%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU647^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 08:30:30 AM UTC 2026
% Result : Theorem 1.45s 0.53s
% Output : Refutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 22
% Syntax : Number of formulae : 137 ( 42 unt; 0 typ; 16 def)
% Number of atoms : 3897 (1072 equ; 0 cnn)
% Maximal formula atoms : 165 ( 28 avg)
% Number of connectives : 2384 ( 162 ~; 167 |; 697 &; 668 @)
% ( 28 <=>; 662 =>; 0 <=; 0 <~>)
% Maximal formula depth : 170 ( 13 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 : 353 ( 350 usr; 206 con; 0-4 aty)
% Number of variables : 163 ( 0 sgn 126 !; 37 ?; 163 :)
% 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_196,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_197,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_198,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_199,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_200,type,
vAND: $o > $o > $o ).
thf(func_def_201,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_202,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_203,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_204,type,
vIMP: $o > $o > $o ).
thf(func_def_205,type,
vNOT: $o > $o ).
thf(func_def_206,type,
sP0: $i > $i > $o ).
thf(func_def_207,type,
sP1: $i > $o ).
thf(func_def_208,type,
sP2: $o ).
thf(func_def_214,type,
sK8: $i > $i ).
thf(func_def_226,type,
sK20: $i > $o ).
thf(func_def_227,type,
sK21: ( $i > $o ) > $i ).
thf(func_def_232,type,
sK26: $i > $o ).
thf(func_def_234,type,
sK28: ( $i > $o ) > $i ).
thf(func_def_235,type,
sK29: ( $i > $o ) > $i ).
thf(func_def_241,type,
sK35: $i > $o ).
thf(func_def_244,type,
sK38: $i > ( $i > $o ) > $i ).
thf(func_def_247,type,
sK41: $i > ( $i > $o ) > $i ).
thf(func_def_248,type,
sK42: $i > $o ).
thf(func_def_257,type,
sK51: $i > $o ).
thf(func_def_258,type,
sK52: $i > $o ).
thf(func_def_259,type,
sK53: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_260,type,
sK54: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_264,type,
sK58: $i > $o ).
thf(func_def_267,type,
sK61: $i > $o ).
thf(func_def_270,type,
sK64: ( $i > $o ) > $i ).
thf(func_def_271,type,
sK65: $i > $o ).
thf(func_def_272,type,
sK66: $i > $i ).
thf(func_def_273,type,
sK67: $i > $o ).
thf(func_def_276,type,
sK70: $i > $i > $i ).
thf(func_def_283,type,
sK77: ( $i > $o ) > $i ).
thf(func_def_284,type,
sK78: $i > $o ).
thf(func_def_285,type,
sK79: $i > $i ).
thf(func_def_298,type,
sK92: $o ).
thf(func_def_299,type,
sK93: ( $i > $o ) > $i > $i ).
thf(func_def_301,type,
sK95: $i > $o ).
thf(func_def_309,type,
sK103: $i > $i > $i ).
thf(func_def_321,type,
sK115: $o ).
thf(func_def_325,type,
sK119: $i > $o ).
thf(func_def_329,type,
sK123: $i > $i > $i ).
thf(func_def_334,type,
sK128: $i > $o ).
thf(func_def_335,type,
sK129: $i > $i > $o ).
thf(func_def_337,type,
sK131: $i > $i ).
thf(func_def_338,type,
sK132: $i > $i ).
thf(func_def_339,type,
sK133: $i > ( $i > $i > $o ) > $i ).
thf(func_def_340,type,
sK134: $i > ( $i > $i > $o ) > $i ).
thf(func_def_341,type,
sK135: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_345,type,
sK139: $o ).
thf(func_def_349,type,
sK143: ( $i > $o ) > $i > $i ).
thf(func_def_350,type,
sK144: ( $i > $o ) > $i > $i ).
thf(func_def_352,type,
sK146: $i > $o ).
thf(func_def_358,type,
sK152: $i > $i ).
thf(func_def_364,type,
sK158: $o ).
thf(func_def_365,type,
sK159: $o > $i > $i > $i ).
thf(func_def_376,type,
sK170: $i > $i > $i ).
thf(func_def_397,type,
sK191: $i > $i ).
thf(func_def_404,type,
sK198: $i > $o ).
thf(func_def_406,type,
sK200: ( $i > $o ) > $i > $i ).
thf(func_def_407,type,
sK201: ( $i > $o ) > $i > $i ).
thf(func_def_410,type,
sK204: $i > $o ).
thf(func_def_412,type,
sK206: $i > $o ).
thf(func_def_414,type,
sK208: ( $i > $o ) > $i > $i ).
thf(func_def_429,type,
sK223: $i > $o ).
thf(func_def_430,type,
sK224: $i > $o ).
thf(func_def_431,type,
sK225: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_432,type,
sK226: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_443,type,
sK237: $i > $o ).
thf(func_def_444,type,
sK238: $i > $o ).
thf(func_def_445,type,
sK239: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_446,type,
sK240: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_449,type,
sK243: $i > $i > $i ).
thf(func_def_450,type,
sK244: $i > $i > $i ).
thf(func_def_453,type,
sK247: $i > $o ).
thf(func_def_461,type,
sK255: $i > $o ).
thf(func_def_465,type,
sK259: $o ).
thf(func_def_470,type,
sK264: $i > $i > $i > $i ).
thf(func_def_471,type,
sK265: $i > $i > $i > $i ).
thf(func_def_479,type,
sK273: $i > $o ).
thf(func_def_484,type,
sK278: $i > $o ).
thf(func_def_488,type,
sK282: $o ).
thf(func_def_495,type,
sK289: $i > $i ).
thf(func_def_496,type,
sK290: $i > $i ).
thf(func_def_497,type,
sK291: $i > $i ).
thf(func_def_498,type,
sK292: $i > $i ).
thf(func_def_499,type,
sK293: $i > $i ).
thf(func_def_500,type,
sK294: $i > $i > $i > $i ).
thf(func_def_501,type,
sK295: $i > $i ).
thf(func_def_502,type,
sK296: $i > $i ).
thf(func_def_503,type,
sK297: $i > $i ).
thf(func_def_504,type,
sK298: $i > $i ).
thf(func_def_505,type,
sK299: $i > $i > $i ).
thf(func_def_506,type,
sK300: $i > $i > $i > $i ).
thf(func_def_507,type,
sK301: $i > $i > $i > $i ).
thf(func_def_508,type,
sK302: $i > $i > $i > $i ).
thf(func_def_509,type,
sK303: $i > $i > $i ).
thf(func_def_510,type,
sK304: $i > $i > $i ).
thf(func_def_511,type,
sK305: $i > $i > $i ).
thf(func_def_512,type,
sK306: $i > $i > $i ).
thf(func_def_514,type,
sK308: $i > $o ).
thf(func_def_516,type,
sK310: $i > ( $i > $o ) > $i ).
thf(func_def_517,type,
sK311: $i > $o ).
thf(func_def_520,type,
sK314: $i > ( $i > $o ) > $i ).
thf(func_def_527,type,
sK321: $i > $i > $i ).
thf(func_def_539,type,
sK333: $o ).
thf(func_def_542,type,
sK336: $o ).
thf(func_def_552,type,
sK346: $i > $i > $i ).
thf(func_def_556,type,
sK350: $i > ( $i > $o ) > $i ).
thf(func_def_557,type,
sK351: $i > $o ).
thf(func_def_560,type,
sK354: $i > $i ).
thf(func_def_578,type,
sK372: $i > $o ).
thf(func_def_603,type,
sK397: $i > $i > $i ).
thf(func_def_607,type,
sK401: $i > $o ).
thf(func_def_609,type,
sK403: $i > ( $i > $o ) > $i ).
thf(func_def_619,type,
sK413: $i > $o ).
thf(func_def_622,type,
sK416: $i > $i > ( $i > $o ) > $i ).
thf(func_def_631,type,
sK425: $i > $i ).
thf(func_def_633,type,
sK427: $i > $i ).
thf(func_def_635,type,
sK429: $i > $i ).
thf(func_def_636,type,
sK430: $i > $o ).
thf(func_def_641,type,
sK435: $i > $i > $i ).
thf(func_def_652,type,
sK446: $i > ( $i > $o ) > $i ).
thf(func_def_653,type,
sK447: $i > $o ).
thf(f3,axiom,
( emptysetAx
= ( ! [X0: $i] :
~ ( in @ X0 @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetAx) ).
thf(f4,axiom,
( setadjoinAx
= ( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
| ( X2 = X0 ) )
<=> ( in @ X2 @ ( setadjoin @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinAx) ).
thf(f31,axiom,
! [X1: $i,X0: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= setadjoinIL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(f48,axiom,
! [X0: $i,X1: $i] :
( ( ( X0 = X1 )
=> ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= eqinunit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqinunit) ).
thf(f145,axiom,
! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( ( X2 = X1 )
| ( X2 = X0 ) ) )
= upairset2E ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2E) ).
