c_236,c_188]) ).
tff(c_297,plain,
! [A_75] : subset('#skF_12',A_75),
inference(demodulation,[status(thm),theory(equality)],[c_257,c_241]) ).
tff(c_370,plain,
! [A_116] :
( empty(relation_rng(A_116))
| ~ empty(A_116) ),
inference(cnfTransformation,[status(thm)],[f_181]) ).
tff(c_382,plain,
! [A_121] :
( ( relation_rng(A_121) = '#skF_12' )
| ~ empty(A_121) ),
inference(resolution,[status(thm)],[c_370,c_344]) ).
tff(c_394,plain,
relation_rng('#skF_12') = '#skF_12',
inference(resolution,[status(thm)],[c_132,c_382]) ).
tff(c_1039,plain,
! [B_179,A_180] :
( transfinite_sequence_of(B_179,A_180)
| ~ subset(relation_rng(B_179),A_180)
| ~ transfinite_sequence(B_179)
| ~ function(B_179)
| ~ relation(B_179) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_1048,plain,
! [A_180] :
( transfinite_sequence_of('#skF_12',A_180)
| ~ subset('#skF_12',A_180)
| ~ transfinite_sequence('#skF_12')
| ~ function('#skF_12')
| ~ relation('#skF_12') ),
inference(superposition,[status(thm),theory(equality)],[c_394,c_1039]) ).
tff(c_1058,plain,
! [A_180] : transfinite_sequence_of('#skF_12',A_180),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_136,c_910,c_297,c_1048]) ).
tff(c_194,plain,
~ transfinite_sequence_of(empty_set,'#skF_21'),
inference(cnfTransformation,[status(thm)],[f_283]) ).
tff(c_249,plain,
~ transfinite_sequence_of('#skF_9','#skF_21'),
inference(demodulation,[status(thm),theory(equality)],[c_236,c_194]) ).
tff(c_290,plain,
~ transfinite_sequence_of('#skF_12','#skF_21'),
inference(demodulation,[status(thm),theory(equality)],[c_257,c_249]) ).
tff(c_1062,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1058,c_290]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM409+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % 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
% 0.14/0.36 % Computer : n028.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 15:37:54 EDT 2023
% 0.14/0.36 % CPUTime :
% 5.71/2.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.71/2.23
% 5.71/2.23 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.71/2.27
% 5.71/2.27 Inference rules
% 5.71/2.27 ----------------------
% 5.71/2.27 #Ref : 0
% 5.71/2.27 #Sup : 181
% 5.71/2.27 #Fact : 0
% 5.71/2.27 #Define : 0
% 5.71/2.27 #Split : 12
% 5.71/2.27 #Chain : 0
% 5.71/2.27 #Close : 0
% 5.71/2.27
% 5.71/2.27 Ordering : KBO
% 5.71/2.27
% 5.71/2.27 Simplification rules
% 5.71/2.27 ----------------------
% 5.71/2.27 #Subsume : 19
% 5.71/2.27 #Demod : 137
% 5.71/2.27 #Tautology : 104
% 5.71/2.27 #SimpNegUnit : 7
% 5.71/2.27 #BackRed : 19
% 5.71/2.27
% 5.71/2.27 #Partial instantiations: 0
% 5.71/2.27 #Strategies tried : 1
% 5.71/2.27
% 5.71/2.27 Timing (in seconds)
% 5.71/2.27 ----------------------
% 5.71/2.27 Preprocessing : 0.61
% 5.71/2.27 Parsing : 0.31
% 5.71/2.27 CNF conversion : 0.06
% 5.71/2.27 Main loop : 0.59
% 5.71/2.27 Inferencing : 0.18
% 5.71/2.27 Reduction : 0.21
% 5.71/2.27 Demodulation : 0.15
% 5.71/2.27 BG Simplification : 0.03
% 5.71/2.27 Subsumption : 0.12
% 5.71/2.27 Abstraction : 0.02
% 5.71/2.27 MUC search : 0.00
% 5.71/2.27 Cooper : 0.00
% 5.71/2.27 Total : 1.25
% 5.71/2.27 Index Insertion : 0.00
% 5.71/2.27 Index Deletion : 0.00
% 5.71/2.27 Index Matching : 0.00
% 5.71/2.27 BG Taut test : 0.00
%------------------------------------------------------------------------------