%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU635^1 : 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 : n004.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 08:30:26 AM UTC 2026
% Result : Theorem 1.95s 0.60s
% Output : Refutation 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 71 ( 23 unt; 0 typ; 7 def)
% Number of atoms : 2687 ( 711 equ; 0 cnn)
% Maximal formula atoms : 153 ( 37 avg)
% Number of connectives : 1496 ( 78 ~; 69 |; 468 &; 259 @)
% ( 12 <=>; 610 =>; 0 <=; 0 <~>)
% Maximal formula depth : 158 ( 19 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 : 307 ( 304 usr; 177 con; 0-4 aty)
% Number of variables : 80 ( 0 sgn 66 !; 14 ?; 80 :)
% 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_177,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_178,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_179,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_180,type,
vAND: $o > $o > $o ).
thf(func_def_181,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_182,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_183,type,
vIMP: $o > $o > $o ).
thf(func_def_184,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_185,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_186,type,
vNOT: $o > $o ).
thf(func_def_187,type,
sP0: $i > $i > $o ).
thf(func_def_188,type,
sP1: $i > $o ).
thf(func_def_189,type,
sP2: $o ).
thf(func_def_191,type,
sK4: $i > $i ).
thf(func_def_197,type,
sK10: $o ).
thf(func_def_200,type,
sK13: $i > $o ).
thf(func_def_201,type,
sK14: $i > $i > $i ).
thf(func_def_213,type,
sK26: $i > $o ).
thf(func_def_215,type,
sK28: ( $i > $o ) > $i ).
thf(func_def_216,type,
sK29: ( $i > $o ) > $i ).
thf(func_def_237,type,
sK50: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_238,type,
sK51: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_239,type,
sK52: $i > $o ).
thf(func_def_240,type,
sK53: $i > $o ).
thf(func_def_250,type,
sK63: $o ).
thf(func_def_254,type,
sK67: $i > $o ).
thf(func_def_260,type,
sK73: ( $i > $o ) > $i ).
thf(func_def_261,type,
sK74: $i > $o ).
thf(func_def_262,type,
sK75: $i > $i ).
thf(func_def_263,type,
sK76: $i > $i > $o ).
thf(func_def_265,type,
sK78: $i > $i ).
thf(func_def_266,type,
sK79: $i > $i ).
thf(func_def_267,type,
sK80: $i > ( $i > $i > $o ) > $i ).
thf(func_def_268,type,
sK81: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_269,type,
sK82: $i > ( $i > $i > $o ) > $i ).
thf(func_def_277,type,
sK90: $o ).
thf(func_def_283,type,
sK96: $i > $o ).
thf(func_def_290,type,
sK103: $i > $i > $i ).
thf(func_def_296,type,
sK109: $i > $o ).
thf(func_def_309,type,
sK122: $i > $i > $i ).
thf(func_def_320,type,
sK133: $i > $i > $i ).
thf(func_def_321,type,
sK134: $i > $o ).
thf(func_def_326,type,
sK139: $i > $i > $i ).
thf(func_def_331,type,
sK144: $o ).
thf(func_def_332,type,
sK145: $o > $i > $i > $i ).
thf(func_def_341,type,
sK154: $i > $i > $i > $i ).
thf(func_def_342,type,
sK155: $i > $i > $i > $i ).
thf(func_def_360,type,
sK173: $i > $o ).
thf(func_def_362,type,
sK175: ( $i > $o ) > $i > $i ).
thf(func_def_363,type,
sK176: $i > $o ).
thf(func_def_366,type,
sK179: $i > ( $i > $o ) > $i ).
thf(func_def_373,type,
sK186: ( $i > $o ) > $i > $i ).
thf(func_def_375,type,
sK188: $i > $o ).
thf(func_def_379,type,
sK192: $i > $o ).
thf(func_def_383,type,
sK196: $o ).
thf(func_def_387,type,
sK200: $o ).
thf(func_def_407,type,
sK220: $i > $o ).
thf(func_def_408,type,
sK221: ( $i > $o ) > $i ).
thf(func_def_412,type,
sK225: $i > $o ).
thf(func_def_413,type,
sK226: $i > $i ).
thf(func_def_414,type,
sK227: ( $i > $o ) > $i ).
thf(func_def_428,type,
sK241: $i > $i > $i ).
thf(func_def_432,type,
sK245: $i > $i ).
thf(func_def_433,type,
sK246: $i > $i ).
thf(func_def_434,type,
sK247: $i > $i ).
thf(func_def_435,type,
sK248: $i > $i ).
thf(func_def_436,type,
sK249: $i > $i ).
thf(func_def_437,type,
sK250: $i > $i > $i > $i ).
thf(func_def_438,type,
sK251: $i > $i ).
thf(func_def_439,type,
sK252: $i > $i ).
thf(func_def_440,type,
sK253: $i > $i ).
thf(func_def_441,type,
sK254: $i > $i ).
thf(func_def_442,type,
sK255: $i > $i > $i ).
thf(func_def_443,type,
sK256: $i > $i > $i > $i ).
thf(func_def_444,type,
sK257: $i > $i > $i > $i ).
thf(func_def_445,type,
sK258: $i > $i > $i > $i ).
thf(func_def_446,type,
sK259: $i > $i > $i ).
thf(func_def_447,type,
sK260: $i > $i > $i ).
thf(func_def_448,type,
sK261: $i > $i > $i ).
thf(func_def_449,type,
sK262: $i > $i > $i ).
thf(func_def_450,type,
sK263: $i > $i ).
thf(func_def_452,type,
sK265: $i > $o ).
thf(func_def_456,type,
sK269: $i > $i > $i ).
thf(func_def_457,type,
sK270: $i > $i > $i ).
thf(func_def_460,type,
sK273: $o ).
thf(func_def_465,type,
sK278: $i > ( $i > $o ) > $i ).
thf(func_def_466,type,
sK279: $i > $o ).
thf(func_def_468,type,
sK281: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_469,type,
sK282: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_472,type,
sK285: $i > $o ).
thf(func_def_473,type,
sK286: $i > $o ).
thf(func_def_476,type,
sK289: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_477,type,
sK290: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_478,type,
sK291: $i > $o ).
thf(func_def_479,type,
sK292: $i > $o ).
thf(func_def_488,type,
sK301: $i > $o ).
thf(func_def_490,type,
sK303: $o ).
thf(func_def_505,type,
sK318: $i > $o ).
thf(func_def_509,type,
sK322: $i > $o ).
thf(func_def_511,type,
sK324: ( $i > $o ) > $i > $i ).
thf(func_def_519,type,
sK332: $i > $i > $i ).
thf(func_def_522,type,
sK335: $i > $i ).
thf(func_def_524,type,
sK337: $i > $o ).
thf(func_def_527,type,
sK340: $i > ( $i > $o ) > $i ).
thf(func_def_531,type,
sK344: $i > $i ).
thf(func_def_534,type,
sK347: $i > $i ).
