%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU676^1 : 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 : n015.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 08:30:41 AM UTC 2026
% Result : Theorem 1.16s 0.49s
% Output : Refutation 1.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 72 ( 24 unt; 0 typ; 8 def)
% Number of atoms : 3966 (1076 equ; 0 cnn)
% Maximal formula atoms : 195 ( 55 avg)
% Number of connectives : 2136 ( 84 ~; 74 |; 791 &; 390 @)
% ( 12 <=>; 785 =>; 0 <=; 0 <~>)
% Maximal formula depth : 206 ( 26 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 : 383 ( 380 usr; 222 con; 0-4 aty)
% Number of variables : 112 ( 0 sgn 86 !; 26 ?; 112 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_3,type,
setextAx: $o ).
thf(func_def_5,type,
emptysetAx: $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_7,type,
setadjoinAx: $o ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_9,type,
powersetAx: $o ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_11,type,
setunionAx: $o ).
thf(func_def_13,type,
omega0Ax: $o ).
thf(func_def_14,type,
omegaSAx: $o ).
thf(func_def_15,type,
omegaIndAx: $o ).
thf(func_def_16,type,
replAx: $o ).
thf(func_def_17,type,
foundationAx: $o ).
thf(func_def_18,type,
wellorderingAx: $o ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_20,type,
descrp: $o ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_22,type,
dsetconstrI: $o ).
thf(func_def_23,type,
dsetconstrEL: $o ).
thf(func_def_24,type,
dsetconstrER: $o ).
thf(func_def_25,type,
exuE1: $o ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_27,type,
prop2setE: $o ).
thf(func_def_28,type,
emptysetE: $o ).
thf(func_def_29,type,
emptysetimpfalse: $o ).
thf(func_def_30,type,
notinemptyset: $o ).
thf(func_def_31,type,
exuE3e: $o ).
thf(func_def_32,type,
setext: $o ).
thf(func_def_33,type,
emptyI: $o ).
thf(func_def_34,type,
noeltsimpempty: $o ).
thf(func_def_35,type,
setbeta: $o ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_37,type,
nonemptyE1: $o ).
thf(func_def_38,type,
nonemptyI: $o ).
thf(func_def_39,type,
nonemptyI1: $o ).
thf(func_def_40,type,
setadjoinIL: $o ).
thf(func_def_41,type,
emptyinunitempty: $o ).
thf(func_def_42,type,
setadjoinIR: $o ).
thf(func_def_43,type,
setadjoinE: $o ).
thf(func_def_44,type,
setadjoinOr: $o ).
thf(func_def_45,type,
setoftrueEq: $o ).
thf(func_def_46,type,
powersetI: $o ).
thf(func_def_47,type,
emptyinPowerset: $o ).
thf(func_def_48,type,
emptyInPowerset: $o ).
thf(func_def_49,type,
powersetE: $o ).
thf(func_def_50,type,
setunionI: $o ).
thf(func_def_51,type,
setunionE: $o ).
thf(func_def_52,type,
subPowSU: $o ).
thf(func_def_53,type,
exuE2: $o ).
thf(func_def_54,type,
nonemptyImpWitness: $o ).
thf(func_def_55,type,
uniqinunit: $o ).
thf(func_def_56,type,
notinsingleton: $o ).
thf(func_def_57,type,
eqinunit: $o ).
thf(func_def_58,type,
singletonsswitch: $o ).
thf(func_def_59,type,
upairsetE: $o ).
thf(func_def_60,type,
upairsetIL: $o ).
thf(func_def_61,type,
upairsetIR: $o ).
thf(func_def_62,type,
emptyE1: $o ).
thf(func_def_63,type,
vacuousDall: $o ).
thf(func_def_64,type,
quantDeMorgan1: $o ).
thf(func_def_65,type,
quantDeMorgan2: $o ).
thf(func_def_66,type,
quantDeMorgan3: $o ).
thf(func_def_67,type,
quantDeMorgan4: $o ).
thf(func_def_68,type,
prop2setI: $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_70,type,
prop2set2propI: $o ).
thf(func_def_71,type,
notdexE: $o ).
thf(func_def_72,type,
notdallE: $o ).
thf(func_def_73,type,
exuI1: $o ).
thf(func_def_74,type,
exuI3: $o ).
thf(func_def_75,type,
exuI2: $o ).
thf(func_def_76,type,
inCongP: $o ).
thf(func_def_77,type,
in__Cong: $o ).
thf(func_def_78,type,
exuE3u: $o ).
thf(func_def_79,type,
exu__Cong: $o ).
thf(func_def_80,type,
emptyset__Cong: $o ).
thf(func_def_81,type,
setadjoin__Cong: $o ).
thf(func_def_82,type,
powerset__Cong: $o ).
thf(func_def_83,type,
setunion__Cong: $o ).
thf(func_def_84,type,
omega__Cong: $o ).
thf(func_def_85,type,
exuEu: $o ).
thf(func_def_86,type,
descr__Cong: $o ).
thf(func_def_87,type,
dsetconstr__Cong: $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_91,type,
subsetI1: $o ).
thf(func_def_92,type,
eqimpsubset2: $o ).
thf(func_def_93,type,
eqimpsubset1: $o ).
thf(func_def_94,type,
subsetI2: $o ).
thf(func_def_95,type,
emptysetsubset: $o ).
thf(func_def_96,type,
subsetE: $o ).
thf(func_def_97,type,
subsetE2: $o ).
thf(func_def_98,type,
notsubsetI: $o ).
thf(func_def_99,type,
notequalI1: $o ).
thf(func_def_100,type,
notequalI2: $o ).
thf(func_def_101,type,
subsetRefl: $o ).
thf(func_def_102,type,
subsetTrans: $o ).
thf(func_def_103,type,
setadjoinSub: $o ).
thf(func_def_104,type,
setadjoinSub2: $o ).
thf(func_def_105,type,
subset2powerset: $o ).
thf(func_def_106,type,
setextsub: $o ).
thf(func_def_107,type,
subsetemptysetimpeq: $o ).
thf(func_def_108,type,
powersetI1: $o ).
thf(func_def_109,type,
powersetE1: $o ).
thf(func_def_110,type,
inPowerset: $o ).
thf(func_def_111,type,
powersetsubset: $o ).
thf(func_def_112,type,
sepInPowerset: $o ).
thf(func_def_113,type,
sepSubset: $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_115,type,
binunionIL: $o ).
thf(func_def_116,type,
upairset2IR: $o ).
thf(func_def_117,type,
binunionIR: $o ).
thf(func_def_118,type,
binunionEcases: $o ).
thf(func_def_119,type,
binunionE: $o ).
thf(func_def_120,type,
binunionLsub: $o ).
thf(func_def_121,type,
binunionRsub: $o ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_123,type,
binintersectI: $o ).
thf(func_def_124,type,
binintersectSubset5: $o ).
thf(func_def_125,type,
binintersectEL: $o ).
thf(func_def_126,type,
binintersectLsub: $o ).
thf(func_def_127,type,
binintersectSubset2: $o ).
thf(func_def_128,type,
binintersectSubset3: $o ).
thf(func_def_129,type,
binintersectER: $o ).
thf(func_def_130,type,
disjointsetsI1: $o ).
thf(func_def_131,type,
binintersectRsub: $o ).
thf(func_def_132,type,
binintersectSubset4: $o ).
thf(func_def_133,type,
binintersectSubset1: $o ).
thf(func_def_134,type,
bs114d: $o ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_137,type,
setminusI: $o ).
thf(func_def_138,type,
setminusEL: $o ).
thf(func_def_139,type,
setminusER: $o ).
thf(func_def_140,type,
setminusSubset2: $o ).
thf(func_def_141,type,
setminusERneg: $o ).
thf(func_def_142,type,
setminusELneg: $o ).
thf(func_def_143,type,
setminusILneg: $o ).
thf(func_def_144,type,
setminusIRneg: $o ).
thf(func_def_145,type,
setminusLsub: $o ).
thf(func_def_146,type,
setminusSubset1: $o ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_148,type,
symdiffE: $o ).
thf(func_def_149,type,
symdiffI1: $o ).
thf(func_def_150,type,
symdiffI2: $o ).
thf(func_def_151,type,
symdiffIneg1: $o ).
thf(func_def_152,type,
symdiffIneg2: $o ).
thf(func_def_153,type,
iskpair: $i > $o ).
thf(func_def_154,type,
secondinupair: $o ).
thf(func_def_155,type,
setukpairIL: $o ).
thf(func_def_156,type,
setukpairIR: $o ).
thf(func_def_157,type,
kpairiskpair: $o ).
thf(func_def_158,type,
kpair: $i > $i > $i ).
thf(func_def_159,type,
kpairp: $o ).
thf(func_def_160,type,
cartprod: $i > $i > $i ).
thf(func_def_161,type,
singletonsubset: $o ).
thf(func_def_162,type,
singletoninpowerset: $o ).
thf(func_def_163,type,
singletoninpowunion: $o ).
thf(func_def_164,type,
upairset2E: $o ).
thf(func_def_165,type,
upairsubunion: $o ).
thf(func_def_166,type,
upairinpowunion: $o ).
thf(func_def_167,type,
ubforcartprodlem1: $o ).
thf(func_def_168,type,
ubforcartprodlem2: $o ).
thf(func_def_169,type,
ubforcartprodlem3: $o ).
thf(func_def_170,type,
cartprodpairin: $o ).
thf(func_def_171,type,
cartprodmempair1: $o ).
thf(func_def_172,type,
cartprodmempair: $o ).
thf(func_def_173,type,
setunionE2: $o ).
thf(func_def_174,type,
setunionsingleton1: $o ).
