%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU649^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:35:56 AM UTC 2026
% Result : Theorem 155.03s 24.02s
% Output : Refutation 155.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 29
% Syntax : Number of formulae : 120 ( 37 unt; 0 typ; 16 def)
% Number of atoms : 3406 ( 946 equ; 0 cnn)
% Maximal formula atoms : 167 ( 28 avg)
% Number of connectives : 2107 ( 168 ~; 155 |; 546 &; 531 @)
% ( 21 <=>; 686 =>; 0 <=; 0 <~>)
% Maximal formula depth : 170 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 338 ( 335 usr; 195 con; 0-4 aty)
% Number of variables : 188 ( 0 ^; 145 !; 43 ?; 188 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_69,type,
set2prop: $i > $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_114,type,
binunion: $i > $i > $i ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_153,type,
iskpair: $i > $o ).
thf(func_def_158,type,
kpair: $i > $i > $i ).
thf(func_def_160,type,
cartprod: $i > $i > $i ).
thf(func_def_177,type,
singleton: $i > $o ).
thf(func_def_179,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_184,type,
atmost1p: $i > $o ).
thf(func_def_185,type,
atleast2p: $i > $o ).
thf(func_def_186,type,
atmost2p: $i > $o ).
thf(func_def_187,type,
upairsetp: $i > $o ).
thf(func_def_191,type,
kfst: $i > $i ).
thf(func_def_208,type,
diff:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > ( X0 > X1 ) > X0 ) ).
thf(func_def_211,type,
sP2: $o > $i > $i > $i > $o ).
thf(func_def_213,type,
sP4: $i > $i > $o ).
thf(func_def_214,type,
sP5: $i > $o ).
thf(func_def_215,type,
sP6: $i > $i > $o ).
thf(func_def_216,type,
sP7: $i > $i > $o ).
thf(func_def_226,type,
sK17: $i > $i > $i ).
thf(func_def_227,type,
sK18: $i > $i > $i ).
thf(func_def_254,type,
sK45: $i > $i > $i ).
thf(func_def_256,type,
sK47: $i > $i ).
thf(func_def_270,type,
sK61: $i > $o ).
thf(func_def_271,type,
sK62: $i > $o ).
thf(func_def_272,type,
sK63: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_273,type,
sK64: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_277,type,
sK68: $i > $i > $o ).
thf(func_def_279,type,
sK70: $i > $i ).
thf(func_def_280,type,
sK71: $i > $i ).
thf(func_def_281,type,
sK72: $i > ( $i > $i > $o ) > $i ).
thf(func_def_282,type,
sK73: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_283,type,
sK74: $i > ( $i > $i > $o ) > $i ).
thf(func_def_292,type,
sK83: $i > $i ).
thf(func_def_308,type,
sK99: $i > $o ).
thf(func_def_311,type,
sK102: $i > ( $i > $o ) > $i ).
thf(func_def_312,type,
sK103: $i > ( $i > $o ) > $i ).
thf(func_def_321,type,
sK112: ( $i > $o ) > $i ).
thf(func_def_322,type,
sK113: $i > $o ).
thf(func_def_323,type,
sK114: $i > $i ).
thf(func_def_328,type,
sK119: $i > $o ).
thf(func_def_331,type,
sK122: $i > ( $i > $o ) > $i ).
thf(func_def_334,type,
sK125: $i > $o ).
thf(func_def_337,type,
sK128: $i > ( $i > $o ) > $i ).
thf(func_def_345,type,
sK136: $i > $i > $i ).
thf(func_def_349,type,
sK140: $i > $i ).
thf(func_def_366,type,
sK157: $i > ( $i > $o ) > $i ).
thf(func_def_367,type,
sK158: $i > $o ).
thf(func_def_370,type,
sK161: ( $i > $o ) > $i > $i ).
thf(func_def_372,type,
sK163: $i > $o ).
thf(func_def_376,type,
sK167: $i > $o ).
thf(func_def_377,type,
sK168: ( $i > $o ) > $i > $i > $i ).
thf(func_def_380,type,
sK171: $i > $o ).
thf(func_def_384,type,
sK175: $i > $o ).
thf(func_def_389,type,
sK180: $i > $o ).
thf(func_def_391,type,
sK182: $i > ( $i > $o ) > $i ).
thf(func_def_405,type,
sK196: $i > $o ).
thf(func_def_411,type,
sK202: $i > $o ).
thf(func_def_412,type,
sK203: $i > $o ).
thf(func_def_413,type,
sK204: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_414,type,
sK205: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_417,type,
sK208: ( $i > $o ) > $i ).
thf(func_def_418,type,
sK209: $i > $o ).
thf(func_def_419,type,
sK210: $i > $o ).
thf(func_def_424,type,
sK215: $i > $o ).
thf(func_def_426,type,
sK217: ( $i > $o ) > $i ).
thf(func_def_427,type,
sK218: ( $i > $o ) > $i ).
thf(func_def_443,type,
sK234: $i > $o ).
thf(func_def_446,type,
sK237: $i > $o ).
thf(func_def_451,type,
sK242: $i > $o ).
thf(func_def_452,type,
sK243: $i > $o ).
thf(func_def_453,type,
sK244: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_454,type,
sK245: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_458,type,
sK249: $i > $o ).
thf(func_def_461,type,
sK252: $i > ( $i > $o ) > $i ).
thf(func_def_471,type,
sK262: $i > ( $i > $o ) > $i ).
thf(func_def_472,type,
sK263: $i > $o ).
thf(func_def_475,type,
sK266: $i > $i ).
thf(func_def_477,type,
sK268: $i > $i ).
thf(func_def_481,type,
sK272: $i > $i ).
thf(func_def_492,type,
sK283: $i > $o ).
thf(func_def_493,type,
sK284: $i > $i ).
thf(func_def_494,type,
sK285: ( $i > $o ) > $i ).
thf(func_def_497,type,
sK288: $i > $i > $i ).
thf(func_def_502,type,
sK293: $i > $i ).
thf(func_def_505,type,
sK296: $i > $i > $i ).
thf(func_def_510,type,
sK301: $i > $o ).
thf(func_def_513,type,
sK304: $o > $i > $i > $i ).
thf(func_def_520,type,
sK311: $i > $i > $i ).
thf(func_def_535,type,
sK326: $i > $o ).
thf(func_def_543,type,
sK334: $i > $o ).
thf(func_def_544,type,
sK335: $i > $o ).
thf(func_def_546,type,
sK337: $i > ( $i > $o ) > $i ).
thf(func_def_553,type,
sK344: $i > $o ).
thf(func_def_556,type,
sK347: $i > $o ).
thf(func_def_561,type,
sK352: $i > $i > $i ).
thf(func_def_576,type,
sK367: $i > $o ).
thf(func_def_579,type,
sK370: $i > ( $i > $o ) > $i ).
thf(func_def_580,type,
sK371: $i > ( $i > $o ) > $i ).
thf(func_def_588,type,
sK379: $i > $i > $i ).
thf(func_def_591,type,
sK382: $i > $i > $i > $i ).
thf(func_def_592,type,
sK383: $i > $i > $i > $i ).
thf(func_def_599,type,
sK390: $i > $i > $i ).
thf(func_def_600,type,
sK391: $i > $i > $i ).
thf(func_def_601,type,
sK392: $i > $i > $i ).
thf(func_def_602,type,
sK393: $i > $i > $i ).
thf(func_def_603,type,
sK394: $i > $i > $i ).
thf(func_def_604,type,
sK395: $i > $i > $i > $i ).
thf(func_def_605,type,
sK396: $i > $i ).
thf(func_def_606,type,
sK397: $i > $i ).
thf(func_def_607,type,
sK398: $i > $i ).
thf(func_def_608,type,
sK399: $i > $i ).
thf(func_def_609,type,
sK400: $i > $i > $i > $i ).
thf(func_def_610,type,
sK401: $i > $i > $i > $i ).
thf(func_def_611,type,
sK402: $i > $i > $i ).
thf(func_def_612,type,
sK403: $i > $i > $i ).
thf(func_def_613,type,
sK404: $i > $i > $i ).
thf(func_def_614,type,
sK405: $i > $i ).
thf(func_def_616,type,
sK407: $i > $i ).
thf(func_def_617,type,
sK408: $i > $i ).
thf(func_def_624,type,
sK415: $i > $o ).
thf(func_def_663,type,
sK454: $i > $i > $i ).
thf(func_def_664,type,
sK455: $i > ( $i > $o ) > $i ).
thf(func_def_665,type,
sK456: $i > $o ).
thf(func_def_671,type,
sF462: $i > $i ).
thf(func_def_672,type,
sF463: $i > $i ).
thf(func_def_677,type,
ph468:
!>[X0: $tType] : X0 ).
thf(f19887,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f2603,f3149,f4255,f4559,f4590,f5104,f5313,f5535,f5743,f5879,f5965,f19873]) ).
thf(f19873,plain,
( ~ spl467_10
| ~ spl467_157
| ~ spl467_173
| ~ spl467_402
| ~ spl467_664
| ~ spl467_708 ),
inference(avatar_contradiction_clause,[status(thm)],[f19872]) ).
thf(f19872,plain,
( $false
| ~ spl467_10
| ~ spl467_157
| ~ spl467_173
| ~ spl467_402
| ~ spl467_664
| ~ spl467_708 ),
inference(trivial_inequality_removal,[status(thm)],[f19851]) ).
thf(f19851,plain,
( ( $true != $true )
| ~ spl467_10
| ~ spl467_157
| ~ spl467_173
| ~ spl467_402
| ~ spl467_664
| ~ spl467_708 ),
inference(superposition,[status(thm)],[f7706,f19499]) ).
thf(f19499,plain,
( ! [X0: $i] :
( ( subset @ sF465 @ ( setadjoin @ sK356 @ X0 ) )
= $true )
| ~ spl467_10
| ~ spl467_173
| ~ spl467_664
| ~ spl467_708 ),
inference(trivial_inequality_removal,[status(thm)],[f19481]) ).
thf(f19481,plain,
( ! [X0: $i] :
( ( ( subset @ sF465 @ ( setadjoin @ sK356 @ X0 ) )
= $true )
| ( $true != $true ) )
| ~ spl467_10
| ~ spl467_173
| ~ spl467_664
| ~ spl467_708 ),
inference(superposition,[status(thm)],[f18760,f2507]) ).
thf(f2507,plain,
( ! [X2: $i,X0: $i] :
( ( in @ X2 @ ( setadjoin @ X2 @ X0 ) )
= $true )
| ~ spl467_10 ),
inference(avatar_component_clause,[status(thm)],[f2506]) ).
thf(f2506,definition,
( spl467_10
<=> ! [X2: $i,X0: $i] :
( ( in @ X2 @ ( setadjoin @ X2 @ X0 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl467_10])],[avatar_definition]) ).
thf(f18760,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ sK356 @ X0 ) )
| ( ( subset @ sF465 @ X0 )
= $true ) )
| ~ spl467_173
| ~ spl467_664
| ~ spl467_708 ),
inference(duplicate_literal_removal,[status(thm)],[f18759]) ).
thf(f18759,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ sK356 @ X0 ) )
| ( ( subset @ sF465 @ X0 )
= $true )
| ( ( subset @ sF465 @ X0 )
= $true ) )
| ~ spl467_173
| ~ spl467_664
| ~ spl467_708 ),
inference(superposition,[status(thm)],[f5534,f16182]) ).
thf(f16182,plain,
( ! [X0: $i] :
( ( ( sK45 @ X0 @ sF465 )
= sK356 )
| ( ( subset @ sF465 @ X0 )
= $true ) )
| ~ spl467_173
| ~ spl467_708 ),
inference(trivial_inequality_removal,[status(thm)],[f16181]) ).
thf(f16181,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( subset @ sF465 @ X0 )
= $true )
| ( ( sK45 @ X0 @ sF465 )
= sK356 ) )
| ~ spl467_173
| ~ spl467_708 ),
inference(superposition,[status(thm)],[f16164,f5742]) ).
thf(f5742,plain,
( ! [X3: $i,X4: $i] :
( ( ( in @ ( sK45 @ X4 @ X3 ) @ X3 )
= $true )
| ( ( subset @ X3 @ X4 )
= $true ) )
| ~ spl467_708 ),
inference(avatar_component_clause,[status(thm)],[f5741]) ).
thf(f5741,definition,
( spl467_708
<=> ! [X4: $i,X3: $i] :
( ( ( in @ ( sK45 @ X4 @ X3 ) @ X3 )
= $true )
| ( ( subset @ X3 @ X4 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl467_708])],[avatar_definition]) ).
thf(f16164,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sF465 )
!= $true )
| ( sK356 = X0 ) )
| ~ spl467_173 ),
inference(duplicate_literal_removal,[status(thm)],[f16155]) ).
thf(f16155,plain,
( ! [X0: $i] :
( ( sK356 = X0 )
| ( sK356 = X0 )
| ( ( in @ X0 @ sF465 )
!= $true ) )
| ~ spl467_173 ),
inference(superposition,[status(thm)],[f3218,f6020]) ).
thf(f6020,plain,
( ( setadjoin @ sK356 @ ( setadjoin @ sK356 @ emptyset ) )
= sF465 ),
inference(superposition,[status(thm)],[f6000,f6004]) ).
thf(f6004,plain,
( ( sF462 @ ( setadjoin @ sK356 @ emptyset ) )
= sF465 ),
inference(backward_demodulation,[status(thm)],[f2346,f6003]) ).
thf(f6003,plain,
( sF464
= ( setadjoin @ sK356 @ emptyset ) ),
inference(backward_demodulation,[status(thm)],[f2345,f6002]) ).
thf(f6002,plain,
! [X1: $i] :
( ( sF463 @ X1 )
= ( setadjoin @ sK356 @ X1 ) ),
inference(argument_congruence,[status(thm)],[f6001]) ).
thf(f6001,plain,
( sF463
= ( setadjoin @ sK356 ) ),
inference(forward_demodulation,[status(thm)],[f2344,f2020]) ).
thf(f2020,plain,
sK357 = sK356,
inference(cnf_transformation,[status(thm)],[f1321]) ).
thf(f1321,plain,
( ( emptyinPowerset = $true )
& ( upairsubunion = $true )
& ( nonemptyE1 = $true )
& ( wellorderingAx = $true )
& ( subset2powerset = $true )
& ( setukpairIR = $true )
& ( exuE1 = $true )
& ( exuI2 = $true )
& ( ex1E1 = $true )
& ( binintersectEL = $true )
& ( exuEu = $true )
& ( inPowerset = $true )
& ( exu__Cong = $true )
& ( emptysetE = $true )
& ( cartprodfstin = $true )
& ( upairsetIR = $true )
& ( setminusER = $true )
& ( dsetconstrEL = $true )
& ( binintersectSubset5 = $true )
& ( setadjoinE = $true )
& ( dsetconstrI = $true )
& ( ubforcartprodlem3 = $true )
& ( theprop = $true )
& ( setminusLsub = $true )
& ( powersetI1 = $true )
& ( singletoninpowunion = $true )
& ( binintersectI = $true )
& ( symdiffI1 = $true )
& ( subsetE = $true )
& ( kpairp = $true )
& ( foundationAx = $true )
& ( subsetI2 = $true )
& ( descrp = $true )
& ( setunionsingleton1 = $true )
& ( setadjoinIR = $true )
& ( emptyInPowerset = $true )
& ( setunion__Cong = $true )
& ( omega0Ax = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( powersetE = $true )
& ( powersetI = $true )
& ( uniqinunit = $true )
& ( emptysetimpfalse = $true )
& ( binunionIL = $true )
& ( vacuousDall = $true )
& ( prop2set2propI = $true )
& ( emptyinunitempty = $true )
& ( quantDeMorgan2 = $true )
& ( sepInPowerset = $true )
& ( setunionsingleton2 = $true )
& ( emptyE1 = $true )
& ( symdiffI2 = $true )
& ( powerset__Cong = $true )
& ( setunionAx = $true )
& ( exuE3e = $true )
& ( setminusILneg = $true )
& ( setextAx = $true )
& ( singletonsubset = $true )
& ( singletonsswitch = $true )
& ( noeltsimpempty = $true )
& ( binintersectSubset2 = $true )
& ( descr__Cong = $true )
& ( disjointsetsI1 = $true )
& ( notinsingleton = $true )
& ( subsetI1 = $true )
& ( emptyI = $true )
& ( exuI3 = $true )
& ( singletonsuniq = $true )
& ( ex1I2 = $true )
& ( prop2setI = $true )
& ( cartprodmempair = $true )
& ( setunionE2 = $true )
& ( nonemptyI1 = $true )
& ( powersetE1 = $true )
& ( binintersectRsub = $true )
& ( upairsetE = $true )
& ( upairset2IR = $true )
& ( omega__Cong = $true )
& ( setunionI = $true )
& ( exuE2 = $true )
& ( binintersectSubset1 = $true )
& ( in__Cong = $true )
& ( emptysetAx = $true )
& ( setminusELneg = $true )
& ( kfstsingleton = $true )
& ( quantDeMorgan1 = $true )
& ( setext = $true )
& ( setadjoin__Cong = $true )
& ( cartprodmempair1 = $true )
& ( notequalI2 = $true )
& ( setukpairinjL = $true )
& ( setadjoinSub2 = $true )
& ( secondinupair = $true )
& ( replAx = $true )
& ( sepSubset = $true )
& ( singletonprop = $true )
& ( notsubsetI = $true )
& ( setukpairIL = $true )
& ( setadjoinIL = $true )
& ( ex1I = $true )
& ( eqinunit = $true )
& ( cartprodpairin = $true )
& ( setminusI = $true )
& ( setunionsingleton = $true )
& ( prop2setE = $true )
& ( kfstpairEq = $true )
& ( setukpairinjL2 = $true )
& ( ubforcartprodlem2 = $true )
& ( upairinpowunion = $true )
& ( nonemptyImpWitness = $true )
& ( symdiffE = $true )
& ( binunionE = $true )
& ( quantDeMorgan3 = $true )
& ( notequalI1 = $true )
& ( ubforcartprodlem1 = $true )
& ( emptysetsubset = $true )
& ( emptyset__Cong = $true )
& ( binintersectSubset4 = $true )
& ( eqimpsubset1 = $true )
& ( symdiffIneg2 = $true )
& ( omegaSAx = $true )
& ( exuI1 = $true )
& ( setminusSubset1 = $true )
& ( powersetsubset = $true )
& ( setukpairinjL1 = $true )
& ( upairset2E = $true )
& ( binintersectSubset3 = $true )
& ( exuE3u = $true )
& ( dsetconstrER = $true )
& ( quantDeMorgan4 = $true )
& ( setextsub = $true )
& ( setminusEL = $true )
& ( symdiffIneg1 = $true )
& ( notdexE = $true )
& ( subsetE2 = $true )
& ( subsetRefl = $true )
& ( setminusERneg = $true )
& ( subsetemptysetimpeq = $true )
& ( bs114d = $true )
& ( ( setadjoin @ sK356 @ ( setadjoin @ sK357 @ emptyset ) )
!= ( setadjoin @ sK356 @ emptyset ) )
& ( sK357 = sK356 )
& ( notinemptyset = $true )
& ( upairsetIL = $true )
& ( singletoninpowerset = $true )
& ( setoftrueEq = $true )
& ( setbeta = $true )
& ( setminusIRneg = $true )
& ( nonemptyI = $true )
& ( binunionRsub = $true )
& ( setminusSubset2 = $true )
& ( notdallE = $true )
& ( omegaIndAx = $true )
& ( setadjoinSub = $true )
& ( kpairiskpair = $true )
& ( subsetTrans = $true )
& ( binunionLsub = $true )
& ( binintersectLsub = $true )
& ( setadjoinOr = $true )
& ( dsetconstr__Cong = $true )
& ( eqimpsubset2 = $true )
& ( binunionEcases = $true )
& ( binintersectER = $true )
& ( inCongP = $true )
& ( subPowSU = $true )
& ( binunionIR = $true )
& ( setunionE = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK356,sK357])],[f589,f1320]) ).
