%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SET016-6 : TPTP v9.0.0. 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 : 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 : Wed Apr 9 08:37:30 PM UTC 2025
% Result : Unsatisfiable 20.72s 8.28s
% Output : CNFRefutation 20.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 25
% Syntax : Number of formulae : 131 ( 52 unt; 0 typ; 0 def)
% Number of atoms : 240 ( 76 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 209 ( 100 ~; 109 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 42 ( 42 usr; 12 con; 0-3 aty)
% Number of variables : 155 ( 155 !; 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 > w > 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(w,type,
w: $i ).
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_651,axiom,
w != y,
file(unknown,unknown) ).
tff(f_646,axiom,
member(w,universal_class),
file(unknown,unknown) ).
tff(f_124,axiom,
! [X] : ( unordered_pair(X,X) = singleton(X) ),
file(unknown,unknown) ).
tff(f_117,axiom,
! [Y,X] :
( ~ member(Y,universal_class)
| member(Y,unordered_pair(X,Y)) ),
file(unknown,unknown) ).
tff(f_229,axiom,
! [Xr,X,Y] : ( intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y) ),
file(unknown,unknown) ).
tff(f_471,axiom,
! [X] :
( ( X = null_class )
| member(regular(X),X) ),
file(unknown,unknown) ).
tff(f_186,axiom,
! [Z,X,Y] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
file(unknown,unknown) ).
tff(f_72,axiom,
! [X] : subclass(X,universal_class),
file(unknown,unknown) ).
tff(f_58,axiom,
! [X,Y,U] :
( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) ),
file(unknown,unknown) ).
tff(f_208,axiom,
! [Z,X] :
( ~ member(Z,complement(X))
| ~ member(Z,X) ),
file(unknown,unknown) ).
tff(f_242,axiom,
! [X,Z] :
( ( restrict(X,singleton(Z),universal_class) != null_class )
| ~ member(Z,domain_of(X)) ),
file(unknown,unknown) ).
tff(f_120,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
file(unknown,unknown) ).
tff(f_490,axiom,
! [Y] :
( ~ member(Y,universal_class)
| ( Y = null_class )
| member(apply(choice,Y),Y) ),
file(unknown,unknown) ).
tff(f_103,axiom,
! [U,X,Y] :
( ~ member(U,unordered_pair(X,Y))
| ( U = X )
| ( U = Y ) ),
file(unknown,unknown) ).
tff(f_151,axiom,
! [U,X,V,Y] :
( ~ member(U,X)
| ~ member(V,Y)
| member(ordered_pair(U,V),cross_product(X,Y)) ),
file(unknown,unknown) ).
tff(f_645,axiom,
ordered_pair(w,x) = ordered_pair(y,z),
file(unknown,unknown) ).
tff(f_137,axiom,
! [U,V,X,Y] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) ),
file(unknown,unknown) ).
tff(f_483,axiom,
function(choice),
file(unknown,unknown) ).
tff(f_465,axiom,
! [Xf,X] :
( ~ function(Xf)
| ~ member(X,universal_class)
| member(image(Xf,X),universal_class) ),
file(unknown,unknown) ).
tff(f_479,axiom,
! [Xf,Y] : ( sum_class(image(Xf,singleton(Y))) = apply(Xf,Y) ),
file(unknown,unknown) ).
tff(f_391,axiom,
! [X] :
( ~ member(X,universal_class)
| member(sum_class(X),universal_class) ),
file(unknown,unknown) ).
tff(f_170,axiom,
! [X,Y] :
( ~ member(ordered_pair(X,Y),element_relation)
| member(X,Y) ),
file(unknown,unknown) ).
tff(f_178,axiom,
! [X,Y] :
( ~ member(ordered_pair(X,Y),cross_product(universal_class,universal_class))
| ~ member(X,Y)
| member(ordered_pair(X,Y),element_relation) ),
file(unknown,unknown) ).
tff(f_129,axiom,
! [X,Y] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ),
file(unknown,unknown) ).
tff(f_110,axiom,
! [X,Y] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ),
file(unknown,unknown) ).
tff(c_188,plain,
y != w,
inference(cnfTransformation,[status(thm)],[f_651]) ).
