TSTP Solution File: SEU144+2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SEU144+2 : TPTP v8.1.2. Released v3.3.0.
% 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 : n008.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 10:57:44 EDT 2023
% Result : Theorem 22.66s 10.44s
% Output : CNFRefutation 22.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 43
% Syntax : Number of formulae : 88 ( 25 unt; 33 typ; 0 def)
% Number of atoms : 89 ( 29 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 56 ( 22 ~; 24 |; 0 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 57 ( 26 >; 31 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 7 con; 0-3 aty)
% Number of variables : 51 (; 50 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ subset > proper_subset > in > disjoint > empty > unordered_pair > set_union2 > set_intersection2 > set_difference > #nlpp > singleton > empty_set > #skF_22 > #skF_18 > #skF_17 > #skF_6 > #skF_15 > #skF_20 > #skF_12 > #skF_4 > #skF_16 > #skF_14 > #skF_19 > #skF_13 > #skF_5 > #skF_8 > #skF_11 > #skF_7 > #skF_9 > #skF_3 > #skF_2 > #skF_1 > #skF_21 > #skF_10
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_22',type,
'#skF_22': ( $i * $i ) > $i ).
tff(set_difference,type,
set_difference: ( $i * $i ) > $i ).
tff('#skF_18',type,
'#skF_18': $i ).
tff(singleton,type,
singleton: $i > $i ).
tff('#skF_17',type,
'#skF_17': $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff('#skF_20',type,
'#skF_20': ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff('#skF_16',type,
'#skF_16': $i ).
tff(proper_subset,type,
proper_subset: ( $i * $i ) > $o ).
tff(in,type,
in: ( $i * $i ) > $o ).
tff('#skF_14',type,
'#skF_14': $i ).
tff('#skF_19',type,
'#skF_19': ( $i * $i ) > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_13',type,
'#skF_13': $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff(set_intersection2,type,
set_intersection2: ( $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i ) > $i ).
tff(empty,type,
empty: $i > $o ).
tff(disjoint,type,
disjoint: ( $i * $i ) > $o ).
tff('#skF_11',type,
'#skF_11': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i * $i ) > $i ).
tff(empty_set,type,
empty_set: $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(set_union2,type,
set_union2: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_21',type,
'#skF_21': ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i * $i ) > $i ).
tff(f_151,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
tff(f_276,axiom,
! [A] :
( empty(A)
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
tff(f_140,lemma,
! [A] : ( singleton(A) != empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
tff(f_145,negated_conjecture,
~ ! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
tff(f_61,axiom,
! [A] :
( ( A = empty_set )
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
tff(f_55,axiom,
! [A,B] :
( ( B = singleton(A) )
<=> ! [C] :
( in(C,B)
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
tff(f_211,lemma,
! [A,B] : ( set_union2(A,set_difference(B,A)) = set_union2(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
tff(f_241,lemma,
! [A,B] :
( subset(A,B)
=> ( B = set_union2(A,set_difference(B,A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_xboole_1) ).
tff(f_79,axiom,
! [A,B,C] :
( ( C = set_union2(A,B) )
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
tff(f_86,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
tff(c_160,plain,
empty('#skF_17'),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_253,plain,
! [A_144] :
( ( empty_set = A_144 )
| ~ empty(A_144) ),
inference(cnfTransformation,[status(thm)],[f_276]) ).
tff(c_262,plain,
empty_set = '#skF_17',
inference(resolution,[status(thm)],[c_160,c_253]) ).
tff(c_146,plain,
! [A_65] : ( singleton(A_65) != empty_set ),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_266,plain,
! [A_65] : ( singleton(A_65) != '#skF_17' ),
inference(demodulation,[status(thm),theory(equality)],[c_262,c_146]) ).
tff(c_150,plain,
( in('#skF_13','#skF_14')
| ~ in('#skF_15','#skF_16') ),
inference(cnfTransformation,[status(thm)],[f_145]) ).
tff(c_263,plain,
~ in('#skF_15','#skF_16'),
inference(splitLeft,[status(thm)],[c_150]) ).
tff(c_32,plain,
! [A_18] :
( ( empty_set = A_18 )
| in('#skF_3'(A_18),A_18) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_944,plain,
! [A_214] :
( ( A_214 = '#skF_17' )
| in('#skF_3'(A_214),A_214) ),
inference(demodulation,[status(thm),theory(equality)],[c_262,c_32]) ).
