%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU733^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 08:31:01 AM UTC 2026
% Result : Theorem 2.43s 0.67s
% Output : Refutation 2.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 90 ( 31 unt; 0 typ; 10 def)
% Number of atoms : 4561 (1190 equ; 0 cnn)
% Maximal formula atoms : 254 ( 50 avg)
% Number of connectives : 2753 ( 167 ~; 138 |; 783 &; 611 @)
% ( 18 <=>;1036 =>; 0 <=; 0 <~>)
% Maximal formula depth : 263 ( 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 : 486 ( 483 usr; 291 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_290,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_291,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_292,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_293,type,
vOR: $o > $o > $o ).
thf(func_def_294,type,
vAND: $o > $o > $o ).
thf(func_def_295,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_296,type,
vNOT: $o > $o ).
thf(func_def_297,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $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,
sP0: $i > $i > $o ).
thf(func_def_302,type,
sP1: $i > $o ).
thf(func_def_303,type,
sP2: $o ).
thf(func_def_304,type,
sP3: $o ).
thf(func_def_309,type,
sK8: $i > $o ).
thf(func_def_316,type,
sK15: $i > $i ).
thf(func_def_318,type,
sK17: $i > ( $i > $i ) > $i > $i ).
thf(func_def_321,type,
sK20: $o ).
thf(func_def_326,type,
sK25: $o ).
thf(func_def_333,type,
sK32: $o ).
thf(func_def_341,type,
sK40: $i > $o ).
thf(func_def_343,type,
sK42: ( $i > $o ) > $i > $i ).
thf(func_def_344,type,
sK43: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_345,type,
sK44: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_348,type,
sK47: $i > $o ).
thf(func_def_349,type,
sK48: $i > $o ).
thf(func_def_352,type,
sK51: $i > $i ).
thf(func_def_355,type,
sK54: $i > $i > ( $i > $i ) > $i ).
thf(func_def_361,type,
sK60: ( $i > $o ) > $i > $i > $i ).
thf(func_def_364,type,
sK63: $i > $o ).
thf(func_def_367,type,
sK66: $i > $o ).
thf(func_def_372,type,
sK71: $i > $i > $i ).
thf(func_def_379,type,
sK78: $o ).
thf(func_def_381,type,
sK80: $i > $i ).
thf(func_def_388,type,
sK87: $o ).
thf(func_def_402,type,
sK101: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_403,type,
sK102: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_404,type,
sK103: $i > $o ).
thf(func_def_405,type,
sK104: $i > $o ).
thf(func_def_409,type,
sK108: $i > $i > $i > $i ).
thf(func_def_410,type,
sK109: $i > $i > $i > $i ).
thf(func_def_413,type,
sK112: $i > $o ).
thf(func_def_415,type,
sK114: $i > $i ).
thf(func_def_416,type,
sK115: $i > $i ).
thf(func_def_417,type,
sK116: $i > $i ).
thf(func_def_418,type,
sK117: $i > $i ).
thf(func_def_419,type,
sK118: $i > $i ).
thf(func_def_420,type,
sK119: $i > $i > $i > $i ).
thf(func_def_421,type,
sK120: $i > $i ).
thf(func_def_422,type,
sK121: $i > $i ).
thf(func_def_423,type,
sK122: $i > $i ).
thf(func_def_424,type,
sK123: $i > $i ).
thf(func_def_425,type,
sK124: $i > $i > $i ).
thf(func_def_426,type,
sK125: $i > $i > $i ).
thf(func_def_427,type,
sK126: $i > $i > $i > $i ).
thf(func_def_428,type,
sK127: $i > $i > $i > $i ).
thf(func_def_429,type,
sK128: $i > $i > $i > $i ).
thf(func_def_430,type,
sK129: $i > $i > $i ).
thf(func_def_431,type,
sK130: $i > $i > $i ).
thf(func_def_432,type,
sK131: $i > $i > $i ).
thf(func_def_448,type,
sK147: $o ).
thf(func_def_450,type,
sK149: $i > $o ).
thf(func_def_452,type,
sK151: $i > ( $i > $o ) > $i ).
thf(func_def_482,type,
sK181: $i > $i > $o ).
thf(func_def_488,type,
sK187: ( $i > $o ) > $i ).
thf(func_def_489,type,
sK188: $i > $o ).
thf(func_def_490,type,
sK189: $i > $i ).
thf(func_def_491,type,
sK190: $i > $i ).
thf(func_def_493,type,
sK192: $i > $i ).
thf(func_def_497,type,
sK196: $i > $i > $i ).
thf(func_def_500,type,
sK199: $i > ( $i > $i ) > $i > $i ).
thf(func_def_502,type,
sK201: $i > $i ).
thf(func_def_511,type,
sK210: $i > $i ).
thf(func_def_518,type,
sK217: $i > $i > $i > $i > $i ).
thf(func_def_520,type,
sK219: $i > $o ).
thf(func_def_533,type,
sK232: $i > $i > $i > $i > $i ).
thf(func_def_534,type,
sK233: $i > $i > $i > $i > $i ).
thf(func_def_535,type,
sK234: $i > $i > $i > $i > $i ).
thf(func_def_536,type,
sK235: $i > $i > $i > $i > $i ).
thf(func_def_559,type,
sK258: $i > $o ).
thf(func_def_560,type,
sK259: $i > $o ).
thf(func_def_561,type,
sK260: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_562,type,
sK261: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_563,type,
sK262: $i > ( $i > $o ) > $i ).
thf(func_def_564,type,
sK263: $i > $o ).
thf(func_def_566,type,
sK265: ( $i > $o ) > $i > $i ).
thf(func_def_567,type,
sK266: ( $i > $o ) > $i > $i ).
thf(func_def_569,type,
sK268: $i > $o ).
thf(func_def_572,type,
sK271: $o ).
thf(func_def_575,type,
sK274: $i > $o ).
thf(func_def_578,type,
sK277: $i > ( $i > $o ) > $i ).
thf(func_def_581,type,
sK280: $i > $i > $i ).
thf(func_def_585,type,
sK284: $o ).
thf(func_def_592,type,
sK291: $i > $i > $i ).
thf(func_def_611,type,
sK310: $i > $o ).
thf(func_def_614,type,
sK313: $i > ( $i > $o ) > $i ).
thf(func_def_617,type,
sK316: $i > $i ).
thf(func_def_625,type,
sK324: $o ).
thf(func_def_628,type,
sK327: $i > $o ).
thf(func_def_630,type,
sK329: ( $i > $o ) > $i > $i ).
thf(func_def_632,type,
sK331: $i > $i > $o ).
thf(func_def_662,type,
sK361: $i > ( $i > $o ) > $i ).
thf(func_def_663,type,
sK362: $i > $o ).
thf(func_def_693,type,
sK392: $i > $o ).
thf(func_def_695,type,
sK394: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_696,type,
sK395: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_700,type,
sK399: $i > $i > $o ).
thf(func_def_706,type,
sK405: $i > $i > $o ).
thf(func_def_714,type,
sK413: $i > $i > $i > $i > $i ).
thf(func_def_718,type,
sK417: $i > $i > $i > $i ).
thf(func_def_719,type,
sK418: $i > $i > $i > $i ).
thf(func_def_732,type,
sK431: $o ).
thf(func_def_738,type,
sK437: $i > $o ).
thf(func_def_740,type,
sK439: ( $i > $o ) > $i > $i ).
thf(func_def_753,type,
sK452: $i > $i > $i ).
thf(func_def_767,type,
sK466: $o ).
thf(func_def_771,type,
sK470: $i > $i > $i > $i > $i ).
thf(func_def_772,type,
sK471: $i > $i > $i > $i > $i ).
thf(func_def_799,type,
sK498: $i > $o ).
thf(func_def_801,type,
sK500: ( $i > $o ) > $i > $i ).
thf(func_def_802,type,
sK501: ( $i > $o ) > $i > $i ).
thf(func_def_809,type,
sK508: $i > $i > $i ).
thf(func_def_815,type,
sK514: $o ).
thf(func_def_816,type,
sK515: ( $i > $o ) > $i ).
thf(func_def_817,type,
sK516: $i > $o ).
thf(func_def_826,type,
sK525: $i > $o ).
thf(func_def_827,type,
sK526: $i > $i ).
thf(func_def_828,type,
sK527: ( $i > $o ) > $i ).
thf(func_def_830,type,
sK529: $o ).
thf(func_def_837,type,
sK536: $i > $i ).
thf(func_def_840,type,
sK539: $i > $i > ( $i > $i ) > $i ).
thf(func_def_842,type,
sK541: $i > $o ).
thf(func_def_854,type,
sK553: $i > $o ).
thf(func_def_857,type,
sK556: $i > $i > $o ).
thf(func_def_872,type,
sK571: ( $i > $i ) > $i > $i > $i ).
thf(func_def_875,type,
sK574: $i > $i ).
thf(func_def_877,type,
sK576: $i > $i > $i ).
thf(func_def_878,type,
sK577: $i > $i > $i ).
thf(func_def_883,type,
sK582: $i > $o ).
thf(func_def_885,type,
sK584: $i > $o ).
thf(func_def_888,type,
sK587: $i > ( $i > $o ) > $i ).
thf(func_def_893,type,
sK592: $i > $i ).
thf(func_def_903,type,
sK602: $o ).
thf(func_def_913,type,
sK612: $i > $o ).
thf(func_def_915,type,
sK614: ( $i > $o ) > $i ).
thf(func_def_916,type,
sK615: ( $i > $o ) > $i ).
thf(func_def_919,type,
sK618: $i > $o ).
thf(func_def_923,type,
sK622: $o ).
thf(func_def_927,type,
sK626: $i > $i > $o ).
thf(func_def_937,type,
sK636: $i > $i > $i > $i ).
thf(func_def_941,type,
sK640: $i > $i > $o ).
thf(func_def_949,type,
sK648: $o ).
thf(func_def_953,type,
sK652: $i > $o ).
thf(func_def_960,type,
sK659: $i > $i > $i > $i ).