thf(func_def_536,type,
sK349: $i > $i ).
thf(func_def_555,type,
sK368: $i > $o ).
thf(func_def_558,type,
sK371: $i > ( $i > $o ) > $i ).
thf(func_def_563,type,
sK376: $i > $o ).
thf(func_def_567,type,
sK380: $i > $i ).
thf(func_def_572,type,
sK385: $i > ( $i > $o ) > $i ).
thf(func_def_573,type,
sK386: $i > $o ).
thf(func_def_586,type,
sK399: $i > $o ).
thf(func_def_591,type,
sK404: $i > $i > $i ).
thf(func_def_596,type,
sK409: $i > $o ).
thf(f31,axiom,
( setadjoinIL
= ( ! [X0: $i,X1: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(f43,axiom,
! [X1: $i,X0: $i] :
( ( ( in @ X1 @ X0 )
=> ( in @ X1 @ ( powerset @ ( setunion @ X0 ) ) ) )
= subPowSU ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subPowSU) ).
thf(f96,axiom,
( powersetE1
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( subset @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).
thf(f156,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
=> ! [X0: $i] : ( subset @ X0 @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton2) ).
thf(f157,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
=> ! [X0: $i] : ( subset @ X0 @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f156]) ).
thf(f278,plain,
( powersetE1
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( subset @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f96]) ).
thf(f279,plain,
( ( powersetE1 = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ( ( subset @ X1 @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f278]) ).
thf(f378,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
=> ( in @ X0 @ ( powerset @ ( setunion @ X1 ) ) ) )
= subPowSU ),
inference(rectify,[],[f43]) ).
thf(f379,plain,
( ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ X1 )
= $true )
=> ( $true
= ( in @ X0 @ ( powerset @ ( setunion @ X1 ) ) ) ) )
<=> ( subPowSU = $true ) ),
inference(fool_elimination,[],[f378]) ).
thf(f382,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
=> ! [X0: $i] : ( subset @ X0 @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f157]) ).
thf(f383,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 )
=> ! [X0: $i] :
( ( subset @ X0 @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f382]) ).
thf(f460,plain,
( setadjoinIL
= ( ! [X0: $i,X1: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f31]) ).
thf(f461,plain,
( ! [X1: $i,X0: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true )
<=> ( setadjoinIL = $true ) ),
inference(fool_elimination,[],[f460]) ).
thf(f502,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( subset @ X1 @ X0 )
= $true ) )
<=> ( powersetE1 = $true ) ),
inference(ennf_transformation,[],[f279]) ).
thf(f564,plain,
( ( subPowSU = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
| ( $true
= ( in @ X0 @ ( powerset @ ( setunion @ X1 ) ) ) ) ) ),
inference(ennf_transformation,[],[f379]) ).
thf(f593,plain,
( ? [X0: $i] :
( ( subset @ X0 @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) )
!= $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,[],[f383]) ).
thf(f594,plain,
( ( kpairiskpair = $true )
& ( notsubsetI = $true )
& ( upairset2E = $true )
& ( emptyinPowerset = $true )
& ( omegaSAx = $true )
& ( emptysetE = $true )
& ( setbeta = $true )
& ( dsetconstr__Cong = $true )
& ( subsetE = $true )
& ( upairsetE = $true )
& ( foundationAx = $true )
& ( noeltsimpempty = $true )
& ( wellorderingAx = $true )
& ( exuI2 = $true )
& ( powersetAx = $true )
& ( uniqinunit = $true )
& ( powersetI1 = $true )
& ( symdiffE = $true )
& ( subsetemptysetimpeq = $true )
& ( setextAx = $true )
& ( exuE1 = $true )
& ( descr__Cong = $true )
& ( setunionE2 = $true )
& ( emptyI = $true )
& ( setextsub = $true )
& ( quantDeMorgan4 = $true )
& ( setukpairIR = $true )
& ( nonemptyI1 = $true )
& ( setminusSubset2 = $true )
& ( powersetE = $true )
& ( setext = $true )
& ( notequalI1 = $true )
& ( setminusELneg = $true )
& ( powersetE1 = $true )
& ( setminusEL = $true )
& ( cartprodmempair = $true )
& ( singletonsswitch = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdexE = $true )
& ( setadjoinSub = $true )
& ( binintersectEL = $true )
& ( inCongP = $true )
& ( subsetTrans = $true )
& ( prop2setE = $true )
& ( ubforcartprodlem1 = $true )
& ( notdallE = $true )
& ( binintersectSubset5 = $true )
& ( upairsetIL = $true )
& ( setunionI = $true )
& ( descrp = $true )
& ( setunionAx = $true )
& ( setminusLsub = $true )
& ( symdiffI2 = $true )
& ( setadjoinSub2 = $true )
& ( kpairp = $true )
& ( setunionE = $true )
& ( inPowerset = $true )
& ( nonemptyImpWitness = $true )
& ( exuEu = $true )
& ( prop2setI = $true )
& ( setadjoinE = $true )
& ( singletonsubset = $true )
& ( binunionIL = $true )
& ( setadjoinOr = $true )
& ( emptyInPowerset = $true )
& ( binintersectSubset1 = $true )
& ( setadjoinIR = $true )
& ( emptyset__Cong = $true )
& ( subsetI1 = $true )
& ( notinemptyset = $true )
& ( emptysetAx = $true )
& ( emptyE1 = $true )
& ( quantDeMorgan3 = $true )
& ( setminusER = $true )
& ( subset2powerset = $true )
& ( binintersectSubset4 = $true )
& ( nonemptyI = $true )
& ( cartprodpairin = $true )
& ( cartprodmempair1 = $true )
& ( emptysetimpfalse = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( notinsingleton = $true )
& ( setadjoin__Cong = $true )
& ( setukpairIL = $true )
& ( subPowSU = $true )
& ( binintersectI = $true )
& ( setunion__Cong = $true )
& ( omegaIndAx = $true )
& ( setunionsingleton1 = $true )
& ( binunionLsub = $true )
& ( exuE2 = $true )
& ( eqinunit = $true )
& ( replAx = $true )
& ( binunionEcases = $true )
& ( setminusI = $true )
& ( setminusILneg = $true )
& ( symdiffIneg2 = $true )
& ( setminusSubset1 = $true )
& ( omega0Ax = $true )
& ( binintersectLsub = $true )
& ( exuE3e = $true )
& ( subsetRefl = $true )
& ( powersetsubset = $true )
& ( binintersectER = $true )
& ( vacuousDall = $true )
& ( upairset2IR = $true )
& ( symdiffIneg1 = $true )
& ( binunionRsub = $true )
& ( exuE3u = $true )
& ( quantDeMorgan2 = $true )
& ( dsetconstrEL = $true )
& ( nonemptyE1 = $true )
& ( upairsubunion = $true )
& ( powersetI = $true )
& ( omega__Cong = $true )
& ( dsetconstrI = $true )
& ( ubforcartprodlem3 = $true )
& ( singletoninpowunion = $true )
& ( bs114d = $true )
& ( setoftrueEq = $true )
& ( symdiffI1 = $true )
& ( sepInPowerset = $true )
& ( emptysetsubset = $true )
& ( upairsetIR = $true )
& ( binintersectSubset2 = $true )
& ( quantDeMorgan1 = $true )
& ( upairinpowunion = $true )
& ( setadjoinAx = $true )
& ( subsetI2 = $true )
& ( notequalI2 = $true )
& ( emptyinunitempty = $true )
& ( setminusERneg = $true )
& ( binunionIR = $true )
& ( dsetconstrER = $true )
& ( prop2set2propI = $true )
& ( eqimpsubset2 = $true )
& ( in__Cong = $true )
& ( setadjoinIL = $true )
& ? [X0: $i] :
( ( subset @ X0 @ ( setunion @ ( setadjoin @ X0 @ emptyset ) ) )
!= $true )
& ( binunionE = $true )
& ( exu__Cong = $true )
& ( secondinupair = $true )
& ( singletoninpowerset = $true )
& ( powerset__Cong = $true )
& ( sepSubset = $true )
& ( binintersectSubset3 = $true )
& ( subsetE2 = $true )
& ( setminusIRneg = $true )
& ( ubforcartprodlem2 = $true )
& ( eqimpsubset1 = $true ) ),
inference(flattening,[],[f593]) ).
