%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU620^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 08:30:21 AM UTC 2026
% Result : Theorem 1.42s 0.52s
% Output : Refutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 49 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 2527 ( 610 equ; 0 cnn)
% Maximal formula atoms : 137 ( 51 avg)
% Number of connectives : 1878 ( 10 ~; 9 |; 427 &; 861 @)
% ( 0 <=>; 544 =>; 0 <=; 0 <~>)
% Maximal formula depth : 143 ( 22 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 258 ( 253 usr; 143 con; 0-4 aty)
% ( 16 !!; 11 ??; 0 @@+; 0 @@-)
% Number of variables : 93 ( 46 ^; 39 !; 8 ?; 93 :)
% 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,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_160,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_161,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_162,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_163,type,
vIMP: $o > $o > $o ).
thf(func_def_164,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_165,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_166,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_167,type,
vAND: $o > $o > $o ).
thf(func_def_168,type,
vNOT: $o > $o ).
thf(func_def_169,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_172,type,
vIFF: $o > $o > $o ).
thf(func_def_173,type,
vOR: $o > $o > $o ).
thf(func_def_174,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_177,type,
sK2: $i > ( $i > $o ) > $i ).
thf(func_def_178,type,
sK3: $i > $i > $i ).
thf(func_def_179,type,
sK4: $i > $i > $i ).
thf(func_def_180,type,
sK5: $i > $i ).
thf(func_def_181,type,
sK6: ( $i > $o ) > $i ).
thf(func_def_182,type,
sK7: ( $i > $o ) > $i > $i ).
thf(func_def_183,type,
sK8: $i > $i > $i ).
thf(func_def_184,type,
sK9: ( $i > $o ) > $i > $i ).
thf(func_def_185,type,
sK10: $o > $i > $i > $i ).
thf(func_def_186,type,
sK11: ( $i > $o ) > $i ).
thf(func_def_187,type,
sK12: ( $i > $o ) > $i > $i ).
thf(func_def_188,type,
sK13: ( $i > $o ) > $i > $i ).
thf(func_def_189,type,
sK14: $i > ( $i > $o ) > $i ).
thf(func_def_190,type,
sK15: $i > $i > $i ).
thf(func_def_191,type,
sK16: ( $i > $o ) > $i > $i ).
thf(func_def_192,type,
sK17: $i > ( $i > $o ) > $i ).
thf(func_def_193,type,
sK18: $i > $i ).
thf(func_def_194,type,
sK19: $i > $i > $i ).
thf(func_def_195,type,
sK20: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_196,type,
sK21: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_197,type,
sK22: ( $i > $o ) > $i ).
thf(func_def_198,type,
sK23: $i > ( $i > $o ) > $i ).
thf(func_def_199,type,
sK24: $i > ( $i > $o ) > $i ).
thf(func_def_200,type,
sK25: ( $i > $o ) > $i ).
thf(func_def_201,type,
sK26: $i > ( $i > $o ) > $i ).
thf(func_def_202,type,
sK27: $i > ( $i > $o ) > $i ).
thf(func_def_203,type,
sK28: ( $i > $o ) > $i ).
thf(func_def_204,type,
sK29: $i > ( $i > $o ) > $i ).
thf(func_def_205,type,
sK30: $i > ( $i > $o ) > $i ).
thf(func_def_206,type,
sK31: ( $i > $o ) > $i ).
thf(func_def_207,type,
sK32: $i > ( $i > $o ) > $i ).
thf(func_def_208,type,
sK33: ( $i > $o ) > $i ).
thf(func_def_209,type,
sK34: $i > ( $i > $o ) > $i ).
thf(func_def_210,type,
sK35: $i > ( $i > $o ) > $i ).
thf(func_def_211,type,
sK36: ( $i > $o ) > $i ).
thf(func_def_212,type,
sK37: $i > ( $i > $o ) > $i ).
thf(func_def_213,type,
sK38: $i > $i ).
thf(func_def_214,type,
sK39: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_215,type,
sK40: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_216,type,
sK41: ( $i > $o ) > $i > $i ).
thf(func_def_217,type,
sK42: $i > ( $i > $o ) > $i ).
thf(func_def_218,type,
sK43: $i > ( $i > $o ) > $i ).
thf(func_def_219,type,
sK44: $i > $i ).
thf(func_def_220,type,
sK45: $i > ( $i > $o ) > $i ).
thf(func_def_221,type,
sK46: $i > $i ).
thf(func_def_222,type,
sK47: $i > ( $i > $o ) > $i ).
thf(func_def_223,type,
sK48: ( $i > $o ) > $i > ( $i > $o ) > $i > $i ).
thf(func_def_224,type,
sK49: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_225,type,
sK50: $i > $i > $i ).
thf(func_def_226,type,
sK51: $i > $i > $i ).
thf(func_def_227,type,
sK52: $i > $i > $i ).
thf(func_def_228,type,
sK53: ( $i > $o ) > $i ).
thf(func_def_229,type,
sK54: ( $i > $o ) > $i > $i ).
thf(func_def_230,type,
sK55: ( $i > $o ) > $i > $i ).
thf(func_def_231,type,
sK56: $i > $i > $i ).
thf(func_def_232,type,
sK57: $i > $i ).
thf(func_def_233,type,
sK58: $i > $i ).
thf(func_def_234,type,
sK59: $i > $i > $i > $i ).
thf(func_def_235,type,
sK60: $i > $i > $i ).
thf(func_def_236,type,
sK61: $i > $i > $i ).
