%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU620^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 08:32:42 AM UTC 2026
% Result : Theorem 3.00s 0.75s
% Output : Refutation 3.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 72 ( 40 unt; 0 typ; 4 def)
% Number of atoms : 2622 ( 661 equ; 0 cnn)
% Maximal formula atoms : 137 ( 36 avg)
% Number of connectives : 1928 ( 12 ~; 34 |; 433 &; 860 @)
% ( 0 <=>; 544 =>; 0 <=; 0 <~>)
% Maximal formula depth : 143 ( 16 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 644 ( 639 usr; 281 con; 0-4 aty)
% ( 28 !!; 17 ??; 0 @@+; 0 @@-)
% Number of variables : 128 ( 71 ^; 49 !; 8 ?; 128 :)
% 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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_160,type,
vAND: $o > $o > $o ).
thf(func_def_161,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_162,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_163,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_164,type,
vIMP: $o > $o > $o ).
thf(func_def_165,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_166,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_167,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_168,type,
vIFF: $o > $o > $o ).
thf(func_def_169,type,
vNOT: $o > $o ).
thf(func_def_170,type,
vOR: $o > $o > $o ).
thf(func_def_171,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_172,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_175,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_178,type,
sF2: $o ).
thf(func_def_179,type,
sF3: $o ).
thf(func_def_180,type,
sF4: $o ).
thf(func_def_181,type,
sF5: $o ).
thf(func_def_182,type,
sF6: $o ).
thf(func_def_183,type,
sF7: $o ).
thf(func_def_184,type,
sF8: $o ).
thf(func_def_185,type,
sF9: $o ).
thf(func_def_186,type,
sF10: $o ).
thf(func_def_187,type,
sF11: $o ).
thf(func_def_188,type,
sF12: $o ).
thf(func_def_189,type,
sF13: $o ).
thf(func_def_190,type,
sF14: $o ).
thf(func_def_191,type,
sF15: $o ).
thf(func_def_192,type,
sF16: $o ).
thf(func_def_193,type,
sF17: $o ).
thf(func_def_194,type,
sF18: $o ).
thf(func_def_195,type,
sF19: $o ).
thf(func_def_196,type,
sF20: $o ).
thf(func_def_197,type,
sF21: $o ).
thf(func_def_198,type,
sF22: $o ).
thf(func_def_199,type,
sF23: $o ).
thf(func_def_200,type,
sF24: $o ).
thf(func_def_201,type,
sF25: $o ).
thf(func_def_202,type,
sF26: $o ).
thf(func_def_203,type,
sF27: $o ).
thf(func_def_204,type,
sF28: $o ).
thf(func_def_205,type,
sF29: $o ).
thf(func_def_207,type,
sF31: $o ).
thf(func_def_208,type,
sF32: $o ).
thf(func_def_209,type,
sF33: $o ).
thf(func_def_210,type,
sF34: $o ).
thf(func_def_211,type,
sF35: $o ).
thf(func_def_212,type,
sF36: $o ).
thf(func_def_213,type,
sF37: $o ).
thf(func_def_214,type,
sF38: $o ).
thf(func_def_215,type,
sF39: $o ).
thf(func_def_216,type,
sF40: $o ).
thf(func_def_217,type,
sF41: $o ).
thf(func_def_218,type,
sF42: $o ).
thf(func_def_219,type,
sF43: $o ).
thf(func_def_220,type,
sF44: $o ).
thf(func_def_221,type,
sF45: $o ).
thf(func_def_222,type,
sF46: $o ).
thf(func_def_223,type,
sF47: $o ).
thf(func_def_224,type,
sF48: $o ).
thf(func_def_225,type,
sF49: $o ).
thf(func_def_226,type,
sF50: $o ).
thf(func_def_227,type,
sF51: $o ).
thf(func_def_228,type,
sF52: $o ).
thf(func_def_229,type,
sF53: $o ).
thf(func_def_230,type,
sF54: $o ).
thf(func_def_231,type,
sF55: $o ).
thf(func_def_232,type,
sF56: $o ).
thf(func_def_233,type,
sF57: $o ).
thf(func_def_234,type,
sF58: $o ).
thf(func_def_235,type,
sF59: $o ).
thf(func_def_236,type,
sF60: $o ).
thf(func_def_237,type,
sF61: $o ).
thf(func_def_238,type,
sF62: $o ).
thf(func_def_239,type,
sF63: $o ).
thf(func_def_240,type,
sF64: $o ).
thf(func_def_241,type,
sF65: $o ).
thf(func_def_242,type,
sF66: $o ).
thf(func_def_243,type,
sF67: $o ).
thf(func_def_244,type,
sF68: $o ).
thf(func_def_245,type,
sF69: $o ).
thf(func_def_246,type,
sF70: $o ).
thf(func_def_247,type,
sF71: $o ).
thf(func_def_248,type,
sF72: $o ).
thf(func_def_249,type,
sF73: $o ).
thf(func_def_250,type,
sF74: $o ).
thf(func_def_251,type,
sF75: $o ).
thf(func_def_252,type,
sF76: $o ).
thf(func_def_253,type,
sF77: $o ).
thf(func_def_254,type,
sF78: $o ).
thf(func_def_255,type,
sF79: $o ).
thf(func_def_256,type,
sF80: $o ).
thf(func_def_257,type,
sF81: $o ).
thf(func_def_258,type,
sF82: $o ).
thf(func_def_259,type,
sF83: $o ).
thf(func_def_260,type,
sF84: $o ).
thf(func_def_261,type,
sF85: $o ).
thf(func_def_262,type,
sF86: $o ).
thf(func_def_263,type,
sF87: $o ).
thf(func_def_264,type,
sF88: $o ).
thf(func_def_265,type,
sF89: $o ).
thf(func_def_266,type,
sF90: $o ).
thf(func_def_267,type,
sF91: $o ).
thf(func_def_268,type,
sF92: $o ).
thf(func_def_269,type,
sF93: $o ).
thf(func_def_270,type,
sF94: $o ).
thf(func_def_271,type,
sF95: $o ).
thf(func_def_272,type,
sF96: $o ).
thf(func_def_273,type,
sF97: $o ).
thf(func_def_274,type,
sF98: $o ).
thf(func_def_275,type,
sF99: $o ).
thf(func_def_276,type,
sF100: $o ).