thf(func_def_971,type,
sK670: $i > $i > $i ).
thf(func_def_990,type,
sK689: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_991,type,
sK690: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_995,type,
sK694: $i > $o ).
thf(func_def_1000,type,
sK699: $i > $i ).
thf(func_def_1001,type,
sK700: ( $i > $i ) > $i > $i > $i ).
thf(func_def_1002,type,
sK701: $i > $o ).
thf(func_def_1011,type,
sK710: $i > $o ).
thf(func_def_1015,type,
sK714: $i > $i > $i ).
thf(func_def_1021,type,
sK720: $i > $o ).
thf(func_def_1034,type,
sK733: $i > $i > $i > $i > $i ).
thf(func_def_1044,type,
sK743: $i > $o ).
thf(func_def_1050,type,
sK749: $o > $i > $i > $i ).
thf(func_def_1053,type,
sK752: $o ).
thf(func_def_1054,type,
sK753: $i > $i ).
thf(func_def_1067,type,
sK766: $i > $i > $o ).
thf(func_def_1069,type,
sK768: $i > $i ).
thf(func_def_1070,type,
sK769: $i > $i ).
thf(func_def_1071,type,
sK770: $i > ( $i > $i > $o ) > $i ).
thf(func_def_1072,type,
sK771: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_1073,type,
sK772: $i > ( $i > $i > $o ) > $i ).
thf(f125,axiom,
! [X2: $i,X0: $i,X1: $i] :
( ( ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ( ~ ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ X0 ) ) )
= setminusELneg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusELneg) ).
thf(f253,axiom,
( complementTnotintersectT
= ( ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementTnotintersectT) ).
thf(f254,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
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
=> ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementImpComplementIntersect) ).
thf(f255,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
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
=> ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f254]) ).
thf(f375,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
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
=> ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f255]) ).
thf(f376,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 )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
= $true )
=> ( ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f375]) ).
thf(f403,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ~ ( in @ X0 @ ( setminus @ X1 @ X2 ) )
=> ( ~ ( in @ X0 @ X2 )
=> ~ ( in @ X0 @ X1 ) ) )
= setminusELneg ),
inference(rectify,[],[f125]) ).
thf(f404,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ ( setminus @ X1 @ X2 ) ) )
=> ( ( $true
!= ( in @ X0 @ X2 ) )
=> ( $true
!= ( in @ X0 @ X1 ) ) ) )
<=> ( setminusELneg = $true ) ),
inference(fool_elimination,[],[f403]) ).
thf(f670,plain,
( complementTnotintersectT
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ ( setminus @ X1 @ X0 ) )
=> ~ ( in @ X3 @ ( binintersect @ X0 @ X2 ) ) ) ) ) ) ) ),
inference(rectify,[],[f253]) ).
thf(f671,plain,
( ( complementTnotintersectT = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( $true
= ( in @ X3 @ ( setminus @ X1 @ X0 ) ) )
=> ( $true
!= ( in @ X3 @ ( binintersect @ X0 @ X2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f670]) ).
thf(f762,plain,
( ! [X1: $i,X2: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ ( setminus @ X1 @ X2 ) ) )
=> ( ( $true
!= ( in @ X0 @ X2 ) )
=> ( $true
!= ( in @ X0 @ X1 ) ) ) )
<=> ( setminusELneg = $true ) ),
inference(flattening,[],[f404]) ).
thf(f788,plain,
( ( complementTnotintersectT = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( $true
= ( in @ X3 @ ( setminus @ X1 @ X0 ) ) )
=> ( $true
!= ( in @ X3 @ ( binintersect @ X0 @ X2 ) ) ) ) ) ) ) ),
inference(flattening,[],[f671]) ).
thf(f848,plain,
( ( complementTnotintersectT = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ ( binintersect @ X0 @ X2 ) ) )
| ( $true
!= ( in @ X3 @ ( setminus @ X1 @ X0 ) ) )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) ) ),
inference(ennf_transformation,[],[f788]) ).
thf(f849,plain,
( ( complementTnotintersectT = $true )
<=> ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ ( setminus @ X1 @ X0 ) ) )
| ( $true
!= ( in @ X3 @ ( binintersect @ X0 @ X2 ) ) )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) ) ),
inference(flattening,[],[f848]) ).
thf(f906,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
!= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $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,[],[f376]) ).
thf(f907,plain,
( ( omega__Cong = $true )
& ( ksndpairEq = $true )
& ( symdiffIneg2 = $true )
& ( nonemptyImpWitness = $true )
& ( binunionE = $true )
& ( eqinunit = $true )
& ( dpsetconstrERa = $true )
& ( eqimpsubset2 = $true )
& ( setextsub = $true )
& ( singletonsubset = $true )
& ( setunionE2 = $true )
& ( setminusER = $true )
& ( subsetRefl = $true )
& ( contrasubsetT2 = $true )
& ( binunionLsub = $true )
& ( setunionsingleton = $true )
& ( setadjoinAx = $true )
& ( cartprodpairmemEL = $true )
& ( sepSubset = $true )
& ( omega0Ax = $true )
& ( descrp = $true )
& ( funcGraphProp2 = $true )
& ( symdiffI1 = $true )
& ( subsetI2 = $true )
& ( emptysetE = $true )
& ( descr__Cong = $true )
& ( doubleComplementI1 = $true )
& ( binintersectSubset5 = $true )
& ( funcext2 = $true )
& ( exuI1 = $true )
& ( ksndsingleton = $true )
& ( complementTE1 = $true )
& ( setadjoinE = $true )
& ( ubforcartprodlem2 = $true )
& ( dsetconstrEL = $true )
& ( ifSingleton = $true )
& ( upairsubunion = $true )
& ( kfstsingleton = $true )
& ( symdiffE = $true )
& ( setadjoinOr = $true )
& ( ap2p = $true )
& ( cartprodfstpairEq = $true )
& ( brelnall2 = $true )
& ( setukpairinjR12 = $true )
& ( notequalI2 = $true )
& ( binintersectLsub = $true )
& ( cartprodmempaircEq = $true )
& ( binunionRsub = $true )
& ( powersetAx = $true )
& ( vacuousDall = $true )
& ( setadjoinIR = $true )
& ( secondinupair = $true )
& ( symdiffIneg1 = $true )
& ( powersetT_lem = $true )
& ( binunionIL = $true )
& ( binintersectT_lem = $true )
& ( binintersectSubset4 = $true )
& ( setukpairinjL2 = $true )
& ( setukpairinjL1 = $true )
& ( binintersectSubset3 = $true )
& ( notsubsetI = $true )
& ( notinemptyset = $true )
& ( doubleComplementSub2 = $true )
& ( complementTnotintersectT = $true )
& ( cartprodmempair1 = $true )
& ( complementTI1 = $true )
& ( lam2lamEq = $true )
& ( subset2powerset = $true )
& ( setadjoinSub = $true )
& ( cartprodpairin = $true )
& ( cartprodfstin = $true )
& ( doubleComplementSub1 = $true )
& ( powersetsubset = $true )
& ( lamp = $true )
& ( setunionE = $true )
& ( kfstpairEq = $true )
& ( setbeta = $true )
& ( nonemptyI1 = $true )
& ( ex1E2 = $true )
& ( beta1 = $true )
& ( eta1 = $true )
& ( setminusERneg = $true )
& ( iftrueorfalse = $true )
& ( ap2apEq2 = $true )
& ( dpsetconstrEL1 = $true )
& ( powersetI = $true )
& ( subsetE2 = $true )
& ( setminusEL = $true )
& ( cartprodmempair = $true )
& ( setadjoinIL = $true )
& ( doubleComplementE1 = $true )
& ( eta2 = $true )
& ( iftrueProp1 = $true )
& ( binintersectI = $true )
& ( prop2setI = $true )
& ( setminusT_lem = $true )
& ( binunionEcases = $true )
& ( funcextLem = $true )
& ( binintersectER = $true )
& ( setunion__Cong = $true )
& ( kpairp = $true )
& ( binunionT_lem = $true )
& ( iffalseProp1 = $true )
& ( upairequniteq = $true )
& ( dpsetconstrER = $true )
& ( quantDeMorgan4 = $true )
& ( emptysetimpfalse = $true )
& ( cartprodsndpairEq = $true )
& ( setukpairinjR11 = $true )
& ( nonemptyE1 = $true )
& ( binintersectSubset1 = $true )
& ( funcext = $true )
& ( exuE2 = $true )
& ( setOfPairsIsBReln = $true )
& ( setukpairIR = $true )
& ( setoftrueEq = $true )
& ( eqbreln = $true )
& ( funcGraphProp3 = $true )
& ( omegaSAx = $true )
& ( singletonsuniq = $true )
& ( notequalI1 = $true )
& ( infuncsetfunc = $true )
& ( upairsetIL = $true )
& ( foundationAx = $true )
& ( singletoninpowerset = $true )
& ( powersetTE1 = $true )
& ( binintersectSubset2 = $true )
& ( upairsetE = $true )
& ( setextT = $true )
& ( binunionIR = $true )