thf(func_def_237,type,
sK62: $i > $i > $i ).
thf(func_def_238,type,
sK63: ( $i > $o ) > $i ).
thf(func_def_239,type,
sK64: ( $i > $o ) > $i ).
thf(func_def_240,type,
sK65: ( $i > $o ) > $i ).
thf(func_def_241,type,
sK66: ( $i > $o ) > $i ).
thf(func_def_242,type,
sK67: ( $i > $i > $o ) > $i > $i ).
thf(func_def_243,type,
sK68: ( $i > $i > $o ) > $i > $i ).
thf(func_def_244,type,
sK69: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_245,type,
sK70: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_246,type,
sK71: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_247,type,
sK72: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_248,type,
sK73: ( $i > $o ) > $i ).
thf(func_def_249,type,
sK74: ( $i > $o ) > $i > $i ).
thf(func_def_250,type,
sK75: ( $i > $o ) > $i > $i ).
thf(func_def_251,type,
sK76: $i > $i > $i ).
thf(func_def_252,type,
sK77: $i > $i > $i ).
thf(func_def_253,type,
sK78: ( $i > $o ) > $i ).
thf(func_def_254,type,
sK79: ( $i > $o ) > $i > $i ).
thf(func_def_255,type,
sK80: ( $i > $o ) > $i > $i ).
thf(f135,axiom,
( iskpair
= ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ ( setunion @ X0 ) )
& ? [X2: $i] :
( ( in @ X2 @ ( setunion @ X0 ) )
& ( X0
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iskpair) ).
thf(f137,axiom,
( setukpairIL
= ( ! [X0: $i,X1: $i] : ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIL) ).
thf(f138,axiom,
( setukpairIR
= ( ! [X0: $i,X1: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIR) ).
thf(f140,axiom,
( ( ^ [X0: $i,X1: $i] : ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= kpair ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpair) ).
thf(f141,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ! [X0: $i,X1: $i] : ( iskpair @ ( kpair @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairp) ).
thf(f142,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ! [X0: $i,X1: $i] : ( iskpair @ ( kpair @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f141]) ).
thf(f235,plain,
( setukpairIR
= ( ! [X0: $i,X1: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(rectify,[],[f138]) ).
thf(f236,plain,
( setukpairIR
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(fool_elimination,[],[f235]) ).
thf(f239,plain,
( setukpairIL
= ( ! [X0: $i,X1: $i] : ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(rectify,[],[f137]) ).
thf(f240,plain,
( setukpairIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(fool_elimination,[],[f239]) ).
thf(f273,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ! [X0: $i,X1: $i] : ( iskpair @ ( kpair @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f142]) ).
thf(f274,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 )
=> ! [X1: $i,X0: $i] :
( ( iskpair @ ( kpair @ X0 @ X1 ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f273]) ).
thf(f400,plain,
( iskpair
= ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ ( setunion @ X0 ) )
& ? [X2: $i] :
( ( in @ X2 @ ( setunion @ X0 ) )
& ( X0
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(rectify,[],[f135]) ).
thf(f401,plain,
( iskpair
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ ( setunion @ Y0 ) ) ) )
& ( in @ Y1 @ ( setunion @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f400]) ).
thf(f408,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(fool_elimination,[],[f140]) ).
thf(f415,plain,
( ? [X0: $i,X1: $i] :
( ( iskpair @ ( kpair @ X0 @ X1 ) )
!= $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[],[f274]) ).
thf(f416,plain,
( ( kpairiskpair = $true )
& ( setunion__Cong = $true )
& ( binintersectSubset4 = $true )
& ( quantDeMorgan4 = $true )
& ( emptysetAx = $true )
& ( upairsetIR = $true )
& ( setminusI = $true )
& ( powerset__Cong = $true )
& ( singletonsswitch = $true )
& ( setminusELneg = $true )
& ( descrp = $true )
& ( setadjoinOr = $true )
& ( inPowerset = $true )
& ( setukpairIR = $true )
& ( subPowSU = $true )
& ( binintersectSubset5 = $true )
& ( setextAx = $true )
& ( sepInPowerset = $true )
& ( dsetconstrER = $true )
& ( binintersectRsub = $true )
& ( binunionIL = $true )
& ( binunionEcases = $true )
& ( setminusLsub = $true )
& ( omegaSAx = $true )
& ( subsetE2 = $true )
& ( eqimpsubset2 = $true )
& ( subset2powerset = $true )
& ( notdexE = $true )
& ( prop2setE = $true )
& ( setunionI = $true )
& ( binintersectSubset2 = $true )
& ( sepSubset = $true )
& ( quantDeMorgan2 = $true )
& ( setminusEL = $true )
& ( binunionIR = $true )
& ( exuI3 = $true )
& ( omega0Ax = $true )
& ( setminusIRneg = $true )
& ( foundationAx = $true )
& ( subsetemptysetimpeq = $true )
& ( setunionE = $true )
& ( emptyI = $true )
& ( descr__Cong = $true )
& ( emptysetimpfalse = $true )
& ( setadjoinAx = $true )
& ( setoftrueEq = $true )
& ( symdiffIneg1 = $true )
& ( setext = $true )
& ( subsetE = $true )
& ( eqinunit = $true )
& ( emptyinPowerset = $true )
& ( eqimpsubset1 = $true )
& ( omegaIndAx = $true )
& ( dsetconstr__Cong = $true )
& ( nonemptyE1 = $true )
& ( subsetI2 = $true )
& ( nonemptyI1 = $true )
& ( binintersectER = $true )
& ( binintersectEL = $true )
& ( binunionRsub = $true )
& ( powersetAx = $true )
& ( emptysetE = $true )
& ( nonemptyI = $true )
& ( emptyset__Cong = $true )
& ( setunionAx = $true )
& ( notequalI2 = $true )
& ( disjointsetsI1 = $true )
& ( exu__Cong = $true )
& ( notinsingleton = $true )
& ( symdiffE = $true )
& ( binintersectLsub = $true )
& ( vacuousDall = $true )
& ( powersetI = $true )
& ( upairsetIL = $true )
& ( binintersectSubset3 = $true )
