TSTP Solution File: SET072-7 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET072-7 : 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 : n005.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 10:55:49 EDT 2023
% Result : Unsatisfiable 6.50s 2.48s
% Output : CNFRefutation 6.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 60
% Syntax : Number of formulae : 90 ( 23 unt; 50 typ; 0 def)
% Number of atoms : 62 ( 21 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 42 ( 20 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 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 : 41 ( 41 usr; 11 con; 0-3 aty)
% Number of variables : 47 (; 47 !; 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 > z > 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(z,type,
z: $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_777,axiom,
x != y,
file(unknown,unknown) ).
tff(f_747,axiom,
! [X,Y] : subclass(singleton(X),unordered_pair(X,Y)),
file(unknown,unknown) ).
tff(f_775,axiom,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
file(unknown,unknown) ).
tff(f_136,axiom,
! [U,V,X,Y] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) ),
file(unknown,unknown) ).
tff(f_123,axiom,
! [X] : ( unordered_pair(X,X) = singleton(X) ),
file(unknown,unknown) ).
tff(f_774,axiom,
unordered_pair(x,z) = unordered_pair(y,z),
file(unknown,unknown) ).
tff(f_109,axiom,
! [X,Y] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ),
file(unknown,unknown) ).
tff(f_142,axiom,
! [U,V,X,Y] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) ),
file(unknown,unknown) ).
tff(f_102,axiom,
! [U,X,Y] :
( ~ member(U,unordered_pair(X,Y))
| ( U = X )
| ( U = Y ) ),
file(unknown,unknown) ).
tff(f_57,axiom,
! [X,Y,U] :
( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) ),
file(unknown,unknown) ).
tff(c_234,plain,
y != x,
inference(cnfTransformation,[status(thm)],[f_777]) ).
tff(c_218,plain,
! [X_213,Y_214] : subclass(singleton(X_213),unordered_pair(X_213,Y_214)),
inference(cnfTransformation,[status(thm)],[f_747]) ).
tff(c_232,plain,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
inference(cnfTransformation,[status(thm)],[f_775]) ).
tff(c_1875,plain,
! [U_375,X_376,V_377,Y_378] :
( member(U_375,X_376)
| ~ member(ordered_pair(U_375,V_377),cross_product(X_376,Y_378)) ),
inference(cnfTransformation,[status(thm)],[f_136]) ).
tff(c_1879,plain,
member(x,universal_class),
inference(resolution,[status(thm)],[c_232,c_1875]) ).
tff(c_24,plain,
! [X_24] : ( unordered_pair(X_24,X_24) = singleton(X_24) ),
inference(cnfTransformation,[status(thm)],[f_123]) ).
tff(c_230,plain,
unordered_pair(y,z) = unordered_pair(x,z),
inference(cnfTransformation,[status(thm)],[f_774]) ).
tff(c_538,plain,
! [X_282,Y_283] :
( member(X_282,unordered_pair(X_282,Y_283))
| ~ member(X_282,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_109]) ).
tff(c_547,plain,
( member(y,unordered_pair(x,z))
| ~ member(y,universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_230,c_538]) ).
tff(c_1424,plain,
~ member(y,universal_class),
inference(splitLeft,[status(thm)],[c_547]) ).
tff(c_1712,plain,
! [V_367,Y_368,U_369,X_370] :
( member(V_367,Y_368)
| ~ member(ordered_pair(U_369,V_367),cross_product(X_370,Y_368)) ),
inference(cnfTransformation,[status(thm)],[f_142]) ).
tff(c_1715,plain,
member(y,universal_class),
inference(resolution,[status(thm)],[c_232,c_1712]) ).
tff(c_1719,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1424,c_1715]) ).
tff(c_1720,plain,
member(y,unordered_pair(x,z)),
inference(splitRight,[status(thm)],[c_547]) ).
tff(c_1753,plain,
! [Y_372,U_373,X_374] :
( ( Y_372 = U_373 )
| ( X_374 = U_373 )
| ~ member(U_373,unordered_pair(X_374,Y_372)) ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_1756,plain,
( ( z = y )
| ( y = x ) ),
inference(resolution,[status(thm)],[c_1720,c_1753]) ).
tff(c_1807,plain,
z = y,
inference(negUnitSimplification,[status(thm)],[c_234,c_1756]) ).
tff(c_1820,plain,
unordered_pair(y,y) = unordered_pair(x,y),
inference(demodulation,[status(thm),theory(equality)],[c_1807,c_1807,c_230]) ).
tff(c_1822,plain,
unordered_pair(x,y) = singleton(y),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_1820]) ).