thf(func_def_277,type,
sF101: $o ).
thf(func_def_278,type,
sF102: $o ).
thf(func_def_279,type,
sF103: $o ).
thf(func_def_280,type,
sF104: $o ).
thf(func_def_281,type,
sF105: $o ).
thf(func_def_282,type,
sF106: $o ).
thf(func_def_283,type,
sF107: $o ).
thf(func_def_284,type,
sF108: $o ).
thf(func_def_285,type,
sF109: $o ).
thf(func_def_286,type,
sF110: $o ).
thf(func_def_287,type,
sF111: $o ).
thf(func_def_288,type,
sF112: $o ).
thf(func_def_289,type,
sF113: $o ).
thf(func_def_290,type,
sF114: $o ).
thf(func_def_291,type,
sF115: $o ).
thf(func_def_292,type,
sF116: $o ).
thf(func_def_293,type,
sF117: $o ).
thf(func_def_294,type,
sF118: $o ).
thf(func_def_295,type,
sF119: $o ).
thf(func_def_296,type,
sF120: $o ).
thf(func_def_297,type,
sF121: $o ).
thf(func_def_298,type,
sF122: $o ).
thf(func_def_299,type,
sF123: $o ).
thf(func_def_300,type,
sF124: $o ).
thf(func_def_301,type,
sF125: $o ).
thf(func_def_302,type,
sF126: $o ).
thf(func_def_303,type,
sF127: $o ).
thf(func_def_304,type,
sF128: $o ).
thf(func_def_305,type,
sF129: $o ).
thf(func_def_306,type,
sF130: $o ).
thf(func_def_308,type,
sF132: $o ).
thf(func_def_311,type,
sK135: $i > $i > $i ).
thf(func_def_319,type,
sK143: $i > $i > $i ).
thf(func_def_323,type,
sK147: $i > $i > $i ).
thf(func_def_327,type,
sK151: $i > $i ).
thf(func_def_329,type,
sK153: $i > $i > $o ).
thf(func_def_330,type,
sK154: $i > $i ).
thf(func_def_331,type,
sK155: $i > $i ).
thf(func_def_332,type,
sK156: $i > $i ).
thf(func_def_333,type,
sK157: $i > ( $i > $i > $o ) > $i ).
thf(func_def_334,type,
sK158: $i > ( $i > $i > $o ) > $i ).
thf(func_def_335,type,
sK159: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_336,type,
sK160: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_337,type,
sK161: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_338,type,
sK162: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_341,type,
sK165: $i > $i ).
thf(func_def_342,type,
sK166: $i > $i ).
thf(func_def_344,type,
sK168: $i > $i ).
thf(func_def_345,type,
sK169: $i > $i ).
thf(func_def_346,type,
sK170: $i > $i ).
thf(func_def_347,type,
sK171: $i > $i ).
thf(func_def_348,type,
sK172: $i > $i ).
thf(func_def_349,type,
sK173: $i > $i ).
thf(func_def_350,type,
sK174: $i > $i ).
thf(func_def_351,type,
sK175: $i > $i ).
thf(func_def_352,type,
sK176: $i > $i ).
thf(func_def_353,type,
sK177: $i > $i ).
thf(func_def_354,type,
sK178: $i > $i ).
thf(func_def_355,type,
sK179: $i > $i ).
thf(func_def_356,type,
sK180: $i > $i ).
thf(func_def_357,type,
sK181: $i > $i ).
thf(func_def_358,type,
sK182: $i > $i ).
thf(func_def_359,type,
sK183: $i > $i ).
thf(func_def_360,type,
sK184: $i > $i ).
thf(func_def_361,type,
sK185: $i > $i ).
thf(func_def_362,type,
sK186: $i > $i ).
thf(func_def_363,type,
sK187: $i > $i ).
thf(func_def_364,type,
sK188: $i > $i ).
thf(func_def_365,type,
sK189: $i > $i > $i > $i ).
thf(func_def_366,type,
sK190: $i > $i > $i ).
thf(func_def_367,type,
sK191: $i > $i > $i > $i ).
thf(func_def_368,type,
sK192: $i > $i > $i > $i ).
thf(func_def_369,type,
sK193: $i > $i > $i ).
thf(func_def_370,type,
sK194: $i > $i > $i > $i ).
thf(func_def_371,type,
sK195: $i > $i > $i > $i ).
thf(func_def_372,type,
sK196: $i > $i > $i ).
thf(func_def_373,type,
sK197: $i > $i > $i > $i ).
thf(func_def_374,type,
sK198: $i > $i > $i > $i ).
thf(func_def_375,type,
sK199: $i > $i > $i ).
thf(func_def_376,type,
sK200: $i > $i > $i > $i ).
thf(func_def_377,type,
sK201: $i > $i > $i > $i ).
thf(func_def_378,type,
sK202: $i > $i > $i ).
thf(func_def_379,type,
sK203: $i > $i > $i > $i ).
thf(func_def_380,type,
sK204: $i > $i > $i > $i ).
thf(func_def_381,type,
sK205: $i > $i > $i ).
thf(func_def_382,type,
sK206: $i > $i > $i > $i ).
thf(func_def_383,type,
sK207: $i > $i > $i > $i ).
thf(func_def_384,type,
sK208: $i > $i > $i ).
thf(func_def_385,type,
sK209: $i > $i > $i > $i ).
thf(func_def_386,type,
sK210: $i > $i > $i > $i ).
thf(func_def_387,type,
sK211: $i > $i > $i ).
thf(func_def_388,type,
sK212: $i > $i > $i > $i ).
thf(func_def_389,type,
sK213: $i > $i ).
thf(func_def_390,type,
sK214: $i > $i > $i > $i ).
thf(func_def_391,type,
sK215: $i > $i > $i ).
thf(func_def_392,type,
sK216: $i > $i > $i > $i ).
thf(func_def_393,type,
sK217: $i > $i > $i ).
thf(func_def_394,type,
sK218: $i > $i > $i > $i ).
thf(func_def_395,type,
sK219: $i > $i > $i > $i ).
thf(func_def_396,type,
sK220: $i > $i > $i ).
thf(func_def_397,type,
sK221: $i > $i > $i > $i ).
thf(func_def_398,type,
sK222: $i > $i > $i ).
thf(func_def_399,type,
sK223: $i > $i > $i > $i ).