& ( dsetconstrI = $true )
& ( powersetE1 = $true )
& ( setminusILneg = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( setminusER = $true )
& ( noeltsimpempty = $true )
& ( symdiffIneg2 = $true )
& ( setextsub = $true )
& ( setukpairIL = $true )
& ( quantDeMorgan3 = $true )
& ( uniqinunit = $true )
& ? [X0: $i,X1: $i] :
( ( iskpair @ ( kpair @ X0 @ X1 ) )
!= $true )
& ( upairsetE = $true )
& ( setminusERneg = $true )
& ( notsubsetI = $true )
& ( emptyinunitempty = $true )
& ( exuE2 = $true )
& ( exuI2 = $true )
& ( notinemptyset = $true )
& ( emptyInPowerset = $true )
& ( setminusSubset2 = $true )
& ( omega__Cong = $true )
& ( powersetE = $true )
& ( bs114d = $true )
& ( powersetI1 = $true )
& ( subsetI1 = $true )
& ( wellorderingAx = $true )
& ( notequalI1 = $true )
& ( binintersectSubset1 = $true )
& ( emptysetsubset = $true )
& ( notdallE = $true )
& ( prop2setI = $true )
& ( subsetTrans = $true )
& ( setadjoinIL = $true )
& ( emptyE1 = $true )
& ( quantDeMorgan1 = $true )
& ( setadjoinE = $true )
& ( setbeta = $true )
& ( symdiffI2 = $true )
& ( setminusSubset1 = $true )
& ( exuE3e = $true )
& ( powersetsubset = $true )
& ( binunionE = $true )
& ( binunionLsub = $true )
& ( prop2set2propI = $true )
& ( upairset2IR = $true )
& ( exuI1 = $true )
& ( exuE3u = $true )
& ( secondinupair = $true )
& ( nonemptyImpWitness = $true )
& ( exuE1 = $true )
& ( replAx = $true )
& ( in__Cong = $true )
& ( dsetconstrEL = $true )
& ( setadjoin__Cong = $true )
& ( binintersectI = $true )
& ( symdiffI1 = $true )
& ( setadjoinIR = $true )
& ( exuEu = $true )
& ( inCongP = $true )
& ( subsetRefl = $true ) ),
inference(flattening,[],[f415]) ).
thf(f417,plain,
( ( kpairiskpair = $true )
& ( setunion__Cong = $true )
& ( binintersectSubset4 = $true )
& ( quantDeMorgan4 = $true )
& ( emptysetAx = $true )
& ( upairsetIR = $true )
& ( setminusI = $true )
& ( powerset__Cong = $true )
& ( singletonsswitch = $true )
& ( setminusELneg = $true )
& ( descrp = $true )
& ( setadjoinOr = $true )
& ( inPowerset = $true )
& ( setukpairIR = $true )
& ( subPowSU = $true )
& ( binintersectSubset5 = $true )
& ( setextAx = $true )
& ( sepInPowerset = $true )
& ( dsetconstrER = $true )
& ( binintersectRsub = $true )
& ( binunionIL = $true )
& ( binunionEcases = $true )
& ( setminusLsub = $true )
& ( omegaSAx = $true )
& ( subsetE2 = $true )
& ( eqimpsubset2 = $true )
& ( subset2powerset = $true )
& ( notdexE = $true )
& ( prop2setE = $true )
& ( setunionI = $true )
& ( binintersectSubset2 = $true )
& ( sepSubset = $true )
& ( quantDeMorgan2 = $true )
& ( setminusEL = $true )
& ( binunionIR = $true )
& ( exuI3 = $true )
& ( omega0Ax = $true )
& ( setminusIRneg = $true )
& ( foundationAx = $true )
& ( subsetemptysetimpeq = $true )
& ( setunionE = $true )
& ( emptyI = $true )
& ( descr__Cong = $true )
& ( emptysetimpfalse = $true )
& ( setadjoinAx = $true )
& ( setoftrueEq = $true )
& ( symdiffIneg1 = $true )
& ( setext = $true )
& ( subsetE = $true )
& ( eqinunit = $true )
& ( emptyinPowerset = $true )
& ( eqimpsubset1 = $true )
& ( omegaIndAx = $true )
& ( dsetconstr__Cong = $true )
& ( nonemptyE1 = $true )
& ( subsetI2 = $true )
& ( nonemptyI1 = $true )
& ( binintersectER = $true )
& ( binintersectEL = $true )
& ( binunionRsub = $true )
& ( powersetAx = $true )
& ( emptysetE = $true )
& ( nonemptyI = $true )
& ( emptyset__Cong = $true )
& ( setunionAx = $true )
& ( notequalI2 = $true )
& ( disjointsetsI1 = $true )
& ( exu__Cong = $true )
& ( notinsingleton = $true )
& ( symdiffE = $true )
& ( binintersectLsub = $true )
& ( vacuousDall = $true )
& ( powersetI = $true )
& ( upairsetIL = $true )
& ( binintersectSubset3 = $true )
& ( dsetconstrI = $true )
& ( powersetE1 = $true )
& ( setminusILneg = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( setminusER = $true )
& ( noeltsimpempty = $true )
& ( symdiffIneg2 = $true )
& ( setextsub = $true )
& ( setukpairIL = $true )
& ( quantDeMorgan3 = $true )
& ( uniqinunit = $true )
& ( $true
!= ( iskpair @ ( kpair @ sK0 @ sK1 ) ) )
& ( upairsetE = $true )
& ( setminusERneg = $true )
& ( notsubsetI = $true )
& ( emptyinunitempty = $true )
& ( exuE2 = $true )
& ( exuI2 = $true )
& ( notinemptyset = $true )
& ( emptyInPowerset = $true )
& ( setminusSubset2 = $true )
& ( omega__Cong = $true )
& ( powersetE = $true )
& ( bs114d = $true )
& ( powersetI1 = $true )
& ( subsetI1 = $true )
& ( wellorderingAx = $true )
& ( notequalI1 = $true )
& ( binintersectSubset1 = $true )
& ( emptysetsubset = $true )
& ( notdallE = $true )
& ( prop2setI = $true )
& ( subsetTrans = $true )
& ( setadjoinIL = $true )
& ( emptyE1 = $true )
& ( quantDeMorgan1 = $true )
& ( setadjoinE = $true )
& ( setbeta = $true )
& ( symdiffI2 = $true )
& ( setminusSubset1 = $true )
& ( exuE3e = $true )
& ( powersetsubset = $true )
& ( binunionE = $true )
& ( binunionLsub = $true )
& ( prop2set2propI = $true )
& ( upairset2IR = $true )
& ( exuI1 = $true )
& ( exuE3u = $true )
& ( secondinupair = $true )
& ( nonemptyImpWitness = $true )
& ( exuE1 = $true )
& ( replAx = $true )
& ( in__Cong = $true )
& ( dsetconstrEL = $true )
& ( setadjoin__Cong = $true )
& ( binintersectI = $true )
& ( symdiffI1 = $true )
& ( setadjoinIR = $true )
& ( exuEu = $true )
& ( inCongP = $true )
& ( subsetRefl = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f416]) ).
thf(f454,plain,
( setukpairIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f240]) ).
thf(f534,plain,
( $true
