%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU688^1 : 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 : n009.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 08:30:47 AM UTC 2026
% Result : Theorem 2.30s 0.67s
% Output : Refutation 2.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 86 ( 31 unt; 0 typ; 10 def)
% Number of atoms : 4372 (1195 equ; 0 cnn)
% Maximal formula atoms : 209 ( 50 avg)
% Number of connectives : 2484 ( 130 ~; 120 |; 853 &; 519 @)
% ( 15 <=>; 847 =>; 0 <=; 0 <~>)
% Maximal formula depth : 219 ( 24 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 414 ( 411 usr; 238 con; 0-4 aty)
% Number of variables : 139 ( 0 sgn 108 !; 31 ?; 139 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_3,type,
setextAx: $o ).
thf(func_def_5,type,
emptysetAx: $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_7,type,
setadjoinAx: $o ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_9,type,
powersetAx: $o ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_11,type,
setunionAx: $o ).
thf(func_def_13,type,
omega0Ax: $o ).
thf(func_def_14,type,
omegaSAx: $o ).
thf(func_def_15,type,
omegaIndAx: $o ).
thf(func_def_16,type,
replAx: $o ).
thf(func_def_17,type,
foundationAx: $o ).
thf(func_def_18,type,
wellorderingAx: $o ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_20,type,
descrp: $o ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_22,type,
dsetconstrI: $o ).
thf(func_def_23,type,
dsetconstrEL: $o ).
thf(func_def_24,type,
dsetconstrER: $o ).
thf(func_def_25,type,
exuE1: $o ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_27,type,
prop2setE: $o ).
thf(func_def_28,type,
emptysetE: $o ).
thf(func_def_29,type,
emptysetimpfalse: $o ).
thf(func_def_30,type,
notinemptyset: $o ).
thf(func_def_31,type,
exuE3e: $o ).
thf(func_def_32,type,
setext: $o ).
thf(func_def_33,type,
emptyI: $o ).
thf(func_def_34,type,
noeltsimpempty: $o ).
thf(func_def_35,type,
setbeta: $o ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_37,type,
nonemptyE1: $o ).
thf(func_def_38,type,
nonemptyI: $o ).
thf(func_def_39,type,
nonemptyI1: $o ).
thf(func_def_40,type,
setadjoinIL: $o ).
thf(func_def_41,type,
emptyinunitempty: $o ).
thf(func_def_42,type,
setadjoinIR: $o ).
thf(func_def_43,type,
setadjoinE: $o ).
thf(func_def_44,type,
setadjoinOr: $o ).
thf(func_def_45,type,
setoftrueEq: $o ).
thf(func_def_46,type,
powersetI: $o ).
thf(func_def_47,type,
emptyinPowerset: $o ).
thf(func_def_48,type,
emptyInPowerset: $o ).
thf(func_def_49,type,
powersetE: $o ).
thf(func_def_50,type,
setunionI: $o ).
thf(func_def_51,type,
setunionE: $o ).
thf(func_def_52,type,
subPowSU: $o ).
thf(func_def_53,type,
exuE2: $o ).
thf(func_def_54,type,
nonemptyImpWitness: $o ).
thf(func_def_55,type,
uniqinunit: $o ).
thf(func_def_56,type,
notinsingleton: $o ).
thf(func_def_57,type,
eqinunit: $o ).
thf(func_def_58,type,
singletonsswitch: $o ).
thf(func_def_59,type,
upairsetE: $o ).
thf(func_def_60,type,
upairsetIL: $o ).
thf(func_def_61,type,
upairsetIR: $o ).
thf(func_def_62,type,
emptyE1: $o ).
thf(func_def_63,type,
vacuousDall: $o ).
thf(func_def_64,type,
quantDeMorgan1: $o ).
thf(func_def_65,type,
quantDeMorgan2: $o ).
thf(func_def_66,type,
quantDeMorgan3: $o ).
thf(func_def_67,type,
quantDeMorgan4: $o ).
thf(func_def_68,type,
prop2setI: $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_70,type,
prop2set2propI: $o ).
thf(func_def_71,type,
notdexE: $o ).
thf(func_def_72,type,
notdallE: $o ).
thf(func_def_73,type,
exuI1: $o ).
thf(func_def_74,type,
exuI3: $o ).
thf(func_def_75,type,
exuI2: $o ).
thf(func_def_76,type,
inCongP: $o ).
thf(func_def_77,type,
in__Cong: $o ).
thf(func_def_78,type,
exuE3u: $o ).
thf(func_def_79,type,
exu__Cong: $o ).
thf(func_def_80,type,
emptyset__Cong: $o ).
thf(func_def_81,type,
setadjoin__Cong: $o ).
thf(func_def_82,type,
powerset__Cong: $o ).
thf(func_def_83,type,
setunion__Cong: $o ).
thf(func_def_84,type,
omega__Cong: $o ).
thf(func_def_85,type,
exuEu: $o ).
thf(func_def_86,type,
descr__Cong: $o ).
thf(func_def_87,type,
dsetconstr__Cong: $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_91,type,
subsetI1: $o ).
thf(func_def_92,type,
eqimpsubset2: $o ).
thf(func_def_93,type,
eqimpsubset1: $o ).
thf(func_def_94,type,
subsetI2: $o ).
thf(func_def_95,type,
emptysetsubset: $o ).
thf(func_def_96,type,
subsetE: $o ).
thf(func_def_97,type,
subsetE2: $o ).
thf(func_def_98,type,
notsubsetI: $o ).
thf(func_def_99,type,
notequalI1: $o ).
thf(func_def_100,type,
notequalI2: $o ).
thf(func_def_101,type,
subsetRefl: $o ).
thf(func_def_102,type,
subsetTrans: $o ).
thf(func_def_103,type,
setadjoinSub: $o ).
thf(func_def_104,type,
setadjoinSub2: $o ).
thf(func_def_105,type,
subset2powerset: $o ).
thf(func_def_106,type,
setextsub: $o ).
thf(func_def_107,type,
subsetemptysetimpeq: $o ).
thf(func_def_108,type,
powersetI1: $o ).
thf(func_def_109,type,
powersetE1: $o ).
thf(func_def_110,type,
inPowerset: $o ).
thf(func_def_111,type,
powersetsubset: $o ).
thf(func_def_112,type,
sepInPowerset: $o ).
thf(func_def_113,type,
sepSubset: $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_115,type,
binunionIL: $o ).
thf(func_def_116,type,
upairset2IR: $o ).
thf(func_def_117,type,
binunionIR: $o ).
thf(func_def_118,type,
binunionEcases: $o ).
thf(func_def_119,type,
binunionE: $o ).
thf(func_def_120,type,
binunionLsub: $o ).
thf(func_def_121,type,
binunionRsub: $o ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_123,type,
binintersectI: $o ).
thf(func_def_124,type,
binintersectSubset5: $o ).
thf(func_def_125,type,
binintersectEL: $o ).
thf(func_def_126,type,
binintersectLsub: $o ).
thf(func_def_127,type,
binintersectSubset2: $o ).
thf(func_def_128,type,
binintersectSubset3: $o ).
thf(func_def_129,type,
binintersectER: $o ).
thf(func_def_130,type,
disjointsetsI1: $o ).
thf(func_def_131,type,
binintersectRsub: $o ).
thf(func_def_132,type,
binintersectSubset4: $o ).
thf(func_def_133,type,
binintersectSubset1: $o ).
thf(func_def_134,type,
bs114d: $o ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_137,type,
setminusI: $o ).
thf(func_def_138,type,
setminusEL: $o ).
thf(func_def_139,type,
setminusER: $o ).
thf(func_def_140,type,
setminusSubset2: $o ).
thf(func_def_141,type,
setminusERneg: $o ).
thf(func_def_142,type,
setminusELneg: $o ).
thf(func_def_143,type,
setminusILneg: $o ).
thf(func_def_144,type,
setminusIRneg: $o ).
thf(func_def_145,type,
setminusLsub: $o ).
thf(func_def_146,type,
setminusSubset1: $o ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_148,type,
symdiffE: $o ).
thf(func_def_149,type,
symdiffI1: $o ).
thf(func_def_150,type,
symdiffI2: $o ).
thf(func_def_151,type,
symdiffIneg1: $o ).
thf(func_def_152,type,
symdiffIneg2: $o ).
thf(func_def_153,type,
iskpair: $i > $o ).
thf(func_def_154,type,
secondinupair: $o ).
thf(func_def_155,type,
setukpairIL: $o ).
thf(func_def_156,type,
setukpairIR: $o ).
thf(func_def_157,type,
kpairiskpair: $o ).
thf(func_def_158,type,
kpair: $i > $i > $i ).
thf(func_def_159,type,
kpairp: $o ).
thf(func_def_160,type,
cartprod: $i > $i > $i ).
thf(func_def_161,type,
singletonsubset: $o ).
thf(func_def_162,type,
singletoninpowerset: $o ).
thf(func_def_163,type,
singletoninpowunion: $o ).
thf(func_def_164,type,
upairset2E: $o ).
thf(func_def_165,type,
upairsubunion: $o ).
thf(func_def_166,type,
upairinpowunion: $o ).
thf(func_def_167,type,
ubforcartprodlem1: $o ).
thf(func_def_168,type,
ubforcartprodlem2: $o ).
thf(func_def_169,type,
ubforcartprodlem3: $o ).
thf(func_def_170,type,
cartprodpairin: $o ).
thf(func_def_171,type,
cartprodmempair1: $o ).
thf(func_def_172,type,
cartprodmempair: $o ).
thf(func_def_173,type,
setunionE2: $o ).
thf(func_def_174,type,
setunionsingleton1: $o ).
thf(func_def_175,type,
setunionsingleton2: $o ).
thf(func_def_176,type,
setunionsingleton: $o ).
thf(func_def_177,type,
singleton: $i > $o ).
thf(func_def_178,type,
singletonprop: $o ).
thf(func_def_179,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_180,type,
ex1E1: $o ).
thf(func_def_181,type,
ex1I: $o ).
thf(func_def_182,type,
ex1I2: $o ).
thf(func_def_183,type,
singletonsuniq: $o ).
thf(func_def_184,type,
atmost1p: $i > $o ).
thf(func_def_185,type,
atleast2p: $i > $o ).
thf(func_def_186,type,
atmost2p: $i > $o ).
thf(func_def_187,type,
upairsetp: $i > $o ).
thf(func_def_188,type,
setukpairinjL1: $o ).
thf(func_def_189,type,
kfstsingleton: $o ).
thf(func_def_190,type,
theprop: $o ).
thf(func_def_191,type,
kfst: $i > $i ).
thf(func_def_192,type,
kfstpairEq: $o ).
thf(func_def_193,type,
cartprodfstin: $o ).
thf(func_def_194,type,
setukpairinjL2: $o ).
thf(func_def_195,type,
setukpairinjL: $o ).
thf(func_def_196,type,
setukpairinjR11: $o ).
thf(func_def_197,type,
setukpairinjR12: $o ).
thf(func_def_198,type,
setukpairinjR1: $o ).
thf(func_def_199,type,
upairequniteq: $o ).
thf(func_def_200,type,
setukpairinjR2: $o ).
thf(func_def_201,type,
setukpairinjR: $o ).
thf(func_def_202,type,
ksndsingleton: $o ).
thf(func_def_203,type,
ksnd: $i > $i ).
thf(func_def_204,type,
ksndpairEq: $o ).
thf(func_def_205,type,
kpairsurjEq: $o ).
thf(func_def_206,type,
cartprodsndin: $o ).
thf(func_def_207,type,
cartprodpairmemEL: $o ).
thf(func_def_208,type,
cartprodpairmemER: $o ).
thf(func_def_209,type,
cartprodmempaircEq: $o ).
thf(func_def_210,type,
cartprodfstpairEq: $o ).
thf(func_def_211,type,
cartprodsndpairEq: $o ).
thf(func_def_212,type,
cartprodpairsurjEq: $o ).
thf(func_def_213,type,
breln: $i > $i > $i > $o ).