tff(c_186,plain,
member(w,universal_class),
inference(cnfTransformation,[status(thm)],[f_646]) ).
tff(c_24,plain,
! [X_24] : ( unordered_pair(X_24,X_24) = singleton(X_24) ),
inference(cnfTransformation,[status(thm)],[f_124]) ).
tff(c_371,plain,
! [Y_226,X_227] :
( member(Y_226,unordered_pair(X_227,Y_226))
| ~ member(Y_226,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_117]) ).
tff(c_374,plain,
! [X_24] :
( member(X_24,singleton(X_24))
| ~ member(X_24,universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_371]) ).
tff(c_56,plain,
! [Xr_63,X_64,Y_65] : ( intersection(Xr_63,cross_product(X_64,Y_65)) = restrict(Xr_63,X_64,Y_65) ),
inference(cnfTransformation,[status(thm)],[f_229]) ).
tff(c_132,plain,
! [X_131] :
( member(regular(X_131),X_131)
| ( null_class = X_131 ) ),
inference(cnfTransformation,[status(thm)],[f_471]) ).
tff(c_338,plain,
! [Z_218,X_219,Y_220] :
( member(Z_218,X_219)
| ~ member(Z_218,intersection(X_219,Y_220)) ),
inference(cnfTransformation,[status(thm)],[f_186]) ).
tff(c_3697,plain,
! [X_535,Y_536] :
( member(regular(intersection(X_535,Y_536)),X_535)
| ( intersection(X_535,Y_536) = null_class ) ),
inference(resolution,[status(thm)],[c_132,c_338]) ).
tff(c_8,plain,
! [X_8] : subclass(X_8,universal_class),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_729,plain,
! [U_273,Y_274,X_275] :
( member(U_273,Y_274)
| ~ member(U_273,X_275)
| ~ subclass(X_275,Y_274) ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_766,plain,
! [X_131,Y_274] :
( member(regular(X_131),Y_274)
| ~ subclass(X_131,Y_274)
| ( null_class = X_131 ) ),
inference(resolution,[status(thm)],[c_132,c_729]) ).
tff(c_1211,plain,
! [X_335,Y_336] :
( member(regular(X_335),Y_336)
| ~ subclass(X_335,Y_336)
| ( null_class = X_335 ) ),
inference(resolution,[status(thm)],[c_132,c_729]) ).
tff(c_255,plain,
! [Z_206,X_207] :
( ~ member(Z_206,X_207)
| ~ member(Z_206,complement(X_207)) ),
inference(cnfTransformation,[status(thm)],[f_208]) ).
tff(c_267,plain,
! [X_207] :
( ~ member(regular(complement(X_207)),X_207)
| ( complement(X_207) = null_class ) ),
inference(resolution,[status(thm)],[c_132,c_255]) ).
tff(c_1261,plain,
! [Y_337] :
( ~ subclass(complement(Y_337),Y_337)
| ( complement(Y_337) = null_class ) ),
inference(resolution,[status(thm)],[c_1211,c_267]) ).
tff(c_1283,plain,
complement(universal_class) = null_class,
inference(resolution,[status(thm)],[c_8,c_1261]) ).
tff(c_48,plain,
! [Z_55,X_56] :
( ~ member(Z_55,X_56)
| ~ member(Z_55,complement(X_56)) ),
inference(cnfTransformation,[status(thm)],[f_208]) ).
tff(c_1368,plain,
! [Z_339] :
( ~ member(Z_339,universal_class)
| ~ member(Z_339,null_class) ),
inference(superposition,[status(thm),theory(equality)],[c_1283,c_48]) ).
tff(c_1376,plain,
! [X_131] :
( ~ member(regular(X_131),null_class)
| ~ subclass(X_131,universal_class)
| ( null_class = X_131 ) ),
inference(resolution,[status(thm)],[c_766,c_1368]) ).
tff(c_1424,plain,
! [X_131] :
( ~ member(regular(X_131),null_class)
| ( null_class = X_131 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_1376]) ).
tff(c_3898,plain,
! [Y_539] : ( intersection(null_class,Y_539) = null_class ),
inference(resolution,[status(thm)],[c_3697,c_1424]) ).
