%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU699^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 08:30:50 AM UTC 2026
% Result : Theorem 1.04s 0.51s
% Output : Refutation 1.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 69 ( 23 unt; 0 typ; 7 def)
% Number of atoms : 4265 (1178 equ; 0 cnn)
% Maximal formula atoms : 217 ( 61 avg)
% Number of connectives : 2261 ( 73 ~; 60 |; 876 &; 371 @)
% ( 11 <=>; 870 =>; 0 <=; 0 <~>)
% Maximal formula depth : 224 ( 29 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 : 432 ( 429 usr; 243 con; 0-4 aty)
% Number of variables : 116 ( 0 sgn 75 !; 21 ?; 116 :)
% 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_255,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_256,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_257,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_258,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_259,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_260,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_261,type,
vAND: $o > $o > $o ).
thf(func_def_262,type,
vNOT: $o > $o ).
thf(func_def_263,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_264,type,
vIMP: $o > $o > $o ).
thf(func_def_265,type,
sP0: $o ).
thf(func_def_266,type,
sP1: $i > $i > $o ).
thf(func_def_267,type,
sP2: $i > $o ).
thf(func_def_268,type,
sP3: $o ).
thf(func_def_272,type,
sK7: $o ).
thf(func_def_275,type,
sK10: $i > $o ).
thf(func_def_281,type,
sK16: $o ).
thf(func_def_282,type,
sK17: $i > $i > $o ).
thf(func_def_284,type,
sK19: $i > $i ).
thf(func_def_285,type,
sK20: $i > $i ).
thf(func_def_286,type,
sK21: $i > ( $i > $i > $o ) > $i ).
thf(func_def_287,type,
sK22: $i > ( $i > $i > $o ) > $i ).
thf(func_def_288,type,
sK23: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_295,type,
sK30: $i > $i > $i ).
thf(func_def_296,type,
sK31: ( $i > $o ) > $i > $i ).
thf(func_def_298,type,
sK33: $i > $o ).
thf(func_def_302,type,
sK37: $o ).
thf(func_def_308,type,
sK43: $i > $i ).
thf(func_def_309,type,
sK44: $i > $o ).
thf(func_def_314,type,
sK49: $i > $o ).
thf(func_def_315,type,
sK50: $i > $o ).
thf(func_def_316,type,
sK51: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_317,type,
sK52: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_321,type,
sK56: $o ).
thf(func_def_322,type,
sK57: $i > ( $i > $i ) > $i > $i ).
thf(func_def_324,type,
sK59: $i > $i ).
thf(func_def_328,type,
sK63: $i > $i > $i ).
thf(func_def_340,type,
sK75: $i > ( $i > $i ) > $i > $i ).
thf(func_def_342,type,
sK77: $i > $i ).
thf(func_def_351,type,
sK86: $i > $i ).
thf(func_def_352,type,
sK87: $i > $i ).
thf(func_def_356,type,
sK91: ( $i > $o ) > $i ).
thf(func_def_357,type,
sK92: $i > $o ).
thf(func_def_358,type,
sK93: $i > $i ).
thf(func_def_359,type,
sK94: $i > $i > $i ).
thf(func_def_367,type,
sK102: $i > $o ).
thf(func_def_372,type,
sK107: $o ).
thf(func_def_375,type,
sK110: $i > $i > $o ).
thf(func_def_382,type,
sK117: $i > $i > $o ).
thf(func_def_387,type,
sK122: $i > ( $i > $o ) > $i ).
thf(func_def_388,type,
sK123: $i > $o ).
thf(func_def_392,type,
sK127: $i > $i ).
thf(func_def_393,type,
sK128: ( $i > $i ) > $i > $i > $i ).
thf(func_def_402,type,
sK137: $i > $o ).
thf(func_def_405,type,
sK140: $i > ( $i > $o ) > $i ).
thf(func_def_406,type,
sK141: $i > ( $i > $o ) > $i ).
thf(func_def_417,type,
sK152: $o > $i > $i > $i ).
thf(func_def_420,type,
sK155: $o ).
thf(func_def_434,type,
sK169: $i > $o ).
thf(func_def_445,type,
sK180: $i > $o ).
thf(func_def_446,type,
sK181: $i > $o ).
thf(func_def_448,type,
sK183: $i > ( $i > $o ) > $i ).
thf(func_def_451,type,
sK186: $i > $i > $i ).
thf(func_def_452,type,
sK187: $i > $i > $i > $i > $i ).
thf(func_def_468,type,
sK203: ( $i > $o ) > $i ).
thf(func_def_469,type,
sK204: ( $i > $o ) > $i ).
thf(func_def_470,type,
sK205: $i > $o ).
thf(func_def_474,type,
sK209: $i > $i > $i ).
thf(func_def_479,type,
sK214: $i > $i ).
thf(func_def_481,type,
sK216: ( $i > $i ) > $i > $i > $i ).
thf(func_def_485,type,
sK220: $i > $i > $i ).
thf(func_def_515,type,
sK250: $i > $i > $o ).
thf(func_def_522,type,
sK257: $i > $i > $o ).
thf(func_def_534,type,
sK269: $i > $i > ( $i > $o ) > $i ).
thf(func_def_535,type,
sK270: $i > $o ).
thf(func_def_548,type,
sK283: $i > $o ).
thf(func_def_555,type,
sK290: $i > $o ).
thf(func_def_565,type,
sK300: $i > $o ).
thf(func_def_566,type,
sK301: ( $i > $o ) > $i ).
thf(func_def_579,type,
sK314: $i > $i > $o ).
thf(func_def_585,type,
sK320: $i > $o ).
thf(func_def_588,type,
sK323: $i > ( $i > $o ) > $i ).
thf(func_def_589,type,
sK324: $i > ( $i > $o ) > $i ).
thf(func_def_603,type,
sK338: $i > $i > $i > $i > $i ).
thf(func_def_607,type,
sK342: $i > $i ).
thf(func_def_612,type,
sK347: $i > $i > $i ).
thf(func_def_622,type,
sK357: $i > $i ).
thf(func_def_624,type,
sK359: $i > ( $i > $i ) > $i > $i ).
thf(func_def_625,type,
sK360: ( $i > $o ) > $i > $i ).
thf(func_def_627,type,
sK362: $i > $o ).
thf(func_def_637,type,
sK372: $i > $o ).
thf(func_def_651,type,
sK386: $i > $i > $i > $i > $i ).
thf(func_def_652,type,
sK387: $i > $i > $i > $i > $i ).
thf(func_def_669,type,
sK404: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_670,type,
sK405: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_671,type,
sK406: $i > $o ).
thf(func_def_672,type,
sK407: $i > $o ).
thf(func_def_677,type,
sK412: $i > $o ).
thf(func_def_678,type,
sK413: $i > $i ).
thf(func_def_679,type,
sK414: ( $i > $o ) > $i ).
thf(func_def_691,type,
sK426: $o ).
thf(func_def_704,type,
sK439: $i > $i ).
thf(func_def_712,type,
sK447: $i > $i ).
thf(func_def_713,type,
sK448: $i > $o ).
thf(func_def_717,type,
sK452: $i > $i > $o ).
thf(func_def_724,type,
sK459: $i > $o ).
thf(func_def_727,type,
sK462: $i > $i ).
thf(func_def_736,type,
sK471: ( $i > $i ) > $i > $i > $i ).
thf(func_def_739,type,
sK474: $i > $i ).
thf(func_def_744,type,
sK479: $i > $o ).
thf(func_def_746,type,
sK481: ( $i > $o ) > $i > $i ).
thf(func_def_747,type,
sK482: $i > $o ).
thf(func_def_750,type,
sK485: $i > ( $i > $o ) > $i ).
thf(func_def_752,type,
sK487: $i > $o ).
thf(func_def_754,type,
sK489: ( $i > $o ) > $i > $i ).
thf(func_def_766,type,
sK501: $i > $o ).
thf(func_def_772,type,
sK507: $i > $o ).
thf(func_def_774,type,
sK509: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_775,type,
sK510: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_776,type,
sK511: $i > $o ).
thf(func_def_785,type,
sK520: $i > $i > $i > $i > $i ).
thf(func_def_786,type,
sK521: $i > $i > $i > $i > $i ).
thf(func_def_787,type,
sK522: $i > $i > $i > $i > $i ).