tff(c_18,plain,
! [C_17,A_13] :
( ( C_17 = A_13 )
| ~ in(C_17,singleton(A_13)) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_948,plain,
! [A_13] :
( ( '#skF_3'(singleton(A_13)) = A_13 )
| ( singleton(A_13) = '#skF_17' ) ),
inference(resolution,[status(thm)],[c_944,c_18]) ).
tff(c_960,plain,
! [A_13] : ( '#skF_3'(singleton(A_13)) = A_13 ),
inference(negUnitSimplification,[status(thm)],[c_266,c_948]) ).
tff(c_943,plain,
! [A_18] :
( ( A_18 = '#skF_17' )
| in('#skF_3'(A_18),A_18) ),
inference(demodulation,[status(thm),theory(equality)],[c_262,c_32]) ).
tff(c_154,plain,
( in('#skF_13','#skF_14')
| subset(singleton('#skF_15'),'#skF_16') ),
inference(cnfTransformation,[status(thm)],[f_145]) ).
tff(c_439,plain,
subset(singleton('#skF_15'),'#skF_16'),
inference(splitLeft,[status(thm)],[c_154]) ).
tff(c_202,plain,
! [A_100,B_101] : ( set_union2(A_100,set_difference(B_101,A_100)) = set_union2(A_100,B_101) ),
inference(cnfTransformation,[status(thm)],[f_211]) ).
tff(c_216,plain,
! [A_111,B_112] :
( ( set_union2(A_111,set_difference(B_112,A_111)) = B_112 )
| ~ subset(A_111,B_112) ),
inference(cnfTransformation,[status(thm)],[f_241]) ).
tff(c_1244,plain,
! [A_237,B_238] :
( ( set_union2(A_237,B_238) = B_238 )
| ~ subset(A_237,B_238) ),
inference(demodulation,[status(thm),theory(equality)],[c_202,c_216]) ).
tff(c_1281,plain,
set_union2(singleton('#skF_15'),'#skF_16') = '#skF_16',
inference(resolution,[status(thm)],[c_439,c_1244]) ).
tff(c_1883,plain,
! [D_254,A_255,B_256] :
( ~ in(D_254,A_255)
| in(D_254,set_union2(A_255,B_256)) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_2195,plain,
! [D_267] :
( ~ in(D_267,singleton('#skF_15'))
| in(D_267,'#skF_16') ),
inference(superposition,[status(thm),theory(equality)],[c_1281,c_1883]) ).
tff(c_2199,plain,
( in('#skF_3'(singleton('#skF_15')),'#skF_16')
| ( singleton('#skF_15') = '#skF_17' ) ),
inference(resolution,[status(thm)],[c_943,c_2195]) ).
tff(c_2205,plain,
( in('#skF_15','#skF_16')
| ( singleton('#skF_15') = '#skF_17' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_960,c_2199]) ).
tff(c_2207,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_266,c_263,c_2205]) ).
tff(c_2209,plain,
~ subset(singleton('#skF_15'),'#skF_16'),
inference(splitRight,[status(thm)],[c_154]) ).
tff(c_152,plain,
( ~ subset(singleton('#skF_13'),'#skF_14')
| subset(singleton('#skF_15'),'#skF_16') ),
inference(cnfTransformation,[status(thm)],[f_145]) ).
tff(c_2260,plain,
~ subset(singleton('#skF_13'),'#skF_14'),
inference(negUnitSimplification,[status(thm)],[c_2209,c_152]) ).
tff(c_2208,plain,
in('#skF_13','#skF_14'),
inference(splitRight,[status(thm)],[c_154]) ).
tff(c_4755,plain,
! [A_427,B_428] :
( in('#skF_8'(A_427,B_428),A_427)
| subset(A_427,B_428) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_41446,plain,
! [A_52514,B_52515] :
( ( '#skF_8'(singleton(A_52514),B_52515) = A_52514 )
| subset(singleton(A_52514),B_52515) ),
inference(resolution,[status(thm)],[c_4755,c_18]) ).
tff(c_41533,plain,
'#skF_8'(singleton('#skF_13'),'#skF_14') = '#skF_13',
inference(resolution,[status(thm)],[c_41446,c_2260]) ).
tff(c_72,plain,
! [A_34,B_35] :
( ~ in('#skF_8'(A_34,B_35),B_35)
| subset(A_34,B_35) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_41567,plain,
( ~ in('#skF_13','#skF_14')
| subset(singleton('#skF_13'),'#skF_14') ),
inference(superposition,[status(thm),theory(equality)],[c_41533,c_72]) ).