thf(func_def_400,type,
sK224: $i > $i > $i > $i ).
thf(func_def_401,type,
sK225: $i > $i > $i ).
thf(func_def_402,type,
sK226: $i > $i > $i > $i ).
thf(func_def_403,type,
sK227: $i > $i > $i ).
thf(func_def_404,type,
sK228: $i > $i > $i > $i ).
thf(func_def_405,type,
sK229: $i > $i > $i > $i ).
thf(func_def_406,type,
sK230: $i > $i > $i ).
thf(func_def_407,type,
sK231: $i > $i > $i > $i ).
thf(func_def_408,type,
sK232: $i > $i > $i ).
thf(func_def_409,type,
sK233: $i > $i > $i > $i ).
thf(func_def_410,type,
sK234: $i > $i ).
thf(func_def_411,type,
sK235: $i > $i > $i > $i ).
thf(func_def_412,type,
sK236: $i > $i > $i ).
thf(func_def_413,type,
sK237: $i > $i > $i > $i ).
thf(func_def_414,type,
sK238: $i > $i > $i ).
thf(func_def_415,type,
sK239: $i > $i > $i > $i ).
thf(func_def_416,type,
sK240: $i > $i > $i > $i ).
thf(func_def_417,type,
sK241: $i > $i > $i ).
thf(func_def_418,type,
sK242: $i > $i > $i > $i ).
thf(func_def_419,type,
sK243: $i > $i > $i ).
thf(func_def_420,type,
sK244: $i > $i > $i > $i ).
thf(func_def_421,type,
sK245: $i > $i > $i > $i ).
thf(func_def_422,type,
sK246: $i > $i > $i ).
thf(func_def_423,type,
sK247: $i > $i > $i > $i ).
thf(func_def_424,type,
sK248: $i > $i > $i ).
thf(func_def_425,type,
sK249: $i > $i > $i > $i ).
thf(func_def_426,type,
sK250: $i > $i > $i > $i ).
thf(func_def_427,type,
sK251: $i > $i > $i ).
thf(func_def_428,type,
sK252: $i > $i > $i > $i ).
thf(func_def_429,type,
sK253: $i > $i > $i ).
thf(func_def_430,type,
sK254: $i > $i > $i > $i ).
thf(func_def_431,type,
sK255: $i > $i ).
thf(func_def_432,type,
sK256: $i > $i > $i > $i ).
thf(func_def_433,type,
sK257: $i > $i > $i ).
thf(func_def_434,type,
sK258: $i > $i > $i > $i ).
thf(func_def_435,type,
sK259: $i > $i > $i > $i ).
thf(func_def_436,type,
sK260: $i > $i > $i ).
thf(func_def_437,type,
sK261: $i > $i > $i > $i ).
thf(func_def_438,type,
sK262: $i > $i > $i > $i ).
thf(func_def_439,type,
sK263: $i > $i > $i ).
thf(func_def_440,type,
sK264: $i > $i > $i > $i ).
thf(func_def_441,type,
sK265: $i > $i > $i > $i ).
thf(func_def_442,type,
sK266: $i > $i > $i ).
thf(func_def_443,type,
sK267: $i > $i > $i > $i ).
thf(func_def_444,type,
sK268: $i > $i > $i > $i ).
thf(func_def_445,type,
sK269: $i > $i > $i ).
thf(func_def_446,type,
sK270: $i > $i > $i > $i ).
thf(func_def_447,type,
sK271: $i > $i > $i > $i ).
thf(func_def_448,type,
sK272: $i > $i > $i ).
thf(func_def_449,type,
sK273: $i > $i > $i > $i ).
thf(func_def_450,type,
sK274: $i > $i > $i > $i ).
thf(func_def_451,type,
sK275: $i > $i > $i ).
thf(func_def_452,type,
sK276: $i > $i > $i > $i ).
thf(func_def_453,type,
sK277: $i > $i > $i > $i ).
thf(func_def_454,type,
sK278: $i > $i > $i ).
thf(func_def_455,type,
sK279: $i > $i > $i > $i ).
thf(func_def_456,type,
sK280: $i > $i > $i > $i ).
thf(func_def_457,type,
sK281: $i > $i > $i ).
thf(func_def_458,type,
sK282: $i > $i > $i > $i ).
thf(func_def_459,type,
sK283: $i > $i > $i > $i ).
thf(func_def_460,type,
sK284: $i > $i > $i ).
thf(func_def_461,type,
sK285: $i > $i > $i > $i ).
thf(func_def_462,type,
sK286: $i > $i > $i > $i ).
thf(func_def_463,type,
sK287: $i > $i > $i ).
thf(func_def_464,type,
sK288: $i > $i > $i > $i ).
thf(func_def_465,type,
sK289: $i > $i > $i > $i ).
thf(func_def_466,type,
sK290: $i > $i > $i ).
thf(func_def_467,type,
sK291: $i > $i > $i > $i ).
thf(func_def_468,type,
sK292: $i > $i > $i > $i ).
thf(func_def_469,type,
sK293: $i > $i > $i ).
thf(func_def_470,type,
sK294: $i > $i > $i > $i ).
thf(func_def_471,type,
sK295: $i > $i > $i > $i ).
thf(func_def_472,type,
sK296: $i > $i > $i ).
thf(func_def_473,type,
sK297: $i > $i > $i > $i ).
thf(func_def_474,type,
sK298: $i > $i > $i > $i ).
thf(func_def_475,type,
sK299: $i > $i > $i ).
thf(func_def_476,type,
sK300: $i > $i > $i > $i ).
thf(func_def_477,type,
sK301: $i > $i > $i > $i ).
thf(func_def_478,type,
sK302: $i > $i > $i ).
thf(func_def_479,type,
sK303: $i > $i > $i > $i ).
thf(func_def_480,type,
sK304: $i > $i ).
thf(func_def_481,type,
sK305: $i > $i > $i > $i ).
thf(func_def_482,type,
sK306: $i > $i > $i ).
thf(func_def_483,type,
sK307: $i > $i > $i > $i ).
thf(func_def_484,type,
sK308: $i > $i > $i ).
thf(func_def_485,type,
sK309: $i > $i > $i > $i ).
thf(func_def_486,type,
sK310: $i > $i > $i > $i ).
