TSTP Solution File: SET577+3 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET577+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 : n003.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 10:56:36 EDT 2023
% Result : Theorem 24.63s 12.78s
% Output : CNFRefutation 24.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 57 ( 11 unt; 9 typ; 0 def)
% Number of atoms : 117 ( 28 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 106 ( 37 ~; 62 |; 0 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 6 >; 6 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 76 (; 76 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > member > union > #nlpp > #skF_3 > #skF_5 > #skF_6 > #skF_4 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(union,type,
union: ( $i * $i ) > $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('#skF_4',type,
'#skF_4': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_43,axiom,
! [B,C] : ( union(B,C) = union(C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
tff(f_73,negated_conjecture,
~ ! [B,C,D] :
( ! [E] :
( member(E,B)
<=> ( member(E,C)
| member(E,D) ) )
=> ( B = union(C,D) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th18) ).
tff(f_62,axiom,
! [B,C] :
( ( B = C )
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
tff(f_33,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,B)
| member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
tff(f_51,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
tff(c_14,plain,
! [C_7,B_6] : ( union(C_7,B_6) = union(B_6,C_7) ),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_36,plain,
union('#skF_5','#skF_6') != '#skF_4',
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_43,plain,
union('#skF_6','#skF_5') != '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_14,c_36]) ).
tff(c_363,plain,
! [B_72,C_73] :
( member('#skF_2'(B_72,C_73),C_73)
| member('#skF_3'(B_72,C_73),B_72)
| ( C_73 = B_72 ) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_2,plain,
! [D_3,C_2,B_1] :
( member(D_3,C_2)
| member(D_3,B_1)
| ~ member(D_3,union(B_1,C_2)) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_3187,plain,
! [B_231,C_232,C_233] :
( member('#skF_3'(union(B_231,C_232),C_233),C_232)
| member('#skF_3'(union(B_231,C_232),C_233),B_231)
| member('#skF_2'(union(B_231,C_232),C_233),C_233)
| ( union(B_231,C_232) = C_233 ) ),
inference(resolution,[status(thm)],[c_363,c_2]) ).
tff(c_42,plain,
! [E_20] :
( ~ member(E_20,'#skF_5')
| member(E_20,'#skF_4') ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_14580,plain,
! [B_371,C_372] :
( member('#skF_3'(union(B_371,'#skF_5'),C_372),'#skF_4')
| member('#skF_3'(union(B_371,'#skF_5'),C_372),B_371)
| member('#skF_2'(union(B_371,'#skF_5'),C_372),C_372)
| ( union(B_371,'#skF_5') = C_372 ) ),
inference(resolution,[status(thm)],[c_3187,c_42]) ).
tff(c_40,plain,
! [E_20] :
( ~ member(E_20,'#skF_6')
| member(E_20,'#skF_4') ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_15558,plain,
! [C_387] :
( member('#skF_3'(union('#skF_6','#skF_5'),C_387),'#skF_4')
| member('#skF_2'(union('#skF_6','#skF_5'),C_387),C_387)
| ( union('#skF_6','#skF_5') = C_387 ) ),
inference(resolution,[status(thm)],[c_14580,c_40]) ).
tff(c_30,plain,
! [B_14,C_15] :
( member('#skF_2'(B_14,C_15),C_15)
| ~ member('#skF_3'(B_14,C_15),C_15)
| ( C_15 = B_14 ) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_15568,plain,
( member('#skF_2'(union('#skF_6','#skF_5'),'#skF_4'),'#skF_4')
| ( union('#skF_6','#skF_5') = '#skF_4' ) ),
inference(resolution,[status(thm)],[c_15558,c_30]) ).
tff(c_15602,plain,
member('#skF_2'(union('#skF_6','#skF_5'),'#skF_4'),'#skF_4'),
inference(negUnitSimplification,[status(thm)],[c_43,c_43,c_15568]) ).
tff(c_38,plain,
! [E_20] :
( member(E_20,'#skF_6')
| member(E_20,'#skF_5')
| ~ member(E_20,'#skF_4') ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_4,plain,
! [D_3,C_2,B_1] :
( ~ member(D_3,C_2)
| member(D_3,union(B_1,C_2)) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_217,plain,
! [B_53,C_54] :
( ~ member('#skF_2'(B_53,C_54),B_53)
| member('#skF_3'(B_53,C_54),B_53)
| ( C_54 = B_53 ) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_3456,plain,
! [B_240,C_241,C_242] :
( member('#skF_3'(union(B_240,C_241),C_242),C_241)
| member('#skF_3'(union(B_240,C_241),C_242),B_240)
| ~ member('#skF_2'(union(B_240,C_241),C_242),union(B_240,C_241))
| ( union(B_240,C_241) = C_242 ) ),
inference(resolution,[status(thm)],[c_217,c_2]) ).