& ( setukpairinjR2 = $true )
& ( setminusIRneg = $true )
& ( singletoninpowunion = $true )
& ( symdiffI2 = $true )
& ( subbreln = $true )
& ( ubforcartprodlem1 = $true )
& ( inPowerset = $true )
& ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ X1 ) )
= $true )
& ( ( in @ X3 @ ( setminus @ X0 @ ( binintersect @ X1 @ X2 ) ) )
!= $true ) ) ) )
& ( ap2apEq1 = $true )
& ( quantDeMorgan2 = $true )
& ( cartprodsndin = $true )
& ( ex1I = $true )
& ( theprop = $true )
& ( beta2 = $true )
& ( cartprodpairsurjEq = $true )
& ( emptyI = $true )
& ( setminusI = $true )
& ( iffalse = $true )
& ( powersetE = $true )
& ( kpairiskpair = $true )
& ( ex1E1 = $true )
& ( disjointsetsI1 = $true )
& ( cartprodpairmemER = $true )
& ( powersetI1 = $true )
& ( emptysetAx = $true )
& ( setminusELneg = $true )
& ( powersetTI1 = $true )
& ( upairsetIR = $true )
& ( kpairsurjEq = $true )
& ( binintersectRsub = $true )
& ( notinsingleton = $true )
& ( emptyinunitempty = $true )
& ( prop2set2propI = $true )
& ( exuE1 = $true )
& ( ifp = $true )
& ( powersetE1 = $true )
& ( subsetI1 = $true )
& ( in__Cong = $true )
& ( notdexE = $true )
& ( iffalseProp2 = $true )
& ( emptysetsubset = $true )
& ( bs114d = $true )
& ( setminusLsub = $true )
& ( subsetTrans = $true )
& ( exuE3e = $true )
& ( theeq = $true )
& ( upairset2E = $true )
& ( exuE3u = $true )
& ( sepInPowerset = $true )
& ( subsetTI = $true )
& ( doubleComplementEq = $true )
& ( funcinfuncset = $true )
& ( dpsetconstrSub = $true )
& ( iftrueProp2 = $true )
& ( lamProp = $true )
& ( subsetemptysetimpeq = $true )
& ( singletonprop = $true )
& ( wellorderingAx = $true )
& ( subPowSU = $true )
& ( eqimpsubset1 = $true )
& ( singletonsswitch = $true )
& ( exuEu = $true )
& ( contrasubsetT3 = $true )
& ( binintersectTELcontra = $true )
& ( brelnall1 = $true )
& ( dsetconstr__Cong = $true )
& ( omegaIndAx = $true )
& ( setminusSubset2 = $true )
& ( setminusILneg = $true )
& ( iftrue = $true )
& ( emptyinPowerset = $true )
& ( inCongP = $true )
& ( contrasubsetT = $true )
& ( contrasubsetT1 = $true )
& ( funcImageSingleton = $true )
& ( replAx = $true )
& ( setunionAx = $true )
& ( prop2setE = $true )
& ( binintersectEL = $true )
& ( lam2p = $true )
& ( exu__Cong = $true )
& ( setextAx = $true )
& ( nonemptyI = $true )
& ( dsetconstrI = $true )
& ( app = $true )
& ( emptyE1 = $true )
& ( setminusSubset1 = $true )
& ( upairset2IR = $true )
& ( setukpairinjR1 = $true )
& ( exuI3 = $true )
& ( setukpairIL = $true )
& ( ex1I2 = $true )
& ( dsetconstrER = $true )
& ( apProp = $true )
& ( setunionsingleton2 = $true )
& ( emptyInPowerset = $true )
& ( setext = $true )
& ( quantDeMorgan1 = $true )
& ( uniqinunit = $true )
& ( dpsetconstrEL2 = $true )
& ( binintersectTERcontra = $true )
& ( subsetE = $true )
& ( funcGraphProp1 = $true )
& ( setadjoin__Cong = $true )
& ( upairinpowunion = $true )
& ( noeltsimpempty = $true )
& ( quantDeMorgan3 = $true )
& ( complementT_lem = $true )
& ( notdallE = $true )
& ( funcGraphProp4 = $true )
& ( exuI2 = $true )
& ( setunionsingleton1 = $true )
& ( dpsetconstrI = $true )
& ( setunionI = $true )
& ( ubforcartprodlem3 = $true )
& ( setadjoinSub2 = $true )
& ( emptyset__Cong = $true )
& ( setukpairinjL = $true )
& ( setukpairinjR = $true )
& ( powerset__Cong = $true ) ),
inference(flattening,[],[f906]) ).
thf(f1058,plain,
( ! [X1: $i,X2: $i,X0: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
= ( in @ X0 @ X2 ) )
| ( $true
= ( in @ X0 @ ( setminus @ X1 @ X2 ) ) ) )
<=> ( setminusELneg = $true ) ),
inference(ennf_transformation,[],[f762]) ).
thf(f1059,plain,
( ( setminusELneg = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( setminus @ X1 @ X2 ) ) )
| ( $true
= ( in @ X0 @ X2 ) )
| ( $true
!= ( in @ X0 @ X1 ) ) ) ),
inference(flattening,[],[f1058]) ).
thf(f1598,plain,
( ( omega__Cong = $true )
& ( ksndpairEq = $true )
& ( symdiffIneg2 = $true )
& ( nonemptyImpWitness = $true )
& ( binunionE = $true )
& ( eqinunit = $true )
& ( dpsetconstrERa = $true )
& ( eqimpsubset2 = $true )
& ( setextsub = $true )
& ( singletonsubset = $true )
& ( setunionE2 = $true )
& ( setminusER = $true )
& ( subsetRefl = $true )
& ( contrasubsetT2 = $true )
& ( binunionLsub = $true )
& ( setunionsingleton = $true )
& ( setadjoinAx = $true )
& ( cartprodpairmemEL = $true )
& ( sepSubset = $true )
& ( omega0Ax = $true )
& ( descrp = $true )
& ( funcGraphProp2 = $true )
& ( symdiffI1 = $true )
& ( subsetI2 = $true )
& ( emptysetE = $true )
& ( descr__Cong = $true )
& ( doubleComplementI1 = $true )
& ( binintersectSubset5 = $true )
& ( funcext2 = $true )
& ( exuI1 = $true )
& ( ksndsingleton = $true )
& ( complementTE1 = $true )
& ( setadjoinE = $true )
& ( ubforcartprodlem2 = $true )
& ( dsetconstrEL = $true )
& ( ifSingleton = $true )
& ( upairsubunion = $true )
& ( kfstsingleton = $true )
& ( symdiffE = $true )
& ( setadjoinOr = $true )
& ( ap2p = $true )
& ( cartprodfstpairEq = $true )
& ( brelnall2 = $true )
& ( setukpairinjR12 = $true )
& ( notequalI2 = $true )
& ( binintersectLsub = $true )
& ( cartprodmempaircEq = $true )
& ( binunionRsub = $true )
& ( powersetAx = $true )
& ( vacuousDall = $true )
& ( setadjoinIR = $true )
& ( secondinupair = $true )
& ( symdiffIneg1 = $true )
& ( powersetT_lem = $true )
& ( binunionIL = $true )
& ( binintersectT_lem = $true )
& ( binintersectSubset4 = $true )
& ( setukpairinjL2 = $true )
& ( setukpairinjL1 = $true )
& ( binintersectSubset3 = $true )
& ( notsubsetI = $true )
& ( notinemptyset = $true )
& ( doubleComplementSub2 = $true )
& ( complementTnotintersectT = $true )
& ( cartprodmempair1 = $true )
& ( complementTI1 = $true )
& ( lam2lamEq = $true )
& ( subset2powerset = $true )
& ( setadjoinSub = $true )
& ( cartprodpairin = $true )
& ( cartprodfstin = $true )
& ( doubleComplementSub1 = $true )
& ( powersetsubset = $true )
& ( lamp = $true )
& ( setunionE = $true )
& ( kfstpairEq = $true )
& ( setbeta = $true )
& ( nonemptyI1 = $true )
& ( ex1E2 = $true )
& ( beta1 = $true )
& ( eta1 = $true )
& ( setminusERneg = $true )
& ( iftrueorfalse = $true )
& ( ap2apEq2 = $true )
& ( dpsetconstrEL1 = $true )
& ( powersetI = $true )
& ( subsetE2 = $true )
& ( setminusEL = $true )
& ( cartprodmempair = $true )
& ( setadjoinIL = $true )
& ( doubleComplementE1 = $true )
& ( eta2 = $true )
& ( iftrueProp1 = $true )
& ( binintersectI = $true )
& ( prop2setI = $true )
& ( setminusT_lem = $true )
& ( binunionEcases = $true )
& ( funcextLem = $true )
& ( binintersectER = $true )
& ( setunion__Cong = $true )
& ( kpairp = $true )
& ( binunionT_lem = $true )
& ( iffalseProp1 = $true )
& ( upairequniteq = $true )
& ( dpsetconstrER = $true )
& ( quantDeMorgan4 = $true )
& ( emptysetimpfalse = $true )
& ( cartprodsndpairEq = $true )
& ( setukpairinjR11 = $true )
& ( nonemptyE1 = $true )
& ( binintersectSubset1 = $true )
& ( funcext = $true )
& ( exuE2 = $true )
& ( setOfPairsIsBReln = $true )
& ( setukpairIR = $true )
& ( setoftrueEq = $true )
& ( eqbreln = $true )
& ( funcGraphProp3 = $true )
& ( omegaSAx = $true )
& ( singletonsuniq = $true )
& ( notequalI1 = $true )
& ( infuncsetfunc = $true )
& ( upairsetIL = $true )
& ( foundationAx = $true )
& ( singletoninpowerset = $true )
& ( powersetTE1 = $true )
& ( binintersectSubset2 = $true )
& ( upairsetE = $true )
& ( setextT = $true )
& ( binunionIR = $true )
& ( setukpairinjR2 = $true )
& ( setminusIRneg = $true )
& ( singletoninpowunion = $true )
& ( symdiffI2 = $true )
& ( subbreln = $true )
& ( ubforcartprodlem1 = $true )
& ( inPowerset = $true )
& ( $true
= ( in @ sK543 @ ( powerset @ sK542 ) ) )
& ( $true
= ( in @ sK544 @ ( powerset @ sK542 ) ) )
& ( $true
= ( in @ sK545 @ sK542 ) )
& ( $true
= ( in @ sK545 @ ( setminus @ sK542 @ sK543 ) ) )
& ( $true
!= ( in @ sK545 @ ( setminus @ sK542 @ ( binintersect @ sK543 @ sK544 ) ) ) )
& ( ap2apEq1 = $true )
& ( quantDeMorgan2 = $true )
& ( cartprodsndin = $true )