thf(func_def_487,type,
sK311: $i > $i > $i ).
thf(func_def_488,type,
sK312: $i > $i > $i > $i ).
thf(func_def_489,type,
sK313: $i > $i > $i ).
thf(func_def_490,type,
sK314: $i > $i > $i > $i ).
thf(func_def_491,type,
sK315: $i > $i > $i > $i ).
thf(func_def_492,type,
sK316: $i > $i > $i ).
thf(func_def_493,type,
sK317: $i > $i > $i > $i ).
thf(func_def_494,type,
sK318: $i > $i > $i ).
thf(func_def_495,type,
sK319: $i > $i > $i > $i ).
thf(func_def_496,type,
sK320: $i > $i > $i > $i ).
thf(func_def_497,type,
sK321: $i > $i > $i ).
thf(func_def_498,type,
sK322: $i > $i > $i > $i ).
thf(func_def_499,type,
sK323: $i > $i > $i ).
thf(func_def_500,type,
sK324: $i > $i > $i > $i ).
thf(func_def_501,type,
sK325: $i > $i > $i > $i ).
thf(func_def_502,type,
sK326: $i > $i > $i ).
thf(func_def_503,type,
sK327: $i > $i > $i > $i ).
thf(func_def_504,type,
sK328: $i > $i > $i ).
thf(func_def_505,type,
sK329: $i > $i > $i > $i ).
thf(func_def_506,type,
sK330: $i > $i > $i > $i ).
thf(func_def_507,type,
sK331: $i > $i > $i ).
thf(func_def_508,type,
sK332: $i > $i > $i > $i ).
thf(func_def_509,type,
sK333: $i > $i > $i ).
thf(func_def_510,type,
sK334: $i > $i > $i > $i ).
thf(func_def_511,type,
sK335: $i > $i > $i > $i ).
thf(func_def_512,type,
sK336: $i > $i > $i ).
thf(func_def_513,type,
sK337: $i > $i > $i > $i ).
thf(func_def_514,type,
sK338: $i > $i > $i ).
thf(func_def_515,type,
sK339: $i > $i > $i > $i ).
thf(func_def_516,type,
sK340: $i > $i > $i > $i ).
thf(func_def_517,type,
sK341: $i > $i > $i ).
thf(func_def_518,type,
sK342: $i > $i > $i > $i ).
thf(func_def_519,type,
sK343: $i > $i > $i ).
thf(func_def_520,type,
sK344: $i > $i > $i > $i ).
thf(func_def_521,type,
sK345: $i > $i ).
thf(func_def_522,type,
sK346: $i > $i > $i > $i ).
thf(func_def_523,type,
sK347: $i > $i > $i ).
thf(func_def_524,type,
sK348: $i > $i > $i > $i ).
thf(func_def_525,type,
sK349: $i > $i > $i ).
thf(func_def_526,type,
sK350: $i > $i > $i > $i ).
thf(func_def_527,type,
sK351: $i > $i > $i > $i ).
thf(func_def_528,type,
sK352: $i > $i > $i ).
thf(func_def_529,type,
sK353: $i > $i > $i > $i ).
thf(func_def_530,type,
sK354: $i > $i > $i ).
thf(func_def_531,type,
sK355: $i > $i > $i > $i ).
thf(func_def_532,type,
sK356: $i > $i > $i > $i ).
thf(func_def_533,type,
sK357: $i > $i > $i ).
thf(func_def_534,type,
sK358: $i > $i > $i > $i ).
thf(func_def_535,type,
sK359: $i > $i > $i ).
thf(func_def_536,type,
sK360: $i > $i > $i > $i ).
thf(func_def_537,type,
sK361: $i > $i > $i > $i ).
thf(func_def_538,type,
sK362: $i > $i > $i ).
thf(func_def_539,type,
sK363: $i > $i > $i > $i ).
thf(func_def_540,type,
sK364: $i > $i > $i ).
thf(func_def_541,type,
sK365: $i > $i > $i > $i ).
thf(func_def_542,type,
sK366: $i > $i > $i > $i ).
thf(func_def_543,type,
sK367: $i > $i > $i ).
thf(func_def_544,type,
sK368: $i > $i > $i > $i ).
thf(func_def_545,type,
sK369: $i > $i > $i ).
thf(func_def_546,type,
sK370: $i > $i > $i > $i ).
thf(func_def_547,type,
sK371: $i > $i > $i > $i ).
thf(func_def_548,type,
sK372: $i > $i > $i ).
thf(func_def_549,type,
sK373: $i > $i > $i > $i ).
thf(func_def_550,type,
sK374: $i > $i > $i ).
thf(func_def_551,type,
sK375: $i > $i > $i > $i ).
thf(func_def_552,type,
sK376: $i > $i > $i > $i ).
thf(func_def_553,type,
sK377: $i > $i > $i ).
thf(func_def_554,type,
sK378: $i > $i > $i > $i ).
thf(func_def_555,type,
sK379: $i > $i > $i ).
thf(func_def_556,type,
sK380: $i > $i > $i > $i ).
thf(func_def_557,type,
sK381: $i > $i > $i > $i ).
thf(func_def_558,type,
sK382: $i > $i > $i ).
thf(func_def_559,type,
sK383: $i > $i > $i > $i ).
thf(func_def_560,type,
sK384: $i > $i > $i ).
thf(func_def_561,type,
sK385: $i > $i > $i > $i ).
thf(func_def_562,type,
sK386: $i > $i ).
thf(func_def_563,type,
sK387: $i > $i > $i > $i ).
thf(func_def_564,type,
sK388: $i > $i > $i ).
thf(func_def_565,type,
sK389: $i > $i > $i ).
thf(func_def_566,type,
sK390: $i > $i > $i ).
thf(func_def_567,type,
sK391: $i > $o ).
thf(func_def_569,type,
sK393: ( $i > $o ) > $i > $i ).
thf(func_def_571,type,
sK395: $i > $o ).
thf(func_def_574,type,
sK398: $i > $o ).
thf(func_def_577,type,
sK401: $i > $o ).
thf(func_def_579,type,
sK403: $i > $o ).
thf(func_def_581,type,
sK405: $i > $i ).
thf(func_def_582,type,
sK406: ( $i > $o ) > $i ).
thf(func_def_583,type,
sK407: ( $i > $o ) > $i > $i ).