thf(f1320,plain,
( ? [X0: $i,X1: $i] :
( ( ( setadjoin @ X0 @ emptyset )
!= ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
& ( X0 = X1 ) )
=> ( ( ( setadjoin @ sK356 @ ( setadjoin @ sK357 @ emptyset ) )
!= ( setadjoin @ sK356 @ emptyset ) )
& ( sK357 = sK356 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f589,plain,
( ( emptyinPowerset = $true )
& ( upairsubunion = $true )
& ( nonemptyE1 = $true )
& ( wellorderingAx = $true )
& ( subset2powerset = $true )
& ( setukpairIR = $true )
& ( exuE1 = $true )
& ( exuI2 = $true )
& ( ex1E1 = $true )
& ( binintersectEL = $true )
& ( exuEu = $true )
& ( inPowerset = $true )
& ( exu__Cong = $true )
& ( emptysetE = $true )
& ( cartprodfstin = $true )
& ( upairsetIR = $true )
& ( setminusER = $true )
& ( dsetconstrEL = $true )
& ( binintersectSubset5 = $true )
& ( setadjoinE = $true )
& ( dsetconstrI = $true )
& ( ubforcartprodlem3 = $true )
& ( theprop = $true )
& ( setminusLsub = $true )
& ( powersetI1 = $true )
& ( singletoninpowunion = $true )
& ( binintersectI = $true )
& ( symdiffI1 = $true )
& ( subsetE = $true )
& ( kpairp = $true )
& ( foundationAx = $true )
& ( subsetI2 = $true )
& ( descrp = $true )
& ( setunionsingleton1 = $true )
& ( setadjoinIR = $true )
& ( emptyInPowerset = $true )
& ( setunion__Cong = $true )
& ( omega0Ax = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( powersetE = $true )
& ( powersetI = $true )
& ( uniqinunit = $true )
& ( emptysetimpfalse = $true )
& ( binunionIL = $true )
& ( vacuousDall = $true )
& ( prop2set2propI = $true )
& ( emptyinunitempty = $true )
& ( quantDeMorgan2 = $true )
& ( sepInPowerset = $true )
& ( setunionsingleton2 = $true )
& ( emptyE1 = $true )
& ( symdiffI2 = $true )
& ( powerset__Cong = $true )
& ( setunionAx = $true )
& ( exuE3e = $true )
& ( setminusILneg = $true )
& ( setextAx = $true )
& ( singletonsubset = $true )
& ( singletonsswitch = $true )
& ( noeltsimpempty = $true )
& ( binintersectSubset2 = $true )
& ( descr__Cong = $true )
& ( disjointsetsI1 = $true )
& ( notinsingleton = $true )
& ( subsetI1 = $true )
& ( emptyI = $true )
& ( exuI3 = $true )
& ( singletonsuniq = $true )
& ( ex1I2 = $true )
& ( prop2setI = $true )
& ( cartprodmempair = $true )
& ( setunionE2 = $true )
& ( nonemptyI1 = $true )
& ( powersetE1 = $true )
& ( binintersectRsub = $true )
& ( upairsetE = $true )
& ( upairset2IR = $true )
& ( omega__Cong = $true )
& ( setunionI = $true )
& ( exuE2 = $true )
& ( binintersectSubset1 = $true )
& ( in__Cong = $true )
& ( emptysetAx = $true )
& ( setminusELneg = $true )
& ( kfstsingleton = $true )
& ( quantDeMorgan1 = $true )
& ( setext = $true )
& ( setadjoin__Cong = $true )
& ( cartprodmempair1 = $true )
& ( notequalI2 = $true )
& ( setukpairinjL = $true )
& ( setadjoinSub2 = $true )
& ( secondinupair = $true )
& ( replAx = $true )
& ( sepSubset = $true )
& ( singletonprop = $true )
& ( notsubsetI = $true )
& ( setukpairIL = $true )
& ( setadjoinIL = $true )
& ( ex1I = $true )
& ( eqinunit = $true )
& ( cartprodpairin = $true )
& ( setminusI = $true )
& ( setunionsingleton = $true )
& ( prop2setE = $true )
& ( kfstpairEq = $true )
& ( setukpairinjL2 = $true )
& ( ubforcartprodlem2 = $true )
& ( upairinpowunion = $true )
& ( nonemptyImpWitness = $true )
& ( symdiffE = $true )
& ( binunionE = $true )
& ( quantDeMorgan3 = $true )
& ( notequalI1 = $true )
& ( ubforcartprodlem1 = $true )
& ( emptysetsubset = $true )
& ( emptyset__Cong = $true )
& ( binintersectSubset4 = $true )
& ( eqimpsubset1 = $true )
& ( symdiffIneg2 = $true )
& ( omegaSAx = $true )
& ( exuI1 = $true )
& ( setminusSubset1 = $true )
& ( powersetsubset = $true )
& ( setukpairinjL1 = $true )
& ( upairset2E = $true )
& ( binintersectSubset3 = $true )
& ( exuE3u = $true )
& ( dsetconstrER = $true )
& ( quantDeMorgan4 = $true )
& ( setextsub = $true )
& ( setminusEL = $true )
& ( symdiffIneg1 = $true )
& ( notdexE = $true )
& ( subsetE2 = $true )
& ( subsetRefl = $true )
& ( setminusERneg = $true )
& ( subsetemptysetimpeq = $true )
& ( bs114d = $true )
& ? [X0: $i,X1: $i] :
( ( ( setadjoin @ X0 @ emptyset )
!= ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
& ( X0 = X1 ) )
& ( notinemptyset = $true )
& ( upairsetIL = $true )
& ( singletoninpowerset = $true )
& ( setoftrueEq = $true )
& ( setbeta = $true )
& ( setminusIRneg = $true )
& ( nonemptyI = $true )
& ( binunionRsub = $true )
& ( setminusSubset2 = $true )
& ( notdallE = $true )
& ( omegaIndAx = $true )
& ( setadjoinSub = $true )
& ( kpairiskpair = $true )
& ( subsetTrans = $true )
& ( binunionLsub = $true )
& ( binintersectLsub = $true )
& ( setadjoinOr = $true )
& ( dsetconstr__Cong = $true )
& ( eqimpsubset2 = $true )
& ( binunionEcases = $true )
& ( binintersectER = $true )
& ( inCongP = $true )
& ( subPowSU = $true )
& ( binunionIR = $true )
& ( setunionE = $true ) ),
inference(flattening,[status(thm)],[f588]) ).
thf(f588,plain,
( ? [X0: $i,X1: $i] :
( ( ( setadjoin @ X0 @ emptyset )
!= ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
& ( X0 = X1 ) )
& ( setukpairinjL = $true )
& ( setukpairinjL2 = $true )
& ( cartprodfstin = $true )
& ( kfstpairEq = $true )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( singletonsuniq = $true )
& ( ex1I2 = $true )
& ( ex1I = $true )
& ( ex1E1 = $true )
& ( singletonprop = $true )
& ( setunionsingleton = $true )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( setunionE2 = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( cartprodpairin = $true )
& ( ubforcartprodlem3 = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( upairsubunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f253]) ).
thf(f253,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( ( setadjoin @ X0 @ emptyset )
= ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f252]) ).
thf(f252,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( ( setadjoin @ X0 @ emptyset )
= ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f173]) ).
thf(f173,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( ( setadjoin @ X1 @ emptyset )
= ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f172]) ).
thf(f172,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( ( setadjoin @ X1 @ emptyset )
= ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.u7Pd4WLIgv/DTF2THF_23265.p',setukpairinjR11) ).
thf(f2344,definition,
( ( setadjoin @ sK357 )
= sF463 ),
introduced(definition,[],[function_definition]) ).
thf(f2345,definition,
( ( sF463 @ emptyset )
= sF464 ),
introduced(definition,[],[function_definition]) ).
thf(f2346,definition,
( ( sF462 @ sF464 )
= sF465 ),
introduced(definition,[],[function_definition]) ).
thf(f6000,plain,
! [X1: $i] :
( ( sF462 @ X1 )
= ( setadjoin @ sK356 @ X1 ) ),
inference(argument_congruence,[status(thm)],[f2343]) ).
thf(f2343,definition,
( sF462
= ( setadjoin @ sK356 ) ),
introduced(definition,[],[function_definition]) ).
thf(f3218,plain,
( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X4 @ ( setadjoin @ X5 @ ( setadjoin @ X3 @ emptyset ) ) ) )
| ( X4 = X5 )
| ( X3 = X4 ) )
| ~ spl467_173 ),
inference(avatar_component_clause,[status(thm)],[f3217]) ).
thf(f3217,definition,
( spl467_173
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( X3 = X4 )
| ( X4 = X5 )
| ( $true
!= ( in @ X4 @ ( setadjoin @ X5 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl467_173])],[avatar_definition]) ).
thf(f5534,plain,
( ! [X3: $i,X4: $i] :
( ( $true
!= ( in @ ( sK45 @ X4 @ X3 ) @ X4 ) )
| ( ( subset @ X3 @ X4 )
= $true ) )
| ~ spl467_664 ),
inference(avatar_component_clause,[status(thm)],[f5533]) ).
thf(f5533,definition,
( spl467_664
<=> ! [X4: $i,X3: $i] :
( ( $true
!= ( in @ ( sK45 @ X4 @ X3 ) @ X4 ) )
| ( ( subset @ X3 @ X4 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl467_664])],[avatar_definition]) ).
thf(f7706,plain,
( ( ( subset @ sF465 @ ( setadjoin @ sK356 @ emptyset ) )
!= $true )
| ~ spl467_157
| ~ spl467_402 ),
inference(subsumption_resolution,[status(thm)],[f7698,f6022]) ).
thf(f6022,plain,
( sF465
!= ( setadjoin @ sK356 @ emptyset ) ),
inference(backward_demodulation,[status(thm)],[f2348,f6019]) ).
thf(f6019,plain,
( sF466
= ( setadjoin @ sK356 @ emptyset ) ),
inference(backward_demodulation,[status(thm)],[f2347,f6000]) ).
thf(f2347,definition,
( ( sF462 @ emptyset )
= sF466 ),
introduced(definition,[],[function_definition]) ).
thf(f2348,plain,
sF466 != sF465,
inference(definition_folding,[status(thm)],[f2021,f2347,f2343,f2346,f2345,f2344,f2343]) ).
thf(f2021,plain,
( ( setadjoin @ sK356 @ ( setadjoin @ sK357 @ emptyset ) )
!= ( setadjoin @ sK356 @ emptyset ) ),
inference(cnf_transformation,[status(thm)],[f1321]) ).
thf(f7698,plain,
( ( sF465
= ( setadjoin @ sK356 @ emptyset ) )
| ( ( subset @ sF465 @ ( setadjoin @ sK356 @ emptyset ) )
!= $true )
| ~ spl467_157
| ~ spl467_402 ),
inference(trivial_inequality_removal,[status(thm)],[f7696]) ).
thf(f7696,plain,
( ( sF465
= ( setadjoin @ sK356 @ emptyset ) )
| ( ( subset @ sF465 @ ( setadjoin @ sK356 @ emptyset ) )
!= $true )
| ( $true != $true )
| ~ spl467_157
| ~ spl467_402 ),
inference(superposition,[status(thm)],[f4254,f6068]) ).
thf(f6068,plain,
( ( ( subset @ ( setadjoin @ sK356 @ emptyset ) @ sF465 )
= $true )
| ~ spl467_157 ),
inference(superposition,[status(thm)],[f3148,f6020]) ).
thf(f3148,plain,
( ! [X0: $i,X1: $i] :
( ( subset @ X1 @ ( setadjoin @ X0 @ X1 ) )
= $true )
| ~ spl467_157 ),
inference(avatar_component_clause,[status(thm)],[f3147]) ).
thf(f3147,definition,
( spl467_157
<=> ! [X0: $i,X1: $i] :
( ( subset @ X1 @ ( setadjoin @ X0 @ X1 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl467_157])],[avatar_definition]) ).
thf(f4254,plain,
( ! [X2: $i,X3: $i] :
( ( $true
!= ( subset @ X2 @ X3 ) )
| ( ( subset @ X3 @ X2 )
!= $true )
| ( X2 = X3 ) )
| ~ spl467_402 ),
inference(avatar_component_clause,[status(thm)],[f4253]) ).
thf(f4253,definition,
( spl467_402
<=> ! [X2: $i,X3: $i] :
( ( ( subset @ X3 @ X2 )
!= $true )
| ( X2 = X3 )
| ( $true
!= ( subset @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl467_402])],[avatar_definition]) ).
thf(f5965,plain,
spl467_483,
inference(avatar_split_clause,[status(thm)],[f2096,f4647]) ).
thf(f4647,definition,
( spl467_483
<=> ( subsetI1 = $true ) ),
introduced(definition,[new_symbols(naming,[spl467_483])],[avatar_definition]) ).
thf(f2096,plain,
subsetI1 = $true,
inference(cnf_transformation,[status(thm)],[f1321]) ).
thf(f5879,plain,
spl467_310,
inference(avatar_split_clause,[status(thm)],[f2035,f3824]) ).
thf(f3824,definition,
( spl467_310
<=> ( upairset2E = $true ) ),
introduced(definition,[new_symbols(naming,[spl467_310])],[avatar_definition]) ).
thf(f2035,plain,
upairset2E = $true,
inference(cnf_transformation,[status(thm)],[f1321]) ).
thf(f5743,plain,
( spl467_708
| ~ spl467_483 ),
inference(avatar_split_clause,[status(thm)],[f1549,f4647,f5741]) ).
thf(f1549,plain,
! [X3: $i,X4: $i] :
( ( ( in @ ( sK45 @ X4 @ X3 ) @ X3 )
= $true )
| ( ( subset @ X3 @ X4 )
= $true )
| ( subsetI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f801]) ).
thf(f801,plain,
( ( ( subsetI1 = $true )
| ( ( ( subset @ sK43 @ sK44 )
!= $true )
& ! [X2: $i] :
( ( $true
= ( in @ X2 @ sK44 ) )
| ( ( in @ X2 @ sK43 )
!= $true ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( ( subset @ X3 @ X4 )
= $true )
| ( ( $true
!= ( in @ ( sK45 @ X4 @ X3 ) @ X4 ) )
& ( ( in @ ( sK45 @ X4 @ X3 ) @ X3 )
= $true ) ) )
| ( subsetI1 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK43,sK44,sK45])],[f798,f800,f799]) ).
thf(f799,plain,
( ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) )
=> ( ( ( subset @ sK43 @ sK44 )
!= $true )
& ! [X2: $i] :
( ( $true
= ( in @ X2 @ sK44 ) )
| ( ( in @ X2 @ sK43 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f800,plain,
! [X3: $i,X4: $i] :
( ? [X5: $i] :
( ( ( in @ X5 @ X4 )
!= $true )
& ( ( in @ X5 @ X3 )
= $true ) )
=> ( ( $true
!= ( in @ ( sK45 @ X4 @ X3 ) @ X4 ) )
& ( ( in @ ( sK45 @ X4 @ X3 ) @ X3 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f798,plain,
( ( ( subsetI1 = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) ) )
& ( ! [X3: $i,X4: $i] :
( ( ( subset @ X3 @ X4 )
= $true )
| ? [X5: $i] :
( ( ( in @ X5 @ X4 )
!= $true )
& ( ( in @ X5 @ X3 )
= $true ) ) )
| ( subsetI1 != $true ) ) ),
inference(rectify,[status(thm)],[f797]) ).
thf(f797,plain,
( ( ( subsetI1 = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
& ! [X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) ) ) )
& ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) ) )
| ( subsetI1 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f650]) ).
thf(f650,plain,
( ( subsetI1 = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ? [X2: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ X0 )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f460]) ).
thf(f460,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) )
=> ( ( subset @ X0 @ X1 )
= $true ) )
<=> ( subsetI1 = $true ) ),
inference(fool_elimination,[status(thm)],[f459]) ).
thf(f459,plain,
! [X0: $i,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) )
=> ( subset @ X0 @ X1 ) )
= subsetI1 ),
inference(rectify,[status(thm)],[f78]) ).
thf(f78,axiom,
! [X3: $i,X4: $i] :
( ( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( in @ X1 @ X4 ) )
=> ( subset @ X3 @ X4 ) )
= subsetI1 ),
file('/export/starexec/sandbox/tmp/tmp.u7Pd4WLIgv/DTF2THF_23265.p',subsetI1) ).
thf(f5535,plain,
( ~ spl467_483
| spl467_664 ),
inference(avatar_split_clause,[status(thm)],[f1550,f5533,f4647]) ).
thf(f1550,plain,
! [X3: $i,X4: $i] :
( ( $true
!= ( in @ ( sK45 @ X4 @ X3 ) @ X4 ) )
| ( subsetI1 != $true )
| ( ( subset @ X3 @ X4 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f801]) ).
thf(f5313,plain,
spl467_156,
inference(avatar_split_clause,[status(thm)],[f2008,f3143]) ).
thf(f3143,definition,
( spl467_156
<=> ( setadjoinSub = $true ) ),
introduced(definition,[new_symbols(naming,[spl467_156])],[avatar_definition]) ).
thf(f2008,plain,
setadjoinSub = $true,
inference(cnf_transformation,[status(thm)],[f1321]) ).
thf(f5104,plain,
( ~ spl467_310
| spl467_173 ),
inference(avatar_split_clause,[status(thm)],[f1621,f3217,f3824]) ).
thf(f1621,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( upairset2E != $true )
| ( X0 = X2 )
| ( X1 = X2 )
| ( ( in @ X2 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f881]) ).
thf(f881,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( ( in @ X2 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
!= $true )
| ( X1 = X2 ) )
| ( upairset2E != $true ) )
& ( ( upairset2E = $true )
| ( ( sK96 != sK98 )
& ( ( in @ sK98 @ ( setadjoin @ sK96 @ ( setadjoin @ sK97 @ emptyset ) ) )
= $true )
& ( sK98 != sK97 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK96,sK97,sK98])],[f879,f880]) ).
thf(f880,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( X3 != X5 )
& ( ( in @ X5 @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) )
= $true )
& ( X4 != X5 ) )
=> ( ( sK96 != sK98 )
& ( ( in @ sK98 @ ( setadjoin @ sK96 @ ( setadjoin @ sK97 @ emptyset ) ) )
= $true )
& ( sK98 != sK97 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f879,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( ( in @ X2 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
!= $true )
| ( X1 = X2 ) )
| ( upairset2E != $true ) )
& ( ( upairset2E = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( X3 != X5 )
& ( ( in @ X5 @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) )
= $true )
& ( X4 != X5 ) ) ) ),
inference(rectify,[status(thm)],[f878]) ).
thf(f878,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( ( in @ X2 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
!= $true )
| ( X1 = X2 ) )
| ( upairset2E != $true ) )
& ( ( upairset2E = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( X0 != X2 )
& ( ( in @ X2 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= $true )
& ( X1 != X2 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f711]) ).
thf(f711,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( ( in @ X2 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
!= $true )
| ( X1 = X2 ) )
<=> ( upairset2E = $true ) ),
inference(flattening,[status(thm)],[f710]) ).
thf(f710,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X1 = X2 )
| ( ( in @ X2 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
!= $true ) )
<=> ( upairset2E = $true ) ),
inference(ennf_transformation,[status(thm)],[f195]) ).
thf(f195,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= $true )
=> ( ( X0 = X2 )
| ( X1 = X2 ) ) )
<=> ( upairset2E = $true ) ),
inference(fool_elimination,[status(thm)],[f194]) ).
thf(f194,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
=> ( ( X0 = X2 )
| ( X1 = X2 ) ) )
= upairset2E ),
inference(rectify,[status(thm)],[f145]) ).