thf(func_def_175,type,
setunionsingleton2: $o ).
thf(func_def_176,type,
setunionsingleton: $o ).
thf(func_def_177,type,
singleton: $i > $o ).
thf(func_def_178,type,
singletonprop: $o ).
thf(func_def_179,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_180,type,
ex1E1: $o ).
thf(func_def_181,type,
ex1I: $o ).
thf(func_def_182,type,
ex1I2: $o ).
thf(func_def_183,type,
singletonsuniq: $o ).
thf(func_def_184,type,
atmost1p: $i > $o ).
thf(func_def_185,type,
atleast2p: $i > $o ).
thf(func_def_186,type,
atmost2p: $i > $o ).
thf(func_def_187,type,
upairsetp: $i > $o ).
thf(func_def_188,type,
setukpairinjL1: $o ).
thf(func_def_189,type,
kfstsingleton: $o ).
thf(func_def_190,type,
theprop: $o ).
thf(func_def_191,type,
kfst: $i > $i ).
thf(func_def_192,type,
kfstpairEq: $o ).
thf(func_def_193,type,
cartprodfstin: $o ).
thf(func_def_194,type,
setukpairinjL2: $o ).
thf(func_def_195,type,
setukpairinjL: $o ).
thf(func_def_196,type,
setukpairinjR11: $o ).
thf(func_def_197,type,
setukpairinjR12: $o ).
thf(func_def_198,type,
setukpairinjR1: $o ).
thf(func_def_199,type,
upairequniteq: $o ).
thf(func_def_200,type,
setukpairinjR2: $o ).
thf(func_def_201,type,
setukpairinjR: $o ).
thf(func_def_202,type,
ksndsingleton: $o ).
thf(func_def_203,type,
ksnd: $i > $i ).
thf(func_def_204,type,
ksndpairEq: $o ).
thf(func_def_205,type,
kpairsurjEq: $o ).
thf(func_def_206,type,
cartprodsndin: $o ).
thf(func_def_207,type,
cartprodpairmemEL: $o ).
thf(func_def_208,type,
cartprodpairmemER: $o ).
thf(func_def_209,type,
cartprodmempaircEq: $o ).
thf(func_def_210,type,
cartprodfstpairEq: $o ).
thf(func_def_211,type,
cartprodsndpairEq: $o ).
thf(func_def_212,type,
cartprodpairsurjEq: $o ).
thf(func_def_213,type,
breln: $i > $i > $i > $o ).
thf(func_def_214,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_215,type,
dpsetconstrI: $o ).
thf(func_def_216,type,
dpsetconstrSub: $o ).
thf(func_def_217,type,
setOfPairsIsBReln: $o ).
thf(func_def_218,type,
dpsetconstrERa: $o ).
thf(func_def_219,type,
dpsetconstrEL1: $o ).
thf(func_def_220,type,
dpsetconstrEL2: $o ).
thf(func_def_221,type,
dpsetconstrER: $o ).
thf(func_def_222,type,
func: $i > $i > $i > $o ).
thf(func_def_223,type,
funcSet: $i > $i > $i ).
thf(func_def_224,type,
funcImageSingleton: $o ).
thf(func_def_225,type,
apProp: $o ).
thf(func_def_226,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_227,type,
app: $o ).
thf(func_def_228,type,
infuncsetfunc: $o ).
thf(func_def_231,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_232,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_233,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_234,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_235,type,
vAND: $o > $o > $o ).
thf(func_def_236,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_237,type,
vIMP: $o > $o > $o ).
thf(func_def_238,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_239,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_240,type,
vNOT: $o > $o ).
thf(func_def_241,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_242,type,
sP0: $i > $i > $o ).
thf(func_def_243,type,
sP1: $i > $o ).
thf(func_def_244,type,
sP2: $o ).
thf(func_def_248,type,
sK6: $i > $i ).
thf(func_def_259,type,
sK17: $i > $i > $o ).
thf(func_def_266,type,
sK24: $i > $o ).
thf(func_def_268,type,
sK26: $i > ( $i > $o ) > $i ).
thf(func_def_278,type,
sK36: $i > $o ).
thf(func_def_279,type,
sK37: $i > ( $i > $o ) > $i ).
thf(func_def_280,type,
sK38: $i > $o ).
thf(func_def_302,type,
sK60: $i > ( $i > $o ) > $i ).
thf(func_def_303,type,
sK61: $i > ( $i > $o ) > $i ).
thf(func_def_304,type,
sK62: $i > $o ).
thf(func_def_315,type,
sK73: $i > $o ).
thf(func_def_319,type,
sK77: $i > $i > $i ).
thf(func_def_323,type,
sK81: $i > $i > $i ).
thf(func_def_329,type,
sK87: $i > $i > $o ).
thf(func_def_344,type,
sK102: $i > $i > $o ).
thf(func_def_350,type,
sK108: $i > $o ).
thf(func_def_352,type,
sK110: ( $i > $o ) > $i > $i ).
thf(func_def_367,type,
sK125: $i > $o ).
thf(func_def_368,type,
sK126: $i > $o ).
thf(func_def_369,type,
sK127: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_370,type,
sK128: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_374,type,
sK132: $i > $i > $o ).
thf(func_def_381,type,
sK139: $i > $o ).
thf(func_def_400,type,
sK158: $i > $i ).
thf(func_def_406,type,
sK164: $i > $o ).
thf(func_def_409,type,
sK167: $i > ( $i > $o ) > $i ).
thf(func_def_410,type,
sK168: $i > $o ).
thf(func_def_422,type,
sK180: $i > $o ).
thf(func_def_425,type,
sK183: $i > ( $i > $o ) > $i ).
thf(func_def_430,type,
sK188: $o ).
thf(func_def_431,type,
sK189: $i > $i > $i > $i ).
thf(func_def_432,type,
sK190: $i > $i > $i > $i ).
thf(func_def_437,type,
sK195: $i > $i ).
thf(func_def_438,type,
sK196: $i > $i ).
thf(func_def_439,type,
sK197: $i > $i ).
thf(func_def_440,type,
sK198: $i > $i ).
thf(func_def_441,type,
sK199: $i > $i ).
thf(func_def_442,type,
sK200: $i > $i > $i > $i ).
thf(func_def_443,type,
sK201: $i > $i ).
thf(func_def_444,type,
sK202: $i > $i ).
thf(func_def_445,type,
sK203: $i > $i ).
thf(func_def_446,type,
sK204: $i > $i ).
thf(func_def_447,type,
sK205: $i > $i > $i ).
thf(func_def_448,type,
sK206: $i > $i > $i ).
thf(func_def_449,type,
sK207: $i > $i > $i > $i ).
thf(func_def_450,type,
sK208: $i > $i > $i > $i ).
thf(func_def_451,type,
sK209: $i > $i > $i > $i ).
thf(func_def_452,type,
sK210: $i > $i > $i ).
thf(func_def_453,type,
sK211: $i > $i > $i ).
thf(func_def_454,type,
sK212: $i > $i > $i ).
thf(func_def_458,type,
sK216: $i > $i > $o ).
thf(func_def_462,type,
sK220: $i > $o ).
thf(func_def_463,type,
sK221: ( $i > $o ) > $i > $i > $i ).
thf(func_def_466,type,
sK224: $i > $i > $i ).
thf(func_def_491,type,
sK249: $o ).
thf(func_def_524,type,
sK282: $i > $o ).
thf(func_def_527,type,
sK285: $i > $i > $o ).
thf(func_def_533,type,
sK291: $i > $o ).
thf(func_def_536,type,
sK294: $i > ( $i > $o ) > $i ).
thf(func_def_537,type,
sK295: $i > $o ).
thf(func_def_538,type,
sK296: $i > $o ).
thf(func_def_539,type,
sK297: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_540,type,
sK298: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_553,type,
sK311: $o ).
thf(func_def_566,type,
sK324: $i > $i ).
thf(func_def_572,type,
sK330: $i > $i ).
thf(func_def_577,type,
sK335: $i > $o ).
thf(func_def_578,type,
sK336: ( $i > $o ) > $i ).
thf(func_def_583,type,
sK341: $i > $o ).
thf(func_def_584,type,
sK342: $i > $i ).
thf(func_def_585,type,
sK343: ( $i > $o ) > $i ).
thf(func_def_588,type,
sK346: $o ).
thf(func_def_595,type,
sK353: $i > $i ).
thf(func_def_598,type,
sK356: ( $i > $o ) > $i ).
thf(func_def_599,type,
sK357: $i > $o ).
thf(func_def_600,type,
sK358: $i > $i ).
thf(func_def_601,type,
sK359: $i > $o ).
thf(func_def_607,type,
sK365: $i > $o ).
thf(func_def_609,type,
sK367: $i > $o ).
thf(func_def_612,type,
sK370: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_613,type,
sK371: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_616,type,
sK374: $i > $o ).
thf(func_def_617,type,
sK375: $i > $o ).
thf(func_def_618,type,
sK376: ( $i > $o ) > $i > $i ).
thf(func_def_620,type,
sK378: $i > $o ).
thf(func_def_627,type,
sK385: $o ).
thf(func_def_631,type,
sK389: $i > $i > $o ).
thf(func_def_634,type,
sK392: $o ).
thf(func_def_637,type,
sK395: $i > $i > $i ).
thf(func_def_644,type,
sK402: $i > $i > $i ).
thf(func_def_646,type,
sK404: ( $i > $i > $o ) > $i > $i ).
thf(func_def_647,type,
sK405: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_648,type,
sK406: ( $i > $i > $o ) > $i > $i ).
thf(func_def_650,type,
sK408: $i > $i > $o ).
