TSTP Solution File: SET638+3 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET638+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 : 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 10:56:46 EDT 2023
% Result : Theorem 5.49s 2.30s
% Output : CNFRefutation 5.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 19
% Syntax : Number of formulae : 34 ( 18 unt; 13 typ; 0 def)
% Number of atoms : 25 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 7 ( 3 ~; 1 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 9 >; 7 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 27 (; 27 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > empty > union > 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(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,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_106,negated_conjecture,
~ ! [B,C,D] :
( ( subset(B,union(C,D))
& ( intersection(B,D) = empty_set ) )
=> subset(B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th120) ).
tff(f_38,axiom,
! [B] : ( union(B,empty_set) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_empty_set) ).
tff(f_41,axiom,
! [B,C,D] : ( intersection(B,union(C,D)) = union(intersection(B,C),intersection(B,D)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_distributes_over_union) ).
tff(f_35,axiom,
! [B,C] :
( subset(B,C)
=> ( intersection(B,C) = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_intersection) ).
tff(f_80,axiom,
! [B,C] : ( intersection(B,C) = intersection(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
tff(f_30,axiom,
! [B,C] : subset(intersection(B,C),B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_is_subset) ).
tff(c_58,plain,
~ subset('#skF_5','#skF_6'),
inference(cnfTransformation,[status(thm)],[f_106]) ).
tff(c_6,plain,
! [B_5] : ( union(B_5,empty_set) = B_5 ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_60,plain,
intersection('#skF_5','#skF_7') = empty_set,
inference(cnfTransformation,[status(thm)],[f_106]) ).
tff(c_2116,plain,
! [B_135,C_136,D_137] : ( union(intersection(B_135,C_136),intersection(B_135,D_137)) = intersection(B_135,union(C_136,D_137)) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_2237,plain,
! [C_136] : ( union(intersection('#skF_5',C_136),empty_set) = intersection('#skF_5',union(C_136,'#skF_7')) ),
inference(superposition,[status(thm),theory(equality)],[c_60,c_2116]) ).
tff(c_2821,plain,
! [C_145] : ( intersection('#skF_5',union(C_145,'#skF_7')) = intersection('#skF_5',C_145) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_2237]) ).
tff(c_62,plain,
subset('#skF_5',union('#skF_6','#skF_7')),
inference(cnfTransformation,[status(thm)],[f_106]) ).
tff(c_233,plain,
! [B_52,C_53] :
( ( intersection(B_52,C_53) = B_52 )
| ~ subset(B_52,C_53) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_254,plain,
intersection('#skF_5',union('#skF_6','#skF_7')) = '#skF_5',
inference(resolution,[status(thm)],[c_62,c_233]) ).
tff(c_2882,plain,
intersection('#skF_5','#skF_6') = '#skF_5',
inference(superposition,[status(thm),theory(equality)],[c_2821,c_254]) ).
tff(c_85,plain,
! [C_44,B_45] : ( intersection(C_44,B_45) = intersection(B_45,C_44) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_2,plain,
! [B_1,C_2] : subset(intersection(B_1,C_2),B_1),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_100,plain,
! [C_44,B_45] : subset(intersection(C_44,B_45),B_45),
inference(superposition,[status(thm),theory(equality)],[c_85,c_2]) ).
tff(c_2988,plain,
subset('#skF_5','#skF_6'),
inference(superposition,[status(thm),theory(equality)],[c_2882,c_100]) ).
tff(c_3017,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_58,c_2988]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET638+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/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
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 3 16:46:33 EDT 2023
% 0.13/0.35 % CPUTime :
% 5.49/2.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.49/2.31
% 5.49/2.31 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.49/2.33
% 5.49/2.33 Inference rules
% 5.49/2.33 ----------------------
% 5.49/2.33 #Ref : 0
% 5.49/2.33 #Sup : 731
% 5.49/2.33 #Fact : 0
% 5.49/2.33 #Define : 0
% 5.49/2.33 #Split : 6
% 5.49/2.33 #Chain : 0
% 5.49/2.33 #Close : 0
% 5.49/2.33
% 5.49/2.33 Ordering : KBO
% 5.49/2.33
% 5.49/2.33 Simplification rules
% 5.49/2.33 ----------------------
% 5.49/2.33 #Subsume : 74
% 5.49/2.33 #Demod : 552
% 5.49/2.33 #Tautology : 402
% 5.49/2.33 #SimpNegUnit : 10
% 5.49/2.33 #BackRed : 13
% 5.49/2.33
% 5.49/2.33 #Partial instantiations: 0
% 5.49/2.33 #Strategies tried : 1
% 5.49/2.33
% 5.49/2.33 Timing (in seconds)
% 5.49/2.33 ----------------------
% 5.49/2.33 Preprocessing : 0.51
% 5.49/2.33 Parsing : 0.26
% 5.49/2.34 CNF conversion : 0.04
% 5.49/2.34 Main loop : 0.77
% 5.49/2.34 Inferencing : 0.26
% 5.49/2.34 Reduction : 0.30
% 5.49/2.34 Demodulation : 0.23
% 5.49/2.34 BG Simplification : 0.03
% 5.49/2.34 Subsumption : 0.14
% 5.49/2.34 Abstraction : 0.03
% 5.49/2.34 MUC search : 0.00
% 5.49/2.34 Cooper : 0.00
% 5.49/2.34 Total : 1.33
% 5.49/2.34 Index Insertion : 0.00
% 5.49/2.34 Index Deletion : 0.00
% 5.49/2.34 Index Matching : 0.00
% 5.49/2.34 BG Taut test : 0.00
%------------------------------------------------------------------------------