thf(f145,axiom,
! [X1: $i,X2: $i,X8: $i] :
( ( ( in @ X8 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
=> ( ( X1 = X8 )
| ( X2 = X8 ) ) )
= upairset2E ),
file('/export/starexec/sandbox/tmp/tmp.u7Pd4WLIgv/DTF2THF_23265.p',upairset2E) ).
thf(f4590,plain,
spl467_32,
inference(avatar_split_clause,[status(thm)],[f2062,f2600]) ).
thf(f2600,definition,
( spl467_32
<=> ( setadjoinIL = $true ) ),
introduced(definition,[new_symbols(naming,[spl467_32])],[avatar_definition]) ).
thf(f2062,plain,
setadjoinIL = $true,
inference(cnf_transformation,[status(thm)],[f1321]) ).
thf(f4559,plain,
spl467_141,
inference(avatar_split_clause,[status(thm)],[f2030,f3077]) ).
thf(f3077,definition,
( spl467_141
<=> ( setextsub = $true ) ),
introduced(definition,[new_symbols(naming,[spl467_141])],[avatar_definition]) ).
thf(f2030,plain,
setextsub = $true,
inference(cnf_transformation,[status(thm)],[f1321]) ).
thf(f4255,plain,
( spl467_402
| ~ spl467_141 ),
inference(avatar_split_clause,[status(thm)],[f2162,f3077,f4253]) ).
thf(f2162,plain,
! [X2: $i,X3: $i] :
( ( ( subset @ X3 @ X2 )
!= $true )
| ( $true
!= ( subset @ X2 @ X3 ) )
| ( X2 = X3 )
| ( setextsub != $true ) ),
inference(cnf_transformation,[status(thm)],[f1325]) ).
thf(f1325,plain,
( ( ( setextsub = $true )
| ( ( ( subset @ sK358 @ sK359 )
= $true )
& ( ( subset @ sK359 @ sK358 )
= $true )
& ( sK358 != sK359 ) ) )
& ( ! [X2: $i,X3: $i] :
( ( $true
!= ( subset @ X2 @ X3 ) )
| ( ( subset @ X3 @ X2 )
!= $true )
| ( X2 = X3 ) )
| ( setextsub != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK358,sK359])],[f1323,f1324]) ).
thf(f1324,plain,
( ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
& ( ( subset @ X1 @ X0 )
= $true )
& ( X0 != X1 ) )
=> ( ( ( subset @ sK358 @ sK359 )
= $true )
& ( ( subset @ sK359 @ sK358 )
= $true )
& ( sK358 != sK359 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1323,plain,
( ( ( setextsub = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
& ( ( subset @ X1 @ X0 )
= $true )
& ( X0 != X1 ) ) )
& ( ! [X2: $i,X3: $i] :
( ( $true
!= ( subset @ X2 @ X3 ) )
| ( ( subset @ X3 @ X2 )
!= $true )
| ( X2 = X3 ) )
| ( setextsub != $true ) ) ),
inference(rectify,[status(thm)],[f1322]) ).
thf(f1322,plain,
( ( ( setextsub = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
& ( ( subset @ X1 @ X0 )
= $true )
& ( X0 != X1 ) ) )
& ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( subset @ X1 @ X0 )
!= $true )
| ( X0 = X1 ) )
| ( setextsub != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f662]) ).
thf(f662,plain,
( ( setextsub = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( subset @ X1 @ X0 )
!= $true )
| ( X0 = X1 ) ) ),
inference(flattening,[status(thm)],[f661]) ).
thf(f661,plain,
( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( subset @ X1 @ X0 )
!= $true )
| ( ( subset @ X0 @ X1 )
!= $true ) )
<=> ( setextsub = $true ) ),
inference(ennf_transformation,[status(thm)],[f379]) ).
thf(f379,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
=> ( ( ( subset @ X1 @ X0 )
= $true )
=> ( X0 = X1 ) ) )
<=> ( setextsub = $true ) ),
inference(fool_elimination,[status(thm)],[f378]) ).
thf(f378,plain,
( setextsub
= ( ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X0 )
=> ( X0 = X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f93]) ).
thf(f93,axiom,
( setextsub
= ( ! [X3: $i,X4: $i] :
( ( subset @ X3 @ X4 )
=> ( ( subset @ X4 @ X3 )
=> ( X3 = X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.u7Pd4WLIgv/DTF2THF_23265.p',setextsub) ).
thf(f3149,plain,
( ~ spl467_156
| spl467_157 ),
inference(avatar_split_clause,[status(thm)],[f2171,f3147,f3143]) ).
thf(f2171,plain,
! [X0: $i,X1: $i] :
( ( setadjoinSub != $true )
| ( ( subset @ X1 @ ( setadjoin @ X0 @ X1 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f1337]) ).
thf(f1337,plain,
( ( ! [X0: $i,X1: $i] :
( ( subset @ X1 @ ( setadjoin @ X0 @ X1 ) )
= $true )
| ( setadjoinSub != $true ) )
& ( ( setadjoinSub = $true )
| ( ( subset @ sK366 @ ( setadjoin @ sK365 @ sK366 ) )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK365,sK366])],[f1335,f1336]) ).
thf(f1336,plain,
( ? [X2: $i,X3: $i] :
( ( subset @ X3 @ ( setadjoin @ X2 @ X3 ) )
!= $true )
=> ( ( subset @ sK366 @ ( setadjoin @ sK365 @ sK366 ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1335,plain,
( ( ! [X0: $i,X1: $i] :
( ( subset @ X1 @ ( setadjoin @ X0 @ X1 ) )
= $true )
| ( setadjoinSub != $true ) )
& ( ( setadjoinSub = $true )
| ? [X2: $i,X3: $i] :
( ( subset @ X3 @ ( setadjoin @ X2 @ X3 ) )
!= $true ) ) ),
inference(rectify,[status(thm)],[f1334]) ).
thf(f1334,plain,
( ( ! [X0: $i,X1: $i] :
( ( subset @ X1 @ ( setadjoin @ X0 @ X1 ) )
= $true )
| ( setadjoinSub != $true ) )
& ( ( setadjoinSub = $true )
| ? [X0: $i,X1: $i] :
( ( subset @ X1 @ ( setadjoin @ X0 @ X1 ) )
!= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f458]) ).
thf(f458,plain,
( ! [X0: $i,X1: $i] :
( ( subset @ X1 @ ( setadjoin @ X0 @ X1 ) )
= $true )
<=> ( setadjoinSub = $true ) ),
inference(fool_elimination,[status(thm)],[f457]) ).
thf(f457,plain,
! [X0: $i,X1: $i] :
( ( subset @ X1 @ ( setadjoin @ X0 @ X1 ) )
= setadjoinSub ),
inference(rectify,[status(thm)],[f90]) ).
thf(f90,axiom,
! [X1: $i,X3: $i] :
( ( subset @ X3 @ ( setadjoin @ X1 @ X3 ) )
= setadjoinSub ),
file('/export/starexec/sandbox/tmp/tmp.u7Pd4WLIgv/DTF2THF_23265.p',setadjoinSub) ).
thf(f2603,plain,
( spl467_10
| ~ spl467_32 ),
inference(avatar_split_clause,[status(thm)],[f1522,f2600,f2506]) ).
thf(f1522,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true )
| ( setadjoinIL != $true ) ),
inference(cnf_transformation,[status(thm)],[f763]) ).
thf(f763,plain,
( ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ( ( in @ sK21 @ ( setadjoin @ sK21 @ sK22 ) )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21,sK22])],[f761,f762]) ).
thf(f762,plain,
( ? [X2: $i,X3: $i] :
( $true
!= ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) )
=> ( ( in @ sK21 @ ( setadjoin @ sK21 @ sK22 ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f761,plain,
( ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ? [X2: $i,X3: $i] :
( $true
!= ( in @ X2 @ ( setadjoin @ X2 @ X3 ) ) ) ) ),
inference(rectify,[status(thm)],[f760]) ).
thf(f760,plain,
( ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ? [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
!= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f367]) ).
thf(f367,plain,
( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true )
<=> ( setadjoinIL = $true ) ),
inference(fool_elimination,[status(thm)],[f366]) ).
thf(f366,plain,
( setadjoinIL
= ( ! [X0: $i,X1: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f31]) ).
thf(f31,axiom,
( setadjoinIL
= ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.u7Pd4WLIgv/DTF2THF_23265.p',setadjoinIL) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU649^1 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n008.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:35:39 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.27/0.50 ---- Original DTF file ---
% 0.27/0.50 thf(spec,logic,$$dhol).
% 0.27/0.50 %------------------------------------------------------------------------------
% 0.27/0.50 % File : SEU649^1 : TPTP v9.2.1. Released v3.7.0.
% 0.27/0.50 % Domain : Set Theory
% 0.27/0.50 % Problem : Ordered Pairs - Properties of Pairs
% 0.27/0.50 % Version : Especial.
% 0.27/0.50 % English : (! x:i.! y:i.x = y -> setadjoin x (setadjoin y emptyset) =
% 0.27/0.50 % setadjoin x emptyset)
% 0.27/0.50
% 0.27/0.50 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.27/0.50 % Source : [Bro08]
% 0.27/0.50 % Names : ZFC151g [Bro08]
% 0.27/0.50
% 0.27/0.50 % Status : Theorem
% 0.27/0.50 % Rating : 0.67 v9.1.0, 0.75 v9.0.0, 0.80 v8.2.0, 0.85 v8.1.0, 0.82 v7.5.0, 0.86 v7.4.0, 0.89 v7.2.0, 0.88 v7.0.0, 1.00 v6.2.0, 0.86 v6.1.0, 1.00 v5.4.0, 0.80 v5.2.0, 1.00 v3.7.0
% 0.27/0.50 % Syntax : Number of formulae : 367 ( 171 unt; 195 typ; 171 def)
% 0.27/0.50 % Number of atoms : 906 ( 247 equ; 0 cnn)
% 0.27/0.50 % Maximal formula atoms : 167 ( 5 avg)
% 0.27/0.50 % Number of connectives : 1580 ( 47 ~; 7 |; 37 &;1075 @)
% 0.27/0.50 % ( 14 <=>; 400 =>; 0 <=; 0 <~>)
% 0.27/0.50 % Maximal formula depth : 169 ( 2 avg)
% 0.27/0.50 % Number of types : 2 ( 0 usr)
% 0.27/0.50 % Number of type conns : 83 ( 83 >; 0 *; 0 +; 0 <<)
% 0.27/0.50 % Number of symbols : 198 ( 195 usr; 169 con; 0-2 aty)
% 0.27/0.50 % Number of variables : 498 ( 42 ^; 418 !; 38 ?; 498 :)
% 0.27/0.50 % SPC : TH0_THM_EQU_NAR
% 0.27/0.50
% 0.27/0.50 % Comments : http://mathgate.info/detsetitem.php?id=205
% 0.27/0.50 %------------------------------------------------------------------------------
% 0.27/0.50 thf(in_type,type,
% 0.27/0.50 in: $i > $i > $o ).
% 0.27/0.50
% 0.27/0.50 thf(exu_type,type,
% 0.27/0.50 exu: ( $i > $o ) > $o ).
% 0.27/0.50
% 0.27/0.50 thf(exu,definition,
% 0.27/0.50 ( exu
% 0.27/0.50 = ( ^ [Xphi: $i > $o] :
% 0.27/0.50 ? [Xx: $i] :
% 0.27/0.50 ( ( Xphi @ Xx )
% 0.27/0.50 & ! [Xy: $i] :
% 0.27/0.50 ( ( Xphi @ Xy )
% 0.27/0.50 => ( Xx = Xy ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(setextAx_type,type,
% 0.27/0.50 setextAx: $o ).
% 0.27/0.50
% 0.27/0.50 thf(setextAx,definition,
% 0.27/0.50 ( setextAx
% 0.27/0.50 = ( ! [A: $i,B: $i] :
% 0.27/0.50 ( ! [Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ A )
% 0.27/0.50 <=> ( in @ Xx @ B ) )
% 0.27/0.50 => ( A = B ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(emptyset_type,type,
% 0.27/0.50 emptyset: $i ).
% 0.27/0.50
% 0.27/0.50 thf(emptysetAx_type,type,
% 0.27/0.50 emptysetAx: $o ).
% 0.27/0.50
% 0.27/0.50 thf(emptysetAx,definition,
% 0.27/0.50 ( emptysetAx
% 0.27/0.50 = ( ! [Xx: $i] :
% 0.27/0.50 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(setadjoin_type,type,
% 0.27/0.50 setadjoin: $i > $i > $i ).
% 0.27/0.50
% 0.27/0.50 thf(setadjoinAx_type,type,
% 0.27/0.50 setadjoinAx: $o ).
% 0.27/0.50
% 0.27/0.50 thf(setadjoinAx,definition,
% 0.27/0.50 ( setadjoinAx
% 0.27/0.50 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.27/0.50 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.27/0.50 <=> ( ( Xy = Xx )
% 0.27/0.50 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(powerset_type,type,
% 0.27/0.50 powerset: $i > $i ).
% 0.27/0.50
% 0.27/0.50 thf(powersetAx_type,type,
% 0.27/0.50 powersetAx: $o ).
% 0.27/0.50
% 0.27/0.50 thf(powersetAx,definition,
% 0.27/0.50 ( powersetAx
% 0.27/0.50 = ( ! [A: $i,B: $i] :
% 0.27/0.50 ( ( in @ B @ ( powerset @ A ) )
% 0.27/0.50 <=> ! [Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ B )
% 0.27/0.50 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(setunion_type,type,
% 0.27/0.50 setunion: $i > $i ).
% 0.27/0.50
% 0.27/0.50 thf(setunionAx_type,type,
% 0.27/0.50 setunionAx: $o ).
% 0.27/0.50
% 0.27/0.50 thf(setunionAx,definition,
% 0.27/0.50 ( setunionAx
% 0.27/0.50 = ( ! [A: $i,Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ ( setunion @ A ) )
% 0.27/0.50 <=> ? [B: $i] :
% 0.27/0.50 ( ( in @ Xx @ B )
% 0.27/0.50 & ( in @ B @ A ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(omega_type,type,
% 0.27/0.50 omega: $i ).
% 0.27/0.50
% 0.27/0.50 thf(omega0Ax_type,type,
% 0.27/0.50 omega0Ax: $o ).
% 0.27/0.50
% 0.27/0.50 thf(omega0Ax,definition,
% 0.27/0.50 ( omega0Ax
% 0.27/0.50 = ( in @ emptyset @ omega ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(omegaSAx_type,type,
% 0.27/0.50 omegaSAx: $o ).
% 0.27/0.50
% 0.27/0.50 thf(omegaSAx,definition,
% 0.27/0.50 ( omegaSAx
% 0.27/0.50 = ( ! [Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ omega )
% 0.27/0.50 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(omegaIndAx_type,type,
% 0.27/0.50 omegaIndAx: $o ).
% 0.27/0.50
% 0.27/0.50 thf(omegaIndAx,definition,
% 0.27/0.50 ( omegaIndAx
% 0.27/0.50 = ( ! [A: $i] :
% 0.27/0.50 ( ( ( in @ emptyset @ A )
% 0.27/0.50 & ! [Xx: $i] :
% 0.27/0.50 ( ( ( in @ Xx @ omega )
% 0.27/0.50 & ( in @ Xx @ A ) )
% 0.27/0.50 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.27/0.50 => ! [Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ omega )
% 0.27/0.50 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(replAx_type,type,
% 0.27/0.50 replAx: $o ).
% 0.27/0.50
% 0.27/0.50 thf(replAx,definition,
% 0.27/0.50 ( replAx
% 0.27/0.50 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.27/0.50 ( ! [Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ A )
% 0.27/0.50 => ( exu
% 0.27/0.50 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.27/0.50 => ? [B: $i] :
% 0.27/0.50 ! [Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ B )
% 0.27/0.50 <=> ? [Xy: $i] :
% 0.27/0.50 ( ( in @ Xy @ A )
% 0.27/0.50 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(foundationAx_type,type,
% 0.27/0.50 foundationAx: $o ).
% 0.27/0.50
% 0.27/0.50 thf(foundationAx,definition,
% 0.27/0.50 ( foundationAx
% 0.27/0.50 = ( ! [A: $i] :
% 0.27/0.50 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.27/0.50 => ? [B: $i] :
% 0.27/0.50 ( ( in @ B @ A )
% 0.27/0.50 & ~ ? [Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ B )
% 0.27/0.50 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(wellorderingAx_type,type,
% 0.27/0.50 wellorderingAx: $o ).
% 0.27/0.50
% 0.27/0.50 thf(wellorderingAx,definition,
% 0.27/0.50 ( wellorderingAx
% 0.27/0.50 = ( ! [A: $i] :
% 0.27/0.50 ? [B: $i] :
% 0.27/0.50 ( ! [C: $i] :
% 0.27/0.50 ( ( in @ C @ B )
% 0.27/0.50 => ! [Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ C )
% 0.27/0.50 => ( in @ Xx @ A ) ) )
% 0.27/0.50 & ! [Xx: $i,Xy: $i] :
% 0.27/0.50 ( ( ( in @ Xx @ A )
% 0.27/0.50 & ( in @ Xy @ A ) )
% 0.27/0.50 => ( ! [C: $i] :
% 0.27/0.50 ( ( in @ C @ B )
% 0.27/0.50 => ( ( in @ Xx @ C )
% 0.27/0.50 <=> ( in @ Xy @ C ) ) )
% 0.27/0.50 => ( Xx = Xy ) ) )
% 0.27/0.50 & ! [C: $i,D: $i] :
% 0.27/0.50 ( ( ( in @ C @ B )
% 0.27/0.50 & ( in @ D @ B ) )
% 0.27/0.50 => ( ! [Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ C )
% 0.27/0.50 => ( in @ Xx @ D ) )
% 0.27/0.50 | ! [Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ D )
% 0.27/0.50 => ( in @ Xx @ C ) ) ) )
% 0.27/0.50 & ! [C: $i] :
% 0.27/0.50 ( ( ! [Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ C )
% 0.27/0.50 => ( in @ Xx @ A ) )
% 0.27/0.50 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.27/0.50 => ? [D: $i,Xx: $i] :
% 0.27/0.50 ( ( in @ D @ B )
% 0.27/0.50 & ( in @ Xx @ C )
% 0.27/0.50 & ~ ? [Xy: $i] :
% 0.27/0.50 ( ( in @ Xy @ D )
% 0.27/0.50 & ( in @ Xy @ C ) )
% 0.27/0.50 & ! [E: $i] :
% 0.27/0.50 ( ( in @ E @ B )
% 0.27/0.50 => ( ! [Xy: $i] :
% 0.27/0.50 ( ( in @ Xy @ E )
% 0.27/0.50 => ( in @ Xy @ D ) )
% 0.27/0.50 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(descr_type,type,
% 0.27/0.50 descr: ( $i > $o ) > $i ).
% 0.27/0.50
% 0.27/0.50 thf(descrp_type,type,
% 0.27/0.50 descrp: $o ).
% 0.27/0.50
% 0.27/0.50 thf(descrp,definition,
% 0.27/0.50 ( descrp
% 0.27/0.50 = ( ! [Xphi: $i > $o] :
% 0.27/0.50 ( ( exu
% 0.27/0.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.50 => ( Xphi
% 0.27/0.50 @ ( descr
% 0.27/0.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(dsetconstr_type,type,
% 0.27/0.50 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.27/0.50
% 0.27/0.50 thf(dsetconstrI_type,type,
% 0.27/0.50 dsetconstrI: $o ).
% 0.27/0.50
% 0.27/0.50 thf(dsetconstrI,definition,
% 0.27/0.50 ( dsetconstrI
% 0.27/0.50 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ A )
% 0.27/0.50 => ( ( Xphi @ Xx )
% 0.27/0.50 => ( in @ Xx
% 0.27/0.50 @ ( dsetconstr @ A
% 0.27/0.50 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(dsetconstrEL_type,type,
% 0.27/0.50 dsetconstrEL: $o ).
