TSTP Solution File: SET017-6 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET017-6 : 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/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 : n027.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 10:55:33 EDT 2023
% Result : Unsatisfiable 7.14s 2.65s
% Output : CNFRefutation 7.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 58
% Syntax : Number of formulae : 86 ( 23 unt; 50 typ; 0 def)
% Number of atoms : 52 ( 19 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 17 ~; 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,
y != z,
file(unknown,unknown) ).
tff(f_644,axiom,
unordered_pair(x,y) = unordered_pair(x,z),
file(unknown,unknown) ).
tff(f_116,axiom,
! [Y,X] :
( ~ member(Y,universal_class)
| member(Y,unordered_pair(X,Y)) ),
file(unknown,unknown) ).
tff(f_645,axiom,
member(ordered_pair(y,z),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_123,axiom,
! [X] : ( unordered_pair(X,X) = singleton(X) ),
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,
z != y,
inference(cnfTransformation,[status(thm)],[f_647]) ).
tff(c_184,plain,
unordered_pair(x,z) = unordered_pair(x,y),
inference(cnfTransformation,[status(thm)],[f_644]) ).
tff(c_527,plain,
! [Y_243,X_244] :
( member(Y_243,unordered_pair(X_244,Y_243))
| ~ member(Y_243,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_530,plain,
( member(z,unordered_pair(x,y))
| ~ member(z,universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_184,c_527]) ).
tff(c_605,plain,
~ member(z,universal_class),
inference(splitLeft,[status(thm)],[c_530]) ).
tff(c_186,plain,
member(ordered_pair(y,z),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(z,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(z,unordered_pair(x,y)),
inference(splitRight,[status(thm)],[c_530]) ).
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 )
| ( z = x ) ),
inference(resolution,[status(thm)],[c_1520,c_1597]) ).
tff(c_1627,plain,
z = x,
inference(negUnitSimplification,[status(thm)],[c_188,c_1600]) ).
tff(c_1639,plain,
y != x,
inference(demodulation,[status(thm),theory(equality)],[c_1627,c_188]) ).
tff(c_24,plain,
! [X_24] : ( unordered_pair(X_24,X_24) = singleton(X_24) ),
inference(cnfTransformation,[status(thm)],[f_123]) ).
tff(c_1638,plain,
unordered_pair(x,y) = unordered_pair(x,x),
inference(demodulation,[status(thm),theory(equality)],[c_1627,c_184]) ).
tff(c_1640,plain,
unordered_pair(x,y) = singleton(x),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_1638]) ).
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_116]) ).
tff(c_1697,plain,
( member(y,singleton(x))
| ~ member(y,universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_1640,c_20]) ).
tff(c_1778,plain,
~ member(y,universal_class),
inference(splitLeft,[status(thm)],[c_1697]) ).
tff(c_1637,plain,
member(ordered_pair(y,x),cross_product(universal_class,universal_class)),
inference(demodulation,[status(thm),theory(equality)],[c_1627,c_186]) ).
tff(c_2492,plain,
! [U_447,X_448,V_449,Y_450] :
( member(U_447,X_448)
| ~ member(ordered_pair(U_447,V_449),cross_product(X_448,Y_450)) ),
inference(cnfTransformation,[status(thm)],[f_136]) ).
tff(c_2499,plain,
member(y,universal_class),
inference(resolution,[status(thm)],[c_1637,c_2492]) ).
tff(c_2504,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1778,c_2499]) ).
tff(c_2505,plain,
member(y,singleton(x)),
inference(splitRight,[status(thm)],[c_1697]) ).
tff(c_2843,plain,
! [X_479,U_480] :
( ( X_479 = U_480 )
| ( X_479 = U_480 )
| ~ member(U_480,singleton(X_479)) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_1597]) ).
tff(c_2850,plain,
y = x,
inference(resolution,[status(thm)],[c_2505,c_2843]) ).
tff(c_2877,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1639,c_1639,c_2850]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET017-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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
% 0.14/0.35 % Computer : n027.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 17:23:24 EDT 2023
% 0.14/0.35 % CPUTime :
% 7.14/2.65 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.14/2.65
% 7.14/2.65 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.14/2.68
% 7.14/2.68 Inference rules
% 7.14/2.68 ----------------------
% 7.14/2.68 #Ref : 0
% 7.14/2.68 #Sup : 612
% 7.14/2.68 #Fact : 0
% 7.14/2.68 #Define : 0
% 7.14/2.68 #Split : 27
% 7.14/2.68 #Chain : 0
% 7.14/2.68 #Close : 0
% 7.14/2.68
% 7.14/2.68 Ordering : KBO
% 7.14/2.68
% 7.14/2.68 Simplification rules
% 7.14/2.68 ----------------------
% 7.14/2.68 #Subsume : 93
% 7.14/2.68 #Demod : 82
% 7.14/2.68 #Tautology : 120
% 7.14/2.68 #SimpNegUnit : 10
% 7.14/2.68 #BackRed : 8
% 7.14/2.68
% 7.14/2.68 #Partial instantiations: 0
% 7.14/2.68 #Strategies tried : 1
% 7.14/2.68
% 7.14/2.68 Timing (in seconds)
% 7.14/2.68 ----------------------
% 7.14/2.68 Preprocessing : 0.69
% 7.14/2.68 Parsing : 0.36
% 7.14/2.68 CNF conversion : 0.05
% 7.14/2.68 Main loop : 0.88
% 7.14/2.68 Inferencing : 0.32
% 7.14/2.68 Reduction : 0.27
% 7.14/2.68 Demodulation : 0.20
% 7.14/2.68 BG Simplification : 0.05
% 7.14/2.69 Subsumption : 0.18
% 7.14/2.69 Abstraction : 0.03
% 7.14/2.69 MUC search : 0.00
% 7.14/2.69 Cooper : 0.00
% 7.14/2.69 Total : 1.62
% 7.14/2.69 Index Insertion : 0.00
% 7.14/2.69 Index Deletion : 0.00
% 7.14/2.69 Index Matching : 0.00
% 7.14/2.69 BG Taut test : 0.00
%------------------------------------------------------------------------------