TSTP Solution File: SET596+3 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET596+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/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 10:56:39 EDT 2023
% Result : Theorem 3.62s 1.94s
% Output : CNFRefutation 3.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 17
% Syntax : Number of formulae : 30 ( 8 unt; 12 typ; 0 def)
% Number of atoms : 33 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 11 ~; 8 |; 2 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 8 >; 6 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 24 (; 24 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > empty > intersection > #nlpp > empty_set > #skF_2 > #skF_7 > #skF_3 > #skF_5 > #skF_6 > #skF_1 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff(intersection,type,
intersection: ( $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,type,
empty: $i > $o ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(f_92,negated_conjecture,
~ ! [B,C,D] :
( ( subset(B,C)
& ( intersection(C,D) = empty_set ) )
=> ( intersection(B,D) = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th55) ).
tff(f_56,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
tff(f_41,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
tff(f_37,axiom,
! [B,C,D] :
( subset(B,C)
=> subset(intersection(B,D),intersection(C,D)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_of_subset) ).
tff(f_63,axiom,
! [B,C] :
( ( B = C )
<=> ( subset(B,C)
& subset(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
tff(c_46,plain,
intersection('#skF_5','#skF_7') != empty_set,
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_50,plain,
subset('#skF_5','#skF_6'),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_110,plain,
! [B_36,C_37] :
( member('#skF_1'(B_36,C_37),B_36)
| subset(B_36,C_37) ),
inference(cnfTransformation,[status(thm)],[f_56]) ).
tff(c_6,plain,
! [B_5] : ~ member(B_5,empty_set),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_119,plain,
! [C_37] : subset(empty_set,C_37),
inference(resolution,[status(thm)],[c_110,c_6]) ).
tff(c_48,plain,
intersection('#skF_6','#skF_7') = empty_set,
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_295,plain,
! [B_64,D_65,C_66] :
( subset(intersection(B_64,D_65),intersection(C_66,D_65))
| ~ subset(B_64,C_66) ),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_326,plain,
! [B_67] :
( subset(intersection(B_67,'#skF_7'),empty_set)
| ~ subset(B_67,'#skF_6') ),
inference(superposition,[status(thm),theory(equality)],[c_48,c_295]) ).
tff(c_20,plain,
! [C_15,B_14] :
( ( C_15 = B_14 )
| ~ subset(C_15,B_14)
| ~ subset(B_14,C_15) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_337,plain,
! [B_67] :
( ( intersection(B_67,'#skF_7') = empty_set )
| ~ subset(empty_set,intersection(B_67,'#skF_7'))
| ~ subset(B_67,'#skF_6') ),
inference(resolution,[status(thm)],[c_326,c_20]) ).
tff(c_365,plain,
! [B_68] :
( ( intersection(B_68,'#skF_7') = empty_set )
| ~ subset(B_68,'#skF_6') ),
inference(demodulation,[status(thm),theory(equality)],[c_119,c_337]) ).
tff(c_380,plain,
intersection('#skF_5','#skF_7') = empty_set,
inference(resolution,[status(thm)],[c_50,c_365]) ).
tff(c_388,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46,c_380]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET596+3 : 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
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 3 16:38:38 EDT 2023
% 0.12/0.34 % CPUTime :
% 3.62/1.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.62/1.94
% 3.62/1.94 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.81/1.97
% 3.81/1.97 Inference rules
% 3.81/1.97 ----------------------
% 3.81/1.97 #Ref : 0
% 3.81/1.97 #Sup : 74
% 3.81/1.97 #Fact : 0
% 3.81/1.97 #Define : 0
% 3.81/1.97 #Split : 1
% 3.81/1.97 #Chain : 0
% 3.81/1.97 #Close : 0
% 3.81/1.97
% 3.81/1.97 Ordering : KBO
% 3.81/1.97
% 3.81/1.97 Simplification rules
% 3.81/1.97 ----------------------
% 3.81/1.97 #Subsume : 11
% 3.81/1.97 #Demod : 14
% 3.81/1.97 #Tautology : 30
% 3.81/1.97 #SimpNegUnit : 1
% 3.81/1.97 #BackRed : 0
% 3.81/1.97
% 3.81/1.97 #Partial instantiations: 0
% 3.81/1.97 #Strategies tried : 1
% 3.81/1.97
% 3.81/1.97 Timing (in seconds)
% 3.81/1.97 ----------------------
% 3.81/1.97 Preprocessing : 0.50
% 3.81/1.97 Parsing : 0.26
% 3.81/1.97 CNF conversion : 0.04
% 3.81/1.97 Main loop : 0.33
% 3.81/1.97 Inferencing : 0.11
% 3.81/1.97 Reduction : 0.10
% 3.81/1.97 Demodulation : 0.08
% 3.81/1.97 BG Simplification : 0.02
% 3.81/1.97 Subsumption : 0.08
% 3.81/1.97 Abstraction : 0.01
% 3.81/1.97 MUC search : 0.00
% 3.81/1.97 Cooper : 0.00
% 3.81/1.97 Total : 0.88
% 3.81/1.97 Index Insertion : 0.00
% 3.81/1.97 Index Deletion : 0.00
% 3.81/1.97 Index Matching : 0.00
% 3.81/1.97 BG Taut test : 0.00
%------------------------------------------------------------------------------