TSTP Solution File: SET762+4 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET762+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 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 : n013.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 10:56:58 EDT 2023
% Result : Theorem 6.37s 2.49s
% Output : CNFRefutation 6.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 78
% Syntax : Number of formulae : 90 ( 8 unt; 73 typ; 0 def)
% Number of atoms : 30 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 9 ~; 6 |; 2 &)
% ( 3 <=>; 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 : 249 ( 69 >; 180 *; 0 +; 0 <<)
% Number of predicates : 16 ( 15 usr; 1 prp; 0-6 aty)
% Number of functors : 58 ( 58 usr; 4 con; 0-8 aty)
% Number of variables : 30 (; 29 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ compose_predicate > isomorphism > increasing > decreasing > inverse_predicate > equal_maps > surjective > one_to_one > maps > injective > apply > subset > member > identity > equal_set > compose_function > inverse_image3 > inverse_function > image3 > unordered_pair > union > inverse_image2 > intersection > image2 > difference > #nlpp > sum > singleton > product > power_set > empty_set > #skF_10 > #skF_41 > #skF_9 > #skF_34 > #skF_6 > #skF_27 > #skF_24 > #skF_17 > #skF_18 > #skF_43 > #skF_35 > #skF_4 > #skF_11 > #skF_3 > #skF_38 > #skF_8 > #skF_40 > #skF_15 > #skF_26 > #skF_36 > #skF_31 > #skF_32 > #skF_13 > #skF_5 > #skF_37 > #skF_19 > #skF_29 > #skF_16 > #skF_7 > #skF_20 > #skF_42 > #skF_28 > #skF_2 > #skF_39 > #skF_12 > #skF_33 > #skF_25 > #skF_21 > #skF_14 > #skF_1 > #skF_30 > #skF_22 > #skF_23
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_10',type,
'#skF_10': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_41',type,
'#skF_41': $i ).
tff(isomorphism,type,
isomorphism: ( $i * $i * $i * $i * $i ) > $o ).
tff(equal_set,type,
equal_set: ( $i * $i ) > $o ).
tff(identity,type,
identity: ( $i * $i ) > $o ).
tff(compose_function,type,
compose_function: ( $i * $i * $i * $i * $i ) > $i ).
tff(power_set,type,
power_set: $i > $i ).
tff(decreasing,type,
decreasing: ( $i * $i * $i * $i * $i ) > $o ).
tff('#skF_9',type,
'#skF_9': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_34',type,
'#skF_34': ( $i * $i * $i * $i * $i ) > $i ).
tff(product,type,
product: $i > $i ).
tff(apply,type,
apply: ( $i * $i * $i ) > $o ).
tff(singleton,type,
singleton: $i > $i ).
tff(maps,type,
maps: ( $i * $i * $i ) > $o ).
tff(equal_maps,type,
equal_maps: ( $i * $i * $i * $i ) > $o ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff('#skF_27',type,
'#skF_27': ( $i * $i * $i ) > $i ).
tff('#skF_24',type,
'#skF_24': ( $i * $i * $i * $i ) > $i ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff('#skF_17',type,
'#skF_17': ( $i * $i ) > $i ).
tff('#skF_18',type,
'#skF_18': ( $i * $i * $i ) > $i ).
tff(sum,type,
sum: $i > $i ).
tff(intersection,type,
intersection: ( $i * $i ) > $i ).
tff(increasing,type,
increasing: ( $i * $i * $i * $i * $i ) > $o ).
tff('#skF_43',type,
'#skF_43': $i ).
tff(union,type,
union: ( $i * $i ) > $i ).
tff(inverse_image2,type,
inverse_image2: ( $i * $i ) > $i ).
tff('#skF_35',type,
'#skF_35': ( $i * $i * $i * $i * $i ) > $i ).