thf(func_def_651,type,
sK409: $i > $i ).
thf(func_def_652,type,
sK410: $i > $i ).
thf(func_def_653,type,
sK411: ( $i > $o ) > $i > $i ).
thf(func_def_655,type,
sK413: $i > $o ).
thf(func_def_664,type,
sK422: $o ).
thf(func_def_673,type,
sK431: $i > $i > $i ).
thf(func_def_701,type,
sK459: $i > $o ).
thf(func_def_704,type,
sK462: $i > $o ).
thf(func_def_724,type,
sK482: $o > $i > $i > $i ).
thf(func_def_727,type,
sK485: $o ).
thf(func_def_747,type,
sK505: $i > $o ).
thf(func_def_749,type,
sK507: $i > $i > $i ).
thf(func_def_750,type,
sK508: $i > $i > $i ).
thf(func_def_755,type,
sK513: $i > $i > $i ).
thf(func_def_763,type,
sK521: $i > $o ).
thf(func_def_765,type,
sK523: $i > $o ).
thf(func_def_767,type,
sK525: ( $i > $o ) > $i ).
thf(func_def_768,type,
sK526: ( $i > $o ) > $i ).
thf(func_def_778,type,
sK536: $i > ( $i > $o ) > $i ).
thf(func_def_779,type,
sK537: $i > ( $i > $o ) > $i ).
thf(func_def_780,type,
sK538: $i > $o ).
thf(func_def_786,type,
sK544: $i > $i > $i ).
thf(func_def_789,type,
sK547: $i > $i ).
thf(func_def_792,type,
sK550: $i > $i ).
thf(func_def_794,type,
sK552: $i > $o ).
thf(func_def_795,type,
sK553: ( $i > $o ) > $i > $i ).
thf(f199,axiom,
( app
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( ap @ X0 @ X1 @ X2 @ X3 ) @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',app) ).
thf(f200,axiom,
( infuncsetfunc
= ( ! [X2: $i,X1: $i,X0: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ( func @ X0 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(f201,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ! [X2: $i,X1: $i,X0: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( ap @ X0 @ X1 @ X2 @ X3 ) @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap2p) ).
thf(f202,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ! [X2: $i,X1: $i,X0: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( ap @ X0 @ X1 @ X2 @ X3 ) @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f201]) ).
thf(f335,plain,
( app
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( in @ ( ap @ X0 @ X1 @ X2 @ X3 ) @ X1 ) ) ) ) ),
inference(rectify,[],[f199]) ).
thf(f336,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( func @ X0 @ X1 @ X2 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( in @ ( ap @ X0 @ X1 @ X2 @ X3 ) @ X1 )
= $true ) ) )
<=> ( app = $true ) ),
inference(fool_elimination,[],[f335]) ).
thf(f400,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ ( funcSet @ X2 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( in @ ( ap @ X2 @ X1 @ X0 @ X3 ) @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f202]) ).
thf(f401,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ( ( setukpairinjR2 = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ( ( ksndpairEq = $true )
=> ( ( kpairsurjEq = $true )
=> ( ( cartprodsndin = $true )
=> ( ( cartprodpairmemEL = $true )
=> ( ( cartprodpairmemER = $true )
=> ( ( cartprodmempaircEq = $true )
=> ( ( cartprodfstpairEq = $true )
=> ( ( cartprodsndpairEq = $true )
=> ( ( cartprodpairsurjEq = $true )
=> ( ( dpsetconstrI = $true )
=> ( ( dpsetconstrSub = $true )
=> ( ( setOfPairsIsBReln = $true )
=> ( ( dpsetconstrERa = $true )
=> ( ( dpsetconstrEL1 = $true )
=> ( ( dpsetconstrEL2 = $true )
=> ( ( dpsetconstrER = $true )
=> ( ( funcImageSingleton = $true )
=> ( ( apProp = $true )
=> ( ( app = $true )
=> ( ( infuncsetfunc = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( funcSet @ X2 @ X1 ) ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
=> ( $true
= ( in @ ( ap @ X2 @ X1 @ X0 @ X3 ) @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f400]) ).
thf(f438,plain,
( infuncsetfunc
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ ( funcSet @ X2 @ X1 ) )
=> ( func @ X2 @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f200]) ).
thf(f439,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( funcSet @ X2 @ X1 ) ) )
=> ( $true
= ( func @ X2 @ X1 @ X0 ) ) )
<=> ( infuncsetfunc = $true ) ),
inference(fool_elimination,[],[f438]) ).
thf(f649,plain,
( ! [X1: $i,X0: $i,X2: $i] :
( ( ( func @ X0 @ X1 @ X2 )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ ( ap @ X0 @ X1 @ X2 @ X3 ) @ X1 )
= $true ) ) )
<=> ( app = $true ) ),
inference(ennf_transformation,[],[f336]) ).
thf(f712,plain,
( ( infuncsetfunc = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( func @ X2 @ X1 @ X0 ) )
| ( $true
!= ( in @ X0 @ ( funcSet @ X2 @ X1 ) ) ) ) ),
inference(ennf_transformation,[],[f439]) ).
thf(f812,plain,
( ? [X1: $i,X0: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( funcSet @ X2 @ X1 ) ) )
& ? [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
& ( $true
!= ( in @ ( ap @ X2 @ X1 @ X0 @ X3 ) @ X1 ) ) ) )
& ( infuncsetfunc = $true )
& ( app = $true )
& ( apProp = $true )
& ( funcImageSingleton = $true )
& ( dpsetconstrER = $true )
& ( dpsetconstrEL2 = $true )
& ( dpsetconstrEL1 = $true )
& ( dpsetconstrERa = $true )
& ( setOfPairsIsBReln = $true )
& ( dpsetconstrSub = $true )
& ( dpsetconstrI = $true )
& ( cartprodpairsurjEq = $true )
& ( cartprodsndpairEq = $true )
& ( cartprodfstpairEq = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodpairmemER = $true )
& ( cartprodpairmemEL = $true )
& ( cartprodsndin = $true )
& ( kpairsurjEq = $true )
& ( ksndpairEq = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR = $true )
& ( setukpairinjR2 = $true )
& ( upairequniteq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjR12 = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjL = $true )
& ( setukpairinjL2 = $true )
& ( cartprodfstin = $true )
& ( kfstpairEq = $true )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( singletonsuniq = $true )
& ( ex1I2 = $true )
& ( ex1I = $true )
& ( ex1E1 = $true )
& ( singletonprop = $true )
& ( setunionsingleton = $true )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( setunionE2 = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( cartprodpairin = $true )
& ( ubforcartprodlem3 = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( upairsubunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[],[f401]) ).
thf(f813,plain,
( ( exuI3 = $true )
& ( dsetconstrEL = $true )
& ( powersetsubset = $true )
& ( cartprodfstin = $true )
& ( emptyInPowerset = $true )
& ( bs114d = $true )
& ( infuncsetfunc = $true )
& ( cartprodsndpairEq = $true )
& ( prop2set2propI = $true )
& ( quantDeMorgan3 = $true )
& ( emptyset__Cong = $true )
& ( upairset2IR = $true )
& ( kpairsurjEq = $true )
& ( setunionsingleton2 = $true )
& ( notinsingleton = $true )
& ( dpsetconstrSub = $true )
& ( powersetAx = $true )
& ( cartprodpairmemEL = $true )
& ( emptyI = $true )
& ( kpairiskpair = $true )
& ( emptyE1 = $true )
& ( uniqinunit = $true )
& ( upairset2E = $true )
& ( omega0Ax = $true )
& ( cartprodfstpairEq = $true )
& ( exuE1 = $true )
& ( cartprodpairin = $true )
& ( setadjoin__Cong = $true )
& ( symdiffE = $true )
& ( app = $true )
& ( emptysetE = $true )
& ( ksndpairEq = $true )
& ( subsetI2 = $true )
& ( setminusERneg = $true )
& ( dpsetconstrER = $true )
& ( dpsetconstrERa = $true )
& ( powersetE1 = $true )
& ( disjointsetsI1 = $true )
& ( singletonsuniq = $true )
& ( setukpairIL = $true )
& ( subsetI1 = $true )
& ( notequalI2 = $true )
& ( setukpairinjR2 = $true )
& ( notequalI1 = $true )
& ( subsetRefl = $true )
& ( setadjoinSub2 = $true )
& ( cartprodmempair1 = $true )
& ? [X1: $i,X0: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( funcSet @ X2 @ X1 ) ) )
& ? [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
& ( $true
!= ( in @ ( ap @ X2 @ X1 @ X0 @ X3 ) @ X1 ) ) ) )
& ( setminusER = $true )
& ( binintersectI = $true )
& ( dpsetconstrEL2 = $true )
& ( binintersectLsub = $true )
& ( omegaSAx = $true )
& ( kfstpairEq = $true )
& ( setadjoinAx = $true )
& ( singletonsswitch = $true )
& ( exuI1 = $true )
& ( setukpairinjL = $true )
& ( vacuousDall = $true )