thf(func_def_214,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_215,type,
dpsetconstrI: $o ).
thf(func_def_216,type,
dpsetconstrSub: $o ).
thf(func_def_217,type,
setOfPairsIsBReln: $o ).
thf(func_def_218,type,
dpsetconstrERa: $o ).
thf(func_def_219,type,
dpsetconstrEL1: $o ).
thf(func_def_220,type,
dpsetconstrEL2: $o ).
thf(func_def_221,type,
dpsetconstrER: $o ).
thf(func_def_222,type,
func: $i > $i > $i > $o ).
thf(func_def_223,type,
funcSet: $i > $i > $i ).
thf(func_def_224,type,
funcImageSingleton: $o ).
thf(func_def_225,type,
apProp: $o ).
thf(func_def_226,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_227,type,
app: $o ).
thf(func_def_228,type,
infuncsetfunc: $o ).
thf(func_def_229,type,
ap2p: $o ).
thf(func_def_230,type,
funcinfuncset: $o ).
thf(func_def_231,type,
lamProp: $o ).
thf(func_def_232,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(func_def_233,type,
lamp: $o ).
thf(func_def_234,type,
lam2p: $o ).
thf(func_def_235,type,
brelnall1: $o ).
thf(func_def_236,type,
brelnall2: $o ).
thf(func_def_237,type,
ex1E2: $o ).
thf(func_def_238,type,
funcGraphProp1: $o ).
thf(func_def_239,type,
funcGraphProp3: $o ).
thf(func_def_240,type,
funcGraphProp2: $o ).
thf(func_def_241,type,
funcextLem: $o ).
thf(func_def_244,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_245,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_246,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_247,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_248,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_249,type,
vNOT: $o > $o ).
thf(func_def_250,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_251,type,
vAND: $o > $o > $o ).
thf(func_def_252,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_253,type,
vIMP: $o > $o > $o ).
thf(func_def_254,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_255,type,
sP0: $i > $i > $o ).
thf(func_def_256,type,
sP1: $i > $o ).
thf(func_def_257,type,
sP2: $o ).
thf(func_def_261,type,
sK6: $i > $o ).
thf(func_def_262,type,
sK7: ( $i > $o ) > $i ).
thf(func_def_265,type,
sK10: $i > $o ).
thf(func_def_268,type,
sK13: $i > $o ).
thf(func_def_271,type,
sK16: $i > $i ).
thf(func_def_276,type,
sK21: $o ).
thf(func_def_277,type,
sK22: $o > $i > $i > $i ).
thf(func_def_283,type,
sK28: $i > $i > $o ).
thf(func_def_292,type,
sK37: $i > $i > $i ).
thf(func_def_295,type,
sK40: $i > $i > $o ).
thf(func_def_316,type,
sK61: ( $i > $o ) > $i ).
thf(func_def_317,type,
sK62: ( $i > $o ) > $i ).
thf(func_def_318,type,
sK63: $i > $o ).
thf(func_def_321,type,
sK66: $i > $o ).
thf(func_def_324,type,
sK69: $o ).
thf(func_def_325,type,
sK70: $i > ( $i > $o ) > $i ).
thf(func_def_326,type,
sK71: $i > $o ).
thf(func_def_328,type,
sK73: $i > $o ).
thf(func_def_344,type,
sK89: $i > $o ).
thf(func_def_346,type,
sK91: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_347,type,
sK92: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_348,type,
sK93: $i > ( $i > $o ) > $i ).
thf(func_def_349,type,
sK94: $i > $o ).
thf(func_def_352,type,
sK97: $o ).
thf(func_def_365,type,
sK110: $i > $o ).
thf(func_def_366,type,
sK111: $i > $i ).
thf(func_def_367,type,
sK112: ( $i > $o ) > $i ).
thf(func_def_369,type,
sK114: $i > $o ).
thf(func_def_371,type,
sK116: ( $i > $o ) > $i > $i ).
thf(func_def_373,type,
sK118: $i > $o ).
thf(func_def_375,type,
sK120: ( $i > $o ) > $i > $i ).
thf(func_def_382,type,
sK127: $i > $i > $i > $i ).
thf(func_def_383,type,
sK128: $i > $i > $i > $i ).
thf(func_def_386,type,
sK131: $i > $i > $i ).
thf(func_def_390,type,
sK135: $i > $i ).
thf(func_def_408,type,
sK153: $i > $o ).
thf(func_def_425,type,
sK170: $i > $i > ( $i > $i ) > $i ).
thf(func_def_426,type,
sK171: $i > $i ).
thf(func_def_432,type,
sK177: $i > $i > $i ).
thf(func_def_436,type,
sK181: $i > $i > $o ).
thf(func_def_453,type,
sK198: $i > $i > $i ).
thf(func_def_462,type,
sK207: $o ).
thf(func_def_464,type,
sK209: $i > $i ).
thf(func_def_465,type,
sK210: $o ).
thf(func_def_492,type,
sK237: $i > $i > $i ).
thf(func_def_503,type,
sK248: $i > $o ).
thf(func_def_505,type,
sK250: ( $i > $o ) > $i > $i > $i ).
thf(func_def_508,type,
sK253: $i > $o ).
thf(func_def_512,type,
sK257: $i > $o ).
thf(func_def_515,type,
sK260: $i > ( $i > $o ) > $i ).
thf(func_def_532,type,
sK277: $i > $o ).
thf(func_def_534,type,
sK279: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_535,type,
sK280: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_539,type,
sK284: $i > $o ).
thf(func_def_546,type,
sK291: $i > $i > $i ).
thf(func_def_547,type,
sK292: $i > $i > $i ).
thf(func_def_562,type,
sK307: ( $i > $o ) > $i ).
thf(func_def_563,type,
sK308: $i > $o ).
thf(func_def_564,type,
sK309: $i > $i ).
thf(func_def_567,type,
sK312: $i > $o ).
thf(func_def_580,type,
sK325: $i > $o ).
thf(func_def_582,type,
sK327: $i > ( $i > $o ) > $i ).
thf(func_def_592,type,
sK337: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_593,type,
sK338: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_594,type,
sK339: $i > $o ).
thf(func_def_595,type,
sK340: $i > $o ).
thf(func_def_597,type,
sK342: $i > $o ).
thf(func_def_606,type,
sK351: ( $i > $i > $o ) > $i > $i ).
thf(func_def_607,type,
sK352: ( $i > $i > $o ) > $i > $i ).
thf(func_def_608,type,
sK353: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_610,type,
sK355: $i > $i > $o ).
thf(func_def_611,type,
sK356: $i > $i ).
thf(func_def_612,type,
sK357: $i > $i ).
thf(func_def_615,type,
sK360: $i > $i > $i ).
thf(func_def_620,type,
sK365: $i > $i > $i ).
thf(func_def_626,type,
sK371: $i > $o ).
thf(func_def_628,type,
sK373: ( $i > $o ) > $i > $i ).
thf(func_def_632,type,
sK377: $i > $o ).
thf(func_def_637,type,
sK382: $i > $i ).
thf(func_def_638,type,
sK383: $i > $i ).
thf(func_def_639,type,
sK384: $i > $i ).
thf(func_def_640,type,
sK385: $i > $i ).
thf(func_def_641,type,
sK386: $i > $i ).
thf(func_def_642,type,
sK387: $i > $i > $i > $i ).
thf(func_def_643,type,
sK388: $i > $i ).
thf(func_def_644,type,
sK389: $i > $i ).
thf(func_def_645,type,
sK390: $i > $i ).
thf(func_def_646,type,
sK391: $i > $i ).
thf(func_def_647,type,
sK392: $i > $i > $i ).
thf(func_def_648,type,
sK393: $i > $i > $i > $i ).
thf(func_def_649,type,
sK394: $i > $i > $i > $i ).
thf(func_def_650,type,
sK395: $i > $i > $i > $i ).
thf(func_def_651,type,
sK396: $i > $i > $i ).
thf(func_def_652,type,
sK397: $i > $i > $i ).
thf(func_def_653,type,
sK398: $i > $i > $i ).
thf(func_def_654,type,
sK399: $i > $i > $i ).
thf(func_def_665,type,
sK410: $i > $o ).
thf(func_def_666,type,
sK411: $i > $o ).
thf(func_def_667,type,
sK412: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_668,type,
sK413: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_673,type,
sK418: $i > $o ).
thf(func_def_674,type,
sK419: $i > $o ).
thf(func_def_675,type,
sK420: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_676,type,
sK421: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_677,type,
sK422: ( $i > $o ) > $i > $i ).
thf(func_def_678,type,
sK423: ( $i > $o ) > $i > $i ).
thf(func_def_680,type,
sK425: $i > $o ).
thf(func_def_695,type,
sK440: $i > $i > $o ).
thf(func_def_699,type,
sK444: ( $i > $i ) > $i > $i > $i ).
thf(func_def_702,type,
sK447: $i > $i ).
thf(func_def_706,type,
sK451: $i > $o ).
thf(func_def_708,type,
sK453: ( $i > $o ) > $i > $i ).
thf(func_def_709,type,
sK454: ( $i > $o ) > $i > $i ).
thf(func_def_710,type,
sK455: $i > $i > $i ).
thf(func_def_719,type,
sK464: $i > $i > $i > $i > $i ).
thf(func_def_724,type,
sK469: $i > $i > $o ).
thf(func_def_728,type,
sK473: $i > $o ).
thf(func_def_740,type,
sK485: $o ).
thf(func_def_742,type,
sK487: $i > $i > $o ).
thf(func_def_751,type,
sK496: $i > $o ).
thf(func_def_753,type,
sK498: $i > $i > ( $i > $i ) > $i ).
thf(func_def_754,type,
sK499: $i > $i ).
thf(func_def_779,type,
sK524: $i > $i > $o ).
thf(func_def_791,type,
sK536: $i > $o ).
thf(func_def_803,type,
sK548: $i > $i ).
thf(func_def_805,type,
sK550: $i > $i ).
thf(func_def_807,type,
sK552: $i > $i ).
thf(func_def_813,type,
sK558: ( $i > $o ) > $i > $i ).
thf(func_def_815,type,
sK560: $i > $o ).
thf(func_def_819,type,
sK564: $o ).
thf(func_def_846,type,
sK591: $i > $i ).
thf(func_def_856,type,
sK601: $o ).
thf(func_def_862,type,
sK607: $i > ( $i > $o ) > $i ).
thf(func_def_863,type,
sK608: $i > $o ).
thf(f198,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ( func @ X0 @ X1 @ X2 ) )
= infuncsetfunc ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(f210,axiom,
! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> ( ( ap @ X0 @ X1 @ X2 @ X3 )
= X4 ) ) ) ) )
= funcGraphProp2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp2) ).
thf(f212,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ! [X1: $i,X0: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> ( ( ap @ X0 @ X1 @ X2 @ X3 )
= X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp4) ).
thf(f213,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ! [X1: $i,X0: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> ( ( ap @ X0 @ X1 @ X2 @ X3 )
= X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f212]) ).
thf(f315,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> ( ( ap @ X0 @ X1 @ X2 @ X3 )
= X4 ) ) ) ) )
= funcGraphProp2 ),
inference(rectify,[],[f210]) ).
thf(f316,plain,
( ( funcGraphProp2 = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( func @ X0 @ X1 @ X2 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ! [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
=> ( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true )
=> ( ( ap @ X0 @ X1 @ X2 @ X3 )
= X4 ) ) ) ) ) ),
inference(fool_elimination,[],[f315]) ).
thf(f371,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ X1 @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> ( ( ap @ X1 @ X0 @ X2 @ X3 )
= X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f213]) ).