thf(f170,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
=> ! [X0: $i,X2: $i,X1: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X0 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL2) ).
thf(f171,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
=> ! [X0: $i,X2: $i,X1: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X0 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f170]) ).
thf(f176,plain,
( setadjoinAx
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
| ( X0 = X1 ) )
<=> ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f177,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
= $true )
<=> ( ( ( in @ X0 @ X2 )
= $true )
| ( X0 = X1 ) ) )
<=> ( setadjoinAx = $true ) ),
inference(fool_elimination,[],[f176]) ).
thf(f180,plain,
! [X0: $i,X1: $i] :
( ( ( X0 = X1 )
=> ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= eqinunit ),
inference(rectify,[],[f48]) ).
thf(f181,plain,
( ! [X1: $i,X0: $i] :
( ( X0 = X1 )
=> ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true ) )
<=> ( eqinunit = $true ) ),
inference(fool_elimination,[],[f180]) ).
thf(f304,plain,
! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X1 @ X0 ) )
= setadjoinIL ),
inference(rectify,[],[f31]) ).
thf(f305,plain,
( ( setadjoinIL = $true )
<=> ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ) ),
inference(fool_elimination,[],[f304]) ).
thf(f414,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
=> ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X0 = X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f171]) ).
thf(f415,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 )
=> ! [X1: $i,X3: $i,X0: $i,X2: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X0 = X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f414]) ).
thf(f429,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) )
=> ( ( X0 = X1 )
| ( X1 = X2 ) ) )
= upairset2E ),
inference(rectify,[],[f145]) ).
thf(f430,plain,
( ( upairset2E = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( $true
= ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) ) )
=> ( ( X1 = X2 )
| ( X0 = X1 ) ) ) ),
inference(fool_elimination,[],[f429]) ).
thf(f495,plain,
( emptysetAx
= ( ! [X0: $i] :
~ ( in @ X0 @ emptyset ) ) ),
inference(rectify,[],[f3]) ).
thf(f496,plain,
( ( emptysetAx = $true )
<=> ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true ) ),
inference(fool_elimination,[],[f495]) ).
thf(f535,plain,
( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
<=> ( emptysetAx = $true ) ),
inference(flattening,[],[f496]) ).
thf(f541,plain,
( ? [X1: $i,X0: $i,X3: $i,X2: $i] :
( ( X0 != X1 )
& ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
& ( 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,[],[f415]) ).
thf(f542,plain,
( ( exuI1 = $true )
& ( setadjoinIR = $true )
& ( ex1E1 = $true )
& ( powersetI1 = $true )
& ( exuI3 = $true )
& ( emptyInPowerset = $true )
& ( setextAx = $true )
& ( singletoninpowunion = $true )
& ( upairsubunion = $true )
& ( setext = $true )
& ( cartprodfstin = $true )
& ( setukpairIR = $true )
& ( quantDeMorgan4 = $true )
& ( symdiffI2 = $true )
& ( binintersectSubset2 = $true )
& ( quantDeMorgan1 = $true )
& ( binintersectLsub = $true )
& ( eqinunit = $true )
& ( setukpairIL = $true )
& ( setadjoinSub = $true )
& ( vacuousDall = $true )
& ( setunionAx = $true )
& ( singletonsuniq = $true )
& ( upairinpowunion = $true )
& ( binintersectSubset1 = $true )
& ( powersetAx = $true )
& ( upairset2IR = $true )
& ( upairsetIR = $true )
& ( powersetsubset = $true )
& ( setminusEL = $true )
& ( setunionsingleton2 = $true )
& ( nonemptyE1 = $true )
& ( omega0Ax = $true )
& ( quantDeMorgan3 = $true )
& ( descr__Cong = $true )
& ( exuE1 = $true )
& ( singletonprop = $true )
& ( symdiffIneg2 = $true )
& ( subPowSU = $true )
& ( powerset__Cong = $true )
& ( inCongP = $true )
& ( notinsingleton = $true )
& ( subsetTrans = $true )
& ( binunionEcases = $true )
& ( setminusELneg = $true )
& ( setminusIRneg = $true )
& ( dsetconstr__Cong = $true )
& ( ex1I2 = $true )
& ( setadjoinAx = $true )
& ( ubforcartprodlem1 = $true )
& ( binunionE = $true )
& ? [X1: $i,X0: $i,X3: $i,X2: $i] :
( ( X0 != X1 )
& ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
& ( setadjoinIL = $true )
& ( setunionI = $true )
& ( descrp = $true )
& ( emptysetAx = $true )
& ( binintersectSubset5 = $true )
& ( setadjoin__Cong = $true )
& ( prop2setE = $true )
& ( emptysetsubset = $true )
& ( kpairiskpair = $true )
& ( binunionIL = $true )
& ( cartprodmempair1 = $true )
& ( notequalI2 = $true )
& ( emptyinunitempty = $true )
& ( eqimpsubset1 = $true )
& ( dsetconstrER = $true )
& ( singletonsswitch = $true )
& ( setunionsingleton1 = $true )
& ( exuE3e = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinE = $true )
& ( ubforcartprodlem3 = $true )
& ( emptyI = $true )
& ( foundationAx = $true )
& ( notinemptyset = $true )
& ( noeltsimpempty = $true )
& ( wellorderingAx = $true )
& ( subsetI1 = $true )
& ( quantDeMorgan2 = $true )
& ( setunionE = $true )
& ( setbeta = $true )
& ( setminusER = $true )
& ( subset2powerset = $true )
& ( binintersectER = $true )
& ( ubforcartprodlem2 = $true )
& ( exuE2 = $true )
& ( powersetE1 = $true )
& ( setminusI = $true )
& ( kpairp = $true )
& ( omega__Cong = $true )
& ( notequalI1 = $true )
& ( ex1I = $true )
& ( powersetI = $true )
& ( prop2setI = $true )
& ( emptysetimpfalse = $true )
& ( setoftrueEq = $true )
& ( subsetRefl = $true )
& ( dsetconstrEL = $true )
& ( exu__Cong = $true )
& ( setminusERneg = $true )
& ( notdallE = $true )
& ( uniqinunit = $true )
& ( singletoninpowerset = $true )
& ( prop2set2propI = $true )
& ( disjointsetsI1 = $true )
& ( eqimpsubset2 = $true )
& ( binintersectI = $true )
& ( omegaIndAx = $true )
& ( nonemptyImpWitness = $true )
& ( setunionE2 = $true )
& ( binunionLsub = $true )
& ( setunion__Cong = $true )
& ( bs114d = $true )
& ( emptysetE = $true )
& ( exuI2 = $true )
& ( exuE3u = $true )
& ( subsetE = $true )
& ( upairset2E = $true )
& ( nonemptyI1 = $true )
& ( powersetE = $true )
& ( setunionsingleton = $true )
& ( kfstsingleton = $true )
& ( exuEu = $true )
& ( setukpairinjL1 = $true )
& ( cartprodpairin = $true )
& ( theprop = $true )
& ( symdiffE = $true )
& ( binintersectEL = $true )
& ( subsetE2 = $true )
& ( binunionIR = $true )
& ( nonemptyI = $true )
& ( upairsetIL = $true )
& ( secondinupair = $true )
& ( binintersectSubset4 = $true )
& ( setadjoinOr = $true )
& ( subsetI2 = $true )
& ( kfstpairEq = $true )
& ( notsubsetI = $true )
& ( sepSubset = $true )
& ( symdiffIneg1 = $true )
& ( notdexE = $true )
& ( inPowerset = $true )
& ( binintersectRsub = $true )
& ( setminusILneg = $true )
& ( setminusSubset1 = $true )
& ( in__Cong = $true )
& ( upairsetE = $true )
& ( omegaSAx = $true )
& ( subsetemptysetimpeq = $true )
& ( binunionRsub = $true )
& ( symdiffI1 = $true )
& ( setextsub = $true )
& ( emptyset__Cong = $true )
& ( cartprodmempair = $true )
& ( dsetconstrI = $true )
& ( emptyinPowerset = $true )
& ( emptyE1 = $true )
& ( binintersectSubset3 = $true )
& ( replAx = $true )
& ( setminusSubset2 = $true )
& ( singletonsubset = $true )
& ( sepInPowerset = $true )
& ( setminusLsub = $true ) ),
inference(flattening,[],[f541]) ).
thf(f594,plain,
( ( upairset2E = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( X1 = X2 )
| ( X0 = X1 )
| ( $true
!= ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ) ),
inference(ennf_transformation,[],[f430]) ).
thf(f595,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) ) )
| ( X1 = X2 )
| ( X0 = X1 ) )
<=> ( upairset2E = $true ) ),
inference(flattening,[],[f594]) ).
thf(f621,plain,
( ( eqinunit = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true )
| ( X0 != X1 ) ) ),
inference(ennf_transformation,[],[f181]) ).
