TSTP Solution File: SET067-7 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET067-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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 : n028.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 10:55:48 EDT 2023
% Result : Unsatisfiable 8.94s 3.25s
% Output : CNFRefutation 9.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 61
% Syntax : Number of formulae : 90 ( 19 unt; 49 typ; 0 def)
% Number of atoms : 69 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 53 ( 25 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 65 ( 39 >; 26 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 40 ( 40 usr; 10 con; 0-3 aty)
% Number of variables : 72 (; 72 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ homomorphism > compatible > subclass > member > single_valued_class > operation > one_to_one > inductive > function > restrict > range > not_homomorphism2 > not_homomorphism1 > domain > unordered_pair > union > symmetric_difference > ordered_pair > not_subclass_element > intersection > image > cross_product > compose > apply > #nlpp > sum_class > successor > singleton > second > rotate > regular > range_of > power_class > inverse > flip > first > domain_of > diagonalise > complement > cantor > y > x > universal_class > successor_relation > subset_relation > omega > null_class > identity_relation > element_relation > choice
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(omega,type,
omega: $i ).
tff(null_class,type,
null_class: $i ).
tff(rotate,type,
rotate: $i > $i ).
tff(subclass,type,
subclass: ( $i * $i ) > $o ).
tff(singleton,type,
singleton: $i > $i ).
tff(single_valued_class,type,
single_valued_class: $i > $o ).
tff(operation,type,
operation: $i > $o ).
tff(sum_class,type,
sum_class: $i > $i ).
tff(x,type,
x: $i ).
tff(apply,type,
apply: ( $i * $i ) > $i ).
tff(compatible,type,
compatible: ( $i * $i * $i ) > $o ).
tff(unordered_pair,type,
unordered_pair: ( $i * $i ) > $i ).
tff(regular,type,
regular: $i > $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(ordered_pair,type,
ordered_pair: ( $i * $i ) > $i ).
tff(one_to_one,type,
one_to_one: $i > $o ).
tff(element_relation,type,
element_relation: $i ).
tff(intersection,type,
intersection: ( $i * $i ) > $i ).
tff(second,type,
second: $i > $i ).
tff(union,type,
union: ( $i * $i ) > $i ).
tff(function,type,
function: $i > $o ).
tff(symmetric_difference,type,
symmetric_difference: ( $i * $i ) > $i ).
tff(flip,type,
flip: $i > $i ).
tff(power_class,type,
power_class: $i > $i ).
tff(cross_product,type,
cross_product: ( $i * $i ) > $i ).
tff(choice,type,
choice: $i ).
tff(y,type,
y: $i ).
tff(subset_relation,type,
subset_relation: $i ).
tff(restrict,type,
restrict: ( $i * $i * $i ) > $i ).
tff(complement,type,
complement: $i > $i ).
tff(member,type,
member: ( $i * $i ) > $o ).
tff(not_subclass_element,type,
not_subclass_element: ( $i * $i ) > $i ).
tff(range,type,
range: ( $i * $i * $i ) > $i ).
tff(first,type,
first: $i > $i ).
tff(diagonalise,type,
diagonalise: $i > $i ).
tff(homomorphism,type,
homomorphism: ( $i * $i * $i ) > $o ).
tff(cantor,type,
cantor: $i > $i ).
tff(image,type,
image: ( $i * $i ) > $i ).
tff(range_of,type,
range_of: $i > $i ).
tff(inductive,type,
inductive: $i > $o ).
tff(domain,type,
domain: ( $i * $i * $i ) > $i ).
tff(compose,type,
compose: ( $i * $i ) > $i ).
tff(domain_of,type,
domain_of: $i > $i ).
tff(not_homomorphism2,type,
not_homomorphism2: ( $i * $i * $i ) > $i ).
tff(successor,type,
successor: $i > $i ).
tff(successor_relation,type,
successor_relation: $i ).
tff(identity_relation,type,
identity_relation: $i ).
tff(not_homomorphism1,type,
not_homomorphism1: ( $i * $i * $i ) > $i ).
tff(universal_class,type,
universal_class: $i ).
tff(f_746,axiom,
~ subclass(singleton(x),unordered_pair(x,y)),
file(unknown,unknown) ).
tff(f_62,axiom,
! [X,Y] :
( member(not_subclass_element(X,Y),X)
| subclass(X,Y) ),
file(unknown,unknown) ).
tff(f_124,axiom,
! [X] : ( unordered_pair(X,X) = singleton(X) ),
file(unknown,unknown) ).