thf(f749,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( subset @ X1 @ X0 )
= $true ) )
| ( powersetE1 != $true ) )
& ( ( powersetE1 = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ( ( subset @ X1 @ X0 )
!= $true ) ) ) ),
inference(nnf_transformation,[],[f502]) ).
thf(f750,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( subset @ X1 @ X0 )
= $true ) )
| ( powersetE1 != $true ) )
& ( ( powersetE1 = $true )
| ? [X2: $i,X3: $i] :
( ( ( in @ X3 @ ( powerset @ X2 ) )
= $true )
& ( ( subset @ X3 @ X2 )
!= $true ) ) ) ),
inference(rectify,[],[f749]) ).
thf(f751,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( subset @ X1 @ X0 )
= $true ) )
| ( powersetE1 != $true ) )
& ( ( powersetE1 = $true )
| ( ( $true
= ( in @ sK86 @ ( powerset @ sK85 ) ) )
& ( $true
!= ( subset @ sK86 @ sK85 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK85,sK86]),skolemize(X2,sK85),skolemize(X3,sK86)],[f750]) ).
thf(f888,plain,
( ( ! [X1: $i,X0: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ? [X1: $i,X0: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
!= $true ) ) ),
inference(nnf_transformation,[],[f461]) ).
thf(f889,plain,
( ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X1 @ X0 ) )
= $true )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ? [X2: $i,X3: $i] :
( ( in @ X3 @ ( setadjoin @ X3 @ X2 ) )
!= $true ) ) ),
inference(rectify,[],[f888]) ).
thf(f890,plain,
( ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X1 @ X0 ) )
= $true )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ( ( in @ sK212 @ ( setadjoin @ sK212 @ sK211 ) )
!= $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK211,sK212]),skolemize(X2,sK211),skolemize(X3,sK212)],[f889]) ).
thf(f988,plain,
( ( ( subPowSU = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
& ( $true
!= ( in @ X0 @ ( powerset @ ( setunion @ X1 ) ) ) ) ) )
& ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
| ( $true
= ( in @ X0 @ ( powerset @ ( setunion @ X1 ) ) ) ) )
| ( subPowSU != $true ) ) ),
inference(nnf_transformation,[],[f564]) ).
thf(f989,plain,
( ( ( subPowSU = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
& ( $true
!= ( in @ X0 @ ( powerset @ ( setunion @ X1 ) ) ) ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X3 )
!= $true )
| ( ( in @ X2 @ ( powerset @ ( setunion @ X3 ) ) )
= $true ) )
| ( subPowSU != $true ) ) ),
inference(rectify,[],[f988]) ).
thf(f990,plain,
( ( ( subPowSU = $true )
| ( ( $true
= ( in @ sK310 @ sK311 ) )
& ( ( in @ sK310 @ ( powerset @ ( setunion @ sK311 ) ) )
!= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X3 )
!= $true )
| ( ( in @ X2 @ ( powerset @ ( setunion @ X3 ) ) )
= $true ) )
| ( subPowSU != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK310,sK311]),skolemize(X0,sK310),skolemize(X1,sK311)],[f989]) ).
thf(f1036,plain,
( ( kpairiskpair = $true )
& ( notsubsetI = $true )
& ( upairset2E = $true )
& ( emptyinPowerset = $true )
& ( omegaSAx = $true )
& ( emptysetE = $true )
& ( setbeta = $true )
& ( dsetconstr__Cong = $true )
& ( subsetE = $true )
& ( upairsetE = $true )
& ( foundationAx = $true )
& ( noeltsimpempty = $true )
& ( wellorderingAx = $true )
& ( exuI2 = $true )
& ( powersetAx = $true )
& ( uniqinunit = $true )
& ( powersetI1 = $true )
& ( symdiffE = $true )
& ( subsetemptysetimpeq = $true )
& ( setextAx = $true )
& ( exuE1 = $true )
& ( descr__Cong = $true )
& ( setunionE2 = $true )
& ( emptyI = $true )
& ( setextsub = $true )
& ( quantDeMorgan4 = $true )
& ( setukpairIR = $true )
& ( nonemptyI1 = $true )
& ( setminusSubset2 = $true )
& ( powersetE = $true )
& ( setext = $true )
& ( notequalI1 = $true )
& ( setminusELneg = $true )
& ( powersetE1 = $true )
& ( setminusEL = $true )
& ( cartprodmempair = $true )
& ( singletonsswitch = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdexE = $true )
& ( setadjoinSub = $true )
& ( binintersectEL = $true )
& ( inCongP = $true )
& ( subsetTrans = $true )
& ( prop2setE = $true )
& ( ubforcartprodlem1 = $true )
& ( notdallE = $true )
& ( binintersectSubset5 = $true )
& ( upairsetIL = $true )
& ( setunionI = $true )
& ( descrp = $true )
& ( setunionAx = $true )
& ( setminusLsub = $true )
& ( symdiffI2 = $true )
& ( setadjoinSub2 = $true )
& ( kpairp = $true )
& ( setunionE = $true )
& ( inPowerset = $true )
& ( nonemptyImpWitness = $true )
& ( exuEu = $true )
& ( prop2setI = $true )
& ( setadjoinE = $true )
& ( singletonsubset = $true )
& ( binunionIL = $true )
& ( setadjoinOr = $true )
& ( emptyInPowerset = $true )
& ( binintersectSubset1 = $true )
& ( setadjoinIR = $true )
& ( emptyset__Cong = $true )
& ( subsetI1 = $true )
& ( notinemptyset = $true )
& ( emptysetAx = $true )
& ( emptyE1 = $true )
& ( quantDeMorgan3 = $true )
& ( setminusER = $true )
& ( subset2powerset = $true )
& ( binintersectSubset4 = $true )
& ( nonemptyI = $true )
& ( cartprodpairin = $true )
& ( cartprodmempair1 = $true )
& ( emptysetimpfalse = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( notinsingleton = $true )
& ( setadjoin__Cong = $true )
& ( setukpairIL = $true )