% 0.27/0.50
% 0.27/0.50 thf(dsetconstrEL,definition,
% 0.27/0.50 ( dsetconstrEL
% 0.27/0.50 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.50 ( ( in @ Xx
% 0.27/0.50 @ ( dsetconstr @ A
% 0.27/0.50 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.27/0.50 => ( in @ Xx @ A ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(dsetconstrER_type,type,
% 0.27/0.50 dsetconstrER: $o ).
% 0.27/0.50
% 0.27/0.50 thf(dsetconstrER,definition,
% 0.27/0.50 ( dsetconstrER
% 0.27/0.50 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.50 ( ( in @ Xx
% 0.27/0.50 @ ( dsetconstr @ A
% 0.27/0.50 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.27/0.50 => ( Xphi @ Xx ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(exuE1_type,type,
% 0.27/0.50 exuE1: $o ).
% 0.27/0.50
% 0.27/0.50 thf(exuE1,definition,
% 0.27/0.50 ( exuE1
% 0.27/0.50 = ( ! [Xphi: $i > $o] :
% 0.27/0.50 ( ( exu
% 0.27/0.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.50 => ? [Xx: $i] :
% 0.27/0.50 ( ( Xphi @ Xx )
% 0.27/0.50 & ! [Xy: $i] :
% 0.27/0.50 ( ( Xphi @ Xy )
% 0.27/0.50 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(prop2set_type,type,
% 0.27/0.50 prop2set: $o > $i ).
% 0.27/0.50
% 0.27/0.50 thf(prop2setE_type,type,
% 0.27/0.50 prop2setE: $o ).
% 0.27/0.50
% 0.27/0.50 thf(prop2setE,definition,
% 0.27/0.50 ( prop2setE
% 0.27/0.50 = ( ! [Xphi: $o,Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.27/0.50 => Xphi ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(emptysetE_type,type,
% 0.27/0.50 emptysetE: $o ).
% 0.27/0.50
% 0.27/0.50 thf(emptysetE,definition,
% 0.27/0.50 ( emptysetE
% 0.27/0.50 = ( ! [Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ emptyset )
% 0.27/0.50 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(emptysetimpfalse_type,type,
% 0.27/0.50 emptysetimpfalse: $o ).
% 0.27/0.50
% 0.27/0.50 thf(emptysetimpfalse,definition,
% 0.27/0.50 ( emptysetimpfalse
% 0.27/0.50 = ( ! [Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ emptyset )
% 0.27/0.50 => $false ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(notinemptyset_type,type,
% 0.27/0.50 notinemptyset: $o ).
% 0.27/0.50
% 0.27/0.50 thf(notinemptyset,definition,
% 0.27/0.50 ( notinemptyset
% 0.27/0.50 = ( ! [Xx: $i] :
% 0.27/0.50 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(exuE3e_type,type,
% 0.27/0.50 exuE3e: $o ).
% 0.27/0.50
% 0.27/0.50 thf(exuE3e,definition,
% 0.27/0.50 ( exuE3e
% 0.27/0.50 = ( ! [Xphi: $i > $o] :
% 0.27/0.50 ( ( exu
% 0.27/0.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.50 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(setext_type,type,
% 0.27/0.50 setext: $o ).
% 0.27/0.50
% 0.27/0.50 thf(setext,definition,
% 0.27/0.50 ( setext
% 0.27/0.50 = ( ! [A: $i,B: $i] :
% 0.27/0.50 ( ! [Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ A )
% 0.27/0.50 => ( in @ Xx @ B ) )
% 0.27/0.50 => ( ! [Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ B )
% 0.27/0.50 => ( in @ Xx @ A ) )
% 0.27/0.50 => ( A = B ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(emptyI_type,type,
% 0.27/0.50 emptyI: $o ).
% 0.27/0.50
% 0.27/0.50 thf(emptyI,definition,
% 0.27/0.50 ( emptyI
% 0.27/0.50 = ( ! [A: $i] :
% 0.27/0.50 ( ! [Xx: $i] :
% 0.27/0.50 ~ ( in @ Xx @ A )
% 0.27/0.50 => ( A = emptyset ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(noeltsimpempty_type,type,
% 0.27/0.50 noeltsimpempty: $o ).
% 0.27/0.50
% 0.27/0.50 thf(noeltsimpempty,definition,
% 0.27/0.50 ( noeltsimpempty
% 0.27/0.50 = ( ! [A: $i] :
% 0.27/0.50 ( ! [Xx: $i] :
% 0.27/0.50 ~ ( in @ Xx @ A )
% 0.27/0.50 => ( A = emptyset ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(setbeta_type,type,
% 0.27/0.50 setbeta: $o ).
% 0.27/0.50
% 0.27/0.50 thf(setbeta,definition,
% 0.27/0.50 ( setbeta
% 0.27/0.50 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ A )
% 0.27/0.50 => ( ( in @ Xx
% 0.27/0.50 @ ( dsetconstr @ A
% 0.27/0.50 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.27/0.50 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(nonempty_type,type,
% 0.27/0.50 nonempty: $i > $o ).
% 0.27/0.50
% 0.27/0.50 thf(nonempty,definition,
% 0.27/0.50 ( nonempty
% 0.27/0.50 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(nonemptyE1_type,type,
% 0.27/0.50 nonemptyE1: $o ).
% 0.27/0.50
% 0.27/0.50 thf(nonemptyE1,definition,
% 0.27/0.50 ( nonemptyE1
% 0.27/0.50 = ( ! [A: $i] :
% 0.27/0.50 ( ( nonempty @ A )
% 0.27/0.50 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(nonemptyI_type,type,
% 0.27/0.50 nonemptyI: $o ).
% 0.27/0.50
% 0.27/0.50 thf(nonemptyI,definition,
% 0.27/0.50 ( nonemptyI
% 0.27/0.50 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ A )
% 0.27/0.50 => ( ( Xphi @ Xx )
% 0.27/0.50 => ( nonempty
% 0.27/0.50 @ ( dsetconstr @ A
% 0.27/0.50 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(nonemptyI1_type,type,
% 0.27/0.50 nonemptyI1: $o ).
% 0.27/0.50
% 0.27/0.50 thf(nonemptyI1,definition,
% 0.27/0.50 ( nonemptyI1
% 0.27/0.50 = ( ! [A: $i] :
% 0.27/0.50 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.27/0.50 => ( nonempty @ A ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(setadjoinIL_type,type,
% 0.27/0.50 setadjoinIL: $o ).
% 0.27/0.50
% 0.27/0.50 thf(setadjoinIL,definition,
% 0.27/0.50 ( setadjoinIL
% 0.27/0.50 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(emptyinunitempty_type,type,
% 0.27/0.50 emptyinunitempty: $o ).
% 0.27/0.50
% 0.27/0.50 thf(emptyinunitempty,definition,
% 0.27/0.50 ( emptyinunitempty
% 0.27/0.50 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(setadjoinIR_type,type,
% 0.27/0.50 setadjoinIR: $o ).
% 0.27/0.50
% 0.27/0.50 thf(setadjoinIR,definition,
% 0.27/0.50 ( setadjoinIR
% 0.27/0.50 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.27/0.50 ( ( in @ Xy @ A )
% 0.27/0.50 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(setadjoinE_type,type,
% 0.27/0.50 setadjoinE: $o ).
% 0.27/0.50
% 0.27/0.50 thf(setadjoinE,definition,
% 0.27/0.50 ( setadjoinE
% 0.27/0.50 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.27/0.50 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.27/0.50 => ! [Xphi: $o] :
% 0.27/0.50 ( ( ( Xy = Xx )
% 0.27/0.50 => Xphi )
% 0.27/0.50 => ( ( ( in @ Xy @ A )
% 0.27/0.50 => Xphi )
% 0.27/0.50 => Xphi ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(setadjoinOr_type,type,
% 0.27/0.50 setadjoinOr: $o ).
% 0.27/0.50
% 0.27/0.50 thf(setadjoinOr,definition,
% 0.27/0.50 ( setadjoinOr
% 0.27/0.50 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.27/0.50 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.27/0.50 => ( ( Xy = Xx )
% 0.27/0.50 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(setoftrueEq_type,type,
% 0.27/0.50 setoftrueEq: $o ).
% 0.27/0.50
% 0.27/0.50 thf(setoftrueEq,definition,
% 0.27/0.50 ( setoftrueEq
% 0.27/0.50 = ( ! [A: $i] :
% 0.27/0.50 ( ( dsetconstr @ A
% 0.27/0.50 @ ^ [Xx: $i] : $true )
% 0.27/0.50 = A ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(powersetI_type,type,
% 0.27/0.50 powersetI: $o ).
% 0.27/0.50
% 0.27/0.50 thf(powersetI,definition,
% 0.27/0.50 ( powersetI
% 0.27/0.50 = ( ! [A: $i,B: $i] :
% 0.27/0.50 ( ! [Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ B )
% 0.27/0.50 => ( in @ Xx @ A ) )
% 0.27/0.50 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(emptyinPowerset_type,type,
% 0.27/0.50 emptyinPowerset: $o ).
% 0.27/0.50
% 0.27/0.50 thf(emptyinPowerset,definition,
% 0.27/0.50 ( emptyinPowerset
% 0.27/0.50 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(emptyInPowerset_type,type,
% 0.27/0.50 emptyInPowerset: $o ).
% 0.27/0.50
% 0.27/0.50 thf(emptyInPowerset,definition,
% 0.27/0.50 ( emptyInPowerset
% 0.27/0.50 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(powersetE_type,type,
% 0.27/0.50 powersetE: $o ).
% 0.27/0.50
% 0.27/0.50 thf(powersetE,definition,
% 0.27/0.50 ( powersetE
% 0.27/0.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.50 ( ( in @ B @ ( powerset @ A ) )
% 0.27/0.50 => ( ( in @ Xx @ B )
% 0.27/0.50 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(setunionI_type,type,
% 0.27/0.50 setunionI: $o ).
% 0.27/0.50
% 0.27/0.50 thf(setunionI,definition,
% 0.27/0.50 ( setunionI
% 0.27/0.50 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.27/0.50 ( ( in @ Xx @ B )
% 0.27/0.50 => ( ( in @ B @ A )
% 0.27/0.50 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(setunionE_type,type,
% 0.27/0.50 setunionE: $o ).
% 0.27/0.50
% 0.27/0.50 thf(setunionE,definition,
% 0.27/0.50 ( setunionE
% 0.27/0.50 = ( ! [A: $i,Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ ( setunion @ A ) )
% 0.27/0.50 => ! [Xphi: $o] :
% 0.27/0.50 ( ! [B: $i] :
% 0.27/0.50 ( ( in @ Xx @ B )
% 0.27/0.50 => ( ( in @ B @ A )
% 0.27/0.50 => Xphi ) )
% 0.27/0.50 => Xphi ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(subPowSU_type,type,
% 0.27/0.50 subPowSU: $o ).
% 0.27/0.50
% 0.27/0.50 thf(subPowSU,definition,
% 0.27/0.50 ( subPowSU
% 0.27/0.50 = ( ! [A: $i,Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ A )
% 0.27/0.50 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(exuE2_type,type,
% 0.27/0.50 exuE2: $o ).
% 0.27/0.50
% 0.27/0.50 thf(exuE2,definition,
% 0.27/0.50 ( exuE2
% 0.27/0.50 = ( ! [Xphi: $i > $o] :
% 0.27/0.50 ( ( exu
% 0.27/0.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.50 => ? [Xx: $i] :
% 0.27/0.50 ! [Xy: $i] :
% 0.27/0.50 ( ( Xphi @ Xy )
% 0.27/0.50 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(nonemptyImpWitness_type,type,
% 0.27/0.50 nonemptyImpWitness: $o ).
% 0.27/0.50
% 0.27/0.50 thf(nonemptyImpWitness,definition,
% 0.27/0.50 ( nonemptyImpWitness
% 0.27/0.50 = ( ! [A: $i] :
% 0.27/0.50 ( ( nonempty @ A )
% 0.27/0.50 => ? [Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ A )
% 0.27/0.50 & $true ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(uniqinunit_type,type,
% 0.27/0.50 uniqinunit: $o ).
% 0.27/0.50
% 0.27/0.50 thf(uniqinunit,definition,
% 0.27/0.50 ( uniqinunit
% 0.27/0.50 = ( ! [Xx: $i,Xy: $i] :
% 0.27/0.50 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.27/0.50 => ( Xx = Xy ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(notinsingleton_type,type,
% 0.27/0.50 notinsingleton: $o ).
% 0.27/0.50
% 0.27/0.50 thf(notinsingleton,definition,
% 0.27/0.50 ( notinsingleton
% 0.27/0.50 = ( ! [Xx: $i,Xy: $i] :
% 0.27/0.50 ( ( Xx != Xy )
% 0.27/0.50 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(eqinunit_type,type,
% 0.27/0.50 eqinunit: $o ).
% 0.27/0.50
% 0.27/0.50 thf(eqinunit,definition,
% 0.27/0.50 ( eqinunit
% 0.27/0.50 = ( ! [Xx: $i,Xy: $i] :
% 0.27/0.50 ( ( Xx = Xy )
% 0.27/0.50 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(singletonsswitch_type,type,
% 0.27/0.50 singletonsswitch: $o ).
% 0.27/0.50
% 0.27/0.50 thf(singletonsswitch,definition,
% 0.27/0.50 ( singletonsswitch
% 0.27/0.50 = ( ! [Xx: $i,Xy: $i] :
% 0.27/0.50 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.27/0.50 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(upairsetE_type,type,
% 0.27/0.50 upairsetE: $o ).
% 0.27/0.50
% 0.27/0.50 thf(upairsetE,definition,
% 0.27/0.50 ( upairsetE
% 0.27/0.50 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.27/0.50 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.27/0.50 => ( ( Xz = Xx )
% 0.27/0.50 | ( Xz = Xy ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(upairsetIL_type,type,
% 0.27/0.50 upairsetIL: $o ).
% 0.27/0.50
% 0.27/0.50 thf(upairsetIL,definition,
% 0.27/0.50 ( upairsetIL
% 0.27/0.50 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(upairsetIR_type,type,
% 0.27/0.50 upairsetIR: $o ).
% 0.27/0.50
% 0.27/0.50 thf(upairsetIR,definition,
% 0.27/0.50 ( upairsetIR
% 0.27/0.50 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(emptyE1_type,type,
% 0.27/0.50 emptyE1: $o ).
% 0.27/0.50
% 0.27/0.50 thf(emptyE1,definition,
% 0.27/0.50 ( emptyE1
% 0.27/0.50 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.50 ( ? [Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ A )
% 0.27/0.50 & ( Xphi @ Xx ) )
% 0.27/0.50 => ( ( ( dsetconstr @ A
% 0.27/0.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.50 = emptyset )
% 0.27/0.50 => $false ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(vacuousDall_type,type,
% 0.27/0.50 vacuousDall: $o ).
% 0.27/0.50
% 0.27/0.50 thf(vacuousDall,definition,
% 0.27/0.50 ( vacuousDall
% 0.27/0.50 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ emptyset )
% 0.27/0.50 => ( Xphi @ Xx ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(quantDeMorgan1_type,type,
% 0.27/0.50 quantDeMorgan1: $o ).
% 0.27/0.50
% 0.27/0.50 thf(quantDeMorgan1,definition,
% 0.27/0.50 ( quantDeMorgan1
% 0.27/0.50 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.50 ( ~ ! [Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ A )
% 0.27/0.50 => ( Xphi @ Xx ) )
% 0.27/0.50 => ? [Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ A )
% 0.27/0.50 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(quantDeMorgan2_type,type,
% 0.27/0.50 quantDeMorgan2: $o ).
% 0.27/0.50
% 0.27/0.50 thf(quantDeMorgan2,definition,
% 0.27/0.50 ( quantDeMorgan2
% 0.27/0.50 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.50 ( ! [Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ A )
% 0.27/0.50 => ~ ( Xphi @ Xx ) )
% 0.27/0.50 => ~ ? [Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ A )
% 0.27/0.50 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(quantDeMorgan3_type,type,
% 0.27/0.50 quantDeMorgan3: $o ).
% 0.27/0.50
% 0.27/0.50 thf(quantDeMorgan3,definition,
% 0.27/0.50 ( quantDeMorgan3
% 0.27/0.50 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.50 ( ~ ? [Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ A )
% 0.27/0.50 & ( Xphi @ Xx ) )
% 0.27/0.50 => ! [Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ A )
% 0.27/0.50 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(quantDeMorgan4_type,type,
% 0.27/0.50 quantDeMorgan4: $o ).
% 0.27/0.50
% 0.27/0.50 thf(quantDeMorgan4,definition,
% 0.27/0.50 ( quantDeMorgan4
% 0.27/0.50 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.50 ( ? [Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ A )
% 0.27/0.50 & ~ ( Xphi @ Xx ) )
% 0.27/0.50 => ~ ! [Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ A )
% 0.27/0.50 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(prop2setI_type,type,
% 0.27/0.50 prop2setI: $o ).
% 0.27/0.50
% 0.27/0.50 thf(prop2setI,definition,
% 0.27/0.50 ( prop2setI
% 0.27/0.50 = ( ! [Xphi: $o] :
% 0.27/0.50 ( Xphi
% 0.27/0.50 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(set2prop_type,type,
% 0.27/0.50 set2prop: $i > $o ).
% 0.27/0.50
% 0.27/0.50 thf(prop2set2propI_type,type,
% 0.27/0.50 prop2set2propI: $o ).
% 0.27/0.50
% 0.27/0.50 thf(prop2set2propI,definition,
% 0.27/0.50 ( prop2set2propI
% 0.27/0.50 = ( ! [Xphi: $o] :
% 0.27/0.50 ( Xphi
% 0.27/0.50 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(notdexE_type,type,
% 0.27/0.50 notdexE: $o ).
% 0.27/0.50
% 0.27/0.50 thf(notdexE,definition,
% 0.27/0.50 ( notdexE
% 0.27/0.50 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.50 ( ~ ? [Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ A )
% 0.27/0.50 & ( Xphi @ Xx ) )
% 0.27/0.50 => ! [Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ A )
% 0.27/0.50 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(notdallE_type,type,
% 0.27/0.50 notdallE: $o ).
% 0.27/0.50
% 0.27/0.50 thf(notdallE,definition,
% 0.27/0.50 ( notdallE
% 0.27/0.50 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.50 ( ~ ! [Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ A )
% 0.27/0.50 => ( Xphi @ Xx ) )
% 0.27/0.50 => ? [Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ A )
% 0.27/0.50 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(exuI1_type,type,
% 0.27/0.50 exuI1: $o ).
% 0.27/0.50
% 0.27/0.50 thf(exuI1,definition,
% 0.27/0.50 ( exuI1
% 0.27/0.50 = ( ! [Xphi: $i > $o] :
% 0.27/0.50 ( ? [Xx: $i] :
% 0.27/0.50 ( ( Xphi @ Xx )
% 0.27/0.50 & ! [Xy: $i] :
% 0.27/0.50 ( ( Xphi @ Xy )
% 0.27/0.50 => ( Xx = Xy ) ) )
% 0.27/0.50 => ( exu
% 0.27/0.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(exuI3_type,type,
% 0.27/0.50 exuI3: $o ).
% 0.27/0.50
% 0.27/0.50 thf(exuI3,definition,
% 0.27/0.50 ( exuI3
% 0.27/0.50 = ( ! [Xphi: $i > $o] :
% 0.27/0.50 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.27/0.50 => ( ! [Xx: $i,Xy: $i] :
% 0.27/0.50 ( ( Xphi @ Xx )
% 0.27/0.50 => ( ( Xphi @ Xy )
% 0.27/0.50 => ( Xx = Xy ) ) )
% 0.27/0.50 => ( exu
% 0.27/0.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(exuI2_type,type,
% 0.27/0.50 exuI2: $o ).