thf(func_def_788,type,
sK523: $i > $i > $i > $i > $i ).
thf(func_def_804,type,
sK539: $i > $o ).
thf(func_def_806,type,
sK541: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_807,type,
sK542: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_810,type,
sK545: $i > $i > $o ).
thf(func_def_815,type,
sK550: $i > $i > $i ).
thf(func_def_816,type,
sK551: $i > $i > $i ).
thf(func_def_821,type,
sK556: $i > $i > $i > $i > $i ).
thf(func_def_828,type,
sK563: $i > $o ).
thf(func_def_848,type,
sK583: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_849,type,
sK584: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_852,type,
sK587: $i > $o ).
thf(func_def_853,type,
sK588: $i > $o ).
thf(func_def_854,type,
sK589: ( $i > $o ) > $i > $i ).
thf(func_def_856,type,
sK591: $i > $o ).
thf(func_def_867,type,
sK602: $i > $i > $i > $i ).
thf(func_def_868,type,
sK603: $i > $i > $i > $i ).
thf(func_def_870,type,
sK605: $o ).
thf(func_def_871,type,
sK606: $i > $i > $i ).
thf(func_def_885,type,
sK620: $i > ( $i > $o ) > $i ).
thf(func_def_886,type,
sK621: $i > $o ).
thf(func_def_893,type,
sK628: $i > $i ).
thf(func_def_894,type,
sK629: $i > $i ).
thf(func_def_895,type,
sK630: $i > $i ).
thf(func_def_896,type,
sK631: $i > $i ).
thf(func_def_897,type,
sK632: $i > $i ).
thf(func_def_898,type,
sK633: $i > $i > $i > $i ).
thf(func_def_899,type,
sK634: $i > $i ).
thf(func_def_900,type,
sK635: $i > $i ).
thf(func_def_901,type,
sK636: $i > $i ).
thf(func_def_902,type,
sK637: $i > $i ).
thf(func_def_903,type,
sK638: $i > $i > $i ).
thf(func_def_904,type,
sK639: $i > $i > $i ).
thf(func_def_905,type,
sK640: $i > $i > $i > $i ).
thf(func_def_906,type,
sK641: $i > $i > $i > $i ).
thf(func_def_907,type,
sK642: $i > $i > $i > $i ).
thf(func_def_908,type,
sK643: $i > $i > $i ).
thf(func_def_909,type,
sK644: $i > $i > $i ).
thf(func_def_910,type,
sK645: $i > $i > $i ).
thf(f197,axiom,
( infuncsetfunc
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ( func @ X0 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(f218,axiom,
( eta1
= ( ! [X0: $i,X2: $i,X1: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ( X2
= ( lam @ X0 @ X1
@ ^ [X3: $i] : ( ap @ X0 @ X1 @ X2 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta1) ).
thf(f221,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
=> ! [X2: $i,X1: $i,X0: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ( ( lam @ X0 @ X1
@ ^ [X3: $i] : ( ap @ X0 @ X1 @ X2 @ X3 ) )
= X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta2) ).
thf(f222,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
=> ! [X2: $i,X1: $i,X0: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ( ( lam @ X0 @ X1
@ ^ [X3: $i] : ( ap @ X0 @ X1 @ X2 @ X3 ) )
= X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f221]) ).
thf(f272,plain,
( eta1
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X0 @ X2 @ X1 )
=> ( X1
= ( lam @ X0 @ X2
@ ^ [X3: $i] : ( ap @ X0 @ X2 @ X1 @ X3 ) ) ) ) ) ),
inference(rectify,[],[f218]) ).
thf(f273,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( func @ X0 @ X2 @ X1 ) )
=> ( ( lam @ X0 @ X2
@ ^ [Y0: $i] : ( ap @ X0 @ X2 @ X1 @ Y0 ) )
= X1 ) )
<=> ( eta1 = $true ) ),
inference(fool_elimination,[],[f272]) ).
thf(f280,plain,
( infuncsetfunc
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ( func @ X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f197]) ).
thf(f281,plain,
( ( infuncsetfunc = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
= $true )
=> ( ( func @ X0 @ X1 @ X2 )
= $true ) ) ),
inference(fool_elimination,[],[f280]) ).
thf(f610,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ ( funcSet @ X2 @ X1 ) )
=> ( ( lam @ X2 @ X1
@ ^ [X3: $i] : ( ap @ X2 @ X1 @ X0 @ X3 ) )
= X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f222]) ).
thf(f611,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 )
=> ! [X1: $i,X0: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( funcSet @ X2 @ X1 ) ) )
=> ( ( lam @ X2 @ X1
@ ^ [Y0: $i] : ( ap @ X2 @ X1 @ X0 @ Y0 ) )
= X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f610]) ).
thf(f693,plain,
( ( infuncsetfunc = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
!= $true )
| ( ( func @ X0 @ X1 @ X2 )
= $true ) ) ),
inference(ennf_transformation,[],[f281]) ).
thf(f720,plain,
( ( eta1 = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( ( lam @ X0 @ X2
@ ^ [Y0: $i] : ( ap @ X0 @ X2 @ X1 @ Y0 ) )
= X1 )
| ( $true
!= ( func @ X0 @ X2 @ X1 ) ) ) ),
inference(ennf_transformation,[],[f273]) ).
thf(f726,plain,
( ? [X2: $i,X1: $i,X0: $i] :
( ( ( lam @ X2 @ X1
@ ^ [Y0: $i] : ( ap @ X2 @ X1 @ X0 @ Y0 ) )
!= X0 )
& ( $true
= ( in @ X0 @ ( funcSet @ X2 @ X1 ) ) ) )
& ( 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,[],[f611]) ).
thf(f727,plain,
( ( ksndsingleton = $true )
& ( funcGraphProp4 = $true )
& ( ubforcartprodlem2 = $true )
& ( subsetemptysetimpeq = $true )
& ( binunionIR = $true )
& ( setbeta = $true )
& ( binintersectSubset4 = $true )
& ( kpairsurjEq = $true )
& ( eqimpsubset1 = $true )
& ( theprop = $true )
& ( nonemptyImpWitness = $true )
& ( singletonprop = $true )
& ( binintersectSubset3 = $true )
& ( funcGraphProp2 = $true )
& ( powersetI1 = $true )
& ( funcImageSingleton = $true )
& ( upairsubunion = $true )
& ( binunionE = $true )
& ( lam2p = $true )
& ( notdexE = $true )
& ( brelnall1 = $true )
& ( dpsetconstrI = $true )
& ( symdiffI1 = $true )
& ( exuE3e = $true )
& ( setunion__Cong = $true )
& ( upairsetIL = $true )
& ( cartprodsndpairEq = $true )
& ( dsetconstr__Cong = $true )
& ( upairinpowunion = $true )
& ( subsetI1 = $true )
& ( setextsub = $true )
& ( exuE1 = $true )
& ( foundationAx = $true )
& ( setminusELneg = $true )
& ( subsetTrans = $true )
& ( ex1I = $true )
& ( brelnall2 = $true )
& ( uniqinunit = $true )
& ( quantDeMorgan4 = $true )
& ( setukpairinjR11 = $true )
& ( emptysetAx = $true )
& ( exuI2 = $true )
& ( singletonsuniq = $true )
& ( omegaIndAx = $true )
& ( powersetE1 = $true )
& ( emptyinPowerset = $true )
& ( cartprodpairsurjEq = $true )
& ( emptysetsubset = $true )
& ( prop2set2propI = $true )
& ( notinemptyset = $true )
& ( emptyInPowerset = $true )
& ( setukpairinjR2 = $true )
& ( symdiffE = $true )
& ( emptyI = $true )
& ( cartprodfstin = $true )
& ( setminusLsub = $true )