& ( subPowSU = $true )
& ( binintersectI = $true )
& ( setunion__Cong = $true )
& ( omegaIndAx = $true )
& ( setunionsingleton1 = $true )
& ( binunionLsub = $true )
& ( exuE2 = $true )
& ( eqinunit = $true )
& ( replAx = $true )
& ( binunionEcases = $true )
& ( setminusI = $true )
& ( setminusILneg = $true )
& ( symdiffIneg2 = $true )
& ( setminusSubset1 = $true )
& ( omega0Ax = $true )
& ( binintersectLsub = $true )
& ( exuE3e = $true )
& ( subsetRefl = $true )
& ( powersetsubset = $true )
& ( binintersectER = $true )
& ( vacuousDall = $true )
& ( upairset2IR = $true )
& ( symdiffIneg1 = $true )
& ( binunionRsub = $true )
& ( exuE3u = $true )
& ( quantDeMorgan2 = $true )
& ( dsetconstrEL = $true )
& ( nonemptyE1 = $true )
& ( upairsubunion = $true )
& ( powersetI = $true )
& ( omega__Cong = $true )
& ( dsetconstrI = $true )
& ( ubforcartprodlem3 = $true )
& ( singletoninpowunion = $true )
& ( bs114d = $true )
& ( setoftrueEq = $true )
& ( symdiffI1 = $true )
& ( sepInPowerset = $true )
& ( emptysetsubset = $true )
& ( upairsetIR = $true )
& ( binintersectSubset2 = $true )
& ( quantDeMorgan1 = $true )
& ( upairinpowunion = $true )
& ( setadjoinAx = $true )
& ( subsetI2 = $true )
& ( notequalI2 = $true )
& ( emptyinunitempty = $true )
& ( setminusERneg = $true )
& ( binunionIR = $true )
& ( dsetconstrER = $true )
& ( prop2set2propI = $true )
& ( eqimpsubset2 = $true )
& ( in__Cong = $true )
& ( setadjoinIL = $true )
& ( ( subset @ sK356 @ ( setunion @ ( setadjoin @ sK356 @ emptyset ) ) )
!= $true )
& ( binunionE = $true )
& ( exu__Cong = $true )
& ( secondinupair = $true )
& ( singletoninpowerset = $true )
& ( powerset__Cong = $true )
& ( sepSubset = $true )
& ( binintersectSubset3 = $true )
& ( subsetE2 = $true )
& ( setminusIRneg = $true )
& ( ubforcartprodlem2 = $true )
& ( eqimpsubset1 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK356]),skolemize(X0,sK356)],[f594]) ).
thf(f1227,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( subset @ X1 @ X0 )
= $true )
| ( powersetE1 != $true ) ),
inference(cnf_transformation,[],[f751]) ).
thf(f1397,plain,
! [X0: $i,X1: $i] :
( ( setadjoinIL != $true )
| ( ( in @ X1 @ ( setadjoin @ X1 @ X0 ) )
= $true ) ),
inference(cnf_transformation,[],[f890]) ).
thf(f1552,plain,
! [X2: $i,X3: $i] :
( ( ( in @ X2 @ ( powerset @ ( setunion @ X3 ) ) )
= $true )
| ( subPowSU != $true )
| ( ( in @ X2 @ X3 )
!= $true ) ),
inference(cnf_transformation,[],[f990]) ).
thf(f1626,plain,
( ( subset @ sK356 @ ( setunion @ ( setadjoin @ sK356 @ emptyset ) ) )
!= $true ),
inference(cnf_transformation,[],[f1036]) ).
thf(f1627,plain,
setadjoinIL = $true,
inference(cnf_transformation,[],[f1036]) ).
thf(f1680,plain,
subPowSU = $true,
inference(cnf_transformation,[],[f1036]) ).
thf(f1733,plain,
powersetE1 = $true,
inference(cnf_transformation,[],[f1036]) ).
thf(f2304,definition,
( spl417_69
<=> ( powersetE1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl417_69])],[avatar_definition]) ).
thf(f2308,definition,
( spl417_70
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( subset @ X1 @ X0 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl417_70])],[avatar_definition]) ).
thf(f2309,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true )
| ( ( subset @ X1 @ X0 )
= $true ) )
| ~ spl417_70 ),
inference(avatar_component_clause,[],[f2308]) ).
thf(f2310,plain,
( ~ spl417_69
| spl417_70 ),
inference(avatar_split_clause,[],[f1227,f2308,f2304]) ).
thf(f2420,definition,
( spl417_95
<=> ( subPowSU = $true ) ),
introduced(definition,[new_symbols(definition,[spl417_95])],[avatar_definition]) ).
thf(f2851,definition,
( spl417_191
<=> ! [X4: $i,X5: $i] :
( ( in @ X4 @ ( setadjoin @ X4 @ X5 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl417_191])],[avatar_definition]) ).
thf(f2852,plain,
( ! [X4: $i,X5: $i] :
( ( in @ X4 @ ( setadjoin @ X4 @ X5 ) )
= $true )
| ~ spl417_191 ),
inference(avatar_component_clause,[],[f2851]) ).
thf(f3173,definition,
( spl417_262
<=> ( setadjoinIL = $true ) ),
introduced(definition,[new_symbols(definition,[spl417_262])],[avatar_definition]) ).
thf(f3176,plain,
spl417_262,
inference(avatar_split_clause,[],[f1627,f3173]) ).
thf(f3630,plain,
spl417_95,
inference(avatar_split_clause,[],[f1680,f2420]) ).
thf(f3996,plain,
( spl417_191
| ~ spl417_262 ),
inference(avatar_split_clause,[],[f1397,f3173,f2851]) ).
thf(f4402,definition,
( spl417_520
<=> ( ( subset @ sK356 @ ( setunion @ ( setadjoin @ sK356 @ emptyset ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl417_520])],[avatar_definition]) ).
thf(f4404,plain,
( ( ( subset @ sK356 @ ( setunion @ ( setadjoin @ sK356 @ emptyset ) ) )
!= $true )
| spl417_520 ),
inference(avatar_component_clause,[],[f4402]) ).
thf(f4405,plain,
~ spl417_520,
inference(avatar_split_clause,[],[f1626,f4402]) ).
thf(f5028,definition,
( spl417_645
<=> ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ ( powerset @ ( setunion @ X3 ) ) )
= $true )
| ( ( in @ X2 @ X3 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl417_645])],[avatar_definition]) ).