!= ( iskpair @ ( kpair @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f417]) ).
thf(f537,plain,
setukpairIL = $true,
inference(cnf_transformation,[],[f417]) ).
thf(f608,plain,
setukpairIR = $true,
inference(cnf_transformation,[],[f417]) ).
thf(f634,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(cnf_transformation,[],[f408]) ).
thf(f639,plain,
( setukpairIR
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f236]) ).
thf(f642,plain,
( iskpair
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ ( setunion @ Y0 ) ) ) )
& ( in @ Y1 @ ( setunion @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f401]) ).
thf(f732,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f454,f537]) ).
thf(f763,plain,
( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ ( setunion @ Y0 ) ) ) )
& ( in @ Y1 @ ( setunion @ Y0 ) ) ) )
@ ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
@ sK0
@ sK1 ) )
!= $true ),
inference(definition_unfolding,[],[f534,f642,f634]) ).
thf(f780,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f639,f608]) ).
thf(f1751,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f780]) ).
thf(f1752,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1751]) ).
thf(f1753,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f1752]) ).
thf(f1754,plain,
! [X2: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(beta-eta_normalization,[],[f1753]) ).
thf(f1757,plain,
( $true
!= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) )
& ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ) ) ) )
& ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f763]) ).
thf(f1758,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) )
& ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ) ) ) )
& ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f1757]) ).
thf(f1759,plain,
! [X1: $i] :
( $false
= ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) )
& ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ) ) ) )
& ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1758]) ).
thf(f1760,plain,
! [X1: $i] :
( ( ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) )
& ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f1759]) ).
thf(f1761,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) )
& ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ) ) )
@ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f1760]) ).
thf(f1762,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) )
& ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f1761]) ).
thf(f1763,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f1762]) ).
thf(f1764,plain,
! [X2: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) )
| ( ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ) )
= $false ) ),
inference(equality_proxy_clausification,[],[f1763]) ).
thf(f1927,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f732]) ).
thf(f1928,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1927]) ).
thf(f1929,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] : ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f1928]) ).
thf(f1930,plain,
! [X2: $i,X1: $i] :
( $true
= ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(beta-eta_normalization,[],[f1929]) ).
thf(f3857,plain,
( ( ( in @ sK0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( $false
= ( in @ sK1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(equality_resolution,[],[f1764]) ).
thf(f3858,plain,
( ( $true = $false )
| ( $false
= ( in @ sK1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(forward_demodulation,[],[f3857,f1930]) ).
thf(f3859,plain,
( $false
= ( in @ sK1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(trivial_inequality_removal,[],[f3858]) ).
thf(f3860,plain,
$true = $false,
inference(forward_demodulation,[],[f3859,f1754]) ).
thf(f3861,plain,
$false,
inference(trivial_inequality_removal,[],[f3860]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU620^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.19 % Computer : n017.cluster.edu
% 0.06/0.19 % Model : x86_64 x86_64
% 0.06/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.19 % Memory : 8046.5625MB
% 0.06/0.19 % OS : Linux 6.8.0-71-generic
% 0.06/0.19 % CPULimit : 300
% 0.06/0.19 % WCLimit : 300
% 0.06/0.19 % DateTime : Tue Sep 29 13:54:08 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running higher-order theorem proving
% 0.06/0.26 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.68/0.39 % (377167)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.68/0.39 % (377176)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4272683299:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.68/0.39 % (377178)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.68/0.39 % (377178)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
% 0.68/0.39 % (377172)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2428411183:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.68/0.39 % (377173)lrs+10_16_si=on:nwc=1.5:random_seed=3091293343:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.68/0.39 % (377177)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3618630206:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.68/0.39 % (377174)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1403455243:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.68/0.39 % (377175)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=2914897539: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)
% 0.68/0.39 % (377176)Instruction limit reached!