tff(c_55845,plain,
! [B_885,C_886,C_887] :
( member('#skF_3'(union(B_885,C_886),C_887),C_886)
| member('#skF_3'(union(B_885,C_886),C_887),B_885)
| ( union(B_885,C_886) = C_887 )
| ~ member('#skF_2'(union(B_885,C_886),C_887),C_886) ),
inference(resolution,[status(thm)],[c_4,c_3456]) ).
tff(c_56326,plain,
! [C_890,C_891] :
( member('#skF_3'(union('#skF_6',C_890),C_891),'#skF_4')
| member('#skF_3'(union('#skF_6',C_890),C_891),C_890)
| ( union('#skF_6',C_890) = C_891 )
| ~ member('#skF_2'(union('#skF_6',C_890),C_891),C_890) ),
inference(resolution,[status(thm)],[c_55845,c_40]) ).
tff(c_56917,plain,
! [C_895] :
( member('#skF_3'(union('#skF_6','#skF_5'),C_895),'#skF_4')
| ( union('#skF_6','#skF_5') = C_895 )
| ~ member('#skF_2'(union('#skF_6','#skF_5'),C_895),'#skF_5') ),
inference(resolution,[status(thm)],[c_56326,c_42]) ).
tff(c_491,plain,
! [B_81,C_82] :
( ~ member('#skF_2'(B_81,C_82),B_81)
| ~ member('#skF_3'(B_81,C_82),C_82)
| ( C_82 = B_81 ) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_502,plain,
! [B_1,C_2,C_82] :
( ~ member('#skF_3'(union(B_1,C_2),C_82),C_82)
| ( union(B_1,C_2) = C_82 )
| ~ member('#skF_2'(union(B_1,C_2),C_82),C_2) ),
inference(resolution,[status(thm)],[c_4,c_491]) ).
tff(c_56945,plain,
( ( union('#skF_6','#skF_5') = '#skF_4' )
| ~ member('#skF_2'(union('#skF_6','#skF_5'),'#skF_4'),'#skF_5') ),
inference(resolution,[status(thm)],[c_56917,c_502]) ).
tff(c_56969,plain,
~ member('#skF_2'(union('#skF_6','#skF_5'),'#skF_4'),'#skF_5'),
inference(negUnitSimplification,[status(thm)],[c_43,c_43,c_56945]) ).
tff(c_56983,plain,
( member('#skF_2'(union('#skF_6','#skF_5'),'#skF_4'),'#skF_6')
| ~ member('#skF_2'(union('#skF_6','#skF_5'),'#skF_4'),'#skF_4') ),
inference(resolution,[status(thm)],[c_38,c_56969]) ).
tff(c_56987,plain,
member('#skF_2'(union('#skF_6','#skF_5'),'#skF_4'),'#skF_6'),
inference(demodulation,[status(thm),theory(equality)],[c_15602,c_56983]) ).
tff(c_6,plain,
! [D_3,B_1,C_2] :
( ~ member(D_3,B_1)
| member(D_3,union(B_1,C_2)) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_63954,plain,
! [B_952,C_953,C_954] :
( member('#skF_3'(union(B_952,C_953),C_954),C_953)
| member('#skF_3'(union(B_952,C_953),C_954),B_952)
| ( union(B_952,C_953) = C_954 )
| ~ member('#skF_2'(union(B_952,C_953),C_954),B_952) ),
inference(resolution,[status(thm)],[c_6,c_3456]) ).
tff(c_65947,plain,
! [C_973,C_974] :
( member('#skF_3'(union('#skF_6',C_973),C_974),'#skF_4')
| member('#skF_3'(union('#skF_6',C_973),C_974),C_973)
| ( union('#skF_6',C_973) = C_974 )
| ~ member('#skF_2'(union('#skF_6',C_973),C_974),'#skF_6') ),
inference(resolution,[status(thm)],[c_63954,c_40]) ).
tff(c_66980,plain,
! [C_984] :
( member('#skF_3'(union('#skF_6','#skF_5'),C_984),'#skF_4')
| ( union('#skF_6','#skF_5') = C_984 )
| ~ member('#skF_2'(union('#skF_6','#skF_5'),C_984),'#skF_6') ),
inference(resolution,[status(thm)],[c_65947,c_42]) ).
tff(c_20,plain,
! [B_8,C_9] :
( member('#skF_1'(B_8,C_9),B_8)
| subset(B_8,C_9) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_107,plain,
! [B_33,C_34] :
( ~ member('#skF_1'(B_33,C_34),C_34)
| subset(B_33,C_34) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_631,plain,
! [B_87,B_88,C_89] :
( subset(B_87,union(B_88,C_89))
| ~ member('#skF_1'(B_87,union(B_88,C_89)),B_88) ),
inference(resolution,[status(thm)],[c_6,c_107]) ).
