TSTP Solution File: SET017-7 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET017-7 : 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 : n029.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 7.41s 2.70s
% Output : CNFRefutation 7.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 61
% Syntax : Number of formulae : 113 ( 40 unt; 50 typ; 0 def)
% Number of atoms : 91 ( 30 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 55 ( 27 ~; 28 |; 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 : 60 (; 60 !; 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_768,axiom,
y != z,
file(unknown,unknown) ).
tff(f_753,axiom,
! [Y,X] :
( member(Y,universal_class)
| ( unordered_pair(X,Y) = singleton(X) ) ),
file(unknown,unknown) ).
tff(f_765,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_766,axiom,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
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(f_747,axiom,
! [X,Y] : subclass(singleton(X),unordered_pair(X,Y)),
file(unknown,unknown) ).
tff(f_57,axiom,
! [X,Y,U] :
( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,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_665,axiom,
! [U,V,X,Y] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,universal_class) ),
file(unknown,unknown) ).
tff(f_123,axiom,
! [X] : ( unordered_pair(X,X) = singleton(X) ),
file(unknown,unknown) ).
tff(c_232,plain,
z != y,
inference(cnfTransformation,[status(thm)],[f_768]) ).
tff(c_222,plain,
! [X_218,Y_217] :
( ( unordered_pair(X_218,Y_217) = singleton(X_218) )
| member(Y_217,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_753]) ).
tff(c_228,plain,
unordered_pair(x,z) = unordered_pair(x,y),
inference(cnfTransformation,[status(thm)],[f_765]) ).
tff(c_636,plain,
! [Y_280,X_281] :
( member(Y_280,unordered_pair(X_281,Y_280))
| ~ member(Y_280,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_116]) ).
tff(c_642,plain,
( member(z,unordered_pair(x,y))
| ~ member(z,universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_228,c_636]) ).
tff(c_951,plain,
~ member(z,universal_class),
inference(splitLeft,[status(thm)],[c_642]) ).
tff(c_958,plain,
! [X_218] : ( unordered_pair(X_218,z) = singleton(X_218) ),
inference(resolution,[status(thm)],[c_222,c_951]) ).
tff(c_960,plain,
unordered_pair(x,y) = singleton(x),
inference(demodulation,[status(thm),theory(equality)],[c_958,c_228]) ).
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_1164,plain,
( member(y,singleton(x))
| ~ member(y,universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_960,c_20]) ).
tff(c_1486,plain,
~ member(y,universal_class),
inference(splitLeft,[status(thm)],[c_1164]) ).
tff(c_230,plain,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
inference(cnfTransformation,[status(thm)],[f_766]) ).
tff(c_1748,plain,
! [U_355,X_356,V_357,Y_358] :
( member(U_355,X_356)
| ~ member(ordered_pair(U_355,V_357),cross_product(X_356,Y_358)) ),
inference(cnfTransformation,[status(thm)],[f_136]) ).
tff(c_1751,plain,
member(y,universal_class),
inference(resolution,[status(thm)],[c_230,c_1748]) ).
tff(c_1755,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1486,c_1751]) ).
tff(c_1757,plain,
member(y,universal_class),
inference(splitRight,[status(thm)],[c_1164]) ).
tff(c_218,plain,
! [X_213,Y_214] : subclass(singleton(X_213),unordered_pair(X_213,Y_214)),
inference(cnfTransformation,[status(thm)],[f_747]) ).
tff(c_1756,plain,
member(y,singleton(x)),
inference(splitRight,[status(thm)],[c_1164]) ).
tff(c_2,plain,
! [U_3,Y_2,X_1] :
( member(U_3,Y_2)
| ~ member(U_3,X_1)
| ~ subclass(X_1,Y_2) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_1823,plain,
! [Y_363] :
( member(y,Y_363)
| ~ subclass(singleton(x),Y_363) ),
inference(resolution,[status(thm)],[c_1756,c_2]) ).
tff(c_1851,plain,
! [Y_364] : member(y,unordered_pair(x,Y_364)),
inference(resolution,[status(thm)],[c_218,c_1823]) ).
tff(c_16,plain,
! [Y_17,U_15,X_16] :
( ( Y_17 = U_15 )
| ( X_16 = U_15 )
| ~ member(U_15,unordered_pair(X_16,Y_17)) ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_1882,plain,
! [Y_364] :
( ( y = Y_364 )
| ( y = x ) ),
inference(resolution,[status(thm)],[c_1851,c_16]) ).
tff(c_1886,plain,
y = x,
inference(splitLeft,[status(thm)],[c_1882]) ).
tff(c_1894,plain,
member(ordered_pair(x,z),cross_product(universal_class,universal_class)),
inference(demodulation,[status(thm),theory(equality)],[c_1886,c_230]) ).
tff(c_2160,plain,
! [V_388,U_389,X_390,Y_391] :
( member(V_388,universal_class)
| ~ member(ordered_pair(U_389,V_388),cross_product(X_390,Y_391)) ),
inference(cnfTransformation,[status(thm)],[f_665]) ).
tff(c_2163,plain,
member(z,universal_class),
inference(resolution,[status(thm)],[c_1894,c_2160]) ).
tff(c_2167,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_951,c_2163]) ).
tff(c_2170,plain,
! [Y_392] : ( y = Y_392 ),
inference(splitRight,[status(thm)],[c_1882]) ).
tff(c_2402,plain,
~ member(y,universal_class),
inference(superposition,[status(thm),theory(equality)],[c_2170,c_951]) ).
tff(c_2631,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1757,c_2402]) ).