tff(c_3971,plain,
! [X_64,Y_65] : ( restrict(null_class,X_64,Y_65) = null_class ),
inference(superposition,[status(thm),theory(equality)],[c_56,c_3898]) ).
tff(c_1525,plain,
! [Z_348,X_349] :
( ~ member(Z_348,domain_of(X_349))
| ( restrict(X_349,singleton(Z_348),universal_class) != null_class ) ),
inference(cnfTransformation,[status(thm)],[f_242]) ).
tff(c_22428,plain,
! [X_1159] :
( ( restrict(X_1159,singleton(regular(domain_of(X_1159))),universal_class) != null_class )
| ( domain_of(X_1159) = null_class ) ),
inference(resolution,[status(thm)],[c_132,c_1525]) ).
tff(c_22442,plain,
domain_of(null_class) = null_class,
inference(superposition,[status(thm),theory(equality)],[c_3971,c_22428]) ).
tff(c_60,plain,
! [Z_70,X_69] :
( ~ member(Z_70,domain_of(X_69))
| ( restrict(X_69,singleton(Z_70),universal_class) != null_class ) ),
inference(cnfTransformation,[status(thm)],[f_242]) ).
tff(c_22508,plain,
! [Z_70] :
( ~ member(Z_70,null_class)
| ( restrict(null_class,singleton(Z_70),universal_class) != null_class ) ),
inference(superposition,[status(thm),theory(equality)],[c_22442,c_60]) ).
tff(c_22530,plain,
! [Z_70] : ~ member(Z_70,null_class),
inference(demodulation,[status(thm),theory(equality)],[c_3971,c_22508]) ).
tff(c_218,plain,
! [X_183,Y_184] : member(unordered_pair(X_183,Y_184),universal_class),
inference(cnfTransformation,[status(thm)],[f_120]) ).
tff(c_220,plain,
! [X_24] : member(singleton(X_24),universal_class),
inference(superposition,[status(thm),theory(equality)],[c_24,c_218]) ).
tff(c_1323,plain,
! [Y_338] :
( member(apply(choice,Y_338),Y_338)
| ( null_class = Y_338 )
| ~ member(Y_338,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_490]) ).
tff(c_695,plain,
! [Y_267,U_268,X_269] :
( ( Y_267 = U_268 )
| ( X_269 = U_268 )
| ~ member(U_268,unordered_pair(X_269,Y_267)) ),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_716,plain,
! [X_24,U_268] :
( ( X_24 = U_268 )
| ( X_24 = U_268 )
| ~ member(U_268,singleton(X_24)) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_695]) ).
tff(c_1331,plain,
! [X_24] :
( ( apply(choice,singleton(X_24)) = X_24 )
| ( singleton(X_24) = null_class )
| ~ member(singleton(X_24),universal_class) ),
inference(resolution,[status(thm)],[c_1323,c_716]) ).
tff(c_2021,plain,
! [X_381] :
( ( apply(choice,singleton(X_381)) = X_381 )
| ( singleton(X_381) = null_class ) ),
inference(demodulation,[status(thm),theory(equality)],[c_220,c_1331]) ).
tff(c_140,plain,
! [Y_135] :
( member(apply(choice,Y_135),Y_135)
| ( null_class = Y_135 )
| ~ member(Y_135,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_490]) ).
tff(c_2027,plain,
! [X_381] :
( member(X_381,singleton(X_381))
| ( singleton(X_381) = null_class )
| ~ member(singleton(X_381),universal_class)
| ( singleton(X_381) = null_class ) ),
inference(superposition,[status(thm),theory(equality)],[c_2021,c_140]) ).
tff(c_2033,plain,
! [X_381] :
( member(X_381,singleton(X_381))
| ( singleton(X_381) = null_class ) ),
inference(demodulation,[status(thm),theory(equality)],[c_220,c_2027]) ).
tff(c_32,plain,
! [U_35,V_37,X_36,Y_38] :
( member(ordered_pair(U_35,V_37),cross_product(X_36,Y_38))
| ~ member(V_37,Y_38)
| ~ member(U_35,X_36) ),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_184,plain,
ordered_pair(y,z) = ordered_pair(w,x),
inference(cnfTransformation,[status(thm)],[f_645]) ).