tff(compose_predicate,type,
compose_predicate: ( $i * $i * $i * $i * $i * $i ) > $o ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff('#skF_11',type,
'#skF_11': ( $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff(inverse_predicate,type,
inverse_predicate: ( $i * $i * $i * $i ) > $o ).
tff('#skF_38',type,
'#skF_38': ( $i * $i * $i * $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i * $i * $i ) > $i ).
tff('#skF_40',type,
'#skF_40': ( $i * $i * $i * $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': ( $i * $i * $i * $i ) > $i ).
tff(inverse_image3,type,
inverse_image3: ( $i * $i * $i ) > $i ).
tff(injective,type,
injective: ( $i * $i * $i ) > $o ).
tff('#skF_26',type,
'#skF_26': ( $i * $i * $i * $i ) > $i ).
tff('#skF_36',type,
'#skF_36': ( $i * $i * $i * $i * $i ) > $i ).
tff('#skF_31',type,
'#skF_31': ( $i * $i * $i * $i * $i ) > $i ).
tff(subset,type,
subset: ( $i * $i ) > $o ).
tff('#skF_32',type,
'#skF_32': ( $i * $i * $i * $i * $i ) > $i ).
tff('#skF_13',type,
'#skF_13': ( $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff('#skF_37',type,
'#skF_37': ( $i * $i * $i * $i * $i ) > $i ).
tff('#skF_19',type,
'#skF_19': ( $i * $i * $i ) > $i ).
tff('#skF_29',type,
'#skF_29': ( $i * $i * $i * $i * $i ) > $i ).
tff('#skF_16',type,
'#skF_16': ( $i * $i * $i * $i ) > $i ).
tff(surjective,type,
surjective: ( $i * $i * $i ) > $o ).
tff(image3,type,
image3: ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i * $i ) > $i ).
tff(empty_set,type,
empty_set: $i ).
tff(image2,type,
image2: ( $i * $i ) > $i ).
tff('#skF_20',type,
'#skF_20': ( $i * $i * $i ) > $i ).
tff('#skF_42',type,
'#skF_42': $i ).
tff('#skF_28',type,
'#skF_28': ( $i * $i * $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff('#skF_39',type,
'#skF_39': ( $i * $i * $i * $i * $i ) > $i ).
tff(difference,type,
difference: ( $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff('#skF_33',type,
'#skF_33': ( $i * $i * $i * $i * $i ) > $i ).
tff('#skF_25',type,
'#skF_25': ( $i * $i * $i ) > $i ).
tff('#skF_21',type,
'#skF_21': ( $i * $i * $i ) > $i ).
tff('#skF_14',type,
'#skF_14': ( $i * $i * $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_30',type,
'#skF_30': ( $i * $i * $i * $i * $i ) > $i ).
tff('#skF_22',type,
'#skF_22': ( $i * $i * $i * $i ) > $i ).
tff(inverse_function,type,
inverse_function: ( $i * $i * $i ) > $i ).
tff('#skF_23',type,
'#skF_23': ( $i * $i * $i * $i ) > $i ).
tff(one_to_one,type,
one_to_one: ( $i * $i * $i ) > $o ).
tff(f_57,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
tff(f_271,axiom,
! [F,A,Y] :
( member(Y,image2(F,A))
<=> ? [X] :
( member(X,A)
& apply(F,X,Y) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',image2) ).
tff(f_82,axiom,
! [X] : ~ member(X,empty_set),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',empty_set) ).
tff(f_63,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(A,B)
& subset(B,A) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',equal_set) ).
tff(f_364,negated_conjecture,
~ ! [F,A,B] :
( maps(F,A,B)
=> equal_set(image2(F,empty_set),empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIIa12) ).
tff(c_6,plain,
! [A_1,B_2] :
( member('#skF_1'(A_1,B_2),A_1)
| subset(A_1,B_2) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_2094,plain,
! [F_439,A_440,Y_441] :
( member('#skF_25'(F_439,A_440,Y_441),A_440)
| ~ member(Y_441,image2(F_439,A_440)) ),
inference(cnfTransformation,[status(thm)],[f_271]) ).