thf(func_def_585,type,
sK409: $o ).
thf(func_def_586,type,
sK410: $o ).
thf(func_def_589,type,
sK413: $i > $o ).
thf(func_def_591,type,
sK415: ( $i > $o ) > $i ).
thf(func_def_592,type,
sK416: ( $i > $o ) > $i > $i ).
thf(func_def_595,type,
sK419: $i > $i > $i ).
thf(func_def_596,type,
sK420: $i > $i > $i ).
thf(func_def_598,type,
sK422: $i > $i ).
thf(func_def_600,type,
sK424: $i > $o ).
thf(func_def_603,type,
sK427: $i > $i ).
thf(func_def_605,type,
sK429: $i > $o ).
thf(func_def_617,type,
sK441: $o ).
thf(func_def_624,type,
sK448: $i > $i > $i ).
thf(func_def_634,type,
sK458: $o ).
thf(func_def_635,type,
sK459: $o > $i > $i > $i ).
thf(func_def_638,type,
sK462: $i > $o ).
thf(func_def_640,type,
sK464: $i > $i ).
thf(func_def_641,type,
sK465: ( $i > $o ) > $i ).
thf(func_def_642,type,
sK466: ( $i > $o ) > $i > $i ).
thf(func_def_644,type,
sK468: $i > $i ).
thf(func_def_660,type,
sK484: $i > $o ).
thf(func_def_664,type,
sK488: $i > $o ).
thf(func_def_665,type,
sK489: $i > $o ).
thf(func_def_668,type,
sK492: ( $i > $o ) > $i > $i ).
thf(func_def_669,type,
sK493: $i > $o ).
thf(func_def_672,type,
sK496: ( $i > $o ) > $i > $i ).
thf(func_def_673,type,
sK497: $i > $o ).
thf(func_def_676,type,
sK500: ( $i > $o ) > $i > $i ).
thf(func_def_677,type,
sK501: $i > $o ).
thf(func_def_680,type,
sK504: ( $i > $o ) > $i > $i ).
thf(func_def_681,type,
sK505: $o ).
thf(func_def_682,type,
sK506: $o ).
thf(func_def_683,type,
sK507: $i > $o ).
thf(func_def_685,type,
sK509: $i > $i ).
thf(func_def_686,type,
sK510: ( $i > $o ) > $i ).
thf(func_def_687,type,
sK511: ( $i > $o ) > $i > $i ).
thf(func_def_688,type,
sK512: $i > $o ).
thf(func_def_690,type,
sK514: $i > $i ).
thf(func_def_691,type,
sK515: ( $i > $o ) > $i ).
thf(func_def_692,type,
sK516: ( $i > $o ) > $i ).
thf(func_def_693,type,
sK517: ( $i > $o ) > $i ).
thf(func_def_694,type,
sK518: $i > $o ).
thf(func_def_696,type,
sK520: $i > $i ).
thf(func_def_697,type,
sK521: ( $i > $o ) > $i ).
thf(func_def_698,type,
sK522: ( $i > $o ) > $i > $i ).
thf(func_def_707,type,
sK531: $i > $o ).
thf(func_def_711,type,
sK535: ( $i > $o ) > $i > $i ).
thf(func_def_712,type,
sK536: $i > $o ).
thf(func_def_713,type,
sK537: $i > $o ).
thf(func_def_714,type,
sK538: $i > $i ).
thf(func_def_715,type,
sK539: $i > $i ).
thf(func_def_718,type,
sK542: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_719,type,
sK543: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_720,type,
sK544: ( $i > $o ) > $i ).
thf(func_def_721,type,
sK545: $i > ( $i > $o ) > $i ).
thf(func_def_722,type,
sK546: ( $i > $o ) > $i ).
thf(func_def_723,type,
sK547: $i > ( $i > $o ) > $i ).
thf(func_def_724,type,
sK548: $i > ( $i > $o ) > $i ).
thf(func_def_725,type,
sK549: ( $i > $o ) > $i ).
thf(func_def_726,type,
sK550: $i > ( $i > $o ) > $i ).
thf(func_def_727,type,
sK551: ( $i > $o ) > $i ).
thf(func_def_728,type,
sK552: $i > ( $i > $o ) > $i ).
thf(func_def_729,type,
sK553: $i > ( $i > $o ) > $i ).
thf(func_def_730,type,
sK554: ( $i > $o ) > $i ).
thf(func_def_731,type,
sK555: $i > ( $i > $o ) > $i ).
thf(func_def_732,type,
sK556: ( $i > $o ) > $i ).
thf(func_def_733,type,
sK557: $i > ( $i > $o ) > $i ).
thf(func_def_734,type,
sK558: $i > ( $i > $o ) > $i ).
thf(func_def_743,type,
sK567: $i > $o ).
thf(func_def_744,type,
sK568: $i > $o ).
thf(func_def_747,type,
sK571: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_748,type,
sK572: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_749,type,
sK573: $i > ( $i > $o ) > $i ).
thf(func_def_750,type,
sK574: ( $i > $o ) > $i > $i ).
thf(func_def_753,type,
sK577: $i > $o ).
thf(func_def_754,type,
sK578: $i > $o ).
thf(func_def_755,type,
sK579: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_756,type,
sK580: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_759,type,
sK583: $i > $i > $i ).
thf(func_def_800,type,
sK624: $i > $o ).
thf(func_def_802,type,
sK626: $i > $o ).
thf(func_def_810,type,
sK634: $o ).
thf(func_def_841,type,
sK665: $i > $i > $i ).
thf(func_def_881,type,
sK705: $o ).
thf(func_def_900,type,
sK724: $i > $i > $i ).
thf(func_def_901,type,
sK725: $i > $i > $i ).
thf(f135,axiom,
( iskpair
= ( ^ [X0: $i] :
? [X1: $i] :
( ? [X2: $i] :
( ( X0
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
& ( in @ X2 @ ( setunion @ X0 ) ) )
& ( in @ X1 @ ( setunion @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iskpair) ).
thf(f137,axiom,
( setukpairIL
= ( ! [X0: $i,X1: $i] : ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairIL) ).
thf(f138,axiom,
( setukpairIR
= ( ! [X0: $i,X1: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairIR) ).
thf(f140,axiom,
( kpair
= ( ^ [X0: $i,X1: $i] : ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpair) ).