tff(c_1059,plain,
! [U_300,X_301,V_302,Y_303] :
( member(U_300,X_301)
| ~ member(ordered_pair(U_300,V_302),cross_product(X_301,Y_303)) ),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_21587,plain,
! [X_1128,Y_1129] :
( member(y,X_1128)
| ~ member(ordered_pair(w,x),cross_product(X_1128,Y_1129)) ),
inference(superposition,[status(thm),theory(equality)],[c_184,c_1059]) ).
tff(c_21598,plain,
! [X_36,Y_38] :
( member(y,X_36)
| ~ member(x,Y_38)
| ~ member(w,X_36) ),
inference(resolution,[status(thm)],[c_32,c_21587]) ).
tff(c_21951,plain,
! [Y_1144] : ~ member(x,Y_1144),
inference(splitLeft,[status(thm)],[c_21598]) ).
tff(c_22008,plain,
singleton(x) = null_class,
inference(resolution,[status(thm)],[c_2033,c_21951]) ).
tff(c_138,plain,
function(choice),
inference(cnfTransformation,[status(thm)],[f_483]) ).
tff(c_1356,plain,
! [X_24] :
( ( apply(choice,singleton(X_24)) = X_24 )
| ( singleton(X_24) = null_class ) ),
inference(demodulation,[status(thm),theory(equality)],[c_220,c_1331]) ).
tff(c_130,plain,
! [Xf_129,X_130] :
( member(image(Xf_129,X_130),universal_class)
| ~ member(X_130,universal_class)
| ~ function(Xf_129) ),
inference(cnfTransformation,[status(thm)],[f_465]) ).
tff(c_461,plain,
! [Xf_238,Y_239] : ( sum_class(image(Xf_238,singleton(Y_239))) = apply(Xf_238,Y_239) ),
inference(cnfTransformation,[status(thm)],[f_479]) ).
tff(c_108,plain,
! [X_111] :
( member(sum_class(X_111),universal_class)
| ~ member(X_111,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_391]) ).
tff(c_23852,plain,
! [Xf_1205,Y_1206] :
( member(apply(Xf_1205,Y_1206),universal_class)
| ~ member(image(Xf_1205,singleton(Y_1206)),universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_461,c_108]) ).
tff(c_23875,plain,
! [Xf_129,Y_1206] :
( member(apply(Xf_129,Y_1206),universal_class)
| ~ member(singleton(Y_1206),universal_class)
| ~ function(Xf_129) ),
inference(resolution,[status(thm)],[c_130,c_23852]) ).
tff(c_23881,plain,
! [Xf_1207,Y_1208] :
( member(apply(Xf_1207,Y_1208),universal_class)
| ~ function(Xf_1207) ),
inference(demodulation,[status(thm),theory(equality)],[c_220,c_23875]) ).
tff(c_23895,plain,
! [X_24] :
( member(X_24,universal_class)
| ~ function(choice)
| ( singleton(X_24) = null_class ) ),
inference(superposition,[status(thm),theory(equality)],[c_1356,c_23881]) ).
tff(c_23898,plain,
! [X_24] :
( member(X_24,universal_class)
| ( singleton(X_24) = null_class ) ),
inference(demodulation,[status(thm),theory(equality)],[c_138,c_23895]) ).
tff(c_2283,plain,
! [U_400,V_401,X_402,Y_403] :
( member(ordered_pair(U_400,V_401),cross_product(X_402,Y_403))
| ~ member(V_401,Y_403)
| ~ member(U_400,X_402) ),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_31179,plain,
! [X_1406,Y_1407] :
( member(ordered_pair(w,x),cross_product(X_1406,Y_1407))
| ~ member(z,Y_1407)
| ~ member(y,X_1406) ),
inference(superposition,[status(thm),theory(equality)],[c_184,c_2283]) ).
tff(c_376,plain,
! [X_229,Y_230] :
( member(X_229,Y_230)
| ~ member(ordered_pair(X_229,Y_230),element_relation) ),
inference(cnfTransformation,[status(thm)],[f_170]) ).