& ( upairequniteq = $true )
& ( binintersectEL = $true )
& ( powersetI = $true )
& ( setminusERneg = $true )
& ( prop2setE = $true )
& ( notinsingleton = $true )
& ( quantDeMorgan1 = $true )
& ( exu__Cong = $true )
& ( singletonsswitch = $true )
& ( powersetsubset = $true )
& ( setukpairinjR12 = $true )
& ( symdiffIneg2 = $true )
& ( dpsetconstrEL2 = $true )
& ( funcinfuncset = $true )
& ( setext = $true )
& ( kfstpairEq = $true )
& ( infuncsetfunc = $true )
& ( lamp = $true )
& ( setminusI = $true )
& ( ex1I2 = $true )
& ( cartprodpairmemER = $true )
& ( setadjoinIR = $true )
& ( setadjoinSub2 = $true )
& ( upairsetIR = $true )
& ( powerset__Cong = $true )
& ( symdiffIneg1 = $true )
& ( cartprodmempair1 = $true )
& ( setunionE = $true )
& ( setunionsingleton = $true )
& ( binintersectLsub = $true )
& ( inPowerset = $true )
& ( setadjoinSub = $true )
& ( dpsetconstrER = $true )
& ( ap2p = $true )
& ( kpairiskpair = $true )
& ( setunionsingleton1 = $true )
& ( quantDeMorgan2 = $true )
& ( eqimpsubset2 = $true )
& ( setadjoinIL = $true )
& ( upairset2E = $true )
& ( binintersectSubset2 = $true )
& ( ap2apEq1 = $true )
& ( exuE2 = $true )
& ( subsetRefl = $true )
& ( setoftrueEq = $true )
& ( omega__Cong = $true )
& ( setadjoinE = $true )
& ( setunionE2 = $true )
& ( funcext2 = $true )
& ( ap2apEq2 = $true )
& ( nonemptyI = $true )
& ( cartprodpairmemEL = $true )
& ( cartprodmempaircEq = $true )
& ( setminusEL = $true )
& ( emptyE1 = $true )
& ( sepSubset = $true )
& ( binunionLsub = $true )
& ( setunionsingleton2 = $true )
& ( exuEu = $true )
& ( notequalI1 = $true )
& ( setOfPairsIsBReln = $true )
& ( binintersectRsub = $true )
& ( setminusIRneg = $true )
& ( funcext = $true )
& ( binunionIL = $true )
& ( descrp = $true )
& ( ex1E1 = $true )
& ( subbreln = $true )
& ( emptyinunitempty = $true )
& ( eqinunit = $true )
& ( setminusSubset2 = $true )
& ( subset2powerset = $true )
& ( replAx = $true )
& ( powersetAx = $true )
& ( setadjoin__Cong = $true )
& ( omega0Ax = $true )
& ( eqbreln = $true )
& ( kfstsingleton = $true )
& ( apProp = $true )
& ( prop2setI = $true )
& ( dsetconstrEL = $true )
& ( setadjoinAx = $true )
& ( setukpairIL = $true )
& ( subsetE2 = $true )
& ( singletoninpowerset = $true )
& ( setunionAx = $true )
& ( ubforcartprodlem3 = $true )
& ( wellorderingAx = $true )
& ( quantDeMorgan3 = $true )
& ( setukpairinjR = $true )
& ( funcextLem = $true )
& ( dpsetconstrERa = $true )
& ( setminusILneg = $true )
& ( eta1 = $true )
& ( binunionRsub = $true )
& ( kpairp = $true )
& ( sepInPowerset = $true )
& ( noeltsimpempty = $true )
& ( setadjoinOr = $true )
& ( funcGraphProp3 = $true )
& ( subsetI2 = $true )
& ( emptyset__Cong = $true )
& ( lamProp = $true )
& ( setukpairinjL2 = $true )
& ( setminusER = $true )
& ( setukpairinjL1 = $true )
& ( dsetconstrER = $true )
& ( upairsetE = $true )
& ( cartprodmempair = $true )
& ( dpsetconstrSub = $true )
& ( subsetE = $true )
& ( dsetconstrI = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( powersetE = $true )
& ( singletonsubset = $true )
& ( symdiffI2 = $true )
& ( beta2 = $true )
& ( setminusSubset1 = $true )
& ( exuE3u = $true )
& ( binunionEcases = $true )
& ( ksndpairEq = $true )
& ( subPowSU = $true )
& ( lam2lamEq = $true )
& ( ex1E2 = $true )
& ( binintersectER = $true )
& ( vacuousDall = $true )
& ( nonemptyI1 = $true )
& ( setunionI = $true )
& ( omegaSAx = $true )
& ( funcGraphProp1 = $true )
& ( notequalI2 = $true )
& ( exuI1 = $true )
& ( disjointsetsI1 = $true )
& ( secondinupair = $true )
& ( binintersectSubset5 = $true )
& ( nonemptyE1 = $true )
& ( binintersectSubset1 = $true )
& ( notdallE = $true )
& ? [X2: $i,X1: $i,X0: $i] :
( ( ( lam @ X2 @ X1
@ ^ [Y0: $i] : ( ap @ X2 @ X1 @ X0 @ Y0 ) )
!= X0 )
& ( $true
= ( in @ X0 @ ( funcSet @ X2 @ X1 ) ) ) )
& ( dpsetconstrEL1 = $true )
& ( beta1 = $true )
& ( app = $true )
& ( notsubsetI = $true )
& ( descr__Cong = $true )
& ( cartprodfstpairEq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjL = $true )
& ( upairset2IR = $true )
& ( setextAx = $true )
& ( ubforcartprodlem1 = $true )
& ( bs114d = $true )
& ( cartprodpairin = $true )
& ( cartprodsndin = $true )
& ( setukpairIR = $true )
& ( binintersectI = $true )
& ( exuI3 = $true )
& ( singletoninpowunion = $true ) ),
inference(flattening,[],[f726]) ).
thf(f1173,plain,
( ( ksndsingleton = $true )
& ( funcGraphProp4 = $true )
& ( ubforcartprodlem2 = $true )
& ( subsetemptysetimpeq = $true )
& ( binunionIR = $true )
& ( setbeta = $true )
& ( binintersectSubset4 = $true )
& ( kpairsurjEq = $true )
& ( eqimpsubset1 = $true )
& ( theprop = $true )
& ( nonemptyImpWitness = $true )
& ( singletonprop = $true )
& ( binintersectSubset3 = $true )
& ( funcGraphProp2 = $true )
& ( powersetI1 = $true )
& ( funcImageSingleton = $true )
& ( upairsubunion = $true )
& ( binunionE = $true )
& ( lam2p = $true )
& ( notdexE = $true )
& ( brelnall1 = $true )
& ( dpsetconstrI = $true )
& ( symdiffI1 = $true )
& ( exuE3e = $true )
& ( setunion__Cong = $true )
& ( upairsetIL = $true )
& ( cartprodsndpairEq = $true )
& ( dsetconstr__Cong = $true )
& ( upairinpowunion = $true )
& ( subsetI1 = $true )
& ( setextsub = $true )
& ( exuE1 = $true )
& ( foundationAx = $true )
& ( setminusELneg = $true )
& ( subsetTrans = $true )
& ( ex1I = $true )
& ( brelnall2 = $true )
& ( uniqinunit = $true )
& ( quantDeMorgan4 = $true )
& ( setukpairinjR11 = $true )
& ( emptysetAx = $true )
& ( exuI2 = $true )
& ( singletonsuniq = $true )
& ( omegaIndAx = $true )
& ( powersetE1 = $true )
& ( emptyinPowerset = $true )
& ( cartprodpairsurjEq = $true )
& ( emptysetsubset = $true )
& ( prop2set2propI = $true )
& ( notinemptyset = $true )
& ( emptyInPowerset = $true )
& ( setukpairinjR2 = $true )
& ( symdiffE = $true )
& ( emptyI = $true )
& ( cartprodfstin = $true )
& ( setminusLsub = $true )
& ( upairequniteq = $true )
& ( binintersectEL = $true )
& ( powersetI = $true )
& ( setminusERneg = $true )
& ( prop2setE = $true )
& ( notinsingleton = $true )
& ( quantDeMorgan1 = $true )
& ( exu__Cong = $true )
& ( singletonsswitch = $true )
& ( powersetsubset = $true )
& ( setukpairinjR12 = $true )
& ( symdiffIneg2 = $true )
& ( dpsetconstrEL2 = $true )
& ( funcinfuncset = $true )
& ( setext = $true )
& ( kfstpairEq = $true )
