%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU736^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:31:02 AM UTC 2026
% Result : Theorem 1.83s 0.62s
% Output : Refutation 1.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 95 ( 33 unt; 0 typ; 11 def)
% Number of atoms : 4707 (1229 equ; 0 cnn)
% Maximal formula atoms : 258 ( 49 avg)
% Number of connectives : 2813 ( 178 ~; 159 |; 798 &; 603 @)
% ( 19 <=>;1056 =>; 0 <=; 0 <~>)
% Maximal formula depth : 266 ( 24 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 490 ( 487 usr; 295 con; 0-4 aty)
% Number of variables : 126 ( 0 sgn 104 !; 22 ?; 126 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_3,type,
setextAx: $o ).
thf(func_def_5,type,
emptysetAx: $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_7,type,
setadjoinAx: $o ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_9,type,
powersetAx: $o ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_11,type,
setunionAx: $o ).
thf(func_def_13,type,
omega0Ax: $o ).
thf(func_def_14,type,
omegaSAx: $o ).
thf(func_def_15,type,
omegaIndAx: $o ).
thf(func_def_16,type,
replAx: $o ).
thf(func_def_17,type,
foundationAx: $o ).
thf(func_def_18,type,
wellorderingAx: $o ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_20,type,
descrp: $o ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_22,type,
dsetconstrI: $o ).
thf(func_def_23,type,
dsetconstrEL: $o ).
thf(func_def_24,type,
dsetconstrER: $o ).
thf(func_def_25,type,
exuE1: $o ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_27,type,
prop2setE: $o ).
thf(func_def_28,type,
emptysetE: $o ).
thf(func_def_29,type,
emptysetimpfalse: $o ).
thf(func_def_30,type,
notinemptyset: $o ).
thf(func_def_31,type,
exuE3e: $o ).
thf(func_def_32,type,
setext: $o ).
thf(func_def_33,type,
emptyI: $o ).
thf(func_def_34,type,
noeltsimpempty: $o ).
thf(func_def_35,type,
setbeta: $o ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_37,type,
nonemptyE1: $o ).
thf(func_def_38,type,
nonemptyI: $o ).
thf(func_def_39,type,
nonemptyI1: $o ).
thf(func_def_40,type,
setadjoinIL: $o ).
thf(func_def_41,type,
emptyinunitempty: $o ).
thf(func_def_42,type,
setadjoinIR: $o ).
thf(func_def_43,type,
setadjoinE: $o ).
thf(func_def_44,type,
setadjoinOr: $o ).
thf(func_def_45,type,
setoftrueEq: $o ).
thf(func_def_46,type,
powersetI: $o ).
thf(func_def_47,type,
emptyinPowerset: $o ).
thf(func_def_48,type,
emptyInPowerset: $o ).
thf(func_def_49,type,
powersetE: $o ).
thf(func_def_50,type,
setunionI: $o ).
thf(func_def_51,type,
setunionE: $o ).
thf(func_def_52,type,
subPowSU: $o ).
thf(func_def_53,type,
exuE2: $o ).
thf(func_def_54,type,
nonemptyImpWitness: $o ).
thf(func_def_55,type,
uniqinunit: $o ).
thf(func_def_56,type,
notinsingleton: $o ).
thf(func_def_57,type,
eqinunit: $o ).
thf(func_def_58,type,
singletonsswitch: $o ).
thf(func_def_59,type,
upairsetE: $o ).
thf(func_def_60,type,
upairsetIL: $o ).
thf(func_def_61,type,
upairsetIR: $o ).
thf(func_def_62,type,
emptyE1: $o ).
thf(func_def_63,type,
vacuousDall: $o ).
thf(func_def_64,type,
quantDeMorgan1: $o ).
thf(func_def_65,type,
quantDeMorgan2: $o ).
thf(func_def_66,type,
quantDeMorgan3: $o ).
thf(func_def_67,type,
quantDeMorgan4: $o ).
thf(func_def_68,type,
prop2setI: $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_70,type,
prop2set2propI: $o ).
thf(func_def_71,type,
notdexE: $o ).
thf(func_def_72,type,
notdallE: $o ).
thf(func_def_73,type,
exuI1: $o ).
thf(func_def_74,type,
exuI3: $o ).
thf(func_def_75,type,
exuI2: $o ).
thf(func_def_76,type,
inCongP: $o ).
thf(func_def_77,type,
in__Cong: $o ).
thf(func_def_78,type,
exuE3u: $o ).
thf(func_def_79,type,
exu__Cong: $o ).
thf(func_def_80,type,
emptyset__Cong: $o ).
thf(func_def_81,type,
setadjoin__Cong: $o ).
thf(func_def_82,type,
powerset__Cong: $o ).
thf(func_def_83,type,
setunion__Cong: $o ).
thf(func_def_84,type,
omega__Cong: $o ).
thf(func_def_85,type,
exuEu: $o ).
thf(func_def_86,type,
descr__Cong: $o ).
thf(func_def_87,type,
dsetconstr__Cong: $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_91,type,
subsetI1: $o ).
thf(func_def_92,type,
eqimpsubset2: $o ).
thf(func_def_93,type,
eqimpsubset1: $o ).
thf(func_def_94,type,
subsetI2: $o ).
thf(func_def_95,type,
emptysetsubset: $o ).
thf(func_def_96,type,
subsetE: $o ).
thf(func_def_97,type,
subsetE2: $o ).
thf(func_def_98,type,
notsubsetI: $o ).
thf(func_def_99,type,
notequalI1: $o ).
thf(func_def_100,type,
notequalI2: $o ).
thf(func_def_101,type,
subsetRefl: $o ).
thf(func_def_102,type,
subsetTrans: $o ).
thf(func_def_103,type,
setadjoinSub: $o ).
thf(func_def_104,type,
setadjoinSub2: $o ).
thf(func_def_105,type,
subset2powerset: $o ).
thf(func_def_106,type,
setextsub: $o ).
thf(func_def_107,type,
subsetemptysetimpeq: $o ).
thf(func_def_108,type,
powersetI1: $o ).
thf(func_def_109,type,
powersetE1: $o ).
thf(func_def_110,type,
inPowerset: $o ).
thf(func_def_111,type,
powersetsubset: $o ).
thf(func_def_112,type,
sepInPowerset: $o ).
thf(func_def_113,type,
sepSubset: $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_115,type,
binunionIL: $o ).
thf(func_def_116,type,
upairset2IR: $o ).
thf(func_def_117,type,
binunionIR: $o ).
thf(func_def_118,type,
binunionEcases: $o ).
thf(func_def_119,type,
binunionE: $o ).
thf(func_def_120,type,
binunionLsub: $o ).
thf(func_def_121,type,
binunionRsub: $o ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_123,type,
binintersectI: $o ).
thf(func_def_124,type,
binintersectSubset5: $o ).
thf(func_def_125,type,
binintersectEL: $o ).
thf(func_def_126,type,
binintersectLsub: $o ).
thf(func_def_127,type,
binintersectSubset2: $o ).
thf(func_def_128,type,
binintersectSubset3: $o ).
thf(func_def_129,type,
binintersectER: $o ).
thf(func_def_130,type,
disjointsetsI1: $o ).
thf(func_def_131,type,
binintersectRsub: $o ).
thf(func_def_132,type,
binintersectSubset4: $o ).
thf(func_def_133,type,
binintersectSubset1: $o ).
thf(func_def_134,type,
bs114d: $o ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_137,type,
setminusI: $o ).
thf(func_def_138,type,
setminusEL: $o ).
thf(func_def_139,type,
setminusER: $o ).
thf(func_def_140,type,
setminusSubset2: $o ).
thf(func_def_141,type,
setminusERneg: $o ).
thf(func_def_142,type,
setminusELneg: $o ).
thf(func_def_143,type,
setminusILneg: $o ).
thf(func_def_144,type,
setminusIRneg: $o ).
thf(func_def_145,type,
setminusLsub: $o ).
thf(func_def_146,type,
setminusSubset1: $o ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_148,type,
symdiffE: $o ).
thf(func_def_149,type,
symdiffI1: $o ).
thf(func_def_150,type,
symdiffI2: $o ).
thf(func_def_151,type,
symdiffIneg1: $o ).
thf(func_def_152,type,
symdiffIneg2: $o ).
thf(func_def_153,type,
iskpair: $i > $o ).
thf(func_def_154,type,
secondinupair: $o ).
thf(func_def_155,type,
setukpairIL: $o ).
thf(func_def_156,type,
setukpairIR: $o ).
thf(func_def_157,type,
kpairiskpair: $o ).
thf(func_def_158,type,
kpair: $i > $i > $i ).
thf(func_def_159,type,
kpairp: $o ).
thf(func_def_160,type,
cartprod: $i > $i > $i ).
thf(func_def_161,type,
singletonsubset: $o ).
thf(func_def_162,type,
singletoninpowerset: $o ).
thf(func_def_163,type,
singletoninpowunion: $o ).
thf(func_def_164,type,
upairset2E: $o ).
thf(func_def_165,type,
upairsubunion: $o ).
thf(func_def_166,type,
upairinpowunion: $o ).
thf(func_def_167,type,
ubforcartprodlem1: $o ).
thf(func_def_168,type,
ubforcartprodlem2: $o ).
thf(func_def_169,type,
ubforcartprodlem3: $o ).
thf(func_def_170,type,
cartprodpairin: $o ).
thf(func_def_171,type,
cartprodmempair1: $o ).
thf(func_def_172,type,
cartprodmempair: $o ).
thf(func_def_173,type,
setunionE2: $o ).
thf(func_def_174,type,
setunionsingleton1: $o ).
thf(func_def_175,type,
setunionsingleton2: $o ).
thf(func_def_176,type,
setunionsingleton: $o ).
thf(func_def_177,type,
singleton: $i > $o ).
thf(func_def_178,type,
singletonprop: $o ).
thf(func_def_179,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_180,type,
ex1E1: $o ).
thf(func_def_181,type,
ex1I: $o ).
thf(func_def_182,type,
ex1I2: $o ).
thf(func_def_183,type,
singletonsuniq: $o ).
thf(func_def_184,type,
atmost1p: $i > $o ).
thf(func_def_185,type,
atleast2p: $i > $o ).
thf(func_def_186,type,
atmost2p: $i > $o ).
thf(func_def_187,type,
upairsetp: $i > $o ).
thf(func_def_188,type,
setukpairinjL1: $o ).
thf(func_def_189,type,
kfstsingleton: $o ).
thf(func_def_190,type,
theprop: $o ).
thf(func_def_191,type,
kfst: $i > $i ).
thf(func_def_192,type,
kfstpairEq: $o ).
thf(func_def_193,type,
cartprodfstin: $o ).
thf(func_def_194,type,
setukpairinjL2: $o ).
thf(func_def_195,type,
setukpairinjL: $o ).
thf(func_def_196,type,
setukpairinjR11: $o ).
thf(func_def_197,type,
setukpairinjR12: $o ).
thf(func_def_198,type,
setukpairinjR1: $o ).
thf(func_def_199,type,
upairequniteq: $o ).
thf(func_def_200,type,
setukpairinjR2: $o ).
thf(func_def_201,type,
setukpairinjR: $o ).
thf(func_def_202,type,
ksndsingleton: $o ).
thf(func_def_203,type,
ksnd: $i > $i ).
thf(func_def_204,type,
ksndpairEq: $o ).
thf(func_def_205,type,
kpairsurjEq: $o ).
thf(func_def_206,type,
cartprodsndin: $o ).
thf(func_def_207,type,
cartprodpairmemEL: $o ).
thf(func_def_208,type,
cartprodpairmemER: $o ).
thf(func_def_209,type,
cartprodmempaircEq: $o ).
thf(func_def_210,type,
cartprodfstpairEq: $o ).
thf(func_def_211,type,
cartprodsndpairEq: $o ).
thf(func_def_212,type,
cartprodpairsurjEq: $o ).
thf(func_def_213,type,
breln: $i > $i > $i > $o ).
thf(func_def_214,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_215,type,
dpsetconstrI: $o ).
thf(func_def_216,type,
dpsetconstrSub: $o ).
thf(func_def_217,type,
setOfPairsIsBReln: $o ).