thf(f801,plain,
( ( exuI1 = $true )
& ( setadjoinIR = $true )
& ( ex1E1 = $true )
& ( powersetI1 = $true )
& ( exuI3 = $true )
& ( emptyInPowerset = $true )
& ( setextAx = $true )
& ( singletoninpowunion = $true )
& ( upairsubunion = $true )
& ( setext = $true )
& ( cartprodfstin = $true )
& ( setukpairIR = $true )
& ( quantDeMorgan4 = $true )
& ( symdiffI2 = $true )
& ( binintersectSubset2 = $true )
& ( quantDeMorgan1 = $true )
& ( binintersectLsub = $true )
& ( eqinunit = $true )
& ( setukpairIL = $true )
& ( setadjoinSub = $true )
& ( vacuousDall = $true )
& ( setunionAx = $true )
& ( singletonsuniq = $true )
& ( upairinpowunion = $true )
& ( binintersectSubset1 = $true )
& ( powersetAx = $true )
& ( upairset2IR = $true )
& ( upairsetIR = $true )
& ( powersetsubset = $true )
& ( setminusEL = $true )
& ( setunionsingleton2 = $true )
& ( nonemptyE1 = $true )
& ( omega0Ax = $true )
& ( quantDeMorgan3 = $true )
& ( descr__Cong = $true )
& ( exuE1 = $true )
& ( singletonprop = $true )
& ( symdiffIneg2 = $true )
& ( subPowSU = $true )
& ( powerset__Cong = $true )
& ( inCongP = $true )
& ( notinsingleton = $true )
& ( subsetTrans = $true )
& ( binunionEcases = $true )
& ( setminusELneg = $true )
& ( setminusIRneg = $true )
& ( dsetconstr__Cong = $true )
& ( ex1I2 = $true )
& ( setadjoinAx = $true )
& ( ubforcartprodlem1 = $true )
& ( binunionE = $true )
& ? [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 != X1 )
& ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
& ( setadjoinIL = $true )
& ( setunionI = $true )
& ( descrp = $true )
& ( emptysetAx = $true )
& ( binintersectSubset5 = $true )
& ( setadjoin__Cong = $true )
& ( prop2setE = $true )
& ( emptysetsubset = $true )
& ( kpairiskpair = $true )
& ( binunionIL = $true )
& ( cartprodmempair1 = $true )
& ( notequalI2 = $true )
& ( emptyinunitempty = $true )
& ( eqimpsubset1 = $true )
& ( dsetconstrER = $true )
& ( singletonsswitch = $true )
& ( setunionsingleton1 = $true )
& ( exuE3e = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinE = $true )
& ( ubforcartprodlem3 = $true )
& ( emptyI = $true )
& ( foundationAx = $true )
& ( notinemptyset = $true )
& ( noeltsimpempty = $true )
& ( wellorderingAx = $true )
& ( subsetI1 = $true )
& ( quantDeMorgan2 = $true )
& ( setunionE = $true )
& ( setbeta = $true )
& ( setminusER = $true )
& ( subset2powerset = $true )
& ( binintersectER = $true )
& ( ubforcartprodlem2 = $true )
& ( exuE2 = $true )
& ( powersetE1 = $true )
& ( setminusI = $true )
& ( kpairp = $true )
& ( omega__Cong = $true )
& ( notequalI1 = $true )
& ( ex1I = $true )
& ( powersetI = $true )
& ( prop2setI = $true )
& ( emptysetimpfalse = $true )
& ( setoftrueEq = $true )
& ( subsetRefl = $true )
& ( dsetconstrEL = $true )
& ( exu__Cong = $true )
& ( setminusERneg = $true )
& ( notdallE = $true )
& ( uniqinunit = $true )
& ( singletoninpowerset = $true )
& ( prop2set2propI = $true )
& ( disjointsetsI1 = $true )
& ( eqimpsubset2 = $true )
& ( binintersectI = $true )
& ( omegaIndAx = $true )
& ( nonemptyImpWitness = $true )
& ( setunionE2 = $true )
& ( binunionLsub = $true )
& ( setunion__Cong = $true )
& ( bs114d = $true )
& ( emptysetE = $true )
& ( exuI2 = $true )
& ( exuE3u = $true )
& ( subsetE = $true )
& ( upairset2E = $true )
& ( nonemptyI1 = $true )
& ( powersetE = $true )
& ( setunionsingleton = $true )
& ( kfstsingleton = $true )
& ( exuEu = $true )
& ( setukpairinjL1 = $true )
& ( cartprodpairin = $true )
& ( theprop = $true )
& ( symdiffE = $true )
& ( binintersectEL = $true )
& ( subsetE2 = $true )
& ( binunionIR = $true )
& ( nonemptyI = $true )
& ( upairsetIL = $true )
& ( secondinupair = $true )
& ( binintersectSubset4 = $true )
& ( setadjoinOr = $true )
& ( subsetI2 = $true )
& ( kfstpairEq = $true )
& ( notsubsetI = $true )
& ( sepSubset = $true )
& ( symdiffIneg1 = $true )
& ( notdexE = $true )
& ( inPowerset = $true )
& ( binintersectRsub = $true )
& ( setminusILneg = $true )
& ( setminusSubset1 = $true )
& ( in__Cong = $true )
& ( upairsetE = $true )
& ( omegaSAx = $true )
& ( subsetemptysetimpeq = $true )
& ( binunionRsub = $true )
& ( symdiffI1 = $true )
& ( setextsub = $true )
& ( emptyset__Cong = $true )
& ( cartprodmempair = $true )
& ( dsetconstrI = $true )
& ( emptyinPowerset = $true )
& ( emptyE1 = $true )
& ( binintersectSubset3 = $true )
& ( replAx = $true )
& ( setminusSubset2 = $true )
& ( singletonsubset = $true )
& ( sepInPowerset = $true )
& ( setminusLsub = $true ) ),
inference(rectify,[],[f542]) ).
thf(f802,plain,
( ( exuI1 = $true )
& ( setadjoinIR = $true )
& ( ex1E1 = $true )
& ( powersetI1 = $true )
& ( exuI3 = $true )
& ( emptyInPowerset = $true )
& ( setextAx = $true )
& ( singletoninpowunion = $true )
& ( upairsubunion = $true )
& ( setext = $true )
& ( cartprodfstin = $true )
& ( setukpairIR = $true )
& ( quantDeMorgan4 = $true )
& ( symdiffI2 = $true )
& ( binintersectSubset2 = $true )
& ( quantDeMorgan1 = $true )
& ( binintersectLsub = $true )
& ( eqinunit = $true )
& ( setukpairIL = $true )
& ( setadjoinSub = $true )
& ( vacuousDall = $true )
& ( setunionAx = $true )
& ( singletonsuniq = $true )
& ( upairinpowunion = $true )
& ( binintersectSubset1 = $true )
& ( powersetAx = $true )
& ( upairset2IR = $true )
& ( upairsetIR = $true )
& ( powersetsubset = $true )
& ( setminusEL = $true )
& ( setunionsingleton2 = $true )
& ( nonemptyE1 = $true )
& ( omega0Ax = $true )
& ( quantDeMorgan3 = $true )
& ( descr__Cong = $true )
& ( exuE1 = $true )
& ( singletonprop = $true )
& ( symdiffIneg2 = $true )
& ( subPowSU = $true )
& ( powerset__Cong = $true )
& ( inCongP = $true )
& ( notinsingleton = $true )
& ( subsetTrans = $true )
& ( binunionEcases = $true )
& ( setminusELneg = $true )
& ( setminusIRneg = $true )
& ( dsetconstr__Cong = $true )
& ( ex1I2 = $true )
& ( setadjoinAx = $true )
& ( ubforcartprodlem1 = $true )
& ( binunionE = $true )
& ( sK80 != sK81 )
& ( ( setadjoin @ ( setadjoin @ sK80 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK80 @ ( setadjoin @ sK82 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK81 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK81 @ ( setadjoin @ sK83 @ emptyset ) ) @ emptyset ) ) )
& ( setadjoinIL = $true )
& ( setunionI = $true )
& ( descrp = $true )
& ( emptysetAx = $true )
& ( binintersectSubset5 = $true )
& ( setadjoin__Cong = $true )
& ( prop2setE = $true )
& ( emptysetsubset = $true )
& ( kpairiskpair = $true )
& ( binunionIL = $true )
& ( cartprodmempair1 = $true )
& ( notequalI2 = $true )
& ( emptyinunitempty = $true )
& ( eqimpsubset1 = $true )
& ( dsetconstrER = $true )
& ( singletonsswitch = $true )
& ( setunionsingleton1 = $true )
& ( exuE3e = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinE = $true )
& ( ubforcartprodlem3 = $true )
& ( emptyI = $true )
& ( foundationAx = $true )
& ( notinemptyset = $true )
& ( noeltsimpempty = $true )
& ( wellorderingAx = $true )
& ( subsetI1 = $true )
& ( quantDeMorgan2 = $true )
& ( setunionE = $true )
& ( setbeta = $true )
& ( setminusER = $true )
& ( subset2powerset = $true )
& ( binintersectER = $true )
& ( ubforcartprodlem2 = $true )
& ( exuE2 = $true )
& ( powersetE1 = $true )
& ( setminusI = $true )
& ( kpairp = $true )
& ( omega__Cong = $true )
& ( notequalI1 = $true )
& ( ex1I = $true )
& ( powersetI = $true )
& ( prop2setI = $true )