tff(c_379,plain,
( member(y,z)
| ~ member(ordered_pair(w,x),element_relation) ),
inference(superposition,[status(thm),theory(equality)],[c_184,c_376]) ).
tff(c_603,plain,
~ member(ordered_pair(w,x),element_relation),
inference(splitLeft,[status(thm)],[c_379]) ).
tff(c_2567,plain,
! [X_433,Y_434] :
( member(ordered_pair(X_433,Y_434),element_relation)
| ~ member(X_433,Y_434)
| ~ member(ordered_pair(X_433,Y_434),cross_product(universal_class,universal_class)) ),
inference(cnfTransformation,[status(thm)],[f_178]) ).
tff(c_2578,plain,
( member(ordered_pair(y,z),element_relation)
| ~ member(y,z)
| ~ member(ordered_pair(w,x),cross_product(universal_class,universal_class)) ),
inference(superposition,[status(thm),theory(equality)],[c_184,c_2567]) ).
tff(c_2581,plain,
( member(ordered_pair(w,x),element_relation)
| ~ member(y,z)
| ~ member(ordered_pair(w,x),cross_product(universal_class,universal_class)) ),
inference(demodulation,[status(thm),theory(equality)],[c_184,c_2578]) ).
tff(c_2582,plain,
( ~ member(y,z)
| ~ member(ordered_pair(w,x),cross_product(universal_class,universal_class)) ),
inference(negUnitSimplification,[status(thm)],[c_603,c_2581]) ).
tff(c_22160,plain,
~ member(ordered_pair(w,x),cross_product(universal_class,universal_class)),
inference(splitLeft,[status(thm)],[c_2582]) ).
tff(c_31211,plain,
( ~ member(z,universal_class)
| ~ member(y,universal_class) ),
inference(resolution,[status(thm)],[c_31179,c_22160]) ).
tff(c_31224,plain,
~ member(y,universal_class),
inference(splitLeft,[status(thm)],[c_31211]) ).
tff(c_31234,plain,
singleton(y) = null_class,
inference(resolution,[status(thm)],[c_23898,c_31224]) ).
tff(c_1469,plain,
! [X_342,Y_343] : ( unordered_pair(singleton(X_342),unordered_pair(X_342,singleton(Y_343))) = ordered_pair(X_342,Y_343) ),
inference(cnfTransformation,[status(thm)],[f_129]) ).
tff(c_18,plain,
! [X_18,Y_19] :
( member(X_18,unordered_pair(X_18,Y_19))
| ~ member(X_18,universal_class) ),
inference(cnfTransformation,[status(thm)],[f_110]) ).
tff(c_1485,plain,
! [X_342,Y_343] :
( member(singleton(X_342),ordered_pair(X_342,Y_343))
| ~ member(singleton(X_342),universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_1469,c_18]) ).
tff(c_1575,plain,
! [X_352,Y_353] : member(singleton(X_352),ordered_pair(X_352,Y_353)),
inference(demodulation,[status(thm),theory(equality)],[c_220,c_1485]) ).
tff(c_1582,plain,
member(singleton(y),ordered_pair(w,x)),
inference(superposition,[status(thm),theory(equality)],[c_184,c_1575]) ).
tff(c_31238,plain,
member(null_class,ordered_pair(w,x)),
inference(demodulation,[status(thm),theory(equality)],[c_31234,c_1582]) ).
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_103]) ).
tff(c_32921,plain,
! [X_1457,Y_1458,U_1459] :
( ( unordered_pair(X_1457,singleton(Y_1458)) = U_1459 )
| ( singleton(X_1457) = U_1459 )
| ~ member(U_1459,ordered_pair(X_1457,Y_1458)) ),
inference(superposition,[status(thm),theory(equality)],[c_1469,c_16]) ).
tff(c_32930,plain,
( ( unordered_pair(w,singleton(x)) = null_class )
| ( singleton(w) = null_class ) ),
inference(resolution,[status(thm)],[c_31238,c_32921]) ).