& ( ex1I = $true )
& ( theprop = $true )
& ( beta2 = $true )
& ( cartprodpairsurjEq = $true )
& ( emptyI = $true )
& ( setminusI = $true )
& ( iffalse = $true )
& ( powersetE = $true )
& ( kpairiskpair = $true )
& ( ex1E1 = $true )
& ( disjointsetsI1 = $true )
& ( cartprodpairmemER = $true )
& ( powersetI1 = $true )
& ( emptysetAx = $true )
& ( setminusELneg = $true )
& ( powersetTI1 = $true )
& ( upairsetIR = $true )
& ( kpairsurjEq = $true )
& ( binintersectRsub = $true )
& ( notinsingleton = $true )
& ( emptyinunitempty = $true )
& ( prop2set2propI = $true )
& ( exuE1 = $true )
& ( ifp = $true )
& ( powersetE1 = $true )
& ( subsetI1 = $true )
& ( in__Cong = $true )
& ( notdexE = $true )
& ( iffalseProp2 = $true )
& ( emptysetsubset = $true )
& ( bs114d = $true )
& ( setminusLsub = $true )
& ( subsetTrans = $true )
& ( exuE3e = $true )
& ( theeq = $true )
& ( upairset2E = $true )
& ( exuE3u = $true )
& ( sepInPowerset = $true )
& ( subsetTI = $true )
& ( doubleComplementEq = $true )
& ( funcinfuncset = $true )
& ( dpsetconstrSub = $true )
& ( iftrueProp2 = $true )
& ( lamProp = $true )
& ( subsetemptysetimpeq = $true )
& ( singletonprop = $true )
& ( wellorderingAx = $true )
& ( subPowSU = $true )
& ( eqimpsubset1 = $true )
& ( singletonsswitch = $true )
& ( exuEu = $true )
& ( contrasubsetT3 = $true )
& ( binintersectTELcontra = $true )
& ( brelnall1 = $true )
& ( dsetconstr__Cong = $true )
& ( omegaIndAx = $true )
& ( setminusSubset2 = $true )
& ( setminusILneg = $true )
& ( iftrue = $true )
& ( emptyinPowerset = $true )
& ( inCongP = $true )
& ( contrasubsetT = $true )
& ( contrasubsetT1 = $true )
& ( funcImageSingleton = $true )
& ( replAx = $true )
& ( setunionAx = $true )
& ( prop2setE = $true )
& ( binintersectEL = $true )
& ( lam2p = $true )
& ( exu__Cong = $true )
& ( setextAx = $true )
& ( nonemptyI = $true )
& ( dsetconstrI = $true )
& ( app = $true )
& ( emptyE1 = $true )
& ( setminusSubset1 = $true )
& ( upairset2IR = $true )
& ( setukpairinjR1 = $true )
& ( exuI3 = $true )
& ( setukpairIL = $true )
& ( ex1I2 = $true )
& ( dsetconstrER = $true )
& ( apProp = $true )
& ( setunionsingleton2 = $true )
& ( emptyInPowerset = $true )
& ( setext = $true )
& ( quantDeMorgan1 = $true )
& ( uniqinunit = $true )
& ( dpsetconstrEL2 = $true )
& ( binintersectTERcontra = $true )
& ( subsetE = $true )
& ( funcGraphProp1 = $true )
& ( setadjoin__Cong = $true )
& ( upairinpowunion = $true )
& ( noeltsimpempty = $true )
& ( quantDeMorgan3 = $true )
& ( complementT_lem = $true )
& ( notdallE = $true )
& ( funcGraphProp4 = $true )
& ( exuI2 = $true )
& ( setunionsingleton1 = $true )
& ( dpsetconstrI = $true )
& ( setunionI = $true )
& ( ubforcartprodlem3 = $true )
& ( setadjoinSub2 = $true )
& ( emptyset__Cong = $true )
& ( setukpairinjL = $true )
& ( setukpairinjR = $true )
& ( powerset__Cong = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK542,sK543,sK544,sK545]),skolemize(X0,sK542),skolemize(X1,sK543),skolemize(X2,sK544),skolemize(X3,sK545)],[f907]) ).
thf(f1810,plain,
( ( ( setminusELneg = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( setminus @ X1 @ X2 ) ) )
& ( $true
!= ( in @ X0 @ X2 ) )
& ( $true
= ( in @ X0 @ X1 ) ) ) )
& ( ! [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( setminus @ X1 @ X2 ) ) )
| ( $true
= ( in @ X0 @ X2 ) )
| ( $true
!= ( in @ X0 @ X1 ) ) )
| ( setminusELneg != $true ) ) ),
inference(nnf_transformation,[],[f1059]) ).
thf(f1811,plain,
( ( ( setminusELneg = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) )
& ( $true
!= ( in @ X0 @ X1 ) )
& ( $true
= ( in @ X0 @ X2 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X3 @ ( setminus @ X5 @ X4 ) ) )
| ( $true
= ( in @ X3 @ X4 ) )
| ( ( in @ X3 @ X5 )
!= $true ) )
| ( setminusELneg != $true ) ) ),
inference(rectify,[],[f1810]) ).
thf(f1812,plain,
( ( ( setminusELneg = $true )
| ( ( ( in @ sK755 @ ( setminus @ sK757 @ sK756 ) )
!= $true )
& ( $true
!= ( in @ sK755 @ sK756 ) )
& ( $true
= ( in @ sK755 @ sK757 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X3 @ ( setminus @ X5 @ X4 ) ) )
| ( $true
= ( in @ X3 @ X4 ) )
| ( ( in @ X3 @ X5 )
!= $true ) )
| ( setminusELneg != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK755,sK756,sK757]),skolemize(X0,sK755),skolemize(X1,sK756),skolemize(X2,sK757)],[f1811]) ).
thf(f1813,plain,
( ( ( complementTnotintersectT = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( setminus @ X1 @ X0 ) ) )
& ( $true
= ( in @ X3 @ ( binintersect @ X0 @ X2 ) ) )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ) )
& ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ ( setminus @ X1 @ X0 ) ) )
| ( $true
!= ( in @ X3 @ ( binintersect @ X0 @ X2 ) ) )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) )
| ( complementTnotintersectT != $true ) ) ),
inference(nnf_transformation,[],[f849]) ).
thf(f1814,plain,
( ( ( complementTnotintersectT = $true )
| ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ ( setminus @ X1 @ X0 ) ) )
& ( $true
= ( in @ X3 @ ( binintersect @ X0 @ X2 ) ) )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ) )
& ( ! [X4: $i,X5: $i] :
( ! [X6: $i] :
( ! [X7: $i] :
( ( $true
!= ( in @ X7 @ ( setminus @ X5 @ X4 ) ) )
| ( $true
!= ( in @ X7 @ ( binintersect @ X4 @ X6 ) ) )
| ( $true
!= ( in @ X7 @ X5 ) ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) ) )
| ( complementTnotintersectT != $true ) ) ),
inference(rectify,[],[f1813]) ).
thf(f1815,plain,
( ( ( complementTnotintersectT = $true )
| ( ( $true
= ( in @ sK761 @ ( setminus @ sK759 @ sK758 ) ) )
& ( $true
= ( in @ sK761 @ ( binintersect @ sK758 @ sK760 ) ) )
& ( $true
= ( in @ sK761 @ sK759 ) )
& ( $true
= ( in @ sK760 @ ( powerset @ sK759 ) ) )
& ( $true
= ( in @ sK758 @ ( powerset @ sK759 ) ) ) ) )
& ( ! [X4: $i,X5: $i] :
( ! [X6: $i] :
( ! [X7: $i] :
( ( $true
!= ( in @ X7 @ ( setminus @ X5 @ X4 ) ) )
| ( $true
!= ( in @ X7 @ ( binintersect @ X4 @ X6 ) ) )
| ( $true
!= ( in @ X7 @ X5 ) ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) ) )
| ( complementTnotintersectT != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK758,sK759,sK760,sK761]),skolemize(X0,sK758),skolemize(X1,sK759),skolemize(X2,sK760),skolemize(X3,sK761)],[f1814]) ).
thf(f2667,plain,
setminusELneg = $true,
inference(cnf_transformation,[],[f1598]) ).
thf(f2685,plain,
( $true
!= ( in @ sK545 @ ( setminus @ sK542 @ ( binintersect @ sK543 @ sK544 ) ) ) ),
inference(cnf_transformation,[],[f1598]) ).
thf(f2686,plain,
( $true
= ( in @ sK545 @ ( setminus @ sK542 @ sK543 ) ) ),
inference(cnf_transformation,[],[f1598]) ).
thf(f2687,plain,
( $true
= ( in @ sK545 @ sK542 ) ),
inference(cnf_transformation,[],[f1598]) ).
thf(f2688,plain,
( $true
= ( in @ sK544 @ ( powerset @ sK542 ) ) ),
inference(cnf_transformation,[],[f1598]) ).
thf(f2689,plain,
( $true
= ( in @ sK543 @ ( powerset @ sK542 ) ) ),
inference(cnf_transformation,[],[f1598]) ).
thf(f2763,plain,
complementTnotintersectT = $true,
inference(cnf_transformation,[],[f1598]) ).
thf(f3100,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X3 @ X4 ) )
| ( $true
= ( in @ X3 @ ( setminus @ X5 @ X4 ) ) )
| ( setminusELneg != $true )
| ( ( in @ X3 @ X5 )
!= $true ) ),
inference(cnf_transformation,[],[f1812]) ).
thf(f3104,plain,
! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X7 @ X5 ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) )
| ( complementTnotintersectT != $true )
| ( $true
!= ( in @ X7 @ ( binintersect @ X4 @ X6 ) ) )
| ( $true
!= ( in @ X7 @ ( setminus @ X5 @ X4 ) ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) ) ),
inference(cnf_transformation,[],[f1815]) ).
thf(f3748,definition,
( spl781_90
<=> ( $true
= ( in @ sK545 @ ( setminus @ sK542 @ sK543 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl781_90])],[avatar_definition]) ).
thf(f3750,plain,
( ( $true
= ( in @ sK545 @ ( setminus @ sK542 @ sK543 ) ) )
| ~ spl781_90 ),
inference(avatar_component_clause,[],[f3748]) ).