% 0.68/0.39 % (377176)------------------------------
% 0.68/0.39 % (377176)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.39 % (377176)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.39 % (377176)CaDiCaL version: 2.1.3
% 0.68/0.39 % (377176)Termination reason: Instruction limit
% 0.68/0.39 % (377176)Termination phase: Preprocessing 3
% 0.68/0.39 % (377176)Time elapsed: 0.007 s
% 0.68/0.39 % (377176)Peak memory usage: 11 MB
% 0.68/0.39 % (377176)Instructions burned: 28 (million)
% 0.68/0.39 % (377178)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=4024694991:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.68/0.39 % (377174)Instruction limit reached!
% 0.68/0.39 % (377174)------------------------------
% 0.68/0.39 % (377174)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.39 % (377174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.39 % (377174)CaDiCaL version: 2.1.3
% 0.68/0.39 % (377174)Termination reason: Instruction limit
% 0.68/0.39 % (377174)Termination phase: shuffling
% 0.68/0.39 % (377174)Time elapsed: 0.002 s
% 0.68/0.39 % (377174)Peak memory usage: 10 MB
% 0.68/0.39 % (377174)Instructions burned: 3 (million)
% 0.68/0.39 % (377173)Instruction limit reached!
% 0.68/0.39 % (377173)------------------------------
% 0.68/0.39 % (377173)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.39 % (377173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.39 % (377173)CaDiCaL version: 2.1.3
% 0.68/0.39 % (377173)Termination reason: Instruction limit
% 0.68/0.39 % (377173)Termination phase: Property scanning
% 0.68/0.39 % (377173)Time elapsed: 0.008 s
% 0.68/0.39 % (377173)Peak memory usage: 10 MB
% 0.68/0.39 % (377173)Instructions burned: 18 (million)
% 0.68/0.39 % (377186)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2029604177:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.68/0.39 % (377187)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=4129620352:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.68/0.39 % (377186)Instruction limit reached!
% 0.68/0.39 % (377186)------------------------------
% 0.68/0.39 % (377186)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.39 % (377186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.39 % (377186)CaDiCaL version: 2.1.3
% 0.68/0.39 % (377186)Termination reason: Instruction limit
% 0.68/0.39 % (377186)Termination phase: shuffling
% 0.68/0.39 % (377186)Time elapsed: 0.002 s
% 0.68/0.39 % (377186)Peak memory usage: 10 MB
% 0.68/0.39 % (377186)Instructions burned: 4 (million)
% 0.68/0.39 % (377188)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.68/0.43 % (377188)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=459874277:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.68/0.43 % (377187)Instruction limit reached!
% 0.68/0.43 % (377187)------------------------------
% 0.68/0.43 % (377187)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.43 % (377187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.43 % (377187)CaDiCaL version: 2.1.3
% 0.68/0.43 % (377187)Termination reason: Instruction limit
% 0.68/0.43 % (377187)Termination phase: Property scanning
% 0.68/0.43 % (377187)Time elapsed: 0.007 s
% 0.68/0.43 % (377187)Peak memory usage: 10 MB
% 0.68/0.43 % (377187)Instructions burned: 20 (million)
% 0.68/0.43 % (377188)Instruction limit reached!
% 0.68/0.43 % (377188)------------------------------
% 0.68/0.43 % (377188)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.43 % (377188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.43 % (377188)CaDiCaL version: 2.1.3
% 0.68/0.43 % (377188)Termination reason: Instruction limit
% 0.68/0.43 % (377188)Termination phase: shuffling
% 0.68/0.43 % (377188)Time elapsed: 0.004 s
% 0.68/0.43 % (377188)Peak memory usage: 10 MB
% 0.68/0.43 % (377188)Instructions burned: 9 (million)
% 0.68/0.43 % (377177)Instruction limit reached!
% 0.68/0.43 % (377177)------------------------------
% 0.68/0.43 % (377177)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.43 % (377177)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.43 % (377177)CaDiCaL version: 2.1.3
% 0.68/0.43 % (377177)Termination reason: Instruction limit
% 0.68/0.43 % (377177)Termination phase: Property scanning
% 0.68/0.43 % (377177)Time elapsed: 0.035 s
% 0.68/0.43 % (377177)Peak memory usage: 12 MB
% 0.68/0.43 % (377177)Instructions burned: 77 (million)
% 0.68/0.43 % (377172)Instruction limit reached!
% 0.68/0.43 % (377172)------------------------------
% 0.68/0.43 % (377172)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.43 % (377172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.43 % (377172)CaDiCaL version: 2.1.3
% 0.68/0.43 % (377172)Termination reason: Instruction limit
% 0.68/0.43 % (377172)Termination phase: Saturation
% 0.68/0.43 % (377172)Time elapsed: 0.039 s
% 0.68/0.43 % (377172)Peak memory usage: 13 MB
% 0.68/0.43 % (377172)Instructions burned: 87 (million)
% 0.68/0.43 % (377191)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=4031327834:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.68/0.43 % (377193)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
% 0.68/0.43 % (377193)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.68/0.43 % (377193)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1902502449:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.68/0.43 % (377191)Instruction limit reached!