tff(c_2632,plain,
member(z,unordered_pair(x,y)),
inference(splitRight,[status(thm)],[c_642]) ).
tff(c_2636,plain,
! [Y_5617,U_5618,X_5619] :
( ( Y_5617 = U_5618 )
| ( X_5619 = U_5618 )
| ~ member(U_5618,unordered_pair(X_5619,Y_5617)) ),
inference(cnfTransformation,[status(thm)],[f_102]) ).
tff(c_2639,plain,
( ( z = y )
| ( z = x ) ),
inference(resolution,[status(thm)],[c_2632,c_2636]) ).
tff(c_2682,plain,
z = x,
inference(negUnitSimplification,[status(thm)],[c_232,c_2639]) ).
tff(c_2696,plain,
y != x,
inference(demodulation,[status(thm),theory(equality)],[c_2682,c_232]) ).
tff(c_24,plain,
! [X_24] : ( unordered_pair(X_24,X_24) = singleton(X_24) ),
inference(cnfTransformation,[status(thm)],[f_123]) ).
tff(c_2695,plain,
unordered_pair(x,y) = unordered_pair(x,x),
inference(demodulation,[status(thm),theory(equality)],[c_2682,c_228]) ).
tff(c_2698,plain,
unordered_pair(x,y) = singleton(x),
inference(demodulation,[status(thm),theory(equality)],[c_24,c_2695]) ).
tff(c_2762,plain,
( member(y,singleton(x))
| ~ member(y,universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_2698,c_20]) ).
tff(c_3017,plain,
~ member(y,universal_class),
inference(splitLeft,[status(thm)],[c_2762]) ).
tff(c_2693,plain,
member(ordered_pair(y,x),cross_product(universal_class,universal_class)),
inference(demodulation,[status(thm),theory(equality)],[c_2682,c_230]) ).
tff(c_3319,plain,
! [U_5650,X_5651,V_5652,Y_5653] :
( member(U_5650,X_5651)
| ~ member(ordered_pair(U_5650,V_5652),cross_product(X_5651,Y_5653)) ),
inference(cnfTransformation,[status(thm)],[f_136]) ).
tff(c_3322,plain,
member(y,universal_class),
inference(resolution,[status(thm)],[c_2693,c_3319]) ).
tff(c_3326,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3017,c_3322]) ).
tff(c_3327,plain,
member(y,singleton(x)),
inference(splitRight,[status(thm)],[c_2762]) ).
tff(c_3516,plain,
! [Y_5664] :
( member(y,Y_5664)
| ~ subclass(singleton(x),Y_5664) ),
inference(resolution,[status(thm)],[c_3327,c_2]) ).
tff(c_3544,plain,
! [Y_5665] : member(y,unordered_pair(x,Y_5665)),
inference(resolution,[status(thm)],[c_218,c_3516]) ).
tff(c_3549,plain,
! [Y_5665] :
( ( y = Y_5665 )
| ( y = x ) ),
inference(resolution,[status(thm)],[c_3544,c_16]) ).
tff(c_3577,plain,
! [Y_5666] : ( y = Y_5666 ),
inference(negUnitSimplification,[status(thm)],[c_2696,c_3549]) ).
tff(c_3833,plain,
y = x,
inference(superposition,[status(thm),theory(equality)],[c_3577,c_2682]) ).
tff(c_4031,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2696,c_3833]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET017-7 : 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
% 0.13/0.34 % Computer : n029.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 17:20:52 EDT 2023
% 0.13/0.34 % CPUTime :
% 7.41/2.70 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.41/2.71
% 7.41/2.71 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.70/2.74
% 7.70/2.74 Inference rules
% 7.70/2.74 ----------------------
% 7.70/2.74 #Ref : 0
% 7.70/2.74 #Sup : 1032
% 7.70/2.74 #Fact : 0
% 7.70/2.74 #Define : 0
% 7.70/2.74 #Split : 6
% 7.70/2.74 #Chain : 0
% 7.70/2.74 #Close : 0
% 7.70/2.74
% 7.70/2.74 Ordering : KBO
% 7.70/2.74
% 7.70/2.74 Simplification rules
% 7.70/2.74 ----------------------
% 7.70/2.74 #Subsume : 70
% 7.70/2.74 #Demod : 200
% 7.70/2.74 #Tautology : 305
% 7.70/2.74 #SimpNegUnit : 18
% 7.70/2.74 #BackRed : 20
% 7.70/2.74
% 7.70/2.74 #Partial instantiations: 1881
% 7.70/2.74 #Strategies tried : 1
% 7.70/2.74
% 7.70/2.74 Timing (in seconds)
% 7.70/2.74 ----------------------
% 7.70/2.74 Preprocessing : 0.71
% 7.70/2.74 Parsing : 0.35
% 7.70/2.74 CNF conversion : 0.05
% 7.70/2.74 Main loop : 0.98
% 7.70/2.74 Inferencing : 0.40
% 7.70/2.74 Reduction : 0.30
% 7.70/2.74 Demodulation : 0.22
% 7.70/2.74 BG Simplification : 0.05
% 7.70/2.74 Subsumption : 0.16
% 7.70/2.74 Abstraction : 0.03
% 7.70/2.74 MUC search : 0.00
% 7.70/2.74 Cooper : 0.00
% 7.70/2.74 Total : 1.75
% 7.70/2.74 Index Insertion : 0.00
% 7.70/2.74 Index Deletion : 0.00
% 7.70/2.74 Index Matching : 0.00
% 7.70/2.74 BG Taut test : 0.00
%------------------------------------------------------------------------------