thf(func_def_218,type,
dpsetconstrERa: $o ).
thf(func_def_219,type,
dpsetconstrEL1: $o ).
thf(func_def_220,type,
dpsetconstrEL2: $o ).
thf(func_def_221,type,
dpsetconstrER: $o ).
thf(func_def_222,type,
func: $i > $i > $i > $o ).
thf(func_def_223,type,
funcSet: $i > $i > $i ).
thf(func_def_224,type,
funcImageSingleton: $o ).
thf(func_def_225,type,
apProp: $o ).
thf(func_def_226,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_227,type,
app: $o ).
thf(func_def_228,type,
infuncsetfunc: $o ).
thf(func_def_229,type,
ap2p: $o ).
thf(func_def_230,type,
funcinfuncset: $o ).
thf(func_def_231,type,
lamProp: $o ).
thf(func_def_232,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(func_def_233,type,
lamp: $o ).
thf(func_def_234,type,
lam2p: $o ).
thf(func_def_235,type,
brelnall1: $o ).
thf(func_def_236,type,
brelnall2: $o ).
thf(func_def_237,type,
ex1E2: $o ).
thf(func_def_238,type,
funcGraphProp1: $o ).
thf(func_def_239,type,
funcGraphProp3: $o ).
thf(func_def_240,type,
funcGraphProp2: $o ).
thf(func_def_241,type,
funcextLem: $o ).
thf(func_def_242,type,
funcGraphProp4: $o ).
thf(func_def_243,type,
subbreln: $o ).
thf(func_def_244,type,
eqbreln: $o ).
thf(func_def_245,type,
funcext: $o ).
thf(func_def_246,type,
funcext2: $o ).
thf(func_def_247,type,
ap2apEq1: $o ).
thf(func_def_248,type,
ap2apEq2: $o ).
thf(func_def_249,type,
beta1: $o ).
thf(func_def_250,type,
eta1: $o ).
thf(func_def_251,type,
lam2lamEq: $o ).
thf(func_def_252,type,
beta2: $o ).
thf(func_def_253,type,
eta2: $o ).
thf(func_def_254,type,
iffalseProp1: $o ).
thf(func_def_255,type,
iffalseProp2: $o ).
thf(func_def_256,type,
iftrueProp1: $o ).
thf(func_def_257,type,
iftrueProp2: $o ).
thf(func_def_258,type,
ifSingleton: $o ).
thf(func_def_259,type,
if: $i > $o > $i > $i > $i ).
thf(func_def_260,type,
ifp: $o ).
thf(func_def_261,type,
theeq: $o ).
thf(func_def_262,type,
iftrue: $o ).
thf(func_def_263,type,
iffalse: $o ).
thf(func_def_264,type,
iftrueorfalse: $o ).
thf(func_def_265,type,
binintersectT_lem: $o ).
thf(func_def_266,type,
binunionT_lem: $o ).
thf(func_def_267,type,
powersetT_lem: $o ).
thf(func_def_268,type,
setminusT_lem: $o ).
thf(func_def_269,type,
complementT_lem: $o ).
thf(func_def_270,type,
setextT: $o ).
thf(func_def_271,type,
subsetTI: $o ).
thf(func_def_272,type,
powersetTI1: $o ).
thf(func_def_273,type,
powersetTE1: $o ).
thf(func_def_274,type,
complementTI1: $o ).
thf(func_def_275,type,
complementTE1: $o ).
thf(func_def_276,type,
binintersectTELcontra: $o ).
thf(func_def_277,type,
binintersectTERcontra: $o ).
thf(func_def_278,type,
contrasubsetT: $o ).
thf(func_def_279,type,
contrasubsetT1: $o ).
thf(func_def_280,type,
contrasubsetT2: $o ).
thf(func_def_281,type,
contrasubsetT3: $o ).
thf(func_def_282,type,
doubleComplementI1: $o ).
thf(func_def_283,type,
doubleComplementE1: $o ).
thf(func_def_284,type,
doubleComplementSub1: $o ).
thf(func_def_285,type,
doubleComplementSub2: $o ).
thf(func_def_286,type,
doubleComplementEq: $o ).
thf(func_def_287,type,
complementTnotintersectT: $o ).
thf(func_def_288,type,
complementImpComplementIntersect: $o ).
thf(func_def_289,type,
complementSubsetComplementIntersect: $o ).
thf(func_def_290,type,
complementInPowersetComplementIntersect: $o ).
thf(func_def_293,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_294,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_295,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_296,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_297,type,
vAND: $o > $o > $o ).
thf(func_def_298,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_299,type,
vIMP: $o > $o > $o ).
thf(func_def_300,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_301,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_302,type,
vOR: $o > $o > $o ).
thf(func_def_303,type,
vNOT: $o > $o ).
thf(func_def_304,type,
sP0: $o ).
thf(func_def_305,type,
sP1: $i > $i > $o ).
thf(func_def_306,type,
sP2: $i > $o ).
thf(func_def_307,type,
sP3: $o ).
thf(func_def_311,type,
sK7: $o ).
thf(func_def_314,type,
sK10: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_315,type,
sK11: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_319,type,
sK15: $i > $o ).
thf(func_def_331,type,
sK27: $i > $i > $i > $i > $i ).
thf(func_def_332,type,
sK28: $i > $i > $i > $i > $i ).
thf(func_def_333,type,
sK29: $i > $i > $i > $i > $i ).
thf(func_def_334,type,
sK30: $i > $i > $i > $i > $i ).
thf(func_def_337,type,
sK33: $o ).
thf(func_def_343,type,
sK39: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_344,type,
sK40: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_345,type,
sK41: $i > $o ).
thf(func_def_346,type,
sK42: $i > $o ).
thf(func_def_358,type,
sK54: $o ).
thf(func_def_373,type,
sK69: $i > $o ).
thf(func_def_375,type,
sK71: $i > $i > $i > $i > $i ).
thf(func_def_376,type,
sK72: $i > $i > $i > $i > $i ).
thf(func_def_384,type,
sK80: $i > $i ).
thf(func_def_404,type,
sK100: $i > $o ).
thf(func_def_405,type,
sK101: ( $i > $o ) > $i ).
thf(func_def_408,type,
sK104: $o ).
thf(func_def_411,type,
sK107: $i > $i ).
thf(func_def_414,type,
sK110: $i > ( $i > $i ) > $i > $i ).
thf(func_def_417,type,
sK113: $i > $o ).
thf(func_def_420,type,
sK116: $i > $o ).
thf(func_def_421,type,
sK117: $i > $i > $o ).
thf(func_def_426,type,
sK122: $i > $o ).
thf(func_def_429,type,
sK125: $i > ( $i > $o ) > $i ).
thf(func_def_431,type,
sK127: ( $i > $i ) > $i > $i > $i ).
thf(func_def_434,type,
sK130: $i > $i ).
thf(func_def_447,type,
sK143: $o ).
thf(func_def_458,type,
sK154: $o ).
thf(func_def_489,type,
sK185: $o > $i > $i > $i ).
thf(func_def_492,type,
sK188: $o ).
thf(func_def_497,type,
sK193: $i > $i ).
thf(func_def_499,type,
sK195: $i > $i ).
thf(func_def_510,type,
sK206: $i > $i > $i ).
thf(func_def_524,type,
sK220: $i > $i > $i ).
thf(func_def_528,type,
sK224: $i > $i > $o ).
thf(func_def_529,type,
sK225: $i > $i ).
thf(func_def_530,type,
sK226: $i > $i ).
thf(func_def_531,type,
sK227: ( $i > $i > $o ) > $i > $i ).
thf(func_def_532,type,
sK228: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_533,type,
sK229: ( $i > $i > $o ) > $i > $i ).
thf(func_def_535,type,
sK231: $i > $o ).
thf(func_def_536,type,
sK232: $i > $o ).
thf(func_def_537,type,
sK233: $i > $o ).
thf(func_def_538,type,
sK234: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_539,type,
sK235: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_540,type,
sK236: ( $i > $i ) > $i > $i > $i ).
thf(func_def_543,type,
sK239: $i > $i ).
thf(func_def_548,type,
sK244: $o ).
thf(func_def_560,type,
sK256: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_561,type,
sK257: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_565,type,
sK261: $i > $o ).
thf(func_def_567,type,
sK263: $i > $o ).
thf(func_def_569,type,
sK265: ( $i > $o ) > $i ).
thf(func_def_570,type,
sK266: ( $i > $o ) > $i ).
thf(func_def_574,type,
sK270: $i > $i > $o ).
thf(func_def_583,type,
sK279: $i > $o ).
thf(func_def_586,type,
sK282: $i > $o ).
thf(func_def_587,type,
sK283: $i > $i ).
thf(func_def_588,type,
sK284: ( $i > $o ) > $i ).
thf(func_def_598,type,
sK294: $i > $o ).
thf(func_def_601,type,
sK297: $i > ( $i > $o ) > $i ).
thf(func_def_602,type,
sK298: $i > ( $i > $o ) > $i ).
thf(func_def_619,type,
sK315: $i > $i ).
thf(func_def_632,type,
sK328: $i > $i > $o ).
thf(func_def_645,type,
sK341: $i > $i > ( $i > $o ) > $i ).
thf(func_def_646,type,
sK342: $i > $o ).
thf(func_def_652,type,
sK348: $i > $i > $o ).
thf(func_def_655,type,
sK351: $i > $o ).
thf(func_def_657,type,
sK353: ( $i > $o ) > $i > $i ).
thf(func_def_658,type,
sK354: $i > $i > $i > $i ).
thf(func_def_664,type,
sK360: $i > $o ).
thf(func_def_666,type,
sK362: $i > $i > $i > $i ).
thf(func_def_667,type,
sK363: $i > $i > $i > $i ).
thf(func_def_675,type,
sK371: $i > ( $i > $o ) > $i ).
thf(func_def_676,type,
sK372: $i > $o ).
thf(func_def_683,type,
sK379: $i > $i > $i > $i ).
thf(func_def_688,type,
sK384: $i > $i > $o ).
thf(func_def_692,type,
sK388: $i > ( $i > $o ) > $i ).
thf(func_def_693,type,
sK389: $i > $o ).
thf(func_def_698,type,
sK394: $i > $i > $o ).
thf(func_def_715,type,
sK411: ( $i > $o ) > $i ).
thf(func_def_716,type,
sK412: $i > $o ).
thf(func_def_717,type,
sK413: $i > $i ).
thf(func_def_726,type,
sK422: $i > $o ).
thf(func_def_740,type,
sK436: $i > ( $i > $i ) > $i > $i ).
thf(func_def_742,type,
sK438: $i > $i ).
thf(func_def_752,type,
sK448: $o ).
thf(func_def_755,type,
sK451: ( $i > $o ) > $i > $i ).
thf(func_def_757,type,
sK453: $i > $o ).
thf(func_def_760,type,
sK456: $i > $o ).
thf(func_def_770,type,
sK466: $i > $i > ( $i > $i ) > $i ).
thf(func_def_771,type,
sK467: $i > $i ).
thf(func_def_784,type,
sK480: $i > $o ).
thf(func_def_787,type,
sK483: ( $i > $o ) > $i > $i ).
thf(func_def_789,type,
sK485: $i > $o ).
thf(func_def_800,type,
sK496: $i > $i > $i ).
thf(func_def_814,type,
sK510: $i > $i > $i > $i > $i ).
thf(func_def_818,type,
sK514: $o ).
thf(func_def_842,type,
sK538: $i > $i > $i ).
thf(func_def_843,type,
sK539: $i > $i > $i ).
thf(func_def_846,type,
sK542: $i > $o ).
thf(func_def_849,type,
sK545: $i > ( $i > $o ) > $i ).
thf(func_def_850,type,
sK546: $i > $o ).
thf(func_def_853,type,
sK549: $o ).
thf(func_def_863,type,
sK559: $i > $i ).
thf(func_def_864,type,
sK560: $i > $i ).
thf(func_def_865,type,
sK561: $i > $i ).
thf(func_def_866,type,
sK562: $i > $i ).
thf(func_def_867,type,
sK563: $i > $i ).
thf(func_def_868,type,
sK564: $i > $i > $i > $i ).