thf(f5029,plain,
( ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ ( powerset @ ( setunion @ X3 ) ) )
= $true )
| ( ( in @ X2 @ X3 )
!= $true ) )
| ~ spl417_645 ),
inference(avatar_component_clause,[],[f5028]) ).
thf(f5030,plain,
( ~ spl417_95
| spl417_645 ),
inference(avatar_split_clause,[],[f1552,f5028,f2420]) ).
thf(f5248,plain,
spl417_69,
inference(avatar_split_clause,[],[f1733,f2304]) ).
thf(f5629,plain,
( ! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( subset @ X0 @ ( setunion @ X1 ) )
= $true )
| ( ( in @ X0 @ X1 )
!= $true ) )
| ~ spl417_70
| ~ spl417_645 ),
inference(superposition,[],[f2309,f5029]) ).
thf(f5633,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ ( setunion @ X1 ) )
= $true )
| ( ( in @ X0 @ X1 )
!= $true ) )
| ~ spl417_70
| ~ spl417_645 ),
inference(trivial_inequality_removal,[],[f5629]) ).
thf(f8720,plain,
( ( $true
!= ( in @ sK356 @ ( setadjoin @ sK356 @ emptyset ) ) )
| ( $true != $true )
| ~ spl417_70
| spl417_520
| ~ spl417_645 ),
inference(superposition,[],[f4404,f5633]) ).
thf(f8733,plain,
( ( $true
!= ( in @ sK356 @ ( setadjoin @ sK356 @ emptyset ) ) )
| ~ spl417_70
| spl417_520
| ~ spl417_645 ),
inference(trivial_inequality_removal,[],[f8720]) ).
thf(f8736,plain,
( $false
| ~ spl417_70
| ~ spl417_191
| spl417_520
| ~ spl417_645 ),
inference(forward_subsumption_resolution,[],[f8733,f2852]) ).
thf(f8737,plain,
( ~ spl417_70
| ~ spl417_191
| spl417_520
| ~ spl417_645 ),
inference(avatar_contradiction_clause,[],[f8736]) ).
cnf(s39,plain,
( ~ spl417_69
| spl417_70 ),
inference(sat_conversion,[],[f2310]) ).
cnf(s187,plain,
spl417_262,
inference(sat_conversion,[],[f3176]) ).
cnf(s279,plain,
spl417_95,
inference(sat_conversion,[],[f3630]) ).
cnf(s372,plain,
( spl417_191
| ~ spl417_262 ),
inference(sat_conversion,[],[f3996]) ).
cnf(s475,plain,
~ spl417_520,
inference(sat_conversion,[],[f4405]) ).
cnf(s653,plain,
( ~ spl417_95
| spl417_645 ),
inference(sat_conversion,[],[f5030]) ).
cnf(s710,plain,
spl417_69,
inference(sat_conversion,[],[f5248]) ).
cnf(s782,plain,
( ~ spl417_70
| ~ spl417_191
| spl417_520
| ~ spl417_645 ),
inference(sat_conversion,[],[f8737]) ).
cnf(s846,plain,
spl417_645,
inference(rat,[],[s653,s279]) ).
cnf(s896,plain,
spl417_191,
inference(rat,[],[s372,s187]) ).
cnf(s897,plain,
~ spl417_70,
inference(rat,[],[s782,s846,s475,s896]) ).
cnf(s970,plain,
$false,
inference(rat,[],[s39,s897,s710]) ).
thf(f8738,plain,
$false,
inference(avatar_sat_refutation,[],[s970]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU635^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n004.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % 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 14:00:22 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.19/0.27 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
% 0.54/0.41 % (1331184)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.54/0.41 % (1331195)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.54/0.41 % (1331195)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
% 0.54/0.41 % (1331191)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=77993383:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.54/0.41 % (1331189)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1156262882:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.54/0.41 % (1331190)lrs+10_16_si=on:nwc=1.5:random_seed=2058231305:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.54/0.41 % (1331193)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3560264241:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.54/0.41 % (1331192)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=460045728: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)
% 0.54/0.41 % (1331194)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=364090643:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.54/0.41 % (1331195)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=4246044889:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.54/0.41 % (1331191)Instruction limit reached!
% 0.54/0.41 % (1331191)------------------------------
% 0.54/0.41 % (1331191)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.41 % (1331191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.41 % (1331191)CaDiCaL version: 2.1.3
% 0.54/0.41 % (1331191)Termination reason: Instruction limit
% 0.54/0.41 % (1331191)Termination phase: shuffling
% 0.54/0.41 % (1331191)Time elapsed: 0.002 s
% 0.54/0.41 % (1331191)Peak memory usage: 10 MB
% 0.54/0.41 % (1331191)Instructions burned: 3 (million)
% 0.54/0.41 % (1331190)Instruction limit reached!
% 0.54/0.41 % (1331190)------------------------------
% 0.54/0.41 % (1331190)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.41 % (1331190)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.41 % (1331190)CaDiCaL version: 2.1.3
% 0.54/0.41 % (1331190)Termination reason: Instruction limit
% 0.54/0.41 % (1331190)Termination phase: Property scanning
% 0.54/0.41 % (1331190)Time elapsed: 0.009 s
% 0.54/0.41 % (1331190)Peak memory usage: 10 MB
% 0.54/0.41 % (1331190)Instructions burned: 19 (million)
% 0.54/0.41 % (1331193)Instruction limit reached!
% 0.54/0.41 % (1331193)------------------------------
% 0.54/0.41 % (1331193)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.41 % (1331193)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.41 % (1331193)CaDiCaL version: 2.1.3
% 0.54/0.41 % (1331193)Termination reason: Instruction limit
% 0.54/0.41 % (1331193)Termination phase: Preprocessing 3
% 0.54/0.41 % (1331193)Time elapsed: 0.011 s
% 0.54/0.41 % (1331193)Peak memory usage: 11 MB
% 0.54/0.41 % (1331193)Instructions burned: 24 (million)
% 0.54/0.41 % (1331203)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3945759282:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.54/0.41 % (1331203)Instruction limit reached!
% 0.54/0.41 % (1331203)------------------------------
% 0.54/0.41 % (1331203)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.41 % (1331203)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.41 % (1331203)CaDiCaL version: 2.1.3
% 0.54/0.41 % (1331203)Termination reason: Instruction limit
% 0.54/0.41 % (1331203)Termination phase: shuffling
% 0.54/0.41 % (1331203)Time elapsed: 0.002 s
% 0.54/0.41 % (1331203)Peak memory usage: 10 MB
% 0.54/0.41 % (1331203)Instructions burned: 3 (million)
% 0.54/0.41 % (1331204)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1332752425:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.54/0.45 % (1331204)Instruction limit reached!