thf(f3751,plain,
spl781_90,
inference(avatar_split_clause,[],[f2686,f3748]) ).
thf(f4070,definition,
( spl781_162
<=> ( complementTnotintersectT = $true ) ),
introduced(definition,[new_symbols(definition,[spl781_162])],[avatar_definition]) ).
thf(f5030,definition,
( spl781_376
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) )
| ( $true
= ( in @ X0 @ X1 ) )
| ( $true
!= ( in @ X0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl781_376])],[avatar_definition]) ).
thf(f5031,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( setminus @ X2 @ X1 ) ) )
| ( $true
= ( in @ X0 @ X1 ) )
| ( $true
!= ( in @ X0 @ X2 ) ) )
| ~ spl781_376 ),
inference(avatar_component_clause,[],[f5030]) ).
thf(f5204,definition,
( spl781_414
<=> ( setminusELneg = $true ) ),
introduced(definition,[new_symbols(definition,[spl781_414])],[avatar_definition]) ).
thf(f5207,plain,
spl781_414,
inference(avatar_split_clause,[],[f2667,f5204]) ).
thf(f5316,plain,
( spl781_376
| ~ spl781_414 ),
inference(avatar_split_clause,[],[f3100,f5204,f5030]) ).
thf(f6671,definition,
( spl781_727
<=> ( $true
= ( in @ sK544 @ ( powerset @ sK542 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl781_727])],[avatar_definition]) ).
thf(f6673,plain,
( ( $true
= ( in @ sK544 @ ( powerset @ sK542 ) ) )
| ~ spl781_727 ),
inference(avatar_component_clause,[],[f6671]) ).
thf(f6674,plain,
spl781_727,
inference(avatar_split_clause,[],[f2688,f6671]) ).
thf(f6940,definition,
( spl781_784
<=> ( $true
= ( in @ sK545 @ sK542 ) ) ),
introduced(definition,[new_symbols(definition,[spl781_784])],[avatar_definition]) ).
thf(f6942,plain,
( ( $true
= ( in @ sK545 @ sK542 ) )
| ~ spl781_784 ),
inference(avatar_component_clause,[],[f6940]) ).
thf(f6943,plain,
spl781_784,
inference(avatar_split_clause,[],[f2687,f6940]) ).
thf(f7131,definition,
( spl781_823
<=> ! [X5: $i,X4: $i,X7: $i,X6: $i] :
( ( $true
!= ( in @ X7 @ X5 ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) )
| ( $true
!= ( in @ X7 @ ( setminus @ X5 @ X4 ) ) )
| ( $true
!= ( in @ X7 @ ( binintersect @ X4 @ X6 ) ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl781_823])],[avatar_definition]) ).
thf(f7132,plain,
( ! [X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X7 @ ( setminus @ X5 @ X4 ) ) )
| ( $true
!= ( in @ X7 @ X5 ) )
| ( $true
!= ( in @ X4 @ ( powerset @ X5 ) ) )
| ( $true
!= ( in @ X7 @ ( binintersect @ X4 @ X6 ) ) )
| ( $true
!= ( in @ X6 @ ( powerset @ X5 ) ) ) )
| ~ spl781_823 ),
inference(avatar_component_clause,[],[f7131]) ).
thf(f7133,plain,
( spl781_823
| ~ spl781_162 ),
inference(avatar_split_clause,[],[f3104,f4070,f7131]) ).
thf(f7383,definition,
( spl781_876
<=> ( $true
= ( in @ sK545 @ ( setminus @ sK542 @ ( binintersect @ sK543 @ sK544 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl781_876])],[avatar_definition]) ).
thf(f7385,plain,
( ( $true
!= ( in @ sK545 @ ( setminus @ sK542 @ ( binintersect @ sK543 @ sK544 ) ) ) )
| spl781_876 ),
inference(avatar_component_clause,[],[f7383]) ).
thf(f7386,plain,
~ spl781_876,
inference(avatar_split_clause,[],[f2685,f7383]) ).
thf(f8567,plain,
spl781_162,
inference(avatar_split_clause,[],[f2763,f4070]) ).
thf(f8593,definition,
( spl781_1120
<=> ( $true
= ( in @ sK543 @ ( powerset @ sK542 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl781_1120])],[avatar_definition]) ).
thf(f8595,plain,
( ( $true
= ( in @ sK543 @ ( powerset @ sK542 ) ) )
| ~ spl781_1120 ),
inference(avatar_component_clause,[],[f8593]) ).
thf(f8596,plain,
spl781_1120,
inference(avatar_split_clause,[],[f2689,f8593]) ).
thf(f9255,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ sK542 ) ) )
| ( $true
!= ( in @ sK545 @ sK542 ) )
| ( $true != $true )
| ( $true
!= ( in @ sK543 @ ( powerset @ sK542 ) ) )
| ( $true
!= ( in @ sK545 @ ( binintersect @ sK543 @ X0 ) ) ) )
| ~ spl781_90
| ~ spl781_823 ),
inference(superposition,[],[f7132,f3750]) ).
thf(f9257,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ sK545 @ sK542 ) )
| ( $true
!= ( in @ sK545 @ ( binintersect @ sK543 @ X0 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ sK542 ) ) )
| ( $true
!= ( in @ sK543 @ ( powerset @ sK542 ) ) ) )
| ~ spl781_90
| ~ spl781_823 ),
inference(trivial_inequality_removal,[],[f9255]) ).
thf(f9259,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ sK545 @ ( binintersect @ sK543 @ X0 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ sK542 ) ) )
| ( $true
!= ( in @ sK543 @ ( powerset @ sK542 ) ) ) )
| ~ spl781_90
| ~ spl781_784
| ~ spl781_823 ),
inference(forward_subsumption_resolution,[],[f9257,f6942]) ).
thf(f9265,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ sK545 @ ( binintersect @ sK543 @ X0 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ sK542 ) ) ) )
| ~ spl781_90
| ~ spl781_784
| ~ spl781_823
| ~ spl781_1120 ),
inference(forward_subsumption_resolution,[],[f9259,f8595]) ).
thf(f11459,plain,
( ( $true
!= ( in @ sK545 @ sK542 ) )
| ( $true
= ( in @ sK545 @ ( binintersect @ sK543 @ sK544 ) ) )
| ( $true != $true )
| ~ spl781_376
| spl781_876 ),
inference(superposition,[],[f7385,f5031]) ).
thf(f11463,plain,
( ( $true
!= ( in @ sK545 @ sK542 ) )
| ( $true
= ( in @ sK545 @ ( binintersect @ sK543 @ sK544 ) ) )
| ~ spl781_376
| spl781_876 ),
inference(trivial_inequality_removal,[],[f11459]) ).
thf(f11483,plain,
( ( $true
= ( in @ sK545 @ ( binintersect @ sK543 @ sK544 ) ) )
| ~ spl781_376
| ~ spl781_784
| spl781_876 ),
inference(forward_subsumption_resolution,[],[f11463,f6942]) ).
thf(f11486,definition,
( spl781_1298
<=> ( $true
= ( in @ sK545 @ ( binintersect @ sK543 @ sK544 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl781_1298])],[avatar_definition]) ).
thf(f11488,plain,
( ( $true
= ( in @ sK545 @ ( binintersect @ sK543 @ sK544 ) ) )
| ~ spl781_1298 ),
inference(avatar_component_clause,[],[f11486]) ).
thf(f11489,plain,
( spl781_1298
| ~ spl781_376
| ~ spl781_784
| spl781_876 ),
inference(avatar_split_clause,[],[f11483,f7383,f6940,f5030,f11486]) ).
thf(f12149,plain,
( ( $true != $true )
| ( $true
!= ( in @ sK544 @ ( powerset @ sK542 ) ) )
| ~ spl781_90
| ~ spl781_784
| ~ spl781_823
| ~ spl781_1120
| ~ spl781_1298 ),
inference(superposition,[],[f9265,f11488]) ).
thf(f12160,plain,
( ( $true
!= ( in @ sK544 @ ( powerset @ sK542 ) ) )
| ~ spl781_90
| ~ spl781_784
| ~ spl781_823
| ~ spl781_1120
| ~ spl781_1298 ),
inference(trivial_inequality_removal,[],[f12149]) ).
thf(f12183,plain,
( $false
| ~ spl781_90
| ~ spl781_727
| ~ spl781_784
| ~ spl781_823
| ~ spl781_1120
| ~ spl781_1298 ),
inference(forward_subsumption_resolution,[],[f12160,f6673]) ).
thf(f12184,plain,
( ~ spl781_90
| ~ spl781_727
| ~ spl781_784
| ~ spl781_823
| ~ spl781_1120
| ~ spl781_1298 ),
inference(avatar_contradiction_clause,[],[f12183]) ).
cnf(s50,plain,
spl781_90,
inference(sat_conversion,[],[f3751]) ).
cnf(s298,plain,
spl781_414,
inference(sat_conversion,[],[f5207]) ).
cnf(s320,plain,
( spl781_376
| ~ spl781_414 ),
inference(sat_conversion,[],[f5316]) ).
cnf(s616,plain,
spl781_727,
inference(sat_conversion,[],[f6674]) ).
cnf(s675,plain,
spl781_784,
inference(sat_conversion,[],[f6943]) ).
cnf(s719,plain,
( ~ spl781_162
| spl781_823 ),
inference(sat_conversion,[],[f7133]) ).
cnf(s781,plain,
~ spl781_876,
inference(sat_conversion,[],[f7386]) ).
cnf(s1098,plain,
spl781_162,
inference(sat_conversion,[],[f8567]) ).
cnf(s1105,plain,
spl781_1120,
inference(sat_conversion,[],[f8596]) ).
cnf(s1327,plain,
( ~ spl781_376
| ~ spl781_784
| spl781_876
| spl781_1298 ),
inference(sat_conversion,[],[f11489]) ).
cnf(s1357,plain,
( ~ spl781_90
| ~ spl781_727
| ~ spl781_784
| ~ spl781_823
| ~ spl781_1120
| ~ spl781_1298 ),
inference(sat_conversion,[],[f12184]) ).
cnf(s1437,plain,
spl781_823,
inference(rat,[],[s719,s1098]) ).
cnf(s1576,plain,
spl781_376,
inference(rat,[],[s320,s298]) ).
cnf(s1577,plain,
spl781_1298,
inference(rat,[],[s1327,s675,s781,s1576]) ).
cnf(s1581,plain,
~ spl781_90,
inference(rat,[],[s1357,s616,s1105,s1437,s675,s1577]) ).
cnf(s1690,plain,
$false,
inference(rat,[],[s50,s1581]) ).
thf(f12185,plain,
$false,
inference(avatar_sat_refutation,[],[s1690]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU733^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n001.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 14:23:51 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.61/0.40 % (1315682)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.61/0.40 % (1315689)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2269228469:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.61/0.40 % (1315689)Instruction limit reached!
