TSTP Solution File: SET102-6 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET102-6 : 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 : n014.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 10:55:58 EDT 2023
% Result : Unsatisfiable 6.06s 2.44s
% Output : CNFRefutation 6.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 53
% Syntax : Number of formulae : 60 ( 8 unt; 49 typ; 0 def)
% Number of atoms : 14 ( 2 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 5 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 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 : 16 (; 16 !; 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_119,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
file(unknown,unknown) ).
tff(f_128,axiom,
! [X,Y] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ),
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(unordered_pair(x,singleton(y)),ordered_pair(x,y)),
file(unknown,unknown) ).
tff(c_22,plain,
! [X_22,Y_23] : member(unordered_pair(X_22,Y_23),universal_class),
inference(cnfTransformation,[status(thm)],[f_119]) ).
tff(c_1143,plain,
! [X_321,Y_322] : ( unordered_pair(singleton(X_321),unordered_pair(X_321,singleton(Y_322))) = ordered_pair(X_321,Y_322) ),
inference(cnfTransformation,[status(thm)],[f_128]) ).
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_1162,plain,
! [X_321,Y_322] :
( member(unordered_pair(X_321,singleton(Y_322)),ordered_pair(X_321,Y_322))
| ~ member(unordered_pair(X_321,singleton(Y_322)),universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_1143,c_20]) ).
tff(c_1176,plain,
! [X_321,Y_322] : member(unordered_pair(X_321,singleton(Y_322)),ordered_pair(X_321,Y_322)),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_1162]) ).
tff(c_184,plain,
~ member(unordered_pair(x,singleton(y)),ordered_pair(x,y)),
inference(cnfTransformation,[status(thm)],[f_645]) ).
tff(c_1248,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1176,c_184]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET102-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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 : n014.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
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 3 16:12:33 EDT 2023
% 0.13/0.35 % CPUTime :
% 6.06/2.44 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.06/2.45
% 6.06/2.45 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.06/2.48
% 6.06/2.48 Inference rules
% 6.06/2.48 ----------------------
% 6.06/2.48 #Ref : 0
% 6.06/2.48 #Sup : 243
% 6.06/2.48 #Fact : 0
% 6.06/2.48 #Define : 0
% 6.06/2.48 #Split : 9
% 6.06/2.48 #Chain : 0
% 6.06/2.48 #Close : 0
% 6.06/2.48
% 6.06/2.48 Ordering : KBO
% 6.06/2.48
% 6.06/2.48 Simplification rules
% 6.06/2.48 ----------------------
% 6.06/2.48 #Subsume : 31
% 6.06/2.48 #Demod : 29
% 6.06/2.48 #Tautology : 56
% 6.06/2.48 #SimpNegUnit : 1
% 6.06/2.48 #BackRed : 2
% 6.06/2.48
% 6.06/2.48 #Partial instantiations: 0
% 6.06/2.48 #Strategies tried : 1
% 6.06/2.48
% 6.06/2.48 Timing (in seconds)
% 6.06/2.48 ----------------------
% 6.28/2.48 Preprocessing : 0.70
% 6.28/2.48 Parsing : 0.38
% 6.28/2.48 CNF conversion : 0.05
% 6.28/2.48 Main loop : 0.68
% 6.28/2.48 Inferencing : 0.25
% 6.28/2.48 Reduction : 0.20
% 6.28/2.48 Demodulation : 0.14
% 6.28/2.48 BG Simplification : 0.04
% 6.28/2.48 Subsumption : 0.14
% 6.28/2.48 Abstraction : 0.03
% 6.28/2.48 MUC search : 0.00
% 6.28/2.48 Cooper : 0.00
% 6.28/2.48 Total : 1.43
% 6.28/2.48 Index Insertion : 0.00
% 6.28/2.48 Index Deletion : 0.00
% 6.28/2.48 Index Matching : 0.00
% 6.28/2.48 BG Taut test : 0.00
%------------------------------------------------------------------------------