TSTP Solution File: SET707+4 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET707+4 : TPTP v8.1.2. Released v2.2.0.
% 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 : n022.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 10:56:55 EDT 2023
% Result : Theorem 10.54s 3.57s
% Output : CNFRefutation 10.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 24
% Syntax : Number of formulae : 75 ( 36 unt; 19 typ; 0 def)
% Number of atoms : 83 ( 33 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 47 ( 20 ~; 19 |; 2 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 14 >; 10 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-2 aty)
% Number of variables : 49 (; 49 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > equal_set > unordered_pair > union > intersection > difference > #nlpp > sum > singleton > product > power_set > empty_set > #skF_7 > #skF_3 > #skF_5 > #skF_6 > #skF_4 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(equal_set,type,
equal_set: ( $i * $i ) > $o ).
tff(power_set,type,
power_set: $i > $i ).
tff(product,type,
product: $i > $i ).
tff(singleton,type,
singleton: $i > $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(sum,type,
sum: $i > $i ).
tff(intersection,type,
intersection: ( $i * $i ) > $i ).
tff(union,type,
union: ( $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': $i ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(difference,type,
difference: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_121,negated_conjecture,
~ ! [A,B,U,V] :
( equal_set(unordered_pair(singleton(A),unordered_pair(A,B)),unordered_pair(singleton(U),unordered_pair(U,V)))
=> ( ( A = U )
& ( B = V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI50) ).
tff(f_62,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(A,B)
& subset(B,A) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',equal_set) ).
tff(f_98,axiom,
! [X,A,B] :
( member(X,unordered_pair(A,B))
<=> ( ( X = A )
| ( X = B ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',unordered_pair) ).
tff(f_56,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
tff(f_92,axiom,
! [X,A] :
( member(X,singleton(A))
<=> ( X = A ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',singleton) ).
tff(c_60,plain,
( ( '#skF_7' != '#skF_5' )
| ( '#skF_6' != '#skF_4' ) ),
inference(cnfTransformation,[status(thm)],[f_121]) ).
tff(c_64,plain,
'#skF_6' != '#skF_4',
inference(splitLeft,[status(thm)],[c_60]) ).
tff(c_62,plain,
equal_set(unordered_pair(singleton('#skF_4'),unordered_pair('#skF_4','#skF_5')),unordered_pair(singleton('#skF_6'),unordered_pair('#skF_6','#skF_7'))),
inference(cnfTransformation,[status(thm)],[f_121]) ).
tff(c_10,plain,
! [B_7,A_6] :
( subset(B_7,A_6)
| ~ equal_set(A_6,B_7) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_46,plain,
! [X_22,B_24] : member(X_22,unordered_pair(X_22,B_24)),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_147,plain,
! [X_75,B_76,A_77] :
( member(X_75,B_76)
| ~ member(X_75,A_77)
| ~ subset(A_77,B_76) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_189,plain,
! [X_86,B_87,B_88] :
( member(X_86,B_87)
| ~ subset(unordered_pair(X_86,B_88),B_87) ),
inference(resolution,[status(thm)],[c_46,c_147]) ).
tff(c_2324,plain,
! [X_214,A_215,B_216] :
( member(X_214,A_215)
| ~ equal_set(A_215,unordered_pair(X_214,B_216)) ),
inference(resolution,[status(thm)],[c_10,c_189]) ).
tff(c_2334,plain,
member(singleton('#skF_6'),unordered_pair(singleton('#skF_4'),unordered_pair('#skF_4','#skF_5'))),
inference(resolution,[status(thm)],[c_62,c_2324]) ).
tff(c_42,plain,
! [X_22,B_24,A_23] :
( ( X_22 = B_24 )
| ( X_22 = A_23 )
| ~ member(X_22,unordered_pair(A_23,B_24)) ),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_2350,plain,
( ( unordered_pair('#skF_4','#skF_5') = singleton('#skF_6') )
| ( singleton('#skF_6') = singleton('#skF_4') ) ),
inference(resolution,[status(thm)],[c_2334,c_42]) ).
tff(c_4112,plain,
singleton('#skF_6') = singleton('#skF_4'),
inference(splitLeft,[status(thm)],[c_2350]) ).
tff(c_40,plain,
! [X_20] : member(X_20,singleton(X_20)),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_4183,plain,
member('#skF_6',singleton('#skF_4')),
inference(superposition,[status(thm),theory(equality)],[c_4112,c_40]) ).
