TSTP Solution File: NUM390+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM390+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 : n010.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 10:51:35 EDT 2023
% Result : Theorem 5.54s 2.37s
% Output : CNFRefutation 5.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 40
% Syntax : Number of formulae : 71 ( 16 unt; 31 typ; 0 def)
% Number of atoms : 84 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 72 ( 28 ~; 25 |; 5 &)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 16 >; 4 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 15 con; 0-1 aty)
% Number of variables : 40 (; 40 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > proper_subset > in > element > relation_non_empty > relation_empty_yielding > relation > ordinal > one_to_one > function > epsilon_transitive > epsilon_connected > empty > #nlpp > powerset > empty_set > #skF_2 > #skF_11 > #skF_15 > #skF_1 > #skF_7 > #skF_10 > #skF_16 > #skF_14 > #skF_5 > #skF_6 > #skF_13 > #skF_3 > #skF_9 > #skF_8 > #skF_4 > #skF_12
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(epsilon_connected,type,
epsilon_connected: $i > $o ).
tff(relation,type,
relation: $i > $o ).
tff('#skF_2',type,
'#skF_2': $i > $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('#skF_1',type,
'#skF_1': $i > $i ).
tff(epsilon_transitive,type,
epsilon_transitive: $i > $o ).
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_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(ordinal,type,
ordinal: $i > $o ).
tff(proper_subset,type,
proper_subset: ( $i * $i ) > $o ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_14',type,
'#skF_14': $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff('#skF_13',type,
'#skF_13': $i ).
tff('#skF_3',type,
'#skF_3': $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_4',type,
'#skF_4': $i ).
tff(powerset,type,
powerset: $i > $i ).
tff('#skF_12',type,
'#skF_12': $i ).
tff(f_185,negated_conjecture,
~ ! [A] :
( epsilon_transitive(A)
=> ! [B] :
( ordinal(B)
=> ! [C] :
( ordinal(C)
=> ( ( subset(A,B)
& in(B,C) )
=> in(A,C) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_ordinal1) ).
tff(f_217,axiom,
! [A,B] :
~ ( in(A,B)
& empty(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
tff(f_191,axiom,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
tff(f_46,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_transitive(A)
& epsilon_connected(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
tff(f_75,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
tff(f_82,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( subset(A,B)
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
tff(f_170,axiom,
! [A] :
( epsilon_transitive(A)
=> ! [B] :
( ordinal(B)
=> ( proper_subset(A,B)
=> in(A,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_ordinal1) ).
tff(f_195,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
tff(f_201,axiom,
! [A,B,C] :
( ( in(A,B)
& element(B,powerset(C)) )
=> element(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
tff(c_110,plain,
in('#skF_15','#skF_16'),
inference(cnfTransformation,[status(thm)],[f_185]) ).
tff(c_215,plain,
! [B_59,A_60] :
( ~ empty(B_59)
| ~ in(A_60,B_59) ),
inference(cnfTransformation,[status(thm)],[f_217]) ).
tff(c_219,plain,
~ empty('#skF_16'),
inference(resolution,[status(thm)],[c_110,c_215]) ).
tff(c_422,plain,
! [A_96,B_97] :
( in(A_96,B_97)
| empty(B_97)
| ~ element(A_96,B_97) ),
inference(cnfTransformation,[status(thm)],[f_191]) ).
tff(c_108,plain,
~ in('#skF_14','#skF_16'),
inference(cnfTransformation,[status(thm)],[f_185]) ).
tff(c_451,plain,
( empty('#skF_16')
| ~ element('#skF_14','#skF_16') ),
inference(resolution,[status(thm)],[c_422,c_108]) ).
tff(c_462,plain,
~ element('#skF_14','#skF_16'),
inference(negUnitSimplification,[status(thm)],[c_219,c_451]) ).
tff(c_114,plain,
ordinal('#skF_16'),
inference(cnfTransformation,[status(thm)],[f_185]) ).
tff(c_142,plain,
! [A_53] :
( epsilon_transitive(A_53)
| ~ ordinal(A_53) ),
inference(cnfTransformation,[status(thm)],[f_46]) ).
tff(c_154,plain,
epsilon_transitive('#skF_16'),
inference(resolution,[status(thm)],[c_114,c_142]) ).
tff(c_22,plain,
! [B_13,A_10] :
( subset(B_13,A_10)
| ~ in(B_13,A_10)
| ~ epsilon_transitive(A_10) ),
inference(cnfTransformation,[status(thm)],[f_75]) ).
tff(c_118,plain,
epsilon_transitive('#skF_14'),
inference(cnfTransformation,[status(thm)],[f_185]) ).
tff(c_116,plain,
ordinal('#skF_15'),
inference(cnfTransformation,[status(thm)],[f_185]) ).
tff(c_112,plain,
subset('#skF_14','#skF_15'),
inference(cnfTransformation,[status(thm)],[f_185]) ).