thf(f372,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ( ( setukpairinjR2 = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ( ( ksndpairEq = $true )
=> ( ( kpairsurjEq = $true )
=> ( ( cartprodsndin = $true )
=> ( ( cartprodpairmemEL = $true )
=> ( ( cartprodpairmemER = $true )
=> ( ( cartprodmempaircEq = $true )
=> ( ( cartprodfstpairEq = $true )
=> ( ( cartprodsndpairEq = $true )
=> ( ( cartprodpairsurjEq = $true )
=> ( ( dpsetconstrI = $true )
=> ( ( dpsetconstrSub = $true )
=> ( ( setOfPairsIsBReln = $true )
=> ( ( dpsetconstrERa = $true )
=> ( ( dpsetconstrEL1 = $true )
=> ( ( dpsetconstrEL2 = $true )
=> ( ( dpsetconstrER = $true )
=> ( ( funcImageSingleton = $true )
=> ( ( apProp = $true )
=> ( ( app = $true )
=> ( ( infuncsetfunc = $true )
=> ( ( ap2p = $true )
=> ( ( funcinfuncset = $true )
=> ( ( lamProp = $true )
=> ( ( lamp = $true )
=> ( ( lam2p = $true )
=> ( ( brelnall1 = $true )
=> ( ( brelnall2 = $true )
=> ( ( ex1E2 = $true )
=> ( ( funcGraphProp1 = $true )
=> ( ( funcGraphProp3 = $true )
=> ( ( funcGraphProp2 = $true )
=> ( ( funcextLem = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( funcSet @ X1 @ X0 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ! [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
=> ( ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true )
=> ( ( ap @ X1 @ X0 @ X2 @ X3 )
= X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f371]) ).
thf(f445,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ( func @ X0 @ X1 @ X2 ) )
= infuncsetfunc ),
inference(rectify,[],[f198]) ).
thf(f446,plain,
( ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
= $true )
=> ( ( func @ X0 @ X1 @ X2 )
= $true ) )
<=> ( infuncsetfunc = $true ) ),
inference(fool_elimination,[],[f445]) ).
thf(f708,plain,
( ( infuncsetfunc = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
!= $true )
| ( ( func @ X0 @ X1 @ X2 )
= $true ) ) ),
inference(ennf_transformation,[],[f446]) ).
thf(f797,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( ap @ X1 @ X0 @ X2 @ X3 )
!= X4 )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true )
& ( ( in @ X4 @ X0 )
= $true ) )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X2 @ ( funcSet @ X1 @ X0 ) )
= $true ) )
& ( funcextLem = $true )
& ( funcGraphProp2 = $true )
& ( funcGraphProp3 = $true )
& ( funcGraphProp1 = $true )
& ( ex1E2 = $true )
& ( brelnall2 = $true )
& ( brelnall1 = $true )
& ( lam2p = $true )
& ( lamp = $true )
& ( lamProp = $true )
& ( funcinfuncset = $true )
& ( ap2p = $true )
& ( infuncsetfunc = $true )
& ( app = $true )
& ( apProp = $true )
& ( funcImageSingleton = $true )
& ( dpsetconstrER = $true )
& ( dpsetconstrEL2 = $true )
& ( dpsetconstrEL1 = $true )
& ( dpsetconstrERa = $true )
& ( setOfPairsIsBReln = $true )
& ( dpsetconstrSub = $true )
& ( dpsetconstrI = $true )
& ( cartprodpairsurjEq = $true )
& ( cartprodsndpairEq = $true )
& ( cartprodfstpairEq = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodpairmemER = $true )
& ( cartprodpairmemEL = $true )
& ( cartprodsndin = $true )
& ( kpairsurjEq = $true )
& ( ksndpairEq = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR = $true )
& ( setukpairinjR2 = $true )
& ( upairequniteq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjR12 = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjL = $true )
& ( setukpairinjL2 = $true )
& ( cartprodfstin = $true )
& ( kfstpairEq = $true )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( singletonsuniq = $true )
& ( ex1I2 = $true )
& ( ex1I = $true )
& ( ex1E1 = $true )
& ( singletonprop = $true )
& ( setunionsingleton = $true )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( setunionE2 = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( cartprodpairin = $true )
& ( ubforcartprodlem3 = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( upairsubunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[],[f372]) ).
thf(f798,plain,
( ( cartprodsndpairEq = $true )
& ( setext = $true )
& ( vacuousDall = $true )
& ( notequalI2 = $true )
& ( funcImageSingleton = $true )
& ( dsetconstrEL = $true )
& ( prop2setI = $true )
& ( exuI3 = $true )
& ( binintersectER = $true )
& ( uniqinunit = $true )
& ( emptysetsubset = $true )
& ( singletoninpowunion = $true )
& ( setadjoinIR = $true )
& ( setunionsingleton = $true )
& ( funcextLem = $true )
& ( powersetAx = $true )
& ( powersetI = $true )
& ( lam2p = $true )
& ( kpairp = $true )
& ( nonemptyI1 = $true )
& ( binunionIL = $true )
& ( singletonsubset = $true )
& ( binunionIR = $true )
& ( setminusERneg = $true )
& ( funcGraphProp1 = $true )
& ( app = $true )
& ( cartprodfstin = $true )
& ( cartprodsndin = $true )
& ( ex1I2 = $true )
& ( infuncsetfunc = $true )
& ( setukpairinjR2 = $true )
& ( setextsub = $true )
& ( setukpairinjR12 = $true )
& ( cartprodmempaircEq = $true )
& ( emptysetimpfalse = $true )
& ( powerset__Cong = $true )
& ( inCongP = $true )
& ( singletonsswitch = $true )
& ( exuI2 = $true )
& ( sepSubset = $true )
& ( binunionRsub = $true )
& ( brelnall1 = $true )
& ? [X0: $i,X2: $i,X1: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( ap @ X1 @ X0 @ X2 @ X3 )
!= X4 )
& ( ( in @ X4 @ X0 )
= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true ) )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X2 @ ( funcSet @ X1 @ X0 ) )
= $true ) )
& ( ksndpairEq = $true )
& ( omega__Cong = $true )
& ( replAx = $true )
& ( setukpairinjL2 = $true )
& ( setukpairinjL = $true )
& ( dsetconstr__Cong = $true )
& ( notdexE = $true )
& ( ubforcartprodlem1 = $true )
& ( upairset2E = $true )
& ( powersetE1 = $true )
& ( funcGraphProp2 = $true )
& ( setminusSubset1 = $true )
& ( omegaIndAx = $true )
& ( ubforcartprodlem2 = $true )
& ( notdallE = $true )
& ( setminusELneg = $true )
& ( quantDeMorgan4 = $true )
& ( nonemptyImpWitness = $true )
& ( setminusI = $true )
& ( kpairiskpair = $true )
& ( setunionI = $true )
& ( apProp = $true )
& ( upairinpowunion = $true )
& ( setunionE2 = $true )
& ( binintersectSubset3 = $true )
& ( cartprodpairsurjEq = $true )
& ( ex1E1 = $true )
& ( descrp = $true )
& ( setunionAx = $true )
& ( subsetE = $true )
& ( nonemptyI = $true )
& ( symdiffE = $true )
& ( prop2setE = $true )
& ( emptysetE = $true )
& ( singletoninpowerset = $true )
& ( omega0Ax = $true )
& ( quantDeMorgan3 = $true )
& ( subPowSU = $true )
& ( emptyI = $true )
& ( ap2p = $true )
& ( symdiffIneg1 = $true )
& ( cartprodpairin = $true )
& ( binunionEcases = $true )
& ( subsetI2 = $true )
& ( emptyE1 = $true )
& ( foundationAx = $true )
& ( exuEu = $true )
& ( emptyinPowerset = $true )
& ( setukpairIL = $true )
& ( dsetconstrI = $true )
& ( exuE1 = $true )
& ( funcinfuncset = $true )
& ( quantDeMorgan1 = $true )
& ( subsetRefl = $true )
& ( lamp = $true )
& ( setunionE = $true )
& ( binintersectSubset5 = $true )
& ( cartprodmempair1 = $true )
& ( symdiffI1 = $true )
& ( kpairsurjEq = $true )
& ( powersetE = $true )
& ( eqimpsubset2 = $true )
& ( setukpairinjR1 = $true )
& ( kfstpairEq = $true )
& ( emptyinunitempty = $true )
& ( powersetsubset = $true )
& ( binintersectSubset1 = $true )
& ( notsubsetI = $true )
& ( powersetI1 = $true )
& ( emptyset__Cong = $true )
& ( setoftrueEq = $true )
& ( setukpairinjR = $true )
& ( dpsetconstrEL1 = $true )
& ( upairsetIL = $true )
& ( setadjoinIL = $true )
& ( singletonprop = $true )
& ( dpsetconstrERa = $true )
& ( dpsetconstrEL2 = $true )
& ( binunionE = $true )
& ( quantDeMorgan2 = $true )
& ( dpsetconstrSub = $true )
& ( inPowerset = $true )
& ( dpsetconstrI = $true )
& ( upairsetIR = $true )
& ( setminusER = $true )
& ( noeltsimpempty = $true )
& ( notinemptyset = $true )
& ( theprop = $true )
& ( exuE3e = $true )
& ( emptyInPowerset = $true )
& ( binintersectI = $true )
& ( exuE2 = $true )
& ( emptysetAx = $true )
& ( disjointsetsI1 = $true )
& ( binunionLsub = $true )
& ( upairequniteq = $true )
& ( setbeta = $true )
& ( setextAx = $true )
& ( ubforcartprodlem3 = $true )
& ( symdiffI2 = $true )
& ( funcGraphProp3 = $true )
& ( cartprodpairmemER = $true )
& ( dpsetconstrER = $true )
& ( setukpairinjL1 = $true )
& ( binintersectSubset2 = $true )
& ( setunionsingleton1 = $true )
& ( dsetconstrER = $true )
& ( cartprodpairmemEL = $true )
& ( exu__Cong = $true )
& ( setadjoinE = $true )
& ( eqinunit = $true )
& ( in__Cong = $true )
& ( setminusSubset2 = $true )
& ( setadjoinAx = $true )
& ( omegaSAx = $true )
& ( setminusILneg = $true )
& ( subset2powerset = $true )
& ( subsetemptysetimpeq = $true )
& ( eqimpsubset1 = $true )
& ( upairset2IR = $true )
& ( upairsubunion = $true )
& ( setadjoinOr = $true )
& ( singletonsuniq = $true )
& ( setadjoinSub2 = $true )
& ( upairsetE = $true )
& ( setminusIRneg = $true )
& ( exuI1 = $true )
& ( setOfPairsIsBReln = $true )
& ( nonemptyE1 = $true )
& ( wellorderingAx = $true )
& ( binintersectRsub = $true )
& ( bs114d = $true )
& ( cartprodfstpairEq = $true )
& ( setadjoin__Cong = $true )
& ( setunion__Cong = $true )
& ( descr__Cong = $true )
& ( kfstsingleton = $true )
& ( subsetI1 = $true )
& ( setminusLsub = $true )
& ( setunionsingleton2 = $true )
& ( sepInPowerset = $true )
& ( setukpairIR = $true )
& ( setadjoinSub = $true )
& ( binintersectSubset4 = $true )
& ( ksndsingleton = $true )
& ( ex1I = $true )
& ( subsetTrans = $true )
& ( setukpairinjR11 = $true )
& ( exuE3u = $true )
& ( cartprodmempair = $true )
& ( ex1E2 = $true )
& ( subsetE2 = $true )
& ( binintersectLsub = $true )
& ( brelnall2 = $true )
& ( lamProp = $true )
& ( secondinupair = $true )
& ( notinsingleton = $true )
& ( setminusEL = $true )
& ( prop2set2propI = $true )
& ( symdiffIneg2 = $true )
& ( binintersectEL = $true )
& ( notequalI1 = $true ) ),
inference(flattening,[],[f797]) ).
thf(f804,plain,
( ( funcGraphProp2 = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( ( ap @ X0 @ X1 @ X2 @ X3 )
= X4 )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
!= $true )
| ( ( in @ X4 @ X1 )
!= $true ) )
| ( ( in @ X3 @ X0 )
!= $true ) )
| ( ( func @ X0 @ X1 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[],[f316]) ).
thf(f805,plain,
( ( funcGraphProp2 = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( ( func @ X0 @ X1 @ X2 )
!= $true )
| ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ X4 @ X1 )
!= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
!= $true )
| ( ( ap @ X0 @ X1 @ X2 @ X3 )
= X4 ) )
| ( ( in @ X3 @ X0 )
!= $true ) ) ) ),
inference(flattening,[],[f804]) ).