% 0.61/0.40 % (1315689)------------------------------
% 0.61/0.40 % (1315689)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.40 % (1315689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.40 % (1315689)CaDiCaL version: 2.1.3
% 0.61/0.40 % (1315689)Termination reason: Instruction limit
% 0.61/0.40 % (1315689)Termination phase: shuffling
% 0.61/0.40 % (1315689)Time elapsed: 0.001 s
% 0.61/0.40 % (1315689)Peak memory usage: 10 MB
% 0.61/0.40 % (1315689)Instructions burned: 3 (million)
% 0.61/0.40 % (1315688)lrs+10_16_si=on:nwc=1.5:random_seed=3617548611:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.61/0.40 % (1315690)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=1360335890: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)
% 0.61/0.40 % (1315691)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=578654129:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.61/0.40 % (1315687)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=48984708:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.61/0.40 % (1315692)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=321006843:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.61/0.40 % (1315688)Instruction limit reached!
% 0.61/0.40 % (1315688)------------------------------
% 0.61/0.40 % (1315688)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.40 % (1315688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.40 % (1315688)CaDiCaL version: 2.1.3
% 0.61/0.40 % (1315688)Termination reason: Instruction limit
% 0.61/0.40 % (1315688)Termination phase: shuffling
% 0.61/0.40 % (1315688)Time elapsed: 0.009 s
% 0.61/0.40 % (1315688)Peak memory usage: 10 MB
% 0.61/0.40 % (1315688)Instructions burned: 19 (million)
% 0.61/0.40 % (1315693)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.61/0.40 % (1315693)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
% 0.61/0.40 % (1315691)Instruction limit reached!
% 0.61/0.40 % (1315691)------------------------------
% 0.61/0.40 % (1315691)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.40 % (1315691)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.40 % (1315691)CaDiCaL version: 2.1.3
% 0.61/0.40 % (1315691)Termination reason: Instruction limit
% 0.61/0.40 % (1315691)Termination phase: Property scanning
% 0.61/0.40 % (1315691)Time elapsed: 0.012 s
% 0.61/0.40 % (1315691)Peak memory usage: 10 MB
% 0.61/0.40 % (1315691)Instructions burned: 25 (million)
% 0.61/0.40 % (1315692)Instruction limit reached!
% 0.61/0.40 % (1315692)------------------------------
% 0.61/0.40 % (1315692)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.40 % (1315692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.40 % (1315692)CaDiCaL version: 2.1.3
% 0.61/0.40 % (1315692)Termination reason: Instruction limit
% 0.61/0.40 % (1315692)Termination phase: Preprocessing 3
% 0.61/0.40 % (1315692)Time elapsed: 0.019 s
% 0.61/0.40 % (1315692)Peak memory usage: 12 MB
% 0.61/0.40 % (1315692)Instructions burned: 77 (million)
% 0.61/0.40 % (1315693)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=1421423814:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.61/0.40 % (1315702)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.61/0.40 % (1315701)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3708345948:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.61/0.43 % (1315703)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2015765415:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.61/0.43 % (1315702)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2129245585:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.61/0.43 % (1315701)Instruction limit reached!
% 0.61/0.43 % (1315701)------------------------------
% 0.61/0.43 % (1315701)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.43 % (1315701)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.43 % (1315701)CaDiCaL version: 2.1.3
% 0.61/0.43 % (1315701)Termination reason: Instruction limit
% 0.61/0.43 % (1315701)Termination phase: shuffling
% 0.61/0.43 % (1315701)Time elapsed: 0.003 s
% 0.61/0.43 % (1315701)Peak memory usage: 10 MB
% 0.61/0.43 % (1315701)Instructions burned: 6 (million)
% 0.61/0.43 % (1315695)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4080022766:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.61/0.43 % (1315703)Instruction limit reached!
% 0.61/0.43 % (1315703)------------------------------
% 0.61/0.43 % (1315703)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.43 % (1315703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.43 % (1315703)CaDiCaL version: 2.1.3
% 0.61/0.43 % (1315703)Termination reason: Instruction limit
% 0.61/0.43 % (1315703)Termination phase: shuffling
% 0.61/0.43 % (1315703)Time elapsed: 0.004 s
% 0.61/0.43 % (1315703)Peak memory usage: 10 MB
% 0.61/0.43 % (1315703)Instructions burned: 17 (million)
% 0.61/0.43 % (1315702)Instruction limit reached!
% 0.61/0.43 % (1315702)------------------------------
% 0.61/0.43 % (1315702)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.43 % (1315702)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.43 % (1315702)CaDiCaL version: 2.1.3
% 0.61/0.43 % (1315702)Termination reason: Instruction limit
% 0.61/0.43 % (1315702)Termination phase: shuffling
% 0.61/0.43 % (1315702)Time elapsed: 0.004 s
% 0.61/0.43 % (1315702)Peak memory usage: 10 MB
% 0.61/0.43 % (1315702)Instructions burned: 9 (million)
% 0.61/0.43 % (1315695)Instruction limit reached!
% 0.61/0.43 % (1315695)------------------------------
% 0.61/0.43 % (1315695)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.43 % (1315695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.43 % (1315695)CaDiCaL version: 2.1.3
% 0.61/0.43 % (1315695)Termination reason: Instruction limit
% 0.61/0.43 % (1315695)Termination phase: shuffling
% 0.61/0.43 % (1315695)Time elapsed: 0.002 s
% 0.61/0.43 % (1315695)Peak memory usage: 10 MB
% 0.61/0.43 % (1315695)Instructions burned: 4 (million)
% 0.61/0.43 % (1315710)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=4146742169:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.61/0.43 % (1315708)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
% 0.61/0.43 % (1315708)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.61/0.43 % (1315687)Instruction limit reached!
% 0.61/0.43 % (1315687)------------------------------
% 0.61/0.43 % (1315687)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.43 % (1315687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.43 % (1315687)CaDiCaL version: 2.1.3
% 0.61/0.43 % (1315687)Termination reason: Instruction limit
% 0.61/0.43 % (1315687)Termination phase: Preprocessing 3
% 0.61/0.43 % (1315687)Time elapsed: 0.050 s
% 0.61/0.43 % (1315687)Peak memory usage: 13 MB
% 0.61/0.43 % (1315687)Instructions burned: 89 (million)
% 0.61/0.43 % (1315708)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2174900293:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.61/0.43 % (1315710)Instruction limit reached!
% 0.61/0.43 % (1315710)------------------------------
% 0.61/0.43 % (1315710)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.46 % (1315710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.46 % (1315710)CaDiCaL version: 2.1.3
% 0.61/0.46 % (1315710)Termination reason: Instruction limit
% 0.61/0.46 % (1315710)Termination phase: Property scanning
% 0.61/0.46 % (1315710)Time elapsed: 0.019 s
% 0.61/0.46 % (1315710)Peak memory usage: 11 MB
% 0.61/0.46 % (1315710)Instructions burned: 90 (million)
% 0.61/0.46 % (1315708)Instruction limit reached!
% 0.61/0.46 % (1315708)------------------------------
% 0.61/0.46 % (1315708)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.46 % (1315712)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.61/0.46 % (1315708)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.46 % (1315708)CaDiCaL version: 2.1.3
% 0.61/0.46 % (1315711)lrs+10_1_si=on:cs=on:random_seed=2161233867:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.61/0.46 % (1315708)Termination reason: Instruction limit
% 0.61/0.46 % (1315708)Termination phase: shuffling
% 0.61/0.46 % (1315708)Time elapsed: 0.013 s
% 0.61/0.46 % (1315708)Peak memory usage: 10 MB
% 0.61/0.46 % (1315708)Instructions burned: 30 (million)
% 0.61/0.46 % (1315714)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2701157154:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.61/0.46 % (1315712)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=2844978827:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.61/0.46 % (1315711)Instruction limit reached!
% 0.61/0.46 % (1315711)------------------------------
% 0.61/0.46 % (1315711)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.46 % (1315711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.46 % (1315711)CaDiCaL version: 2.1.3
% 0.61/0.46 % (1315711)Termination reason: Instruction limit
% 0.61/0.46 % (1315711)Termination phase: shuffling
% 0.61/0.46 % (1315711)Time elapsed: 0.005 s
% 0.61/0.46 % (1315711)Peak memory usage: 10 MB
% 0.61/0.46 % (1315711)Instructions burned: 9 (million)
% 0.61/0.46 % (1315712)Instruction limit reached!
% 0.61/0.46 % (1315712)------------------------------
% 0.61/0.46 % (1315712)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.46 % (1315712)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.46 % (1315712)CaDiCaL version: 2.1.3
% 0.61/0.46 % (1315712)Termination reason: Instruction limit
% 0.61/0.46 % (1315712)Termination phase: shuffling
% 0.61/0.46 % (1315712)Time elapsed: 0.002 s
% 0.61/0.46 % (1315712)Peak memory usage: 10 MB
% 0.61/0.46 % (1315712)Instructions burned: 4 (million)
% 0.61/0.46 % (1315717)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3925072313:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.61/0.46 % (1315718)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=987831539:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.61/0.46 % (1315714)Instruction limit reached!