thf(func_def_869,type,
sK565: $i > $i ).
thf(func_def_870,type,
sK566: $i > $i ).
thf(func_def_871,type,
sK567: $i > $i ).
thf(func_def_872,type,
sK568: $i > $i ).
thf(func_def_873,type,
sK569: $i > $i > $i ).
thf(func_def_874,type,
sK570: $i > $i > $i ).
thf(func_def_875,type,
sK571: $i > $i > $i > $i ).
thf(func_def_876,type,
sK572: $i > $i > $i > $i ).
thf(func_def_877,type,
sK573: $i > $i > $i > $i ).
thf(func_def_878,type,
sK574: $i > $i > $i ).
thf(func_def_879,type,
sK575: $i > $i > $i ).
thf(func_def_880,type,
sK576: $i > $i > $i ).
thf(func_def_885,type,
sK581: $i > ( $i > $o ) > $i ).
thf(func_def_886,type,
sK582: $i > $o ).
thf(func_def_890,type,
sK586: $i > $i > $i ).
thf(func_def_896,type,
sK592: $i > $o ).
thf(func_def_899,type,
sK595: $i > ( $i > $o ) > $i ).
thf(func_def_900,type,
sK596: $i > ( $i > $o ) > $i ).
thf(func_def_901,type,
sK597: $i > $o ).
thf(func_def_904,type,
sK600: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_905,type,
sK601: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_908,type,
sK604: $i > $o ).
thf(func_def_909,type,
sK605: $i > $o ).
thf(func_def_914,type,
sK610: $i > $i > $i > $i ).
thf(func_def_915,type,
sK611: $i > $i > $i > $i ).
thf(func_def_923,type,
sK619: ( $i > $o ) > $i > $i ).
thf(func_def_925,type,
sK621: $i > $o ).
thf(func_def_929,type,
sK625: $i > $i > $i ).
thf(func_def_931,type,
sK627: $i > $i > $o ).
thf(func_def_945,type,
sK641: $i > $i > $i ).
thf(func_def_946,type,
sK642: $o ).
thf(func_def_958,type,
sK654: $i > $o ).
thf(func_def_963,type,
sK659: $i > $i ).
thf(func_def_968,type,
sK664: $i > $i ).
thf(func_def_970,type,
sK666: $i > ( $i > $i ) > $i > $i ).
thf(func_def_976,type,
sK672: $o ).
thf(func_def_982,type,
sK678: $o ).
thf(func_def_985,type,
sK681: $i > $o ).
thf(func_def_996,type,
sK692: $o ).
thf(func_def_1007,type,
sK703: $o ).
thf(func_def_1019,type,
sK715: $i > $i ).
thf(func_def_1020,type,
sK716: $i > $i > $i > $i > $i ).
thf(func_def_1055,type,
sK751: $i > $i > $i ).
thf(func_def_1060,type,
sK756: $o ).
thf(func_def_1068,type,
sK764: $i > $i ).
thf(func_def_1072,type,
sK768: $i > $i > $i ).
thf(func_def_1084,type,
sK780: $i > $i > $i > $i > $i ).
thf(f124,axiom,
( setminusERneg
= ( ! [X2: $i,X0: $i,X1: $i] :
( ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusERneg) ).
thf(f244,axiom,
( contrasubsetT
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
=> ( ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ X1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contrasubsetT) ).
thf(f257,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X2 )
=> ( in @ X3 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contraSubsetComplement) ).
thf(f258,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X2 )
=> ( in @ X3 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f257]) ).
thf(f456,plain,
( setminusERneg
= ( ! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X0 @ ( setminus @ X1 @ X2 ) )
=> ( ( in @ X0 @ X1 )
=> ( in @ X0 @ X2 ) ) ) ) ),
inference(rectify,[],[f124]) ).
thf(f457,plain,
( ( setminusERneg = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
!= $true )
=> ( ( ( in @ X0 @ X1 )
= $true )
=> ( ( in @ X0 @ X2 )
= $true ) ) ) ),
inference(fool_elimination,[],[f456]) ).
thf(f469,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ X2 )
=> ( in @ X3 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f258]) ).
thf(f470,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ( ( setukpairinjR2 = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ( ( ksndpairEq = $true )
=> ( ( kpairsurjEq = $true )
=> ( ( cartprodsndin = $true )
=> ( ( cartprodpairmemEL = $true )
=> ( ( cartprodpairmemER = $true )
=> ( ( cartprodmempaircEq = $true )
=> ( ( cartprodfstpairEq = $true )
=> ( ( cartprodsndpairEq = $true )
=> ( ( cartprodpairsurjEq = $true )
=> ( ( dpsetconstrI = $true )
=> ( ( dpsetconstrSub = $true )
=> ( ( setOfPairsIsBReln = $true )
=> ( ( dpsetconstrERa = $true )
=> ( ( dpsetconstrEL1 = $true )
=> ( ( dpsetconstrEL2 = $true )
=> ( ( dpsetconstrER = $true )
=> ( ( funcImageSingleton = $true )
=> ( ( apProp = $true )
=> ( ( app = $true )
=> ( ( infuncsetfunc = $true )
=> ( ( ap2p = $true )
=> ( ( funcinfuncset = $true )
=> ( ( lamProp = $true )
=> ( ( lamp = $true )
=> ( ( lam2p = $true )
=> ( ( brelnall1 = $true )
=> ( ( brelnall2 = $true )
=> ( ( ex1E2 = $true )
=> ( ( funcGraphProp1 = $true )
=> ( ( funcGraphProp3 = $true )
=> ( ( funcGraphProp2 = $true )
=> ( ( funcextLem = $true )
=> ( ( funcGraphProp4 = $true )
=> ( ( subbreln = $true )
=> ( ( eqbreln = $true )
=> ( ( funcext = $true )
=> ( ( funcext2 = $true )
=> ( ( ap2apEq1 = $true )
=> ( ( ap2apEq2 = $true )
=> ( ( beta1 = $true )
=> ( ( eta1 = $true )
=> ( ( lam2lamEq = $true )
=> ( ( beta2 = $true )
=> ( ( eta2 = $true )
=> ( ( iffalseProp1 = $true )
=> ( ( iffalseProp2 = $true )
=> ( ( iftrueProp1 = $true )
=> ( ( iftrueProp2 = $true )
=> ( ( ifSingleton = $true )
=> ( ( ifp = $true )
=> ( ( theeq = $true )
=> ( ( iftrue = $true )
=> ( ( iffalse = $true )
=> ( ( iftrueorfalse = $true )
=> ( ( binintersectT_lem = $true )
=> ( ( binunionT_lem = $true )
=> ( ( powersetT_lem = $true )
=> ( ( setminusT_lem = $true )
=> ( ( complementT_lem = $true )
=> ( ( setextT = $true )
=> ( ( subsetTI = $true )
=> ( ( powersetTI1 = $true )
=> ( ( powersetTE1 = $true )
=> ( ( complementTI1 = $true )
=> ( ( complementTE1 = $true )
=> ( ( binintersectTELcontra = $true )
=> ( ( binintersectTERcontra = $true )
=> ( ( contrasubsetT = $true )
=> ( ( contrasubsetT1 = $true )
=> ( ( contrasubsetT2 = $true )
=> ( ( contrasubsetT3 = $true )
=> ( ( doubleComplementI1 = $true )
=> ( ( doubleComplementE1 = $true )
=> ( ( doubleComplementSub1 = $true )
=> ( ( doubleComplementSub2 = $true )
=> ( ( doubleComplementEq = $true )
=> ( ( complementTnotintersectT = $true )
=> ( ( complementImpComplementIntersect = $true )
=> ( ( complementSubsetComplementIntersect = $true )
=> ( ( complementInPowersetComplementIntersect = $true )
=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ( ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( in @ X3 @ X2 )
= $true )
=> ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f469]) ).
thf(f543,plain,
( contrasubsetT
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
=> ( ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ X1 ) ) ) ) ) ) ) ),
inference(rectify,[],[f244]) ).
thf(f544,plain,
( ( contrasubsetT = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
=> ( ( ( in @ X3 @ X2 )
= $true )
=> ( ( in @ X3 @ X1 )
!= $true ) ) ) ) ) ) ),
inference(fool_elimination,[],[f543]) ).
thf(f780,plain,
( ( setminusERneg = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
!= $true )
=> ( ( ( in @ X0 @ X1 )
= $true )
=> ( ( in @ X0 @ X2 )
= $true ) ) ) ),
inference(flattening,[],[f457]) ).
thf(f792,plain,
( ( contrasubsetT = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
=> ( ( ( in @ X3 @ X2 )
= $true )
=> ( ( in @ X3 @ X1 )
!= $true ) ) ) ) ) ) ),
inference(flattening,[],[f544]) ).
thf(f968,plain,
( ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
!= $true )
& ( ( in @ X3 @ X2 )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( complementInPowersetComplementIntersect = $true )
& ( complementSubsetComplementIntersect = $true )
& ( complementImpComplementIntersect = $true )
& ( complementTnotintersectT = $true )
& ( doubleComplementEq = $true )
& ( doubleComplementSub2 = $true )
& ( doubleComplementSub1 = $true )
& ( doubleComplementE1 = $true )
& ( doubleComplementI1 = $true )
& ( contrasubsetT3 = $true )
& ( contrasubsetT2 = $true )
& ( contrasubsetT1 = $true )
& ( contrasubsetT = $true )
& ( binintersectTERcontra = $true )
& ( binintersectTELcontra = $true )
& ( complementTE1 = $true )
& ( complementTI1 = $true )
& ( powersetTE1 = $true )
& ( powersetTI1 = $true )
& ( subsetTI = $true )
& ( setextT = $true )
& ( complementT_lem = $true )
& ( setminusT_lem = $true )
& ( powersetT_lem = $true )
& ( binunionT_lem = $true )
& ( binintersectT_lem = $true )
& ( iftrueorfalse = $true )
& ( iffalse = $true )
& ( iftrue = $true )
& ( theeq = $true )
& ( ifp = $true )
& ( ifSingleton = $true )
& ( iftrueProp2 = $true )
& ( iftrueProp1 = $true )
& ( iffalseProp2 = $true )
& ( iffalseProp1 = $true )
& ( eta2 = $true )
& ( beta2 = $true )
& ( lam2lamEq = $true )
& ( eta1 = $true )
& ( beta1 = $true )
& ( ap2apEq2 = $true )
& ( ap2apEq1 = $true )
& ( funcext2 = $true )
& ( funcext = $true )
& ( eqbreln = $true )
& ( subbreln = $true )
& ( funcGraphProp4 = $true )
& ( funcextLem = $true )
& ( funcGraphProp2 = $true )
& ( funcGraphProp3 = $true )
& ( funcGraphProp1 = $true )
& ( ex1E2 = $true )
& ( brelnall2 = $true )
& ( brelnall1 = $true )
& ( lam2p = $true )
& ( lamp = $true )
& ( lamProp = $true )
& ( funcinfuncset = $true )
& ( ap2p = $true )
& ( infuncsetfunc = $true )
& ( app = $true )
& ( apProp = $true )
& ( funcImageSingleton = $true )
& ( dpsetconstrER = $true )
& ( dpsetconstrEL2 = $true )
& ( dpsetconstrEL1 = $true )
& ( dpsetconstrERa = $true )
& ( setOfPairsIsBReln = $true )
& ( dpsetconstrSub = $true )
& ( dpsetconstrI = $true )
& ( cartprodpairsurjEq = $true )
& ( cartprodsndpairEq = $true )
& ( cartprodfstpairEq = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodpairmemER = $true )
& ( cartprodpairmemEL = $true )
& ( cartprodsndin = $true )
& ( kpairsurjEq = $true )
& ( ksndpairEq = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR = $true )
& ( setukpairinjR2 = $true )
& ( upairequniteq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjR12 = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjL = $true )
& ( setukpairinjL2 = $true )
& ( cartprodfstin = $true )
& ( kfstpairEq = $true )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( singletonsuniq = $true )
& ( ex1I2 = $true )
& ( ex1I = $true )
& ( ex1E1 = $true )
& ( singletonprop = $true )
& ( setunionsingleton = $true )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( setunionE2 = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( cartprodpairin = $true )
& ( ubforcartprodlem3 = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( upairsubunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[],[f470]) ).