& ( infuncsetfunc = $true )
& ( lamp = $true )
& ( setminusI = $true )
& ( ex1I2 = $true )
& ( cartprodpairmemER = $true )
& ( setadjoinIR = $true )
& ( setadjoinSub2 = $true )
& ( upairsetIR = $true )
& ( powerset__Cong = $true )
& ( symdiffIneg1 = $true )
& ( cartprodmempair1 = $true )
& ( setunionE = $true )
& ( setunionsingleton = $true )
& ( binintersectLsub = $true )
& ( inPowerset = $true )
& ( setadjoinSub = $true )
& ( dpsetconstrER = $true )
& ( ap2p = $true )
& ( kpairiskpair = $true )
& ( setunionsingleton1 = $true )
& ( quantDeMorgan2 = $true )
& ( eqimpsubset2 = $true )
& ( setadjoinIL = $true )
& ( upairset2E = $true )
& ( binintersectSubset2 = $true )
& ( ap2apEq1 = $true )
& ( exuE2 = $true )
& ( subsetRefl = $true )
& ( setoftrueEq = $true )
& ( omega__Cong = $true )
& ( setadjoinE = $true )
& ( setunionE2 = $true )
& ( funcext2 = $true )
& ( ap2apEq2 = $true )
& ( nonemptyI = $true )
& ( cartprodpairmemEL = $true )
& ( cartprodmempaircEq = $true )
& ( setminusEL = $true )
& ( emptyE1 = $true )
& ( sepSubset = $true )
& ( binunionLsub = $true )
& ( setunionsingleton2 = $true )
& ( exuEu = $true )
& ( notequalI1 = $true )
& ( setOfPairsIsBReln = $true )
& ( binintersectRsub = $true )
& ( setminusIRneg = $true )
& ( funcext = $true )
& ( binunionIL = $true )
& ( descrp = $true )
& ( ex1E1 = $true )
& ( subbreln = $true )
& ( emptyinunitempty = $true )
& ( eqinunit = $true )
& ( setminusSubset2 = $true )
& ( subset2powerset = $true )
& ( replAx = $true )
& ( powersetAx = $true )
& ( setadjoin__Cong = $true )
& ( omega0Ax = $true )
& ( eqbreln = $true )
& ( kfstsingleton = $true )
& ( apProp = $true )
& ( prop2setI = $true )
& ( dsetconstrEL = $true )
& ( setadjoinAx = $true )
& ( setukpairIL = $true )
& ( subsetE2 = $true )
& ( singletoninpowerset = $true )
& ( setunionAx = $true )
& ( ubforcartprodlem3 = $true )
& ( wellorderingAx = $true )
& ( quantDeMorgan3 = $true )
& ( setukpairinjR = $true )
& ( funcextLem = $true )
& ( dpsetconstrERa = $true )
& ( setminusILneg = $true )
& ( eta1 = $true )
& ( binunionRsub = $true )
& ( kpairp = $true )
& ( sepInPowerset = $true )
& ( noeltsimpempty = $true )
& ( setadjoinOr = $true )
& ( funcGraphProp3 = $true )
& ( subsetI2 = $true )
& ( emptyset__Cong = $true )
& ( lamProp = $true )
& ( setukpairinjL2 = $true )
& ( setminusER = $true )
& ( setukpairinjL1 = $true )
& ( dsetconstrER = $true )
& ( upairsetE = $true )
& ( cartprodmempair = $true )
& ( dpsetconstrSub = $true )
& ( subsetE = $true )
& ( dsetconstrI = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( powersetE = $true )
& ( singletonsubset = $true )
& ( symdiffI2 = $true )
& ( beta2 = $true )
& ( setminusSubset1 = $true )
& ( exuE3u = $true )
& ( binunionEcases = $true )
& ( ksndpairEq = $true )
& ( subPowSU = $true )
& ( lam2lamEq = $true )
& ( ex1E2 = $true )
& ( binintersectER = $true )
& ( vacuousDall = $true )
& ( nonemptyI1 = $true )
& ( setunionI = $true )
& ( omegaSAx = $true )
& ( funcGraphProp1 = $true )
& ( notequalI2 = $true )
& ( exuI1 = $true )
& ( disjointsetsI1 = $true )
& ( secondinupair = $true )
& ( binintersectSubset5 = $true )
& ( nonemptyE1 = $true )
& ( binintersectSubset1 = $true )
& ( notdallE = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( lam @ X0 @ X1
@ ^ [Y0: $i] : ( ap @ X0 @ X1 @ X2 @ Y0 ) )
!= X2 )
& ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
= $true ) )
& ( dpsetconstrEL1 = $true )
& ( beta1 = $true )
& ( app = $true )
& ( notsubsetI = $true )
& ( descr__Cong = $true )
& ( cartprodfstpairEq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjL = $true )
& ( upairset2IR = $true )
& ( setextAx = $true )
& ( ubforcartprodlem1 = $true )
& ( bs114d = $true )
& ( cartprodpairin = $true )
& ( cartprodsndin = $true )
& ( setukpairIR = $true )
& ( binintersectI = $true )
& ( exuI3 = $true )
& ( singletoninpowunion = $true ) ),
inference(rectify,[],[f727]) ).
thf(f1174,plain,
( ( ksndsingleton = $true )
& ( funcGraphProp4 = $true )
& ( ubforcartprodlem2 = $true )
& ( subsetemptysetimpeq = $true )
& ( binunionIR = $true )
& ( setbeta = $true )
& ( binintersectSubset4 = $true )
& ( kpairsurjEq = $true )
& ( eqimpsubset1 = $true )
& ( theprop = $true )
& ( nonemptyImpWitness = $true )
& ( singletonprop = $true )
& ( binintersectSubset3 = $true )
& ( funcGraphProp2 = $true )
& ( powersetI1 = $true )
& ( funcImageSingleton = $true )
& ( upairsubunion = $true )
& ( binunionE = $true )
& ( lam2p = $true )
& ( notdexE = $true )
& ( brelnall1 = $true )
& ( dpsetconstrI = $true )
& ( symdiffI1 = $true )
& ( exuE3e = $true )
& ( setunion__Cong = $true )
& ( upairsetIL = $true )
& ( cartprodsndpairEq = $true )
& ( dsetconstr__Cong = $true )
& ( upairinpowunion = $true )
& ( subsetI1 = $true )
& ( setextsub = $true )
& ( exuE1 = $true )
& ( foundationAx = $true )
& ( setminusELneg = $true )
& ( subsetTrans = $true )
& ( ex1I = $true )
& ( brelnall2 = $true )
& ( uniqinunit = $true )
& ( quantDeMorgan4 = $true )
& ( setukpairinjR11 = $true )
& ( emptysetAx = $true )
& ( exuI2 = $true )
& ( singletonsuniq = $true )
& ( omegaIndAx = $true )
& ( powersetE1 = $true )
& ( emptyinPowerset = $true )
& ( cartprodpairsurjEq = $true )
& ( emptysetsubset = $true )
& ( prop2set2propI = $true )
& ( notinemptyset = $true )
& ( emptyInPowerset = $true )
& ( setukpairinjR2 = $true )
& ( symdiffE = $true )
& ( emptyI = $true )
& ( cartprodfstin = $true )
& ( setminusLsub = $true )
& ( upairequniteq = $true )
& ( binintersectEL = $true )
& ( powersetI = $true )
& ( setminusERneg = $true )
& ( prop2setE = $true )
& ( notinsingleton = $true )
& ( quantDeMorgan1 = $true )
& ( exu__Cong = $true )
& ( singletonsswitch = $true )
& ( powersetsubset = $true )
& ( setukpairinjR12 = $true )
& ( symdiffIneg2 = $true )
& ( dpsetconstrEL2 = $true )
& ( funcinfuncset = $true )
& ( setext = $true )
& ( kfstpairEq = $true )
& ( infuncsetfunc = $true )
& ( lamp = $true )
& ( setminusI = $true )
& ( ex1I2 = $true )
& ( cartprodpairmemER = $true )
& ( setadjoinIR = $true )
& ( setadjoinSub2 = $true )
& ( upairsetIR = $true )
& ( powerset__Cong = $true )
& ( symdiffIneg1 = $true )
& ( cartprodmempair1 = $true )
& ( setunionE = $true )
& ( setunionsingleton = $true )
& ( binintersectLsub = $true )