% 0.27/0.50
% 0.27/0.50 thf(exuI2,definition,
% 0.27/0.50 ( exuI2
% 0.27/0.50 = ( ! [Xphi: $i > $o] :
% 0.27/0.50 ( ? [Xx: $i] :
% 0.27/0.50 ! [Xy: $i] :
% 0.27/0.50 ( ( Xphi @ Xy )
% 0.27/0.50 <=> ( Xy = Xx ) )
% 0.27/0.50 => ( exu
% 0.27/0.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(inCongP_type,type,
% 0.27/0.50 inCongP: $o ).
% 0.27/0.50
% 0.27/0.50 thf(inCongP,definition,
% 0.27/0.50 ( inCongP
% 0.27/0.50 = ( ! [A: $i,B: $i] :
% 0.27/0.50 ( ( A = B )
% 0.27/0.50 => ! [Xx: $i,Xy: $i] :
% 0.27/0.50 ( ( Xx = Xy )
% 0.27/0.50 => ( ( in @ Xx @ A )
% 0.27/0.50 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(in__Cong_type,type,
% 0.27/0.50 in__Cong: $o ).
% 0.27/0.50
% 0.27/0.50 thf(in__Cong,definition,
% 0.27/0.50 ( in__Cong
% 0.27/0.50 = ( ! [A: $i,B: $i] :
% 0.27/0.50 ( ( A = B )
% 0.27/0.50 => ! [Xx: $i,Xy: $i] :
% 0.27/0.50 ( ( Xx = Xy )
% 0.27/0.50 => ( ( in @ Xx @ A )
% 0.27/0.50 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(exuE3u_type,type,
% 0.27/0.50 exuE3u: $o ).
% 0.27/0.50
% 0.27/0.50 thf(exuE3u,definition,
% 0.27/0.50 ( exuE3u
% 0.27/0.50 = ( ! [Xphi: $i > $o] :
% 0.27/0.50 ( ( exu
% 0.27/0.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.50 => ! [Xx: $i,Xy: $i] :
% 0.27/0.50 ( ( Xphi @ Xx )
% 0.27/0.50 => ( ( Xphi @ Xy )
% 0.27/0.50 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(exu__Cong_type,type,
% 0.27/0.50 exu__Cong: $o ).
% 0.27/0.50
% 0.27/0.50 thf(exu__Cong,definition,
% 0.27/0.50 ( exu__Cong
% 0.27/0.50 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.27/0.50 ( ! [Xx: $i,Xy: $i] :
% 0.27/0.50 ( ( Xx = Xy )
% 0.27/0.50 => ( ( Xphi @ Xx )
% 0.27/0.50 <=> ( Xpsi @ Xy ) ) )
% 0.27/0.50 => ( ( exu
% 0.27/0.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.50 <=> ( exu
% 0.27/0.50 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(emptyset__Cong_type,type,
% 0.27/0.50 emptyset__Cong: $o ).
% 0.27/0.50
% 0.27/0.50 thf(emptyset__Cong,definition,
% 0.27/0.50 ( emptyset__Cong
% 0.27/0.50 = ( emptyset = emptyset ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(setadjoin__Cong_type,type,
% 0.27/0.50 setadjoin__Cong: $o ).
% 0.27/0.50
% 0.27/0.50 thf(setadjoin__Cong,definition,
% 0.27/0.50 ( setadjoin__Cong
% 0.27/0.50 = ( ! [Xx: $i,Xy: $i] :
% 0.27/0.50 ( ( Xx = Xy )
% 0.27/0.50 => ! [Xz: $i,Xu: $i] :
% 0.27/0.50 ( ( Xz = Xu )
% 0.27/0.50 => ( ( setadjoin @ Xx @ Xz )
% 0.27/0.50 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(powerset__Cong_type,type,
% 0.27/0.50 powerset__Cong: $o ).
% 0.27/0.50
% 0.27/0.50 thf(powerset__Cong,definition,
% 0.27/0.50 ( powerset__Cong
% 0.27/0.50 = ( ! [A: $i,B: $i] :
% 0.27/0.50 ( ( A = B )
% 0.27/0.50 => ( ( powerset @ A )
% 0.27/0.50 = ( powerset @ B ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(setunion__Cong_type,type,
% 0.27/0.50 setunion__Cong: $o ).
% 0.27/0.50
% 0.27/0.50 thf(setunion__Cong,definition,
% 0.27/0.50 ( setunion__Cong
% 0.27/0.50 = ( ! [A: $i,B: $i] :
% 0.27/0.50 ( ( A = B )
% 0.27/0.50 => ( ( setunion @ A )
% 0.27/0.50 = ( setunion @ B ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(omega__Cong_type,type,
% 0.27/0.50 omega__Cong: $o ).
% 0.27/0.50
% 0.27/0.50 thf(omega__Cong,definition,
% 0.27/0.50 ( omega__Cong
% 0.27/0.50 = ( omega = omega ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(exuEu_type,type,
% 0.27/0.50 exuEu: $o ).
% 0.27/0.50
% 0.27/0.50 thf(exuEu,definition,
% 0.27/0.50 ( exuEu
% 0.27/0.50 = ( ! [Xphi: $i > $o] :
% 0.27/0.50 ( ( exu
% 0.27/0.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.50 => ! [Xx: $i,Xy: $i] :
% 0.27/0.50 ( ( Xphi @ Xx )
% 0.27/0.50 => ( ( Xphi @ Xy )
% 0.27/0.50 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(descr__Cong_type,type,
% 0.27/0.50 descr__Cong: $o ).
% 0.27/0.50
% 0.27/0.50 thf(descr__Cong,definition,
% 0.27/0.50 ( descr__Cong
% 0.27/0.50 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.27/0.50 ( ! [Xx: $i,Xy: $i] :
% 0.27/0.50 ( ( Xx = Xy )
% 0.27/0.50 => ( ( Xphi @ Xx )
% 0.27/0.50 <=> ( Xpsi @ Xy ) ) )
% 0.27/0.50 => ( ( exu
% 0.27/0.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.50 => ( ( exu
% 0.27/0.50 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.27/0.50 => ( ( descr
% 0.27/0.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.50 = ( descr
% 0.27/0.50 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(dsetconstr__Cong_type,type,
% 0.27/0.50 dsetconstr__Cong: $o ).
% 0.27/0.50
% 0.27/0.50 thf(dsetconstr__Cong,definition,
% 0.27/0.50 ( dsetconstr__Cong
% 0.27/0.50 = ( ! [A: $i,B: $i] :
% 0.27/0.50 ( ( A = B )
% 0.27/0.50 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.27/0.50 ( ! [Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ A )
% 0.27/0.50 => ! [Xy: $i] :
% 0.27/0.50 ( ( in @ Xy @ B )
% 0.27/0.50 => ( ( Xx = Xy )
% 0.27/0.50 => ( ( Xphi @ Xx )
% 0.27/0.50 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.27/0.50 => ( ( dsetconstr @ A
% 0.27/0.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.50 = ( dsetconstr @ B
% 0.27/0.50 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(subset_type,type,
% 0.27/0.50 subset: $i > $i > $o ).
% 0.27/0.50
% 0.27/0.50 thf(disjoint_type,type,
% 0.27/0.50 disjoint: $i > $i > $o ).
% 0.27/0.50
% 0.27/0.50 thf(setsmeet_type,type,
% 0.27/0.50 setsmeet: $i > $i > $o ).
% 0.27/0.50
% 0.27/0.50 thf(subsetI1_type,type,
% 0.27/0.50 subsetI1: $o ).
% 0.27/0.50
% 0.27/0.50 thf(subsetI1,definition,
% 0.27/0.50 ( subsetI1
% 0.27/0.50 = ( ! [A: $i,B: $i] :
% 0.27/0.50 ( ! [Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ A )
% 0.27/0.50 => ( in @ Xx @ B ) )
% 0.27/0.50 => ( subset @ A @ B ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(eqimpsubset2_type,type,
% 0.27/0.50 eqimpsubset2: $o ).
% 0.27/0.50
% 0.27/0.50 thf(eqimpsubset2,definition,
% 0.27/0.50 ( eqimpsubset2
% 0.27/0.50 = ( ! [A: $i,B: $i] :
% 0.27/0.50 ( ( A = B )
% 0.27/0.50 => ( subset @ B @ A ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(eqimpsubset1_type,type,
% 0.27/0.50 eqimpsubset1: $o ).
% 0.27/0.50
% 0.27/0.50 thf(eqimpsubset1,definition,
% 0.27/0.50 ( eqimpsubset1
% 0.27/0.50 = ( ! [A: $i,B: $i] :
% 0.27/0.50 ( ( A = B )
% 0.27/0.50 => ( subset @ A @ B ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(subsetI2_type,type,
% 0.27/0.50 subsetI2: $o ).
% 0.27/0.50
% 0.27/0.50 thf(subsetI2,definition,
% 0.27/0.50 ( subsetI2
% 0.27/0.50 = ( ! [A: $i,B: $i] :
% 0.27/0.50 ( ! [Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ A )
% 0.27/0.50 => ( in @ Xx @ B ) )
% 0.27/0.50 => ( subset @ A @ B ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(emptysetsubset_type,type,
% 0.27/0.50 emptysetsubset: $o ).
% 0.27/0.50
% 0.27/0.50 thf(emptysetsubset,definition,
% 0.27/0.50 ( emptysetsubset
% 0.27/0.50 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(subsetE_type,type,
% 0.27/0.50 subsetE: $o ).
% 0.27/0.50
% 0.27/0.50 thf(subsetE,definition,
% 0.27/0.50 ( subsetE
% 0.27/0.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.50 ( ( subset @ A @ B )
% 0.27/0.50 => ( ( in @ Xx @ A )
% 0.27/0.50 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(subsetE2_type,type,
% 0.27/0.50 subsetE2: $o ).
% 0.27/0.50
% 0.27/0.50 thf(subsetE2,definition,
% 0.27/0.50 ( subsetE2
% 0.27/0.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.50 ( ( subset @ A @ B )
% 0.27/0.50 => ( ~ ( in @ Xx @ B )
% 0.27/0.50 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(notsubsetI_type,type,
% 0.27/0.50 notsubsetI: $o ).
% 0.27/0.50
% 0.27/0.50 thf(notsubsetI,definition,
% 0.27/0.50 ( notsubsetI
% 0.27/0.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ A )
% 0.27/0.50 => ( ~ ( in @ Xx @ B )
% 0.27/0.50 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(notequalI1_type,type,
% 0.27/0.50 notequalI1: $o ).
% 0.27/0.50
% 0.27/0.50 thf(notequalI1,definition,
% 0.27/0.50 ( notequalI1
% 0.27/0.50 = ( ! [A: $i,B: $i] :
% 0.27/0.50 ( ~ ( subset @ A @ B )
% 0.27/0.50 => ( A != B ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(notequalI2_type,type,
% 0.27/0.50 notequalI2: $o ).
% 0.27/0.50
% 0.27/0.50 thf(notequalI2,definition,
% 0.27/0.50 ( notequalI2
% 0.27/0.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.50 ( ( in @ Xx @ A )
% 0.27/0.50 => ( ~ ( in @ Xx @ B )
% 0.27/0.50 => ( A != B ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(subsetRefl_type,type,
% 0.27/0.50 subsetRefl: $o ).
% 0.27/0.50
% 0.27/0.50 thf(subsetRefl,definition,
% 0.27/0.50 ( subsetRefl
% 0.27/0.50 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(subsetTrans_type,type,
% 0.27/0.50 subsetTrans: $o ).
% 0.27/0.50
% 0.27/0.50 thf(subsetTrans,definition,
% 0.27/0.50 ( subsetTrans
% 0.27/0.50 = ( ! [A: $i,B: $i,C: $i] :
% 0.27/0.50 ( ( subset @ A @ B )
% 0.27/0.50 => ( ( subset @ B @ C )
% 0.27/0.50 => ( subset @ A @ C ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(setadjoinSub_type,type,
% 0.27/0.50 setadjoinSub: $o ).
% 0.27/0.50
% 0.27/0.50 thf(setadjoinSub,definition,
% 0.27/0.50 ( setadjoinSub
% 0.27/0.50 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(setadjoinSub2_type,type,
% 0.27/0.50 setadjoinSub2: $o ).
% 0.27/0.50
% 0.27/0.50 thf(setadjoinSub2,definition,
% 0.27/0.50 ( setadjoinSub2
% 0.27/0.50 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.27/0.50 ( ( subset @ A @ B )
% 0.27/0.50 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(subset2powerset_type,type,
% 0.27/0.50 subset2powerset: $o ).
% 0.27/0.50
% 0.27/0.50 thf(subset2powerset,definition,
% 0.27/0.50 ( subset2powerset
% 0.27/0.50 = ( ! [A: $i,B: $i] :
% 0.27/0.50 ( ( subset @ A @ B )
% 0.27/0.50 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(setextsub_type,type,
% 0.27/0.50 setextsub: $o ).
% 0.27/0.50
% 0.27/0.50 thf(setextsub,definition,
% 0.27/0.50 ( setextsub
% 0.27/0.50 = ( ! [A: $i,B: $i] :
% 0.27/0.50 ( ( subset @ A @ B )
% 0.27/0.50 => ( ( subset @ B @ A )
% 0.27/0.50 => ( A = B ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(subsetemptysetimpeq_type,type,
% 0.27/0.50 subsetemptysetimpeq: $o ).
% 0.27/0.50
% 0.27/0.50 thf(subsetemptysetimpeq,definition,
% 0.27/0.50 ( subsetemptysetimpeq
% 0.27/0.50 = ( ! [A: $i] :
% 0.27/0.50 ( ( subset @ A @ emptyset )
% 0.27/0.50 => ( A = emptyset ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(powersetI1_type,type,
% 0.27/0.50 powersetI1: $o ).
% 0.27/0.50
% 0.27/0.50 thf(powersetI1,definition,
% 0.27/0.50 ( powersetI1
% 0.27/0.50 = ( ! [A: $i,B: $i] :
% 0.27/0.50 ( ( subset @ B @ A )
% 0.27/0.50 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(powersetE1_type,type,
% 0.27/0.50 powersetE1: $o ).
% 0.27/0.50
% 0.27/0.50 thf(powersetE1,definition,
% 0.27/0.50 ( powersetE1
% 0.27/0.50 = ( ! [A: $i,B: $i] :
% 0.27/0.50 ( ( in @ B @ ( powerset @ A ) )
% 0.27/0.50 => ( subset @ B @ A ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(inPowerset_type,type,
% 0.27/0.50 inPowerset: $o ).
% 0.27/0.50
% 0.27/0.50 thf(inPowerset,definition,
% 0.27/0.50 ( inPowerset
% 0.27/0.50 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(powersetsubset_type,type,
% 0.27/0.50 powersetsubset: $o ).
% 0.27/0.50
% 0.27/0.50 thf(powersetsubset,definition,
% 0.27/0.50 ( powersetsubset
% 0.27/0.50 = ( ! [A: $i,B: $i] :
% 0.27/0.50 ( ( subset @ A @ B )
% 0.27/0.50 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(sepInPowerset_type,type,
% 0.27/0.50 sepInPowerset: $o ).
% 0.27/0.50
% 0.27/0.50 thf(sepInPowerset,definition,
% 0.27/0.50 ( sepInPowerset
% 0.27/0.50 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.50 ( in
% 0.27/0.50 @ ( dsetconstr @ A
% 0.27/0.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.50 @ ( powerset @ A ) ) ) ) ).
% 0.27/0.50
% 0.27/0.50 thf(sepSubset_type,type,
% 0.27/0.50 sepSubset: $o ).
% 0.27/0.50
% 0.27/0.50 thf(sepSubset,definition,
% 0.27/0.50 ( sepSubset
% 0.27/0.50 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.50 ( subset
% 0.27/0.50 @ ( dsetconstr @ A
% 0.27/0.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.51 @ A ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(binunion_type,type,
% 0.27/0.51 binunion: $i > $i > $i ).
% 0.27/0.51
% 0.27/0.51 thf(binunionIL_type,type,
% 0.27/0.51 binunionIL: $o ).
% 0.27/0.51
% 0.27/0.51 thf(binunionIL,definition,
% 0.27/0.51 ( binunionIL
% 0.27/0.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.51 ( ( in @ Xx @ A )
% 0.27/0.51 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(upairset2IR_type,type,
% 0.27/0.51 upairset2IR: $o ).
% 0.27/0.51
% 0.27/0.51 thf(upairset2IR,definition,
% 0.27/0.51 ( upairset2IR
% 0.27/0.51 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(binunionIR_type,type,
% 0.27/0.51 binunionIR: $o ).
% 0.27/0.51
% 0.27/0.51 thf(binunionIR,definition,
% 0.27/0.51 ( binunionIR
% 0.27/0.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.51 ( ( in @ Xx @ B )
% 0.27/0.51 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(binunionEcases_type,type,
% 0.27/0.51 binunionEcases: $o ).
% 0.27/0.51
% 0.27/0.51 thf(binunionEcases,definition,
% 0.27/0.51 ( binunionEcases
% 0.27/0.51 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.27/0.51 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.27/0.51 => ( ( ( in @ Xx @ A )
% 0.27/0.51 => Xphi )
% 0.27/0.51 => ( ( ( in @ Xx @ B )
% 0.27/0.51 => Xphi )
% 0.27/0.51 => Xphi ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(binunionE_type,type,
% 0.27/0.51 binunionE: $o ).
% 0.27/0.51
% 0.27/0.51 thf(binunionE,definition,
% 0.27/0.51 ( binunionE
% 0.27/0.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.51 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.27/0.51 => ( ( in @ Xx @ A )
% 0.27/0.51 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(binunionLsub_type,type,
% 0.27/0.51 binunionLsub: $o ).
% 0.27/0.51
% 0.27/0.51 thf(binunionLsub,definition,
% 0.27/0.51 ( binunionLsub
% 0.27/0.51 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(binunionRsub_type,type,
% 0.27/0.51 binunionRsub: $o ).
% 0.27/0.51
% 0.27/0.51 thf(binunionRsub,definition,
% 0.27/0.51 ( binunionRsub
% 0.27/0.51 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(binintersect_type,type,
% 0.27/0.51 binintersect: $i > $i > $i ).
% 0.27/0.51
% 0.27/0.51 thf(binintersectI_type,type,
% 0.27/0.51 binintersectI: $o ).
% 0.27/0.51
% 0.27/0.51 thf(binintersectI,definition,
% 0.27/0.51 ( binintersectI
% 0.27/0.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.51 ( ( in @ Xx @ A )
% 0.27/0.51 => ( ( in @ Xx @ B )
% 0.27/0.51 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(binintersectSubset5_type,type,
% 0.27/0.51 binintersectSubset5: $o ).
% 0.27/0.51
% 0.27/0.51 thf(binintersectSubset5,definition,
% 0.27/0.51 ( binintersectSubset5
% 0.27/0.51 = ( ! [A: $i,B: $i,C: $i] :
% 0.27/0.51 ( ( subset @ C @ A )
% 0.27/0.51 => ( ( subset @ C @ B )
% 0.27/0.51 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(binintersectEL_type,type,
% 0.27/0.51 binintersectEL: $o ).
% 0.27/0.51
% 0.27/0.51 thf(binintersectEL,definition,
% 0.27/0.51 ( binintersectEL
% 0.27/0.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.51 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.27/0.51 => ( in @ Xx @ A ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(binintersectLsub_type,type,
% 0.27/0.51 binintersectLsub: $o ).
% 0.27/0.51
% 0.27/0.51 thf(binintersectLsub,definition,
% 0.27/0.51 ( binintersectLsub
% 0.27/0.51 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(binintersectSubset2_type,type,
% 0.27/0.51 binintersectSubset2: $o ).
% 0.27/0.51
% 0.27/0.51 thf(binintersectSubset2,definition,
% 0.27/0.51 ( binintersectSubset2
% 0.27/0.51 = ( ! [A: $i,B: $i] :
% 0.27/0.51 ( ( subset @ A @ B )
% 0.27/0.51 => ( ( binintersect @ A @ B )
% 0.27/0.51 = A ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(binintersectSubset3_type,type,
% 0.27/0.51 binintersectSubset3: $o ).