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_109]) ).
tff(c_1853,plain,
( member(x,singleton(y))
| ~ member(x,universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_1822,c_18]) ).
tff(c_2049,plain,
member(x,singleton(y)),
inference(demodulation,[status(thm),theory(equality)],[c_1879,c_1853]) ).
tff(c_2,plain,
! [U_3,Y_2,X_1] :
( member(U_3,Y_2)
| ~ member(U_3,X_1)
| ~ subclass(X_1,Y_2) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_2094,plain,
! [Y_390] :
( member(x,Y_390)
| ~ subclass(singleton(y),Y_390) ),
inference(resolution,[status(thm)],[c_2049,c_2]) ).
tff(c_2133,plain,
! [Y_391] : member(x,unordered_pair(y,Y_391)),
inference(resolution,[status(thm)],[c_218,c_2094]) ).
tff(c_16,plain,
! [Y_17,U_15,X_16] :
( ( Y_17 = U_15 )
| ( X_16 = U_15 )
| ~ member(U_15,unordered_pair(X_16,Y_17)) ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_2136,plain,
! [Y_391] :
( ( x = Y_391 )
| ( y = x ) ),
inference(resolution,[status(thm)],[c_2133,c_16]) ).
tff(c_2163,plain,
! [Y_392] : ( x = Y_392 ),
inference(negUnitSimplification,[status(thm)],[c_234,c_2136]) ).
tff(c_2384,plain,
y = x,
inference(superposition,[status(thm),theory(equality)],[c_2163,c_1807]) ).
tff(c_2642,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_234,c_2384]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET072-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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
% 0.14/0.35 % Computer : n005.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 16:38:41 EDT 2023
% 0.14/0.35 % CPUTime :
% 6.50/2.48 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.50/2.49
% 6.50/2.49 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.50/2.52
% 6.50/2.52 Inference rules
% 6.50/2.52 ----------------------
% 6.50/2.52 #Ref : 0
% 6.50/2.52 #Sup : 652
% 6.50/2.52 #Fact : 0
% 6.50/2.52 #Define : 0
% 6.50/2.52 #Split : 7
% 6.50/2.52 #Chain : 0
% 6.50/2.52 #Close : 0
% 6.50/2.52
% 6.50/2.52 Ordering : KBO
% 6.50/2.52
% 6.50/2.52 Simplification rules
% 6.50/2.52 ----------------------
% 6.50/2.52 #Subsume : 61
% 6.50/2.52 #Demod : 96
% 6.50/2.52 #Tautology : 167
% 6.50/2.52 #SimpNegUnit : 9
% 6.50/2.52 #BackRed : 8
% 6.50/2.52
% 6.50/2.52 #Partial instantiations: 960
% 6.50/2.52 #Strategies tried : 1
% 6.50/2.52
% 6.50/2.52 Timing (in seconds)
% 6.50/2.52 ----------------------
% 6.50/2.52 Preprocessing : 0.68
% 6.50/2.52 Parsing : 0.33
% 6.50/2.52 CNF conversion : 0.05
% 6.50/2.52 Main loop : 0.81
% 6.50/2.52 Inferencing : 0.30
% 6.50/2.52 Reduction : 0.25
% 6.50/2.52 Demodulation : 0.18
% 6.50/2.52 BG Simplification : 0.05
% 6.50/2.52 Subsumption : 0.14
% 6.50/2.52 Abstraction : 0.03
% 6.50/2.52 MUC search : 0.00
% 6.50/2.52 Cooper : 0.00
% 6.50/2.52 Total : 1.53
% 6.50/2.52 Index Insertion : 0.00
% 6.50/2.52 Index Deletion : 0.00
% 6.50/2.52 Index Matching : 0.00
% 6.50/2.52 BG Taut test : 0.00
%------------------------------------------------------------------------------