tff(f_103,axiom,
! [U,X,Y] :
( ~ member(U,unordered_pair(X,Y))
| ( U = X )
| ( U = Y ) ),
file(unknown,unknown) ).
tff(f_151,axiom,
! [U,X,V,Y] :
( ~ member(U,X)
| ~ member(V,Y)
| member(ordered_pair(U,V),cross_product(X,Y)) ),
file(unknown,unknown) ).
tff(f_661,axiom,
! [U,V,X,Y] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,universal_class) ),
file(unknown,unknown) ).
tff(f_744,axiom,
! [X,Y] : ( unordered_pair(X,Y) = unordered_pair(Y,X) ),
file(unknown,unknown) ).
tff(f_120,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
file(unknown,unknown) ).
tff(f_129,axiom,
! [X,Y] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ),
file(unknown,unknown) ).
tff(f_117,axiom,
! [Y,X] :
( ~ member(Y,universal_class)
| member(Y,unordered_pair(X,Y)) ),
file(unknown,unknown) ).
tff(f_110,axiom,
! [X,Y] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ),
file(unknown,unknown) ).
tff(f_67,axiom,
! [X,Y] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
file(unknown,unknown) ).
tff(c_218,plain,
~ subclass(singleton(x),unordered_pair(x,y)),
inference(cnfTransformation,[status(thm)],[f_746]) ).
tff(c_4,plain,
! [X_4,Y_5] :
( subclass(X_4,Y_5)
| member(not_subclass_element(X_4,Y_5),X_4) ),
inference(cnfTransformation,[status(thm)],[f_62]) ).
tff(c_24,plain,
! [X_24] : ( unordered_pair(X_24,X_24) = singleton(X_24) ),
inference(cnfTransformation,[status(thm)],[f_124]) ).
tff(c_767,plain,
! [Y_304,U_305,X_306] :
( ( Y_304 = U_305 )
| ( X_306 = U_305 )
| ~ member(U_305,unordered_pair(X_306,Y_304)) ),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_837,plain,
! [X_311,U_312] :
( ( X_311 = U_312 )
| ( X_311 = U_312 )
| ~ member(U_312,singleton(X_311)) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_767]) ).
tff(c_4088,plain,
! [X_519,Y_520] :
( ( not_subclass_element(singleton(X_519),Y_520) = X_519 )
| subclass(singleton(X_519),Y_520) ),
inference(resolution,[status(thm)],[c_4,c_837]) ).
tff(c_4139,plain,
not_subclass_element(singleton(x),unordered_pair(x,y)) = x,
inference(resolution,[status(thm)],[c_4088,c_218]) ).
tff(c_3328,plain,
! [U_478,V_479,X_480,Y_481] :
( member(ordered_pair(U_478,V_479),cross_product(X_480,Y_481))
| ~ member(V_479,Y_481)
| ~ member(U_478,X_480) ),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_188,plain,
! [U_185,V_186,X_187,Y_188] :
( member(U_185,universal_class)
| ~ member(ordered_pair(U_185,V_186),cross_product(X_187,Y_188)) ),
inference(cnfTransformation,[status(thm)],[f_661]) ).
tff(c_3358,plain,
! [U_478,V_479,Y_481,X_480] :
( member(U_478,universal_class)
| ~ member(V_479,Y_481)
| ~ member(U_478,X_480) ),
inference(resolution,[status(thm)],[c_3328,c_188]) ).
tff(c_3501,plain,
! [V_479,Y_481] : ~ member(V_479,Y_481),
inference(splitLeft,[status(thm)],[c_3358]) ).
tff(c_216,plain,
! [Y_212,X_211] : ( unordered_pair(Y_212,X_211) = unordered_pair(X_211,Y_212) ),
inference(cnfTransformation,[status(thm)],[f_744]) ).
tff(c_22,plain,
! [X_22,Y_23] : member(unordered_pair(X_22,Y_23),universal_class),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_1505,plain,
! [X_359,Y_360] : ( unordered_pair(singleton(X_359),unordered_pair(X_359,singleton(Y_360))) = ordered_pair(X_359,Y_360) ),
inference(cnfTransformation,[status(thm)],[f_129]) ).
tff(c_20,plain,
! [Y_20,X_21] :
( member(Y_20,unordered_pair(X_21,Y_20))
| ~ member(Y_20,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_1519,plain,
! [X_359,Y_360] :
( member(unordered_pair(X_359,singleton(Y_360)),ordered_pair(X_359,Y_360))
| ~ member(unordered_pair(X_359,singleton(Y_360)),universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_1505,c_20]) ).