% 0.27/0.51
% 0.27/0.51 thf(binintersectSubset3,definition,
% 0.27/0.51 ( binintersectSubset3
% 0.27/0.51 = ( ! [A: $i,B: $i] :
% 0.27/0.51 ( ( ( binintersect @ A @ B )
% 0.27/0.51 = B )
% 0.27/0.51 => ( subset @ B @ A ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(binintersectER_type,type,
% 0.27/0.51 binintersectER: $o ).
% 0.27/0.51
% 0.27/0.51 thf(binintersectER,definition,
% 0.27/0.51 ( binintersectER
% 0.27/0.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.51 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.27/0.51 => ( in @ Xx @ B ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(disjointsetsI1_type,type,
% 0.27/0.51 disjointsetsI1: $o ).
% 0.27/0.51
% 0.27/0.51 thf(disjointsetsI1,definition,
% 0.27/0.51 ( disjointsetsI1
% 0.27/0.51 = ( ! [A: $i,B: $i] :
% 0.27/0.51 ( ~ ? [Xx: $i] :
% 0.27/0.51 ( ( in @ Xx @ A )
% 0.27/0.51 & ( in @ Xx @ B ) )
% 0.27/0.51 => ( ( binintersect @ A @ B )
% 0.27/0.51 = emptyset ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(binintersectRsub_type,type,
% 0.27/0.51 binintersectRsub: $o ).
% 0.27/0.51
% 0.27/0.51 thf(binintersectRsub,definition,
% 0.27/0.51 ( binintersectRsub
% 0.27/0.51 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(binintersectSubset4_type,type,
% 0.27/0.51 binintersectSubset4: $o ).
% 0.27/0.51
% 0.27/0.51 thf(binintersectSubset4,definition,
% 0.27/0.51 ( binintersectSubset4
% 0.27/0.51 = ( ! [A: $i,B: $i] :
% 0.27/0.51 ( ( subset @ B @ A )
% 0.27/0.51 => ( ( binintersect @ A @ B )
% 0.27/0.51 = B ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(binintersectSubset1_type,type,
% 0.27/0.51 binintersectSubset1: $o ).
% 0.27/0.51
% 0.27/0.51 thf(binintersectSubset1,definition,
% 0.27/0.51 ( binintersectSubset1
% 0.27/0.51 = ( ! [A: $i,B: $i] :
% 0.27/0.51 ( ( ( binintersect @ A @ B )
% 0.27/0.51 = A )
% 0.27/0.51 => ( subset @ A @ B ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(bs114d_type,type,
% 0.27/0.51 bs114d: $o ).
% 0.27/0.51
% 0.27/0.51 thf(bs114d,definition,
% 0.27/0.51 ( bs114d
% 0.27/0.51 = ( ! [A: $i,B: $i,C: $i] :
% 0.27/0.51 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.27/0.51 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(regular_type,type,
% 0.27/0.51 regular: $i > $o ).
% 0.27/0.51
% 0.27/0.51 thf(setminus_type,type,
% 0.27/0.51 setminus: $i > $i > $i ).
% 0.27/0.51
% 0.27/0.51 thf(setminusI_type,type,
% 0.27/0.51 setminusI: $o ).
% 0.27/0.51
% 0.27/0.51 thf(setminusI,definition,
% 0.27/0.51 ( setminusI
% 0.27/0.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.51 ( ( in @ Xx @ A )
% 0.27/0.51 => ( ~ ( in @ Xx @ B )
% 0.27/0.51 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(setminusEL_type,type,
% 0.27/0.51 setminusEL: $o ).
% 0.27/0.51
% 0.27/0.51 thf(setminusEL,definition,
% 0.27/0.51 ( setminusEL
% 0.27/0.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.51 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.27/0.51 => ( in @ Xx @ A ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(setminusER_type,type,
% 0.27/0.51 setminusER: $o ).
% 0.27/0.51
% 0.27/0.51 thf(setminusER,definition,
% 0.27/0.51 ( setminusER
% 0.27/0.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.51 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.27/0.51 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(setminusSubset2_type,type,
% 0.27/0.51 setminusSubset2: $o ).
% 0.27/0.51
% 0.27/0.51 thf(setminusSubset2,definition,
% 0.27/0.51 ( setminusSubset2
% 0.27/0.51 = ( ! [A: $i,B: $i] :
% 0.27/0.51 ( ( subset @ A @ B )
% 0.27/0.51 => ( ( setminus @ A @ B )
% 0.27/0.51 = emptyset ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(setminusERneg_type,type,
% 0.27/0.51 setminusERneg: $o ).
% 0.27/0.51
% 0.27/0.51 thf(setminusERneg,definition,
% 0.27/0.51 ( setminusERneg
% 0.27/0.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.51 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.27/0.51 => ( ( in @ Xx @ A )
% 0.27/0.51 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(setminusELneg_type,type,
% 0.27/0.51 setminusELneg: $o ).
% 0.27/0.51
% 0.27/0.51 thf(setminusELneg,definition,
% 0.27/0.51 ( setminusELneg
% 0.27/0.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.51 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.27/0.51 => ( ~ ( in @ Xx @ B )
% 0.27/0.51 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(setminusILneg_type,type,
% 0.27/0.51 setminusILneg: $o ).
% 0.27/0.51
% 0.27/0.51 thf(setminusILneg,definition,
% 0.27/0.51 ( setminusILneg
% 0.27/0.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.51 ( ~ ( in @ Xx @ A )
% 0.27/0.51 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(setminusIRneg_type,type,
% 0.27/0.51 setminusIRneg: $o ).
% 0.27/0.51
% 0.27/0.51 thf(setminusIRneg,definition,
% 0.27/0.51 ( setminusIRneg
% 0.27/0.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.51 ( ( in @ Xx @ B )
% 0.27/0.51 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(setminusLsub_type,type,
% 0.27/0.51 setminusLsub: $o ).
% 0.27/0.51
% 0.27/0.51 thf(setminusLsub,definition,
% 0.27/0.51 ( setminusLsub
% 0.27/0.51 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(setminusSubset1_type,type,
% 0.27/0.51 setminusSubset1: $o ).
% 0.27/0.51
% 0.27/0.51 thf(setminusSubset1,definition,
% 0.27/0.51 ( setminusSubset1
% 0.27/0.51 = ( ! [A: $i,B: $i] :
% 0.27/0.51 ( ( ( setminus @ A @ B )
% 0.27/0.51 = emptyset )
% 0.27/0.51 => ( subset @ A @ B ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(symdiff_type,type,
% 0.27/0.51 symdiff: $i > $i > $i ).
% 0.27/0.51
% 0.27/0.51 thf(symdiffE_type,type,
% 0.27/0.51 symdiffE: $o ).
% 0.27/0.51
% 0.27/0.51 thf(symdiffE,definition,
% 0.27/0.51 ( symdiffE
% 0.27/0.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.51 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.27/0.51 => ! [Xphi: $o] :
% 0.27/0.51 ( ( ( in @ Xx @ A )
% 0.27/0.51 => ( ~ ( in @ Xx @ B )
% 0.27/0.51 => Xphi ) )
% 0.27/0.51 => ( ( ~ ( in @ Xx @ A )
% 0.27/0.51 => ( ( in @ Xx @ B )
% 0.27/0.51 => Xphi ) )
% 0.27/0.51 => Xphi ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(symdiffI1_type,type,
% 0.27/0.51 symdiffI1: $o ).
% 0.27/0.51
% 0.27/0.51 thf(symdiffI1,definition,
% 0.27/0.51 ( symdiffI1
% 0.27/0.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.51 ( ( in @ Xx @ A )
% 0.27/0.51 => ( ~ ( in @ Xx @ B )
% 0.27/0.51 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(symdiffI2_type,type,
% 0.27/0.51 symdiffI2: $o ).
% 0.27/0.51
% 0.27/0.51 thf(symdiffI2,definition,
% 0.27/0.51 ( symdiffI2
% 0.27/0.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.51 ( ~ ( in @ Xx @ A )
% 0.27/0.51 => ( ( in @ Xx @ B )
% 0.27/0.51 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(symdiffIneg1_type,type,
% 0.27/0.51 symdiffIneg1: $o ).
% 0.27/0.51
% 0.27/0.51 thf(symdiffIneg1,definition,
% 0.27/0.51 ( symdiffIneg1
% 0.27/0.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.51 ( ( in @ Xx @ A )
% 0.27/0.51 => ( ( in @ Xx @ B )
% 0.27/0.51 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(symdiffIneg2_type,type,
% 0.27/0.51 symdiffIneg2: $o ).
% 0.27/0.51
% 0.27/0.51 thf(symdiffIneg2,definition,
% 0.27/0.51 ( symdiffIneg2
% 0.27/0.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.51 ( ~ ( in @ Xx @ A )
% 0.27/0.51 => ( ~ ( in @ Xx @ B )
% 0.27/0.51 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(iskpair_type,type,
% 0.27/0.51 iskpair: $i > $o ).
% 0.27/0.51
% 0.27/0.51 thf(iskpair,definition,
% 0.27/0.51 ( iskpair
% 0.27/0.51 = ( ^ [A: $i] :
% 0.27/0.51 ? [Xx: $i] :
% 0.27/0.51 ( ( in @ Xx @ ( setunion @ A ) )
% 0.27/0.51 & ? [Xy: $i] :
% 0.27/0.51 ( ( in @ Xy @ ( setunion @ A ) )
% 0.27/0.51 & ( A
% 0.27/0.51 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(secondinupair_type,type,
% 0.27/0.51 secondinupair: $o ).
% 0.27/0.51
% 0.27/0.51 thf(secondinupair,definition,
% 0.27/0.51 ( secondinupair
% 0.27/0.51 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(setukpairIL_type,type,
% 0.27/0.51 setukpairIL: $o ).
% 0.27/0.51
% 0.27/0.51 thf(setukpairIL,definition,
% 0.27/0.51 ( setukpairIL
% 0.27/0.51 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(setukpairIR_type,type,
% 0.27/0.51 setukpairIR: $o ).
% 0.27/0.51
% 0.27/0.51 thf(setukpairIR,definition,
% 0.27/0.51 ( setukpairIR
% 0.27/0.51 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(kpairiskpair_type,type,
% 0.27/0.51 kpairiskpair: $o ).
% 0.27/0.51
% 0.27/0.51 thf(kpairiskpair,definition,
% 0.27/0.51 ( kpairiskpair
% 0.27/0.51 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(kpair_type,type,
% 0.27/0.51 kpair: $i > $i > $i ).
% 0.27/0.51
% 0.27/0.51 thf(kpair,definition,
% 0.27/0.51 ( kpair
% 0.27/0.51 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(kpairp_type,type,
% 0.27/0.51 kpairp: $o ).
% 0.27/0.51
% 0.27/0.51 thf(kpairp,definition,
% 0.27/0.51 ( kpairp
% 0.27/0.51 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(cartprod_type,type,
% 0.27/0.51 cartprod: $i > $i > $i ).
% 0.27/0.51
% 0.27/0.51 thf(singletonsubset_type,type,
% 0.27/0.51 singletonsubset: $o ).
% 0.27/0.51
% 0.27/0.51 thf(singletonsubset,definition,
% 0.27/0.51 ( singletonsubset
% 0.27/0.51 = ( ! [A: $i,Xx: $i] :
% 0.27/0.51 ( ( in @ Xx @ A )
% 0.27/0.51 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(singletoninpowerset_type,type,
% 0.27/0.51 singletoninpowerset: $o ).
% 0.27/0.51
% 0.27/0.51 thf(singletoninpowerset,definition,
% 0.27/0.51 ( singletoninpowerset
% 0.27/0.51 = ( ! [A: $i,Xx: $i] :
% 0.27/0.51 ( ( in @ Xx @ A )
% 0.27/0.51 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(singletoninpowunion_type,type,
% 0.27/0.51 singletoninpowunion: $o ).
% 0.27/0.51
% 0.27/0.51 thf(singletoninpowunion,definition,
% 0.27/0.51 ( singletoninpowunion
% 0.27/0.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.51 ( ( in @ Xx @ A )
% 0.27/0.51 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(upairset2E_type,type,
% 0.27/0.51 upairset2E: $o ).
% 0.27/0.51
% 0.27/0.51 thf(upairset2E,definition,
% 0.27/0.51 ( upairset2E
% 0.27/0.51 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.27/0.51 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.27/0.51 => ( ( Xz = Xx )
% 0.27/0.51 | ( Xz = Xy ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(upairsubunion_type,type,
% 0.27/0.51 upairsubunion: $o ).
% 0.27/0.51
% 0.27/0.51 thf(upairsubunion,definition,
% 0.27/0.51 ( upairsubunion
% 0.27/0.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.51 ( ( in @ Xx @ A )
% 0.27/0.51 => ! [Xy: $i] :
% 0.27/0.51 ( ( in @ Xy @ B )
% 0.27/0.51 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(upairinpowunion_type,type,
% 0.27/0.51 upairinpowunion: $o ).
% 0.27/0.51
% 0.27/0.51 thf(upairinpowunion,definition,
% 0.27/0.51 ( upairinpowunion
% 0.27/0.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.51 ( ( in @ Xx @ A )
% 0.27/0.51 => ! [Xy: $i] :
% 0.27/0.51 ( ( in @ Xy @ B )
% 0.27/0.51 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(ubforcartprodlem1_type,type,
% 0.27/0.51 ubforcartprodlem1: $o ).
% 0.27/0.51
% 0.27/0.51 thf(ubforcartprodlem1,definition,
% 0.27/0.51 ( ubforcartprodlem1
% 0.27/0.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.51 ( ( in @ Xx @ A )
% 0.27/0.51 => ! [Xy: $i] :
% 0.27/0.51 ( ( in @ Xy @ B )
% 0.27/0.51 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(ubforcartprodlem2_type,type,
% 0.27/0.51 ubforcartprodlem2: $o ).
% 0.27/0.51
% 0.27/0.51 thf(ubforcartprodlem2,definition,
% 0.27/0.51 ( ubforcartprodlem2
% 0.27/0.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.51 ( ( in @ Xx @ A )
% 0.27/0.51 => ! [Xy: $i] :
% 0.27/0.51 ( ( in @ Xy @ B )
% 0.27/0.51 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(ubforcartprodlem3_type,type,
% 0.27/0.51 ubforcartprodlem3: $o ).
% 0.27/0.51
% 0.27/0.51 thf(ubforcartprodlem3,definition,
% 0.27/0.51 ( ubforcartprodlem3
% 0.27/0.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.51 ( ( in @ Xx @ A )
% 0.27/0.51 => ! [Xy: $i] :
% 0.27/0.51 ( ( in @ Xy @ B )
% 0.27/0.51 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(cartprodpairin_type,type,
% 0.27/0.51 cartprodpairin: $o ).
% 0.27/0.51
% 0.27/0.51 thf(cartprodpairin,definition,
% 0.27/0.51 ( cartprodpairin
% 0.27/0.51 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.51 ( ( in @ Xx @ A )
% 0.27/0.51 => ! [Xy: $i] :
% 0.27/0.51 ( ( in @ Xy @ B )
% 0.27/0.51 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(cartprodmempair1_type,type,
% 0.27/0.51 cartprodmempair1: $o ).
% 0.27/0.51
% 0.27/0.51 thf(cartprodmempair1,definition,
% 0.27/0.51 ( cartprodmempair1
% 0.27/0.51 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.27/0.51 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.27/0.51 => ? [Xx: $i] :
% 0.27/0.51 ( ( in @ Xx @ A )
% 0.27/0.51 & ? [Xy: $i] :
% 0.27/0.51 ( ( in @ Xy @ B )
% 0.27/0.51 & ( Xu
% 0.27/0.51 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(cartprodmempair_type,type,
% 0.27/0.51 cartprodmempair: $o ).
% 0.27/0.51
% 0.27/0.51 thf(cartprodmempair,definition,
% 0.27/0.51 ( cartprodmempair
% 0.27/0.51 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.27/0.51 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.27/0.51 => ( iskpair @ Xu ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(setunionE2_type,type,
% 0.27/0.51 setunionE2: $o ).
% 0.27/0.51
% 0.27/0.51 thf(setunionE2,definition,
% 0.27/0.51 ( setunionE2
% 0.27/0.51 = ( ! [A: $i,Xx: $i] :
% 0.27/0.51 ( ( in @ Xx @ ( setunion @ A ) )
% 0.27/0.51 => ? [X: $i] :
% 0.27/0.51 ( ( in @ X @ A )
% 0.27/0.51 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(setunionsingleton1_type,type,
% 0.27/0.51 setunionsingleton1: $o ).
% 0.27/0.51
% 0.27/0.51 thf(setunionsingleton1,definition,
% 0.27/0.51 ( setunionsingleton1
% 0.27/0.51 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(setunionsingleton2_type,type,
% 0.27/0.51 setunionsingleton2: $o ).
% 0.27/0.51
% 0.27/0.51 thf(setunionsingleton2,definition,
% 0.27/0.51 ( setunionsingleton2
% 0.27/0.51 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(setunionsingleton_type,type,
% 0.27/0.51 setunionsingleton: $o ).
% 0.27/0.51
% 0.27/0.51 thf(setunionsingleton,definition,
% 0.27/0.51 ( setunionsingleton
% 0.27/0.51 = ( ! [Xx: $i] :
% 0.27/0.51 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.27/0.51 = Xx ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(singleton_type,type,
% 0.27/0.51 singleton: $i > $o ).
% 0.27/0.51
% 0.27/0.51 thf(singleton,definition,
% 0.27/0.51 ( singleton
% 0.27/0.51 = ( ^ [A: $i] :
% 0.27/0.51 ? [Xx: $i] :
% 0.27/0.51 ( ( in @ Xx @ A )
% 0.27/0.51 & ( A
% 0.27/0.51 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(singletonprop_type,type,
% 0.27/0.51 singletonprop: $o ).
% 0.27/0.51
% 0.27/0.51 thf(singletonprop,definition,
% 0.27/0.51 ( singletonprop
% 0.27/0.51 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.51 ( ! [Xx: $i] :
% 0.27/0.51 ( ( in @ Xx @ A )
% 0.27/0.51 => ! [Xy: $i] :
% 0.27/0.51 ( ( in @ Xy @ A )
% 0.27/0.51 => ( ( Xphi @ Xx )
% 0.27/0.51 => ( ( Xphi @ Xy )
% 0.27/0.51 => ( Xx = Xy ) ) ) ) )
% 0.27/0.51 => ( ? [Xx: $i] :
% 0.27/0.51 ( ( in @ Xx @ A )
% 0.27/0.51 & ( Xphi @ Xx ) )
% 0.27/0.51 => ( singleton
% 0.27/0.51 @ ( dsetconstr @ A
% 0.27/0.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(ex1_type,type,
% 0.27/0.51 ex1: $i > ( $i > $o ) > $o ).
% 0.27/0.51
% 0.27/0.51 thf(ex1,definition,
% 0.27/0.51 ( ex1
% 0.27/0.51 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.27/0.51 ( singleton
% 0.27/0.51 @ ( dsetconstr @ A
% 0.27/0.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(ex1E1_type,type,
% 0.27/0.51 ex1E1: $o ).
% 0.27/0.51
% 0.27/0.51 thf(ex1E1,definition,
% 0.27/0.51 ( ex1E1
% 0.27/0.51 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.51 ( ( ex1 @ A
% 0.27/0.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.51 => ? [Xx: $i] :
% 0.27/0.51 ( ( in @ Xx @ A )
% 0.27/0.51 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(ex1I_type,type,
% 0.27/0.51 ex1I: $o ).
