TSTP Solution File: SET591+3 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET591+3 : 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/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 : n025.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 10:56:38 EDT 2023
% Result : Theorem 4.14s 2.15s
% Output : CNFRefutation 4.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of formulae : 45 ( 14 unt; 9 typ; 0 def)
% Number of atoms : 67 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 58 ( 27 ~; 23 |; 2 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 6 >; 4 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 47 (; 47 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > empty > difference > #nlpp > empty_set > #skF_2 > #skF_3 > #skF_4 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(empty,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_4',type,
'#skF_4': $i ).
tff(difference,type,
difference: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_70,negated_conjecture,
~ ! [B,C] :
( subset(B,difference(C,B))
=> ( B = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th50) ).
tff(f_64,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_defn) ).
tff(f_35,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
tff(f_43,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( member(D,B)
& ~ member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
tff(f_47,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
tff(f_54,axiom,
! [B,C] :
( ( B = C )
<=> ( subset(B,C)
& subset(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
tff(f_57,axiom,
! [B] : subset(B,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
tff(c_28,plain,
empty_set != '#skF_3',
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_30,plain,
subset('#skF_3',difference('#skF_4','#skF_3')),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_26,plain,
! [B_13] :
( empty(B_13)
| member('#skF_2'(B_13),B_13) ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_155,plain,
! [D_43,C_44,B_45] :
( member(D_43,C_44)
| ~ member(D_43,B_45)
| ~ subset(B_45,C_44) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_162,plain,
! [B_46,C_47] :
( member('#skF_2'(B_46),C_47)
| ~ subset(B_46,C_47)
| empty(B_46) ),
inference(resolution,[status(thm)],[c_26,c_155]) ).
tff(c_12,plain,
! [D_8,B_6,C_7] :
( member(D_8,B_6)
| ~ member(D_8,difference(B_6,C_7)) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_1425,plain,
! [B_147,B_148,C_149] :
( member('#skF_2'(B_147),B_148)
| ~ subset(B_147,difference(B_148,C_149))
| empty(B_147) ),
inference(resolution,[status(thm)],[c_162,c_12]) ).
tff(c_1475,plain,
( member('#skF_2'('#skF_3'),'#skF_4')
| empty('#skF_3') ),
inference(resolution,[status(thm)],[c_30,c_1425]) ).
tff(c_1477,plain,
empty('#skF_3'),
inference(splitLeft,[status(thm)],[c_1475]) ).
tff(c_46,plain,
! [B_22,C_23] :
( member('#skF_1'(B_22,C_23),B_22)
| subset(B_22,C_23) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_24,plain,
! [C_16,B_13] :
( ~ member(C_16,B_13)
| ~ empty(B_13) ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_54,plain,
! [B_22,C_23] :
( ~ empty(B_22)
| subset(B_22,C_23) ),
inference(resolution,[status(thm)],[c_46,c_24]) ).
tff(c_14,plain,
! [B_9] : ~ member(B_9,empty_set),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_55,plain,
! [C_23] : subset(empty_set,C_23),
inference(resolution,[status(thm)],[c_46,c_14]) ).
tff(c_57,plain,
! [C_25,B_26] :
( ( C_25 = B_26 )
| ~ subset(C_25,B_26)
| ~ subset(B_26,C_25) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_74,plain,
! [C_29] :
( ( empty_set = C_29 )
| ~ subset(C_29,empty_set) ),
inference(resolution,[status(thm)],[c_55,c_57]) ).
tff(c_87,plain,
! [B_22] :
( ( empty_set = B_22 )
| ~ empty(B_22) ),
inference(resolution,[status(thm)],[c_54,c_74]) ).
tff(c_1492,plain,
empty_set = '#skF_3',
inference(resolution,[status(thm)],[c_1477,c_87]) ).
tff(c_1502,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28,c_1492]) ).
tff(c_1504,plain,
~ empty('#skF_3'),
inference(splitRight,[status(thm)],[c_1475]) ).
tff(c_22,plain,
! [B_12] : subset(B_12,B_12),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_161,plain,
! [B_13,C_44] :
( member('#skF_2'(B_13),C_44)
| ~ subset(B_13,C_44)
| empty(B_13) ),
inference(resolution,[status(thm)],[c_26,c_155]) ).
tff(c_10,plain,
! [D_8,C_7,B_6] :
( ~ member(D_8,C_7)
| ~ member(D_8,difference(B_6,C_7)) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_1722,plain,
! [B_165,C_166,B_167] :
( ~ member('#skF_2'(B_165),C_166)
| ~ subset(B_165,difference(B_167,C_166))
| empty(B_165) ),
inference(resolution,[status(thm)],[c_162,c_10]) ).
tff(c_1760,plain,
( ~ member('#skF_2'('#skF_3'),'#skF_3')
| empty('#skF_3') ),
inference(resolution,[status(thm)],[c_30,c_1722]) ).
tff(c_1773,plain,
~ member('#skF_2'('#skF_3'),'#skF_3'),
inference(negUnitSimplification,[status(thm)],[c_1504,c_1760]) ).
tff(c_1780,plain,
( ~ subset('#skF_3','#skF_3')
| empty('#skF_3') ),
inference(resolution,[status(thm)],[c_161,c_1773]) ).
tff(c_1787,plain,
empty('#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_1780]) ).
tff(c_1789,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1504,c_1787]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET591+3 : TPTP v8.1.2. Released v2.2.0.
% 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
% 0.13/0.35 % Computer : n025.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 16:46:20 EDT 2023
% 0.13/0.35 % CPUTime :
% 4.14/2.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.14/2.16
% 4.14/2.16 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.58/2.19
% 4.58/2.19 Inference rules
% 4.58/2.19 ----------------------
% 4.58/2.19 #Ref : 0
% 4.58/2.19 #Sup : 430
% 4.58/2.19 #Fact : 0
% 4.58/2.19 #Define : 0
% 4.58/2.19 #Split : 3
% 4.58/2.19 #Chain : 0
% 4.58/2.19 #Close : 0
% 4.58/2.19
% 4.58/2.19 Ordering : KBO
% 4.58/2.19
% 4.58/2.19 Simplification rules
% 4.58/2.19 ----------------------
% 4.58/2.19 #Subsume : 162
% 4.58/2.19 #Demod : 181
% 4.58/2.19 #Tautology : 132
% 4.58/2.19 #SimpNegUnit : 14
% 4.58/2.19 #BackRed : 2
% 4.58/2.19
% 4.58/2.19 #Partial instantiations: 0
% 4.58/2.19 #Strategies tried : 1
% 4.58/2.19
% 4.58/2.19 Timing (in seconds)
% 4.58/2.19 ----------------------
% 4.58/2.19 Preprocessing : 0.48
% 4.58/2.19 Parsing : 0.25
% 4.58/2.19 CNF conversion : 0.03
% 4.58/2.19 Main loop : 0.59
% 4.58/2.19 Inferencing : 0.23
% 4.58/2.19 Reduction : 0.15
% 4.58/2.19 Demodulation : 0.11
% 4.58/2.19 BG Simplification : 0.03
% 4.58/2.19 Subsumption : 0.13
% 4.58/2.19 Abstraction : 0.02
% 4.58/2.19 MUC search : 0.00
% 4.58/2.19 Cooper : 0.00
% 4.58/2.19 Total : 1.12
% 4.58/2.19 Index Insertion : 0.00
% 4.58/2.19 Index Deletion : 0.00
% 4.58/2.19 Index Matching : 0.00
% 4.58/2.19 BG Taut test : 0.00
%------------------------------------------------------------------------------