% 0.68/0.43 % (377191)------------------------------
% 0.68/0.43 % (377191)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.43 % (377191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.43 % (377191)CaDiCaL version: 2.1.3
% 0.68/0.43 % (377191)Termination reason: Instruction limit
% 0.68/0.43 % (377191)Termination phase: shuffling
% 0.68/0.43 % (377191)Time elapsed: 0.006 s
% 0.68/0.43 % (377191)Peak memory usage: 10 MB
% 0.68/0.43 % (377191)Instructions burned: 12 (million)
% 0.68/0.43 % (377194)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=1715320882:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.68/0.43 % (377193)Instruction limit reached!
% 0.68/0.43 % (377193)------------------------------
% 0.68/0.43 % (377193)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.43 % (377193)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.46 % (377193)CaDiCaL version: 2.1.3
% 0.68/0.46 % (377193)Termination reason: Instruction limit
% 0.68/0.46 % (377193)Termination phase: Unused predicate definition removal
% 0.68/0.46 % (377193)Time elapsed: 0.007 s
% 0.68/0.46 % (377193)Peak memory usage: 10 MB
% 0.68/0.46 % (377193)Instructions burned: 29 (million)
% 0.68/0.46 % (377195)lrs+10_1_si=on:cs=on:random_seed=4118224026:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.68/0.46 % (377196)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.68/0.46 % (377196)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=3704813916:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.68/0.46 % (377195)Instruction limit reached!
% 0.68/0.46 % (377195)------------------------------
% 0.68/0.46 % (377195)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.46 % (377195)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.46 % (377195)CaDiCaL version: 2.1.3
% 0.68/0.46 % (377195)Termination reason: Instruction limit
% 0.68/0.46 % (377195)Termination phase: shuffling
% 0.68/0.46 % (377195)Time elapsed: 0.004 s
% 0.68/0.46 % (377195)Peak memory usage: 10 MB
% 0.68/0.46 % (377195)Instructions burned: 9 (million)
% 0.68/0.46 % (377196)Instruction limit reached!
% 0.68/0.46 % (377196)------------------------------
% 0.68/0.46 % (377196)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.46 % (377196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.46 % (377196)CaDiCaL version: 2.1.3
% 0.68/0.46 % (377196)Termination reason: Instruction limit
% 0.68/0.46 % (377196)Termination phase: shuffling
% 0.68/0.46 % (377196)Time elapsed: 0.001 s
% 0.68/0.46 % (377196)Peak memory usage: 10 MB
% 0.68/0.46 % (377196)Instructions burned: 3 (million)
% 0.68/0.46 % (377201)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=753345708:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.68/0.46 % (377199)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=4108679710:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.68/0.46 % (377178)Instruction limit reached!
% 0.68/0.46 % (377178)------------------------------
% 0.68/0.46 % (377178)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.46 % (377178)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.46 % (377178)CaDiCaL version: 2.1.3
% 0.68/0.46 % (377178)Termination reason: Instruction limit
% 0.68/0.46 % (377178)Termination phase: Saturation
% 0.68/0.46 % (377178)Time elapsed: 0.067 s
% 0.68/0.46 % (377178)Peak memory usage: 14 MB
% 0.68/0.46 % (377178)Instructions burned: 157 (million)
% 0.68/0.46 % (377204)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3186562027:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.68/0.46 % (377205)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=461693711:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.68/0.46 % (377199)Instruction limit reached!
% 0.68/0.46 % (377199)------------------------------
% 0.68/0.46 % (377199)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.46 % (377199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.46 % (377199)CaDiCaL version: 2.1.3
% 0.68/0.46 % (377199)Termination reason: Instruction limit
% 0.68/0.46 % (377199)Termination phase: Preprocessing 3
% 0.68/0.46 % (377199)Time elapsed: 0.018 s
% 0.68/0.46 % (377199)Peak memory usage: 12 MB
% 0.68/0.46 % (377199)Instructions burned: 38 (million)
% 0.68/0.46 % (377205)Instruction limit reached!
% 0.68/0.46 % (377205)------------------------------
% 0.68/0.46 % (377205)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.46 % (377205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.46 % (377205)CaDiCaL version: 2.1.3
% 0.68/0.46 % (377205)Termination reason: Instruction limit
% 0.68/0.46 % (377205)Termination phase: shuffling
% 0.68/0.46 % (377205)Time elapsed: 0.006 s
% 0.68/0.46 % (377205)Peak memory usage: 10 MB
% 0.68/0.46 % (377205)Instructions burned: 14 (million)
% 0.68/0.46 % (377208)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2230823460:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.42/0.51 % (377194)Instruction limit reached!
% 1.42/0.51 % (377194)------------------------------
% 1.42/0.51 % (377194)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.51 % (377194)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.51 % (377194)CaDiCaL version: 2.1.3
% 1.42/0.51 % (377194)Termination reason: Instruction limit
% 1.42/0.51 % (377194)Termination phase: Saturation
% 1.42/0.51 % (377194)Time elapsed: 0.038 s
% 1.42/0.51 % (377194)Peak memory usage: 13 MB
% 1.42/0.51 % (377194)Instructions burned: 88 (million)
% 1.42/0.51 % (377204)Instruction limit reached!