& ( notdexE = $true )
& ( setminusIRneg = $true )
& ( upairsetIR = $true )
& ( notsubsetI = $true )
& ( setadjoinIR = $true )
& ( sepInPowerset = $true )
& ( setminusELneg = $true )
& ( subset2powerset = $true )
& ( symdiffIneg1 = $true )
& ( ex1E1 = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( symdiffI2 = $true )
& ( powersetI1 = $true )
& ( exuEu = $true )
& ( exuI2 = $true )
& ( binintersectER = $true )
& ( subsetemptysetimpeq = $true )
& ( subPowSU = $true )
& ( binintersectRsub = $true )
& ( binunionE = $true )
& ( nonemptyI = $true )
& ( inPowerset = $true )
& ( singletoninpowerset = $true )
& ( nonemptyE1 = $true )
& ( cartprodpairsurjEq = $true )
& ( binunionRsub = $true )
& ( upairinpowunion = $true )
& ( setadjoinSub = $true )
& ( binintersectSubset3 = $true )
& ( binunionIL = $true )
& ( nonemptyI1 = $true )
& ( ksndsingleton = $true )
& ( subsetE = $true )
& ( binunionEcases = $true )
& ( ex1I = $true )
& ( ubforcartprodlem1 = $true )
& ( wellorderingAx = $true )
& ( setukpairinjR1 = $true )
& ( funcImageSingleton = $true )
& ( binintersectEL = $true )
& ( emptysetsubset = $true )
& ( upairsetIL = $true )
& ( setukpairinjL2 = $true )
& ( descrp = $true )
& ( subsetE2 = $true )
& ( binintersectSubset4 = $true )
& ( powerset__Cong = $true )
& ( binunionIR = $true )
& ( emptyinPowerset = $true )
& ( setminusSubset1 = $true )
& ( sepSubset = $true )
& ( binintersectSubset2 = $true )
& ( singletonsubset = $true )
& ( omega__Cong = $true )
& ( in__Cong = $true )
& ( eqimpsubset1 = $true )
& ( ex1I2 = $true )
& ( singletonprop = $true )
& ( powersetI = $true )
& ( binintersectSubset1 = $true )
& ( exuE3u = $true )
& ( setminusSubset2 = $true )
& ( quantDeMorgan4 = $true )
& ( setoftrueEq = $true )
& ( setukpairinjR12 = $true )
& ( dsetconstr__Cong = $true )
& ( symdiffIneg2 = $true )
& ( cartprodmempair = $true )
& ( eqinunit = $true )
& ( exuE2 = $true )
& ( setunionI = $true )
& ( notdallE = $true )
& ( setminusEL = $true )
& ( cartprodsndin = $true )
& ( binunionLsub = $true )
& ( prop2setI = $true )
& ( setukpairinjR = $true )
& ( nonemptyImpWitness = $true )
& ( emptysetAx = $true )
& ( setadjoinOr = $true )
& ( apProp = $true )
& ( emptysetimpfalse = $true )
& ( setukpairIR = $true )
& ( setminusI = $true )
& ( upairsetE = $true )
& ( secondinupair = $true )
& ( symdiffI1 = $true )
& ( prop2setE = $true )
& ( descr__Cong = $true )
& ( setadjoinIL = $true )
& ( eqimpsubset2 = $true )
& ( setunionE = $true )
& ( singletoninpowunion = $true )
& ( setunionsingleton1 = $true )
& ( kfstsingleton = $true )
& ( dsetconstrER = $true )
& ( cartprodpairmemER = $true )
& ( setukpairinjR11 = $true )
& ( setunionAx = $true )
& ( powersetE = $true )
& ( setOfPairsIsBReln = $true )
& ( inCongP = $true )
& ( setunionsingleton = $true )
& ( setunion__Cong = $true )
& ( setext = $true )
& ( dsetconstrI = $true )
& ( exu__Cong = $true )
& ( upairsubunion = $true )
& ( notinemptyset = $true )
& ( theprop = $true )
& ( setunionE2 = $true )
& ( noeltsimpempty = $true )
& ( dpsetconstrI = $true )
& ( setbeta = $true )
& ( ubforcartprodlem2 = $true )
& ( omegaIndAx = $true )
& ( ubforcartprodlem3 = $true )
& ( quantDeMorgan2 = $true )
& ( setminusLsub = $true )
& ( kpairp = $true )
& ( setextAx = $true )
& ( setadjoinE = $true )
& ( cartprodmempaircEq = $true )
& ( setextsub = $true )
& ( quantDeMorgan1 = $true )
& ( setukpairinjL1 = $true )
& ( emptyinunitempty = $true )
& ( exuE3e = $true )
& ( subsetTrans = $true )
& ( dpsetconstrEL1 = $true )
& ( upairequniteq = $true )
& ( setminusILneg = $true )
& ( binintersectSubset5 = $true ) ),
inference(flattening,[],[f812]) ).
thf(f876,plain,
( ( ( infuncsetfunc = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( func @ X2 @ X1 @ X0 ) )
& ( $true
= ( in @ X0 @ ( funcSet @ X2 @ X1 ) ) ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( func @ X2 @ X1 @ X0 ) )
| ( $true
!= ( in @ X0 @ ( funcSet @ X2 @ X1 ) ) ) )
| ( infuncsetfunc != $true ) ) ),
inference(nnf_transformation,[],[f712]) ).
thf(f877,plain,
( ( ( infuncsetfunc = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( func @ X2 @ X1 @ X0 ) )
& ( $true
= ( in @ X0 @ ( funcSet @ X2 @ X1 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( func @ X5 @ X4 @ X3 ) )
| ( $true
!= ( in @ X3 @ ( funcSet @ X5 @ X4 ) ) ) )
| ( infuncsetfunc != $true ) ) ),
inference(rectify,[],[f876]) ).
thf(f878,plain,
( ( ( infuncsetfunc = $true )
| ( ( $true
!= ( func @ sK46 @ sK45 @ sK44 ) )
& ( $true
= ( in @ sK44 @ ( funcSet @ sK46 @ sK45 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( func @ X5 @ X4 @ X3 ) )
| ( $true
!= ( in @ X3 @ ( funcSet @ X5 @ X4 ) ) ) )
| ( infuncsetfunc != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44,sK45,sK46]),skolemize(X0,sK44),skolemize(X1,sK45),skolemize(X2,sK46)],[f877]) ).
thf(f930,plain,
( ( exuI3 = $true )
& ( dsetconstrEL = $true )
& ( powersetsubset = $true )
& ( cartprodfstin = $true )
& ( emptyInPowerset = $true )
& ( bs114d = $true )
& ( infuncsetfunc = $true )
& ( cartprodsndpairEq = $true )
& ( prop2set2propI = $true )
& ( quantDeMorgan3 = $true )
& ( emptyset__Cong = $true )
& ( upairset2IR = $true )
& ( kpairsurjEq = $true )
& ( setunionsingleton2 = $true )
& ( notinsingleton = $true )
& ( dpsetconstrSub = $true )
& ( powersetAx = $true )
& ( cartprodpairmemEL = $true )
& ( emptyI = $true )
& ( kpairiskpair = $true )
& ( emptyE1 = $true )
& ( uniqinunit = $true )
& ( upairset2E = $true )
& ( omega0Ax = $true )
& ( cartprodfstpairEq = $true )
& ( exuE1 = $true )
& ( cartprodpairin = $true )
& ( setadjoin__Cong = $true )
& ( symdiffE = $true )
& ( app = $true )
& ( emptysetE = $true )
& ( ksndpairEq = $true )
& ( subsetI2 = $true )
& ( setminusERneg = $true )
& ( dpsetconstrER = $true )
& ( dpsetconstrERa = $true )
& ( powersetE1 = $true )
& ( disjointsetsI1 = $true )
& ( singletonsuniq = $true )
& ( setukpairIL = $true )
& ( subsetI1 = $true )
& ( notequalI2 = $true )
& ( setukpairinjR2 = $true )
& ( notequalI1 = $true )
& ( subsetRefl = $true )
& ( setadjoinSub2 = $true )
& ( cartprodmempair1 = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( funcSet @ X2 @ X0 ) ) )
& ? [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
& ( $true
!= ( in @ ( ap @ X2 @ X0 @ X1 @ X3 ) @ X0 ) ) ) )
& ( setminusER = $true )
& ( binintersectI = $true )
& ( dpsetconstrEL2 = $true )
& ( binintersectLsub = $true )
& ( omegaSAx = $true )
& ( kfstpairEq = $true )
& ( setadjoinAx = $true )
& ( singletonsswitch = $true )
& ( exuI1 = $true )
& ( setukpairinjL = $true )
& ( vacuousDall = $true )
& ( notdexE = $true )
& ( setminusIRneg = $true )
& ( upairsetIR = $true )
& ( notsubsetI = $true )
& ( setadjoinIR = $true )
& ( sepInPowerset = $true )
& ( setminusELneg = $true )
& ( subset2powerset = $true )
& ( symdiffIneg1 = $true )
& ( ex1E1 = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( symdiffI2 = $true )
& ( powersetI1 = $true )
& ( exuEu = $true )
& ( exuI2 = $true )
& ( binintersectER = $true )
& ( subsetemptysetimpeq = $true )
& ( subPowSU = $true )
& ( binintersectRsub = $true )
& ( binunionE = $true )
& ( nonemptyI = $true )
& ( inPowerset = $true )
& ( singletoninpowerset = $true )
& ( nonemptyE1 = $true )
& ( cartprodpairsurjEq = $true )
& ( binunionRsub = $true )
& ( upairinpowunion = $true )
& ( setadjoinSub = $true )
& ( binintersectSubset3 = $true )
& ( binunionIL = $true )
& ( nonemptyI1 = $true )
& ( ksndsingleton = $true )
& ( subsetE = $true )
& ( binunionEcases = $true )
& ( ex1I = $true )
& ( ubforcartprodlem1 = $true )
& ( wellorderingAx = $true )
& ( setukpairinjR1 = $true )
& ( funcImageSingleton = $true )
& ( binintersectEL = $true )
& ( emptysetsubset = $true )
& ( upairsetIL = $true )
& ( setukpairinjL2 = $true )
& ( descrp = $true )
& ( subsetE2 = $true )
& ( binintersectSubset4 = $true )
& ( powerset__Cong = $true )