thf(f1184,plain,
( ( cartprodsndpairEq = $true )
& ( setext = $true )
& ( vacuousDall = $true )
& ( notequalI2 = $true )
& ( funcImageSingleton = $true )
& ( dsetconstrEL = $true )
& ( prop2setI = $true )
& ( exuI3 = $true )
& ( binintersectER = $true )
& ( uniqinunit = $true )
& ( emptysetsubset = $true )
& ( singletoninpowunion = $true )
& ( setadjoinIR = $true )
& ( setunionsingleton = $true )
& ( funcextLem = $true )
& ( powersetAx = $true )
& ( powersetI = $true )
& ( lam2p = $true )
& ( kpairp = $true )
& ( nonemptyI1 = $true )
& ( binunionIL = $true )
& ( singletonsubset = $true )
& ( binunionIR = $true )
& ( setminusERneg = $true )
& ( funcGraphProp1 = $true )
& ( app = $true )
& ( cartprodfstin = $true )
& ( cartprodsndin = $true )
& ( ex1I2 = $true )
& ( infuncsetfunc = $true )
& ( setukpairinjR2 = $true )
& ( setextsub = $true )
& ( setukpairinjR12 = $true )
& ( cartprodmempaircEq = $true )
& ( emptysetimpfalse = $true )
& ( powerset__Cong = $true )
& ( inCongP = $true )
& ( singletonsswitch = $true )
& ( exuI2 = $true )
& ( sepSubset = $true )
& ( binunionRsub = $true )
& ( brelnall1 = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( ap @ X2 @ X0 @ X1 @ X3 )
!= X4 )
& ( ( in @ X4 @ X0 )
= $true )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ X1 ) ) )
& ( ( in @ X3 @ X2 )
= $true ) )
& ( $true
= ( in @ X1 @ ( funcSet @ X2 @ X0 ) ) ) )
& ( ksndpairEq = $true )
& ( omega__Cong = $true )
& ( replAx = $true )
& ( setukpairinjL2 = $true )
& ( setukpairinjL = $true )
& ( dsetconstr__Cong = $true )
& ( notdexE = $true )
& ( ubforcartprodlem1 = $true )
& ( upairset2E = $true )
& ( powersetE1 = $true )
& ( funcGraphProp2 = $true )
& ( setminusSubset1 = $true )
& ( omegaIndAx = $true )
& ( ubforcartprodlem2 = $true )
& ( notdallE = $true )
& ( setminusELneg = $true )
& ( quantDeMorgan4 = $true )
& ( nonemptyImpWitness = $true )
& ( setminusI = $true )
& ( kpairiskpair = $true )
& ( setunionI = $true )
& ( apProp = $true )
& ( upairinpowunion = $true )
& ( setunionE2 = $true )
& ( binintersectSubset3 = $true )
& ( cartprodpairsurjEq = $true )
& ( ex1E1 = $true )
& ( descrp = $true )
& ( setunionAx = $true )
& ( subsetE = $true )
& ( nonemptyI = $true )
& ( symdiffE = $true )
& ( prop2setE = $true )
& ( emptysetE = $true )
& ( singletoninpowerset = $true )
& ( omega0Ax = $true )
& ( quantDeMorgan3 = $true )
& ( subPowSU = $true )
& ( emptyI = $true )
& ( ap2p = $true )
& ( symdiffIneg1 = $true )
& ( cartprodpairin = $true )
& ( binunionEcases = $true )
& ( subsetI2 = $true )
& ( emptyE1 = $true )
& ( foundationAx = $true )
& ( exuEu = $true )
& ( emptyinPowerset = $true )
& ( setukpairIL = $true )
& ( dsetconstrI = $true )
& ( exuE1 = $true )
& ( funcinfuncset = $true )
& ( quantDeMorgan1 = $true )
& ( subsetRefl = $true )
& ( lamp = $true )
& ( setunionE = $true )
& ( binintersectSubset5 = $true )
& ( cartprodmempair1 = $true )
& ( symdiffI1 = $true )
& ( kpairsurjEq = $true )
& ( powersetE = $true )
& ( eqimpsubset2 = $true )
& ( setukpairinjR1 = $true )
& ( kfstpairEq = $true )
& ( emptyinunitempty = $true )
& ( powersetsubset = $true )
& ( binintersectSubset1 = $true )
& ( notsubsetI = $true )
& ( powersetI1 = $true )
& ( emptyset__Cong = $true )
& ( setoftrueEq = $true )
& ( setukpairinjR = $true )
& ( dpsetconstrEL1 = $true )
& ( upairsetIL = $true )
& ( setadjoinIL = $true )
& ( singletonprop = $true )
& ( dpsetconstrERa = $true )
& ( dpsetconstrEL2 = $true )
& ( binunionE = $true )
& ( quantDeMorgan2 = $true )
& ( dpsetconstrSub = $true )
& ( inPowerset = $true )
& ( dpsetconstrI = $true )
& ( upairsetIR = $true )
& ( setminusER = $true )
& ( noeltsimpempty = $true )
& ( notinemptyset = $true )
& ( theprop = $true )
& ( exuE3e = $true )
& ( emptyInPowerset = $true )
& ( binintersectI = $true )
& ( exuE2 = $true )
& ( emptysetAx = $true )
& ( disjointsetsI1 = $true )
& ( binunionLsub = $true )
& ( upairequniteq = $true )
& ( setbeta = $true )
& ( setextAx = $true )
& ( ubforcartprodlem3 = $true )
& ( symdiffI2 = $true )
& ( funcGraphProp3 = $true )
& ( cartprodpairmemER = $true )
& ( dpsetconstrER = $true )
& ( setukpairinjL1 = $true )
& ( binintersectSubset2 = $true )
& ( setunionsingleton1 = $true )
& ( dsetconstrER = $true )
& ( cartprodpairmemEL = $true )
& ( exu__Cong = $true )
& ( setadjoinE = $true )
& ( eqinunit = $true )
& ( in__Cong = $true )
& ( setminusSubset2 = $true )
& ( setadjoinAx = $true )
& ( omegaSAx = $true )
& ( setminusILneg = $true )
& ( subset2powerset = $true )
& ( subsetemptysetimpeq = $true )
& ( eqimpsubset1 = $true )
& ( upairset2IR = $true )
& ( upairsubunion = $true )
& ( setadjoinOr = $true )
& ( singletonsuniq = $true )
& ( setadjoinSub2 = $true )
& ( upairsetE = $true )
& ( setminusIRneg = $true )
& ( exuI1 = $true )
& ( setOfPairsIsBReln = $true )
& ( nonemptyE1 = $true )
& ( wellorderingAx = $true )
& ( binintersectRsub = $true )
& ( bs114d = $true )
& ( cartprodfstpairEq = $true )
& ( setadjoin__Cong = $true )
& ( setunion__Cong = $true )
& ( descr__Cong = $true )
& ( kfstsingleton = $true )
& ( subsetI1 = $true )
& ( setminusLsub = $true )
& ( setunionsingleton2 = $true )
& ( sepInPowerset = $true )
& ( setukpairIR = $true )
& ( setadjoinSub = $true )
& ( binintersectSubset4 = $true )
& ( ksndsingleton = $true )
& ( ex1I = $true )
& ( subsetTrans = $true )
& ( setukpairinjR11 = $true )
& ( exuE3u = $true )
& ( cartprodmempair = $true )
& ( ex1E2 = $true )
& ( subsetE2 = $true )
& ( binintersectLsub = $true )
& ( brelnall2 = $true )
& ( lamProp = $true )
& ( secondinupair = $true )
& ( notinsingleton = $true )
& ( setminusEL = $true )
& ( prop2set2propI = $true )
& ( symdiffIneg2 = $true )
& ( binintersectEL = $true )
& ( notequalI1 = $true ) ),
inference(rectify,[],[f798]) ).
thf(f1185,plain,
( ( cartprodsndpairEq = $true )
& ( setext = $true )
& ( vacuousDall = $true )
& ( notequalI2 = $true )
& ( funcImageSingleton = $true )
& ( dsetconstrEL = $true )
& ( prop2setI = $true )
& ( exuI3 = $true )
& ( binintersectER = $true )
& ( uniqinunit = $true )
& ( emptysetsubset = $true )
& ( singletoninpowunion = $true )
& ( setadjoinIR = $true )
& ( setunionsingleton = $true )
& ( funcextLem = $true )
& ( powersetAx = $true )
& ( powersetI = $true )
& ( lam2p = $true )
& ( kpairp = $true )
& ( nonemptyI1 = $true )
& ( binunionIL = $true )
& ( singletonsubset = $true )
& ( binunionIR = $true )
& ( setminusERneg = $true )
& ( funcGraphProp1 = $true )
& ( app = $true )
& ( cartprodfstin = $true )
& ( cartprodsndin = $true )
& ( ex1I2 = $true )
& ( infuncsetfunc = $true )
& ( setukpairinjR2 = $true )
& ( setextsub = $true )
& ( setukpairinjR12 = $true )
& ( cartprodmempaircEq = $true )
& ( emptysetimpfalse = $true )
& ( powerset__Cong = $true )
& ( inCongP = $true )
& ( singletonsswitch = $true )
& ( exuI2 = $true )
& ( sepSubset = $true )
& ( binunionRsub = $true )
& ( brelnall1 = $true )
& ( ( ap @ sK297 @ sK295 @ sK296 @ sK298 )
!= sK299 )
& ( ( in @ sK299 @ sK295 )
= $true )
& ( $true
= ( in @ ( kpair @ sK298 @ sK299 ) @ sK296 ) )
& ( ( in @ sK298 @ sK297 )
= $true )
& ( ( in @ sK296 @ ( funcSet @ sK297 @ sK295 ) )
= $true )
& ( ksndpairEq = $true )
& ( omega__Cong = $true )
& ( replAx = $true )
& ( setukpairinjL2 = $true )
& ( setukpairinjL = $true )
& ( dsetconstr__Cong = $true )
& ( notdexE = $true )
& ( ubforcartprodlem1 = $true )
& ( upairset2E = $true )
& ( powersetE1 = $true )
& ( funcGraphProp2 = $true )
& ( setminusSubset1 = $true )
& ( omegaIndAx = $true )
& ( ubforcartprodlem2 = $true )
& ( notdallE = $true )
& ( setminusELneg = $true )
& ( quantDeMorgan4 = $true )
& ( nonemptyImpWitness = $true )
& ( setminusI = $true )
& ( kpairiskpair = $true )
& ( setunionI = $true )
& ( apProp = $true )
& ( upairinpowunion = $true )
& ( setunionE2 = $true )
& ( binintersectSubset3 = $true )
& ( cartprodpairsurjEq = $true )
& ( ex1E1 = $true )
& ( descrp = $true )
& ( setunionAx = $true )
& ( subsetE = $true )
& ( nonemptyI = $true )
& ( symdiffE = $true )
& ( prop2setE = $true )
& ( emptysetE = $true )
& ( singletoninpowerset = $true )
& ( omega0Ax = $true )
& ( quantDeMorgan3 = $true )
& ( subPowSU = $true )
& ( emptyI = $true )
& ( ap2p = $true )
& ( symdiffIneg1 = $true )
& ( cartprodpairin = $true )
& ( binunionEcases = $true )
& ( subsetI2 = $true )
& ( emptyE1 = $true )
& ( foundationAx = $true )
& ( exuEu = $true )
& ( emptyinPowerset = $true )
& ( setukpairIL = $true )
& ( dsetconstrI = $true )
& ( exuE1 = $true )
& ( funcinfuncset = $true )
& ( quantDeMorgan1 = $true )
& ( subsetRefl = $true )
& ( lamp = $true )
& ( setunionE = $true )
& ( binintersectSubset5 = $true )
& ( cartprodmempair1 = $true )
& ( symdiffI1 = $true )
& ( kpairsurjEq = $true )
& ( powersetE = $true )
& ( eqimpsubset2 = $true )
& ( setukpairinjR1 = $true )