% 0.27/0.51
% 0.27/0.51 thf(ex1I,definition,
% 0.27/0.51 ( ex1I
% 0.27/0.51 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.51 ( ( in @ Xx @ A )
% 0.27/0.51 => ( ( Xphi @ Xx )
% 0.27/0.51 => ( ! [Xy: $i] :
% 0.27/0.51 ( ( in @ Xy @ A )
% 0.27/0.51 => ( ( Xphi @ Xy )
% 0.27/0.51 => ( Xy = Xx ) ) )
% 0.27/0.51 => ( ex1 @ A
% 0.27/0.51 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(ex1I2_type,type,
% 0.27/0.51 ex1I2: $o ).
% 0.27/0.51
% 0.27/0.51 thf(ex1I2,definition,
% 0.27/0.51 ( ex1I2
% 0.27/0.51 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.51 ( ! [Xx: $i] :
% 0.27/0.51 ( ( in @ Xx @ A )
% 0.27/0.51 => ! [Xy: $i] :
% 0.27/0.51 ( ( in @ Xy @ A )
% 0.27/0.51 => ( ( Xphi @ Xx )
% 0.27/0.51 => ( ( Xphi @ Xy )
% 0.27/0.51 => ( Xx = Xy ) ) ) ) )
% 0.27/0.51 => ( ? [Xx: $i] :
% 0.27/0.51 ( ( in @ Xx @ A )
% 0.27/0.51 & ( Xphi @ Xx ) )
% 0.27/0.51 => ( ex1 @ A
% 0.27/0.51 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(singletonsuniq_type,type,
% 0.27/0.51 singletonsuniq: $o ).
% 0.27/0.51
% 0.27/0.51 thf(singletonsuniq,definition,
% 0.27/0.51 ( singletonsuniq
% 0.27/0.51 = ( ! [Xx: $i,Xy: $i] :
% 0.27/0.51 ( ( ( setadjoin @ Xx @ emptyset )
% 0.27/0.51 = ( setadjoin @ Xy @ emptyset ) )
% 0.27/0.51 => ( Xx = Xy ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(atmost1p_type,type,
% 0.27/0.51 atmost1p: $i > $o ).
% 0.27/0.51
% 0.27/0.51 thf(atleast2p_type,type,
% 0.27/0.51 atleast2p: $i > $o ).
% 0.27/0.51
% 0.27/0.51 thf(atmost2p_type,type,
% 0.27/0.51 atmost2p: $i > $o ).
% 0.27/0.51
% 0.27/0.51 thf(upairsetp_type,type,
% 0.27/0.51 upairsetp: $i > $o ).
% 0.27/0.51
% 0.27/0.51 thf(setukpairinjL1_type,type,
% 0.27/0.51 setukpairinjL1: $o ).
% 0.27/0.51
% 0.27/0.51 thf(setukpairinjL1,definition,
% 0.27/0.51 ( setukpairinjL1
% 0.27/0.51 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.27/0.51 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.27/0.51 => ( Xx = Xz ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(kfstsingleton_type,type,
% 0.27/0.51 kfstsingleton: $o ).
% 0.27/0.51
% 0.27/0.51 thf(kfstsingleton,definition,
% 0.27/0.51 ( kfstsingleton
% 0.27/0.51 = ( ! [Xu: $i] :
% 0.27/0.51 ( ( iskpair @ Xu )
% 0.27/0.51 => ( singleton
% 0.27/0.51 @ ( dsetconstr @ ( setunion @ Xu )
% 0.27/0.51 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(theprop_type,type,
% 0.27/0.51 theprop: $o ).
% 0.27/0.51
% 0.27/0.51 thf(theprop,definition,
% 0.27/0.51 ( theprop
% 0.27/0.51 = ( ! [X: $i] :
% 0.27/0.51 ( ( singleton @ X )
% 0.27/0.51 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(kfst_type,type,
% 0.27/0.51 kfst: $i > $i ).
% 0.27/0.51
% 0.27/0.51 thf(kfstpairEq_type,type,
% 0.27/0.51 kfstpairEq: $o ).
% 0.27/0.51
% 0.27/0.51 thf(kfstpairEq,definition,
% 0.27/0.51 ( kfstpairEq
% 0.27/0.51 = ( ! [Xx: $i,Xy: $i] :
% 0.27/0.51 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.27/0.51 = Xx ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(cartprodfstin_type,type,
% 0.27/0.51 cartprodfstin: $o ).
% 0.27/0.51
% 0.27/0.51 thf(cartprodfstin,definition,
% 0.27/0.51 ( cartprodfstin
% 0.27/0.51 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.27/0.51 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.27/0.51 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(setukpairinjL2_type,type,
% 0.27/0.51 setukpairinjL2: $o ).
% 0.27/0.51
% 0.27/0.51 thf(setukpairinjL2,definition,
% 0.27/0.51 ( setukpairinjL2
% 0.27/0.51 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.27/0.51 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.27/0.51 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.27/0.51 => ( Xx = Xz ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(setukpairinjL_type,type,
% 0.27/0.51 setukpairinjL: $o ).
% 0.27/0.51
% 0.27/0.51 thf(setukpairinjL,definition,
% 0.27/0.51 ( setukpairinjL
% 0.27/0.51 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.27/0.51 ( ( ( kpair @ Xx @ Xy )
% 0.27/0.51 = ( kpair @ Xz @ Xu ) )
% 0.27/0.51 => ( Xx = Xz ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 thf(setukpairinjR11,conjecture,
% 0.27/0.51 ( setextAx
% 0.27/0.51 => ( emptysetAx
% 0.27/0.51 => ( setadjoinAx
% 0.27/0.51 => ( powersetAx
% 0.27/0.51 => ( setunionAx
% 0.27/0.51 => ( omega0Ax
% 0.27/0.51 => ( omegaSAx
% 0.27/0.51 => ( omegaIndAx
% 0.27/0.51 => ( replAx
% 0.27/0.51 => ( foundationAx
% 0.27/0.51 => ( wellorderingAx
% 0.27/0.51 => ( descrp
% 0.27/0.51 => ( dsetconstrI
% 0.27/0.51 => ( dsetconstrEL
% 0.27/0.51 => ( dsetconstrER
% 0.27/0.51 => ( exuE1
% 0.27/0.51 => ( prop2setE
% 0.27/0.51 => ( emptysetE
% 0.27/0.51 => ( emptysetimpfalse
% 0.27/0.51 => ( notinemptyset
% 0.27/0.51 => ( exuE3e
% 0.27/0.51 => ( setext
% 0.27/0.51 => ( emptyI
% 0.27/0.51 => ( noeltsimpempty
% 0.27/0.51 => ( setbeta
% 0.27/0.51 => ( nonemptyE1
% 0.27/0.51 => ( nonemptyI
% 0.27/0.51 => ( nonemptyI1
% 0.27/0.51 => ( setadjoinIL
% 0.27/0.51 => ( emptyinunitempty
% 0.27/0.51 => ( setadjoinIR
% 0.27/0.51 => ( setadjoinE
% 0.27/0.51 => ( setadjoinOr
% 0.27/0.51 => ( setoftrueEq
% 0.27/0.51 => ( powersetI
% 0.27/0.51 => ( emptyinPowerset
% 0.27/0.51 => ( emptyInPowerset
% 0.27/0.51 => ( powersetE
% 0.27/0.51 => ( setunionI
% 0.27/0.51 => ( setunionE
% 0.27/0.51 => ( subPowSU
% 0.27/0.51 => ( exuE2
% 0.27/0.51 => ( nonemptyImpWitness
% 0.27/0.51 => ( uniqinunit
% 0.27/0.51 => ( notinsingleton
% 0.27/0.51 => ( eqinunit
% 0.27/0.51 => ( singletonsswitch
% 0.27/0.51 => ( upairsetE
% 0.27/0.51 => ( upairsetIL
% 0.27/0.51 => ( upairsetIR
% 0.27/0.51 => ( emptyE1
% 0.27/0.51 => ( vacuousDall
% 0.27/0.51 => ( quantDeMorgan1
% 0.27/0.51 => ( quantDeMorgan2
% 0.27/0.51 => ( quantDeMorgan3
% 0.27/0.51 => ( quantDeMorgan4
% 0.27/0.51 => ( prop2setI
% 0.27/0.51 => ( prop2set2propI
% 0.27/0.51 => ( notdexE
% 0.27/0.51 => ( notdallE
% 0.27/0.51 => ( exuI1
% 0.27/0.51 => ( exuI3
% 0.27/0.51 => ( exuI2
% 0.27/0.51 => ( inCongP
% 0.27/0.51 => ( in__Cong
% 0.27/0.51 => ( exuE3u
% 0.27/0.51 => ( exu__Cong
% 0.27/0.51 => ( emptyset__Cong
% 0.27/0.51 => ( setadjoin__Cong
% 0.27/0.51 => ( powerset__Cong
% 0.27/0.51 => ( setunion__Cong
% 0.27/0.51 => ( omega__Cong
% 0.27/0.51 => ( exuEu
% 0.27/0.51 => ( descr__Cong
% 0.27/0.51 => ( dsetconstr__Cong
% 0.27/0.51 => ( subsetI1
% 0.27/0.51 => ( eqimpsubset2
% 0.27/0.51 => ( eqimpsubset1
% 0.27/0.51 => ( subsetI2
% 0.27/0.51 => ( emptysetsubset
% 0.27/0.51 => ( subsetE
% 0.27/0.51 => ( subsetE2
% 0.27/0.51 => ( notsubsetI
% 0.27/0.51 => ( notequalI1
% 0.27/0.51 => ( notequalI2
% 0.27/0.51 => ( subsetRefl
% 0.27/0.51 => ( subsetTrans
% 0.27/0.51 => ( setadjoinSub
% 0.27/0.51 => ( setadjoinSub2
% 0.27/0.51 => ( subset2powerset
% 0.27/0.51 => ( setextsub
% 0.27/0.51 => ( subsetemptysetimpeq
% 0.27/0.51 => ( powersetI1
% 0.27/0.51 => ( powersetE1
% 0.27/0.51 => ( inPowerset
% 0.27/0.51 => ( powersetsubset
% 0.27/0.51 => ( sepInPowerset
% 0.27/0.51 => ( sepSubset
% 0.27/0.51 => ( binunionIL
% 0.27/0.51 => ( upairset2IR
% 0.27/0.51 => ( binunionIR
% 0.27/0.51 => ( binunionEcases
% 0.27/0.51 => ( binunionE
% 0.27/0.51 => ( binunionLsub
% 0.27/0.51 => ( binunionRsub
% 0.27/0.51 => ( binintersectI
% 0.27/0.51 => ( binintersectSubset5
% 0.27/0.51 => ( binintersectEL
% 0.27/0.51 => ( binintersectLsub
% 0.27/0.51 => ( binintersectSubset2
% 0.27/0.51 => ( binintersectSubset3
% 0.27/0.51 => ( binintersectER
% 0.27/0.51 => ( disjointsetsI1
% 0.27/0.51 => ( binintersectRsub
% 0.27/0.51 => ( binintersectSubset4
% 0.27/0.51 => ( binintersectSubset1
% 0.27/0.51 => ( bs114d
% 0.27/0.51 => ( setminusI
% 0.27/0.51 => ( setminusEL
% 0.27/0.51 => ( setminusER
% 0.27/0.51 => ( setminusSubset2
% 0.27/0.51 => ( setminusERneg
% 0.27/0.51 => ( setminusELneg
% 0.27/0.51 => ( setminusILneg
% 0.27/0.51 => ( setminusIRneg
% 0.27/0.51 => ( setminusLsub
% 0.27/0.51 => ( setminusSubset1
% 0.27/0.51 => ( symdiffE
% 0.27/0.51 => ( symdiffI1
% 0.27/0.51 => ( symdiffI2
% 0.27/0.51 => ( symdiffIneg1
% 0.27/0.51 => ( symdiffIneg2
% 0.27/0.51 => ( secondinupair
% 0.27/0.51 => ( setukpairIL
% 0.27/0.51 => ( setukpairIR
% 0.27/0.51 => ( kpairiskpair
% 0.27/0.51 => ( kpairp
% 0.27/0.51 => ( singletonsubset
% 0.27/0.51 => ( singletoninpowerset
% 0.27/0.51 => ( singletoninpowunion
% 0.27/0.51 => ( upairset2E
% 0.27/0.51 => ( upairsubunion
% 0.27/0.51 => ( upairinpowunion
% 0.27/0.51 => ( ubforcartprodlem1
% 0.27/0.51 => ( ubforcartprodlem2
% 0.27/0.51 => ( ubforcartprodlem3
% 0.27/0.51 => ( cartprodpairin
% 0.27/0.51 => ( cartprodmempair1
% 0.27/0.51 => ( cartprodmempair
% 0.27/0.51 => ( setunionE2
% 0.27/0.51 => ( setunionsingleton1
% 0.27/0.51 => ( setunionsingleton2
% 0.27/0.51 => ( setunionsingleton
% 0.27/0.51 => ( singletonprop
% 0.27/0.51 => ( ex1E1
% 0.27/0.51 => ( ex1I
% 0.27/0.51 => ( ex1I2
% 0.27/0.51 => ( singletonsuniq
% 0.27/0.51 => ( setukpairinjL1
% 0.27/0.51 => ( kfstsingleton
% 0.27/0.51 => ( theprop
% 0.27/0.51 => ( kfstpairEq
% 0.27/0.51 => ( cartprodfstin
% 0.27/0.51 => ( setukpairinjL2
% 0.27/0.51 => ( setukpairinjL
% 0.27/0.51 => ! [Xx: $i,Xy: $i] :
% 0.27/0.51 ( ( Xx = Xy )
% 0.27/0.51 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.27/0.51 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.51
% 0.27/0.51 %------------------------------------------------------------------------------
% 0.27/0.51 ------------------------
% 3.11/1.83 ---- Embedded in THF ---
% 3.11/1.83 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.11/1.83 %%% Generated on Tue Feb 24 12:35:41 EST 2026
% 3.11/1.83 %%% using '$$dhol' embedding, version 1.3.0.
% 3.11/1.83 %%% Logic specification used:
% 3.11/1.83 %%% thf(spec, logic, $$dhol).
% 3.11/1.83
% 3.11/1.83 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.u7Pd4WLIgv/DTF2DTF23265.p
% See solution above
% 3.11/1.83 ------------------------
% 3.11/1.87 ---- Cleaned THF ---
% 3.11/1.87 thf(in_type,type,
% 3.11/1.87 in: $i > $i > $o ).
% 3.11/1.87
% 3.11/1.87 thf(exu_type,type,
% 3.11/1.87 exu: ( $i > $o ) > $o ).
% 3.11/1.87
% 3.11/1.87 thf(exu,definition,
% 3.11/1.87 ( exu
% 3.11/1.87 = ( ^ [Xphi: $i > $o] :
% 3.11/1.87 ? [Xx: $i] :
% 3.11/1.87 ( ( Xphi @ Xx )
% 3.11/1.87 & ! [Xy: $i] :
% 3.11/1.87 ( ( Xphi @ Xy )
% 3.11/1.87 => ( Xx = Xy ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setextAx_type,type,
% 3.11/1.87 setextAx: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setextAx,definition,
% 3.11/1.87 ( setextAx
% 3.11/1.87 = ( ! [A: $i,B: $i] :
% 3.11/1.87 ( ! [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 <=> ( in @ Xx @ B ) )
% 3.11/1.87 => ( A = B ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(emptyset_type,type,
% 3.11/1.87 emptyset: $i ).
% 3.11/1.87
% 3.11/1.87 thf(emptysetAx_type,type,
% 3.11/1.87 emptysetAx: $o ).
% 3.11/1.87
% 3.11/1.87 thf(emptysetAx,definition,
% 3.11/1.87 ( emptysetAx
% 3.11/1.87 = ( ! [Xx: $i] :
% 3.11/1.87 ~ ( in @ Xx @ emptyset ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setadjoin_type,type,
% 3.11/1.87 setadjoin: $i > $i > $i ).
% 3.11/1.87
% 3.11/1.87 thf(setadjoinAx_type,type,
% 3.11/1.87 setadjoinAx: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setadjoinAx,definition,
% 3.11/1.87 ( setadjoinAx
% 3.11/1.87 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.11/1.87 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.11/1.87 <=> ( ( Xy = Xx )
% 3.11/1.87 | ( in @ Xy @ A ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(powerset_type,type,
% 3.11/1.87 powerset: $i > $i ).
% 3.11/1.87
% 3.11/1.87 thf(powersetAx_type,type,
% 3.11/1.87 powersetAx: $o ).
% 3.11/1.87
% 3.11/1.87 thf(powersetAx,definition,
% 3.11/1.87 ( powersetAx
% 3.11/1.87 = ( ! [A: $i,B: $i] :
% 3.11/1.87 ( ( in @ B @ ( powerset @ A ) )
% 3.11/1.87 <=> ! [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ B )
% 3.11/1.87 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setunion_type,type,
% 3.11/1.87 setunion: $i > $i ).
% 3.11/1.87
% 3.11/1.87 thf(setunionAx_type,type,
% 3.11/1.87 setunionAx: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setunionAx,definition,
% 3.11/1.87 ( setunionAx
% 3.11/1.87 = ( ! [A: $i,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ ( setunion @ A ) )
% 3.11/1.87 <=> ? [B: $i] :
% 3.11/1.87 ( ( in @ Xx @ B )
% 3.11/1.87 & ( in @ B @ A ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(omega_type,type,
% 3.11/1.87 omega: $i ).
% 3.11/1.87
% 3.11/1.87 thf(omega0Ax_type,type,
% 3.11/1.87 omega0Ax: $o ).
% 3.11/1.87
% 3.11/1.87 thf(omega0Ax,definition,
% 3.11/1.87 ( omega0Ax
% 3.11/1.87 = ( in @ emptyset @ omega ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(omegaSAx_type,type,
% 3.11/1.87 omegaSAx: $o ).
% 3.11/1.87
% 3.11/1.87 thf(omegaSAx,definition,
% 3.11/1.87 ( omegaSAx
% 3.11/1.87 = ( ! [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ omega )
% 3.11/1.87 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(omegaIndAx_type,type,
% 3.11/1.87 omegaIndAx: $o ).
% 3.11/1.87
% 3.11/1.87 thf(omegaIndAx,definition,
% 3.11/1.87 ( omegaIndAx
% 3.11/1.87 = ( ! [A: $i] :
% 3.11/1.87 ( ( ( in @ emptyset @ A )
% 3.11/1.87 & ! [Xx: $i] :
% 3.11/1.87 ( ( ( in @ Xx @ omega )
% 3.11/1.87 & ( in @ Xx @ A ) )
% 3.11/1.87 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 3.11/1.87 => ! [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ omega )
% 3.11/1.87 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(replAx_type,type,
% 3.11/1.87 replAx: $o ).
% 3.11/1.87
% 3.11/1.87 thf(replAx,definition,
% 3.11/1.87 ( replAx
% 3.11/1.87 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 3.11/1.87 ( ! [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 => ( exu
% 3.11/1.87 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 3.11/1.87 => ? [B: $i] :
% 3.11/1.87 ! [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ B )
% 3.11/1.87 <=> ? [Xy: $i] :
% 3.11/1.87 ( ( in @ Xy @ A )
% 3.11/1.87 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(foundationAx_type,type,
% 3.11/1.87 foundationAx: $o ).
% 3.11/1.87
% 3.11/1.87 thf(foundationAx,definition,
% 3.11/1.87 ( foundationAx
% 3.11/1.87 = ( ! [A: $i] :
% 3.11/1.87 ( ? [Xx: $i] : ( in @ Xx @ A )
% 3.11/1.87 => ? [B: $i] :
% 3.11/1.87 ( ( in @ B @ A )
% 3.11/1.87 & ~ ? [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ B )
% 3.11/1.87 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(wellorderingAx_type,type,
% 3.11/1.87 wellorderingAx: $o ).