& ( binunionIR = $true )
& ( emptyinPowerset = $true )
& ( setminusSubset1 = $true )
& ( sepSubset = $true )
& ( binintersectSubset2 = $true )
& ( singletonsubset = $true )
& ( omega__Cong = $true )
& ( in__Cong = $true )
& ( eqimpsubset1 = $true )
& ( ex1I2 = $true )
& ( singletonprop = $true )
& ( powersetI = $true )
& ( binintersectSubset1 = $true )
& ( exuE3u = $true )
& ( setminusSubset2 = $true )
& ( quantDeMorgan4 = $true )
& ( setoftrueEq = $true )
& ( setukpairinjR12 = $true )
& ( dsetconstr__Cong = $true )
& ( symdiffIneg2 = $true )
& ( cartprodmempair = $true )
& ( eqinunit = $true )
& ( exuE2 = $true )
& ( setunionI = $true )
& ( notdallE = $true )
& ( setminusEL = $true )
& ( cartprodsndin = $true )
& ( binunionLsub = $true )
& ( prop2setI = $true )
& ( setukpairinjR = $true )
& ( nonemptyImpWitness = $true )
& ( emptysetAx = $true )
& ( setadjoinOr = $true )
& ( apProp = $true )
& ( emptysetimpfalse = $true )
& ( setukpairIR = $true )
& ( setminusI = $true )
& ( upairsetE = $true )
& ( secondinupair = $true )
& ( symdiffI1 = $true )
& ( prop2setE = $true )
& ( descr__Cong = $true )
& ( setadjoinIL = $true )
& ( eqimpsubset2 = $true )
& ( setunionE = $true )
& ( singletoninpowunion = $true )
& ( setunionsingleton1 = $true )
& ( kfstsingleton = $true )
& ( dsetconstrER = $true )
& ( cartprodpairmemER = $true )
& ( setukpairinjR11 = $true )
& ( setunionAx = $true )
& ( powersetE = $true )
& ( setOfPairsIsBReln = $true )
& ( inCongP = $true )
& ( setunionsingleton = $true )
& ( setunion__Cong = $true )
& ( setext = $true )
& ( dsetconstrI = $true )
& ( exu__Cong = $true )
& ( upairsubunion = $true )
& ( notinemptyset = $true )
& ( theprop = $true )
& ( setunionE2 = $true )
& ( noeltsimpempty = $true )
& ( dpsetconstrI = $true )
& ( setbeta = $true )
& ( ubforcartprodlem2 = $true )
& ( omegaIndAx = $true )
& ( ubforcartprodlem3 = $true )
& ( quantDeMorgan2 = $true )
& ( setminusLsub = $true )
& ( kpairp = $true )
& ( setextAx = $true )
& ( setadjoinE = $true )
& ( cartprodmempaircEq = $true )
& ( setextsub = $true )
& ( quantDeMorgan1 = $true )
& ( setukpairinjL1 = $true )
& ( emptyinunitempty = $true )
& ( exuE3e = $true )
& ( subsetTrans = $true )
& ( dpsetconstrEL1 = $true )
& ( upairequniteq = $true )
& ( setminusILneg = $true )
& ( binintersectSubset5 = $true ) ),
inference(rectify,[],[f813]) ).
thf(f931,plain,
( ( exuI3 = $true )
& ( dsetconstrEL = $true )
& ( powersetsubset = $true )
& ( cartprodfstin = $true )
& ( emptyInPowerset = $true )
& ( bs114d = $true )
& ( infuncsetfunc = $true )
& ( cartprodsndpairEq = $true )
& ( prop2set2propI = $true )
& ( quantDeMorgan3 = $true )
& ( emptyset__Cong = $true )
& ( upairset2IR = $true )
& ( kpairsurjEq = $true )
& ( setunionsingleton2 = $true )
& ( notinsingleton = $true )
& ( dpsetconstrSub = $true )
& ( powersetAx = $true )
& ( cartprodpairmemEL = $true )
& ( emptyI = $true )
& ( kpairiskpair = $true )
& ( emptyE1 = $true )
& ( uniqinunit = $true )
& ( upairset2E = $true )
& ( omega0Ax = $true )
& ( cartprodfstpairEq = $true )
& ( exuE1 = $true )
& ( cartprodpairin = $true )
& ( setadjoin__Cong = $true )
& ( symdiffE = $true )
& ( app = $true )
& ( emptysetE = $true )
& ( ksndpairEq = $true )
& ( subsetI2 = $true )
& ( setminusERneg = $true )
& ( dpsetconstrER = $true )
& ( dpsetconstrERa = $true )
& ( powersetE1 = $true )
& ( disjointsetsI1 = $true )
& ( singletonsuniq = $true )
& ( setukpairIL = $true )
& ( subsetI1 = $true )
& ( notequalI2 = $true )
& ( setukpairinjR2 = $true )
& ( notequalI1 = $true )
& ( subsetRefl = $true )
& ( setadjoinSub2 = $true )
& ( cartprodmempair1 = $true )
& ( $true
= ( in @ sK95 @ ( funcSet @ sK96 @ sK94 ) ) )
& ( $true
= ( in @ sK97 @ sK96 ) )
& ( $true
!= ( in @ ( ap @ sK96 @ sK94 @ sK95 @ sK97 ) @ sK94 ) )
& ( setminusER = $true )
& ( binintersectI = $true )
& ( dpsetconstrEL2 = $true )
& ( binintersectLsub = $true )
& ( omegaSAx = $true )
& ( kfstpairEq = $true )
& ( setadjoinAx = $true )
& ( singletonsswitch = $true )
& ( exuI1 = $true )
& ( setukpairinjL = $true )
& ( vacuousDall = $true )
& ( notdexE = $true )
& ( setminusIRneg = $true )
& ( upairsetIR = $true )
& ( notsubsetI = $true )
& ( setadjoinIR = $true )
& ( sepInPowerset = $true )
& ( setminusELneg = $true )
& ( subset2powerset = $true )
& ( symdiffIneg1 = $true )
& ( ex1E1 = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( symdiffI2 = $true )
& ( powersetI1 = $true )
& ( exuEu = $true )
& ( exuI2 = $true )
& ( binintersectER = $true )
& ( subsetemptysetimpeq = $true )
& ( subPowSU = $true )
& ( binintersectRsub = $true )
& ( binunionE = $true )
& ( nonemptyI = $true )
& ( inPowerset = $true )
& ( singletoninpowerset = $true )
& ( nonemptyE1 = $true )
& ( cartprodpairsurjEq = $true )
& ( binunionRsub = $true )
& ( upairinpowunion = $true )
& ( setadjoinSub = $true )
& ( binintersectSubset3 = $true )
& ( binunionIL = $true )
& ( nonemptyI1 = $true )
& ( ksndsingleton = $true )
& ( subsetE = $true )
& ( binunionEcases = $true )
& ( ex1I = $true )
& ( ubforcartprodlem1 = $true )
& ( wellorderingAx = $true )
& ( setukpairinjR1 = $true )
& ( funcImageSingleton = $true )
& ( binintersectEL = $true )
& ( emptysetsubset = $true )
& ( upairsetIL = $true )
& ( setukpairinjL2 = $true )
& ( descrp = $true )
& ( subsetE2 = $true )
& ( binintersectSubset4 = $true )
& ( powerset__Cong = $true )
& ( binunionIR = $true )
& ( emptyinPowerset = $true )
& ( setminusSubset1 = $true )
& ( sepSubset = $true )
& ( binintersectSubset2 = $true )
& ( singletonsubset = $true )
& ( omega__Cong = $true )
& ( in__Cong = $true )
& ( eqimpsubset1 = $true )
& ( ex1I2 = $true )
& ( singletonprop = $true )
& ( powersetI = $true )
& ( binintersectSubset1 = $true )
& ( exuE3u = $true )
& ( setminusSubset2 = $true )
& ( quantDeMorgan4 = $true )
& ( setoftrueEq = $true )
& ( setukpairinjR12 = $true )
& ( dsetconstr__Cong = $true )
& ( symdiffIneg2 = $true )
& ( cartprodmempair = $true )
& ( eqinunit = $true )
& ( exuE2 = $true )
& ( setunionI = $true )
& ( notdallE = $true )
& ( setminusEL = $true )
& ( cartprodsndin = $true )
& ( binunionLsub = $true )
& ( prop2setI = $true )
& ( setukpairinjR = $true )
& ( nonemptyImpWitness = $true )
& ( emptysetAx = $true )
& ( setadjoinOr = $true )
& ( apProp = $true )
& ( emptysetimpfalse = $true )
& ( setukpairIR = $true )
& ( setminusI = $true )
& ( upairsetE = $true )
& ( secondinupair = $true )
& ( symdiffI1 = $true )
& ( prop2setE = $true )
& ( descr__Cong = $true )
& ( setadjoinIL = $true )
& ( eqimpsubset2 = $true )
& ( setunionE = $true )
& ( singletoninpowunion = $true )
& ( setunionsingleton1 = $true )
& ( kfstsingleton = $true )
& ( dsetconstrER = $true )
& ( cartprodpairmemER = $true )
& ( setukpairinjR11 = $true )
& ( setunionAx = $true )
& ( powersetE = $true )
& ( setOfPairsIsBReln = $true )
& ( inCongP = $true )
& ( setunionsingleton = $true )
& ( setunion__Cong = $true )
& ( setext = $true )
& ( dsetconstrI = $true )
& ( exu__Cong = $true )
& ( upairsubunion = $true )
& ( notinemptyset = $true )
& ( theprop = $true )
& ( setunionE2 = $true )
& ( noeltsimpempty = $true )
& ( dpsetconstrI = $true )
& ( setbeta = $true )
& ( ubforcartprodlem2 = $true )
& ( omegaIndAx = $true )
& ( ubforcartprodlem3 = $true )
& ( quantDeMorgan2 = $true )
& ( setminusLsub = $true )
& ( kpairp = $true )
& ( setextAx = $true )
& ( setadjoinE = $true )
& ( cartprodmempaircEq = $true )
& ( setextsub = $true )
& ( quantDeMorgan1 = $true )
& ( setukpairinjL1 = $true )
& ( emptyinunitempty = $true )
& ( exuE3e = $true )
& ( subsetTrans = $true )
& ( dpsetconstrEL1 = $true )
& ( upairequniteq = $true )
& ( setminusILneg = $true )
& ( binintersectSubset5 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK94,sK95,sK96,sK97]),skolemize(X0,sK94),skolemize(X1,sK95),skolemize(X2,sK96),skolemize(X3,sK97)],[f930]) ).