% 0.54/0.45 % (1331204)------------------------------
% 0.54/0.45 % (1331204)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.45 % (1331204)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.45 % (1331204)CaDiCaL version: 2.1.3
% 0.54/0.45 % (1331204)Termination reason: Instruction limit
% 0.54/0.45 % (1331204)Termination phase: shuffling
% 0.54/0.45 % (1331204)Time elapsed: 0.003 s
% 0.54/0.45 % (1331204)Peak memory usage: 10 MB
% 0.54/0.45 % (1331204)Instructions burned: 6 (million)
% 0.54/0.45 % (1331194)Instruction limit reached!
% 0.54/0.45 % (1331194)------------------------------
% 0.54/0.45 % (1331194)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.45 % (1331194)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.45 % (1331194)CaDiCaL version: 2.1.3
% 0.54/0.45 % (1331194)Termination reason: Instruction limit
% 0.54/0.45 % (1331194)Termination phase: Property scanning
% 0.54/0.45 % (1331194)Time elapsed: 0.035 s
% 0.54/0.45 % (1331194)Peak memory usage: 12 MB
% 0.54/0.45 % (1331194)Instructions burned: 77 (million)
% 0.54/0.45 % (1331205)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.54/0.45 % (1331207)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=4110658605:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.54/0.45 % (1331189)Instruction limit reached!
% 0.54/0.45 % (1331189)------------------------------
% 0.54/0.45 % (1331189)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.45 % (1331189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.45 % (1331189)CaDiCaL version: 2.1.3
% 0.54/0.45 % (1331189)Termination reason: Instruction limit
% 0.54/0.45 % (1331189)Termination phase: Property scanning
% 0.54/0.45 % (1331189)Time elapsed: 0.043 s
% 0.54/0.45 % (1331189)Peak memory usage: 12 MB
% 0.54/0.45 % (1331189)Instructions burned: 88 (million)
% 0.54/0.45 % (1331205)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=665602476:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.54/0.45 % (1331209)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
% 0.54/0.45 % (1331209)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.54/0.45 % (1331207)Instruction limit reached!
% 0.54/0.45 % (1331207)------------------------------
% 0.54/0.45 % (1331207)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.45 % (1331207)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.45 % (1331207)CaDiCaL version: 2.1.3
% 0.54/0.45 % (1331207)Termination reason: Instruction limit
% 0.54/0.45 % (1331207)Termination phase: shuffling
% 0.54/0.45 % (1331207)Time elapsed: 0.005 s
% 0.54/0.45 % (1331207)Peak memory usage: 10 MB
% 0.54/0.45 % (1331207)Instructions burned: 12 (million)
% 0.54/0.45 % (1331205)Instruction limit reached!
% 0.54/0.45 % (1331205)------------------------------
% 0.54/0.45 % (1331205)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.45 % (1331205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.45 % (1331205)CaDiCaL version: 2.1.3
% 0.54/0.45 % (1331205)Termination reason: Instruction limit
% 0.54/0.45 % (1331205)Termination phase: shuffling
% 0.54/0.45 % (1331205)Time elapsed: 0.003 s
% 0.54/0.45 % (1331205)Peak memory usage: 10 MB
% 0.54/0.45 % (1331205)Instructions burned: 7 (million)
% 0.54/0.45 % (1331209)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1146915707:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.54/0.45 % (1331210)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=3292366480:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.54/0.45 % (1331214)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.23/0.49 % (1331212)lrs+10_1_si=on:cs=on:random_seed=3572249148:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 1.23/0.49 % (1331209)Instruction limit reached!
% 1.23/0.49 % (1331209)------------------------------
% 1.23/0.49 % (1331209)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.49 % (1331209)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.49 % (1331209)CaDiCaL version: 2.1.3
% 1.23/0.49 % (1331209)Termination reason: Instruction limit
% 1.23/0.49 % (1331209)Termination phase: Property scanning
% 1.23/0.49 % (1331209)Time elapsed: 0.012 s
% 1.23/0.49 % (1331209)Peak memory usage: 10 MB
% 1.23/0.49 % (1331209)Instructions burned: 28 (million)
% 1.23/0.49 % (1331214)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=1365111987:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.23/0.49 % (1331212)Instruction limit reached!
% 1.23/0.49 % (1331212)------------------------------
% 1.23/0.49 % (1331212)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.49 % (1331212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.49 % (1331212)CaDiCaL version: 2.1.3
% 1.23/0.49 % (1331212)Termination reason: Instruction limit
% 1.23/0.49 % (1331212)Termination phase: shuffling
% 1.23/0.49 % (1331212)Time elapsed: 0.004 s
% 1.23/0.49 % (1331212)Peak memory usage: 10 MB
% 1.23/0.49 % (1331212)Instructions burned: 8 (million)
% 1.23/0.49 % (1331215)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=4274908219:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 1.23/0.49 % (1331214)Instruction limit reached!
% 1.23/0.49 % (1331214)------------------------------
% 1.23/0.49 % (1331214)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.49 % (1331214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.49 % (1331214)CaDiCaL version: 2.1.3
% 1.23/0.49 % (1331214)Termination reason: Instruction limit
% 1.23/0.49 % (1331214)Termination phase: shuffling
% 1.23/0.49 % (1331214)Time elapsed: 0.003 s
% 1.23/0.49 % (1331214)Peak memory usage: 10 MB
% 1.23/0.49 % (1331214)Instructions burned: 6 (million)
% 1.23/0.49 % (1331219)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1212090510:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.23/0.49 % (1331195)Instruction limit reached!
% 1.23/0.49 % (1331195)------------------------------
% 1.23/0.49 % (1331195)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.49 % (1331195)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.49 % (1331195)CaDiCaL version: 2.1.3
% 1.23/0.49 % (1331195)Termination reason: Instruction limit
% 1.23/0.49 % (1331195)Termination phase: Saturation
% 1.23/0.49 % (1331195)Time elapsed: 0.083 s
% 1.23/0.49 % (1331195)Peak memory usage: 14 MB
% 1.23/0.49 % (1331195)Instructions burned: 159 (million)
% 1.23/0.49 % (1331215)Instruction limit reached!
% 1.23/0.49 % (1331215)------------------------------
% 1.23/0.49 % (1331215)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.49 % (1331215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.49 % (1331215)CaDiCaL version: 2.1.3
% 1.23/0.49 % (1331215)Termination reason: Instruction limit
% 1.23/0.49 % (1331215)Termination phase: Preprocessing 3
% 1.23/0.49 % (1331215)Time elapsed: 0.018 s
% 1.23/0.49 % (1331215)Peak memory usage: 11 MB
% 1.23/0.49 % (1331215)Instructions burned: 38 (million)
% 1.23/0.49 % (1331222)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2345092189:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.23/0.49 % (1331223)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3348592654:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.23/0.49 % (1331210)Instruction limit reached!
% 1.23/0.49 % (1331210)------------------------------
% 1.23/0.49 % (1331210)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.49 % (1331210)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.49 % (1331210)CaDiCaL version: 2.1.3
% 1.23/0.49 % (1331210)Termination reason: Instruction limit
% 1.23/0.49 % (1331210)Termination phase: Saturation
% 1.95/0.57 % (1331210)Time elapsed: 0.036 s
% 1.95/0.57 % (1331210)Peak memory usage: 12 MB
% 1.95/0.57 % (1331210)Instructions burned: 88 (million)
% 1.95/0.57 % (1331223)Instruction limit reached!