thf(f141,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
=> ! [X0: $i,X1: $i] : ( iskpair @ ( kpair @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairp) ).
thf(f142,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
=> ! [X0: $i,X1: $i] : ( iskpair @ ( kpair @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f141]) ).
thf(f400,plain,
( iskpair
= ( ^ [X0: $i] :
? [X1: $i] :
( ? [X2: $i] :
( ( X0
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
& ( in @ X2 @ ( setunion @ X0 ) ) )
& ( in @ X1 @ ( setunion @ X0 ) ) ) ) ),
inference(rectify,[],[f135]) ).
thf(f401,plain,
( iskpair
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y0 ) )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f400]) ).
thf(f404,plain,
( setukpairIL
= ( ! [X0: $i,X1: $i] : ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(rectify,[],[f137]) ).
thf(f405,plain,
( setukpairIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(fool_elimination,[],[f404]) ).
thf(f406,plain,
( setukpairIR
= ( ! [X0: $i,X1: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(rectify,[],[f138]) ).
thf(f407,plain,
( setukpairIR
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(fool_elimination,[],[f406]) ).
thf(f410,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(fool_elimination,[],[f140]) ).
thf(f411,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
=> ! [X0: $i,X1: $i] : ( iskpair @ ( kpair @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f142]) ).
thf(f412,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 )
=> ! [X0: $i,X1: $i] :
( ( iskpair @ ( kpair @ X0 @ X1 ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f411]) ).
thf(f413,plain,
( ? [X0: $i,X1: $i] :
( ( iskpair @ ( kpair @ X0 @ X1 ) )
!= $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,[],[f412]) ).
thf(f414,plain,
( ? [X0: $i,X1: $i] :
( ( iskpair @ ( kpair @ X0 @ X1 ) )
!= $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(flattening,[],[f413]) ).
thf(f415,plain,
( ( $true
!= ( iskpair @ ( kpair @ sK0 @ sK1 ) ) )
& ( 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(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f414]) ).
thf(f550,plain,
( iskpair
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y0 ) )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f401]) ).
thf(f552,plain,
( setukpairIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f405]) ).
thf(f553,plain,
( setukpairIR
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f407]) ).
thf(f555,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(cnf_transformation,[],[f410]) ).
thf(f689,plain,
setukpairIL = $true,
inference(cnf_transformation,[],[f415]) ).
thf(f690,plain,
setukpairIR = $true,
inference(cnf_transformation,[],[f415]) ).
thf(f692,plain,
( $true
!= ( iskpair @ ( kpair @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f415]) ).
thf(f828,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f552,f689]) ).
thf(f829,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f553,f690]) ).
thf(f831,plain,
( $true
!= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y0 ) )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) ) ) )
@ ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
@ sK0
@ sK1 ) ) ),
inference(definition_unfolding,[],[f692,f550,f555]) ).
thf(f1217,definition,
( sF128
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF128])],[function_definition]) ).
thf(f1218,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= sF128 ),
inference(reorient_equations,[],[f1217]) ).
thf(f1219,plain,
$true = sF128,
inference(definition_folding,[],[f828,f1218]) ).
thf(f1220,definition,
( sF129
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF129])],[function_definition]) ).
thf(f1221,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= sF129 ),
inference(reorient_equations,[],[f1220]) ).
thf(f1222,plain,
$true = sF129,
inference(definition_folding,[],[f829,f1221]) ).
thf(f1226,definition,
( sF131
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
@ sK0
@ sK1 ) ),
introduced(definition,[new_symbols(definition,[sF131])],[function_definition]) ).
thf(f1227,plain,
( ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
@ sK0
@ sK1 )
= sF131 ),
inference(reorient_equations,[],[f1226]) ).
thf(f1228,definition,
( sF132
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y0 ) )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) ) ) )
@ sF131 ) ),
introduced(definition,[new_symbols(definition,[sF132])],[function_definition]) ).
thf(f1229,plain,
( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y0 ) )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) ) ) )
@ sF131 )
= sF132 ),
inference(reorient_equations,[],[f1228]) ).
thf(f1230,plain,
$true != sF132,
inference(definition_folding,[],[f831,f1229,f1227]) ).
thf(f7029,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
| ( $false = sF128 ) ),
inference(iff_proxy_clausification,[],[f1218]) ).
thf(f7035,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) )
@ X1 ) )
| ( $false = sF128 ) ),
inference(pi_proxy_clausification,[],[f7029]) ).
thf(f7036,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) )
| ( $false = sF128 ) ),
inference(beta-eta_normalization,[],[f7035]) ).
thf(f7037,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] : ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
@ X2 ) )
| ( $false = sF128 ) ),
inference(pi_proxy_clausification,[],[f7036]) ).
thf(f7038,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( $false = sF128 ) ),
inference(beta-eta_normalization,[],[f7037]) ).
thf(f7039,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
| ( $false = sF129 ) ),
inference(iff_proxy_clausification,[],[f1221]) ).
thf(f7045,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) )
@ X1 ) )
| ( $false = sF129 ) ),
inference(pi_proxy_clausification,[],[f7039]) ).
thf(f7046,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) )
| ( $false = sF129 ) ),
inference(beta-eta_normalization,[],[f7045]) ).
thf(f7047,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
@ X2 ) )
| ( $false = sF129 ) ),
inference(pi_proxy_clausification,[],[f7046]) ).
thf(f7048,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( $false = sF129 ) ),
inference(beta-eta_normalization,[],[f7047]) ).
thf(f7075,plain,
( sF131
= ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ),
inference(beta-eta_normalization,[],[f1227]) ).
thf(f7077,plain,
( ( $false
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y0 ) )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) ) ) )
@ sF131 ) )
| ( $true = sF132 ) ),
inference(iff_proxy_clausification,[],[f1229]) ).
thf(f7078,plain,
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sF131 ) )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ sF131 ) )
& ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= sF131 ) ) ) ) ) )
| ( $true = sF132 ) ),
inference(beta-eta_normalization,[],[f7077]) ).
thf(f7079,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sF131 ) )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ sF131 ) )
& ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= sF131 ) ) ) )
@ X1 ) )
| ( $true = sF132 ) ),
inference(pi_proxy_clausification,[],[f7078]) ).