% 1.42/0.51 % (377204)------------------------------
% 1.42/0.51 % (377204)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.51 % (377204)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.51 % (377204)CaDiCaL version: 2.1.3
% 1.42/0.51 % (377204)Termination reason: Instruction limit
% 1.42/0.51 % (377204)Termination phase: Preprocessing 3
% 1.42/0.51 % (377204)Time elapsed: 0.013 s
% 1.42/0.51 % (377204)Peak memory usage: 11 MB
% 1.42/0.51 % (377204)Instructions burned: 27 (million)
% 1.42/0.51 % (377211)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1690805878:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.42/0.51 % (377212)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1587958218: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)
% 1.42/0.51 % (377212)Instruction limit reached!
% 1.42/0.51 % (377212)------------------------------
% 1.42/0.51 % (377212)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.51 % (377212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.51 % (377212)CaDiCaL version: 2.1.3
% 1.42/0.51 % (377212)Termination reason: Instruction limit
% 1.42/0.51 % (377212)Termination phase: shuffling
% 1.42/0.51 % (377212)Time elapsed: 0.002 s
% 1.42/0.51 % (377212)Peak memory usage: 10 MB
% 1.42/0.51 % (377212)Instructions burned: 4 (million)
% 1.42/0.51 % (377214)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3784207490:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.42/0.51 % (377215)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=4144203152:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.42/0.51 % (377211)Instruction limit reached!
% 1.42/0.51 % (377211)------------------------------
% 1.42/0.51 % (377211)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.51 % (377211)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.51 % (377211)CaDiCaL version: 2.1.3
% 1.42/0.51 % (377211)Termination reason: Instruction limit
% 1.42/0.51 % (377211)Termination phase: Property scanning
% 1.42/0.51 % (377211)Time elapsed: 0.007 s
% 1.42/0.51 % (377211)Peak memory usage: 10 MB
% 1.42/0.51 % (377211)Instructions burned: 16 (million)
% 1.42/0.51 % (377215)Instruction limit reached!
% 1.42/0.51 % (377215)------------------------------
% 1.42/0.51 % (377215)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.51 % (377215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.51 % (377215)CaDiCaL version: 2.1.3
% 1.42/0.51 % (377215)Termination reason: Instruction limit
% 1.42/0.51 % (377215)Termination phase: Property scanning
% 1.42/0.51 % (377215)Time elapsed: 0.010 s
% 1.42/0.51 % (377215)Peak memory usage: 10 MB
% 1.42/0.51 % (377215)Instructions burned: 24 (million)
% 1.42/0.51 % (377214)Instruction limit reached!
% 1.42/0.51 % (377214)------------------------------
% 1.42/0.51 % (377214)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.51 % (377214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.51 % (377214)CaDiCaL version: 2.1.3
% 1.42/0.51 % (377214)Termination reason: Instruction limit
% 1.42/0.51 % (377214)Termination phase: Property scanning
% 1.42/0.51 % (377214)Time elapsed: 0.012 s
% 1.42/0.51 % (377214)Peak memory usage: 10 MB
% 1.42/0.51 % (377214)Instructions burned: 27 (million)
% 1.42/0.51 % (377218)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=4201626709:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.42/0.52 % (377221)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
% 1.42/0.52 % (377221)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.42/0.52 % (377201)Instruction limit reached!
% 1.42/0.52 % (377201)------------------------------
% 1.42/0.52 % (377201)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.52 % (377201)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.52 % (377201)CaDiCaL version: 2.1.3
% 1.42/0.52 % (377201)Termination reason: Instruction limit
% 1.42/0.52 % (377201)Termination phase: Saturation
% 1.42/0.52 % (377201)Time elapsed: 0.066 s
% 1.42/0.52 % (377201)Peak memory usage: 14 MB
% 1.42/0.52 % (377201)Instructions burned: 250 (million)
% 1.42/0.52 % (377221)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=3470392723:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.42/0.52 % (377222)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.42/0.52 % (377222)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=1689685162:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.42/0.52 % (377221)Instruction limit reached!
% 1.42/0.52 % (377221)------------------------------
% 1.42/0.52 % (377221)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.52 % (377221)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.52 % (377221)CaDiCaL version: 2.1.3
% 1.42/0.52 % (377221)Termination reason: Instruction limit
% 1.42/0.52 % (377221)Termination phase: shuffling
% 1.42/0.52 % (377221)Time elapsed: 0.006 s
% 1.42/0.52 % (377221)Peak memory usage: 10 MB
% 1.42/0.52 % (377221)Instructions burned: 14 (million)
% 1.42/0.52 % (377225)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=837652717:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.42/0.52 % (377223)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=2554649244:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.42/0.52 % (377225)Instruction limit reached!
% 1.42/0.52 % (377225)------------------------------
% 1.42/0.52 % (377225)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.52 % (377225)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.52 % (377225)CaDiCaL version: 2.1.3
% 1.42/0.52 % (377225)Termination reason: Instruction limit
% 1.42/0.52 % (377225)Termination phase: shuffling
% 1.42/0.52 % (377225)Time elapsed: 0.002 s
% 1.42/0.52 % (377225)Peak memory usage: 10 MB
% 1.42/0.52 % (377225)Instructions burned: 9 (million)
% 1.42/0.52 % (377222)Instruction limit reached!