thf(f1388,plain,
( ( ! [X1: $i,X0: $i,X2: $i] :
( ( ( func @ X0 @ X1 @ X2 )
!= $true )
| ! [X3: $i] :
( ( ( in @ X3 @ X0 )
!= $true )
| ( ( in @ ( ap @ X0 @ X1 @ X2 @ X3 ) @ X1 )
= $true ) ) )
| ( app != $true ) )
& ( ( app = $true )
| ? [X1: $i,X0: $i,X2: $i] :
( ( ( func @ X0 @ X1 @ X2 )
= $true )
& ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ ( ap @ X0 @ X1 @ X2 @ X3 ) @ X1 )
!= $true ) ) ) ) ),
inference(nnf_transformation,[],[f649]) ).
thf(f1389,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( func @ X1 @ X0 @ X2 ) )
| ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( $true
= ( in @ ( ap @ X1 @ X0 @ X2 @ X3 ) @ X0 ) ) ) )
| ( app != $true ) )
& ( ( app = $true )
| ? [X4: $i,X5: $i,X6: $i] :
( ( ( func @ X5 @ X4 @ X6 )
= $true )
& ? [X7: $i] :
( ( $true
= ( in @ X7 @ X5 ) )
& ( ( in @ ( ap @ X5 @ X4 @ X6 @ X7 ) @ X4 )
!= $true ) ) ) ) ),
inference(rectify,[],[f1388]) ).
thf(f1390,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( func @ X1 @ X0 @ X2 ) )
| ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( $true
= ( in @ ( ap @ X1 @ X0 @ X2 @ X3 ) @ X0 ) ) ) )
| ( app != $true ) )
& ( ( app = $true )
| ( ( ( func @ sK533 @ sK532 @ sK534 )
= $true )
& ( ( in @ sK535 @ sK533 )
= $true )
& ( $true
!= ( in @ ( ap @ sK533 @ sK532 @ sK534 @ sK535 ) @ sK532 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK532,sK533,sK534,sK535]),skolemize(X4,sK532),skolemize(X5,sK533),skolemize(X6,sK534),skolemize(X7,sK535)],[f1389]) ).
thf(f1460,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( funcSet @ X5 @ X4 ) ) )
| ( infuncsetfunc != $true )
| ( $true
= ( func @ X5 @ X4 @ X3 ) ) ),
inference(cnf_transformation,[],[f878]) ).
thf(f1669,plain,
( $true
!= ( in @ ( ap @ sK96 @ sK94 @ sK95 @ sK97 ) @ sK94 ) ),
inference(cnf_transformation,[],[f931]) ).
thf(f1670,plain,
( $true
= ( in @ sK97 @ sK96 ) ),
inference(cnf_transformation,[],[f931]) ).
thf(f1671,plain,
( $true
= ( in @ sK95 @ ( funcSet @ sK96 @ sK94 ) ) ),
inference(cnf_transformation,[],[f931]) ).
thf(f1689,plain,
app = $true,
inference(cnf_transformation,[],[f931]) ).
thf(f1712,plain,
infuncsetfunc = $true,
inference(cnf_transformation,[],[f931]) ).
thf(f2311,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( func @ X1 @ X0 @ X2 ) )
| ( ( in @ X3 @ X1 )
!= $true )
| ( app != $true )
| ( $true
= ( in @ ( ap @ X1 @ X0 @ X2 @ X3 ) @ X0 ) ) ),
inference(cnf_transformation,[],[f1390]) ).
thf(f2683,definition,
( spl554_36
<=> ! [X0: $i,X3: $i,X2: $i,X1: $i] :
( ( $true
!= ( func @ X1 @ X0 @ X2 ) )
| ( $true
= ( in @ ( ap @ X1 @ X0 @ X2 @ X3 ) @ X0 ) )
| ( ( in @ X3 @ X1 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl554_36])],[avatar_definition]) ).
thf(f2684,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( ap @ X1 @ X0 @ X2 @ X3 ) @ X0 ) )
| ( $true
!= ( func @ X1 @ X0 @ X2 ) )
| ( ( in @ X3 @ X1 )
!= $true ) )
| ~ spl554_36 ),
inference(avatar_component_clause,[],[f2683]) ).
thf(f2686,definition,
( spl554_37
<=> ( app = $true ) ),
introduced(definition,[new_symbols(definition,[spl554_37])],[avatar_definition]) ).
thf(f2689,plain,
( spl554_36
| ~ spl554_37 ),
inference(avatar_split_clause,[],[f2311,f2686,f2683]) ).
thf(f3312,plain,
spl554_37,
inference(avatar_split_clause,[],[f1689,f2686]) ).
thf(f3553,definition,
( spl554_232
<=> ( $true
= ( in @ sK95 @ ( funcSet @ sK96 @ sK94 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl554_232])],[avatar_definition]) ).
thf(f3555,plain,
( ( $true
= ( in @ sK95 @ ( funcSet @ sK96 @ sK94 ) ) )
| ~ spl554_232 ),
inference(avatar_component_clause,[],[f3553]) ).
thf(f3556,plain,
spl554_232,
inference(avatar_split_clause,[],[f1671,f3553]) ).
thf(f3818,definition,
( spl554_290
<=> ( $true
= ( in @ ( ap @ sK96 @ sK94 @ sK95 @ sK97 ) @ sK94 ) ) ),
introduced(definition,[new_symbols(definition,[spl554_290])],[avatar_definition]) ).
thf(f3820,plain,
( ( $true
!= ( in @ ( ap @ sK96 @ sK94 @ sK95 @ sK97 ) @ sK94 ) )
| spl554_290 ),
inference(avatar_component_clause,[],[f3818]) ).
thf(f3821,plain,
~ spl554_290,
inference(avatar_split_clause,[],[f1669,f3818]) ).
thf(f4409,definition,
( spl554_416
<=> ( infuncsetfunc = $true ) ),
introduced(definition,[new_symbols(definition,[spl554_416])],[avatar_definition]) ).
thf(f4412,plain,
spl554_416,
inference(avatar_split_clause,[],[f1712,f4409]) ).
thf(f5452,definition,
( spl554_638
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( $true
!= ( in @ X3 @ ( funcSet @ X5 @ X4 ) ) )
| ( $true
= ( func @ X5 @ X4 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl554_638])],[avatar_definition]) ).
thf(f5453,plain,
( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ ( funcSet @ X5 @ X4 ) ) )
| ( $true
= ( func @ X5 @ X4 @ X3 ) ) )
| ~ spl554_638 ),
inference(avatar_component_clause,[],[f5452]) ).
thf(f5454,plain,
( spl554_638
| ~ spl554_416 ),
inference(avatar_split_clause,[],[f1460,f4409,f5452]) ).
thf(f6345,definition,
( spl554_818
<=> ( $true
= ( in @ sK97 @ sK96 ) ) ),
introduced(definition,[new_symbols(definition,[spl554_818])],[avatar_definition]) ).
thf(f6347,plain,
( ( $true
= ( in @ sK97 @ sK96 ) )
| ~ spl554_818 ),
inference(avatar_component_clause,[],[f6345]) ).
thf(f6348,plain,
spl554_818,
inference(avatar_split_clause,[],[f1670,f6345]) ).
thf(f8316,plain,
( ( $true != $true )
| ( ( func @ sK96 @ sK94 @ sK95 )
= $true )
| ~ spl554_232
| ~ spl554_638 ),
inference(superposition,[],[f5453,f3555]) ).
thf(f8317,plain,
( ( ( func @ sK96 @ sK94 @ sK95 )
= $true )
| ~ spl554_232
| ~ spl554_638 ),
inference(trivial_inequality_removal,[],[f8316]) ).
thf(f8335,definition,
( spl554_910
<=> ( ( func @ sK96 @ sK94 @ sK95 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl554_910])],[avatar_definition]) ).
thf(f8337,plain,
( ( ( func @ sK96 @ sK94 @ sK95 )
= $true )
| ~ spl554_910 ),
inference(avatar_component_clause,[],[f8335]) ).
thf(f8338,plain,
( spl554_910
| ~ spl554_232
| ~ spl554_638 ),
inference(avatar_split_clause,[],[f8317,f5452,f3553,f8335]) ).
thf(f9806,plain,
( ( $true
!= ( in @ sK97 @ sK96 ) )
| ( ( func @ sK96 @ sK94 @ sK95 )
!= $true )
| ( $true != $true )
| ~ spl554_36
| spl554_290 ),
inference(superposition,[],[f3820,f2684]) ).
thf(f9852,plain,
( ( ( func @ sK96 @ sK94 @ sK95 )
!= $true )
| ( $true
!= ( in @ sK97 @ sK96 ) )
| ~ spl554_36
| spl554_290 ),
inference(trivial_inequality_removal,[],[f9806]) ).