& ( kfstpairEq = $true )
& ( emptyinunitempty = $true )
& ( powersetsubset = $true )
& ( binintersectSubset1 = $true )
& ( notsubsetI = $true )
& ( powersetI1 = $true )
& ( emptyset__Cong = $true )
& ( setoftrueEq = $true )
& ( setukpairinjR = $true )
& ( dpsetconstrEL1 = $true )
& ( upairsetIL = $true )
& ( setadjoinIL = $true )
& ( singletonprop = $true )
& ( dpsetconstrERa = $true )
& ( dpsetconstrEL2 = $true )
& ( binunionE = $true )
& ( quantDeMorgan2 = $true )
& ( dpsetconstrSub = $true )
& ( inPowerset = $true )
& ( dpsetconstrI = $true )
& ( upairsetIR = $true )
& ( setminusER = $true )
& ( noeltsimpempty = $true )
& ( notinemptyset = $true )
& ( theprop = $true )
& ( exuE3e = $true )
& ( emptyInPowerset = $true )
& ( binintersectI = $true )
& ( exuE2 = $true )
& ( emptysetAx = $true )
& ( disjointsetsI1 = $true )
& ( binunionLsub = $true )
& ( upairequniteq = $true )
& ( setbeta = $true )
& ( setextAx = $true )
& ( ubforcartprodlem3 = $true )
& ( symdiffI2 = $true )
& ( funcGraphProp3 = $true )
& ( cartprodpairmemER = $true )
& ( dpsetconstrER = $true )
& ( setukpairinjL1 = $true )
& ( binintersectSubset2 = $true )
& ( setunionsingleton1 = $true )
& ( dsetconstrER = $true )
& ( cartprodpairmemEL = $true )
& ( exu__Cong = $true )
& ( setadjoinE = $true )
& ( eqinunit = $true )
& ( in__Cong = $true )
& ( setminusSubset2 = $true )
& ( setadjoinAx = $true )
& ( omegaSAx = $true )
& ( setminusILneg = $true )
& ( subset2powerset = $true )
& ( subsetemptysetimpeq = $true )
& ( eqimpsubset1 = $true )
& ( upairset2IR = $true )
& ( upairsubunion = $true )
& ( setadjoinOr = $true )
& ( singletonsuniq = $true )
& ( setadjoinSub2 = $true )
& ( upairsetE = $true )
& ( setminusIRneg = $true )
& ( exuI1 = $true )
& ( setOfPairsIsBReln = $true )
& ( nonemptyE1 = $true )
& ( wellorderingAx = $true )
& ( binintersectRsub = $true )
& ( bs114d = $true )
& ( cartprodfstpairEq = $true )
& ( setadjoin__Cong = $true )
& ( setunion__Cong = $true )
& ( descr__Cong = $true )
& ( kfstsingleton = $true )
& ( subsetI1 = $true )
& ( setminusLsub = $true )
& ( setunionsingleton2 = $true )
& ( sepInPowerset = $true )
& ( setukpairIR = $true )
& ( setadjoinSub = $true )
& ( binintersectSubset4 = $true )
& ( ksndsingleton = $true )
& ( ex1I = $true )
& ( subsetTrans = $true )
& ( setukpairinjR11 = $true )
& ( exuE3u = $true )
& ( cartprodmempair = $true )
& ( ex1E2 = $true )
& ( subsetE2 = $true )
& ( binintersectLsub = $true )
& ( brelnall2 = $true )
& ( lamProp = $true )
& ( secondinupair = $true )
& ( notinsingleton = $true )
& ( setminusEL = $true )
& ( prop2set2propI = $true )
& ( symdiffIneg2 = $true )
& ( binintersectEL = $true )
& ( notequalI1 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK295,sK296,sK297,sK298,sK299]),skolemize(X0,sK295),skolemize(X1,sK296),skolemize(X2,sK297),skolemize(X3,sK298),skolemize(X4,sK299)],[f1184]) ).
thf(f1278,plain,
( ( ( funcGraphProp2 = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( ( func @ X0 @ X1 @ X2 )
= $true )
& ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
= $true )
& ( ( ap @ X0 @ X1 @ X2 @ X3 )
!= X4 ) )
& ( ( in @ X3 @ X0 )
= $true ) ) ) )
& ( ! [X1: $i,X2: $i,X0: $i] :
( ( ( func @ X0 @ X1 @ X2 )
!= $true )
| ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ X4 @ X1 )
!= $true )
| ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
!= $true )
| ( ( ap @ X0 @ X1 @ X2 @ X3 )
= X4 ) )
| ( ( in @ X3 @ X0 )
!= $true ) ) )
| ( funcGraphProp2 != $true ) ) ),
inference(nnf_transformation,[],[f805]) ).
thf(f1279,plain,
( ( ( funcGraphProp2 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X2 @ X0 @ X1 )
= $true )
& ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ X1 ) )
& ( ( ap @ X2 @ X0 @ X1 @ X3 )
!= X4 ) )
& ( ( in @ X3 @ X2 )
= $true ) ) ) )
& ( ! [X5: $i,X6: $i,X7: $i] :
( ( $true
!= ( func @ X7 @ X5 @ X6 ) )
| ! [X8: $i] :
( ! [X9: $i] :
( ( ( in @ X9 @ X5 )
!= $true )
| ( ( in @ ( kpair @ X8 @ X9 ) @ X6 )
!= $true )
| ( ( ap @ X7 @ X5 @ X6 @ X8 )
= X9 ) )
| ( ( in @ X8 @ X7 )
!= $true ) ) )
| ( funcGraphProp2 != $true ) ) ),
inference(rectify,[],[f1278]) ).
thf(f1280,plain,
( ( ( funcGraphProp2 = $true )
| ( ( ( func @ sK405 @ sK403 @ sK404 )
= $true )
& ( $true
= ( in @ sK407 @ sK403 ) )
& ( ( in @ ( kpair @ sK406 @ sK407 ) @ sK404 )
= $true )
& ( sK407
!= ( ap @ sK405 @ sK403 @ sK404 @ sK406 ) )
& ( ( in @ sK406 @ sK405 )
= $true ) ) )
& ( ! [X5: $i,X6: $i,X7: $i] :
( ( $true
!= ( func @ X7 @ X5 @ X6 ) )
| ! [X8: $i] :
( ! [X9: $i] :
( ( ( in @ X9 @ X5 )
!= $true )
| ( ( in @ ( kpair @ X8 @ X9 ) @ X6 )
!= $true )
| ( ( ap @ X7 @ X5 @ X6 @ X8 )
= X9 ) )
| ( ( in @ X8 @ X7 )
!= $true ) ) )
| ( funcGraphProp2 != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK403,sK404,sK405,sK406,sK407]),skolemize(X0,sK403),skolemize(X1,sK404),skolemize(X2,sK405),skolemize(X3,sK406),skolemize(X4,sK407)],[f1279]) ).
thf(f1474,plain,
( ( ( infuncsetfunc = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
= $true )
& ( ( func @ X0 @ X1 @ X2 )
!= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
!= $true )
| ( ( func @ X0 @ X1 @ X2 )
= $true ) )
| ( infuncsetfunc != $true ) ) ),
inference(nnf_transformation,[],[f708]) ).
thf(f1475,plain,
( ( ( infuncsetfunc = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
= $true )
& ( ( func @ X0 @ X1 @ X2 )
!= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( funcSet @ X3 @ X4 ) )
!= $true )
| ( ( func @ X3 @ X4 @ X5 )
= $true ) )
| ( infuncsetfunc != $true ) ) ),
inference(rectify,[],[f1474]) ).
thf(f1476,plain,
( ( ( infuncsetfunc = $true )
| ( ( ( in @ sK597 @ ( funcSet @ sK595 @ sK596 ) )
= $true )
& ( $true
!= ( func @ sK595 @ sK596 @ sK597 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( funcSet @ X3 @ X4 ) )
!= $true )
| ( ( func @ X3 @ X4 @ X5 )
= $true ) )
| ( infuncsetfunc != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK595,sK596,sK597]),skolemize(X0,sK595),skolemize(X1,sK596),skolemize(X2,sK597)],[f1475]) ).
thf(f2016,plain,
funcGraphProp2 = $true,
inference(cnf_transformation,[],[f1185]) ).
thf(f2027,plain,
( ( in @ sK296 @ ( funcSet @ sK297 @ sK295 ) )
= $true ),
inference(cnf_transformation,[],[f1185]) ).
thf(f2028,plain,
( ( in @ sK298 @ sK297 )
= $true ),
inference(cnf_transformation,[],[f1185]) ).
thf(f2029,plain,
( $true
= ( in @ ( kpair @ sK298 @ sK299 ) @ sK296 ) ),
inference(cnf_transformation,[],[f1185]) ).
thf(f2030,plain,
( ( in @ sK299 @ sK295 )
= $true ),
inference(cnf_transformation,[],[f1185]) ).
thf(f2031,plain,
( ( ap @ sK297 @ sK295 @ sK296 @ sK298 )
!= sK299 ),
inference(cnf_transformation,[],[f1185]) ).
thf(f2044,plain,
infuncsetfunc = $true,
inference(cnf_transformation,[],[f1185]) ).
thf(f2224,plain,
! [X8: $i,X6: $i,X9: $i,X7: $i,X5: $i] :
( ( funcGraphProp2 != $true )
| ( ( ap @ X7 @ X5 @ X6 @ X8 )
= X9 )
| ( ( in @ X9 @ X5 )
!= $true )
| ( ( in @ X8 @ X7 )
!= $true )
| ( ( in @ ( kpair @ X8 @ X9 ) @ X6 )
!= $true )
| ( $true
!= ( func @ X7 @ X5 @ X6 ) ) ),
inference(cnf_transformation,[],[f1280]) ).
thf(f2473,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( infuncsetfunc != $true )
| ( ( func @ X3 @ X4 @ X5 )
= $true )
| ( ( in @ X5 @ ( funcSet @ X3 @ X4 ) )
!= $true ) ),
inference(cnf_transformation,[],[f1476]) ).
thf(f3211,definition,
( spl612_115
<=> ( $true
= ( in @ ( kpair @ sK298 @ sK299 ) @ sK296 ) ) ),
introduced(definition,[new_symbols(definition,[spl612_115])],[avatar_definition]) ).
thf(f3213,plain,
( ( $true
= ( in @ ( kpair @ sK298 @ sK299 ) @ sK296 ) )
| ~ spl612_115 ),
inference(avatar_component_clause,[],[f3211]) ).
thf(f3214,plain,
spl612_115,
inference(avatar_split_clause,[],[f2029,f3211]) ).
thf(f3226,definition,
( spl612_118
<=> ( infuncsetfunc = $true ) ),
introduced(definition,[new_symbols(definition,[spl612_118])],[avatar_definition]) ).
thf(f3229,plain,
spl612_118,
inference(avatar_split_clause,[],[f2044,f3226]) ).
thf(f4953,definition,
( spl612_496
<=> ( funcGraphProp2 = $true ) ),
introduced(definition,[new_symbols(definition,[spl612_496])],[avatar_definition]) ).
thf(f4956,plain,
spl612_496,
inference(avatar_split_clause,[],[f2016,f4953]) ).
thf(f5344,definition,
( spl612_578
<=> ( ( in @ sK296 @ ( funcSet @ sK297 @ sK295 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl612_578])],[avatar_definition]) ).
thf(f5346,plain,
( ( ( in @ sK296 @ ( funcSet @ sK297 @ sK295 ) )
= $true )
| ~ spl612_578 ),
inference(avatar_component_clause,[],[f5344]) ).
thf(f5347,plain,
spl612_578,
inference(avatar_split_clause,[],[f2027,f5344]) ).
thf(f5454,definition,
( spl612_600
<=> ( ( in @ sK298 @ sK297 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl612_600])],[avatar_definition]) ).
thf(f5456,plain,
( ( ( in @ sK298 @ sK297 )
= $true )
| ~ spl612_600 ),
inference(avatar_component_clause,[],[f5454]) ).