tff(c_30,plain,
! [X_16] : ~ member(X_16,empty_set),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_2190,plain,
! [Y_442,F_443] : ~ member(Y_442,image2(F_443,empty_set)),
inference(resolution,[status(thm)],[c_2094,c_30]) ).
tff(c_2237,plain,
! [F_446,B_447] : subset(image2(F_446,empty_set),B_447),
inference(resolution,[status(thm)],[c_6,c_2190]) ).
tff(c_308,plain,
! [A_250,B_251] :
( member('#skF_1'(A_250,B_251),A_250)
| subset(A_250,B_251) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_328,plain,
! [B_251] : subset(empty_set,B_251),
inference(resolution,[status(thm)],[c_308,c_30]) ).
tff(c_604,plain,
! [A_311,B_312] :
( equal_set(A_311,B_312)
| ~ subset(B_312,A_311)
| ~ subset(A_311,B_312) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_619,plain,
! [B_251] :
( equal_set(B_251,empty_set)
| ~ subset(B_251,empty_set) ),
inference(resolution,[status(thm)],[c_328,c_604]) ).
tff(c_2249,plain,
! [F_446] : equal_set(image2(F_446,empty_set),empty_set),
inference(resolution,[status(thm)],[c_2237,c_619]) ).
tff(c_286,plain,
~ equal_set(image2('#skF_41',empty_set),empty_set),
inference(cnfTransformation,[status(thm)],[f_364]) ).
tff(c_2253,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2249,c_286]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET762+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.00/0.14 % 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
% 0.18/0.35 % Computer : n013.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Thu Aug 3 16:19:32 EDT 2023
% 0.18/0.36 % CPUTime :
% 6.37/2.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.37/2.50
% 6.37/2.50 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.54/2.54
% 6.54/2.54 Inference rules
% 6.54/2.54 ----------------------
% 6.54/2.54 #Ref : 0
% 6.54/2.54 #Sup : 418
% 6.54/2.54 #Fact : 0
% 6.54/2.54 #Define : 0
% 6.54/2.54 #Split : 0
% 6.54/2.54 #Chain : 0
% 6.54/2.54 #Close : 0
% 6.54/2.54
% 6.54/2.54 Ordering : KBO
% 6.54/2.54
% 6.54/2.54 Simplification rules
% 6.54/2.54 ----------------------
% 6.54/2.54 #Subsume : 0
% 6.54/2.54 #Demod : 70
% 6.54/2.54 #Tautology : 83
% 6.54/2.54 #SimpNegUnit : 0
% 6.54/2.54 #BackRed : 1
% 6.54/2.54
% 6.54/2.54 #Partial instantiations: 0
% 6.54/2.54 #Strategies tried : 1
% 6.54/2.54
% 6.54/2.54 Timing (in seconds)
% 6.54/2.54 ----------------------
% 6.64/2.54 Preprocessing : 0.70
% 6.64/2.54 Parsing : 0.33
% 6.64/2.54 CNF conversion : 0.07
% 6.64/2.54 Main loop : 0.70
% 6.64/2.54 Inferencing : 0.25
% 6.64/2.54 Reduction : 0.21
% 6.64/2.54 Demodulation : 0.15
% 6.64/2.54 BG Simplification : 0.05
% 6.64/2.54 Subsumption : 0.15
% 6.64/2.54 Abstraction : 0.04
% 6.64/2.54 MUC search : 0.00
% 6.64/2.54 Cooper : 0.00
% 6.64/2.54 Total : 1.45
% 6.64/2.54 Index Insertion : 0.00
% 6.64/2.54 Index Deletion : 0.00
% 6.64/2.54 Index Matching : 0.00
% 6.64/2.54 BG Taut test : 0.00
%------------------------------------------------------------------------------