thf(f9866,plain,
( ( $true
!= ( in @ sK97 @ sK96 ) )
| ~ spl554_36
| spl554_290
| ~ spl554_910 ),
inference(forward_subsumption_resolution,[],[f9852,f8337]) ).
thf(f9869,plain,
( $false
| ~ spl554_36
| spl554_290
| ~ spl554_818
| ~ spl554_910 ),
inference(forward_subsumption_resolution,[],[f9866,f6347]) ).
thf(f9870,plain,
( ~ spl554_36
| spl554_290
| ~ spl554_818
| ~ spl554_910 ),
inference(avatar_contradiction_clause,[],[f9869]) ).
cnf(s22,plain,
( spl554_36
| ~ spl554_37 ),
inference(sat_conversion,[],[f2689]) ).
cnf(s107,plain,
spl554_37,
inference(sat_conversion,[],[f3312]) ).
cnf(s147,plain,
spl554_232,
inference(sat_conversion,[],[f3556]) ).
cnf(s191,plain,
~ spl554_290,
inference(sat_conversion,[],[f3821]) ).
cnf(s321,plain,
spl554_416,
inference(sat_conversion,[],[f4412]) ).
cnf(s566,plain,
( ~ spl554_416
| spl554_638 ),
inference(sat_conversion,[],[f5454]) ).
cnf(s807,plain,
spl554_818,
inference(sat_conversion,[],[f6348]) ).
cnf(s941,plain,
( ~ spl554_232
| ~ spl554_638
| spl554_910 ),
inference(sat_conversion,[],[f8338]) ).
cnf(s964,plain,
( ~ spl554_36
| spl554_290
| ~ spl554_818
| ~ spl554_910 ),
inference(sat_conversion,[],[f9870]) ).
cnf(s1081,plain,
spl554_638,
inference(rat,[],[s566,s321]) ).
cnf(s1151,plain,
spl554_910,
inference(rat,[],[s941,s1081,s147]) ).
cnf(s1154,plain,
~ spl554_36,
inference(rat,[],[s964,s191,s807,s1151]) ).
cnf(s1217,plain,
$false,
inference(rat,[],[s22,s107,s1154]) ).
thf(f9874,plain,
$false,
inference(avatar_sat_refutation,[],[s1217]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU676^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n015.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 14:10:48 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running higher-order theorem proving
% 0.22/0.29 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
% 0.47/0.43 % (3582213)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.47/0.43 % (3582221)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=2308777903: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)
% 0.47/0.43 % (3582224)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.47/0.43 % (3582224)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
% 0.47/0.43 % (3582218)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=48256815:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.47/0.43 % (3582222)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=632613078:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.47/0.43 % (3582220)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=35355351:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.47/0.43 % (3582224)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=4151519377:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.47/0.43 % (3582223)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3178037209:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.47/0.43 % (3582219)lrs+10_16_si=on:nwc=1.5:random_seed=3716485798:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.47/0.43 % (3582220)Instruction limit reached!
% 0.47/0.43 % (3582220)------------------------------
% 0.47/0.43 % (3582220)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.43 % (3582220)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.43 % (3582220)CaDiCaL version: 2.1.3
% 0.47/0.43 % (3582220)Termination reason: Instruction limit
% 0.47/0.43 % (3582220)Termination phase: shuffling
% 0.47/0.43 % (3582220)Time elapsed: 0.002 s
% 0.47/0.43 % (3582220)Peak memory usage: 10 MB
% 0.47/0.43 % (3582220)Instructions burned: 4 (million)
% 0.47/0.43 % (3582219)Instruction limit reached!
% 0.47/0.43 % (3582219)------------------------------
% 0.47/0.43 % (3582219)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.43 % (3582219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.43 % (3582219)CaDiCaL version: 2.1.3
% 0.47/0.43 % (3582219)Termination reason: Instruction limit
% 0.47/0.43 % (3582219)Termination phase: shuffling
% 0.47/0.43 % (3582219)Time elapsed: 0.009 s
% 0.47/0.43 % (3582219)Peak memory usage: 10 MB
% 0.47/0.43 % (3582219)Instructions burned: 18 (million)
% 0.47/0.43 % (3582222)Instruction limit reached!
% 0.47/0.43 % (3582222)------------------------------
% 0.47/0.43 % (3582222)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.43 % (3582222)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.43 % (3582222)CaDiCaL version: 2.1.3
% 0.47/0.43 % (3582222)Termination reason: Instruction limit
% 0.47/0.43 % (3582222)Termination phase: Property scanning
% 0.47/0.43 % (3582222)Time elapsed: 0.011 s
% 0.47/0.43 % (3582222)Peak memory usage: 10 MB
% 0.47/0.43 % (3582222)Instructions burned: 25 (million)
% 0.47/0.43 % (3582232)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3977820076:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.47/0.43 % (3582232)Instruction limit reached!
% 0.47/0.43 % (3582232)------------------------------
% 0.47/0.43 % (3582232)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.43 % (3582232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.43 % (3582232)CaDiCaL version: 2.1.3
% 0.47/0.43 % (3582232)Termination reason: Instruction limit
% 0.47/0.43 % (3582232)Termination phase: shuffling
% 0.47/0.43 % (3582232)Time elapsed: 0.002 s
% 0.47/0.43 % (3582232)Peak memory usage: 10 MB
% 0.47/0.43 % (3582232)Instructions burned: 3 (million)
% 0.47/0.43 % (3582234)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.16/0.47 % (3582233)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2014799704:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.16/0.47 % (3582234)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=543608067:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.16/0.47 % (3582233)Instruction limit reached!
% 1.16/0.47 % (3582233)------------------------------
% 1.16/0.47 % (3582233)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.47 % (3582233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.47 % (3582233)CaDiCaL version: 2.1.3
% 1.16/0.47 % (3582233)Termination reason: Instruction limit
% 1.16/0.47 % (3582233)Termination phase: shuffling
% 1.16/0.47 % (3582233)Time elapsed: 0.003 s
% 1.16/0.47 % (3582233)Peak memory usage: 10 MB
% 1.16/0.47 % (3582233)Instructions burned: 6 (million)
% 1.16/0.47 % (3582234)Instruction limit reached!
% 1.16/0.47 % (3582234)------------------------------
% 1.16/0.47 % (3582234)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.47 % (3582234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.47 % (3582234)CaDiCaL version: 2.1.3
% 1.16/0.47 % (3582234)Termination reason: Instruction limit
% 1.16/0.47 % (3582234)Termination phase: shuffling
% 1.16/0.47 % (3582234)Time elapsed: 0.004 s
% 1.16/0.47 % (3582234)Peak memory usage: 10 MB
% 1.16/0.47 % (3582234)Instructions burned: 9 (million)
% 1.16/0.47 % (3582223)Instruction limit reached!
% 1.16/0.47 % (3582223)------------------------------
% 1.16/0.47 % (3582223)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.47 % (3582223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.47 % (3582223)CaDiCaL version: 2.1.3
% 1.16/0.47 % (3582223)Termination reason: Instruction limit
% 1.16/0.47 % (3582223)Termination phase: Property scanning
% 1.16/0.47 % (3582223)Time elapsed: 0.036 s
% 1.16/0.47 % (3582223)Peak memory usage: 12 MB
% 1.16/0.47 % (3582223)Instructions burned: 77 (million)
% 1.16/0.47 % (3582218)Instruction limit reached!
% 1.16/0.47 % (3582218)------------------------------
% 1.16/0.47 % (3582218)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.47 % (3582218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.47 % (3582218)CaDiCaL version: 2.1.3
% 1.16/0.47 % (3582218)Termination reason: Instruction limit
% 1.16/0.47 % (3582218)Termination phase: Property scanning
% 1.16/0.47 % (3582218)Time elapsed: 0.040 s
% 1.16/0.47 % (3582218)Peak memory usage: 12 MB
% 1.16/0.47 % (3582218)Instructions burned: 87 (million)
% 1.16/0.47 % (3582236)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1831166971:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.16/0.47 % (3582239)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.16/0.47 % (3582239)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.16/0.47 % (3582236)Instruction limit reached!
% 1.16/0.47 % (3582236)------------------------------
% 1.16/0.47 % (3582236)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.47 % (3582236)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.47 % (3582236)CaDiCaL version: 2.1.3
% 1.16/0.47 % (3582236)Termination reason: Instruction limit
% 1.16/0.47 % (3582236)Termination phase: shuffling
% 1.16/0.47 % (3582236)Time elapsed: 0.006 s
% 1.16/0.47 % (3582236)Peak memory usage: 10 MB
% 1.16/0.47 % (3582236)Instructions burned: 13 (million)
% 1.16/0.47 % (3582239)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3370845424:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.16/0.47 % (3582240)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=1260758067:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.16/0.47 % (3582241)lrs+10_1_si=on:cs=on:random_seed=1480513905:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 1.16/0.47 % (3582242)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.16/0.49 % (3582242)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=453637855:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.16/0.49 % (3582241)Instruction limit reached!
% 1.16/0.49 % (3582241)------------------------------
% 1.16/0.49 % (3582241)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.49 % (3582241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.49 % (3582241)CaDiCaL version: 2.1.3
% 1.16/0.49 % (3582241)Termination reason: Instruction limit
% 1.16/0.49 % (3582241)Termination phase: shuffling
% 1.16/0.49 % (3582241)Time elapsed: 0.004 s
% 1.16/0.49 % (3582241)Peak memory usage: 10 MB
% 1.16/0.49 % (3582241)Instructions burned: 8 (million)
% 1.16/0.49 % (3582242)Instruction limit reached!