thf(f5457,plain,
spl612_600,
inference(avatar_split_clause,[],[f2028,f5454]) ).
thf(f5468,definition,
( spl612_603
<=> ( ( in @ sK299 @ sK295 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl612_603])],[avatar_definition]) ).
thf(f5470,plain,
( ( ( in @ sK299 @ sK295 )
= $true )
| ~ spl612_603 ),
inference(avatar_component_clause,[],[f5468]) ).
thf(f5471,plain,
spl612_603,
inference(avatar_split_clause,[],[f2030,f5468]) ).
thf(f6348,definition,
( spl612_785
<=> ! [X5: $i,X9: $i,X7: $i,X6: $i,X8: $i] :
( ( ( ap @ X7 @ X5 @ X6 @ X8 )
= X9 )
| ( $true
!= ( func @ X7 @ X5 @ X6 ) )
| ( ( in @ ( kpair @ X8 @ X9 ) @ X6 )
!= $true )
| ( ( in @ X8 @ X7 )
!= $true )
| ( ( in @ X9 @ X5 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl612_785])],[avatar_definition]) ).
thf(f6349,plain,
( ! [X8: $i,X6: $i,X9: $i,X7: $i,X5: $i] :
( ( ( ap @ X7 @ X5 @ X6 @ X8 )
= X9 )
| ( ( in @ X8 @ X7 )
!= $true )
| ( $true
!= ( func @ X7 @ X5 @ X6 ) )
| ( ( in @ X9 @ X5 )
!= $true )
| ( ( in @ ( kpair @ X8 @ X9 ) @ X6 )
!= $true ) )
| ~ spl612_785 ),
inference(avatar_component_clause,[],[f6348]) ).
thf(f6350,plain,
( ~ spl612_496
| spl612_785 ),
inference(avatar_split_clause,[],[f2224,f6348,f4953]) ).
thf(f6362,definition,
( spl612_788
<=> ( ( ap @ sK297 @ sK295 @ sK296 @ sK298 )
= sK299 ) ),
introduced(definition,[new_symbols(definition,[spl612_788])],[avatar_definition]) ).
thf(f6364,plain,
( ( ( ap @ sK297 @ sK295 @ sK296 @ sK298 )
!= sK299 )
| spl612_788 ),
inference(avatar_component_clause,[],[f6362]) ).
thf(f6365,plain,
~ spl612_788,
inference(avatar_split_clause,[],[f2031,f6362]) ).
thf(f7107,definition,
( spl612_939
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( ( func @ X3 @ X4 @ X5 )
= $true )
| ( ( in @ X5 @ ( funcSet @ X3 @ X4 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl612_939])],[avatar_definition]) ).
thf(f7108,plain,
( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( funcSet @ X3 @ X4 ) )
!= $true )
| ( ( func @ X3 @ X4 @ X5 )
= $true ) )
| ~ spl612_939 ),
inference(avatar_component_clause,[],[f7107]) ).
thf(f7109,plain,
( spl612_939
| ~ spl612_118 ),
inference(avatar_split_clause,[],[f2473,f3226,f7107]) ).
thf(f8762,plain,
( ( $true
= ( func @ sK297 @ sK295 @ sK296 ) )
| ( $true != $true )
| ~ spl612_578
| ~ spl612_939 ),
inference(superposition,[],[f7108,f5346]) ).
thf(f8769,plain,
( ( $true
= ( func @ sK297 @ sK295 @ sK296 ) )
| ~ spl612_578
| ~ spl612_939 ),
inference(trivial_inequality_removal,[],[f8762]) ).
thf(f8781,definition,
( spl612_982
<=> ( $true
= ( func @ sK297 @ sK295 @ sK296 ) ) ),
introduced(definition,[new_symbols(definition,[spl612_982])],[avatar_definition]) ).
thf(f8783,plain,
( ( $true
= ( func @ sK297 @ sK295 @ sK296 ) )
| ~ spl612_982 ),
inference(avatar_component_clause,[],[f8781]) ).
thf(f8784,plain,
( spl612_982
| ~ spl612_578
| ~ spl612_939 ),
inference(avatar_split_clause,[],[f8769,f7107,f5344,f8781]) ).
thf(f10297,plain,
( ! [X0: $i] :
( ( ( in @ sK298 @ sK297 )
!= $true )
| ( ( in @ ( kpair @ sK298 @ X0 ) @ sK296 )
!= $true )
| ( sK299 != X0 )
| ( $true
!= ( func @ sK297 @ sK295 @ sK296 ) )
| ( ( in @ X0 @ sK295 )
!= $true ) )
| ~ spl612_785
| spl612_788 ),
inference(superposition,[],[f6364,f6349]) ).
thf(f10307,plain,
( ! [X0: $i] :
( ( ( in @ ( kpair @ sK298 @ X0 ) @ sK296 )
!= $true )
| ( sK299 != X0 )
| ( $true
!= ( func @ sK297 @ sK295 @ sK296 ) )
| ( ( in @ X0 @ sK295 )
!= $true ) )
| ~ spl612_600
| ~ spl612_785
| spl612_788 ),
inference(forward_subsumption_resolution,[],[f10297,f5456]) ).
thf(f10308,plain,
( ! [X0: $i] :
( ( ( in @ ( kpair @ sK298 @ X0 ) @ sK296 )
!= $true )
| ( ( in @ X0 @ sK295 )
!= $true )
| ( sK299 != X0 ) )
| ~ spl612_600
| ~ spl612_785
| spl612_788
| ~ spl612_982 ),
inference(forward_subsumption_resolution,[],[f10307,f8783]) ).
thf(f10309,plain,
( ( $true != $true )
| ( sK299 != sK299 )
| ( ( in @ sK299 @ sK295 )
!= $true )
| ~ spl612_115
| ~ spl612_600
| ~ spl612_785
| spl612_788
| ~ spl612_982 ),
inference(superposition,[],[f10308,f3213]) ).
thf(f10315,plain,
( ( ( in @ sK299 @ sK295 )
!= $true )
| ~ spl612_115
| ~ spl612_600
| ~ spl612_785
| spl612_788
| ~ spl612_982 ),
inference(trivial_inequality_removal,[],[f10309]) ).
thf(f10317,plain,
( $false
| ~ spl612_115
| ~ spl612_600
| ~ spl612_603
| ~ spl612_785
| spl612_788
| ~ spl612_982 ),
inference(forward_subsumption_resolution,[],[f10315,f5470]) ).
thf(f10318,plain,
( ~ spl612_115
| ~ spl612_600
| ~ spl612_603
| ~ spl612_785
| spl612_788
| ~ spl612_982 ),
inference(avatar_contradiction_clause,[],[f10317]) ).
cnf(s68,plain,
spl612_115,
inference(sat_conversion,[],[f3214]) ).
cnf(s71,plain,
spl612_118,
inference(sat_conversion,[],[f3229]) ).
cnf(s401,plain,
spl612_496,
inference(sat_conversion,[],[f4956]) ).
cnf(s496,plain,
spl612_578,
inference(sat_conversion,[],[f5347]) ).
cnf(s526,plain,
spl612_600,
inference(sat_conversion,[],[f5457]) ).
cnf(s528,plain,
spl612_603,
inference(sat_conversion,[],[f5471]) ).
cnf(s751,plain,
( ~ spl612_496
| spl612_785 ),
inference(sat_conversion,[],[f6350]) ).
cnf(s754,plain,
~ spl612_788,
inference(sat_conversion,[],[f6365]) ).
cnf(s955,plain,
( ~ spl612_118
| spl612_939 ),
inference(sat_conversion,[],[f7109]) ).
cnf(s1015,plain,
( ~ spl612_578
| ~ spl612_939
| spl612_982 ),
inference(sat_conversion,[],[f8784]) ).
cnf(s1030,plain,
( ~ spl612_115
| ~ spl612_600
| ~ spl612_603
| ~ spl612_785
| spl612_788
| ~ spl612_982 ),
inference(sat_conversion,[],[f10318]) ).
cnf(s1127,plain,
spl612_785,
inference(rat,[],[s751,s401]) ).
cnf(s1256,plain,
spl612_939,
inference(rat,[],[s955,s71]) ).
cnf(s1257,plain,
spl612_982,
inference(rat,[],[s1015,s496,s1256]) ).
cnf(s1258,plain,
~ spl612_115,
inference(rat,[],[s1030,s1127,s754,s526,s528,s1257]) ).
cnf(s1264,plain,
$false,
inference(rat,[],[s68,s1258]) ).
thf(f10319,plain,
$false,
inference(avatar_sat_refutation,[],[s1264]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU688^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n009.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 14:09:15 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.19/0.28 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
% 0.53/0.43 % (4058472)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.53/0.43 % (4058477)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3453434304:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.53/0.43 % (4058483)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.53/0.43 % (4058483)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
% 0.53/0.43 % (4058482)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2806905087:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.53/0.43 % (4058479)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1637523592:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.53/0.43 % (4058483)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=1143400073:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.53/0.43 % (4058480)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=3911225743: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)
% 0.53/0.43 % (4058481)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1694780029:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.53/0.43 % (4058479)Instruction limit reached!
% 0.53/0.43 % (4058479)------------------------------
% 0.53/0.43 % (4058479)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.43 % (4058479)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.43 % (4058479)CaDiCaL version: 2.1.3
% 0.53/0.43 % (4058479)Termination reason: Instruction limit
% 0.53/0.43 % (4058479)Termination phase: shuffling
% 0.53/0.43 % (4058479)Time elapsed: 0.002 s
% 0.53/0.43 % (4058479)Peak memory usage: 10 MB
% 0.53/0.43 % (4058479)Instructions burned: 3 (million)
% 0.53/0.43 % (4058478)lrs+10_16_si=on:nwc=1.5:random_seed=2196521696:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.53/0.43 % (4058481)Instruction limit reached!
% 0.53/0.43 % (4058481)------------------------------
% 0.53/0.43 % (4058481)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.43 % (4058481)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.43 % (4058481)CaDiCaL version: 2.1.3
% 0.53/0.43 % (4058481)Termination reason: Instruction limit
% 0.53/0.43 % (4058481)Termination phase: Property scanning
% 0.53/0.43 % (4058481)Time elapsed: 0.012 s
% 0.53/0.43 % (4058481)Peak memory usage: 10 MB
% 0.53/0.43 % (4058481)Instructions burned: 26 (million)
% 0.53/0.43 % (4058477)Instruction limit reached!
% 0.53/0.43 % (4058477)------------------------------
% 0.53/0.43 % (4058477)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.43 % (4058477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.43 % (4058477)CaDiCaL version: 2.1.3
% 0.53/0.43 % (4058477)Termination reason: Instruction limit
% 0.53/0.43 % (4058477)Termination phase: Property scanning
% 0.53/0.43 % (4058477)Time elapsed: 0.023 s
% 0.53/0.43 % (4058477)Peak memory usage: 13 MB
% 0.53/0.43 % (4058477)Instructions burned: 92 (million)
% 0.53/0.43 % (4058490)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2224039448:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.53/0.43 % (4058493)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.53/0.43 % (4058490)Instruction limit reached!
% 0.53/0.43 % (4058490)------------------------------
% 0.53/0.43 % (4058490)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.43 % (4058490)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.43 % (4058490)CaDiCaL version: 2.1.3
% 0.53/0.43 % (4058490)Termination reason: Instruction limit
% 0.53/0.43 % (4058490)Termination phase: shuffling
% 0.53/0.43 % (4058490)Time elapsed: 0.002 s
% 0.53/0.43 % (4058490)Peak memory usage: 10 MB
% 0.53/0.43 % (4058490)Instructions burned: 3 (million)
% 0.53/0.47 % (4058493)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3504558455:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.53/0.47 % (4058478)Instruction limit reached!