& ( inPowerset = $true )
& ( setadjoinSub = $true )
& ( dpsetconstrER = $true )
& ( ap2p = $true )
& ( kpairiskpair = $true )
& ( setunionsingleton1 = $true )
& ( quantDeMorgan2 = $true )
& ( eqimpsubset2 = $true )
& ( setadjoinIL = $true )
& ( upairset2E = $true )
& ( binintersectSubset2 = $true )
& ( ap2apEq1 = $true )
& ( exuE2 = $true )
& ( subsetRefl = $true )
& ( setoftrueEq = $true )
& ( omega__Cong = $true )
& ( setadjoinE = $true )
& ( setunionE2 = $true )
& ( funcext2 = $true )
& ( ap2apEq2 = $true )
& ( nonemptyI = $true )
& ( cartprodpairmemEL = $true )
& ( cartprodmempaircEq = $true )
& ( setminusEL = $true )
& ( emptyE1 = $true )
& ( sepSubset = $true )
& ( binunionLsub = $true )
& ( setunionsingleton2 = $true )
& ( exuEu = $true )
& ( notequalI1 = $true )
& ( setOfPairsIsBReln = $true )
& ( binintersectRsub = $true )
& ( setminusIRneg = $true )
& ( funcext = $true )
& ( binunionIL = $true )
& ( descrp = $true )
& ( ex1E1 = $true )
& ( subbreln = $true )
& ( emptyinunitempty = $true )
& ( eqinunit = $true )
& ( setminusSubset2 = $true )
& ( subset2powerset = $true )
& ( replAx = $true )
& ( powersetAx = $true )
& ( setadjoin__Cong = $true )
& ( omega0Ax = $true )
& ( eqbreln = $true )
& ( kfstsingleton = $true )
& ( apProp = $true )
& ( prop2setI = $true )
& ( dsetconstrEL = $true )
& ( setadjoinAx = $true )
& ( setukpairIL = $true )
& ( subsetE2 = $true )
& ( singletoninpowerset = $true )
& ( setunionAx = $true )
& ( ubforcartprodlem3 = $true )
& ( wellorderingAx = $true )
& ( quantDeMorgan3 = $true )
& ( setukpairinjR = $true )
& ( funcextLem = $true )
& ( dpsetconstrERa = $true )
& ( setminusILneg = $true )
& ( eta1 = $true )
& ( binunionRsub = $true )
& ( kpairp = $true )
& ( sepInPowerset = $true )
& ( noeltsimpempty = $true )
& ( setadjoinOr = $true )
& ( funcGraphProp3 = $true )
& ( subsetI2 = $true )
& ( emptyset__Cong = $true )
& ( lamProp = $true )
& ( setukpairinjL2 = $true )
& ( setminusER = $true )
& ( setukpairinjL1 = $true )
& ( dsetconstrER = $true )
& ( upairsetE = $true )
& ( cartprodmempair = $true )
& ( dpsetconstrSub = $true )
& ( subsetE = $true )
& ( dsetconstrI = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( powersetE = $true )
& ( singletonsubset = $true )
& ( symdiffI2 = $true )
& ( beta2 = $true )
& ( setminusSubset1 = $true )
& ( exuE3u = $true )
& ( binunionEcases = $true )
& ( ksndpairEq = $true )
& ( subPowSU = $true )
& ( lam2lamEq = $true )
& ( ex1E2 = $true )
& ( binintersectER = $true )
& ( vacuousDall = $true )
& ( nonemptyI1 = $true )
& ( setunionI = $true )
& ( omegaSAx = $true )
& ( funcGraphProp1 = $true )
& ( notequalI2 = $true )
& ( exuI1 = $true )
& ( disjointsetsI1 = $true )
& ( secondinupair = $true )
& ( binintersectSubset5 = $true )
& ( nonemptyE1 = $true )
& ( binintersectSubset1 = $true )
& ( notdallE = $true )
& ( ( lam @ sK239 @ sK240
@ ^ [Y0: $i] : ( ap @ sK239 @ sK240 @ sK241 @ Y0 ) )
!= sK241 )
& ( $true
= ( in @ sK241 @ ( funcSet @ sK239 @ sK240 ) ) )
& ( dpsetconstrEL1 = $true )
& ( beta1 = $true )
& ( app = $true )
& ( notsubsetI = $true )
& ( descr__Cong = $true )
& ( cartprodfstpairEq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjL = $true )
& ( upairset2IR = $true )
& ( setextAx = $true )
& ( ubforcartprodlem1 = $true )
& ( bs114d = $true )
& ( cartprodpairin = $true )
& ( cartprodsndin = $true )
& ( setukpairIR = $true )
& ( binintersectI = $true )
& ( exuI3 = $true )
& ( singletoninpowunion = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK239,sK240,sK241]),skolemize(X0,sK239),skolemize(X1,sK240),skolemize(X2,sK241)],[f1173]) ).
thf(f1377,plain,
( ( ( infuncsetfunc = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
= $true )
& ( ( func @ X0 @ X1 @ X2 )
!= $true ) ) )
& ( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
!= $true )
| ( ( func @ X0 @ X1 @ X2 )
= $true ) )
| ( infuncsetfunc != $true ) ) ),
inference(nnf_transformation,[],[f693]) ).
thf(f1378,plain,
( ( ( infuncsetfunc = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( funcSet @ X2 @ X1 ) ) )
& ( $true
!= ( func @ X2 @ X1 @ X0 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( funcSet @ X5 @ X4 ) ) )
| ( $true
= ( func @ X5 @ X4 @ X3 ) ) )
| ( infuncsetfunc != $true ) ) ),
inference(rectify,[],[f1377]) ).
thf(f1379,plain,
( ( ( infuncsetfunc = $true )
| ( ( $true
= ( in @ sK440 @ ( funcSet @ sK442 @ sK441 ) ) )
& ( ( func @ sK442 @ sK441 @ sK440 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( funcSet @ X5 @ X4 ) ) )
| ( $true
= ( func @ X5 @ X4 @ X3 ) ) )
| ( infuncsetfunc != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK440,sK441,sK442]),skolemize(X0,sK440),skolemize(X1,sK441),skolemize(X2,sK442)],[f1378]) ).
thf(f1566,plain,
( ( ( eta1 = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( ( lam @ X0 @ X2
@ ^ [Y0: $i] : ( ap @ X0 @ X2 @ X1 @ Y0 ) )
!= X1 )
& ( $true
= ( func @ X0 @ X2 @ X1 ) ) ) )
& ( ! [X1: $i,X2: $i,X0: $i] :
( ( ( lam @ X0 @ X2
@ ^ [Y0: $i] : ( ap @ X0 @ X2 @ X1 @ Y0 ) )
= X1 )
| ( $true
!= ( func @ X0 @ X2 @ X1 ) ) )
| ( eta1 != $true ) ) ),
inference(nnf_transformation,[],[f720]) ).
thf(f1567,plain,
( ( ( eta1 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( lam @ X2 @ X1
@ ^ [Y0: $i] : ( ap @ X2 @ X1 @ X0 @ Y0 ) )
!= X0 )
& ( $true
= ( func @ X2 @ X1 @ X0 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( lam @ X5 @ X4
@ ^ [Y0: $i] : ( ap @ X5 @ X4 @ X3 @ Y0 ) )
= X3 )
| ( $true
!= ( func @ X5 @ X4 @ X3 ) ) )
| ( eta1 != $true ) ) ),
inference(rectify,[],[f1566]) ).
thf(f1568,plain,
( ( ( eta1 = $true )
| ( ( sK659
!= ( lam @ sK661 @ sK660
@ ^ [Y0: $i] : ( ap @ sK661 @ sK660 @ sK659 @ Y0 ) ) )
& ( $true
= ( func @ sK661 @ sK660 @ sK659 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( lam @ X5 @ X4
@ ^ [Y0: $i] : ( ap @ X5 @ X4 @ X3 @ Y0 ) )
= X3 )
| ( $true
!= ( func @ X5 @ X4 @ X3 ) ) )
| ( eta1 != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK659,sK660,sK661]),skolemize(X0,sK659),skolemize(X1,sK660),skolemize(X2,sK661)],[f1567]) ).
thf(f1907,plain,
( $true
= ( in @ sK241 @ ( funcSet @ sK239 @ sK240 ) ) ),
inference(cnf_transformation,[],[f1174]) ).
thf(f1908,plain,
( ( lam @ sK239 @ sK240
@ ^ [Y0: $i] : ( ap @ sK239 @ sK240 @ sK241 @ Y0 ) )
!= sK241 ),
inference(cnf_transformation,[],[f1174]) ).