% 1.95/0.57 % (1331223)------------------------------
% 1.95/0.57 % (1331223)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.95/0.57 % (1331223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.95/0.57 % (1331223)CaDiCaL version: 2.1.3
% 1.95/0.57 % (1331223)Termination reason: Instruction limit
% 1.95/0.57 % (1331223)Termination phase: shuffling
% 1.95/0.57 % (1331223)Time elapsed: 0.007 s
% 1.95/0.57 % (1331223)Peak memory usage: 10 MB
% 1.95/0.57 % (1331223)Instructions burned: 16 (million)
% 1.95/0.57 % (1331222)Instruction limit reached!
% 1.95/0.57 % (1331222)------------------------------
% 1.95/0.57 % (1331222)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.95/0.57 % (1331222)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.95/0.57 % (1331222)CaDiCaL version: 2.1.3
% 1.95/0.57 % (1331222)Termination reason: Instruction limit
% 1.95/0.57 % (1331222)Termination phase: Preprocessing 3
% 1.95/0.57 % (1331222)Time elapsed: 0.012 s
% 1.95/0.57 % (1331222)Peak memory usage: 11 MB
% 1.95/0.57 % (1331222)Instructions burned: 26 (million)
% 1.95/0.57 % (1331225)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2414765606:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.95/0.57 % (1331227)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1458385425:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.95/0.57 % (1331229)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3021508457: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)
% 1.95/0.57 % (1331227)Instruction limit reached!
% 1.95/0.57 % (1331227)------------------------------
% 1.95/0.57 % (1331227)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.95/0.57 % (1331227)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.95/0.57 % (1331227)CaDiCaL version: 2.1.3
% 1.95/0.57 % (1331227)Termination reason: Instruction limit
% 1.95/0.57 % (1331227)Termination phase: shuffling
% 1.95/0.57 % (1331227)Time elapsed: 0.007 s
% 1.95/0.57 % (1331227)Peak memory usage: 10 MB
% 1.95/0.57 % (1331227)Instructions burned: 16 (million)
% 1.95/0.57 % (1331229)Instruction limit reached!
% 1.95/0.57 % (1331229)------------------------------
% 1.95/0.57 % (1331229)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.95/0.57 % (1331229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.95/0.57 % (1331229)CaDiCaL version: 2.1.3
% 1.95/0.57 % (1331229)Termination reason: Instruction limit
% 1.95/0.57 % (1331229)Termination phase: shuffling
% 1.95/0.57 % (1331229)Time elapsed: 0.004 s
% 1.95/0.57 % (1331230)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2722182396:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.95/0.57 % (1331229)Peak memory usage: 10 MB
% 1.95/0.57 % (1331229)Instructions burned: 7 (million)
% 1.95/0.57 % (1331231)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=986224749:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.95/0.57 % (1331230)Instruction limit reached!
% 1.95/0.57 % (1331230)------------------------------
% 1.95/0.57 % (1331230)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.95/0.57 % (1331230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.95/0.57 % (1331230)CaDiCaL version: 2.1.3
% 1.95/0.57 % (1331230)Termination reason: Instruction limit
% 1.95/0.57 % (1331230)Termination phase: Property scanning
% 1.95/0.57 % (1331230)Time elapsed: 0.012 s
% 1.95/0.57 % (1331230)Peak memory usage: 10 MB
% 1.95/0.57 % (1331230)Instructions burned: 27 (million)
% 1.95/0.57 % (1331231)Instruction limit reached!
% 1.95/0.57 % (1331231)------------------------------
% 1.95/0.57 % (1331231)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.95/0.57 % (1331231)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.95/0.57 % (1331231)CaDiCaL version: 2.1.3
% 1.95/0.57 % (1331231)Termination reason: Instruction limit
% 1.95/0.57 % (1331231)Termination phase: Property scanning
% 1.95/0.57 % (1331231)Time elapsed: 0.010 s
% 1.95/0.57 % (1331231)Peak memory usage: 10 MB
% 1.95/0.60 % (1331231)Instructions burned: 23 (million)
% 1.95/0.60 % (1331235)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=163455778:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.95/0.60 % (1331238)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
% 1.95/0.60 % (1331238)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.95/0.60 % (1331238)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=2456803252:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.95/0.60 % (1331239)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.95/0.60 % (1331239)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=2000545601:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.95/0.60 % (1331238)Instruction limit reached!
% 1.95/0.60 % (1331238)------------------------------
% 1.95/0.60 % (1331238)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.95/0.60 % (1331238)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.95/0.60 % (1331238)CaDiCaL version: 2.1.3
% 1.95/0.60 % (1331238)Termination reason: Instruction limit
% 1.95/0.60 % (1331238)Termination phase: shuffling
% 1.95/0.60 % (1331238)Time elapsed: 0.007 s
% 1.95/0.60 % (1331238)Peak memory usage: 10 MB
% 1.95/0.60 % (1331238)Instructions burned: 14 (million)
% 1.95/0.60 % (1331240)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=2895319531:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.95/0.60 % (1331239)Instruction limit reached!
% 1.95/0.60 % (1331239)------------------------------
% 1.95/0.60 % (1331239)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.95/0.60 % (1331239)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.95/0.60 % (1331239)CaDiCaL version: 2.1.3
% 1.95/0.60 % (1331239)Termination reason: Instruction limit
% 1.95/0.60 % (1331239)Termination phase: shuffling
% 1.95/0.60 % (1331239)Time elapsed: 0.004 s
% 1.95/0.60 % (1331239)Peak memory usage: 10 MB
% 1.95/0.60 % (1331239)Instructions burned: 9 (million)
% 1.95/0.60 % (1331235)Instruction limit reached!
% 1.95/0.60 % (1331235)------------------------------
% 1.95/0.60 % (1331235)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.95/0.60 % (1331235)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.95/0.60 % (1331235)CaDiCaL version: 2.1.3
% 1.95/0.60 % (1331235)Termination reason: Instruction limit
% 1.95/0.60 % (1331235)Termination phase: Property scanning
% 1.95/0.60 % (1331235)Time elapsed: 0.027 s
% 1.95/0.60 % (1331235)Peak memory usage: 12 MB
% 1.95/0.60 % (1331235)Instructions burned: 60 (million)
% 1.95/0.60 % (1331240)Instruction limit reached!
% 1.95/0.60 % (1331240)------------------------------
% 1.95/0.60 % (1331240)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.95/0.60 % (1331240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.95/0.60 % (1331240)CaDiCaL version: 2.1.3
% 1.95/0.60 % (1331240)Termination reason: Instruction limit
% 1.95/0.60 % (1331240)Termination phase: Property scanning
% 1.95/0.60 % (1331240)Time elapsed: 0.014 s
% 1.95/0.60 % (1331240)Peak memory usage: 10 MB
% 1.95/0.60 % (1331240)Instructions burned: 33 (million)
% 1.95/0.60 % (1331245)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=3995121866:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.95/0.60 % (1331246)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=911171681:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.95/0.60 % (1331245)Instruction limit reached!
