TSTP Solution File: SET102-7 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET102-7 : 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/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 : n025.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 8.06s 2.86s
% Output : CNFRefutation 8.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 55
% Syntax : Number of formulae : 62 ( 8 unt; 51 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 : 67 ( 41 >; 26 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 42 ( 42 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 > member_of1 > member_of > 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(member_of1,type,
member_of1: $i > $i ).
tff(not_subclass_element,type,
not_subclass_element: ( $i * $i ) > $i ).
tff(member_of,type,
member_of: $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_976,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_3446,plain,
! [X_526,Y_527] : ( unordered_pair(singleton(X_526),unordered_pair(X_526,singleton(Y_527))) = ordered_pair(X_526,Y_527) ),
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_3472,plain,
! [X_526,Y_527] :
( member(unordered_pair(X_526,singleton(Y_527)),ordered_pair(X_526,Y_527))
| ~ member(unordered_pair(X_526,singleton(Y_527)),universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_3446,c_20]) ).
tff(c_3562,plain,
! [X_526,Y_527] : member(unordered_pair(X_526,singleton(Y_527)),ordered_pair(X_526,Y_527)),
inference(demodulation,[status(thm),theory(equality)],[c_22,c_3472]) ).
tff(c_292,plain,
~ member(unordered_pair(x,singleton(y)),ordered_pair(x,y)),
inference(cnfTransformation,[status(thm)],[f_976]) ).
tff(c_3623,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_3562,c_292]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET102-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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
% 0.14/0.34 % Computer : n025.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 3 16:46:04 EDT 2023
% 0.14/0.34 % CPUTime :
% 8.06/2.86 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.06/2.87
% 8.06/2.87 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.06/2.92
% 8.06/2.92 Inference rules
% 8.06/2.92 ----------------------
% 8.06/2.92 #Ref : 3
% 8.06/2.92 #Sup : 854
% 8.06/2.92 #Fact : 0
% 8.06/2.92 #Define : 0
% 8.06/2.92 #Split : 9
% 8.06/2.92 #Chain : 0
% 8.06/2.92 #Close : 0
% 8.06/2.92
% 8.06/2.92 Ordering : KBO
% 8.06/2.92
% 8.06/2.92 Simplification rules
% 8.06/2.92 ----------------------
% 8.06/2.92 #Subsume : 157
% 8.06/2.92 #Demod : 129
% 8.06/2.92 #Tautology : 205
% 8.06/2.92 #SimpNegUnit : 1
% 8.06/2.92 #BackRed : 7
% 8.06/2.92
% 8.06/2.92 #Partial instantiations: 0
% 8.06/2.92 #Strategies tried : 1
% 8.06/2.92
% 8.06/2.92 Timing (in seconds)
% 8.06/2.92 ----------------------
% 8.06/2.92 Preprocessing : 0.76
% 8.06/2.92 Parsing : 0.36
% 8.06/2.92 CNF conversion : 0.06
% 8.06/2.92 Main loop : 1.05
% 8.06/2.92 Inferencing : 0.33
% 8.06/2.92 Reduction : 0.38
% 8.06/2.92 Demodulation : 0.27
% 8.06/2.92 BG Simplification : 0.06
% 8.06/2.93 Subsumption : 0.22
% 8.06/2.93 Abstraction : 0.04
% 8.06/2.93 MUC search : 0.00
% 8.06/2.93 Cooper : 0.00
% 8.06/2.93 Total : 1.89
% 8.06/2.93 Index Insertion : 0.00
% 8.06/2.93 Index Deletion : 0.00
% 8.06/2.93 Index Matching : 0.00
% 8.06/2.93 BG Taut test : 0.00
%------------------------------------------------------------------------------