TSTP Solution File: SET108-6 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET108-6 : 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 : n032.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 10:56:00 EDT 2023
% Result : Unsatisfiable 11.56s 3.93s
% Output : CNFRefutation 12.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 52
% Syntax : Number of formulae : 58 ( 7 unt; 49 typ; 0 def)
% Number of atoms : 11 ( 3 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 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 : 6 (; 6 !; 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 > 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(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_646,axiom,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
file(unknown,unknown) ).
tff(f_161,axiom,
! [Z,X,Y] :
( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) ),
file(unknown,unknown) ).
tff(f_652,axiom,
~ member(ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))),cross_product(universal_class,universal_class)),
file(unknown,unknown) ).
tff(c_184,plain,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
inference(cnfTransformation,[status(thm)],[f_646]) ).
tff(c_1710,plain,
! [Z_371,X_372,Y_373] :
( ( ordered_pair(first(Z_371),second(Z_371)) = Z_371 )
| ~ member(Z_371,cross_product(X_372,Y_373)) ),
inference(cnfTransformation,[status(thm)],[f_161]) ).
tff(c_1744,plain,
ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))) = ordered_pair(y,z),
inference(resolution,[status(thm)],[c_184,c_1710]) ).
tff(c_186,plain,
~ member(ordered_pair(first(ordered_pair(y,z)),second(ordered_pair(y,z))),cross_product(universal_class,universal_class)),
inference(cnfTransformation,[status(thm)],[f_652]) ).
tff(c_8602,plain,
~ member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
inference(demodulation,[status(thm),theory(equality)],[c_1744,c_186]) ).
tff(c_8605,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_184,c_8602]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET108-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.11 % 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
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Thu Aug 3 16:43:06 EDT 2023
% 0.10/0.30 % CPUTime :
% 11.56/3.93 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.56/3.93
% 11.56/3.93 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.34/3.96
% 12.34/3.96 Inference rules
% 12.34/3.96 ----------------------
% 12.34/3.96 #Ref : 0
% 12.34/3.96 #Sup : 2123
% 12.34/3.96 #Fact : 0
% 12.34/3.96 #Define : 0
% 12.34/3.96 #Split : 55
% 12.34/3.96 #Chain : 0
% 12.34/3.96 #Close : 0
% 12.34/3.96
% 12.34/3.96 Ordering : KBO
% 12.34/3.96
% 12.34/3.96 Simplification rules
% 12.34/3.96 ----------------------
% 12.34/3.96 #Subsume : 526
% 12.34/3.96 #Demod : 584
% 12.34/3.96 #Tautology : 347
% 12.34/3.96 #SimpNegUnit : 29
% 12.34/3.96 #BackRed : 98
% 12.34/3.96
% 12.34/3.96 #Partial instantiations: 0
% 12.34/3.96 #Strategies tried : 1
% 12.34/3.96
% 12.34/3.96 Timing (in seconds)
% 12.34/3.96 ----------------------
% 12.34/3.96 Preprocessing : 0.72
% 12.34/3.96 Parsing : 0.38
% 12.34/3.97 CNF conversion : 0.05
% 12.34/3.97 Main loop : 2.22
% 12.34/3.97 Inferencing : 0.71
% 12.34/3.97 Reduction : 0.76
% 12.34/3.97 Demodulation : 0.52
% 12.34/3.97 BG Simplification : 0.07
% 12.34/3.97 Subsumption : 0.49
% 12.34/3.97 Abstraction : 0.06
% 12.34/3.97 MUC search : 0.00
% 12.34/3.97 Cooper : 0.00
% 12.34/3.97 Total : 2.99
% 12.34/3.97 Index Insertion : 0.00
% 12.34/3.97 Index Deletion : 0.00
% 12.34/3.97 Index Matching : 0.00
% 12.34/3.97 BG Taut test : 0.00
%------------------------------------------------------------------------------