& ( emptysetimpfalse = $true )
& ( setoftrueEq = $true )
& ( subsetRefl = $true )
& ( dsetconstrEL = $true )
& ( exu__Cong = $true )
& ( setminusERneg = $true )
& ( notdallE = $true )
& ( uniqinunit = $true )
& ( singletoninpowerset = $true )
& ( prop2set2propI = $true )
& ( disjointsetsI1 = $true )
& ( eqimpsubset2 = $true )
& ( binintersectI = $true )
& ( omegaIndAx = $true )
& ( nonemptyImpWitness = $true )
& ( setunionE2 = $true )
& ( binunionLsub = $true )
& ( setunion__Cong = $true )
& ( bs114d = $true )
& ( emptysetE = $true )
& ( exuI2 = $true )
& ( exuE3u = $true )
& ( subsetE = $true )
& ( upairset2E = $true )
& ( nonemptyI1 = $true )
& ( powersetE = $true )
& ( setunionsingleton = $true )
& ( kfstsingleton = $true )
& ( exuEu = $true )
& ( setukpairinjL1 = $true )
& ( cartprodpairin = $true )
& ( theprop = $true )
& ( symdiffE = $true )
& ( binintersectEL = $true )
& ( subsetE2 = $true )
& ( binunionIR = $true )
& ( nonemptyI = $true )
& ( upairsetIL = $true )
& ( secondinupair = $true )
& ( binintersectSubset4 = $true )
& ( setadjoinOr = $true )
& ( subsetI2 = $true )
& ( kfstpairEq = $true )
& ( notsubsetI = $true )
& ( sepSubset = $true )
& ( symdiffIneg1 = $true )
& ( notdexE = $true )
& ( inPowerset = $true )
& ( binintersectRsub = $true )
& ( setminusILneg = $true )
& ( setminusSubset1 = $true )
& ( in__Cong = $true )
& ( upairsetE = $true )
& ( omegaSAx = $true )
& ( subsetemptysetimpeq = $true )
& ( binunionRsub = $true )
& ( symdiffI1 = $true )
& ( setextsub = $true )
& ( emptyset__Cong = $true )
& ( cartprodmempair = $true )
& ( dsetconstrI = $true )
& ( emptyinPowerset = $true )
& ( emptyE1 = $true )
& ( binintersectSubset3 = $true )
& ( replAx = $true )
& ( setminusSubset2 = $true )
& ( singletonsubset = $true )
& ( sepInPowerset = $true )
& ( setminusLsub = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK80,sK81,sK82,sK83]),skolemize(X0,sK80),skolemize(X1,sK81),skolemize(X2,sK82),skolemize(X3,sK83)],[f801]) ).
thf(f803,plain,
( ( ( setadjoinIL = $true )
| ? [X0: $i,X1: $i] :
( $true
!= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ) )
& ( ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
| ( setadjoinIL != $true ) ) ),
inference(nnf_transformation,[],[f305]) ).
thf(f804,plain,
( ( ( setadjoinIL = $true )
| ? [X0: $i,X1: $i] :
( $true
!= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ) )
& ( ! [X2: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X3 @ X2 ) )
= $true )
| ( setadjoinIL != $true ) ) ),
inference(rectify,[],[f803]) ).
thf(f805,plain,
( ( ( setadjoinIL = $true )
| ( $true
!= ( in @ sK85 @ ( setadjoin @ sK85 @ sK84 ) ) ) )
& ( ! [X2: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X3 @ X2 ) )
= $true )
| ( setadjoinIL != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK84,sK85]),skolemize(X0,sK84),skolemize(X1,sK85)],[f804]) ).
thf(f998,plain,
( ( ! [X2: $i,X0: $i,X1: $i] :
( ( ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
= $true )
| ( ( ( in @ X0 @ X2 )
!= $true )
& ( X0 != X1 ) ) )
& ( ( ( in @ X0 @ X2 )
= $true )
| ( X0 = X1 )
| ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
!= $true ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ? [X2: $i,X0: $i,X1: $i] :
( ( ( ( ( in @ X0 @ X2 )
!= $true )
& ( X0 != X1 ) )
| ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
!= $true ) )
& ( ( ( in @ X0 @ X2 )
= $true )
| ( X0 = X1 )
| ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
= $true ) ) ) ) ),
inference(nnf_transformation,[],[f177]) ).
thf(f999,plain,
( ( ! [X2: $i,X0: $i,X1: $i] :
( ( ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
= $true )
| ( ( ( in @ X0 @ X2 )
!= $true )
& ( X0 != X1 ) ) )
& ( ( ( in @ X0 @ X2 )
= $true )
| ( X0 = X1 )
| ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
!= $true ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ? [X2: $i,X0: $i,X1: $i] :
( ( ( ( ( in @ X0 @ X2 )
!= $true )
& ( X0 != X1 ) )
| ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
!= $true ) )
& ( ( ( in @ X0 @ X2 )
= $true )
| ( X0 = X1 )
| ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
= $true ) ) ) ) ),
inference(flattening,[],[f998]) ).
thf(f1000,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( $true
= ( in @ X1 @ ( setadjoin @ X2 @ X0 ) ) )
| ( ( ( in @ X1 @ X0 )
!= $true )
& ( X1 != X2 ) ) )
& ( ( ( in @ X1 @ X0 )
= $true )
| ( X1 = X2 )
| ( $true
!= ( in @ X1 @ ( setadjoin @ X2 @ X0 ) ) ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( ( $true
!= ( in @ X4 @ X3 ) )
& ( X4 != X5 ) )
| ( $true
!= ( in @ X4 @ ( setadjoin @ X5 @ X3 ) ) ) )
& ( ( $true
= ( in @ X4 @ X3 ) )
| ( X4 = X5 )
| ( $true
= ( in @ X4 @ ( setadjoin @ X5 @ X3 ) ) ) ) ) ) ),
inference(rectify,[],[f999]) ).
thf(f1001,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( $true
= ( in @ X1 @ ( setadjoin @ X2 @ X0 ) ) )
| ( ( ( in @ X1 @ X0 )
!= $true )
& ( X1 != X2 ) ) )
& ( ( ( in @ X1 @ X0 )
= $true )
| ( X1 = X2 )
| ( $true
!= ( in @ X1 @ ( setadjoin @ X2 @ X0 ) ) ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ( ( ( ( ( in @ sK268 @ sK267 )
!= $true )
& ( sK268 != sK269 ) )
| ( $true
!= ( in @ sK268 @ ( setadjoin @ sK269 @ sK267 ) ) ) )
& ( ( ( in @ sK268 @ sK267 )
= $true )
| ( sK268 = sK269 )
| ( $true
= ( in @ sK268 @ ( setadjoin @ sK269 @ sK267 ) ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK267,sK268,sK269]),skolemize(X3,sK267),skolemize(X4,sK268),skolemize(X5,sK269)],[f1000]) ).
thf(f1127,plain,
( ( ( eqinunit = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
& ( X0 = X1 ) ) )
& ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true )
| ( X0 != X1 ) )
| ( eqinunit != $true ) ) ),
inference(nnf_transformation,[],[f621]) ).
thf(f1128,plain,
( ( ( eqinunit = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
& ( X0 = X1 ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= $true )
| ( X2 != X3 ) )
| ( eqinunit != $true ) ) ),
inference(rectify,[],[f1127]) ).
thf(f1129,plain,
( ( ( eqinunit = $true )
| ( ( $true
!= ( in @ sK388 @ ( setadjoin @ sK389 @ emptyset ) ) )
& ( sK389 = sK388 ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= $true )
| ( X2 != X3 ) )
| ( eqinunit != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK388,sK389]),skolemize(X0,sK388),skolemize(X1,sK389)],[f1128]) ).
thf(f1133,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) ) )
| ( X1 = X2 )
| ( X0 = X1 ) )
| ( upairset2E != $true ) )
& ( ( upairset2E = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) ) )
& ( X1 != X2 )
& ( X0 != X1 ) ) ) ),
inference(nnf_transformation,[],[f595]) ).
thf(f1134,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) ) )
| ( X1 = X2 )
| ( X0 = X1 ) )
| ( upairset2E != $true ) )
& ( ( upairset2E = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setadjoin @ X5 @ ( setadjoin @ X3 @ emptyset ) ) )
= $true )
& ( X4 != X5 )
& ( X3 != X4 ) ) ) ),
inference(rectify,[],[f1133]) ).
thf(f1135,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) ) )
| ( X1 = X2 )
| ( X0 = X1 ) )
| ( upairset2E != $true ) )
& ( ( upairset2E = $true )
| ( ( $true
= ( in @ sK393 @ ( setadjoin @ sK394 @ ( setadjoin @ sK392 @ emptyset ) ) ) )
& ( sK394 != sK393 )
& ( sK392 != sK393 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK392,sK393,sK394]),skolemize(X3,sK392),skolemize(X4,sK393),skolemize(X5,sK394)],[f1134]) ).