tff(c_38,plain,
! [X_20,A_21] :
( ( X_20 = A_21 )
| ~ member(X_20,singleton(A_21)) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_4198,plain,
'#skF_6' = '#skF_4',
inference(resolution,[status(thm)],[c_4183,c_38]) ).
tff(c_4205,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_64,c_4198]) ).
tff(c_4206,plain,
unordered_pair('#skF_4','#skF_5') = singleton('#skF_6'),
inference(splitRight,[status(thm)],[c_2350]) ).
tff(c_4281,plain,
member('#skF_4',singleton('#skF_6')),
inference(superposition,[status(thm),theory(equality)],[c_4206,c_46]) ).
tff(c_4532,plain,
'#skF_6' = '#skF_4',
inference(resolution,[status(thm)],[c_4281,c_38]) ).
tff(c_4539,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_64,c_4532]) ).
tff(c_4540,plain,
'#skF_7' != '#skF_5',
inference(splitRight,[status(thm)],[c_60]) ).
tff(c_4541,plain,
'#skF_6' = '#skF_4',
inference(splitRight,[status(thm)],[c_60]) ).
tff(c_4542,plain,
equal_set(unordered_pair(singleton('#skF_4'),unordered_pair('#skF_4','#skF_5')),unordered_pair(singleton('#skF_4'),unordered_pair('#skF_4','#skF_7'))),
inference(demodulation,[status(thm),theory(equality)],[c_4541,c_4541,c_62]) ).
tff(c_44,plain,
! [X_22,A_23] : member(X_22,unordered_pair(A_23,X_22)),
inference(cnfTransformation,[status(thm)],[f_98]) ).
tff(c_4731,plain,
! [X_347,B_348,A_349] :
( member(X_347,B_348)
| ~ member(X_347,A_349)
| ~ subset(A_349,B_348) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_5211,plain,
! [X_393,B_394,A_395] :
( member(X_393,B_394)
| ~ subset(unordered_pair(A_395,X_393),B_394) ),
inference(resolution,[status(thm)],[c_44,c_4731]) ).
tff(c_6576,plain,
! [X_467,A_468,A_469] :
( member(X_467,A_468)
| ~ equal_set(A_468,unordered_pair(A_469,X_467)) ),
inference(resolution,[status(thm)],[c_10,c_5211]) ).
tff(c_6590,plain,
member(unordered_pair('#skF_4','#skF_7'),unordered_pair(singleton('#skF_4'),unordered_pair('#skF_4','#skF_5'))),
inference(resolution,[status(thm)],[c_4542,c_6576]) ).
tff(c_6799,plain,
( ( unordered_pair('#skF_4','#skF_7') = unordered_pair('#skF_4','#skF_5') )
| ( unordered_pair('#skF_4','#skF_7') = singleton('#skF_4') ) ),
inference(resolution,[status(thm)],[c_6590,c_42]) ).
tff(c_8064,plain,
unordered_pair('#skF_4','#skF_7') = singleton('#skF_4'),
inference(splitLeft,[status(thm)],[c_6799]) ).
tff(c_8134,plain,
member('#skF_7',singleton('#skF_4')),
inference(superposition,[status(thm),theory(equality)],[c_8064,c_44]) ).
tff(c_8155,plain,
'#skF_7' = '#skF_4',
inference(resolution,[status(thm)],[c_8134,c_38]) ).
tff(c_8159,plain,
'#skF_5' != '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_8155,c_4540]) ).
tff(c_12,plain,
! [A_6,B_7] :
( subset(A_6,B_7)
| ~ equal_set(A_6,B_7) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_6607,plain,
! [X_473,B_474,A_475] :
( member(X_473,B_474)
| ~ equal_set(unordered_pair(A_475,X_473),B_474) ),
inference(resolution,[status(thm)],[c_12,c_5211]) ).
tff(c_6621,plain,
member(unordered_pair('#skF_4','#skF_5'),unordered_pair(singleton('#skF_4'),unordered_pair('#skF_4','#skF_7'))),
inference(resolution,[status(thm)],[c_4542,c_6607]) ).
tff(c_8067,plain,
member(unordered_pair('#skF_4','#skF_5'),unordered_pair(singleton('#skF_4'),singleton('#skF_4'))),
inference(demodulation,[status(thm),theory(equality)],[c_8064,c_6621]) ).