thf(f969,plain,
( ( binintersectSubset2 = $true )
& ( emptysetE = $true )
& ( setukpairinjR12 = $true )
& ( setadjoinE = $true )
& ( notdallE = $true )
& ( dpsetconstrI = $true )
& ( exuE1 = $true )
& ( iftrueProp2 = $true )
& ( dpsetconstrEL2 = $true )
& ( eta1 = $true )
& ( notequalI1 = $true )
& ( brelnall2 = $true )
& ( cartprodpairsurjEq = $true )
& ( dsetconstrI = $true )
& ( doubleComplementSub2 = $true )
& ( iffalseProp1 = $true )
& ( funcGraphProp2 = $true )
& ( binintersectEL = $true )
& ( ubforcartprodlem1 = $true )
& ( emptyI = $true )
& ( binintersectI = $true )
& ( upairinpowunion = $true )
& ( upairset2E = $true )
& ( symdiffIneg2 = $true )
& ( cartprodpairmemEL = $true )
& ( binunionIL = $true )
& ( upairset2IR = $true )
& ( complementSubsetComplementIntersect = $true )
& ( emptysetimpfalse = $true )
& ( notinsingleton = $true )
& ( binunionLsub = $true )
& ( setunionsingleton2 = $true )
& ( exuE3u = $true )
& ( noeltsimpempty = $true )
& ( contrasubsetT2 = $true )
& ( dpsetconstrERa = $true )
& ( doubleComplementSub1 = $true )
& ( lamProp = $true )
& ( uniqinunit = $true )
& ( dsetconstrEL = $true )
& ( symdiffI2 = $true )
& ( setOfPairsIsBReln = $true )
& ( kpairp = $true )
& ( kfstpairEq = $true )
& ( contrasubsetT = $true )
& ( upairsetIR = $true )
& ( ksndpairEq = $true )
& ( setminusEL = $true )
& ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
!= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ X2 )
= $true ) ) ) )
& ( funcext2 = $true )
& ( setbeta = $true )
& ( binintersectTELcontra = $true )
& ( kpairiskpair = $true )
& ( setunionsingleton1 = $true )
& ( vacuousDall = $true )
& ( funcextLem = $true )
& ( singletonsswitch = $true )
& ( binintersectSubset1 = $true )
& ( setextAx = $true )
& ( lam2p = $true )
& ( singletoninpowunion = $true )
& ( descr__Cong = $true )
& ( prop2set2propI = $true )
& ( eqinunit = $true )
& ( setminusT_lem = $true )
& ( setukpairinjL2 = $true )
& ( setext = $true )
& ( contrasubsetT1 = $true )
& ( foundationAx = $true )
& ( powersetAx = $true )
& ( setadjoin__Cong = $true )
& ( dpsetconstrEL1 = $true )
& ( setminusIRneg = $true )
& ( doubleComplementI1 = $true )
& ( powersetI = $true )
& ( iftrue = $true )
& ( emptyInPowerset = $true )
& ( setminusER = $true )
& ( cartprodmempaircEq = $true )
& ( upairequniteq = $true )
& ( nonemptyImpWitness = $true )
& ( dsetconstr__Cong = $true )
& ( setadjoinAx = $true )
& ( cartprodfstin = $true )
& ( upairsetIL = $true )
& ( setadjoinSub = $true )
& ( emptysetAx = $true )
& ( iffalseProp2 = $true )
& ( subsetTrans = $true )
& ( exuI1 = $true )
& ( powersetE1 = $true )
& ( complementTnotintersectT = $true )
& ( exuI3 = $true )
& ( theeq = $true )
& ( binintersectSubset4 = $true )
& ( subbreln = $true )
& ( setextsub = $true )
& ( subsetI1 = $true )
& ( ex1I = $true )
& ( symdiffIneg1 = $true )
& ( ex1I2 = $true )
& ( powersetI1 = $true )
& ( quantDeMorgan4 = $true )
& ( sepSubset = $true )
& ( symdiffI1 = $true )
& ( quantDeMorgan1 = $true )
& ( setukpairinjR11 = $true )
& ( quantDeMorgan2 = $true )
& ( inPowerset = $true )
& ( omega__Cong = $true )
& ( binintersectRsub = $true )
& ( binunionIR = $true )
& ( binintersectTERcontra = $true )
& ( exu__Cong = $true )
& ( setunionAx = $true )
& ( setadjoinOr = $true )
& ( powersetT_lem = $true )
& ( binunionRsub = $true )
& ( ubforcartprodlem2 = $true )
& ( emptyE1 = $true )
& ( eta2 = $true )
& ( binintersectLsub = $true )
& ( setukpairIL = $true )
& ( iftrueProp1 = $true )
& ( binunionT_lem = $true )
& ( setunion__Cong = $true )
& ( iffalse = $true )
& ( emptyinPowerset = $true )
& ( setukpairinjL = $true )
& ( descrp = $true )
& ( notinemptyset = $true )
& ( setunionE2 = $true )
& ( ubforcartprodlem3 = $true )
& ( setadjoinIL = $true )
& ( complementTI1 = $true )
& ( kpairsurjEq = $true )
& ( prop2setI = $true )
& ( emptyinunitempty = $true )
& ( subset2powerset = $true )
& ( app = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( subsetRefl = $true )
& ( emptyset__Cong = $true )
& ( funcinfuncset = $true )
& ( powersetTE1 = $true )
& ( ex1E1 = $true )
& ( dsetconstrER = $true )
& ( powersetsubset = $true )
& ( nonemptyE1 = $true )
& ( powersetTI1 = $true )
& ( wellorderingAx = $true )
& ( setunionI = $true )
& ( setukpairIR = $true )
& ( contrasubsetT3 = $true )
& ( replAx = $true )
& ( setadjoinIR = $true )
& ( subsetI2 = $true )
& ( cartprodfstpairEq = $true )
& ( dpsetconstrER = $true )
& ( omegaIndAx = $true )
& ( beta1 = $true )
& ( setoftrueEq = $true )
& ( iftrueorfalse = $true )
& ( setukpairinjR = $true )
& ( kfstsingleton = $true )
& ( exuE2 = $true )
& ( exuEu = $true )
& ( exuI2 = $true )
& ( cartprodsndin = $true )
& ( setminusSubset2 = $true )
& ( cartprodpairin = $true )
& ( prop2setE = $true )
& ( cartprodpairmemER = $true )
& ( setminusLsub = $true )
& ( funcImageSingleton = $true )
& ( eqbreln = $true )
& ( setminusSubset1 = $true )
& ( setukpairinjR2 = $true )
& ( singletonprop = $true )
& ( setadjoinSub2 = $true )
& ( upairsubunion = $true )
& ( binintersectSubset3 = $true )
& ( setextT = $true )
& ( lamp = $true )
& ( nonemptyI1 = $true )
& ( singletonsubset = $true )
& ( subsetE = $true )
& ( upairsetE = $true )
& ( singletoninpowerset = $true )
& ( secondinupair = $true )
& ( emptysetsubset = $true )
& ( inCongP = $true )
& ( exuE3e = $true )
& ( symdiffE = $true )
& ( ap2p = $true )
& ( bs114d = $true )
& ( funcGraphProp3 = $true )
& ( funcext = $true )
& ( complementImpComplementIntersect = $true )
& ( ifp = $true )
& ( doubleComplementE1 = $true )
& ( cartprodmempair1 = $true )
& ( setukpairinjR1 = $true )
& ( binunionE = $true )
& ( theprop = $true )
& ( subPowSU = $true )
& ( eqimpsubset2 = $true )
& ( ap2apEq1 = $true )
& ( doubleComplementEq = $true )
& ( cartprodsndpairEq = $true )
& ( ifSingleton = $true )
& ( setminusELneg = $true )
& ( complementT_lem = $true )
& ( sepInPowerset = $true )
& ( singletonsuniq = $true )
& ( binunionEcases = $true )
& ( powersetE = $true )
& ( disjointsetsI1 = $true )
& ( ap2apEq2 = $true )
& ( nonemptyI = $true )
& ( binintersectT_lem = $true )
& ( setminusILneg = $true )
& ( notdexE = $true )
& ( complementTE1 = $true )
& ( setminusERneg = $true )
& ( in__Cong = $true )
& ( setminusI = $true )
& ( infuncsetfunc = $true )
& ( subsetemptysetimpeq = $true )
& ( binintersectSubset5 = $true )
& ( ksndsingleton = $true )
& ( omega0Ax = $true )
& ( binintersectER = $true )
& ( powerset__Cong = $true )
& ( dpsetconstrSub = $true )
& ( quantDeMorgan3 = $true )
& ( lam2lamEq = $true )
& ( apProp = $true )
& ( funcGraphProp1 = $true )
& ( omegaSAx = $true )
& ( setukpairinjL1 = $true )
& ( subsetE2 = $true )
& ( subsetTI = $true )
& ( notsubsetI = $true )
& ( setunionsingleton = $true )
& ( funcGraphProp4 = $true )
& ( beta2 = $true )
& ( notequalI2 = $true )
& ( cartprodmempair = $true )
& ( setunionE = $true )
& ( ex1E2 = $true )
& ( eqimpsubset1 = $true )
& ( brelnall1 = $true ) ),
inference(flattening,[],[f968]) ).
thf(f1054,plain,
( ( contrasubsetT = $true )
<=> ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ X2 )
!= $true )
| ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ) ),
inference(ennf_transformation,[],[f792]) ).
thf(f1055,plain,
( ( contrasubsetT = $true )
<=> ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ) ),
inference(flattening,[],[f1054]) ).
thf(f1084,plain,
( ( setminusERneg = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X0 @ X1 )
!= $true )
| ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
= $true ) ) ),
inference(ennf_transformation,[],[f780]) ).
thf(f1085,plain,
( ( setminusERneg = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
= $true )
| ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X0 @ X1 )
!= $true ) ) ),
inference(flattening,[],[f1084]) ).
thf(f1191,plain,
( ( ( setminusERneg = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
!= $true )
& ( ( in @ X0 @ X2 )
!= $true )
& ( ( in @ X0 @ X1 )
= $true ) ) )
& ( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
= $true )
| ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X0 @ X1 )
!= $true ) )
| ( setminusERneg != $true ) ) ),
inference(nnf_transformation,[],[f1085]) ).
thf(f1192,plain,
( ( ( setminusERneg = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
!= $true )
& ( ( in @ X0 @ X1 )
!= $true )
& ( ( in @ X0 @ X2 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( setminus @ X5 @ X4 ) )
= $true )
| ( ( in @ X3 @ X4 )
= $true )
| ( ( in @ X3 @ X5 )
!= $true ) )
| ( setminusERneg != $true ) ) ),
inference(rectify,[],[f1191]) ).
thf(f1193,plain,
( ( ( setminusERneg = $true )
| ( ( ( in @ sK94 @ ( setminus @ sK96 @ sK95 ) )
!= $true )
& ( ( in @ sK94 @ sK95 )
!= $true )
& ( ( in @ sK94 @ sK96 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ ( setminus @ X5 @ X4 ) )
= $true )
| ( ( in @ X3 @ X4 )
= $true )
| ( ( in @ X3 @ X5 )
!= $true ) )
| ( setminusERneg != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK94,sK95,sK96]),skolemize(X0,sK94),skolemize(X1,sK95),skolemize(X2,sK96)],[f1192]) ).