% 1.16/0.49 % (3582242)------------------------------
% 1.16/0.49 % (3582242)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.49 % (3582242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.49 % (3582242)CaDiCaL version: 2.1.3
% 1.16/0.49 % (3582242)Termination reason: Instruction limit
% 1.16/0.49 % (3582242)Termination phase: shuffling
% 1.16/0.49 % (3582242)Time elapsed: 0.002 s
% 1.16/0.49 % (3582242)Peak memory usage: 10 MB
% 1.16/0.49 % (3582242)Instructions burned: 3 (million)
% 1.16/0.49 % (3582239)Instruction limit reached!
% 1.16/0.49 % (3582239)------------------------------
% 1.16/0.49 % (3582239)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.49 % (3582239)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.49 % (3582239)CaDiCaL version: 2.1.3
% 1.16/0.49 % (3582239)Termination reason: Instruction limit
% 1.16/0.49 % (3582239)Termination phase: Property scanning
% 1.16/0.49 % (3582239)Time elapsed: 0.013 s
% 1.16/0.49 % (3582239)Peak memory usage: 10 MB
% 1.16/0.49 % (3582239)Instructions burned: 30 (million)
% 1.16/0.49 % (3582224)Instruction limit reached!
% 1.16/0.49 % (3582224)------------------------------
% 1.16/0.49 % (3582224)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.49 % (3582224)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.49 % (3582224)CaDiCaL version: 2.1.3
% 1.16/0.49 % (3582224)Termination reason: Instruction limit
% 1.16/0.49 % (3582224)Termination phase: Saturation
% 1.16/0.49 % (3582224)Time elapsed: 0.069 s
% 1.16/0.49 % (3582224)Peak memory usage: 14 MB
% 1.16/0.49 % (3582224)Instructions burned: 158 (million)
% 1.16/0.49 % (3582245)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=305848218:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 1.16/0.49 % (3582249)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=4268460961:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.16/0.49 % (3582250)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=4103868286:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.16/0.49 % (3582251)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1792318389:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.16/0.49 % (3582252)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=4154089683:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.16/0.49 % (3582240)Instruction limit reached!
% 1.16/0.49 % (3582240)------------------------------
% 1.16/0.49 % (3582240)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.49 % (3582240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.49 % (3582240)CaDiCaL version: 2.1.3
% 1.16/0.49 % (3582240)Termination reason: Instruction limit
% 1.16/0.49 % (3582240)Termination phase: Property scanning
% 1.16/0.49 % (3582240)Time elapsed: 0.035 s
% 1.16/0.49 % (3582240)Peak memory usage: 11 MB
% 1.16/0.49 % (3582240)Instructions burned: 86 (million)
% 1.16/0.49 % (3582245)Instruction limit reached!
% 1.16/0.49 % (3582245)------------------------------
% 1.16/0.49 % (3582245)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.49 % (3582245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.49 % (3582245)CaDiCaL version: 2.1.3
% 1.16/0.49 % (3582245)Termination reason: Instruction limit
% 1.16/0.49 % (3582245)Termination phase: Preprocessing 3
% 1.16/0.49 % (3582245)Time elapsed: 0.018 s
% 1.16/0.49 % (3582245)Peak memory usage: 11 MB
% 1.16/0.49 % (3582245)Instructions burned: 39 (million)
% 1.16/0.49 % (3582251)Instruction limit reached!
% 1.16/0.49 % (3582251)------------------------------
% 1.16/0.49 % (3582251)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.49 % (3582251)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.49 % (3582251)CaDiCaL version: 2.1.3
% 1.16/0.49 % (3582251)Termination reason: Instruction limit
% 1.16/0.49 % (3582251)Termination phase: shuffling
% 1.16/0.49 % (3582251)Time elapsed: 0.007 s
% 1.16/0.49 % (3582251)Peak memory usage: 10 MB
% 1.16/0.49 % (3582251)Instructions burned: 16 (million)
% 1.16/0.49 % (3582250)Instruction limit reached!
% 1.16/0.49 % (3582250)------------------------------
% 1.16/0.49 % (3582250)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.49 % (3582250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.49 % (3582250)CaDiCaL version: 2.1.3
% 1.16/0.49 % (3582250)Termination reason: Instruction limit
% 1.16/0.49 % (3582250)Termination phase: SInE selection
% 1.16/0.49 % (3582250)Time elapsed: 0.012 s
% 1.16/0.49 % (3582250)Peak memory usage: 11 MB
% 1.16/0.49 % (3582250)Instructions burned: 25 (million)
% 1.16/0.49 % (3582259)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=468208651: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)
% 1.16/0.49 % (3582258)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3321615710:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.16/0.49 % (3582260)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3764834041:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.16/0.49 % (3582259)Instruction limit reached!
% 1.16/0.49 % (3582259)------------------------------
% 1.16/0.49 % (3582259)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.49 % (3582259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.49 % (3582259)CaDiCaL version: 2.1.3
% 1.16/0.49 % (3582259)Termination reason: Instruction limit
% 1.16/0.49 % (3582259)Termination phase: shuffling
% 1.16/0.49 % (3582259)Time elapsed: 0.002 s
% 1.16/0.49 % (3582259)Peak memory usage: 10 MB
% 1.16/0.49 % (3582259)Instructions burned: 3 (million)
% 1.16/0.49 % (3582261)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3860820402:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.16/0.49 % (3582258)Instruction limit reached!
% 1.16/0.49 % (3582258)------------------------------
% 1.16/0.49 % (3582258)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.49 % (3582258)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.49 % (3582258)CaDiCaL version: 2.1.3
% 1.16/0.49 % (3582258)Termination reason: Instruction limit
% 1.16/0.49 % (3582258)Termination phase: shuffling
% 1.16/0.49 % (3582258)Time elapsed: 0.007 s
% 1.16/0.49 % (3582258)Peak memory usage: 10 MB
% 1.16/0.49 % (3582258)Instructions burned: 14 (million)
% 1.16/0.49 % (3582260)Instruction limit reached!
% 1.16/0.49 % (3582260)------------------------------
% 1.16/0.49 % (3582260)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.49 % (3582260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.49 % (3582260)CaDiCaL version: 2.1.3
% 1.16/0.49 % (3582260)Termination reason: Instruction limit
% 1.16/0.49 % (3582260)Termination phase: Property scanning
% 1.16/0.49 % (3582260)Time elapsed: 0.011 s
% 1.16/0.49 % (3582260)Peak memory usage: 10 MB
% 1.16/0.49 % (3582260)Instructions burned: 27 (million)
% 1.16/0.49 % (3582261)Instruction limit reached!
% 1.16/0.49 % (3582261)------------------------------
% 1.16/0.49 % (3582261)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.49 % (3582261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.49 % (3582261)CaDiCaL version: 2.1.3
% 1.16/0.49 % (3582261)Termination reason: Instruction limit
% 1.16/0.49 % (3582261)Termination phase: shuffling
% 1.16/0.49 % (3582261)Time elapsed: 0.011 s
% 1.16/0.49 % (3582261)Peak memory usage: 10 MB
% 1.16/0.49 % (3582261)Instructions burned: 23 (million)
% 1.16/0.49 % (3582265)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=473461340:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.16/0.49 % (3582267)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
% 1.16/0.49 % (3582267)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.16/0.49 % (3582267)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=2309470596:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.16/0.49 % (3582268)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.16/0.49 % (3582268)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=588420512:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.16/0.49 % (3582267)Instruction limit reached!
% 1.16/0.49 % (3582267)------------------------------
% 1.16/0.49 % (3582267)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.49 % (3582267)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.49 % (3582267)CaDiCaL version: 2.1.3
% 1.16/0.49 % (3582267)Termination reason: Instruction limit
% 1.16/0.49 % (3582267)Termination phase: shuffling
% 1.16/0.49 % (3582267)Time elapsed: 0.006 s
% 1.16/0.49 % (3582267)Peak memory usage: 10 MB
% 1.16/0.49 % (3582267)Instructions burned: 14 (million)
% 1.16/0.49 % (3582269)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=763881438:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.16/0.49 % (3582221) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3582213-3582221"...
% 1.16/0.49 % (3582268)Instruction limit reached!
% 1.16/0.49 % (3582268)------------------------------
% 1.16/0.49 % (3582268)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.49 % (3582268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.49 % (3582268)CaDiCaL version: 2.1.3
% 1.16/0.49 % (3582268)Termination reason: Instruction limit
% 1.16/0.49 % (3582268)Termination phase: shuffling
% 1.16/0.49 % (3582268)Time elapsed: 0.004 s
% 1.16/0.49 % (3582268)Peak memory usage: 10 MB
% 1.16/0.49 % (3582268)Instructions burned: 9 (million)
% 1.16/0.49 % (3582221)...printing done.
% 1.16/0.49 % (3582221)Refutation found. Thanks to Tanya!
% 1.16/0.49 % SZS status Theorem for theBenchmark
% 1.16/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 1.16/0.50 % (3582221)------------------------------
% 1.16/0.50 % (3582221)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.16/0.50 % (3582221)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.16/0.50 % (3582221)CaDiCaL version: 2.1.3
% 1.16/0.50 % (3582221)Termination reason: Refutation
% 1.16/0.50 % (3582221)Time elapsed: 0.158 s
% 1.16/0.50 % (3582221)Peak memory usage: 20 MB
% 1.16/0.50 % (3582221)Instructions burned: 544 (million)
% 1.16/0.50 % (3582213)Success in time 0.198 s
% 1.16/0.50 % Vampire exiting
%------------------------------------------------------------------------------