thf(f7080,plain,
! [X1: $i] :
( ( $false
= ( ( in @ X1 @ ( setunion @ sF131 ) )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sF131 ) )
& ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sF131 ) ) ) ) )
| ( $true = sF132 ) ),
inference(beta-eta_normalization,[],[f7079]) ).
thf(f7081,plain,
! [X1: $i] :
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sF131 ) )
& ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sF131 ) ) ) )
| ( $true = sF132 )
| ( $false
= ( in @ X1 @ ( setunion @ sF131 ) ) ) ),
inference(and_proxy_clausification,[],[f7080]) ).
thf(f7082,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ sF131 ) )
& ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sF131 ) )
@ X2 ) )
| ( $true = sF132 )
| ( $false
= ( in @ X1 @ ( setunion @ sF131 ) ) ) ),
inference(pi_proxy_clausification,[],[f7081]) ).
thf(f7083,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( in @ X2 @ ( setunion @ sF131 ) )
& ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= sF131 ) ) )
| ( $true = sF132 )
| ( $false
= ( in @ X1 @ ( setunion @ sF131 ) ) ) ),
inference(beta-eta_normalization,[],[f7082]) ).
thf(f7084,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= sF131 ) )
| ( $true = sF132 )
| ( $false
= ( in @ X1 @ ( setunion @ sF131 ) ) )
| ( $false
= ( in @ X2 @ ( setunion @ sF131 ) ) ) ),
inference(and_proxy_clausification,[],[f7083]) ).
thf(f7085,plain,
! [X2: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
!= sF131 )
| ( $true = sF132 )
| ( $false
= ( in @ X1 @ ( setunion @ sF131 ) ) )
| ( $false
= ( in @ X2 @ ( setunion @ sF131 ) ) ) ),
inference(equality_proxy_clausification,[],[f7084]) ).
thf(f7561,plain,
! [X2: $i,X1: $i] :
( ( $false = $true )
| ( $true
= ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(forward_demodulation,[],[f7038,f1219]) ).
thf(f7562,plain,
! [X2: $i,X1: $i] :
( $true
= ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(trivial_inequality_removal,[],[f7561]) ).
thf(f7563,plain,
! [X2: $i,X1: $i] :
( ( $false = $true )
| ( $true
= ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(forward_demodulation,[],[f7048,f1222]) ).
thf(f7564,plain,
! [X2: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(trivial_inequality_removal,[],[f7563]) ).
thf(f7571,plain,
! [X2: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
!= sF131 )
| ( $false
= ( in @ X1 @ ( setunion @ sF131 ) ) )
| ( $false
= ( in @ X2 @ ( setunion @ sF131 ) ) ) ),
inference(forward_subsumption_resolution,[],[f7085,f1230]) ).
thf(f10622,plain,
( $true
= ( in @ sK0 @ ( setunion @ sF131 ) ) ),
inference(constrained_superposition,[],[f7562,f7075]) ).
thf(f10688,plain,
( $true
= ( in @ sK1 @ ( setunion @ sF131 ) ) ),
inference(constrained_superposition,[],[f7564,f7075]) ).
thf(f10754,plain,
( ( sF131 != sF131 )
| ( $false
= ( in @ sK0 @ ( setunion @ sF131 ) ) )
| ( $false
= ( in @ sK1 @ ( setunion @ sF131 ) ) ) ),
inference(constrained_superposition,[],[f7571,f7075]) ).
thf(f10757,plain,
( ( $false
= ( in @ sK0 @ ( setunion @ sF131 ) ) )
| ( $false
= ( in @ sK1 @ ( setunion @ sF131 ) ) ) ),
inference(trivial_inequality_removal,[],[f10754]) ).
thf(f10758,plain,
( ( $false = $true )
| ( $false
= ( in @ sK1 @ ( setunion @ sF131 ) ) ) ),
inference(forward_demodulation,[],[f10757,f10622]) ).
thf(f10759,plain,
( $false
= ( in @ sK1 @ ( setunion @ sF131 ) ) ),
inference(trivial_inequality_removal,[],[f10758]) ).
thf(f10799,plain,
$false = $true,
inference(constrained_superposition,[],[f10688,f10759]) ).
thf(f10806,plain,
$false,
inference(trivial_inequality_removal,[],[f10799]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU620^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n003.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 14:00:29 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.24 Running first-order model finding
% 0.09/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.00/0.75 % (2549404)Will run a generic schedule for satisfiability detection.
% 3.00/0.75 % (2549410)% WARNING: option uhcvi not known.
% 3.00/0.75 % (2549410)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3578436959:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.00/0.75 % (2549410)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.00/0.75 % (2549409)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2800372025_2999 on theBenchmark for (2999ds/0Mi)
% 3.00/0.75 % (2549411)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=942492039:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.00/0.75 % (2549412)dis+10_1_sil=32000:sp=arity:random_seed=2797745824:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.00/0.75 % (2549415)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3036741042:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.00/0.75 % (2549410)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.00/0.75 % (2549413)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2084883576:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.00/0.75 % (2549414)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3074410549:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.00/0.75 % (2549413)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.00/0.75 % Exception at run slice level
% 3.00/0.75 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.00/0.75 % (2549423)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=86868463:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.00/0.75 % (2549412)Instruction limit reached!
% 3.00/0.75 % (2549412)------------------------------
% 3.00/0.75 % (2549412)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.00/0.75 % (2549412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/0.75 % (2549412)CaDiCaL version: 2.1.3
% 3.00/0.75 % (2549412)Termination reason: Instruction limit
% 3.00/0.75 % (2549412)Termination phase: Saturation
% 3.00/0.75 % (2549412)Time elapsed: 0.046 s
% 3.00/0.75 % (2549412)Peak memory usage: 13 MB
% 3.00/0.75 % (2549412)Instructions burned: 103 (million)
% 3.00/0.75 % Exception at run slice level
% 3.00/0.75 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.00/0.75 % (2549425)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=777106548:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.00/0.75 % (2549413)Instruction limit reached!
% 3.00/0.75 % (2549413)------------------------------
% 3.00/0.75 % (2549413)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.00/0.75 % (2549413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/0.75 % (2549413)CaDiCaL version: 2.1.3
% 3.00/0.75 % (2549413)Termination reason: Instruction limit
% 3.00/0.75 % (2549413)Termination phase: Saturation
% 3.00/0.75 % (2549413)Time elapsed: 0.062 s
% 3.00/0.75 % (2549413)Peak memory usage: 13 MB
% 3.00/0.75 % (2549413)Instructions burned: 116 (million)
% 3.00/0.75 % (2549415)Instruction limit reached!