tff(c_374,plain,
! [A_93,B_94] :
( proper_subset(A_93,B_94)
| ( B_94 = A_93 )
| ~ subset(A_93,B_94) ),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_397,plain,
( proper_subset('#skF_14','#skF_15')
| ( '#skF_15' = '#skF_14' ) ),
inference(resolution,[status(thm)],[c_112,c_374]) ).
tff(c_399,plain,
'#skF_15' = '#skF_14',
inference(splitLeft,[status(thm)],[c_397]) ).
tff(c_406,plain,
in('#skF_14','#skF_16'),
inference(demodulation,[status(thm),theory(equality)],[c_399,c_110]) ).
tff(c_411,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_108,c_406]) ).
tff(c_412,plain,
proper_subset('#skF_14','#skF_15'),
inference(splitRight,[status(thm)],[c_397]) ).
tff(c_725,plain,
! [A_129,B_130] :
( in(A_129,B_130)
| ~ proper_subset(A_129,B_130)
| ~ ordinal(B_130)
| ~ epsilon_transitive(A_129) ),
inference(cnfTransformation,[status(thm)],[f_170]) ).
tff(c_728,plain,
( in('#skF_14','#skF_15')
| ~ ordinal('#skF_15')
| ~ epsilon_transitive('#skF_14') ),
inference(resolution,[status(thm)],[c_412,c_725]) ).
tff(c_731,plain,
in('#skF_14','#skF_15'),
inference(demodulation,[status(thm),theory(equality)],[c_118,c_116,c_728]) ).
tff(c_124,plain,
! [A_36,B_37] :
( element(A_36,powerset(B_37))
| ~ subset(A_36,B_37) ),
inference(cnfTransformation,[status(thm)],[f_195]) ).
tff(c_687,plain,
! [A_124,C_125,B_126] :
( element(A_124,C_125)
| ~ element(B_126,powerset(C_125))
| ~ in(A_124,B_126) ),
inference(cnfTransformation,[status(thm)],[f_201]) ).
tff(c_871,plain,
! [A_139,B_140,A_141] :
( element(A_139,B_140)
| ~ in(A_139,A_141)
| ~ subset(A_141,B_140) ),
inference(resolution,[status(thm)],[c_124,c_687]) ).
tff(c_906,plain,
! [B_143] :
( element('#skF_14',B_143)
| ~ subset('#skF_15',B_143) ),
inference(resolution,[status(thm)],[c_731,c_871]) ).
tff(c_1389,plain,
! [A_173] :
( element('#skF_14',A_173)
| ~ in('#skF_15',A_173)
| ~ epsilon_transitive(A_173) ),
inference(resolution,[status(thm)],[c_22,c_906]) ).
tff(c_1396,plain,
( element('#skF_14','#skF_16')
| ~ epsilon_transitive('#skF_16') ),
inference(resolution,[status(thm)],[c_110,c_1389]) ).
tff(c_1400,plain,
element('#skF_14','#skF_16'),
inference(demodulation,[status(thm),theory(equality)],[c_154,c_1396]) ).
tff(c_1402,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_462,c_1400]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM390+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/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
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % 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 14:38:43 EDT 2023
% 0.14/0.36 % CPUTime :
% 5.54/2.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.54/2.39
% 5.54/2.39 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.54/2.42
% 5.54/2.42 Inference rules
% 5.54/2.42 ----------------------
% 5.54/2.42 #Ref : 0
% 5.54/2.42 #Sup : 260
% 5.54/2.42 #Fact : 0
% 5.54/2.42 #Define : 0
% 5.54/2.42 #Split : 12
% 5.54/2.42 #Chain : 0
% 5.54/2.42 #Close : 0
% 5.54/2.42
% 5.54/2.42 Ordering : KBO
% 5.54/2.42
% 5.54/2.42 Simplification rules
% 5.54/2.42 ----------------------
% 5.54/2.42 #Subsume : 67
% 5.54/2.42 #Demod : 72
% 5.54/2.42 #Tautology : 49
% 5.54/2.42 #SimpNegUnit : 9
% 5.54/2.42 #BackRed : 19
% 5.54/2.42
% 5.54/2.42 #Partial instantiations: 0
% 5.54/2.42 #Strategies tried : 1
% 5.54/2.42
% 5.54/2.42 Timing (in seconds)
% 5.54/2.42 ----------------------
% 5.54/2.42 Preprocessing : 0.58
% 5.54/2.42 Parsing : 0.31
% 5.54/2.42 CNF conversion : 0.05
% 5.54/2.42 Main loop : 0.67
% 5.54/2.42 Inferencing : 0.24
% 5.54/2.42 Reduction : 0.20
% 5.54/2.42 Demodulation : 0.13
% 5.54/2.42 BG Simplification : 0.03
% 5.54/2.42 Subsumption : 0.15
% 5.54/2.42 Abstraction : 0.02
% 5.54/2.42 MUC search : 0.00
% 5.54/2.42 Cooper : 0.00
% 5.54/2.42 Total : 1.32
% 5.54/2.42 Index Insertion : 0.00
% 5.54/2.42 Index Deletion : 0.00
% 5.54/2.42 Index Matching : 0.00
% 5.54/2.42 BG Taut test : 0.00
%------------------------------------------------------------------------------