% 1.42/0.52 % (377222)------------------------------
% 1.42/0.52 % (377222)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.52 % (377222)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.52 % (377222)CaDiCaL version: 2.1.3
% 1.42/0.52 % (377222)Termination reason: Instruction limit
% 1.42/0.52 % (377222)Termination phase: shuffling
% 1.42/0.52 % (377222)Time elapsed: 0.004 s
% 1.42/0.52 % (377222)Peak memory usage: 10 MB
% 1.42/0.52 % (377222)Instructions burned: 8 (million)
% 1.42/0.52 % (377231)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1187716630:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.42/0.52 % (377218)Instruction limit reached!
% 1.42/0.52 % (377218)------------------------------
% 1.42/0.52 % (377218)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.52 % (377218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.52 % (377218)CaDiCaL version: 2.1.3
% 1.42/0.52 % (377223)Instruction limit reached!
% 1.42/0.52 % (377223)------------------------------
% 1.42/0.52 % (377223)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.52 % (377218)Termination reason: Instruction limit
% 1.42/0.52 % (377218)Termination phase: Property scanning
% 1.42/0.52 % (377223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.52 % (377223)CaDiCaL version: 2.1.3
% 1.42/0.52 % (377223)Termination reason: Instruction limit
% 1.42/0.52 % (377223)Termination phase: Property scanning
% 1.42/0.52 % (377223)Time elapsed: 0.014 s
% 1.42/0.52 % (377218)Time elapsed: 0.028 s
% 1.42/0.52 % (377218)Peak memory usage: 12 MB
% 1.42/0.52 % (377223)Peak memory usage: 10 MB
% 1.42/0.52 % (377223)Instructions burned: 32 (million)
% 1.42/0.52 % (377218)Instructions burned: 60 (million)
% 1.42/0.52 % (377229)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2275179030:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.42/0.52 % (377231)Instruction limit reached!
% 1.42/0.52 % (377231)------------------------------
% 1.42/0.52 % (377231)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.52 % (377231)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.52 % (377231)CaDiCaL version: 2.1.3
% 1.42/0.52 % (377231)Termination reason: Instruction limit
% 1.42/0.52 % (377231)Termination phase: Property scanning
% 1.42/0.52 % (377231)Time elapsed: 0.005 s
% 1.42/0.52 % (377231)Peak memory usage: 10 MB
% 1.42/0.52 % (377231)Instructions burned: 24 (million)
% 1.42/0.52 % (377232)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=605146406:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 1.42/0.52 % (377237)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3726679030:i=42:hud=10:rtra=on_2998 on theBenchmark for (2998ds/42Mi)
% 1.42/0.52 % (377229)Instruction limit reached!
% 1.42/0.52 % (377229)------------------------------
% 1.42/0.52 % (377229)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.52 % (377229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.52 % (377229)CaDiCaL version: 2.1.3
% 1.42/0.52 % (377229)Termination reason: Instruction limit
% 1.42/0.52 % (377229)Termination phase: Property scanning
% 1.42/0.52 % (377229)Time elapsed: 0.010 s
% 1.42/0.52 % (377229)Peak memory usage: 10 MB
% 1.42/0.52 % (377229)Instructions burned: 24 (million)
% 1.42/0.52 % (377234)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=2855268887:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 1.42/0.52 % (377235)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=1775519589:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/193Mi)
% 1.42/0.52 % (377237)Instruction limit reached!
% 1.42/0.52 % (377237)------------------------------
% 1.42/0.52 % (377237)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.52 % (377237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.52 % (377237)CaDiCaL version: 2.1.3
% 1.42/0.52 % (377237)Termination reason: Instruction limit
% 1.42/0.52 % (377237)Termination phase: Function definition elimination
% 1.42/0.52 % (377237)Time elapsed: 0.009 s
% 1.42/0.52 % (377237)Peak memory usage: 11 MB
% 1.42/0.52 % (377237)Instructions burned: 43 (million)
% 1.42/0.52 % (377240)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.42/0.52 % (377240)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4086429904:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 1.42/0.52 % (377243)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=884252470:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 1.42/0.52 % (377240)Instruction limit reached!
% 1.42/0.52 % (377240)------------------------------
% 1.42/0.52 % (377240)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.52 % (377240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.52 % (377240)CaDiCaL version: 2.1.3
% 1.42/0.52 % (377240)Termination reason: Instruction limit
% 1.42/0.52 % (377240)Termination phase: shuffling
% 1.42/0.52 % (377240)Time elapsed: 0.004 s
% 1.42/0.52 % (377240)Peak memory usage: 10 MB
% 1.42/0.52 % (377240)Instructions burned: 9 (million)
% 1.42/0.52 % (377208) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-377167-377208"...
% 1.42/0.52 % (377246)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=987314338: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)
% 1.42/0.52 % (377208)...printing done.
% 1.42/0.52 % (377208)Refutation found. Thanks to Tanya!
% 1.42/0.52 % SZS status Theorem for theBenchmark
% 1.42/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 1.42/0.52 % (377208)------------------------------
% 1.42/0.52 % (377208)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.52 % (377208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.52 % (377208)CaDiCaL version: 2.1.3
% 1.42/0.52 % (377208)Termination reason: Refutation
% 1.42/0.52 % (377208)Time elapsed: 0.123 s
% 1.42/0.52 % (377208)Peak memory usage: 14 MB
% 1.42/0.52 % (377208)Instructions burned: 251 (million)
% 1.42/0.52 % (377167)Success in time 0.254 s
% 1.42/0.52 % Vampire exiting
%------------------------------------------------------------------------------