thf(f1194,plain,
( ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
| ( emptysetAx != $true ) )
& ( ( emptysetAx = $true )
| ? [X0: $i] :
( ( in @ X0 @ emptyset )
= $true ) ) ),
inference(nnf_transformation,[],[f535]) ).
thf(f1195,plain,
( ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
| ( emptysetAx != $true ) )
& ( ( emptysetAx = $true )
| ? [X1: $i] :
( ( in @ X1 @ emptyset )
= $true ) ) ),
inference(rectify,[],[f1194]) ).
thf(f1196,plain,
( ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
| ( emptysetAx != $true ) )
& ( ( emptysetAx = $true )
| ( $true
= ( in @ sK450 @ emptyset ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK450]),skolemize(X1,sK450)],[f1195]) ).
thf(f1352,plain,
upairset2E = $true,
inference(cnf_transformation,[],[f802]) ).
thf(f1415,plain,
emptysetAx = $true,
inference(cnf_transformation,[],[f802]) ).
thf(f1418,plain,
setadjoinIL = $true,
inference(cnf_transformation,[],[f802]) ).
thf(f1419,plain,
( ( setadjoin @ ( setadjoin @ sK80 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK80 @ ( setadjoin @ sK82 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK81 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK81 @ ( setadjoin @ sK83 @ emptyset ) ) @ emptyset ) ) ),
inference(cnf_transformation,[],[f802]) ).
thf(f1420,plain,
sK80 != sK81,
inference(cnf_transformation,[],[f802]) ).
thf(f1423,plain,
setadjoinAx = $true,
inference(cnf_transformation,[],[f802]) ).
thf(f1454,plain,
eqinunit = $true,
inference(cnf_transformation,[],[f802]) ).
thf(f1472,plain,
! [X2: $i,X3: $i] :
( ( ( in @ X3 @ ( setadjoin @ X3 @ X2 ) )
= $true )
| ( setadjoinIL != $true ) ),
inference(cnf_transformation,[],[f805]) ).
thf(f1733,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( X1 = X2 )
| ( $true
!= ( in @ X1 @ ( setadjoin @ X2 @ X0 ) ) )
| ( ( in @ X1 @ X0 )
= $true )
| ( setadjoinAx != $true ) ),
inference(cnf_transformation,[],[f1001]) ).
thf(f1920,plain,
! [X2: $i,X3: $i] :
( ( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= $true )
| ( X2 != X3 )
| ( eqinunit != $true ) ),
inference(cnf_transformation,[],[f1129]) ).
thf(f1929,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) ) )
| ( X1 = X2 )
| ( X0 = X1 )
| ( upairset2E != $true ) ),
inference(cnf_transformation,[],[f1135]) ).
thf(f2002,plain,
! [X0: $i] :
( ( ( in @ X0 @ emptyset )
!= $true )
| ( emptysetAx != $true ) ),
inference(cnf_transformation,[],[f1196]) ).
thf(f2040,plain,
! [X3: $i] :
( ( ( in @ X3 @ ( setadjoin @ X3 @ emptyset ) )
= $true )
| ( eqinunit != $true ) ),
inference(equality_resolution,[],[f1920]) ).
thf(f2355,definition,
( spl451_42
<=> ( setadjoinAx = $true ) ),
introduced(definition,[new_symbols(definition,[spl451_42])],[avatar_definition]) ).
thf(f2403,definition,
( spl451_53
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) ) )
| ( X0 = X1 )
| ( X1 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl451_53])],[avatar_definition]) ).
thf(f2404,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X0 @ emptyset ) ) ) )
| ( X0 = X1 )
| ( X1 = X2 ) )
| ~ spl451_53 ),
inference(avatar_component_clause,[],[f2403]) ).
thf(f2503,definition,
( spl451_75
<=> ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true ) ),
introduced(definition,[new_symbols(definition,[spl451_75])],[avatar_definition]) ).
thf(f2504,plain,
( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
| ~ spl451_75 ),
inference(avatar_component_clause,[],[f2503]) ).
thf(f2726,definition,
( spl451_124
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( X1 = X2 )
| ( ( in @ X2 @ X0 )
= $true )
| ( $true
!= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl451_124])],[avatar_definition]) ).
thf(f2727,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) )
| ( ( in @ X2 @ X0 )
= $true )
| ( X1 = X2 ) )
| ~ spl451_124 ),
inference(avatar_component_clause,[],[f2726]) ).
thf(f2745,definition,
( spl451_128
<=> ( upairset2E = $true ) ),
introduced(definition,[new_symbols(definition,[spl451_128])],[avatar_definition]) ).
thf(f3084,definition,
( spl451_204
<=> ( emptysetAx = $true ) ),
introduced(definition,[new_symbols(definition,[spl451_204])],[avatar_definition]) ).
thf(f3169,plain,
( ~ spl451_204
| spl451_75 ),
inference(avatar_split_clause,[],[f2002,f2503,f3084]) ).
thf(f3392,plain,
( ~ spl451_128
| spl451_53 ),
inference(avatar_split_clause,[],[f1929,f2403,f2745]) ).
thf(f3887,definition,
( spl451_381
<=> ( sK80 = sK81 ) ),
introduced(definition,[new_symbols(definition,[spl451_381])],[avatar_definition]) ).
thf(f3889,plain,
( ( sK80 != sK81 )
| spl451_381 ),
inference(avatar_component_clause,[],[f3887]) ).
thf(f3890,plain,
~ spl451_381,
inference(avatar_split_clause,[],[f1420,f3887]) ).
thf(f4034,definition,
( spl451_412
<=> ( setadjoinIL = $true ) ),
introduced(definition,[new_symbols(definition,[spl451_412])],[avatar_definition]) ).
thf(f4461,plain,
( ~ spl451_42
| spl451_124 ),
inference(avatar_split_clause,[],[f1733,f2726,f2355]) ).
thf(f4493,plain,
spl451_42,
inference(avatar_split_clause,[],[f1423,f2355]) ).
thf(f4513,plain,
spl451_204,
inference(avatar_split_clause,[],[f1415,f3084]) ).
thf(f4586,definition,
( spl451_525
<=> ( eqinunit = $true ) ),
introduced(definition,[new_symbols(definition,[spl451_525])],[avatar_definition]) ).
thf(f4956,plain,
spl451_412,
inference(avatar_split_clause,[],[f1418,f4034]) ).
thf(f5240,plain,
spl451_525,
inference(avatar_split_clause,[],[f1454,f4586]) ).
thf(f5296,definition,
( spl451_670
<=> ! [X3: $i] :
( ( in @ X3 @ ( setadjoin @ X3 @ emptyset ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl451_670])],[avatar_definition]) ).
thf(f5297,plain,
( ! [X3: $i] :
( ( in @ X3 @ ( setadjoin @ X3 @ emptyset ) )
= $true )
| ~ spl451_670 ),
inference(avatar_component_clause,[],[f5296]) ).
thf(f5298,plain,
( spl451_670
| ~ spl451_525 ),
inference(avatar_split_clause,[],[f2040,f4586,f5296]) ).
thf(f5310,definition,
( spl451_673
<=> ! [X2: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X3 @ X2 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl451_673])],[avatar_definition]) ).
thf(f5311,plain,
( ! [X2: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X3 @ X2 ) )
= $true )
| ~ spl451_673 ),
inference(avatar_component_clause,[],[f5310]) ).
thf(f5312,plain,
( ~ spl451_412
| spl451_673 ),
inference(avatar_split_clause,[],[f1472,f5310,f4034]) ).
thf(f5461,definition,
( spl451_704
<=> ( ( setadjoin @ ( setadjoin @ sK80 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK80 @ ( setadjoin @ sK82 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK81 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK81 @ ( setadjoin @ sK83 @ emptyset ) ) @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[spl451_704])],[avatar_definition]) ).
thf(f5463,plain,
( ( ( setadjoin @ ( setadjoin @ sK80 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK80 @ ( setadjoin @ sK82 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK81 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK81 @ ( setadjoin @ sK83 @ emptyset ) ) @ emptyset ) ) )
| ~ spl451_704 ),
inference(avatar_component_clause,[],[f5461]) ).
thf(f5464,plain,
spl451_704,
inference(avatar_split_clause,[],[f1419,f5461]) ).
thf(f5614,plain,
spl451_128,
inference(avatar_split_clause,[],[f1352,f2745]) ).
thf(f5984,plain,
( ( $true
= ( in @ ( setadjoin @ sK81 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK80 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK80 @ ( setadjoin @ sK82 @ emptyset ) ) @ emptyset ) ) ) )
| ~ spl451_673
| ~ spl451_704 ),
inference(superposition,[],[f5311,f5463]) ).
thf(f5990,definition,
( spl451_765
<=> ( $true
= ( in @ ( setadjoin @ sK81 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK80 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK80 @ ( setadjoin @ sK82 @ emptyset ) ) @ emptyset ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl451_765])],[avatar_definition]) ).