tff(c_692,plain,
! [B_8,C_89] : subset(B_8,union(B_8,C_89)),
inference(resolution,[status(thm)],[c_20,c_631]) ).
tff(c_16,plain,
! [D_12,C_9,B_8] :
( member(D_12,C_9)
| ~ member(D_12,B_8)
| ~ subset(B_8,C_9) ),
inference(cnfTransformation,[status(thm)],[f_51]) ).
tff(c_57427,plain,
! [C_899] :
( member('#skF_2'(union('#skF_6','#skF_5'),'#skF_4'),C_899)
| ~ subset('#skF_6',C_899) ),
inference(resolution,[status(thm)],[c_56987,c_16]) ).
tff(c_28,plain,
! [B_14,C_15] :
( ~ member('#skF_2'(B_14,C_15),B_14)
| ~ member('#skF_3'(B_14,C_15),C_15)
| ( C_15 = B_14 ) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_57453,plain,
( ~ member('#skF_3'(union('#skF_6','#skF_5'),'#skF_4'),'#skF_4')
| ( union('#skF_6','#skF_5') = '#skF_4' )
| ~ subset('#skF_6',union('#skF_6','#skF_5')) ),
inference(resolution,[status(thm)],[c_57427,c_28]) ).
tff(c_57494,plain,
( ~ member('#skF_3'(union('#skF_6','#skF_5'),'#skF_4'),'#skF_4')
| ( union('#skF_6','#skF_5') = '#skF_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_692,c_57453]) ).
tff(c_57495,plain,
~ member('#skF_3'(union('#skF_6','#skF_5'),'#skF_4'),'#skF_4'),
inference(negUnitSimplification,[status(thm)],[c_43,c_57494]) ).
tff(c_66986,plain,
( ( union('#skF_6','#skF_5') = '#skF_4' )
| ~ member('#skF_2'(union('#skF_6','#skF_5'),'#skF_4'),'#skF_6') ),
inference(resolution,[status(thm)],[c_66980,c_57495]) ).
tff(c_67024,plain,
union('#skF_6','#skF_5') = '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_56987,c_66986]) ).
tff(c_67026,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_43,c_67024]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET577+3 : TPTP v8.1.2. Released v2.2.0.
% 0.14/0.15 % 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
% 0.15/0.36 % Computer : n003.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 3 16:21:53 EDT 2023
% 0.15/0.36 % CPUTime :
% 24.63/12.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.63/12.79
% 24.63/12.79 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 24.63/12.82
% 24.63/12.82 Inference rules
% 24.63/12.82 ----------------------
% 24.63/12.82 #Ref : 0
% 24.63/12.82 #Sup : 15937
% 24.63/12.82 #Fact : 94
% 24.63/12.82 #Define : 0
% 24.63/12.82 #Split : 10
% 24.63/12.82 #Chain : 0
% 24.63/12.82 #Close : 0
% 24.63/12.82
% 24.63/12.82 Ordering : KBO
% 24.63/12.82
% 24.63/12.82 Simplification rules
% 24.63/12.82 ----------------------
% 24.63/12.82 #Subsume : 4826
% 24.63/12.82 #Demod : 16623
% 24.63/12.82 #Tautology : 4141
% 24.63/12.82 #SimpNegUnit : 199
% 24.63/12.82 #BackRed : 28
% 24.63/12.82
% 24.63/12.82 #Partial instantiations: 0
% 24.63/12.82 #Strategies tried : 1
% 24.63/12.82
% 24.63/12.82 Timing (in seconds)
% 24.63/12.82 ----------------------
% 24.63/12.82 Preprocessing : 0.48
% 24.63/12.82 Parsing : 0.25
% 24.63/12.82 CNF conversion : 0.04
% 24.63/12.82 Main loop : 11.26
% 24.63/12.82 Inferencing : 1.74
% 24.63/12.82 Reduction : 5.00
% 24.63/12.82 Demodulation : 4.33
% 24.63/12.82 BG Simplification : 0.12
% 24.63/12.82 Subsumption : 3.78
% 24.63/12.82 Abstraction : 0.16
% 24.63/12.82 MUC search : 0.00
% 24.63/12.82 Cooper : 0.00
% 24.63/12.82 Total : 11.79
% 24.63/12.82 Index Insertion : 0.00
% 24.63/12.83 Index Deletion : 0.00
% 24.63/12.83 Index Matching : 0.00
% 24.63/12.83 BG Taut test : 0.00
%------------------------------------------------------------------------------