thf(f1956,plain,
eta1 = $true,
inference(cnf_transformation,[],[f1174]) ).
thf(f2033,plain,
infuncsetfunc = $true,
inference(cnf_transformation,[],[f1174]) ).
thf(f2359,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( infuncsetfunc != $true )
| ( $true
= ( func @ X5 @ X4 @ X3 ) )
| ( $true
!= ( in @ X3 @ ( funcSet @ X5 @ X4 ) ) ) ),
inference(cnf_transformation,[],[f1379]) ).
thf(f2656,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( func @ X5 @ X4 @ X3 ) )
| ( ( lam @ X5 @ X4
@ ^ [Y0: $i] : ( ap @ X5 @ X4 @ X3 @ Y0 ) )
= X3 )
| ( eta1 != $true ) ),
inference(cnf_transformation,[],[f1568]) ).
thf(f2789,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( func @ X5 @ X4 @ X3 ) )
| ( ( lam @ X5 @ X4 @ ( ap @ X5 @ X4 @ X3 ) )
= X3 )
| ( eta1 != $true ) ),
inference(beta-eta_normalization,[],[f2656]) ).
thf(f2824,plain,
( sK241
!= ( lam @ sK239 @ sK240 @ ( ap @ sK239 @ sK240 @ sK241 ) ) ),
inference(beta-eta_normalization,[],[f1908]) ).
thf(f3480,definition,
( spl665_139
<=> ( eta1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl665_139])],[avatar_definition]) ).
thf(f3587,definition,
( spl665_163
<=> ( infuncsetfunc = $true ) ),
introduced(definition,[new_symbols(definition,[spl665_163])],[avatar_definition]) ).
thf(f3590,plain,
spl665_163,
inference(avatar_split_clause,[],[f2033,f3587]) ).
thf(f3813,plain,
spl665_139,
inference(avatar_split_clause,[],[f1956,f3480]) ).
thf(f5122,definition,
( spl665_500
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( $true
!= ( func @ X5 @ X4 @ X3 ) )
| ( ( lam @ X5 @ X4 @ ( ap @ X5 @ X4 @ X3 ) )
= X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl665_500])],[avatar_definition]) ).
thf(f5123,plain,
( ! [X3: $i,X4: $i,X5: $i] :
( ( ( lam @ X5 @ X4 @ ( ap @ X5 @ X4 @ X3 ) )
= X3 )
| ( $true
!= ( func @ X5 @ X4 @ X3 ) ) )
| ~ spl665_500 ),
inference(avatar_component_clause,[],[f5122]) ).
thf(f5124,plain,
( ~ spl665_139
| spl665_500 ),
inference(avatar_split_clause,[],[f2789,f5122,f3480]) ).
thf(f6335,definition,
( spl665_753
<=> ( sK241
= ( lam @ sK239 @ sK240 @ ( ap @ sK239 @ sK240 @ sK241 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl665_753])],[avatar_definition]) ).
thf(f6337,plain,
( ( sK241
!= ( lam @ sK239 @ sK240 @ ( ap @ sK239 @ sK240 @ sK241 ) ) )
| spl665_753 ),
inference(avatar_component_clause,[],[f6335]) ).
thf(f6338,plain,
~ spl665_753,
inference(avatar_split_clause,[],[f2824,f6335]) ).
thf(f6791,definition,
( spl665_845
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( $true
= ( func @ X5 @ X4 @ X3 ) )
| ( $true
!= ( in @ X3 @ ( funcSet @ X5 @ X4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl665_845])],[avatar_definition]) ).
thf(f6792,plain,
( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( funcSet @ X5 @ X4 ) ) )
| ( $true
= ( func @ X5 @ X4 @ X3 ) ) )
| ~ spl665_845 ),
inference(avatar_component_clause,[],[f6791]) ).
thf(f6793,plain,
( ~ spl665_163
| spl665_845 ),
inference(avatar_split_clause,[],[f2359,f6791,f3587]) ).
thf(f6982,definition,
( spl665_884
<=> ( $true
= ( in @ sK241 @ ( funcSet @ sK239 @ sK240 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl665_884])],[avatar_definition]) ).
thf(f6984,plain,
( ( $true
= ( in @ sK241 @ ( funcSet @ sK239 @ sK240 ) ) )
| ~ spl665_884 ),
inference(avatar_component_clause,[],[f6982]) ).
thf(f6985,plain,
spl665_884,
inference(avatar_split_clause,[],[f1907,f6982]) ).
thf(f9355,plain,
( ( $true != $true )
| ( $true
= ( func @ sK239 @ sK240 @ sK241 ) )
| ~ spl665_845
| ~ spl665_884 ),
inference(superposition,[],[f6792,f6984]) ).
thf(f9373,plain,
( ( $true
= ( func @ sK239 @ sK240 @ sK241 ) )
| ~ spl665_845
| ~ spl665_884 ),
inference(trivial_inequality_removal,[],[f9355]) ).
thf(f9390,definition,
( spl665_1048
<=> ( $true
= ( func @ sK239 @ sK240 @ sK241 ) ) ),
introduced(definition,[new_symbols(definition,[spl665_1048])],[avatar_definition]) ).
thf(f9392,plain,
( ( $true
= ( func @ sK239 @ sK240 @ sK241 ) )
| ~ spl665_1048 ),
inference(avatar_component_clause,[],[f9390]) ).
thf(f9393,plain,
( spl665_1048
| ~ spl665_845
| ~ spl665_884 ),
inference(avatar_split_clause,[],[f9373,f6982,f6791,f9390]) ).
thf(f10520,plain,
( ( $true
!= ( func @ sK239 @ sK240 @ sK241 ) )
| ( sK241 != sK241 )
| ~ spl665_500
| spl665_753 ),
inference(superposition,[],[f6337,f5123]) ).
thf(f10521,plain,
( ( $true
!= ( func @ sK239 @ sK240 @ sK241 ) )
| ~ spl665_500
| spl665_753 ),
inference(trivial_inequality_removal,[],[f10520]) ).
thf(f10522,plain,
( $false
| ~ spl665_500
| spl665_753
| ~ spl665_1048 ),
inference(forward_subsumption_resolution,[],[f10521,f9392]) ).
thf(f10523,plain,
( ~ spl665_500
| spl665_753
| ~ spl665_1048 ),
inference(avatar_contradiction_clause,[],[f10522]) ).
cnf(s99,plain,
spl665_163,
inference(sat_conversion,[],[f3590]) ).
cnf(s137,plain,
spl665_139,
inference(sat_conversion,[],[f3813]) ).
cnf(s394,plain,
( ~ spl665_139
| spl665_500 ),
inference(sat_conversion,[],[f5124]) ).
cnf(s689,plain,
~ spl665_753,
inference(sat_conversion,[],[f6338]) ).
cnf(s806,plain,
( ~ spl665_163
| spl665_845 ),
inference(sat_conversion,[],[f6793]) ).
cnf(s855,plain,
spl665_884,
inference(sat_conversion,[],[f6985]) ).
cnf(s1081,plain,
( ~ spl665_845
| ~ spl665_884
| spl665_1048 ),
inference(sat_conversion,[],[f9393]) ).
cnf(s1091,plain,
( ~ spl665_500
| spl665_753
| ~ spl665_1048 ),
inference(sat_conversion,[],[f10523]) ).
cnf(s1317,plain,
spl665_500,
inference(rat,[],[s394,s137]) ).
cnf(s1318,plain,
~ spl665_1048,
inference(rat,[],[s1091,s689,s1317]) ).
cnf(s1319,plain,
~ spl665_845,
inference(rat,[],[s1081,s855,s1318]) ).
cnf(s1320,plain,
~ spl665_163,
inference(rat,[],[s806,s1319]) ).
cnf(s1346,plain,
$false,
inference(rat,[],[s99,s1320]) ).
thf(f10524,plain,
$false,
inference(avatar_sat_refutation,[],[s1346]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU699^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n007.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 14:09:41 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.21/0.29 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.30/0.45 % (3424867)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.30/0.45 % (3424875)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=3384999613: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)
% 0.30/0.45 % (3424874)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2417143284:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.30/0.45 % (3424873)lrs+10_16_si=on:nwc=1.5:random_seed=1121803303:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.30/0.45 % (3424872)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=758562560:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.30/0.45 % (3424876)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=956654912:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.30/0.45 % (3424874)Instruction limit reached!