% 3.00/0.75 % (2549415)------------------------------
% 3.00/0.75 % (2549415)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.00/0.75 % (2549415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/0.75 % (2549415)CaDiCaL version: 2.1.3
% 3.00/0.75 % (2549415)Termination reason: Instruction limit
% 3.00/0.75 % (2549415)Termination phase: Saturation
% 3.00/0.75 % (2549415)Time elapsed: 0.076 s
% 3.00/0.75 % (2549415)Peak memory usage: 14 MB
% 3.00/0.75 % (2549415)Instructions burned: 159 (million)
% 3.00/0.75 % (2549414)Instruction limit reached!
% 3.00/0.75 % (2549414)------------------------------
% 3.00/0.75 % (2549414)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.00/0.75 % (2549414)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/0.75 % (2549414)CaDiCaL version: 2.1.3
% 3.00/0.75 % (2549414)Termination reason: Instruction limit
% 3.00/0.75 % (2549414)Termination phase: Saturation
% 3.00/0.75 % (2549414)Time elapsed: 0.076 s
% 3.00/0.75 % (2549414)Peak memory usage: 13 MB
% 3.00/0.75 % (2549414)Instructions burned: 133 (million)
% 3.00/0.75 % (2549426)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1213421989:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 3.00/0.75 % (2549428)ott-21_1_sil=16000:fs=off:random_seed=1451941533:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 3.00/0.75 % (2549429)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1754157221:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 3.00/0.75 % (2549426)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.00/0.75 % (2549431)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2774037039:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 3.00/0.75 % (2549426)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.00/0.75 % (2549425)Instruction limit reached!
% 3.00/0.75 % (2549425)------------------------------
% 3.00/0.75 % (2549425)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.00/0.75 % (2549425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/0.75 % (2549425)CaDiCaL version: 2.1.3
% 3.00/0.75 % (2549425)Termination reason: Instruction limit
% 3.00/0.75 % (2549425)Termination phase: Saturation
% 3.00/0.75 % (2549425)Time elapsed: 0.060 s
% 3.00/0.75 % (2549425)Peak memory usage: 13 MB
% 3.00/0.75 % (2549425)Instructions burned: 132 (million)
% 3.00/0.75 % Exception at run slice level
% 3.00/0.75 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.00/0.75 % (2549435)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2842362809:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 3.00/0.75 % (2549436)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3857157943:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 3.00/0.75 % Exception at run slice level
% 3.00/0.75 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.00/0.75 % (2549439)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=3821491241:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 3.00/0.75 % (2549439)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.00/0.75 % (2549428)Instruction limit reached!
% 3.00/0.75 % (2549428)------------------------------
% 3.00/0.75 % (2549428)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.00/0.75 % (2549428)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/0.75 % (2549428)CaDiCaL version: 2.1.3
% 3.00/0.75 % (2549428)Termination reason: Instruction limit
% 3.00/0.75 % (2549428)Termination phase: Saturation
% 3.00/0.75 % (2549428)Time elapsed: 0.154 s
% 3.00/0.75 % (2549428)Peak memory usage: 13 MB
% 3.00/0.75 % (2549428)Instructions burned: 180 (million)
% 3.00/0.75 % (2549441)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2416279445:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 3.00/0.75 % (2549441)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.00/0.75 % (2549429)Instruction limit reached!
% 3.00/0.75 % (2549429)------------------------------
% 3.00/0.75 % (2549429)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.00/0.75 % (2549429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/0.75 % (2549429)CaDiCaL version: 2.1.3
% 3.00/0.75 % (2549429)Termination reason: Instruction limit
% 3.00/0.75 % (2549429)Termination phase: Saturation
% 3.00/0.75 % (2549429)Time elapsed: 0.257 s
% 3.00/0.75 % (2549429)Peak memory usage: 14 MB
% 3.00/0.75 % (2549429)Instructions burned: 478 (million)
% 3.00/0.75 % (2549443)fmb+10_1_sil=64000:random_seed=1650881617:i=22061:nm=2:gsp=on_2995 on theBenchmark for (2995ds/22061Mi)
% 3.00/0.75 % (2549426)Instruction limit reached!
% 3.00/0.75 % (2549426)------------------------------
% 3.00/0.75 % (2549426)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.00/0.75 % (2549426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/0.75 % (2549426)CaDiCaL version: 2.1.3
% 3.00/0.75 % (2549426)Termination reason: Instruction limit
% 3.00/0.75 % (2549426)Termination phase: Saturation
% 3.00/0.75 % (2549426)Time elapsed: 0.299 s
% 3.00/0.75 % (2549426)Peak memory usage: 14 MB
% 3.00/0.75 % (2549426)Instructions burned: 684 (million)
% 3.00/0.75 % (2549443)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.00/0.75 % Exception at run slice level
% 3.00/0.75 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.00/0.75 % (2549445)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3093037881:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 3.00/0.75 % (2549446)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1317617510:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 3.00/0.75 % Exception at run slice level
% 3.00/0.75 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.00/0.75 % Exception at run slice level
% 3.00/0.75 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.00/0.75 % (2549435) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2549404-2549435"...
% 3.00/0.75 % (2549449)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=125292508:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 3.00/0.75 % (2549435)...printing done.
% 3.00/0.75 % (2549435)Refutation found. Thanks to Tanya!
% 3.00/0.75 % SZS status Theorem for theBenchmark
% 3.00/0.75 % SZS output start Proof for theBenchmark
% See solution above
% 3.00/0.75 % (2549435)------------------------------
% 3.00/0.75 % (2549435)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.00/0.75 % (2549435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/0.75 % (2549435)CaDiCaL version: 2.1.3
% 3.00/0.75 % (2549435)Termination reason: Refutation
% 3.00/0.75 % (2549435)Time elapsed: 0.307 s
% 3.00/0.75 % (2549435)Peak memory usage: 17 MB
% 3.00/0.75 % (2549435)Instructions burned: 666 (million)
% 3.00/0.75 % (2549404)Success in time 0.504 s
% 3.00/0.75 % Vampire exiting
%------------------------------------------------------------------------------