tff(c_1595,plain,
! [X_366,Y_367] : member(unordered_pair(X_366,singleton(Y_367)),ordered_pair(X_366,Y_367)),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_1519]) ).
tff(c_1605,plain,
! [Y_367,Y_212] : member(unordered_pair(singleton(Y_367),Y_212),ordered_pair(Y_212,Y_367)),
inference(superposition,[status(thm),theory(equality)],[c_216,c_1595]) ).
tff(c_3554,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3501,c_1605]) ).
tff(c_3565,plain,
! [U_487,X_488] :
( member(U_487,universal_class)
| ~ member(U_487,X_488) ),
inference(splitRight,[status(thm)],[c_3358]) ).
tff(c_3666,plain,
! [X_4,Y_5] :
( member(not_subclass_element(X_4,Y_5),universal_class)
| subclass(X_4,Y_5) ),
inference(resolution,[status(thm)],[c_4,c_3565]) ).
tff(c_4144,plain,
( member(x,universal_class)
| subclass(singleton(x),unordered_pair(x,y)) ),
inference(superposition,[status(thm),theory(equality)],[c_4139,c_3666]) ).
tff(c_4159,plain,
member(x,universal_class),
inference(negUnitSimplification,[status(thm)],[c_218,c_4144]) ).
tff(c_18,plain,
! [X_18,Y_19] :
( member(X_18,unordered_pair(X_18,Y_19))
| ~ member(X_18,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_6,plain,
! [X_6,Y_7] :
( subclass(X_6,Y_7)
| ~ member(not_subclass_element(X_6,Y_7),Y_7) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_4153,plain,
( subclass(singleton(x),unordered_pair(x,y))
| ~ member(x,unordered_pair(x,y)) ),
inference(superposition,[status(thm),theory(equality)],[c_4139,c_6]) ).
tff(c_4160,plain,
~ member(x,unordered_pair(x,y)),
inference(negUnitSimplification,[status(thm)],[c_218,c_4153]) ).
tff(c_4197,plain,
~ member(x,universal_class),
inference(resolution,[status(thm)],[c_18,c_4160]) ).
tff(c_4201,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4159,c_4197]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET067-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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
% 0.12/0.35 % Computer : n028.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Thu Aug 3 16:25:24 EDT 2023
% 0.12/0.35 % CPUTime :
% 8.94/3.25 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.23/3.26
% 9.23/3.26 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.30/3.31
% 9.30/3.31 Inference rules
% 9.30/3.31 ----------------------
% 9.30/3.31 #Ref : 0
% 9.30/3.31 #Sup : 962
% 9.30/3.31 #Fact : 2
% 9.30/3.31 #Define : 0
% 9.30/3.31 #Split : 25
% 9.30/3.31 #Chain : 0
% 9.30/3.31 #Close : 0
% 9.30/3.31
% 9.30/3.31 Ordering : KBO
% 9.30/3.31
% 9.30/3.31 Simplification rules
% 9.30/3.31 ----------------------
% 9.30/3.31 #Subsume : 213
% 9.30/3.31 #Demod : 147
% 9.30/3.31 #Tautology : 191
% 9.30/3.31 #SimpNegUnit : 74
% 9.30/3.31 #BackRed : 29
% 9.30/3.31
% 9.30/3.31 #Partial instantiations: 0
% 9.30/3.31 #Strategies tried : 1
% 9.30/3.31
% 9.30/3.31 Timing (in seconds)
% 9.30/3.31 ----------------------
% 9.30/3.31 Preprocessing : 0.77
% 9.30/3.31 Parsing : 0.39
% 9.30/3.31 CNF conversion : 0.05
% 9.30/3.31 Main loop : 1.28
% 9.30/3.31 Inferencing : 0.42
% 9.30/3.31 Reduction : 0.43
% 9.30/3.31 Demodulation : 0.30
% 9.30/3.31 BG Simplification : 0.06
% 9.30/3.31 Subsumption : 0.27
% 9.30/3.31 Abstraction : 0.04
% 9.30/3.31 MUC search : 0.00
% 9.30/3.31 Cooper : 0.00
% 9.50/3.31 Total : 2.13
% 9.50/3.31 Index Insertion : 0.00
% 9.50/3.31 Index Deletion : 0.00
% 9.50/3.31 Index Matching : 0.00
% 9.50/3.31 BG Taut test : 0.00
%------------------------------------------------------------------------------