% 0.30/0.45 % (3424874)------------------------------
% 0.30/0.45 % (3424874)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.45 % (3424874)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.45 % (3424874)CaDiCaL version: 2.1.3
% 0.30/0.45 % (3424874)Termination reason: Instruction limit
% 0.30/0.45 % (3424874)Termination phase: shuffling
% 0.30/0.45 % (3424874)Time elapsed: 0.002 s
% 0.30/0.45 % (3424874)Peak memory usage: 10 MB
% 0.30/0.45 % (3424874)Instructions burned: 4 (million)
% 0.30/0.45 % (3424873)Instruction limit reached!
% 0.30/0.45 % (3424873)------------------------------
% 0.30/0.45 % (3424873)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.45 % (3424873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.45 % (3424873)CaDiCaL version: 2.1.3
% 0.30/0.45 % (3424873)Termination reason: Instruction limit
% 0.30/0.45 % (3424873)Termination phase: shuffling
% 0.30/0.45 % (3424873)Time elapsed: 0.011 s
% 0.30/0.45 % (3424873)Peak memory usage: 10 MB
% 0.30/0.45 % (3424873)Instructions burned: 23 (million)
% 0.30/0.45 % (3424878)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.30/0.45 % (3424878)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
% 0.30/0.45 % (3424876)Instruction limit reached!
% 0.30/0.45 % (3424876)------------------------------
% 0.30/0.45 % (3424876)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.45 % (3424876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.45 % (3424876)CaDiCaL version: 2.1.3
% 0.30/0.45 % (3424876)Termination reason: Instruction limit
% 0.30/0.45 % (3424876)Termination phase: Property scanning
% 0.30/0.45 % (3424876)Time elapsed: 0.011 s
% 0.30/0.45 % (3424876)Peak memory usage: 10 MB
% 0.30/0.45 % (3424876)Instructions burned: 24 (million)
% 0.30/0.45 % (3424878)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=2939218542:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.30/0.45 % (3424877)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1340798345:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.30/0.45 % (3424884)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1648265813:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.30/0.45 % (3424884)Instruction limit reached!
% 0.30/0.45 % (3424884)------------------------------
% 0.30/0.45 % (3424884)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.30/0.45 % (3424884)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/0.45 % (3424884)CaDiCaL version: 2.1.3
% 0.30/0.45 % (3424884)Termination reason: Instruction limit
% 0.30/0.45 % (3424884)Termination phase: shuffling
% 0.30/0.45 % (3424884)Time elapsed: 0.003 s
% 0.30/0.45 % (3424884)Peak memory usage: 10 MB
% 0.30/0.45 % (3424884)Instructions burned: 4 (million)
% 0.30/0.45 % (3424886)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.04/0.49 % (3424885)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=790695388:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.04/0.49 % (3424886)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2101627095:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.04/0.49 % (3424885)Instruction limit reached!
% 1.04/0.49 % (3424885)------------------------------
% 1.04/0.49 % (3424885)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.49 % (3424885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.49 % (3424885)CaDiCaL version: 2.1.3
% 1.04/0.49 % (3424885)Termination reason: Instruction limit
% 1.04/0.49 % (3424885)Termination phase: shuffling
% 1.04/0.49 % (3424886)Instruction limit reached!
% 1.04/0.49 % (3424886)------------------------------
% 1.04/0.49 % (3424886)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.49 % (3424885)Time elapsed: 0.004 s
% 1.04/0.49 % (3424885)Peak memory usage: 10 MB
% 1.04/0.49 % (3424885)Instructions burned: 7 (million)
% 1.04/0.49 % (3424886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.49 % (3424886)CaDiCaL version: 2.1.3
% 1.04/0.49 % (3424886)Termination reason: Instruction limit
% 1.04/0.49 % (3424886)Termination phase: shuffling
% 1.04/0.49 % (3424886)Time elapsed: 0.003 s
% 1.04/0.49 % (3424886)Peak memory usage: 10 MB
% 1.04/0.49 % (3424886)Instructions burned: 7 (million)
% 1.04/0.49 % (3424872)Instruction limit reached!
% 1.04/0.49 % (3424872)------------------------------
% 1.04/0.49 % (3424872)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.49 % (3424872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.49 % (3424872)CaDiCaL version: 2.1.3
% 1.04/0.49 % (3424872)Termination reason: Instruction limit
% 1.04/0.49 % (3424872)Termination phase: Property scanning
% 1.04/0.49 % (3424872)Time elapsed: 0.042 s
% 1.04/0.49 % (3424872)Peak memory usage: 13 MB
% 1.04/0.49 % (3424872)Instructions burned: 90 (million)
% 1.04/0.49 % (3424890)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=228232843:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.04/0.49 % (3424877)Instruction limit reached!
% 1.04/0.49 % (3424877)------------------------------
% 1.04/0.49 % (3424877)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.49 % (3424877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.49 % (3424877)CaDiCaL version: 2.1.3
% 1.04/0.49 % (3424877)Termination reason: Instruction limit
% 1.04/0.49 % (3424877)Termination phase: Preprocessing 3
% 1.04/0.49 % (3424877)Time elapsed: 0.036 s
% 1.04/0.49 % (3424877)Peak memory usage: 12 MB
% 1.04/0.49 % (3424877)Instructions burned: 76 (million)
% 1.04/0.49 % (3424893)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.04/0.49 % (3424893)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.04/0.49 % (3424890)Instruction limit reached!
% 1.04/0.49 % (3424890)------------------------------
% 1.04/0.49 % (3424890)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.49 % (3424890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.49 % (3424890)CaDiCaL version: 2.1.3
% 1.04/0.49 % (3424890)Termination reason: Instruction limit
% 1.04/0.49 % (3424890)Termination phase: shuffling
% 1.04/0.49 % (3424890)Time elapsed: 0.007 s
% 1.04/0.49 % (3424890)Peak memory usage: 10 MB
% 1.04/0.49 % (3424890)Instructions burned: 14 (million)
% 1.04/0.49 % (3424893)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2279904716:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.04/0.49 % (3424894)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=2276219453:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.04/0.49 % (3424895)lrs+10_1_si=on:cs=on:random_seed=1577539400:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 1.04/0.49 % (3424895)Instruction limit reached!
% 1.04/0.51 % (3424895)------------------------------
% 1.04/0.51 % (3424895)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.51 % (3424895)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.51 % (3424895)CaDiCaL version: 2.1.3
% 1.04/0.51 % (3424895)Termination reason: Instruction limit
% 1.04/0.51 % (3424895)Termination phase: shuffling
% 1.04/0.51 % (3424895)Time elapsed: 0.004 s
% 1.04/0.51 % (3424895)Peak memory usage: 10 MB
% 1.04/0.51 % (3424895)Instructions burned: 9 (million)
% 1.04/0.51 % (3424897)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.04/0.51 % (3424893)Instruction limit reached!
% 1.04/0.51 % (3424893)------------------------------
% 1.04/0.51 % (3424893)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.51 % (3424893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.51 % (3424893)CaDiCaL version: 2.1.3
% 1.04/0.51 % (3424893)Termination reason: Instruction limit
% 1.04/0.51 % (3424893)Termination phase: shuffling
% 1.04/0.51 % (3424893)Time elapsed: 0.013 s
% 1.04/0.51 % (3424893)Peak memory usage: 10 MB
% 1.04/0.51 % (3424893)Instructions burned: 29 (million)
% 1.04/0.51 % (3424898)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3661282421:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.04/0.51 % (3424897)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=3774518404:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.04/0.51 % (3424897)Instruction limit reached!
% 1.04/0.51 % (3424897)------------------------------
% 1.04/0.51 % (3424897)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.51 % (3424897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.51 % (3424897)CaDiCaL version: 2.1.3
% 1.04/0.51 % (3424897)Termination reason: Instruction limit
% 1.04/0.51 % (3424897)Termination phase: shuffling
% 1.04/0.51 % (3424897)Time elapsed: 0.003 s
% 1.04/0.51 % (3424897)Peak memory usage: 10 MB
% 1.04/0.51 % (3424897)Instructions burned: 5 (million)
% 1.04/0.51 % (3424878)Instruction limit reached!