thf(f5992,plain,
( ( $true
= ( in @ ( setadjoin @ sK81 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK80 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK80 @ ( setadjoin @ sK82 @ emptyset ) ) @ emptyset ) ) ) )
| ~ spl451_765 ),
inference(avatar_component_clause,[],[f5990]) ).
thf(f5993,plain,
( spl451_765
| ~ spl451_673
| ~ spl451_704 ),
inference(avatar_split_clause,[],[f5984,f5461,f5310,f5990]) ).
thf(f6631,plain,
( ( ( setadjoin @ sK81 @ emptyset )
= ( setadjoin @ sK80 @ emptyset ) )
| ( ( setadjoin @ sK81 @ emptyset )
= ( setadjoin @ sK80 @ ( setadjoin @ sK82 @ emptyset ) ) )
| ( $true != $true )
| ~ spl451_53
| ~ spl451_765 ),
inference(superposition,[],[f2404,f5992]) ).
thf(f6644,plain,
( ( ( setadjoin @ sK81 @ emptyset )
= ( setadjoin @ sK80 @ emptyset ) )
| ( ( setadjoin @ sK81 @ emptyset )
= ( setadjoin @ sK80 @ ( setadjoin @ sK82 @ emptyset ) ) )
| ~ spl451_53
| ~ spl451_765 ),
inference(trivial_inequality_removal,[],[f6631]) ).
thf(f6658,definition,
( spl451_781
<=> ( ( setadjoin @ sK81 @ emptyset )
= ( setadjoin @ sK80 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[spl451_781])],[avatar_definition]) ).
thf(f6660,plain,
( ( ( setadjoin @ sK81 @ emptyset )
= ( setadjoin @ sK80 @ emptyset ) )
| ~ spl451_781 ),
inference(avatar_component_clause,[],[f6658]) ).
thf(f6662,definition,
( spl451_782
<=> ( ( setadjoin @ sK81 @ emptyset )
= ( setadjoin @ sK80 @ ( setadjoin @ sK82 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[spl451_782])],[avatar_definition]) ).
thf(f6664,plain,
( ( ( setadjoin @ sK81 @ emptyset )
= ( setadjoin @ sK80 @ ( setadjoin @ sK82 @ emptyset ) ) )
| ~ spl451_782 ),
inference(avatar_component_clause,[],[f6662]) ).
thf(f6665,plain,
( spl451_781
| spl451_782
| ~ spl451_53
| ~ spl451_765 ),
inference(avatar_split_clause,[],[f6644,f5990,f2403,f6662,f6658]) ).
thf(f6887,plain,
( ( ( in @ sK80 @ ( setadjoin @ sK81 @ emptyset ) )
= $true )
| ~ spl451_670
| ~ spl451_781 ),
inference(superposition,[],[f5297,f6660]) ).
thf(f6910,definition,
( spl451_793
<=> ( ( in @ sK80 @ ( setadjoin @ sK81 @ emptyset ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl451_793])],[avatar_definition]) ).
thf(f6912,plain,
( ( ( in @ sK80 @ ( setadjoin @ sK81 @ emptyset ) )
= $true )
| ~ spl451_793 ),
inference(avatar_component_clause,[],[f6910]) ).
thf(f6913,plain,
( spl451_793
| ~ spl451_670
| ~ spl451_781 ),
inference(avatar_split_clause,[],[f6887,f6658,f5296,f6910]) ).
thf(f6988,plain,
( ( ( in @ sK80 @ ( setadjoin @ sK81 @ emptyset ) )
= $true )
| ~ spl451_673
| ~ spl451_782 ),
inference(superposition,[],[f5311,f6664]) ).
thf(f7020,plain,
( spl451_793
| ~ spl451_673
| ~ spl451_782 ),
inference(avatar_split_clause,[],[f6988,f6662,f5310,f6910]) ).
thf(f7072,plain,
( ( $true
= ( in @ sK80 @ emptyset ) )
| ( $true != $true )
| ( sK80 = sK81 )
| ~ spl451_124
| ~ spl451_793 ),
inference(superposition,[],[f2727,f6912]) ).
thf(f7078,plain,
( ( $true
= ( in @ sK80 @ emptyset ) )
| ( sK80 = sK81 )
| ~ spl451_124
| ~ spl451_793 ),
inference(trivial_inequality_removal,[],[f7072]) ).
thf(f7091,plain,
( ( sK80 = sK81 )
| ~ spl451_75
| ~ spl451_124
| ~ spl451_793 ),
inference(forward_subsumption_resolution,[],[f7078,f2504]) ).
thf(f7092,plain,
( $false
| ~ spl451_75
| ~ spl451_124
| spl451_381
| ~ spl451_793 ),
inference(forward_subsumption_resolution,[],[f7091,f3889]) ).
thf(f7093,plain,
( ~ spl451_75
| ~ spl451_124
| spl451_381
| ~ spl451_793 ),
inference(avatar_contradiction_clause,[],[f7092]) ).
cnf(s149,plain,
( spl451_75
| ~ spl451_204 ),
inference(sat_conversion,[],[f3169]) ).
cnf(s193,plain,
( spl451_53
| ~ spl451_128 ),
inference(sat_conversion,[],[f3392]) ).
cnf(s294,plain,
~ spl451_381,
inference(sat_conversion,[],[f3890]) ).
cnf(s436,plain,
( ~ spl451_42
| spl451_124 ),
inference(sat_conversion,[],[f4461]) ).
cnf(s446,plain,
spl451_42,
inference(sat_conversion,[],[f4493]) ).
cnf(s453,plain,
spl451_204,
inference(sat_conversion,[],[f4513]) ).
cnf(s564,plain,
spl451_412,
inference(sat_conversion,[],[f4956]) ).
cnf(s639,plain,
spl451_525,
inference(sat_conversion,[],[f5240]) ).
cnf(s657,plain,
( ~ spl451_525
| spl451_670 ),
inference(sat_conversion,[],[f5298]) ).
cnf(s661,plain,
( ~ spl451_412
| spl451_673 ),
inference(sat_conversion,[],[f5312]) ).
cnf(s703,plain,
spl451_704,
inference(sat_conversion,[],[f5464]) ).
cnf(s751,plain,
spl451_128,
inference(sat_conversion,[],[f5614]) ).
cnf(s786,plain,
( ~ spl451_673
| ~ spl451_704
| spl451_765 ),
inference(sat_conversion,[],[f5993]) ).
cnf(s804,plain,
( ~ spl451_53
| ~ spl451_765
| spl451_781
| spl451_782 ),
inference(sat_conversion,[],[f6665]) ).
cnf(s816,plain,
( ~ spl451_670
| ~ spl451_781
| spl451_793 ),
inference(sat_conversion,[],[f6913]) ).
cnf(s827,plain,
( ~ spl451_673
| ~ spl451_782
| spl451_793 ),
inference(sat_conversion,[],[f7020]) ).
cnf(s832,plain,
( ~ spl451_75
| ~ spl451_124
| spl451_381
| ~ spl451_793 ),
inference(sat_conversion,[],[f7093]) ).
cnf(s841,plain,
spl451_670,
inference(rat,[],[s657,s639]) ).
cnf(s857,plain,
spl451_673,
inference(rat,[],[s661,s564]) ).
cnf(s858,plain,
spl451_765,
inference(rat,[],[s786,s703,s857]) ).
cnf(s876,plain,
spl451_124,
inference(rat,[],[s436,s446]) ).
cnf(s968,plain,
spl451_53,
inference(rat,[],[s193,s751]) ).
cnf(s985,plain,
spl451_75,
inference(rat,[],[s149,s453]) ).
cnf(s986,plain,
~ spl451_793,
inference(rat,[],[s832,s294,s876,s985]) ).
cnf(s992,plain,
~ spl451_781,
inference(rat,[],[s816,s841,s986]) ).
cnf(s993,plain,
~ spl451_782,
inference(rat,[],[s827,s857,s986]) ).
cnf(s995,plain,
$false,
inference(rat,[],[s804,s968,s858,s993,s992]) ).
thf(f7094,plain,
$false,
inference(avatar_sat_refutation,[],[s995]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU647^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n018.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 14:04:26 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.21/0.26 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.57/0.44 % (123976)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.57/0.44 % (123986)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2084530683:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.57/0.44 % (123987)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.57/0.44 % (123987)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
% 0.57/0.44 % (123985)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1011661493:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.57/0.44 % (123982)lrs+10_16_si=on:nwc=1.5:random_seed=2258176348:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.57/0.44 % (123983)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2722106167:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.57/0.44 % (123984)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=861983122: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)
% 0.57/0.44 % (123981)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=818643192:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.57/0.44 % (123987)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=3930297282:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.57/0.44 % (123983)Instruction limit reached!