tff(c_33054,plain,
( ( unordered_pair(w,null_class) = null_class )
| ( singleton(w) = null_class ) ),
inference(demodulation,[status(thm),theory(equality)],[c_22008,c_32930]) ).
tff(c_33095,plain,
singleton(w) = null_class,
inference(splitLeft,[status(thm)],[c_33054]) ).
tff(c_33265,plain,
( member(w,null_class)
| ~ member(w,universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_33095,c_374]) ).
tff(c_33297,plain,
member(w,null_class),
inference(demodulation,[status(thm),theory(equality)],[c_186,c_33265]) ).
tff(c_33299,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_22530,c_33297]) ).
tff(c_33300,plain,
unordered_pair(w,null_class) = null_class,
inference(splitRight,[status(thm)],[c_33054]) ).
tff(c_33459,plain,
( member(w,null_class)
| ~ member(w,universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_33300,c_18]) ).
tff(c_33473,plain,
member(w,null_class),
inference(demodulation,[status(thm),theory(equality)],[c_186,c_33459]) ).
tff(c_33475,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_22530,c_33473]) ).
tff(c_33477,plain,
member(y,universal_class),
inference(splitRight,[status(thm)],[c_31211]) ).
tff(c_34691,plain,
! [X_1488,Y_1489,U_1490] :
( ( unordered_pair(X_1488,singleton(Y_1489)) = U_1490 )
| ( singleton(X_1488) = U_1490 )
| ~ member(U_1490,ordered_pair(X_1488,Y_1489)) ),
inference(superposition,[status(thm),theory(equality)],[c_1469,c_16]) ).
tff(c_34792,plain,
( ( unordered_pair(w,singleton(x)) = singleton(y) )
| ( singleton(y) = singleton(w) ) ),
inference(resolution,[status(thm)],[c_1582,c_34691]) ).
tff(c_34861,plain,
( ( unordered_pair(w,null_class) = singleton(y) )
| ( singleton(y) = singleton(w) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_22008,c_34792]) ).
tff(c_34896,plain,
singleton(y) = singleton(w),
inference(splitLeft,[status(thm)],[c_34861]) ).
tff(c_35064,plain,
( member(y,singleton(w))
| ~ member(y,universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_34896,c_374]) ).
tff(c_35101,plain,
member(y,singleton(w)),
inference(demodulation,[status(thm),theory(equality)],[c_33477,c_35064]) ).
tff(c_35106,plain,
y = w,
inference(resolution,[status(thm)],[c_35101,c_716]) ).
tff(c_35112,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_188,c_188,c_35106]) ).
tff(c_35113,plain,
unordered_pair(w,null_class) = singleton(y),
inference(splitRight,[status(thm)],[c_34861]) ).
tff(c_35297,plain,
( member(w,singleton(y))
| ~ member(w,universal_class) ),
inference(superposition,[status(thm),theory(equality)],[c_35113,c_18]) ).
tff(c_35312,plain,
member(w,singleton(y)),
inference(demodulation,[status(thm),theory(equality)],[c_186,c_35297]) ).
tff(c_35319,plain,
y = w,
inference(resolution,[status(thm)],[c_35312,c_716]) ).
tff(c_35325,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_188,c_188,c_35319]) ).
tff(c_35332,plain,
! [X_1495] :
( member(y,X_1495)
| ~ member(w,X_1495) ),
inference(splitRight,[status(thm)],[c_21598]) ).
tff(c_35542,plain,
! [X_1497] :
( ( y = X_1497 )
| ~ member(w,singleton(X_1497)) ),
inference(resolution,[status(thm)],[c_35332,c_716]) ).
tff(c_35550,plain,
( ( y = w )
| ~ member(w,universal_class) ),
inference(resolution,[status(thm)],[c_374,c_35542]) ).
tff(c_35556,plain,
y = w,
inference(demodulation,[status(thm),theory(equality)],[c_186,c_35550]) ).
tff(c_35558,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_188,c_35556]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET016-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.07/0.13 % 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
% 0.14/0.34 % Computer : n014.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 : Tue Apr 8 19:42:04 EDT 2025
% 0.14/0.34 % CPUTime :
% 20.72/8.28 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.78/8.29
% 20.78/8.29 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------