thf(f1338,plain,
( ( binintersectSubset2 = $true )
& ( emptysetE = $true )
& ( setukpairinjR12 = $true )
& ( setadjoinE = $true )
& ( notdallE = $true )
& ( dpsetconstrI = $true )
& ( exuE1 = $true )
& ( iftrueProp2 = $true )
& ( dpsetconstrEL2 = $true )
& ( eta1 = $true )
& ( notequalI1 = $true )
& ( brelnall2 = $true )
& ( cartprodpairsurjEq = $true )
& ( dsetconstrI = $true )
& ( doubleComplementSub2 = $true )
& ( iffalseProp1 = $true )
& ( funcGraphProp2 = $true )
& ( binintersectEL = $true )
& ( ubforcartprodlem1 = $true )
& ( emptyI = $true )
& ( binintersectI = $true )
& ( upairinpowunion = $true )
& ( upairset2E = $true )
& ( symdiffIneg2 = $true )
& ( cartprodpairmemEL = $true )
& ( binunionIL = $true )
& ( upairset2IR = $true )
& ( complementSubsetComplementIntersect = $true )
& ( emptysetimpfalse = $true )
& ( notinsingleton = $true )
& ( binunionLsub = $true )
& ( setunionsingleton2 = $true )
& ( exuE3u = $true )
& ( noeltsimpempty = $true )
& ( contrasubsetT2 = $true )
& ( dpsetconstrERa = $true )
& ( doubleComplementSub1 = $true )
& ( lamProp = $true )
& ( uniqinunit = $true )
& ( dsetconstrEL = $true )
& ( symdiffI2 = $true )
& ( setOfPairsIsBReln = $true )
& ( kpairp = $true )
& ( kfstpairEq = $true )
& ( contrasubsetT = $true )
& ( upairsetIR = $true )
& ( ksndpairEq = $true )
& ( setminusEL = $true )
& ( ( in @ sK246 @ ( powerset @ sK245 ) )
= $true )
& ( ( in @ sK247 @ ( powerset @ sK245 ) )
= $true )
& ( ( subset @ sK246 @ ( setminus @ sK245 @ sK247 ) )
= $true )
& ( ( in @ sK248 @ ( setminus @ sK245 @ sK246 ) )
!= $true )
& ( ( in @ sK248 @ sK245 )
= $true )
& ( ( in @ sK248 @ sK247 )
= $true )
& ( funcext2 = $true )
& ( setbeta = $true )
& ( binintersectTELcontra = $true )
& ( kpairiskpair = $true )
& ( setunionsingleton1 = $true )
& ( vacuousDall = $true )
& ( funcextLem = $true )
& ( singletonsswitch = $true )
& ( binintersectSubset1 = $true )
& ( setextAx = $true )
& ( lam2p = $true )
& ( singletoninpowunion = $true )
& ( descr__Cong = $true )
& ( prop2set2propI = $true )
& ( eqinunit = $true )
& ( setminusT_lem = $true )
& ( setukpairinjL2 = $true )
& ( setext = $true )
& ( contrasubsetT1 = $true )
& ( foundationAx = $true )
& ( powersetAx = $true )
& ( setadjoin__Cong = $true )
& ( dpsetconstrEL1 = $true )
& ( setminusIRneg = $true )
& ( doubleComplementI1 = $true )
& ( powersetI = $true )
& ( iftrue = $true )
& ( emptyInPowerset = $true )
& ( setminusER = $true )
& ( cartprodmempaircEq = $true )
& ( upairequniteq = $true )
& ( nonemptyImpWitness = $true )
& ( dsetconstr__Cong = $true )
& ( setadjoinAx = $true )
& ( cartprodfstin = $true )
& ( upairsetIL = $true )
& ( setadjoinSub = $true )
& ( emptysetAx = $true )
& ( iffalseProp2 = $true )
& ( subsetTrans = $true )
& ( exuI1 = $true )
& ( powersetE1 = $true )
& ( complementTnotintersectT = $true )
& ( exuI3 = $true )
& ( theeq = $true )
& ( binintersectSubset4 = $true )
& ( subbreln = $true )
& ( setextsub = $true )
& ( subsetI1 = $true )
& ( ex1I = $true )
& ( symdiffIneg1 = $true )
& ( ex1I2 = $true )
& ( powersetI1 = $true )
& ( quantDeMorgan4 = $true )
& ( sepSubset = $true )
& ( symdiffI1 = $true )
& ( quantDeMorgan1 = $true )
& ( setukpairinjR11 = $true )
& ( quantDeMorgan2 = $true )
& ( inPowerset = $true )
& ( omega__Cong = $true )
& ( binintersectRsub = $true )
& ( binunionIR = $true )
& ( binintersectTERcontra = $true )
& ( exu__Cong = $true )
& ( setunionAx = $true )
& ( setadjoinOr = $true )
& ( powersetT_lem = $true )
& ( binunionRsub = $true )
& ( ubforcartprodlem2 = $true )
& ( emptyE1 = $true )
& ( eta2 = $true )
& ( binintersectLsub = $true )
& ( setukpairIL = $true )
& ( iftrueProp1 = $true )
& ( binunionT_lem = $true )
& ( setunion__Cong = $true )
& ( iffalse = $true )
& ( emptyinPowerset = $true )
& ( setukpairinjL = $true )
& ( descrp = $true )
& ( notinemptyset = $true )
& ( setunionE2 = $true )
& ( ubforcartprodlem3 = $true )
& ( setadjoinIL = $true )
& ( complementTI1 = $true )
& ( kpairsurjEq = $true )
& ( prop2setI = $true )
& ( emptyinunitempty = $true )
& ( subset2powerset = $true )
& ( app = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( subsetRefl = $true )
& ( emptyset__Cong = $true )
& ( funcinfuncset = $true )
& ( powersetTE1 = $true )
& ( ex1E1 = $true )
& ( dsetconstrER = $true )
& ( powersetsubset = $true )
& ( nonemptyE1 = $true )
& ( powersetTI1 = $true )
& ( wellorderingAx = $true )
& ( setunionI = $true )
& ( setukpairIR = $true )
& ( contrasubsetT3 = $true )
& ( replAx = $true )
& ( setadjoinIR = $true )
& ( subsetI2 = $true )
& ( cartprodfstpairEq = $true )
& ( dpsetconstrER = $true )
& ( omegaIndAx = $true )
& ( beta1 = $true )
& ( setoftrueEq = $true )
& ( iftrueorfalse = $true )
& ( setukpairinjR = $true )
& ( kfstsingleton = $true )
& ( exuE2 = $true )
& ( exuEu = $true )
& ( exuI2 = $true )
& ( cartprodsndin = $true )
& ( setminusSubset2 = $true )
& ( cartprodpairin = $true )
& ( prop2setE = $true )
& ( cartprodpairmemER = $true )
& ( setminusLsub = $true )
& ( funcImageSingleton = $true )
& ( eqbreln = $true )
& ( setminusSubset1 = $true )
& ( setukpairinjR2 = $true )
& ( singletonprop = $true )
& ( setadjoinSub2 = $true )
& ( upairsubunion = $true )
& ( binintersectSubset3 = $true )
& ( setextT = $true )
& ( lamp = $true )
& ( nonemptyI1 = $true )
& ( singletonsubset = $true )
& ( subsetE = $true )
& ( upairsetE = $true )
& ( singletoninpowerset = $true )
& ( secondinupair = $true )
& ( emptysetsubset = $true )
& ( inCongP = $true )
& ( exuE3e = $true )
& ( symdiffE = $true )
& ( ap2p = $true )
& ( bs114d = $true )
& ( funcGraphProp3 = $true )
& ( funcext = $true )
& ( complementImpComplementIntersect = $true )
& ( ifp = $true )
& ( doubleComplementE1 = $true )
& ( cartprodmempair1 = $true )
& ( setukpairinjR1 = $true )
& ( binunionE = $true )
& ( theprop = $true )
& ( subPowSU = $true )
& ( eqimpsubset2 = $true )
& ( ap2apEq1 = $true )
& ( doubleComplementEq = $true )
& ( cartprodsndpairEq = $true )
& ( ifSingleton = $true )
& ( setminusELneg = $true )
& ( complementT_lem = $true )
& ( sepInPowerset = $true )
& ( singletonsuniq = $true )
& ( binunionEcases = $true )
& ( powersetE = $true )
& ( disjointsetsI1 = $true )
& ( ap2apEq2 = $true )
& ( nonemptyI = $true )
& ( binintersectT_lem = $true )
& ( setminusILneg = $true )
& ( notdexE = $true )
& ( complementTE1 = $true )
& ( setminusERneg = $true )
& ( in__Cong = $true )
& ( setminusI = $true )
& ( infuncsetfunc = $true )
& ( subsetemptysetimpeq = $true )
& ( binintersectSubset5 = $true )
& ( ksndsingleton = $true )
& ( omega0Ax = $true )
& ( binintersectER = $true )
& ( powerset__Cong = $true )
& ( dpsetconstrSub = $true )
& ( quantDeMorgan3 = $true )
& ( lam2lamEq = $true )
& ( apProp = $true )
& ( funcGraphProp1 = $true )
& ( omegaSAx = $true )
& ( setukpairinjL1 = $true )
& ( subsetE2 = $true )
& ( subsetTI = $true )
& ( notsubsetI = $true )
& ( setunionsingleton = $true )
& ( funcGraphProp4 = $true )
& ( beta2 = $true )
& ( notequalI2 = $true )
& ( cartprodmempair = $true )
& ( setunionE = $true )
& ( ex1E2 = $true )
& ( eqimpsubset1 = $true )
& ( brelnall1 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK245,sK246,sK247,sK248]),skolemize(X0,sK245),skolemize(X1,sK246),skolemize(X2,sK247),skolemize(X3,sK248)],[f969]) ).
thf(f1787,plain,
( ( ( contrasubsetT = $true )
| ? [X1: $i,X0: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
& ( ( in @ X3 @ X1 )
= $true ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) )
& ( ! [X1: $i,X0: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true )
| ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true ) ) )
| ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) )
| ( contrasubsetT != $true ) ) ),
inference(nnf_transformation,[],[f1055]) ).
thf(f1788,plain,
( ( ( contrasubsetT = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( ( subset @ X0 @ ( setminus @ X1 @ X2 ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ) )
& ( ! [X4: $i,X5: $i] :
( ! [X6: $i] :
( ( ( in @ X6 @ ( powerset @ X5 ) )
!= $true )
| ! [X7: $i] :
( ( ( in @ X7 @ X6 )
!= $true )
| ( ( in @ X7 @ X5 )
!= $true )
| ( ( subset @ X4 @ ( setminus @ X5 @ X6 ) )
!= $true )
| ( ( in @ X7 @ X4 )
!= $true ) ) )
| ( ( in @ X4 @ ( powerset @ X5 ) )
!= $true ) )
| ( contrasubsetT != $true ) ) ),
inference(rectify,[],[f1787]) ).
thf(f1789,plain,
( ( ( contrasubsetT = $true )
| ( ( ( in @ sK723 @ ( powerset @ sK722 ) )
= $true )
& ( ( in @ sK724 @ sK723 )
= $true )
& ( ( in @ sK724 @ sK722 )
= $true )
& ( ( subset @ sK721 @ ( setminus @ sK722 @ sK723 ) )
= $true )
& ( ( in @ sK724 @ sK721 )
= $true )
& ( ( in @ sK721 @ ( powerset @ sK722 ) )
= $true ) ) )
& ( ! [X4: $i,X5: $i] :
( ! [X6: $i] :
( ( ( in @ X6 @ ( powerset @ X5 ) )
!= $true )
| ! [X7: $i] :
( ( ( in @ X7 @ X6 )
!= $true )
| ( ( in @ X7 @ X5 )
!= $true )
| ( ( subset @ X4 @ ( setminus @ X5 @ X6 ) )
!= $true )
| ( ( in @ X7 @ X4 )
!= $true ) ) )
| ( ( in @ X4 @ ( powerset @ X5 ) )
!= $true ) )
| ( contrasubsetT != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK721,sK722,sK723,sK724]),skolemize(X0,sK721),skolemize(X1,sK722),skolemize(X2,sK723),skolemize(X3,sK724)],[f1788]) ).
thf(f1978,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
= $true )
| ( ( in @ X3 @ X5 )
!= $true )
| ( ( in @ X3 @ ( setminus @ X5 @ X4 ) )
= $true )
| ( setminusERneg != $true ) ),
inference(cnf_transformation,[],[f1193]) ).
thf(f2196,plain,
setminusERneg = $true,
inference(cnf_transformation,[],[f1338]) ).
thf(f2372,plain,
( ( in @ sK248 @ sK247 )
= $true ),
inference(cnf_transformation,[],[f1338]) ).
thf(f2373,plain,
( ( in @ sK248 @ sK245 )
= $true ),
inference(cnf_transformation,[],[f1338]) ).