% 1.04/0.51 % (3424878)------------------------------
% 1.04/0.51 % (3424878)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.51 % (3424878)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.51 % (3424878)CaDiCaL version: 2.1.3
% 1.04/0.51 % (3424878)Termination reason: Instruction limit
% 1.04/0.51 % (3424878)Termination phase: Saturation
% 1.04/0.51 % (3424878)Time elapsed: 0.068 s
% 1.04/0.51 % (3424878)Peak memory usage: 14 MB
% 1.04/0.51 % (3424878)Instructions burned: 158 (million)
% 1.04/0.51 % (3424907)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1012158702:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.04/0.51 % (3424908)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2517439605:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.04/0.51 % (3424898)Instruction limit reached!
% 1.04/0.51 % (3424898)------------------------------
% 1.04/0.51 % (3424898)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.51 % (3424898)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.51 % (3424898)CaDiCaL version: 2.1.3
% 1.04/0.51 % (3424898)Termination reason: Instruction limit
% 1.04/0.51 % (3424898)Termination phase: Preprocessing 1
% 1.04/0.51 % (3424898)Time elapsed: 0.018 s
% 1.04/0.51 % (3424898)Peak memory usage: 11 MB
% 1.04/0.51 % (3424898)Instructions burned: 39 (million)
% 1.04/0.51 % (3424894)Instruction limit reached!
% 1.04/0.51 % (3424894)------------------------------
% 1.04/0.51 % (3424894)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.51 % (3424894)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.51 % (3424894)CaDiCaL version: 2.1.3
% 1.04/0.51 % (3424894)Termination reason: Instruction limit
% 1.04/0.51 % (3424894)Termination phase: Property scanning
% 1.04/0.51 % (3424894)Time elapsed: 0.037 s
% 1.04/0.51 % (3424894)Peak memory usage: 11 MB
% 1.04/0.51 % (3424894)Instructions burned: 87 (million)
% 1.04/0.51 % (3424914)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3182239599:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.04/0.51 % (3424908)Instruction limit reached!
% 1.04/0.51 % (3424908)------------------------------
% 1.04/0.51 % (3424908)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.51 % (3424908)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.51 % (3424908)CaDiCaL version: 2.1.3
% 1.04/0.51 % (3424908)Termination reason: Instruction limit
% 1.04/0.51 % (3424908)Termination phase: Property scanning
% 1.04/0.51 % (3424908)Time elapsed: 0.012 s
% 1.04/0.51 % (3424908)Peak memory usage: 10 MB
% 1.04/0.51 % (3424908)Instructions burned: 26 (million)
% 1.04/0.51 % (3424914)Instruction limit reached!
% 1.04/0.51 % (3424914)------------------------------
% 1.04/0.51 % (3424914)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.51 % (3424914)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.51 % (3424914)CaDiCaL version: 2.1.3
% 1.04/0.51 % (3424914)Termination reason: Instruction limit
% 1.04/0.51 % (3424914)Termination phase: shuffling
% 1.04/0.51 % (3424914)Time elapsed: 0.007 s
% 1.04/0.51 % (3424914)Peak memory usage: 10 MB
% 1.04/0.51 % (3424914)Instructions burned: 16 (million)
% 1.04/0.51 % (3424916)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1549073524:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.04/0.51 % (3424920)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3248345368: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)
% 1.04/0.51 % (3424919)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1090200558:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.04/0.51 % (3424920)Instruction limit reached!
% 1.04/0.51 % (3424920)------------------------------
% 1.04/0.51 % (3424920)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.51 % (3424920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.51 % (3424920)CaDiCaL version: 2.1.3
% 1.04/0.51 % (3424920)Termination reason: Instruction limit
% 1.04/0.51 % (3424920)Termination phase: shuffling
% 1.04/0.51 % (3424920)Time elapsed: 0.002 s
% 1.04/0.51 % (3424920)Peak memory usage: 10 MB
% 1.04/0.51 % (3424920)Instructions burned: 3 (million)
% 1.04/0.51 % (3424924)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=4261376154:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.04/0.51 % (3424919)Instruction limit reached!
% 1.04/0.51 % (3424919)------------------------------
% 1.04/0.51 % (3424919)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.51 % (3424919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.51 % (3424919)CaDiCaL version: 2.1.3
% 1.04/0.51 % (3424919)Termination reason: Instruction limit
% 1.04/0.51 % (3424919)Termination phase: shuffling
% 1.04/0.51 % (3424919)Time elapsed: 0.007 s
% 1.04/0.51 % (3424919)Peak memory usage: 10 MB
% 1.04/0.51 % (3424919)Instructions burned: 15 (million)
% 1.04/0.51 % (3424927)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2859861698:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.04/0.51 % (3424924)Instruction limit reached!
% 1.04/0.51 % (3424924)------------------------------
% 1.04/0.51 % (3424924)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.51 % (3424924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.51 % (3424924)CaDiCaL version: 2.1.3
% 1.04/0.51 % (3424924)Termination reason: Instruction limit
% 1.04/0.51 % (3424924)Termination phase: shuffling
% 1.04/0.51 % (3424924)Time elapsed: 0.012 s
% 1.04/0.51 % (3424924)Peak memory usage: 10 MB
% 1.04/0.51 % (3424924)Instructions burned: 26 (million)
% 1.04/0.51 % (3424932)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=1428353321:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.04/0.51 % (3424927)Instruction limit reached!
% 1.04/0.51 % (3424927)------------------------------
% 1.04/0.51 % (3424927)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.51 % (3424927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.51 % (3424927)CaDiCaL version: 2.1.3
% 1.04/0.51 % (3424927)Termination reason: Instruction limit
% 1.04/0.51 % (3424927)Termination phase: shuffling
% 1.04/0.51 % (3424927)Time elapsed: 0.010 s
% 1.04/0.51 % (3424927)Peak memory usage: 10 MB
% 1.04/0.51 % (3424927)Instructions burned: 23 (million)
% 1.04/0.51 % (3424935)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.04/0.51 % (3424935)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.04/0.51 % (3424935)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=2335444186:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.04/0.51 % (3424935)Instruction limit reached!
% 1.04/0.51 % (3424935)------------------------------
% 1.04/0.51 % (3424935)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.51 % (3424935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.51 % (3424935)CaDiCaL version: 2.1.3
% 1.04/0.51 % (3424935)Termination reason: Instruction limit
% 1.04/0.51 % (3424935)Termination phase: shuffling
% 1.04/0.51 % (3424935)Time elapsed: 0.007 s
% 1.04/0.51 % (3424935)Peak memory usage: 10 MB
% 1.04/0.51 % (3424935)Instructions burned: 16 (million)
% 1.04/0.51 % (3424939)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.04/0.51 % (3424875) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3424867-3424875"...
% 1.04/0.51 % (3424939)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=3411266480:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.04/0.51 % (3424942)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=4275162952:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.04/0.51 % (3424875)...printing done.
% 1.04/0.51 % (3424939)Instruction limit reached!
% 1.04/0.51 % (3424939)------------------------------
% 1.04/0.51 % (3424939)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.51 % (3424939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.51 % (3424939)CaDiCaL version: 2.1.3
% 1.04/0.51 % (3424939)Termination reason: Instruction limit
% 1.04/0.51 % (3424939)Termination phase: shuffling
% 1.04/0.51 % (3424939)Time elapsed: 0.004 s
% 1.04/0.51 % (3424939)Peak memory usage: 10 MB
% 1.04/0.51 % (3424939)Instructions burned: 8 (million)
% 1.04/0.51 % (3424875)Refutation found. Thanks to Tanya!
% 1.04/0.51 % SZS status Theorem for theBenchmark
% 1.04/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 1.04/0.52 % (3424875)------------------------------
% 1.04/0.52 % (3424875)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.04/0.52 % (3424875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.04/0.52 % (3424875)CaDiCaL version: 2.1.3
% 1.04/0.52 % (3424875)Termination reason: Refutation
% 1.04/0.52 % (3424875)Time elapsed: 0.162 s
% 1.04/0.52 % (3424875)Peak memory usage: 20 MB
% 1.04/0.52 % (3424875)Instructions burned: 559 (million)
% 1.04/0.52 % (3424867)Success in time 0.212 s
% 1.04/0.52 % Vampire exiting
%------------------------------------------------------------------------------