tff(c_41577,plain,
subset(singleton('#skF_13'),'#skF_14'),
inference(demodulation,[status(thm),theory(equality)],[c_2208,c_41567]) ).
tff(c_41579,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2260,c_41577]) ).
tff(c_41581,plain,
in('#skF_15','#skF_16'),
inference(splitRight,[status(thm)],[c_150]) ).
tff(c_148,plain,
( ~ subset(singleton('#skF_13'),'#skF_14')
| ~ in('#skF_15','#skF_16') ),
inference(cnfTransformation,[status(thm)],[f_145]) ).
tff(c_41626,plain,
~ subset(singleton('#skF_13'),'#skF_14'),
inference(demodulation,[status(thm),theory(equality)],[c_41581,c_148]) ).
tff(c_41580,plain,
in('#skF_13','#skF_14'),
inference(splitRight,[status(thm)],[c_150]) ).
tff(c_46182,plain,
! [A_53029,B_53030] :
( in('#skF_8'(A_53029,B_53030),A_53029)
| subset(A_53029,B_53030) ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_84875,plain,
! [A_110465,B_110466] :
( ( '#skF_8'(singleton(A_110465),B_110466) = A_110465 )
| subset(singleton(A_110465),B_110466) ),
inference(resolution,[status(thm)],[c_46182,c_18]) ).
tff(c_84950,plain,
'#skF_8'(singleton('#skF_13'),'#skF_14') = '#skF_13',
inference(resolution,[status(thm)],[c_84875,c_41626]) ).
tff(c_84992,plain,
( ~ in('#skF_13','#skF_14')
| subset(singleton('#skF_13'),'#skF_14') ),
inference(superposition,[status(thm),theory(equality)],[c_84950,c_72]) ).
tff(c_85001,plain,
subset(singleton('#skF_13'),'#skF_14'),
inference(demodulation,[status(thm),theory(equality)],[c_41580,c_84992]) ).
tff(c_85003,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_41626,c_85001]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU144+2 : TPTP v8.1.2. Released v3.3.0.
% 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 : n008.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 11:53:33 EDT 2023
% 0.13/0.34 % CPUTime :
% 22.66/10.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.66/10.45
% 22.66/10.45 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 22.74/10.48
% 22.74/10.48 Inference rules
% 22.74/10.48 ----------------------
% 22.74/10.48 #Ref : 5
% 22.74/10.48 #Sup : 20431
% 22.74/10.48 #Fact : 20
% 22.74/10.48 #Define : 0
% 22.74/10.48 #Split : 28
% 22.74/10.48 #Chain : 0
% 22.74/10.48 #Close : 0
% 22.74/10.48
% 22.74/10.48 Ordering : KBO
% 22.74/10.48
% 22.74/10.48 Simplification rules
% 22.74/10.48 ----------------------
% 22.74/10.48 #Subsume : 9487
% 22.74/10.48 #Demod : 5460
% 22.74/10.48 #Tautology : 4850
% 22.74/10.48 #SimpNegUnit : 249
% 22.74/10.48 #BackRed : 32
% 22.74/10.48
% 22.74/10.48 #Partial instantiations: 63112
% 22.74/10.48 #Strategies tried : 1
% 22.74/10.48
% 22.74/10.48 Timing (in seconds)
% 22.74/10.48 ----------------------
% 22.74/10.48 Preprocessing : 0.66
% 22.74/10.48 Parsing : 0.32
% 22.74/10.48 CNF conversion : 0.06
% 22.74/10.48 Main loop : 8.77
% 22.74/10.48 Inferencing : 2.15
% 22.74/10.48 Reduction : 3.70
% 22.74/10.48 Demodulation : 2.60
% 22.74/10.48 BG Simplification : 0.12
% 22.74/10.48 Subsumption : 2.31
% 22.74/10.48 Abstraction : 0.14
% 22.74/10.48 MUC search : 0.00
% 22.74/10.48 Cooper : 0.00
% 22.74/10.48 Total : 9.48
% 22.74/10.48 Index Insertion : 0.00
% 22.74/10.48 Index Deletion : 0.00
% 22.74/10.48 Index Matching : 0.00
% 22.74/10.48 BG Taut test : 0.00
%------------------------------------------------------------------------------