% 0.57/0.44 % (123983)------------------------------
% 0.57/0.44 % (123983)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.44 % (123983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.44 % (123983)CaDiCaL version: 2.1.3
% 0.57/0.44 % (123983)Termination reason: Instruction limit
% 0.57/0.44 % (123983)Termination phase: shuffling
% 0.57/0.44 % (123983)Time elapsed: 0.002 s
% 0.57/0.44 % (123983)Peak memory usage: 10 MB
% 0.57/0.44 % (123983)Instructions burned: 3 (million)
% 0.57/0.44 % (123982)Instruction limit reached!
% 0.57/0.44 % (123982)------------------------------
% 0.57/0.44 % (123982)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.44 % (123982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.44 % (123982)CaDiCaL version: 2.1.3
% 0.57/0.44 % (123982)Termination reason: Instruction limit
% 0.57/0.44 % (123982)Termination phase: shuffling
% 0.57/0.44 % (123982)Time elapsed: 0.016 s
% 0.57/0.44 % (123982)Peak memory usage: 10 MB
% 0.57/0.44 % (123982)Instructions burned: 18 (million)
% 0.57/0.44 % (123986)Instruction limit reached!
% 0.57/0.44 % (123986)------------------------------
% 0.57/0.44 % (123986)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.44 % (123986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.44 % (123986)CaDiCaL version: 2.1.3
% 0.57/0.44 % (123986)Termination reason: Instruction limit
% 0.57/0.44 % (123986)Termination phase: Equality resolution with deletion
% 0.57/0.44 % (123986)Time elapsed: 0.024 s
% 0.57/0.44 % (123986)Peak memory usage: 12 MB
% 0.57/0.44 % (123986)Instructions burned: 77 (million)
% 0.57/0.44 % (123985)Instruction limit reached!
% 0.57/0.44 % (123985)------------------------------
% 0.57/0.44 % (123985)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.44 % (123985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.44 % (123985)CaDiCaL version: 2.1.3
% 0.57/0.44 % (123985)Termination reason: Instruction limit
% 0.57/0.44 % (123985)Termination phase: Preprocessing 3
% 0.57/0.44 % (123985)Time elapsed: 0.017 s
% 0.57/0.44 % (123985)Peak memory usage: 11 MB
% 0.57/0.44 % (123985)Instructions burned: 25 (million)
% 0.57/0.44 % (123995)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3926403771:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.57/0.44 % (123995)Instruction limit reached!
% 0.57/0.44 % (123995)------------------------------
% 0.57/0.44 % (123995)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.48 % (123995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.48 % (123995)CaDiCaL version: 2.1.3
% 0.57/0.48 % (123995)Termination reason: Instruction limit
% 0.57/0.48 % (123995)Termination phase: shuffling
% 0.57/0.48 % (123995)Time elapsed: 0.003 s
% 0.57/0.48 % (123995)Peak memory usage: 10 MB
% 0.57/0.48 % (123995)Instructions burned: 3 (million)
% 0.57/0.48 % (123997)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.57/0.48 % (123998)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1822809109:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.57/0.48 % (123996)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=625924984:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.57/0.48 % (123997)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1517258347:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.57/0.48 % (123996)Instruction limit reached!
% 0.57/0.48 % (123996)------------------------------
% 0.57/0.48 % (123996)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.48 % (123996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.48 % (123996)CaDiCaL version: 2.1.3
% 0.57/0.48 % (123996)Termination reason: Instruction limit
% 0.57/0.48 % (123996)Termination phase: shuffling
% 0.57/0.48 % (123996)Time elapsed: 0.006 s
% 0.57/0.48 % (123996)Peak memory usage: 10 MB
% 0.57/0.48 % (123996)Instructions burned: 5 (million)
% 0.57/0.48 % (123998)Instruction limit reached!
% 0.57/0.48 % (123998)------------------------------
% 0.57/0.48 % (123998)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.48 % (123998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.48 % (123998)CaDiCaL version: 2.1.3
% 0.57/0.48 % (123998)Termination reason: Instruction limit
% 0.57/0.48 % (123998)Termination phase: shuffling
% 0.57/0.48 % (123998)Time elapsed: 0.011 s
% 0.57/0.48 % (123998)Peak memory usage: 10 MB
% 0.57/0.48 % (123998)Instructions burned: 12 (million)
% 0.57/0.48 % (123997)Instruction limit reached!
% 0.57/0.48 % (123997)------------------------------
% 0.57/0.48 % (123997)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.48 % (123997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.48 % (123997)CaDiCaL version: 2.1.3
% 0.57/0.48 % (123997)Termination reason: Instruction limit
% 0.57/0.48 % (123997)Termination phase: shuffling
% 0.57/0.48 % (123997)Time elapsed: 0.009 s
% 0.57/0.48 % (123997)Peak memory usage: 10 MB
% 0.57/0.48 % (123997)Instructions burned: 8 (million)
% 0.57/0.48 % (124000)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
% 0.57/0.48 % (124000)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.57/0.48 % (123981)Instruction limit reached!
% 0.57/0.48 % (123981)------------------------------
% 0.57/0.48 % (123981)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.48 % (123981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.48 % (123981)CaDiCaL version: 2.1.3
% 0.57/0.48 % (123981)Termination reason: Instruction limit
% 0.57/0.48 % (123981)Termination phase: Property scanning
% 0.57/0.48 % (123981)Time elapsed: 0.069 s
% 0.57/0.48 % (123981)Peak memory usage: 12 MB
% 0.57/0.48 % (123981)Instructions burned: 87 (million)
% 0.57/0.48 % (124000)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=313159361:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.57/0.48 % (124004)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=2030649487:i=86:piset=equals:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/86Mi)
% 0.57/0.48 % (124006)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.57/0.48 % (124000)Instruction limit reached!
% 0.57/0.48 % (124000)------------------------------
% 1.45/0.52 % (124000)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.52 % (124000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.52 % (124000)CaDiCaL version: 2.1.3
% 1.45/0.52 % (124000)Termination reason: Instruction limit
% 1.45/0.52 % (124000)Termination phase: Property scanning
% 1.45/0.52 % (124000)Time elapsed: 0.016 s
% 1.45/0.52 % (124000)Peak memory usage: 10 MB
% 1.45/0.52 % (124000)Instructions burned: 29 (million)
% 1.45/0.52 % (124006)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=3610257610:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.45/0.52 % (124006)Instruction limit reached!
% 1.45/0.52 % (124006)------------------------------
% 1.45/0.52 % (124006)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.52 % (124006)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.52 % (124006)CaDiCaL version: 2.1.3
% 1.45/0.52 % (124006)Termination reason: Instruction limit
% 1.45/0.52 % (124006)Termination phase: shuffling
% 1.45/0.52 % (124006)Time elapsed: 0.002 s
% 1.45/0.52 % (124006)Peak memory usage: 10 MB
% 1.45/0.52 % (124006)Instructions burned: 4 (million)
% 1.45/0.52 % (124007)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3934063980:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.45/0.52 % (124005)lrs+10_1_si=on:cs=on:random_seed=3910323500:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.45/0.52 % (124004)Instruction limit reached!
% 1.45/0.52 % (124004)------------------------------
% 1.45/0.52 % (124004)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.52 % (124004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.52 % (124004)CaDiCaL version: 2.1.3
% 1.45/0.52 % (124004)Termination reason: Instruction limit
% 1.45/0.52 % (124004)Termination phase: Saturation
% 1.45/0.52 % (124004)Time elapsed: 0.021 s
% 1.45/0.52 % (124004)Peak memory usage: 12 MB
% 1.45/0.52 % (124004)Instructions burned: 87 (million)
% 1.45/0.52 % (124005)Instruction limit reached!
% 1.45/0.52 % (124005)------------------------------
% 1.45/0.52 % (124005)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.52 % (124005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.52 % (124005)CaDiCaL version: 2.1.3
% 1.45/0.52 % (124005)Termination reason: Instruction limit
% 1.45/0.52 % (124005)Termination phase: shuffling
% 1.45/0.52 % (124005)Time elapsed: 0.007 s
% 1.45/0.52 % (124005)Peak memory usage: 10 MB
% 1.45/0.52 % (124005)Instructions burned: 8 (million)
% 1.45/0.52 % (123987)Instruction limit reached!
% 1.45/0.52 % (123987)------------------------------
% 1.45/0.52 % (123987)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.52 % (123987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.52 % (123987)CaDiCaL version: 2.1.3
% 1.45/0.52 % (123987)Termination reason: Instruction limit
% 1.45/0.52 % (123987)Termination phase: Saturation
% 1.45/0.52 % (123987)Time elapsed: 0.106 s
% 1.45/0.52 % (123987)Peak memory usage: 14 MB
% 1.45/0.52 % (123987)Instructions burned: 162 (million)
% 1.45/0.52 % (124015)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2736932689:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.45/0.52 % (124011)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=710452133:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.45/0.52 % (124015)Instruction limit reached!