% 0.61/0.46 % (1315714)------------------------------
% 0.61/0.46 % (1315714)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.46 % (1315714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.46 % (1315714)CaDiCaL version: 2.1.3
% 0.61/0.46 % (1315714)Termination reason: Instruction limit
% 0.61/0.46 % (1315714)Termination phase: SInE selection
% 0.61/0.46 % (1315714)Time elapsed: 0.018 s
% 0.61/0.46 % (1315714)Peak memory usage: 11 MB
% 0.61/0.46 % (1315714)Instructions burned: 38 (million)
% 0.61/0.46 % (1315721)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3353113818:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.61/0.46 % (1315722)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2960570272:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.61/0.46 % (1315718)Instruction limit reached!
% 0.61/0.46 % (1315718)------------------------------
% 0.61/0.46 % (1315718)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.46 % (1315718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.52 % (1315718)CaDiCaL version: 2.1.3
% 1.38/0.52 % (1315718)Termination reason: Instruction limit
% 1.38/0.52 % (1315718)Termination phase: Property scanning
% 1.38/0.52 % (1315718)Time elapsed: 0.012 s
% 1.38/0.52 % (1315718)Peak memory usage: 10 MB
% 1.38/0.52 % (1315718)Instructions burned: 26 (million)
% 1.38/0.52 % (1315721)Instruction limit reached!
% 1.38/0.52 % (1315721)------------------------------
% 1.38/0.52 % (1315721)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.52 % (1315721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.52 % (1315721)CaDiCaL version: 2.1.3
% 1.38/0.52 % (1315721)Termination reason: Instruction limit
% 1.38/0.52 % (1315721)Termination phase: shuffling
% 1.38/0.52 % (1315721)Time elapsed: 0.008 s
% 1.38/0.52 % (1315721)Peak memory usage: 10 MB
% 1.38/0.52 % (1315721)Instructions burned: 16 (million)
% 1.38/0.52 % (1315693)Instruction limit reached!
% 1.38/0.52 % (1315693)------------------------------
% 1.38/0.52 % (1315693)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.52 % (1315693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.52 % (1315693)CaDiCaL version: 2.1.3
% 1.38/0.52 % (1315693)Termination reason: Instruction limit
% 1.38/0.52 % (1315693)Termination phase: Saturation
% 1.38/0.52 % (1315693)Time elapsed: 0.075 s
% 1.38/0.52 % (1315693)Peak memory usage: 13 MB
% 1.38/0.52 % (1315693)Instructions burned: 160 (million)
% 1.38/0.52 % (1315725)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2610939944:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.38/0.52 % (1315728)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=4291894803: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)
% 1.38/0.52 % (1315729)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2555805492:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.38/0.52 % (1315725)Instruction limit reached!
% 1.38/0.52 % (1315725)------------------------------
% 1.38/0.52 % (1315725)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.52 % (1315725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.52 % (1315725)CaDiCaL version: 2.1.3
% 1.38/0.52 % (1315725)Termination reason: Instruction limit
% 1.38/0.52 % (1315725)Termination phase: shuffling
% 1.38/0.52 % (1315725)Time elapsed: 0.007 s
% 1.38/0.52 % (1315725)Peak memory usage: 10 MB
% 1.38/0.52 % (1315725)Instructions burned: 15 (million)
% 1.38/0.52 % (1315728)Instruction limit reached!
% 1.38/0.52 % (1315728)------------------------------
% 1.38/0.52 % (1315728)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.52 % (1315728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.52 % (1315728)CaDiCaL version: 2.1.3
% 1.38/0.52 % (1315728)Termination reason: Instruction limit
% 1.38/0.52 % (1315728)Termination phase: shuffling
% 1.38/0.52 % (1315728)Time elapsed: 0.002 s
% 1.38/0.52 % (1315728)Peak memory usage: 10 MB
% 1.38/0.52 % (1315728)Instructions burned: 3 (million)
% 1.38/0.52 % (1315730)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2360089616:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.38/0.52 % (1315729)Instruction limit reached!
% 1.38/0.52 % (1315729)------------------------------
% 1.38/0.52 % (1315729)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.52 % (1315729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.52 % (1315729)CaDiCaL version: 2.1.3
% 1.38/0.52 % (1315729)Termination reason: Instruction limit
% 1.38/0.52 % (1315729)Termination phase: shuffling
% 1.38/0.52 % (1315729)Time elapsed: 0.012 s
% 1.38/0.52 % (1315729)Peak memory usage: 10 MB
% 1.38/0.52 % (1315729)Instructions burned: 27 (million)
% 1.38/0.52 % (1315730)Instruction limit reached!
% 1.38/0.52 % (1315730)------------------------------
% 1.38/0.52 % (1315730)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.52 % (1315730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.52 % (1315730)CaDiCaL version: 2.1.3
% 1.38/0.52 % (1315730)Termination reason: Instruction limit
% 1.38/0.52 % (1315730)Termination phase: shuffling
% 1.38/0.52 % (1315730)Time elapsed: 0.010 s
% 1.38/0.52 % (1315730)Peak memory usage: 10 MB
% 1.38/0.52 % (1315730)Instructions burned: 23 (million)
% 2.20/0.58 % (1315717)Instruction limit reached!
% 2.20/0.58 % (1315717)------------------------------
% 2.20/0.58 % (1315717)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.58 % (1315717)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.58 % (1315717)CaDiCaL version: 2.1.3
% 2.20/0.58 % (1315717)Termination reason: Instruction limit
% 2.20/0.58 % (1315717)Termination phase: Saturation
% 2.20/0.58 % (1315717)Time elapsed: 0.058 s
% 2.20/0.58 % (1315717)Peak memory usage: 15 MB
% 2.20/0.58 % (1315717)Instructions burned: 252 (million)
% 2.20/0.58 % (1315735)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
% 2.20/0.58 % (1315735)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.20/0.58 % (1315734)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=4172843079:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 2.20/0.58 % (1315735)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=871269786:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.20/0.58 % (1315739)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=2039049289:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 2.20/0.58 % (1315737)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.20/0.58 % (1315735)Instruction limit reached!
% 2.20/0.58 % (1315735)------------------------------
% 2.20/0.58 % (1315735)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.58 % (1315735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.58 % (1315735)CaDiCaL version: 2.1.3
% 2.20/0.58 % (1315735)Termination reason: Instruction limit
% 2.20/0.58 % (1315735)Termination phase: shuffling
% 2.20/0.58 % (1315735)Time elapsed: 0.007 s
% 2.20/0.58 % (1315735)Peak memory usage: 10 MB
% 2.20/0.58 % (1315735)Instructions burned: 15 (million)
% 2.20/0.58 % (1315739)Instruction limit reached!
% 2.20/0.58 % (1315739)------------------------------
% 2.20/0.58 % (1315739)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.58 % (1315739)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.58 % (1315739)CaDiCaL version: 2.1.3
% 2.20/0.58 % (1315739)Termination reason: Instruction limit
% 2.20/0.58 % (1315739)Termination phase: shuffling
% 2.20/0.58 % (1315739)Time elapsed: 0.002 s
% 2.20/0.58 % (1315739)Peak memory usage: 10 MB
% 2.20/0.58 % (1315739)Instructions burned: 8 (million)
% 2.20/0.58 % (1315737)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=2459904620:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 2.20/0.58 % (1315738)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=854688027:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 2.20/0.58 % (1315737)Instruction limit reached!
% 2.20/0.58 % (1315737)------------------------------
% 2.20/0.58 % (1315737)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.58 % (1315737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.58 % (1315737)CaDiCaL version: 2.1.3
% 2.20/0.58 % (1315737)Termination reason: Instruction limit
% 2.20/0.58 % (1315737)Termination phase: shuffling
% 2.20/0.58 % (1315737)Time elapsed: 0.005 s
% 2.20/0.58 % (1315737)Peak memory usage: 10 MB
% 2.20/0.58 % (1315737)Instructions burned: 10 (million)
% 2.20/0.58 % (1315744)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2455031912:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 2.20/0.58 % (1315744)Instruction limit reached!
% 2.20/0.58 % (1315744)------------------------------
% 2.20/0.58 % (1315744)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.20/0.58 % (1315744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/0.58 % (1315744)CaDiCaL version: 2.1.3
% 2.43/0.67 % (1315744)Termination reason: Instruction limit
% 2.43/0.67 % (1315744)Termination phase: shuffling
% 2.43/0.67 % (1315744)Time elapsed: 0.006 s
% 2.43/0.67 % (1315744)Peak memory usage: 10 MB
% 2.43/0.67 % (1315744)Instructions burned: 24 (million)
% 2.43/0.67 % (1315743)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2696384447:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.43/0.67 % (1315734)Instruction limit reached!
% 2.43/0.67 % (1315734)------------------------------
% 2.43/0.67 % (1315734)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.67 % (1315734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.67 % (1315734)CaDiCaL version: 2.1.3
% 2.43/0.67 % (1315734)Termination reason: Instruction limit
% 2.43/0.67 % (1315734)Termination phase: Preprocessing 3
% 2.43/0.67 % (1315734)Time elapsed: 0.028 s
% 2.43/0.67 % (1315734)Peak memory usage: 12 MB
% 2.43/0.67 % (1315734)Instructions burned: 60 (million)
% 2.43/0.67 % (1315747)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=180934117:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 2.43/0.67 % (1315749)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=703513302:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.43/0.67 % (1315738)Instruction limit reached!
% 2.43/0.67 % (1315738)------------------------------
% 2.43/0.67 % (1315738)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.67 % (1315738)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.67 % (1315738)CaDiCaL version: 2.1.3
% 2.43/0.67 % (1315738)Termination reason: Instruction limit
% 2.43/0.67 % (1315738)Termination phase: shuffling
% 2.43/0.67 % (1315738)Time elapsed: 0.022 s
% 2.43/0.67 % (1315738)Peak memory usage: 11 MB
% 2.43/0.67 % (1315738)Instructions burned: 31 (million)
% 2.43/0.67 % (1315743)Instruction limit reached!