thf(f2374,plain,
( ( in @ sK248 @ ( setminus @ sK245 @ sK246 ) )
!= $true ),
inference(cnf_transformation,[],[f1338]) ).
thf(f2375,plain,
( ( subset @ sK246 @ ( setminus @ sK245 @ sK247 ) )
= $true ),
inference(cnf_transformation,[],[f1338]) ).
thf(f2376,plain,
( ( in @ sK247 @ ( powerset @ sK245 ) )
= $true ),
inference(cnf_transformation,[],[f1338]) ).
thf(f2377,plain,
( ( in @ sK246 @ ( powerset @ sK245 ) )
= $true ),
inference(cnf_transformation,[],[f1338]) ).
thf(f2381,plain,
contrasubsetT = $true,
inference(cnf_transformation,[],[f1338]) ).
thf(f3079,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( subset @ X4 @ ( setminus @ X5 @ X6 ) )
!= $true )
| ( ( in @ X7 @ X6 )
!= $true )
| ( contrasubsetT != $true )
| ( ( in @ X6 @ ( powerset @ X5 ) )
!= $true )
| ( ( in @ X7 @ X4 )
!= $true )
| ( ( in @ X4 @ ( powerset @ X5 ) )
!= $true )
| ( ( in @ X7 @ X5 )
!= $true ) ),
inference(cnf_transformation,[],[f1789]) ).
thf(f3778,definition,
( spl791_86
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( ( in @ X4 @ X5 )
!= $true )
| ( ( in @ X4 @ ( setminus @ X5 @ X3 ) )
= $true )
| ( ( in @ X4 @ X3 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl791_86])],[avatar_definition]) ).
thf(f3779,plain,
( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setminus @ X5 @ X3 ) )
= $true )
| ( ( in @ X4 @ X5 )
!= $true )
| ( ( in @ X4 @ X3 )
= $true ) )
| ~ spl791_86 ),
inference(avatar_component_clause,[],[f3778]) ).
thf(f3838,definition,
( spl791_100
<=> ( setminusERneg = $true ) ),
introduced(definition,[new_symbols(definition,[spl791_100])],[avatar_definition]) ).
thf(f4160,definition,
( spl791_173
<=> ( ( in @ sK248 @ sK245 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl791_173])],[avatar_definition]) ).
thf(f4162,plain,
( ( ( in @ sK248 @ sK245 )
= $true )
| ~ spl791_173 ),
inference(avatar_component_clause,[],[f4160]) ).
thf(f4163,plain,
spl791_173,
inference(avatar_split_clause,[],[f2373,f4160]) ).
thf(f4690,definition,
( spl791_292
<=> ( ( in @ sK248 @ sK247 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl791_292])],[avatar_definition]) ).
thf(f4692,plain,
( ( ( in @ sK248 @ sK247 )
= $true )
| ~ spl791_292 ),
inference(avatar_component_clause,[],[f4690]) ).
thf(f4693,plain,
spl791_292,
inference(avatar_split_clause,[],[f2372,f4690]) ).
thf(f5171,plain,
spl791_100,
inference(avatar_split_clause,[],[f2196,f3838]) ).
thf(f5442,definition,
( spl791_454
<=> ( contrasubsetT = $true ) ),
introduced(definition,[new_symbols(definition,[spl791_454])],[avatar_definition]) ).
thf(f5786,plain,
( spl791_86
| ~ spl791_100 ),
inference(avatar_split_clause,[],[f1978,f3838,f3778]) ).
thf(f5929,definition,
( spl791_556
<=> ( ( in @ sK247 @ ( powerset @ sK245 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl791_556])],[avatar_definition]) ).
thf(f5931,plain,
( ( ( in @ sK247 @ ( powerset @ sK245 ) )
= $true )
| ~ spl791_556 ),
inference(avatar_component_clause,[],[f5929]) ).
thf(f5932,plain,
spl791_556,
inference(avatar_split_clause,[],[f2376,f5929]) ).
thf(f6677,definition,
( spl791_713
<=> ( ( subset @ sK246 @ ( setminus @ sK245 @ sK247 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl791_713])],[avatar_definition]) ).
thf(f6679,plain,
( ( ( subset @ sK246 @ ( setminus @ sK245 @ sK247 ) )
= $true )
| ~ spl791_713 ),
inference(avatar_component_clause,[],[f6677]) ).
thf(f6680,plain,
spl791_713,
inference(avatar_split_clause,[],[f2375,f6677]) ).
thf(f8443,definition,
( spl791_1078
<=> ( ( in @ sK248 @ ( setminus @ sK245 @ sK246 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl791_1078])],[avatar_definition]) ).
thf(f8445,plain,
( ( ( in @ sK248 @ ( setminus @ sK245 @ sK246 ) )
!= $true )
| spl791_1078 ),
inference(avatar_component_clause,[],[f8443]) ).
thf(f8446,plain,
~ spl791_1078,
inference(avatar_split_clause,[],[f2374,f8443]) ).
thf(f8793,definition,
( spl791_1151
<=> ! [X5: $i,X4: $i,X7: $i,X6: $i] :
( ( ( subset @ X4 @ ( setminus @ X5 @ X6 ) )
!= $true )
| ( ( in @ X7 @ X5 )
!= $true )
| ( ( in @ X4 @ ( powerset @ X5 ) )
!= $true )
| ( ( in @ X7 @ X4 )
!= $true )
| ( ( in @ X6 @ ( powerset @ X5 ) )
!= $true )
| ( ( in @ X7 @ X6 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl791_1151])],[avatar_definition]) ).
thf(f8794,plain,
( ! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( subset @ X4 @ ( setminus @ X5 @ X6 ) )
!= $true )
| ( ( in @ X7 @ X4 )
!= $true )
| ( ( in @ X7 @ X6 )
!= $true )
| ( ( in @ X4 @ ( powerset @ X5 ) )
!= $true )
| ( ( in @ X7 @ X5 )
!= $true )
| ( ( in @ X6 @ ( powerset @ X5 ) )
!= $true ) )
| ~ spl791_1151 ),
inference(avatar_component_clause,[],[f8793]) ).
thf(f8795,plain,
( ~ spl791_454
| spl791_1151 ),
inference(avatar_split_clause,[],[f3079,f8793,f5442]) ).
thf(f8890,definition,
( spl791_1170
<=> ( ( in @ sK246 @ ( powerset @ sK245 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl791_1170])],[avatar_definition]) ).
thf(f8892,plain,
( ( ( in @ sK246 @ ( powerset @ sK245 ) )
= $true )
| ~ spl791_1170 ),
inference(avatar_component_clause,[],[f8890]) ).
thf(f8893,plain,
spl791_1170,
inference(avatar_split_clause,[],[f2377,f8890]) ).
thf(f9133,plain,
spl791_454,
inference(avatar_split_clause,[],[f2381,f5442]) ).
thf(f9391,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sK247 )
!= $true )
| ( ( in @ X0 @ sK246 )
!= $true )
| ( ( in @ sK247 @ ( powerset @ sK245 ) )
!= $true )
| ( ( in @ X0 @ sK245 )
!= $true )
| ( $true != $true )
| ( ( in @ sK246 @ ( powerset @ sK245 ) )
!= $true ) )
| ~ spl791_713
| ~ spl791_1151 ),
inference(superposition,[],[f8794,f6679]) ).
thf(f9392,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sK247 )
!= $true )
| ( ( in @ X0 @ sK246 )
!= $true )
| ( ( in @ sK247 @ ( powerset @ sK245 ) )
!= $true )
| ( ( in @ sK246 @ ( powerset @ sK245 ) )
!= $true )
| ( ( in @ X0 @ sK245 )
!= $true ) )
| ~ spl791_713
| ~ spl791_1151 ),
inference(trivial_inequality_removal,[],[f9391]) ).
thf(f9393,plain,
( ! [X0: $i] :
( ( ( in @ sK246 @ ( powerset @ sK245 ) )
!= $true )
| ( ( in @ X0 @ sK247 )
!= $true )
| ( ( in @ X0 @ sK246 )
!= $true )
| ( ( in @ X0 @ sK245 )
!= $true ) )
| ~ spl791_556
| ~ spl791_713
| ~ spl791_1151 ),
inference(forward_subsumption_resolution,[],[f9392,f5931]) ).
thf(f9394,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sK247 )
!= $true )
| ( ( in @ X0 @ sK246 )
!= $true )
| ( ( in @ X0 @ sK245 )
!= $true ) )
| ~ spl791_556
| ~ spl791_713
| ~ spl791_1151
| ~ spl791_1170 ),
inference(forward_subsumption_resolution,[],[f9393,f8892]) ).
thf(f9395,plain,
( ( ( in @ sK248 @ sK246 )
!= $true )
| ( $true != $true )
| ( ( in @ sK248 @ sK245 )
!= $true )
| ~ spl791_292
| ~ spl791_556
| ~ spl791_713
| ~ spl791_1151
| ~ spl791_1170 ),
inference(superposition,[],[f9394,f4692]) ).
thf(f9396,plain,
( ( ( in @ sK248 @ sK246 )
!= $true )
| ( ( in @ sK248 @ sK245 )
!= $true )
| ~ spl791_292
| ~ spl791_556
| ~ spl791_713
| ~ spl791_1151
| ~ spl791_1170 ),
inference(trivial_inequality_removal,[],[f9395]) ).
thf(f9397,plain,
( ( ( in @ sK248 @ sK246 )
!= $true )
| ~ spl791_173
| ~ spl791_292
| ~ spl791_556
| ~ spl791_713
| ~ spl791_1151
| ~ spl791_1170 ),
inference(forward_subsumption_resolution,[],[f9396,f4162]) ).
thf(f9399,definition,
( spl791_1263
<=> ( ( in @ sK248 @ sK246 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl791_1263])],[avatar_definition]) ).
thf(f9401,plain,
( ( ( in @ sK248 @ sK246 )
!= $true )
| spl791_1263 ),
inference(avatar_component_clause,[],[f9399]) ).
thf(f9402,plain,
( ~ spl791_1263
| ~ spl791_173
| ~ spl791_292
| ~ spl791_556
| ~ spl791_713
| ~ spl791_1151
| ~ spl791_1170 ),
inference(avatar_split_clause,[],[f9397,f8890,f8793,f6677,f5929,f4690,f4160,f9399]) ).
thf(f11530,plain,
( ( ( in @ sK248 @ sK246 )
= $true )
| ( ( in @ sK248 @ sK245 )
!= $true )
| ( $true != $true )
| ~ spl791_86
| spl791_1078 ),
inference(superposition,[],[f8445,f3779]) ).
thf(f11532,plain,
( ( ( in @ sK248 @ sK245 )
!= $true )
| ( ( in @ sK248 @ sK246 )
= $true )
| ~ spl791_86
| spl791_1078 ),
inference(trivial_inequality_removal,[],[f11530]) ).
thf(f11546,plain,
( ( ( in @ sK248 @ sK246 )
= $true )
| ~ spl791_86
| ~ spl791_173
| spl791_1078 ),
inference(forward_subsumption_resolution,[],[f11532,f4162]) ).
thf(f11547,plain,
( $false
| ~ spl791_86
| ~ spl791_173
| spl791_1078
| spl791_1263 ),
inference(forward_subsumption_resolution,[],[f11546,f9401]) ).
thf(f11548,plain,
( ~ spl791_86
| ~ spl791_173
| spl791_1078
| spl791_1263 ),
inference(avatar_contradiction_clause,[],[f11547]) ).
cnf(s105,plain,
spl791_173,
inference(sat_conversion,[],[f4163]) ).
cnf(s193,plain,
spl791_292,
inference(sat_conversion,[],[f4693]) ).
cnf(s278,plain,
spl791_100,
inference(sat_conversion,[],[f5171]) ).
cnf(s398,plain,
( spl791_86
| ~ spl791_100 ),
inference(sat_conversion,[],[f5786]) ).
cnf(s436,plain,
spl791_556,
inference(sat_conversion,[],[f5932]) ).
cnf(s604,plain,
spl791_713,
inference(sat_conversion,[],[f6680]) ).
cnf(s1061,plain,
~ spl791_1078,
inference(sat_conversion,[],[f8446]) ).
cnf(s1147,plain,
( ~ spl791_454
| spl791_1151 ),
inference(sat_conversion,[],[f8795]) ).
cnf(s1173,plain,
spl791_1170,
inference(sat_conversion,[],[f8893]) ).
cnf(s1237,plain,
spl791_454,
inference(sat_conversion,[],[f9133]) ).
cnf(s1288,plain,
( ~ spl791_173
| ~ spl791_292
| ~ spl791_556
| ~ spl791_713
| ~ spl791_1151
| ~ spl791_1170
| ~ spl791_1263 ),
inference(sat_conversion,[],[f9402]) ).
cnf(s1354,plain,
( ~ spl791_86
| ~ spl791_173
| spl791_1078
| spl791_1263 ),
inference(sat_conversion,[],[f11548]) ).
cnf(s1359,plain,
spl791_1151,
inference(rat,[],[s1147,s1237]) ).
cnf(s1559,plain,
spl791_86,
inference(rat,[],[s398,s278]) ).
cnf(s1649,plain,
spl791_1263,
inference(rat,[],[s1354,s1559,s1061,s105]) ).
cnf(s1652,plain,
$false,
inference(rat,[],[s1288,s193,s1173,s1359,s604,s436,s1649,s105]) ).
thf(f11549,plain,
$false,
inference(avatar_sat_refutation,[],[s1652]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU736^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 % Computer : n004.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 14:18:07 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running higher-order theorem proving
% 0.23/0.30 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.33/0.46 % (1353292)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.33/0.46 % (1353299)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=472275317:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.33/0.46 % (1353299)Instruction limit reached!