% 0.53/0.47 % (4058478)------------------------------
% 0.53/0.47 % (4058478)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.47 % (4058478)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.47 % (4058478)CaDiCaL version: 2.1.3
% 0.53/0.47 % (4058478)Termination reason: Instruction limit
% 0.53/0.47 % (4058478)Termination phase: shuffling
% 0.53/0.47 % (4058478)Time elapsed: 0.019 s
% 0.53/0.47 % (4058478)Peak memory usage: 10 MB
% 0.53/0.47 % (4058478)Instructions burned: 18 (million)
% 0.53/0.47 % (4058493)Instruction limit reached!
% 0.53/0.47 % (4058493)------------------------------
% 0.53/0.47 % (4058493)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.47 % (4058493)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.47 % (4058493)CaDiCaL version: 2.1.3
% 0.53/0.47 % (4058493)Termination reason: Instruction limit
% 0.53/0.47 % (4058493)Termination phase: shuffling
% 0.53/0.47 % (4058493)Time elapsed: 0.002 s
% 0.53/0.47 % (4058493)Peak memory usage: 10 MB
% 0.53/0.47 % (4058493)Instructions burned: 9 (million)
% 0.53/0.47 % (4058492)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3981128753:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.53/0.47 % (4058482)Instruction limit reached!
% 0.53/0.47 % (4058482)------------------------------
% 0.53/0.47 % (4058482)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.47 % (4058482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.47 % (4058482)CaDiCaL version: 2.1.3
% 0.53/0.47 % (4058482)Termination reason: Instruction limit
% 0.53/0.47 % (4058482)Termination phase: Preprocessing 3
% 0.53/0.47 % (4058482)Time elapsed: 0.035 s
% 0.53/0.47 % (4058482)Peak memory usage: 12 MB
% 0.53/0.47 % (4058482)Instructions burned: 75 (million)
% 0.53/0.47 % (4058492)Instruction limit reached!
% 0.53/0.47 % (4058492)------------------------------
% 0.53/0.47 % (4058492)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.47 % (4058492)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.47 % (4058492)CaDiCaL version: 2.1.3
% 0.53/0.47 % (4058492)Termination reason: Instruction limit
% 0.53/0.47 % (4058492)Termination phase: shuffling
% 0.53/0.47 % (4058492)Time elapsed: 0.003 s
% 0.53/0.47 % (4058492)Peak memory usage: 10 MB
% 0.53/0.47 % (4058492)Instructions burned: 7 (million)
% 0.53/0.47 % (4058497)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
% 0.53/0.47 % (4058497)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.53/0.47 % (4058497)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1632621096:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.53/0.47 % (4058497)Instruction limit reached!
% 0.53/0.47 % (4058497)------------------------------
% 0.53/0.47 % (4058497)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.47 % (4058497)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.47 % (4058497)CaDiCaL version: 2.1.3
% 0.53/0.47 % (4058497)Termination reason: Instruction limit
% 0.53/0.47 % (4058497)Termination phase: Property scanning
% 0.53/0.47 % (4058497)Time elapsed: 0.007 s
% 0.53/0.47 % (4058497)Peak memory usage: 10 MB
% 0.53/0.47 % (4058497)Instructions burned: 30 (million)
% 0.53/0.47 % (4058495)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2759518367:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.53/0.47 % (4058498)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=2925497598:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.53/0.47 % (4058500)lrs+10_1_si=on:cs=on:random_seed=2961549000:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.53/0.47 % (4058495)Instruction limit reached!
% 1.24/0.53 % (4058495)------------------------------
% 1.24/0.53 % (4058495)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.24/0.53 % (4058495)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.24/0.53 % (4058495)CaDiCaL version: 2.1.3
% 1.24/0.53 % (4058495)Termination reason: Instruction limit
% 1.24/0.53 % (4058495)Termination phase: shuffling
% 1.24/0.53 % (4058495)Time elapsed: 0.006 s
% 1.24/0.53 % (4058495)Peak memory usage: 10 MB
% 1.24/0.53 % (4058495)Instructions burned: 14 (million)
% 1.24/0.53 % (4058501)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.24/0.53 % (4058504)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=874773829:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 1.24/0.53 % (4058500)Instruction limit reached!
% 1.24/0.53 % (4058500)------------------------------
% 1.24/0.53 % (4058500)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.24/0.53 % (4058500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.24/0.53 % (4058500)CaDiCaL version: 2.1.3
% 1.24/0.53 % (4058500)Termination reason: Instruction limit
% 1.24/0.53 % (4058500)Termination phase: shuffling
% 1.24/0.53 % (4058500)Time elapsed: 0.004 s
% 1.24/0.53 % (4058500)Peak memory usage: 10 MB
% 1.24/0.53 % (4058500)Instructions burned: 8 (million)
% 1.24/0.53 % (4058501)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=3766799223:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.24/0.53 % (4058483)Instruction limit reached!
% 1.24/0.53 % (4058483)------------------------------
% 1.24/0.53 % (4058483)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.24/0.53 % (4058483)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.24/0.53 % (4058483)CaDiCaL version: 2.1.3
% 1.24/0.53 % (4058483)Termination reason: Instruction limit
% 1.24/0.53 % (4058483)Termination phase: Saturation
% 1.24/0.53 % (4058483)Time elapsed: 0.068 s
% 1.24/0.53 % (4058483)Peak memory usage: 14 MB
% 1.24/0.53 % (4058483)Instructions burned: 159 (million)
% 1.24/0.53 % (4058501)Instruction limit reached!
% 1.24/0.53 % (4058501)------------------------------
% 1.24/0.53 % (4058501)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.24/0.53 % (4058501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.24/0.53 % (4058501)CaDiCaL version: 2.1.3
% 1.24/0.53 % (4058501)Termination reason: Instruction limit
% 1.24/0.53 % (4058501)Termination phase: shuffling
% 1.24/0.53 % (4058501)Time elapsed: 0.002 s
% 1.24/0.53 % (4058501)Peak memory usage: 10 MB
% 1.24/0.53 % (4058501)Instructions burned: 2 (million)
% 1.24/0.53 % (4058504)Instruction limit reached!
% 1.24/0.53 % (4058504)------------------------------
% 1.24/0.53 % (4058504)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.24/0.53 % (4058504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.24/0.53 % (4058504)CaDiCaL version: 2.1.3
% 1.24/0.53 % (4058504)Termination reason: Instruction limit
% 1.24/0.53 % (4058504)Termination phase: Naming
% 1.24/0.53 % (4058504)Time elapsed: 0.009 s
% 1.24/0.53 % (4058504)Peak memory usage: 11 MB
% 1.24/0.53 % (4058504)Instructions burned: 39 (million)
% 1.24/0.53 % (4058507)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3074259386:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.24/0.53 % (4058509)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2822293011:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.24/0.53 % (4058512)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1106468293:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.24/0.53 % (4058511)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2168277113:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.24/0.53 % (4058498)Instruction limit reached!
% 1.24/0.53 % (4058498)------------------------------
% 1.24/0.53 % (4058498)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.24/0.53 % (4058498)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.24/0.57 % (4058498)CaDiCaL version: 2.1.3
% 1.24/0.57 % (4058498)Termination reason: Instruction limit
% 1.24/0.57 % (4058498)Termination phase: Property scanning
% 1.24/0.57 % (4058509)Instruction limit reached!
% 1.24/0.57 % (4058509)------------------------------
% 1.24/0.57 % (4058509)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.24/0.57 % (4058498)Time elapsed: 0.037 s
% 1.24/0.57 % (4058509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.24/0.57 % (4058498)Peak memory usage: 11 MB
% 1.24/0.57 % (4058498)Instructions burned: 89 (million)
% 1.24/0.57 % (4058509)CaDiCaL version: 2.1.3
% 1.24/0.57 % (4058509)Termination reason: Instruction limit
% 1.24/0.57 % (4058509)Termination phase: Property scanning
% 1.24/0.57 % (4058509)Time elapsed: 0.011 s
% 1.24/0.57 % (4058509)Peak memory usage: 10 MB
% 1.24/0.57 % (4058509)Instructions burned: 26 (million)
% 1.24/0.57 % (4058511)Instruction limit reached!
% 1.24/0.57 % (4058511)------------------------------
% 1.24/0.57 % (4058511)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.24/0.57 % (4058511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.24/0.57 % (4058511)CaDiCaL version: 2.1.3
% 1.24/0.57 % (4058511)Termination reason: Instruction limit
% 1.24/0.57 % (4058511)Termination phase: shuffling
% 1.24/0.57 % (4058511)Time elapsed: 0.007 s
% 1.24/0.57 % (4058511)Peak memory usage: 10 MB
% 1.24/0.57 % (4058511)Instructions burned: 16 (million)
% 1.24/0.57 % (4058513)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1348163161:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.24/0.57 % (4058518)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=2213097215: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)
% 1.24/0.57 % (4058519)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=45177406:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.24/0.57 % (4058518)Instruction limit reached!
% 1.24/0.57 % (4058518)------------------------------
% 1.24/0.57 % (4058518)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.24/0.57 % (4058518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.24/0.57 % (4058518)CaDiCaL version: 2.1.3
% 1.24/0.57 % (4058518)Termination reason: Instruction limit
% 1.24/0.57 % (4058518)Termination phase: shuffling
% 1.24/0.57 % (4058518)Time elapsed: 0.002 s
% 1.24/0.57 % (4058518)Peak memory usage: 10 MB
% 1.24/0.57 % (4058518)Instructions burned: 3 (million)
% 1.24/0.57 % (4058513)Instruction limit reached!
% 1.24/0.57 % (4058513)------------------------------
% 1.24/0.57 % (4058513)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.24/0.57 % (4058513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.24/0.57 % (4058513)CaDiCaL version: 2.1.3
% 1.24/0.57 % (4058513)Termination reason: Instruction limit
% 1.24/0.57 % (4058513)Termination phase: shuffling
% 1.24/0.57 % (4058513)Time elapsed: 0.011 s
% 1.24/0.57 % (4058513)Peak memory usage: 10 MB
% 1.24/0.57 % (4058513)Instructions burned: 14 (million)
% 1.24/0.57 % (4058520)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3620784106:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.24/0.57 % (4058520)Instruction limit reached!
% 1.24/0.57 % (4058520)------------------------------
% 1.24/0.57 % (4058520)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.24/0.57 % (4058520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.24/0.57 % (4058520)CaDiCaL version: 2.1.3
% 1.24/0.57 % (4058520)Termination reason: Instruction limit
% 1.24/0.57 % (4058520)Termination phase: shuffling
% 1.24/0.57 % (4058520)Time elapsed: 0.011 s
% 1.24/0.57 % (4058520)Peak memory usage: 10 MB
% 1.24/0.57 % (4058520)Instructions burned: 25 (million)
% 1.24/0.57 % (4058519)Instruction limit reached!
% 1.24/0.57 % (4058519)------------------------------
% 1.24/0.57 % (4058519)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.24/0.57 % (4058519)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.24/0.57 % (4058519)CaDiCaL version: 2.1.3
% 1.24/0.57 % (4058519)Termination reason: Instruction limit
% 1.24/0.57 % (4058519)Termination phase: shuffling
% 1.24/0.57 % (4058519)Time elapsed: 0.020 s
% 1.24/0.57 % (4058519)Peak memory usage: 10 MB
% 1.24/0.57 % (4058519)Instructions burned: 27 (million)
% 1.98/0.64 % (4058524)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=4252593925:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.98/0.64 % (4058526)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
% 1.98/0.64 % (4058526)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.98/0.64 % (4058526)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=127490890:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.98/0.64 % (4058527)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.98/0.64 % (4058527)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=1339984274:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.98/0.64 % (4058526)Instruction limit reached!
% 1.98/0.64 % (4058526)------------------------------
% 1.98/0.64 % (4058526)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.98/0.64 % (4058526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.98/0.64 % (4058526)CaDiCaL version: 2.1.3
% 1.98/0.64 % (4058526)Termination reason: Instruction limit
% 1.98/0.64 % (4058526)Termination phase: shuffling
% 1.98/0.64 % (4058526)Time elapsed: 0.013 s
% 1.98/0.64 % (4058526)Peak memory usage: 10 MB
% 1.98/0.64 % (4058526)Instructions burned: 14 (million)
% 1.98/0.64 % (4058527)Instruction limit reached!