% 2.43/0.67 % (1315743)------------------------------
% 2.43/0.67 % (1315743)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.67 % (1315743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.67 % (1315743)CaDiCaL version: 2.1.3
% 2.43/0.67 % (1315743)Termination reason: Instruction limit
% 2.43/0.67 % (1315743)Termination phase: shuffling
% 2.43/0.67 % (1315743)Time elapsed: 0.011 s
% 2.43/0.67 % (1315743)Peak memory usage: 10 MB
% 2.43/0.67 % (1315743)Instructions burned: 24 (million)
% 2.43/0.67 % (1315751)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=1368962987:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.43/0.67 % (1315755)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.43/0.67 % (1315754)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=206946930:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.43/0.67 % (1315755)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1960995214:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.43/0.67 % (1315755)Instruction limit reached!
% 2.43/0.67 % (1315755)------------------------------
% 2.43/0.67 % (1315755)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.67 % (1315755)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.67 % (1315755)CaDiCaL version: 2.1.3
% 2.43/0.67 % (1315755)Termination reason: Instruction limit
% 2.43/0.67 % (1315755)Termination phase: shuffling
% 2.43/0.67 % (1315755)Time elapsed: 0.004 s
% 2.43/0.67 % (1315755)Peak memory usage: 10 MB
% 2.43/0.67 % (1315755)Instructions burned: 9 (million)
% 2.43/0.67 % (1315749)Instruction limit reached!
% 2.43/0.67 % (1315749)------------------------------
% 2.43/0.67 % (1315749)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.67 % (1315749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.67 % (1315749)CaDiCaL version: 2.1.3
% 2.43/0.67 % (1315749)Termination reason: Instruction limit
% 2.43/0.67 % (1315749)Termination phase: Property scanning
% 2.43/0.67 % (1315749)Time elapsed: 0.032 s
% 2.43/0.67 % (1315749)Peak memory usage: 12 MB
% 2.43/0.67 % (1315749)Instructions burned: 143 (million)
% 2.43/0.67 % (1315754)Instruction limit reached!
% 2.43/0.67 % (1315754)------------------------------
% 2.43/0.67 % (1315754)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.67 % (1315754)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.67 % (1315754)CaDiCaL version: 2.1.3
% 2.43/0.67 % (1315754)Termination reason: Instruction limit
% 2.43/0.67 % (1315754)Termination phase: Property scanning
% 2.43/0.67 % (1315754)Time elapsed: 0.019 s
% 2.43/0.67 % (1315754)Peak memory usage: 11 MB
% 2.43/0.67 % (1315754)Instructions burned: 43 (million)
% 2.43/0.67 % (1315760)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=1480696545: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)
% 2.43/0.67 % (1315759)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=1864010988:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.43/0.67 % (1315761)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.43/0.67 % (1315761)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=2846348981:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.43/0.67 % (1315761)Instruction limit reached!
% 2.43/0.67 % (1315761)------------------------------
% 2.43/0.67 % (1315761)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.67 % (1315761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.67 % (1315761)CaDiCaL version: 2.1.3
% 2.43/0.67 % (1315761)Termination reason: Instruction limit
% 2.43/0.67 % (1315761)Termination phase: shuffling
% 2.43/0.67 % (1315761)Time elapsed: 0.003 s
% 2.43/0.67 % (1315761)Peak memory usage: 10 MB
% 2.43/0.67 % (1315761)Instructions burned: 6 (million)
% 2.43/0.67 % (1315760)Instruction limit reached!
% 2.43/0.67 % (1315760)------------------------------
% 2.43/0.67 % (1315760)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.67 % (1315760)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.67 % (1315760)CaDiCaL version: 2.1.3
% 2.43/0.67 % (1315760)Termination reason: Instruction limit
% 2.43/0.67 % (1315760)Termination phase: Saturation
% 2.43/0.67 % (1315760)Time elapsed: 0.038 s
% 2.43/0.67 % (1315760)Peak memory usage: 13 MB
% 2.43/0.67 % (1315760)Instructions burned: 169 (million)
% 2.43/0.67 % (1315766)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=3787470530:i=19:add=on:rtra=on_2996 on theBenchmark for (2996ds/19Mi)
% 2.43/0.67 % (1315751)Instruction limit reached!
% 2.43/0.67 % (1315751)------------------------------
% 2.43/0.67 % (1315751)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.67 % (1315751)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.67 % (1315751)CaDiCaL version: 2.1.3
% 2.43/0.67 % (1315751)Termination reason: Instruction limit
% 2.43/0.67 % (1315751)Termination phase: Saturation
% 2.43/0.67 % (1315751)Time elapsed: 0.082 s
% 2.43/0.67 % (1315751)Peak memory usage: 13 MB
% 2.43/0.67 % (1315751)Instructions burned: 195 (million)
% 2.43/0.67 % (1315765)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=2802981111:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.43/0.67 % (1315766)Instruction limit reached!
% 2.43/0.67 % (1315766)------------------------------
% 2.43/0.67 % (1315766)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.67 % (1315766)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.67 % (1315766)CaDiCaL version: 2.1.3
% 2.43/0.67 % (1315766)Termination reason: Instruction limit
% 2.43/0.67 % (1315766)Termination phase: shuffling
% 2.43/0.67 % (1315766)Time elapsed: 0.005 s
% 2.43/0.67 % (1315766)Peak memory usage: 10 MB
% 2.43/0.67 % (1315766)Instructions burned: 22 (million)
% 2.43/0.67 % (1315765)Instruction limit reached!
% 2.43/0.67 % (1315765)------------------------------
% 2.43/0.67 % (1315765)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.67 % (1315765)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.67 % (1315765)CaDiCaL version: 2.1.3
% 2.43/0.67 % (1315765)Termination reason: Instruction limit
% 2.43/0.67 % (1315765)Termination phase: shuffling
% 2.43/0.67 % (1315765)Time elapsed: 0.012 s
% 2.43/0.67 % (1315765)Peak memory usage: 11 MB
% 2.43/0.67 % (1315765)Instructions burned: 22 (million)
% 2.43/0.67 % (1315770)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=166594347:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2996 on theBenchmark for (2996ds/853Mi)
% 2.43/0.67 % (1315768)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=2295250142:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/316Mi)
% 2.43/0.67 % (1315759)Instruction limit reached!
% 2.43/0.67 % (1315759)------------------------------
% 2.43/0.67 % (1315759)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.67 % (1315759)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.67 % (1315759)CaDiCaL version: 2.1.3
% 2.43/0.67 % (1315759)Termination reason: Instruction limit
% 2.43/0.67 % (1315759)Termination phase: Saturation
% 2.43/0.67 % (1315759)Time elapsed: 0.077 s
% 2.43/0.67 % (1315759)Peak memory usage: 13 MB
% 2.43/0.67 % (1315759)Instructions burned: 181 (million)
% 2.43/0.67 % (1315771)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=334447345:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2996 on theBenchmark for (2996ds/45Mi)
% 2.43/0.67 % (1315774)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=3840448877:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 2.43/0.67 % (1315771)Instruction limit reached!
% 2.43/0.67 % (1315771)------------------------------
% 2.43/0.67 % (1315771)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.67 % (1315771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.67 % (1315771)CaDiCaL version: 2.1.3
% 2.43/0.67 % (1315771)Termination reason: Instruction limit
% 2.43/0.67 % (1315771)Termination phase: Property scanning
% 2.43/0.67 % (1315771)Time elapsed: 0.020 s
% 2.43/0.67 % (1315771)Peak memory usage: 11 MB
% 2.43/0.67 % (1315771)Instructions burned: 47 (million)
% 2.43/0.67 % (1315722)Instruction limit reached!
% 2.43/0.67 % (1315722)------------------------------
% 2.43/0.67 % (1315722)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.67 % (1315722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.67 % (1315722)CaDiCaL version: 2.1.3
% 2.43/0.67 % (1315722)Termination reason: Instruction limit
% 2.43/0.67 % (1315722)Termination phase: Saturation
% 2.43/0.67 % (1315722)Time elapsed: 0.249 s
% 2.43/0.67 % (1315722)Peak memory usage: 15 MB
% 2.43/0.67 % (1315722)Instructions burned: 327 (million)
% 2.43/0.67 % (1315777)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=2335252848:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2996 on theBenchmark for (2996ds/21Mi)
% 2.43/0.67 % (1315690) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1315682-1315690"...
% 2.43/0.67 % (1315777)Instruction limit reached!
% 2.43/0.67 % (1315777)------------------------------
% 2.43/0.67 % (1315777)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.67 % (1315777)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.67 % (1315777)CaDiCaL version: 2.1.3
% 2.43/0.67 % (1315777)Termination reason: Instruction limit
% 2.43/0.67 % (1315777)Termination phase: shuffling
% 2.43/0.67 % (1315777)Time elapsed: 0.010 s
% 2.43/0.67 % (1315777)Peak memory usage: 10 MB
% 2.43/0.67 % (1315777)Instructions burned: 22 (million)
% 2.43/0.67 % (1315778)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 2.43/0.67 % (1315690)...printing done.
% 2.43/0.67 % (1315778)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=2073656449:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 2.43/0.67 % (1315690)Refutation found. Thanks to Tanya!
% 2.43/0.67 % SZS status Theorem for theBenchmark
% 2.43/0.67 % SZS output start Proof for theBenchmark
% See solution above
% 2.43/0.67 % (1315690)------------------------------
% 2.43/0.67 % (1315690)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.67 % (1315690)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.67 % (1315690)CaDiCaL version: 2.1.3
% 2.43/0.67 % (1315690)Termination reason: Refutation
% 2.43/0.67 % (1315690)Time elapsed: 0.361 s
% 2.43/0.67 % (1315690)Peak memory usage: 21 MB
% 2.43/0.67 % (1315690)Instructions burned: 605 (million)
% 2.43/0.67 % (1315682)Success in time 0.415 s
% 2.43/0.67 % Vampire exiting
%------------------------------------------------------------------------------