% 0.33/0.46 % (1353299)------------------------------
% 0.33/0.46 % (1353299)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.46 % (1353299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.46 % (1353299)CaDiCaL version: 2.1.3
% 0.33/0.46 % (1353299)Termination reason: Instruction limit
% 0.33/0.46 % (1353299)Termination phase: shuffling
% 0.33/0.46 % (1353299)Time elapsed: 0.002 s
% 0.33/0.46 % (1353299)Peak memory usage: 10 MB
% 0.33/0.46 % (1353299)Instructions burned: 8 (million)
% 0.33/0.46 % (1353298)lrs+10_16_si=on:nwc=1.5:random_seed=2906580632:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.33/0.46 % (1353297)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3124390402:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.33/0.46 % (1353300)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=710394077:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.33/0.46 % (1353305)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3475730344:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.33/0.46 % (1353305)Instruction limit reached!
% 0.33/0.46 % (1353305)------------------------------
% 0.33/0.46 % (1353305)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.46 % (1353305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.46 % (1353305)CaDiCaL version: 2.1.3
% 0.33/0.46 % (1353305)Termination reason: Instruction limit
% 0.33/0.46 % (1353305)Termination phase: shuffling
% 0.33/0.46 % (1353305)Time elapsed: 0.003 s
% 0.33/0.46 % (1353305)Peak memory usage: 10 MB
% 0.33/0.46 % (1353305)Instructions burned: 12 (million)
% 0.33/0.46 % (1353303)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.33/0.46 % (1353303)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.33/0.46 % (1353298)Instruction limit reached!
% 0.33/0.46 % (1353298)------------------------------
% 0.33/0.46 % (1353298)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.46 % (1353298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.46 % (1353298)CaDiCaL version: 2.1.3
% 0.33/0.46 % (1353298)Termination reason: Instruction limit
% 0.33/0.46 % (1353298)Termination phase: shuffling
% 0.33/0.46 % (1353298)Time elapsed: 0.009 s
% 0.33/0.46 % (1353298)Peak memory usage: 10 MB
% 0.33/0.46 % (1353298)Instructions burned: 18 (million)
% 0.33/0.46 % (1353301)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2262882911:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.33/0.46 % (1353303)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=215353624:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.33/0.46 % (1353302)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1251188783:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.33/0.46 % (1353310)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=533213219:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.33/0.46 % (1353310)Instruction limit reached!
% 0.33/0.46 % (1353310)------------------------------
% 0.33/0.46 % (1353310)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.46 % (1353310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.46 % (1353310)CaDiCaL version: 2.1.3
% 0.33/0.46 % (1353310)Termination reason: Instruction limit
% 0.33/0.46 % (1353310)Termination phase: shuffling
% 0.33/0.46 % (1353310)Time elapsed: 0.002 s
% 0.33/0.46 % (1353310)Peak memory usage: 10 MB
% 0.33/0.46 % (1353310)Instructions burned: 8 (million)
% 1.13/0.52 % (1353311)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.13/0.52 % (1353311)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3950589833:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.13/0.52 % (1353316)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=4115613501:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.13/0.52 % (1353301)Instruction limit reached!
% 1.13/0.52 % (1353301)------------------------------
% 1.13/0.52 % (1353301)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.13/0.52 % (1353301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.13/0.52 % (1353301)CaDiCaL version: 2.1.3
% 1.13/0.52 % (1353301)Termination reason: Instruction limit
% 1.13/0.52 % (1353301)Termination phase: shuffling
% 1.13/0.52 % (1353301)Time elapsed: 0.020 s
% 1.13/0.52 % (1353301)Peak memory usage: 10 MB
% 1.13/0.52 % (1353301)Instructions burned: 24 (million)
% 1.13/0.52 % (1353316)Instruction limit reached!
% 1.13/0.52 % (1353316)------------------------------
% 1.13/0.52 % (1353316)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.13/0.52 % (1353316)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.13/0.52 % (1353316)CaDiCaL version: 2.1.3
% 1.13/0.52 % (1353316)Termination reason: Instruction limit
% 1.13/0.52 % (1353316)Termination phase: shuffling
% 1.13/0.52 % (1353316)Time elapsed: 0.003 s
% 1.13/0.52 % (1353316)Peak memory usage: 10 MB
% 1.13/0.52 % (1353316)Instructions burned: 12 (million)
% 1.13/0.52 % (1353311)Instruction limit reached!
% 1.13/0.52 % (1353311)------------------------------
% 1.13/0.52 % (1353311)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.13/0.52 % (1353311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.13/0.52 % (1353311)CaDiCaL version: 2.1.3
% 1.13/0.52 % (1353311)Termination reason: Instruction limit
% 1.13/0.52 % (1353311)Termination phase: shuffling
% 1.13/0.52 % (1353311)Time elapsed: 0.004 s
% 1.13/0.52 % (1353311)Peak memory usage: 10 MB
% 1.13/0.53 % (1353311)Instructions burned: 9 (million)
% 1.13/0.53 % (1353297)Instruction limit reached!
% 1.13/0.53 % (1353297)------------------------------
% 1.13/0.53 % (1353297)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.13/0.53 % (1353297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.13/0.53 % (1353297)CaDiCaL version: 2.1.3
% 1.13/0.53 % (1353297)Termination reason: Instruction limit
% 1.13/0.53 % (1353297)Termination phase: Preprocessing 3
% 1.13/0.53 % (1353297)Time elapsed: 0.041 s
% 1.13/0.53 % (1353297)Peak memory usage: 13 MB
% 1.13/0.53 % (1353297)Instructions burned: 88 (million)
% 1.13/0.53 % (1353319)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.13/0.53 % (1353319)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.13/0.53 % (1353319)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1486589672:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.13/0.53 % (1353321)lrs+10_1_si=on:cs=on:random_seed=3435536782:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 1.13/0.53 % (1353320)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=3406273984:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.13/0.53 % (1353322)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.13/0.53 % (1353321)Instruction limit reached!
% 1.13/0.53 % (1353321)------------------------------
% 1.13/0.53 % (1353321)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.13/0.53 % (1353321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.13/0.53 % (1353321)CaDiCaL version: 2.1.3
% 1.13/0.53 % (1353321)Termination reason: Instruction limit
% 1.13/0.53 % (1353321)Termination phase: shuffling
% 1.13/0.57 % (1353321)Time elapsed: 0.004 s
% 1.13/0.57 % (1353321)Peak memory usage: 10 MB
% 1.13/0.57 % (1353321)Instructions burned: 8 (million)
% 1.13/0.57 % (1353322)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=3143293609:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.13/0.57 % (1353322)Instruction limit reached!
% 1.13/0.57 % (1353322)------------------------------
% 1.13/0.57 % (1353322)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.13/0.57 % (1353322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.13/0.57 % (1353322)CaDiCaL version: 2.1.3
% 1.13/0.57 % (1353322)Termination reason: Instruction limit
% 1.13/0.57 % (1353322)Termination phase: shuffling
% 1.13/0.57 % (1353322)Time elapsed: 0.002 s
% 1.13/0.57 % (1353322)Peak memory usage: 10 MB
% 1.13/0.57 % (1353322)Instructions burned: 3 (million)
% 1.13/0.57 % (1353319)Instruction limit reached!
% 1.13/0.57 % (1353319)------------------------------
% 1.13/0.57 % (1353319)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.13/0.57 % (1353319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.13/0.57 % (1353319)CaDiCaL version: 2.1.3
% 1.13/0.57 % (1353319)Termination reason: Instruction limit
% 1.13/0.57 % (1353319)Termination phase: shuffling
% 1.13/0.57 % (1353319)Time elapsed: 0.018 s
% 1.13/0.57 % (1353319)Peak memory usage: 11 MB
% 1.13/0.57 % (1353319)Instructions burned: 31 (million)
% 1.13/0.57 % (1353302)Instruction limit reached!
% 1.13/0.57 % (1353302)------------------------------
% 1.13/0.57 % (1353302)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.13/0.57 % (1353302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.13/0.57 % (1353302)CaDiCaL version: 2.1.3
% 1.13/0.57 % (1353302)Termination reason: Instruction limit
% 1.13/0.57 % (1353302)Termination phase: Preprocessing 3
% 1.13/0.57 % (1353302)Time elapsed: 0.063 s
% 1.13/0.57 % (1353302)Peak memory usage: 12 MB
% 1.13/0.57 % (1353302)Instructions burned: 76 (million)
% 1.13/0.57 % (1353326)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=756747382:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.13/0.57 % (1353328)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2669302779:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.13/0.57 % (1353320)Instruction limit reached!
% 1.13/0.57 % (1353320)------------------------------
% 1.13/0.57 % (1353320)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.13/0.57 % (1353320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.13/0.57 % (1353320)CaDiCaL version: 2.1.3
% 1.13/0.57 % (1353320)Termination reason: Instruction limit
% 1.13/0.57 % (1353320)Termination phase: Property scanning
% 1.13/0.57 % (1353320)Time elapsed: 0.031 s
% 1.13/0.57 % (1353320)Peak memory usage: 11 MB
% 1.13/0.57 % (1353320)Instructions burned: 87 (million)
% 1.13/0.57 % (1353329)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=341023114:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.13/0.57 % (1353330)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=798379550:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.13/0.57 % (1353329)Instruction limit reached!
% 1.13/0.57 % (1353329)------------------------------
% 1.13/0.57 % (1353329)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.13/0.57 % (1353329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.13/0.57 % (1353329)CaDiCaL version: 2.1.3
% 1.13/0.57 % (1353329)Termination reason: Instruction limit
% 1.13/0.57 % (1353329)Termination phase: Property scanning
% 1.13/0.57 % (1353329)Time elapsed: 0.012 s
% 1.13/0.57 % (1353329)Peak memory usage: 11 MB
% 1.13/0.57 % (1353329)Instructions burned: 27 (million)
% 1.13/0.57 % (1353330)Instruction limit reached!
% 1.13/0.57 % (1353330)------------------------------
% 1.13/0.57 % (1353330)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.13/0.57 % (1353330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.13/0.57 % (1353330)CaDiCaL version: 2.1.3
% 1.13/0.57 % (1353330)Termination reason: Instruction limit
% 1.13/0.57 % (1353330)Termination phase: shuffling
% 1.13/0.57 % (1353330)Time elapsed: 0.003 s
% 1.83/0.61 % (1353330)Peak memory usage: 10 MB
% 1.83/0.61 % (1353330)Instructions burned: 15 (million)
% 1.83/0.61 % (1353333)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=6500258:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.83/0.61 % (1353326)Instruction limit reached!