% 1.95/0.60 % (1331245)------------------------------
% 1.95/0.60 % (1331245)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.95/0.60 % (1331245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.95/0.60 % (1331245)CaDiCaL version: 2.1.3
% 1.95/0.60 % (1331245)Termination reason: Instruction limit
% 1.95/0.60 % (1331245)Termination phase: shuffling
% 1.95/0.60 % (1331245)Time elapsed: 0.004 s
% 1.95/0.60 % (1331245)Peak memory usage: 10 MB
% 1.95/0.60 % (1331245)Instructions burned: 7 (million)
% 1.95/0.60 % (1331247)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3689049215:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 1.95/0.60 % (1331246)Instruction limit reached!
% 1.95/0.60 % (1331246)------------------------------
% 1.95/0.60 % (1331246)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.95/0.60 % (1331246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.95/0.60 % (1331246)CaDiCaL version: 2.1.3
% 1.95/0.60 % (1331246)Termination reason: Instruction limit
% 1.95/0.60 % (1331246)Termination phase: Property scanning
% 1.95/0.60 % (1331246)Time elapsed: 0.010 s
% 1.95/0.60 % (1331246)Peak memory usage: 10 MB
% 1.95/0.60 % (1331246)Instructions burned: 23 (million)
% 1.95/0.60 % (1331248)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=335725683:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 1.95/0.60 % (1331251)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=103111622:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 1.95/0.60 % (1331247)Instruction limit reached!
% 1.95/0.60 % (1331247)------------------------------
% 1.95/0.60 % (1331247)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.95/0.60 % (1331247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.95/0.60 % (1331247)CaDiCaL version: 2.1.3
% 1.95/0.60 % (1331247)Termination reason: Instruction limit
% 1.95/0.60 % (1331247)Termination phase: Property scanning
% 1.95/0.60 % (1331247)Time elapsed: 0.009 s
% 1.95/0.60 % (1331247)Peak memory usage: 10 MB
% 1.95/0.60 % (1331247)Instructions burned: 21 (million)
% 1.95/0.60 % (1331254)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=2128808288:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 1.95/0.60 % (1331219)Instruction limit reached!
% 1.95/0.60 % (1331219)------------------------------
% 1.95/0.60 % (1331219)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.95/0.60 % (1331219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.95/0.60 % (1331219)CaDiCaL version: 2.1.3
% 1.95/0.60 % (1331219)Termination reason: Instruction limit
% 1.95/0.60 % (1331219)Termination phase: Saturation
% 1.95/0.60 % (1331219)Time elapsed: 0.125 s
% 1.95/0.60 % (1331219)Peak memory usage: 14 MB
% 1.95/0.60 % (1331219)Instructions burned: 250 (million)
% 1.95/0.60 % (1331256)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1623163915:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 1.95/0.60 % (1331259)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.95/0.60 % (1331256)Instruction limit reached!
% 1.95/0.60 % (1331256)------------------------------
% 1.95/0.60 % (1331256)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.95/0.60 % (1331256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.95/0.60 % (1331256)CaDiCaL version: 2.1.3
% 1.95/0.60 % (1331256)Termination reason: Instruction limit
% 1.95/0.60 % (1331256)Termination phase: Property scanning
% 1.95/0.60 % (1331256)Time elapsed: 0.019 s
% 1.95/0.60 % (1331256)Peak memory usage: 11 MB
% 1.95/0.60 % (1331256)Instructions burned: 44 (million)
% 1.95/0.60 % (1331259)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4081750108:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 1.95/0.60 % (1331259)Instruction limit reached!
% 1.95/0.60 % (1331259)------------------------------
% 1.95/0.60 % (1331259)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.95/0.60 % (1331259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.95/0.60 % (1331259)CaDiCaL version: 2.1.3
% 1.95/0.60 % (1331259)Termination reason: Instruction limit
% 1.95/0.60 % (1331259)Termination phase: shuffling
% 1.95/0.60 % (1331259)Time elapsed: 0.003 s
% 1.95/0.60 % (1331259)Peak memory usage: 10 MB
% 1.95/0.60 % (1331259)Instructions burned: 7 (million)
% 1.95/0.60 % (1331261)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=224459831:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 1.95/0.60 % (1331262)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=3605205712: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)
% 1.95/0.60 % (1331251)Instruction limit reached!
% 1.95/0.60 % (1331251)------------------------------
% 1.95/0.60 % (1331251)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.95/0.60 % (1331251)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.95/0.60 % (1331251)CaDiCaL version: 2.1.3
% 1.95/0.60 % (1331251)Termination reason: Instruction limit
% 1.95/0.60 % (1331251)Termination phase: Saturation
% 1.95/0.60 % (1331251)Time elapsed: 0.066 s
% 1.95/0.60 % (1331251)Peak memory usage: 13 MB
% 1.95/0.60 % (1331251)Instructions burned: 144 (million)
% 1.95/0.60 % (1331225)Instruction limit reached!
% 1.95/0.60 % (1331225)------------------------------
% 1.95/0.60 % (1331225)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.95/0.60 % (1331225)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.95/0.60 % (1331225)CaDiCaL version: 2.1.3
% 1.95/0.60 % (1331225)Termination reason: Instruction limit
% 1.95/0.60 % (1331225)Termination phase: Saturation
% 1.95/0.60 % (1331225)Time elapsed: 0.157 s
% 1.95/0.60 % (1331225)Peak memory usage: 14 MB
% 1.95/0.60 % (1331225)Instructions burned: 328 (million)
% 1.95/0.60 % (1331192) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1331184-1331192"...
% 1.95/0.60 % (1331265)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 1.95/0.60 % (1331265)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=911917926:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 1.95/0.60 % (1331192)...printing done.
% 1.95/0.60 % (1331192)Refutation found. Thanks to Tanya!
% 1.95/0.60 % SZS status Theorem for theBenchmark
% 1.95/0.60 % SZS output start Proof for theBenchmark
% See solution above
% 1.95/0.60 % (1331192)------------------------------
% 1.95/0.60 % (1331192)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.95/0.60 % (1331192)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.95/0.60 % (1331192)CaDiCaL version: 2.1.3
% 1.95/0.60 % (1331192)Termination reason: Refutation
% 1.95/0.60 % (1331192)Time elapsed: 0.272 s
% 1.95/0.60 % (1331192)Peak memory usage: 19 MB
% 1.95/0.60 % (1331192)Instructions burned: 507 (million)
% 1.95/0.60 % (1331184)Success in time 0.321 s
% 1.95/0.60 % Vampire exiting
%------------------------------------------------------------------------------