TSTP Solution File: SET072-6 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET072-6 : 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 : n006.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 7.25s 2.75s
% Output : CNFRefutation 7.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 58
% Syntax : Number of formulae : 84 ( 21 unt; 50 typ; 0 def)
% Number of atoms : 50 ( 18 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 32 ( 16 ~; 16 |; 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 : 32 (; 32 !; 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_647,axiom,
x != y,
file(unknown,unknown) ).
tff(f_123,axiom,
! [X] : ( unordered_pair(X,X) = singleton(X) ),
file(unknown,unknown) ).
tff(f_644,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_645,axiom,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
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_136,axiom,
! [U,V,X,Y] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) ),
file(unknown,unknown) ).
tff(c_188,plain,
y != x,
inference(cnfTransformation,[status(thm)],[f_647]) ).
tff(c_24,plain,
! [X_24] : ( unordered_pair(X_24,X_24) = singleton(X_24) ),
inference(cnfTransformation,[status(thm)],[f_123]) ).
tff(c_184,plain,
unordered_pair(y,z) = unordered_pair(x,z),
inference(cnfTransformation,[status(thm)],[f_644]) ).
tff(c_535,plain,
! [X_246,Y_247] :
( member(X_246,unordered_pair(X_246,Y_247))
| ~ member(X_246,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_109]) ).
tff(c_538,plain,
( member(y,unordered_pair(x,z))
| ~ member(y,universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_184,c_535]) ).
tff(c_605,plain,
~ member(y,universal_class),
inference(splitLeft,[status(thm)],[c_538]) ).
tff(c_186,plain,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
inference(cnfTransformation,[status(thm)],[f_645]) ).
tff(c_1507,plain,
! [V_355,Y_356,U_357,X_358] :
( member(V_355,Y_356)
| ~ member(ordered_pair(U_357,V_355),cross_product(X_358,Y_356)) ),
inference(cnfTransformation,[status(thm)],[f_142]) ).
tff(c_1514,plain,
member(y,universal_class),
inference(resolution,[status(thm)],[c_186,c_1507]) ).
tff(c_1519,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_605,c_1514]) ).
tff(c_1520,plain,
member(y,unordered_pair(x,z)),
inference(splitRight,[status(thm)],[c_538]) ).
tff(c_1597,plain,
! [Y_369,U_370,X_371] :
( ( Y_369 = U_370 )
| ( X_371 = U_370 )
| ~ member(U_370,unordered_pair(X_371,Y_369)) ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_1600,plain,
( ( z = y )
| ( y = x ) ),
inference(resolution,[status(thm)],[c_1520,c_1597]) ).
tff(c_1627,plain,
z = y,
inference(negUnitSimplification,[status(thm)],[c_188,c_1600]) ).
tff(c_1636,plain,
unordered_pair(y,y) = unordered_pair(x,y),
inference(demodulation,[status(thm),theory(equality)],[c_1627,c_1627,c_184]) ).
tff(c_1637,plain,
unordered_pair(x,y) = singleton(y),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_1636]) ).
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_1656,plain,
( member(x,singleton(y))
| ~ member(x,universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_1637,c_18]) ).
tff(c_1715,plain,
~ member(x,universal_class),
inference(splitLeft,[status(thm)],[c_1656]) ).
tff(c_1889,plain,
! [U_391,X_392,V_393,Y_394] :
( member(U_391,X_392)
| ~ member(ordered_pair(U_391,V_393),cross_product(X_392,Y_394)) ),
inference(cnfTransformation,[status(thm)],[f_136]) ).
tff(c_1892,plain,
member(x,universal_class),
inference(resolution,[status(thm)],[c_186,c_1889]) ).
tff(c_1896,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1715,c_1892]) ).
tff(c_1897,plain,
member(x,singleton(y)),
inference(splitRight,[status(thm)],[c_1656]) ).
tff(c_2253,plain,
! [X_431,U_432] :
( ( X_431 = U_432 )
| ( X_431 = U_432 )
| ~ member(U_432,singleton(X_431)) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_1597]) ).
tff(c_2260,plain,
y = x,
inference(resolution,[status(thm)],[c_1897,c_2253]) ).
tff(c_2283,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_188,c_188,c_2260]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET072-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.12/0.13 % 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
% 0.13/0.34 % Computer : n006.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
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 16:54:58 EDT 2023
% 0.13/0.35 % CPUTime :
% 7.25/2.75 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.25/2.76
% 7.25/2.76 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.57/2.82
% 7.57/2.82 Inference rules
% 7.57/2.82 ----------------------
% 7.57/2.82 #Ref : 0
% 7.57/2.82 #Sup : 481
% 7.57/2.82 #Fact : 0
% 7.57/2.82 #Define : 0
% 7.57/2.82 #Split : 23
% 7.57/2.82 #Chain : 0
% 7.57/2.82 #Close : 0
% 7.57/2.82
% 7.57/2.82 Ordering : KBO
% 7.57/2.82
% 7.57/2.82 Simplification rules
% 7.57/2.82 ----------------------
% 7.57/2.82 #Subsume : 62
% 7.57/2.82 #Demod : 65
% 7.57/2.82 #Tautology : 102
% 7.57/2.82 #SimpNegUnit : 7
% 7.57/2.82 #BackRed : 5
% 7.57/2.82
% 7.57/2.82 #Partial instantiations: 0
% 7.57/2.82 #Strategies tried : 1
% 7.57/2.82
% 7.57/2.82 Timing (in seconds)
% 7.57/2.82 ----------------------
% 7.57/2.82 Preprocessing : 0.69
% 7.57/2.83 Parsing : 0.35
% 7.57/2.83 CNF conversion : 0.05
% 7.57/2.83 Main loop : 0.92
% 7.57/2.83 Inferencing : 0.32
% 7.57/2.83 Reduction : 0.28
% 7.57/2.83 Demodulation : 0.19
% 7.57/2.83 BG Simplification : 0.05
% 7.57/2.83 Subsumption : 0.19
% 7.57/2.83 Abstraction : 0.04
% 7.57/2.83 MUC search : 0.00
% 7.57/2.83 Cooper : 0.00
% 7.57/2.83 Total : 1.70
% 7.57/2.83 Index Insertion : 0.00
% 7.57/2.83 Index Deletion : 0.00
% 7.57/2.83 Index Matching : 0.00
% 7.57/2.83 BG Taut test : 0.00
%------------------------------------------------------------------------------