% 1.83/0.61 % (1353326)------------------------------
% 1.83/0.61 % (1353326)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.61 % (1353326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.61 % (1353326)CaDiCaL version: 2.1.3
% 1.83/0.61 % (1353326)Termination reason: Instruction limit
% 1.83/0.61 % (1353326)Termination phase: Property scanning
% 1.83/0.61 % (1353326)Time elapsed: 0.030 s
% 1.83/0.61 % (1353326)Peak memory usage: 10 MB
% 1.83/0.61 % (1353326)Instructions burned: 38 (million)
% 1.83/0.61 % (1353336)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1193439792:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.83/0.61 % (1353303)Instruction limit reached!
% 1.83/0.61 % (1353303)------------------------------
% 1.83/0.61 % (1353303)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.61 % (1353303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.61 % (1353303)CaDiCaL version: 2.1.3
% 1.83/0.61 % (1353303)Termination reason: Instruction limit
% 1.83/0.61 % (1353303)Termination phase: Saturation
% 1.83/0.61 % (1353303)Time elapsed: 0.118 s
% 1.83/0.61 % (1353303)Peak memory usage: 13 MB
% 1.83/0.61 % (1353303)Instructions burned: 157 (million)
% 1.83/0.61 % (1353339)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2469524262:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.83/0.61 % (1353338)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1668524478:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.83/0.61 % (1353338)Instruction limit reached!
% 1.83/0.61 % (1353338)------------------------------
% 1.83/0.61 % (1353338)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.61 % (1353338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.61 % (1353338)CaDiCaL version: 2.1.3
% 1.83/0.61 % (1353338)Termination reason: Instruction limit
% 1.83/0.61 % (1353338)Termination phase: shuffling
% 1.83/0.61 % (1353338)Time elapsed: 0.002 s
% 1.83/0.61 % (1353338)Peak memory usage: 10 MB
% 1.83/0.61 % (1353338)Instructions burned: 2 (million)
% 1.83/0.61 % (1353336)Instruction limit reached!
% 1.83/0.61 % (1353336)------------------------------
% 1.83/0.61 % (1353336)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.61 % (1353336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.61 % (1353336)CaDiCaL version: 2.1.3
% 1.83/0.61 % (1353336)Termination reason: Instruction limit
% 1.83/0.61 % (1353336)Termination phase: shuffling
% 1.83/0.61 % (1353336)Time elapsed: 0.013 s
% 1.83/0.61 % (1353336)Peak memory usage: 10 MB
% 1.83/0.61 % (1353336)Instructions burned: 14 (million)
% 1.83/0.61 % (1353339)Instruction limit reached!
% 1.83/0.61 % (1353339)------------------------------
% 1.83/0.61 % (1353339)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.61 % (1353339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.61 % (1353339)CaDiCaL version: 2.1.3
% 1.83/0.61 % (1353339)Termination reason: Instruction limit
% 1.83/0.61 % (1353339)Termination phase: shuffling
% 1.83/0.61 % (1353339)Time elapsed: 0.016 s
% 1.83/0.61 % (1353339)Peak memory usage: 10 MB
% 1.83/0.61 % (1353339)Instructions burned: 27 (million)
% 1.83/0.61 % (1353341)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2533099984:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.83/0.61 % (1353345)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.83/0.61 % (1353345)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.83/0.61 % (1353345)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=915702733:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.83/0.62 % (1353344)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3746261134:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.83/0.62 % (1353345)Instruction limit reached!
% 1.83/0.62 % (1353345)------------------------------
% 1.83/0.62 % (1353345)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.62 % (1353345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.62 % (1353345)CaDiCaL version: 2.1.3
% 1.83/0.62 % (1353345)Termination reason: Instruction limit
% 1.83/0.62 % (1353345)Termination phase: shuffling
% 1.83/0.62 % (1353345)Time elapsed: 0.007 s
% 1.83/0.62 % (1353345)Peak memory usage: 10 MB
% 1.83/0.62 % (1353345)Instructions burned: 15 (million)
% 1.83/0.62 % (1353341)Instruction limit reached!
% 1.83/0.62 % (1353341)------------------------------
% 1.83/0.62 % (1353341)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.62 % (1353341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.62 % (1353341)CaDiCaL version: 2.1.3
% 1.83/0.62 % (1353341)Termination reason: Instruction limit
% 1.83/0.62 % (1353341)Termination phase: shuffling
% 1.83/0.62 % (1353341)Time elapsed: 0.019 s
% 1.83/0.62 % (1353341)Peak memory usage: 11 MB
% 1.83/0.62 % (1353341)Instructions burned: 23 (million)
% 1.83/0.62 % (1353346)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.83/0.62 % (1353333)Instruction limit reached!
% 1.83/0.62 % (1353333)------------------------------
% 1.83/0.62 % (1353333)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.62 % (1353333)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.62 % (1353333)CaDiCaL version: 2.1.3
% 1.83/0.62 % (1353333)Termination reason: Instruction limit
% 1.83/0.62 % (1353333)Termination phase: Saturation
% 1.83/0.62 % (1353333)Time elapsed: 0.081 s
% 1.83/0.62 % (1353333)Peak memory usage: 15 MB
% 1.83/0.62 % (1353333)Instructions burned: 335 (million)
% 1.83/0.62 % (1353328)Instruction limit reached!
% 1.83/0.62 % (1353328)------------------------------
% 1.83/0.62 % (1353328)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.62 % (1353328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.62 % (1353328)CaDiCaL version: 2.1.3
% 1.83/0.62 % (1353328)Termination reason: Instruction limit
% 1.83/0.62 % (1353328)Termination phase: Saturation
% 1.83/0.62 % (1353328)Time elapsed: 0.108 s
% 1.83/0.62 % (1353328)Peak memory usage: 15 MB
% 1.83/0.62 % (1353328)Instructions burned: 250 (million)
% 1.83/0.62 % (1353346)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=1765388847:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2997 on theBenchmark for (2997ds/8Mi)
% 1.83/0.62 % (1353346)Instruction limit reached!
% 1.83/0.62 % (1353346)------------------------------
% 1.83/0.62 % (1353346)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.62 % (1353346)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.62 % (1353346)CaDiCaL version: 2.1.3
% 1.83/0.62 % (1353346)Termination reason: Instruction limit
% 1.83/0.62 % (1353346)Termination phase: shuffling
% 1.83/0.62 % (1353346)Time elapsed: 0.008 s
% 1.83/0.62 % (1353346)Peak memory usage: 10 MB
% 1.83/0.62 % (1353346)Instructions burned: 9 (million)
% 1.83/0.62 % (1353350)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=950877904:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 1.83/0.62 % (1353351)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=1458582378:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 1.83/0.62 % (1353353)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=665386880:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 1.83/0.62 % (1353344)Instruction limit reached!
% 1.83/0.62 % (1353344)------------------------------
% 1.83/0.62 % (1353344)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.62 % (1353344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.62 % (1353344)CaDiCaL version: 2.1.3
% 1.83/0.62 % (1353344)Termination reason: Instruction limit
% 1.83/0.62 % (1353344)Termination phase: Preprocessing 3
% 1.83/0.62 % (1353344)Time elapsed: 0.040 s
% 1.83/0.62 % (1353344)Peak memory usage: 12 MB
% 1.83/0.62 % (1353344)Instructions burned: 60 (million)
% 1.83/0.62 % (1353352)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2715142708:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 1.83/0.62 % (1353351)Instruction limit reached!
% 1.83/0.62 % (1353351)------------------------------
% 1.83/0.62 % (1353351)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.62 % (1353351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.62 % (1353351)CaDiCaL version: 2.1.3
% 1.83/0.62 % (1353351)Termination reason: Instruction limit
% 1.83/0.62 % (1353351)Termination phase: shuffling
% 1.83/0.62 % (1353351)Time elapsed: 0.006 s
% 1.83/0.62 % (1353351)Peak memory usage: 10 MB
% 1.83/0.62 % (1353351)Instructions burned: 8 (million)
% 1.83/0.62 % (1353350)Instruction limit reached!
% 1.83/0.62 % (1353350)------------------------------
% 1.83/0.62 % (1353350)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.62 % (1353350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.62 % (1353350)CaDiCaL version: 2.1.3
% 1.83/0.62 % (1353350)Termination reason: Instruction limit
% 1.83/0.62 % (1353350)Termination phase: shuffling
% 1.83/0.62 % (1353350)Time elapsed: 0.014 s
% 1.83/0.62 % (1353350)Peak memory usage: 11 MB
% 1.83/0.62 % (1353350)Instructions burned: 32 (million)
% 1.83/0.62 % (1353353)Instruction limit reached!
% 1.83/0.62 % (1353353)------------------------------
% 1.83/0.62 % (1353353)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.62 % (1353353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.62 % (1353353)CaDiCaL version: 2.1.3
% 1.83/0.62 % (1353353)Termination reason: Instruction limit
% 1.83/0.62 % (1353353)Termination phase: shuffling
% 1.83/0.62 % (1353353)Time elapsed: 0.010 s
% 1.83/0.62 % (1353353)Peak memory usage: 10 MB
% 1.83/0.62 % (1353353)Instructions burned: 22 (million)
% 1.83/0.62 % (1353352)Instruction limit reached!
% 1.83/0.62 % (1353352)------------------------------
% 1.83/0.62 % (1353352)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.62 % (1353352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.62 % (1353352)CaDiCaL version: 2.1.3
% 1.83/0.62 % (1353352)Termination reason: Instruction limit
% 1.83/0.62 % (1353352)Termination phase: shuffling
% 1.83/0.62 % (1353352)Time elapsed: 0.010 s
% 1.83/0.62 % (1353352)Peak memory usage: 10 MB
% 1.83/0.62 % (1353352)Instructions burned: 25 (million)
% 1.83/0.62 % (1353361)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=4159383762:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 1.83/0.62 % (1353356)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=31487874:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 1.83/0.62 % (1353362)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=505080060:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 1.83/0.62 % (1353363)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.83/0.62 % (1353363)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2579133965:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 1.83/0.62 % (1353363)Instruction limit reached!
% 1.83/0.62 % (1353363)------------------------------
% 1.83/0.62 % (1353363)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.62 % (1353363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.62 % (1353363)CaDiCaL version: 2.1.3
% 1.83/0.62 % (1353363)Termination reason: Instruction limit
% 1.83/0.62 % (1353363)Termination phase: shuffling
% 1.83/0.62 % (1353363)Time elapsed: 0.004 s
% 1.83/0.62 % (1353363)Peak memory usage: 10 MB
% 1.83/0.62 % (1353363)Instructions burned: 8 (million)
% 1.83/0.62 % (1353300) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1353292-1353300"...
% 1.83/0.62 % (1353362)Instruction limit reached!
% 1.83/0.62 % (1353362)------------------------------
% 1.83/0.62 % (1353362)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.62 % (1353362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.62 % (1353362)CaDiCaL version: 2.1.3
% 1.83/0.62 % (1353362)Termination reason: Instruction limit
% 1.83/0.62 % (1353362)Termination phase: Property scanning
% 1.83/0.62 % (1353362)Time elapsed: 0.020 s
% 1.83/0.62 % (1353362)Peak memory usage: 11 MB
% 1.83/0.62 % (1353362)Instructions burned: 46 (million)
% 1.83/0.62 % (1353360)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=839064268:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 1.83/0.62 % (1353300)...printing done.
% 1.83/0.62 % (1353369)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=3671266608:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 1.83/0.62 % (1353300)Refutation found. Thanks to Tanya!
% 1.83/0.62 % SZS status Theorem for theBenchmark
% 1.83/0.62 % SZS output start Proof for theBenchmark
% See solution above
% 1.83/0.63 % (1353300)------------------------------
% 1.83/0.63 % (1353300)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.83/0.63 % (1353300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.83/0.63 % (1353300)CaDiCaL version: 2.1.3
% 1.83/0.63 % (1353300)Termination reason: Refutation
% 1.83/0.63 % (1353300)Time elapsed: 0.261 s
% 1.83/0.63 % (1353300)Peak memory usage: 21 MB
% 1.83/0.63 % (1353300)Instructions burned: 514 (million)
% 1.83/0.63 % (1353292)Success in time 0.312 s
% 1.83/0.63 % Vampire exiting
%------------------------------------------------------------------------------