% 1.98/0.64 % (4058527)------------------------------
% 1.98/0.64 % (4058527)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.98/0.64 % (4058527)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.98/0.64 % (4058527)CaDiCaL version: 2.1.3
% 1.98/0.64 % (4058527)Termination reason: Instruction limit
% 1.98/0.64 % (4058527)Termination phase: shuffling
% 1.98/0.64 % (4058527)Time elapsed: 0.007 s
% 1.98/0.64 % (4058527)Peak memory usage: 10 MB
% 1.98/0.64 % (4058527)Instructions burned: 8 (million)
% 1.98/0.64 % (4058529)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=2066710178:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.98/0.64 % (4058512)Instruction limit reached!
% 1.98/0.64 % (4058512)------------------------------
% 1.98/0.64 % (4058512)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.98/0.64 % (4058512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.98/0.64 % (4058512)CaDiCaL version: 2.1.3
% 1.98/0.64 % (4058512)Termination reason: Instruction limit
% 1.98/0.64 % (4058512)Termination phase: Saturation
% 1.98/0.64 % (4058512)Time elapsed: 0.103 s
% 1.98/0.64 % (4058512)Peak memory usage: 15 MB
% 1.98/0.64 % (4058512)Instructions burned: 328 (million)
% 1.98/0.64 % (4058524)Instruction limit reached!
% 1.98/0.64 % (4058524)------------------------------
% 1.98/0.64 % (4058524)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.98/0.64 % (4058524)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.98/0.64 % (4058524)CaDiCaL version: 2.1.3
% 1.98/0.64 % (4058524)Termination reason: Instruction limit
% 1.98/0.64 % (4058524)Termination phase: Preprocessing 3
% 1.98/0.64 % (4058524)Time elapsed: 0.053 s
% 1.98/0.64 % (4058524)Peak memory usage: 12 MB
% 1.98/0.64 % (4058524)Instructions burned: 60 (million)
% 1.98/0.64 % (4058529)Instruction limit reached!
% 1.98/0.64 % (4058529)------------------------------
% 1.98/0.64 % (4058529)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.98/0.64 % (4058529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.98/0.64 % (4058529)CaDiCaL version: 2.1.3
% 1.98/0.64 % (4058529)Termination reason: Instruction limit
% 1.98/0.64 % (4058529)Termination phase: Property scanning
% 1.98/0.64 % (4058529)Time elapsed: 0.027 s
% 1.98/0.64 % (4058529)Peak memory usage: 11 MB
% 1.98/0.64 % (4058529)Instructions burned: 33 (million)
% 1.98/0.64 % (4058534)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=4275870880:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.30/0.67 % (4058532)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=698562118:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 2.30/0.67 % (4058535)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2724900245:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 2.30/0.67 % (4058532)Instruction limit reached!
% 2.30/0.67 % (4058532)------------------------------
% 2.30/0.67 % (4058532)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.67 % (4058532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.67 % (4058532)CaDiCaL version: 2.1.3
% 2.30/0.67 % (4058532)Termination reason: Instruction limit
% 2.30/0.67 % (4058532)Termination phase: shuffling
% 2.30/0.67 % (4058532)Time elapsed: 0.005 s
% 2.30/0.67 % (4058532)Peak memory usage: 10 MB
% 2.30/0.67 % (4058532)Instructions burned: 9 (million)
% 2.30/0.67 % (4058535)Instruction limit reached!
% 2.30/0.67 % (4058535)------------------------------
% 2.30/0.67 % (4058535)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.67 % (4058535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.67 % (4058535)CaDiCaL version: 2.1.3
% 2.30/0.67 % (4058535)Termination reason: Instruction limit
% 2.30/0.67 % (4058535)Termination phase: shuffling
% 2.30/0.67 % (4058535)Time elapsed: 0.005 s
% 2.30/0.67 % (4058535)Peak memory usage: 10 MB
% 2.30/0.67 % (4058535)Instructions burned: 21 (million)
% 2.30/0.67 % (4058534)Instruction limit reached!
% 2.30/0.67 % (4058534)------------------------------
% 2.30/0.67 % (4058534)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.67 % (4058534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.67 % (4058534)CaDiCaL version: 2.1.3
% 2.30/0.67 % (4058534)Termination reason: Instruction limit
% 2.30/0.67 % (4058534)Termination phase: shuffling
% 2.30/0.67 % (4058534)Time elapsed: 0.011 s
% 2.30/0.67 % (4058534)Peak memory usage: 10 MB
% 2.30/0.67 % (4058534)Instructions burned: 25 (million)
% 2.30/0.67 % (4058537)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=578601221:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.30/0.67 % (4058542)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2661424067:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.30/0.67 % (4058536)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=434987827:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 2.30/0.67 % (4058507)Instruction limit reached!
% 2.30/0.67 % (4058507)------------------------------
% 2.30/0.67 % (4058507)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.67 % (4058507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.67 % (4058507)CaDiCaL version: 2.1.3
% 2.30/0.67 % (4058507)Termination reason: Instruction limit
% 2.30/0.67 % (4058507)Termination phase: Saturation
% 2.30/0.67 % (4058507)Time elapsed: 0.145 s
% 2.30/0.67 % (4058507)Peak memory usage: 15 MB
% 2.30/0.67 % (4058507)Instructions burned: 250 (million)
% 2.30/0.67 % (4058543)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.30/0.67 % (4058542)Instruction limit reached!
% 2.30/0.67 % (4058542)------------------------------
% 2.30/0.67 % (4058542)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.67 % (4058542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.67 % (4058542)CaDiCaL version: 2.1.3
% 2.30/0.67 % (4058542)Termination reason: Instruction limit
% 2.30/0.67 % (4058542)Termination phase: Property scanning
% 2.30/0.67 % (4058542)Time elapsed: 0.010 s
% 2.30/0.67 % (4058542)Peak memory usage: 11 MB
% 2.30/0.67 % (4058542)Instructions burned: 46 (million)
% 2.30/0.67 % (4058543)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1045422295:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.30/0.67 % (4058543)Instruction limit reached!
% 2.30/0.67 % (4058543)------------------------------
% 2.30/0.67 % (4058543)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.67 % (4058543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.67 % (4058543)CaDiCaL version: 2.1.3
% 2.30/0.67 % (4058543)Termination reason: Instruction limit
% 2.30/0.67 % (4058543)Termination phase: shuffling
% 2.30/0.67 % (4058543)Time elapsed: 0.004 s
% 2.30/0.67 % (4058543)Peak memory usage: 10 MB
% 2.30/0.67 % (4058543)Instructions burned: 9 (million)
% 2.30/0.67 % (4058548)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=141167870:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 2.30/0.67 % (4058541)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=4210537777:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.30/0.67 % (4058547)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=554571443:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.30/0.67 % (4058550)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.30/0.67 % (4058550)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=1123987579:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.30/0.67 % (4058550)Instruction limit reached!
% 2.30/0.67 % (4058550)------------------------------
% 2.30/0.67 % (4058550)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.67 % (4058550)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.67 % (4058550)CaDiCaL version: 2.1.3
% 2.30/0.67 % (4058550)Termination reason: Instruction limit
% 2.30/0.67 % (4058550)Termination phase: shuffling
% 2.30/0.67 % (4058550)Time elapsed: 0.003 s
% 2.30/0.67 % (4058550)Peak memory usage: 10 MB
% 2.30/0.67 % (4058550)Instructions burned: 6 (million)
% 2.30/0.67 % (4058537)Instruction limit reached!
% 2.30/0.67 % (4058537)------------------------------
% 2.30/0.67 % (4058537)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.67 % (4058537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.67 % (4058537)CaDiCaL version: 2.1.3
% 2.30/0.67 % (4058537)Termination reason: Instruction limit
% 2.30/0.67 % (4058537)Termination phase: Saturation
% 2.30/0.67 % (4058537)Time elapsed: 0.060 s
% 2.30/0.67 % (4058537)Peak memory usage: 13 MB
% 2.30/0.67 % (4058537)Instructions burned: 144 (million)
% 2.30/0.67 % (4058548)Instruction limit reached!
% 2.30/0.67 % (4058548)------------------------------
% 2.30/0.67 % (4058548)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.67 % (4058548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.67 % (4058548)CaDiCaL version: 2.1.3
% 2.30/0.67 % (4058548)Termination reason: Instruction limit
% 2.30/0.67 % (4058548)Termination phase: Saturation
% 2.30/0.67 % (4058548)Time elapsed: 0.038 s
% 2.30/0.67 % (4058548)Peak memory usage: 13 MB
% 2.30/0.67 % (4058548)Instructions burned: 170 (million)
% 2.30/0.67 % (4058555)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1791713485:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2996 on theBenchmark for (2996ds/22Mi)
% 2.30/0.67 % (4058557)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=4205889615:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/316Mi)
% 2.30/0.67 % (4058555)Instruction limit reached!
% 2.30/0.67 % (4058555)------------------------------
% 2.30/0.67 % (4058555)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.67 % (4058555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.67 % (4058555)CaDiCaL version: 2.1.3
% 2.30/0.67 % (4058555)Termination reason: Instruction limit
% 2.30/0.67 % (4058555)Termination phase: shuffling
% 2.30/0.67 % (4058555)Time elapsed: 0.010 s
% 2.30/0.67 % (4058555)Peak memory usage: 10 MB
% 2.30/0.67 % (4058555)Instructions burned: 23 (million)
% 2.30/0.67 % (4058556)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=1983412136:i=19:add=on:rtra=on_2996 on theBenchmark for (2996ds/19Mi)
% 2.30/0.67 % (4058556)Instruction limit reached!
% 2.30/0.67 % (4058556)------------------------------
% 2.30/0.67 % (4058556)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.67 % (4058556)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.67 % (4058556)CaDiCaL version: 2.1.3
% 2.30/0.67 % (4058556)Termination reason: Instruction limit
% 2.30/0.67 % (4058556)Termination phase: shuffling
% 2.30/0.67 % (4058556)Time elapsed: 0.009 s
% 2.30/0.67 % (4058556)Peak memory usage: 10 MB
% 2.30/0.67 % (4058556)Instructions burned: 21 (million)
% 2.30/0.67 % (4058560)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=3893582931:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2996 on theBenchmark for (2996ds/853Mi)
% 2.30/0.67 % (4058547)Instruction limit reached!
% 2.30/0.67 % (4058547)------------------------------
% 2.30/0.67 % (4058547)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.67 % (4058547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.67 % (4058547)CaDiCaL version: 2.1.3
% 2.30/0.67 % (4058547)Termination reason: Instruction limit
% 2.30/0.67 % (4058547)Termination phase: Saturation
% 2.30/0.67 % (4058547)Time elapsed: 0.078 s
% 2.30/0.67 % (4058547)Peak memory usage: 14 MB
% 2.30/0.67 % (4058547)Instructions burned: 182 (million)
% 2.30/0.67 % (4058480) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4058472-4058480"...
% 2.30/0.67 % (4058562)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=2638898816:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2996 on theBenchmark for (2996ds/45Mi)
% 2.30/0.67 % (4058480)...printing done.
% 2.30/0.67 % (4058480)Refutation found. Thanks to Tanya!
% 2.30/0.67 % SZS status Theorem for theBenchmark
% 2.30/0.67 % SZS output start Proof for theBenchmark
% See solution above
% 2.30/0.67 % (4058480)------------------------------
% 2.30/0.67 % (4058480)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.30/0.67 % (4058480)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.30/0.67 % (4058480)CaDiCaL version: 2.1.3
% 2.30/0.67 % (4058480)Termination reason: Refutation
% 2.30/0.67 % (4058480)Time elapsed: 0.325 s
% 2.30/0.67 % (4058480)Peak memory usage: 20 MB
% 2.30/0.67 % (4058480)Instructions burned: 565 (million)
% 2.30/0.67 % (4058472)Success in time 0.378 s
% 2.30/0.67 % Vampire exiting
%------------------------------------------------------------------------------