tff(c_8628,plain,
unordered_pair('#skF_4','#skF_5') = singleton('#skF_4'),
inference(resolution,[status(thm)],[c_8067,c_42]) ).
tff(c_8696,plain,
member('#skF_5',singleton('#skF_4')),
inference(superposition,[status(thm),theory(equality)],[c_8628,c_44]) ).
tff(c_8713,plain,
'#skF_5' = '#skF_4',
inference(resolution,[status(thm)],[c_8696,c_38]) ).
tff(c_8720,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8159,c_8713]) ).
tff(c_8721,plain,
unordered_pair('#skF_4','#skF_7') = unordered_pair('#skF_4','#skF_5'),
inference(splitRight,[status(thm)],[c_6799]) ).
tff(c_8797,plain,
member('#skF_7',unordered_pair('#skF_4','#skF_5')),
inference(superposition,[status(thm),theory(equality)],[c_8721,c_44]) ).
tff(c_9002,plain,
( ( '#skF_7' = '#skF_5' )
| ( '#skF_7' = '#skF_4' ) ),
inference(resolution,[status(thm)],[c_8797,c_42]) ).
tff(c_9008,plain,
'#skF_7' = '#skF_4',
inference(negUnitSimplification,[status(thm)],[c_4540,c_9002]) ).
tff(c_9127,plain,
'#skF_5' != '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_9008,c_4540]) ).
tff(c_9125,plain,
unordered_pair('#skF_4','#skF_5') = unordered_pair('#skF_4','#skF_4'),
inference(demodulation,[status(thm),theory(equality)],[c_9008,c_8721]) ).
tff(c_10494,plain,
member('#skF_5',unordered_pair('#skF_4','#skF_4')),
inference(superposition,[status(thm),theory(equality)],[c_9125,c_44]) ).
tff(c_10512,plain,
'#skF_5' = '#skF_4',
inference(resolution,[status(thm)],[c_10494,c_42]) ).
tff(c_10519,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_9127,c_9127,c_10512]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET707+4 : TPTP v8.1.2. Released v2.2.0.
% 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 : n022.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 16:16:18 EDT 2023
% 0.14/0.34 % CPUTime :
% 10.54/3.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.54/3.58
% 10.54/3.58 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.54/3.61
% 10.54/3.61 Inference rules
% 10.54/3.61 ----------------------
% 10.54/3.61 #Ref : 0
% 10.54/3.61 #Sup : 2333
% 10.54/3.61 #Fact : 0
% 10.54/3.61 #Define : 0
% 10.54/3.61 #Split : 3
% 10.54/3.61 #Chain : 0
% 10.54/3.61 #Close : 0
% 10.54/3.61
% 10.54/3.61 Ordering : KBO
% 10.54/3.61
% 10.54/3.61 Simplification rules
% 10.54/3.61 ----------------------
% 10.54/3.61 #Subsume : 62
% 10.54/3.61 #Demod : 686
% 10.54/3.61 #Tautology : 690
% 10.54/3.61 #SimpNegUnit : 6
% 10.54/3.61 #BackRed : 46
% 10.54/3.61
% 10.54/3.61 #Partial instantiations: 0
% 10.54/3.61 #Strategies tried : 1
% 10.54/3.61
% 10.54/3.61 Timing (in seconds)
% 10.54/3.61 ----------------------
% 10.54/3.61 Preprocessing : 0.54
% 10.54/3.61 Parsing : 0.28
% 10.54/3.61 CNF conversion : 0.04
% 10.54/3.61 Main loop : 2.01
% 10.54/3.61 Inferencing : 0.69
% 10.54/3.61 Reduction : 0.68
% 10.54/3.61 Demodulation : 0.48
% 10.54/3.61 BG Simplification : 0.05
% 10.54/3.61 Subsumption : 0.42
% 10.54/3.61 Abstraction : 0.05
% 10.54/3.61 MUC search : 0.00
% 10.54/3.61 Cooper : 0.00
% 10.54/3.61 Total : 2.60
% 10.54/3.61 Index Insertion : 0.00
% 10.54/3.61 Index Deletion : 0.00
% 10.54/3.61 Index Matching : 0.00
% 10.54/3.61 BG Taut test : 0.00
%------------------------------------------------------------------------------