% 1.45/0.52 % (124015)------------------------------
% 1.45/0.52 % (124015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.52 % (124015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.52 % (124015)CaDiCaL version: 2.1.3
% 1.45/0.52 % (124015)Termination reason: Instruction limit
% 1.45/0.52 % (124015)Termination phase: shuffling
% 1.45/0.52 % (124015)Time elapsed: 0.004 s
% 1.45/0.52 % (124015)Peak memory usage: 10 MB
% 1.45/0.52 % (124015)Instructions burned: 16 (million)
% 1.45/0.52 % (124007)Instruction limit reached!
% 1.45/0.52 % (124007)------------------------------
% 1.45/0.52 % (124007)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.52 % (124007)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.52 % (124007)CaDiCaL version: 2.1.3
% 1.45/0.52 % (124007)Termination reason: Instruction limit
% 1.45/0.52 % (124007)Termination phase: Preprocessing 3
% 1.45/0.52 % (124007)Time elapsed: 0.019 s
% 1.45/0.52 % (124007)Peak memory usage: 11 MB
% 1.45/0.52 % (124007)Instructions burned: 39 (million)
% 1.45/0.52 % (124014)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=4207687077:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.45/0.52 % (124016)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1686612179:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.45/0.52 % (124020)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1329260404: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)
% 1.45/0.52 % (124020)Instruction limit reached!
% 1.45/0.52 % (124020)------------------------------
% 1.45/0.52 % (124020)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.52 % (124020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.52 % (124020)CaDiCaL version: 2.1.3
% 1.45/0.52 % (124020)Termination reason: Instruction limit
% 1.45/0.52 % (124020)Termination phase: shuffling
% 1.45/0.52 % (124020)Time elapsed: 0.001 s
% 1.45/0.52 % (124020)Peak memory usage: 10 MB
% 1.45/0.52 % (124020)Instructions burned: 4 (million)
% 1.45/0.52 % (124014)Instruction limit reached!
% 1.45/0.52 % (124014)------------------------------
% 1.45/0.52 % (124014)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.52 % (124014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.52 % (124014)CaDiCaL version: 2.1.3
% 1.45/0.52 % (124014)Termination reason: Instruction limit
% 1.45/0.52 % (124014)Termination phase: Preprocessing 1
% 1.45/0.52 % (124014)Time elapsed: 0.012 s
% 1.45/0.52 % (124014)Peak memory usage: 10 MB
% 1.45/0.52 % (124014)Instructions burned: 26 (million)
% 1.45/0.52 % (124017)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1186531302:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.45/0.52 % (124017)Instruction limit reached!
% 1.45/0.52 % (124017)------------------------------
% 1.45/0.52 % (124017)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.52 % (124017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.52 % (124017)CaDiCaL version: 2.1.3
% 1.45/0.52 % (124017)Termination reason: Instruction limit
% 1.45/0.52 % (124017)Termination phase: shuffling
% 1.45/0.52 % (124017)Time elapsed: 0.007 s
% 1.45/0.52 % (124017)Peak memory usage: 10 MB
% 1.45/0.52 % (124017)Instructions burned: 14 (million)
% 1.45/0.52 % (124022)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1250148213:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.45/0.52 % (124028)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
% 1.45/0.52 % (124028)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.45/0.52 % (124028)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=2114727186:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.45/0.52 % (124028)Instruction limit reached!
% 1.45/0.52 % (124028)------------------------------
% 1.45/0.52 % (124028)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.52 % (124028)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.52 % (124028)CaDiCaL version: 2.1.3
% 1.45/0.52 % (124028)Termination reason: Instruction limit
% 1.45/0.52 % (124028)Termination phase: shuffling
% 1.45/0.52 % (124028)Time elapsed: 0.004 s
% 1.45/0.52 % (124028)Peak memory usage: 10 MB
% 1.45/0.52 % (124028)Instructions burned: 15 (million)
% 1.45/0.52 % (124025)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3004893250:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.45/0.52 % (124031)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.45/0.52 % (124031)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=1080003286:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2997 on theBenchmark for (2997ds/8Mi)
% 1.45/0.52 % (124031)Instruction limit reached!
% 1.45/0.52 % (124031)------------------------------
% 1.45/0.52 % (124031)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.52 % (124031)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.52 % (124031)CaDiCaL version: 2.1.3
% 1.45/0.52 % (124031)Termination reason: Instruction limit
% 1.45/0.52 % (124031)Termination phase: shuffling
% 1.45/0.52 % (124031)Time elapsed: 0.002 s
% 1.45/0.52 % (124031)Peak memory usage: 10 MB
% 1.45/0.52 % (124031)Instructions burned: 10 (million)
% 1.45/0.52 % (124027)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2674579645:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.45/0.52 % (124025)Instruction limit reached!
% 1.45/0.52 % (124025)------------------------------
% 1.45/0.52 % (124025)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.52 % (124025)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.52 % (124025)CaDiCaL version: 2.1.3
% 1.45/0.52 % (124025)Termination reason: Instruction limit
% 1.45/0.52 % (124025)Termination phase: Property scanning
% 1.45/0.52 % (124025)Time elapsed: 0.011 s
% 1.45/0.52 % (124025)Peak memory usage: 10 MB
% 1.45/0.52 % (124025)Instructions burned: 24 (million)
% 1.45/0.52 % (124022)Instruction limit reached!
% 1.45/0.52 % (124022)------------------------------
% 1.45/0.52 % (124022)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.52 % (124022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.52 % (124022)CaDiCaL version: 2.1.3
% 1.45/0.52 % (124022)Termination reason: Instruction limit
% 1.45/0.52 % (124022)Termination phase: Property scanning
% 1.45/0.52 % (124022)Time elapsed: 0.026 s
% 1.45/0.52 % (124022)Peak memory usage: 10 MB
% 1.45/0.52 % (124022)Instructions burned: 26 (million)
% 1.45/0.52 % (124034)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=2863055133:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 1.45/0.53 % (124034)Instruction limit reached!
% 1.45/0.53 % (124034)------------------------------
% 1.45/0.53 % (124034)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.53 % (124034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.53 % (124034)CaDiCaL version: 2.1.3
% 1.45/0.53 % (124034)Termination reason: Instruction limit
% 1.45/0.53 % (124034)Termination phase: Property scanning
% 1.45/0.53 % (124034)Time elapsed: 0.007 s
% 1.45/0.53 % (124034)Peak memory usage: 10 MB
% 1.45/0.53 % (124034)Instructions burned: 33 (million)
% 1.45/0.53 % (124036)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=1291372081:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 1.45/0.53 % (124037)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2759715578:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 1.45/0.53 % (123984) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-123976-123984"...
% 1.45/0.53 % (124036)Instruction limit reached!
% 1.45/0.53 % (124036)------------------------------
% 1.45/0.53 % (124036)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.53 % (124036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.53 % (124036)CaDiCaL version: 2.1.3
% 1.45/0.53 % (124036)Termination reason: Instruction limit
% 1.45/0.53 % (124036)Termination phase: shuffling
% 1.45/0.53 % (124036)Time elapsed: 0.004 s
% 1.45/0.53 % (124036)Peak memory usage: 10 MB
% 1.45/0.53 % (124036)Instructions burned: 9 (million)
% 1.45/0.53 % (124039)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1470004943:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 1.45/0.53 % (124039)Instruction limit reached!
% 1.45/0.53 % (124039)------------------------------
% 1.45/0.53 % (124039)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.53 % (124039)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.53 % (124039)CaDiCaL version: 2.1.3
% 1.45/0.53 % (124039)Termination reason: Instruction limit
% 1.45/0.53 % (124039)Termination phase: Property scanning
% 1.45/0.53 % (124039)Time elapsed: 0.005 s
% 1.45/0.53 % (124039)Peak memory usage: 10 MB
% 1.45/0.53 % (124039)Instructions burned: 22 (million)
% 1.45/0.53 % (123984)...printing done.
% 1.45/0.53 % (124037)Instruction limit reached!
% 1.45/0.53 % (124037)------------------------------
% 1.45/0.53 % (124037)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.53 % (124037)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.53 % (124037)CaDiCaL version: 2.1.3
% 1.45/0.53 % (124037)Termination reason: Instruction limit
% 1.45/0.53 % (124037)Termination phase: Property scanning
% 1.45/0.53 % (124037)Time elapsed: 0.010 s
% 1.45/0.53 % (124037)Peak memory usage: 10 MB
% 1.45/0.53 % (124037)Instructions burned: 23 (million)
% 1.45/0.53 % (123984)Refutation found. Thanks to Tanya!
% 1.45/0.53 % SZS status Theorem for theBenchmark
% 1.45/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 1.45/0.53 % (123984)------------------------------
% 1.45/0.53 % (123984)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.45/0.53 % (123984)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.45/0.53 % (123984)CaDiCaL version: 2.1.3
% 1.45/0.53 % (123984)Termination reason: Refutation
% 1.45/0.53 % (123984)Time elapsed: 0.197 s
% 1.45/0.53 % (123984)Peak memory usage: 17 MB
% 1.45/0.53 % (123984)Instructions burned: 298 (million)
% 1.45/0.53 % (123976)Success in time 0.255 s
% 1.45/0.53 % Vampire exiting
%------------------------------------------------------------------------------