% 3.11/1.87
% 3.11/1.87 thf(wellorderingAx,definition,
% 3.11/1.87 ( wellorderingAx
% 3.11/1.87 = ( ! [A: $i] :
% 3.11/1.87 ? [B: $i] :
% 3.11/1.87 ( ! [C: $i] :
% 3.11/1.87 ( ( in @ C @ B )
% 3.11/1.87 => ! [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ C )
% 3.11/1.87 => ( in @ Xx @ A ) ) )
% 3.11/1.87 & ! [Xx: $i,Xy: $i] :
% 3.11/1.87 ( ( ( in @ Xx @ A )
% 3.11/1.87 & ( in @ Xy @ A ) )
% 3.11/1.87 => ( ! [C: $i] :
% 3.11/1.87 ( ( in @ C @ B )
% 3.11/1.87 => ( ( in @ Xx @ C )
% 3.11/1.87 <=> ( in @ Xy @ C ) ) )
% 3.11/1.87 => ( Xx = Xy ) ) )
% 3.11/1.87 & ! [C: $i,D: $i] :
% 3.11/1.87 ( ( ( in @ C @ B )
% 3.11/1.87 & ( in @ D @ B ) )
% 3.11/1.87 => ( ! [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ C )
% 3.11/1.87 => ( in @ Xx @ D ) )
% 3.11/1.87 | ! [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ D )
% 3.11/1.87 => ( in @ Xx @ C ) ) ) )
% 3.11/1.87 & ! [C: $i] :
% 3.11/1.87 ( ( ! [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ C )
% 3.11/1.87 => ( in @ Xx @ A ) )
% 3.11/1.87 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 3.11/1.87 => ? [D: $i,Xx: $i] :
% 3.11/1.87 ( ( in @ D @ B )
% 3.11/1.87 & ( in @ Xx @ C )
% 3.11/1.87 & ~ ? [Xy: $i] :
% 3.11/1.87 ( ( in @ Xy @ D )
% 3.11/1.87 & ( in @ Xy @ C ) )
% 3.11/1.87 & ! [E: $i] :
% 3.11/1.87 ( ( in @ E @ B )
% 3.11/1.87 => ( ! [Xy: $i] :
% 3.11/1.87 ( ( in @ Xy @ E )
% 3.11/1.87 => ( in @ Xy @ D ) )
% 3.11/1.87 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(descr_type,type,
% 3.11/1.87 descr: ( $i > $o ) > $i ).
% 3.11/1.87
% 3.11/1.87 thf(descrp_type,type,
% 3.11/1.87 descrp: $o ).
% 3.11/1.87
% 3.11/1.87 thf(descrp,definition,
% 3.11/1.87 ( descrp
% 3.11/1.87 = ( ! [Xphi: $i > $o] :
% 3.11/1.87 ( ( exu
% 3.11/1.87 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.11/1.87 => ( Xphi
% 3.11/1.87 @ ( descr
% 3.11/1.87 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(dsetconstr_type,type,
% 3.11/1.87 dsetconstr: $i > ( $i > $o ) > $i ).
% 3.11/1.87
% 3.11/1.87 thf(dsetconstrI_type,type,
% 3.11/1.87 dsetconstrI: $o ).
% 3.11/1.87
% 3.11/1.87 thf(dsetconstrI,definition,
% 3.11/1.87 ( dsetconstrI
% 3.11/1.87 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 => ( ( Xphi @ Xx )
% 3.11/1.87 => ( in @ Xx
% 3.11/1.87 @ ( dsetconstr @ A
% 3.11/1.87 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(dsetconstrEL_type,type,
% 3.11/1.87 dsetconstrEL: $o ).
% 3.11/1.87
% 3.11/1.87 thf(dsetconstrEL,definition,
% 3.11/1.87 ( dsetconstrEL
% 3.11/1.87 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx
% 3.11/1.87 @ ( dsetconstr @ A
% 3.11/1.87 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.11/1.87 => ( in @ Xx @ A ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(dsetconstrER_type,type,
% 3.11/1.87 dsetconstrER: $o ).
% 3.11/1.87
% 3.11/1.87 thf(dsetconstrER,definition,
% 3.11/1.87 ( dsetconstrER
% 3.11/1.87 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx
% 3.11/1.87 @ ( dsetconstr @ A
% 3.11/1.87 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.11/1.87 => ( Xphi @ Xx ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(exuE1_type,type,
% 3.11/1.87 exuE1: $o ).
% 3.11/1.87
% 3.11/1.87 thf(exuE1,definition,
% 3.11/1.87 ( exuE1
% 3.11/1.87 = ( ! [Xphi: $i > $o] :
% 3.11/1.87 ( ( exu
% 3.11/1.87 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.11/1.87 => ? [Xx: $i] :
% 3.11/1.87 ( ( Xphi @ Xx )
% 3.11/1.87 & ! [Xy: $i] :
% 3.11/1.87 ( ( Xphi @ Xy )
% 3.11/1.87 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(prop2set_type,type,
% 3.11/1.87 prop2set: $o > $i ).
% 3.11/1.87
% 3.11/1.87 thf(prop2setE_type,type,
% 3.11/1.87 prop2setE: $o ).
% 3.11/1.87
% 3.11/1.87 thf(prop2setE,definition,
% 3.11/1.87 ( prop2setE
% 3.11/1.87 = ( ! [Xphi: $o,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 3.11/1.87 => Xphi ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(emptysetE_type,type,
% 3.11/1.87 emptysetE: $o ).
% 3.11/1.87
% 3.11/1.87 thf(emptysetE,definition,
% 3.11/1.87 ( emptysetE
% 3.11/1.87 = ( ! [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ emptyset )
% 3.11/1.87 => ! [Xphi: $o] : Xphi ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(emptysetimpfalse_type,type,
% 3.11/1.87 emptysetimpfalse: $o ).
% 3.11/1.87
% 3.11/1.87 thf(emptysetimpfalse,definition,
% 3.11/1.87 ( emptysetimpfalse
% 3.11/1.87 = ( ! [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ emptyset )
% 3.11/1.87 => $false ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(notinemptyset_type,type,
% 3.11/1.87 notinemptyset: $o ).
% 3.11/1.87
% 3.11/1.87 thf(notinemptyset,definition,
% 3.11/1.87 ( notinemptyset
% 3.11/1.87 = ( ! [Xx: $i] :
% 3.11/1.87 ~ ( in @ Xx @ emptyset ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(exuE3e_type,type,
% 3.11/1.87 exuE3e: $o ).
% 3.11/1.87
% 3.11/1.87 thf(exuE3e,definition,
% 3.11/1.87 ( exuE3e
% 3.11/1.87 = ( ! [Xphi: $i > $o] :
% 3.11/1.87 ( ( exu
% 3.11/1.87 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.11/1.87 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setext_type,type,
% 3.11/1.87 setext: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setext,definition,
% 3.11/1.87 ( setext
% 3.11/1.87 = ( ! [A: $i,B: $i] :
% 3.11/1.87 ( ! [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 => ( in @ Xx @ B ) )
% 3.11/1.87 => ( ! [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ B )
% 3.11/1.87 => ( in @ Xx @ A ) )
% 3.11/1.87 => ( A = B ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(emptyI_type,type,
% 3.11/1.87 emptyI: $o ).
% 3.11/1.87
% 3.11/1.87 thf(emptyI,definition,
% 3.11/1.87 ( emptyI
% 3.11/1.87 = ( ! [A: $i] :
% 3.11/1.87 ( ! [Xx: $i] :
% 3.11/1.87 ~ ( in @ Xx @ A )
% 3.11/1.87 => ( A = emptyset ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(noeltsimpempty_type,type,
% 3.11/1.87 noeltsimpempty: $o ).
% 3.11/1.87
% 3.11/1.87 thf(noeltsimpempty,definition,
% 3.11/1.87 ( noeltsimpempty
% 3.11/1.87 = ( ! [A: $i] :
% 3.11/1.87 ( ! [Xx: $i] :
% 3.11/1.87 ~ ( in @ Xx @ A )
% 3.11/1.87 => ( A = emptyset ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setbeta_type,type,
% 3.11/1.87 setbeta: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setbeta,definition,
% 3.11/1.87 ( setbeta
% 3.11/1.87 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 => ( ( in @ Xx
% 3.11/1.87 @ ( dsetconstr @ A
% 3.11/1.87 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.11/1.87 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(nonempty_type,type,
% 3.11/1.87 nonempty: $i > $o ).
% 3.11/1.87
% 3.11/1.87 thf(nonempty,definition,
% 3.11/1.87 ( nonempty
% 3.11/1.87 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(nonemptyE1_type,type,
% 3.11/1.87 nonemptyE1: $o ).
% 3.11/1.87
% 3.11/1.87 thf(nonemptyE1,definition,
% 3.11/1.87 ( nonemptyE1
% 3.11/1.87 = ( ! [A: $i] :
% 3.11/1.87 ( ( nonempty @ A )
% 3.11/1.87 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(nonemptyI_type,type,
% 3.11/1.87 nonemptyI: $o ).
% 3.11/1.87
% 3.11/1.87 thf(nonemptyI,definition,
% 3.11/1.87 ( nonemptyI
% 3.11/1.87 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 => ( ( Xphi @ Xx )
% 3.11/1.87 => ( nonempty
% 3.11/1.87 @ ( dsetconstr @ A
% 3.11/1.87 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(nonemptyI1_type,type,
% 3.11/1.87 nonemptyI1: $o ).
% 3.11/1.87
% 3.11/1.87 thf(nonemptyI1,definition,
% 3.11/1.87 ( nonemptyI1
% 3.11/1.87 = ( ! [A: $i] :
% 3.11/1.87 ( ? [Xx: $i] : ( in @ Xx @ A )
% 3.11/1.87 => ( nonempty @ A ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setadjoinIL_type,type,
% 3.11/1.87 setadjoinIL: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setadjoinIL,definition,
% 3.11/1.87 ( setadjoinIL
% 3.11/1.87 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(emptyinunitempty_type,type,
% 3.11/1.87 emptyinunitempty: $o ).
% 3.11/1.87
% 3.11/1.87 thf(emptyinunitempty,definition,
% 3.11/1.87 ( emptyinunitempty
% 3.11/1.87 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setadjoinIR_type,type,
% 3.11/1.87 setadjoinIR: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setadjoinIR,definition,
% 3.11/1.87 ( setadjoinIR
% 3.11/1.87 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.11/1.87 ( ( in @ Xy @ A )
% 3.11/1.87 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setadjoinE_type,type,
% 3.11/1.87 setadjoinE: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setadjoinE,definition,
% 3.11/1.87 ( setadjoinE
% 3.11/1.87 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.11/1.87 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.11/1.87 => ! [Xphi: $o] :
% 3.11/1.87 ( ( ( Xy = Xx )
% 3.11/1.87 => Xphi )
% 3.11/1.87 => ( ( ( in @ Xy @ A )
% 3.11/1.87 => Xphi )
% 3.11/1.87 => Xphi ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setadjoinOr_type,type,
% 3.11/1.87 setadjoinOr: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setadjoinOr,definition,
% 3.11/1.87 ( setadjoinOr
% 3.11/1.87 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.11/1.87 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.11/1.87 => ( ( Xy = Xx )
% 3.11/1.87 | ( in @ Xy @ A ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setoftrueEq_type,type,
% 3.11/1.87 setoftrueEq: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setoftrueEq,definition,
% 3.11/1.87 ( setoftrueEq
% 3.11/1.87 = ( ! [A: $i] :
% 3.11/1.87 ( ( dsetconstr @ A
% 3.11/1.87 @ ^ [Xx: $i] : $true )
% 3.11/1.87 = A ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(powersetI_type,type,
% 3.11/1.87 powersetI: $o ).
% 3.11/1.87
% 3.11/1.87 thf(powersetI,definition,
% 3.11/1.87 ( powersetI
% 3.11/1.87 = ( ! [A: $i,B: $i] :
% 3.11/1.87 ( ! [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ B )
% 3.11/1.87 => ( in @ Xx @ A ) )
% 3.11/1.87 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(emptyinPowerset_type,type,
% 3.11/1.87 emptyinPowerset: $o ).
% 3.11/1.87
% 3.11/1.87 thf(emptyinPowerset,definition,
% 3.11/1.87 ( emptyinPowerset
% 3.11/1.87 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(emptyInPowerset_type,type,
% 3.11/1.87 emptyInPowerset: $o ).
% 3.11/1.87
% 3.11/1.87 thf(emptyInPowerset,definition,
% 3.11/1.87 ( emptyInPowerset
% 3.11/1.87 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(powersetE_type,type,
% 3.11/1.87 powersetE: $o ).
% 3.11/1.87
% 3.11/1.87 thf(powersetE,definition,
% 3.11/1.87 ( powersetE
% 3.11/1.87 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.87 ( ( in @ B @ ( powerset @ A ) )
% 3.11/1.87 => ( ( in @ Xx @ B )
% 3.11/1.87 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setunionI_type,type,
% 3.11/1.87 setunionI: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setunionI,definition,
% 3.11/1.87 ( setunionI
% 3.11/1.87 = ( ! [A: $i,Xx: $i,B: $i] :
% 3.11/1.87 ( ( in @ Xx @ B )
% 3.11/1.87 => ( ( in @ B @ A )
% 3.11/1.87 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setunionE_type,type,
% 3.11/1.87 setunionE: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setunionE,definition,
% 3.11/1.87 ( setunionE
% 3.11/1.87 = ( ! [A: $i,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ ( setunion @ A ) )
% 3.11/1.87 => ! [Xphi: $o] :
% 3.11/1.87 ( ! [B: $i] :
% 3.11/1.87 ( ( in @ Xx @ B )
% 3.11/1.87 => ( ( in @ B @ A )
% 3.11/1.87 => Xphi ) )
% 3.11/1.87 => Xphi ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(subPowSU_type,type,
% 3.11/1.87 subPowSU: $o ).
% 3.11/1.87
% 3.11/1.87 thf(subPowSU,definition,
% 3.11/1.87 ( subPowSU
% 3.11/1.87 = ( ! [A: $i,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(exuE2_type,type,
% 3.11/1.87 exuE2: $o ).
% 3.11/1.87
% 3.11/1.87 thf(exuE2,definition,
% 3.11/1.87 ( exuE2
% 3.11/1.87 = ( ! [Xphi: $i > $o] :
% 3.11/1.87 ( ( exu
% 3.11/1.87 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.11/1.87 => ? [Xx: $i] :
% 3.11/1.87 ! [Xy: $i] :
% 3.11/1.87 ( ( Xphi @ Xy )
% 3.11/1.87 <=> ( Xy = Xx ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(nonemptyImpWitness_type,type,
% 3.11/1.87 nonemptyImpWitness: $o ).
% 3.11/1.87
% 3.11/1.87 thf(nonemptyImpWitness,definition,
% 3.11/1.87 ( nonemptyImpWitness
% 3.11/1.87 = ( ! [A: $i] :
% 3.11/1.87 ( ( nonempty @ A )
% 3.11/1.87 => ? [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 & $true ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(uniqinunit_type,type,
% 3.11/1.87 uniqinunit: $o ).
% 3.11/1.87
% 3.11/1.87 thf(uniqinunit,definition,
% 3.11/1.87 ( uniqinunit
% 3.11/1.87 = ( ! [Xx: $i,Xy: $i] :
% 3.11/1.87 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.11/1.87 => ( Xx = Xy ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(notinsingleton_type,type,
% 3.11/1.87 notinsingleton: $o ).
% 3.11/1.87
% 3.11/1.87 thf(notinsingleton,definition,
% 3.11/1.87 ( notinsingleton
% 3.11/1.87 = ( ! [Xx: $i,Xy: $i] :
% 3.11/1.87 ( ( Xx != Xy )
% 3.11/1.87 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(eqinunit_type,type,
% 3.11/1.87 eqinunit: $o ).
% 3.11/1.87
% 3.11/1.87 thf(eqinunit,definition,
% 3.11/1.87 ( eqinunit
% 3.11/1.87 = ( ! [Xx: $i,Xy: $i] :
% 3.11/1.87 ( ( Xx = Xy )
% 3.11/1.87 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(singletonsswitch_type,type,
% 3.11/1.87 singletonsswitch: $o ).
% 3.11/1.87
% 3.11/1.87 thf(singletonsswitch,definition,
% 3.11/1.87 ( singletonsswitch
% 3.11/1.87 = ( ! [Xx: $i,Xy: $i] :
% 3.11/1.87 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.11/1.87 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(upairsetE_type,type,
% 3.11/1.87 upairsetE: $o ).
% 3.11/1.87
% 3.11/1.87 thf(upairsetE,definition,
% 3.11/1.87 ( upairsetE
% 3.11/1.87 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.11/1.87 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 3.11/1.87 => ( ( Xz = Xx )
% 3.11/1.87 | ( Xz = Xy ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(upairsetIL_type,type,
% 3.11/1.87 upairsetIL: $o ).
% 3.11/1.87
% 3.11/1.87 thf(upairsetIL,definition,
% 3.11/1.87 ( upairsetIL
% 3.11/1.87 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(upairsetIR_type,type,
% 3.11/1.87 upairsetIR: $o ).
% 3.11/1.87
% 3.11/1.87 thf(upairsetIR,definition,
% 3.11/1.87 ( upairsetIR
% 3.11/1.87 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(emptyE1_type,type,
% 3.11/1.87 emptyE1: $o ).
% 3.11/1.87
% 3.11/1.87 thf(emptyE1,definition,
% 3.11/1.87 ( emptyE1
% 3.11/1.87 = ( ! [A: $i,Xphi: $i > $o] :
% 3.11/1.87 ( ? [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 & ( Xphi @ Xx ) )
% 3.11/1.87 => ( ( ( dsetconstr @ A
% 3.11/1.87 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.11/1.87 = emptyset )
% 3.11/1.87 => $false ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(vacuousDall_type,type,
% 3.11/1.87 vacuousDall: $o ).
% 3.11/1.87
% 3.11/1.87 thf(vacuousDall,definition,
% 3.11/1.87 ( vacuousDall
% 3.11/1.87 = ( ! [Xphi: $i > $o,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ emptyset )
% 3.11/1.87 => ( Xphi @ Xx ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(quantDeMorgan1_type,type,
% 3.11/1.87 quantDeMorgan1: $o ).
% 3.11/1.87
% 3.11/1.87 thf(quantDeMorgan1,definition,
% 3.11/1.87 ( quantDeMorgan1
% 3.11/1.87 = ( ! [A: $i,Xphi: $i > $o] :
% 3.11/1.87 ( ~ ! [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 => ( Xphi @ Xx ) )
% 3.11/1.87 => ? [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(quantDeMorgan2_type,type,
% 3.11/1.87 quantDeMorgan2: $o ).
% 3.11/1.87
% 3.11/1.87 thf(quantDeMorgan2,definition,
% 3.11/1.87 ( quantDeMorgan2
% 3.11/1.87 = ( ! [A: $i,Xphi: $i > $o] :
% 3.11/1.87 ( ! [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 => ~ ( Xphi @ Xx ) )
% 3.11/1.87 => ~ ? [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 & ( Xphi @ Xx ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(quantDeMorgan3_type,type,
% 3.11/1.87 quantDeMorgan3: $o ).
% 3.11/1.87
% 3.11/1.87 thf(quantDeMorgan3,definition,
% 3.11/1.87 ( quantDeMorgan3
% 3.11/1.87 = ( ! [A: $i,Xphi: $i > $o] :
% 3.11/1.87 ( ~ ? [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 & ( Xphi @ Xx ) )
% 3.11/1.87 => ! [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(quantDeMorgan4_type,type,
% 3.11/1.87 quantDeMorgan4: $o ).
% 3.11/1.87
% 3.11/1.87 thf(quantDeMorgan4,definition,
% 3.11/1.87 ( quantDeMorgan4
% 3.11/1.87 = ( ! [A: $i,Xphi: $i > $o] :
% 3.11/1.87 ( ? [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 & ~ ( Xphi @ Xx ) )
% 3.11/1.87 => ~ ! [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 => ( Xphi @ Xx ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(prop2setI_type,type,
% 3.11/1.87 prop2setI: $o ).
% 3.11/1.87
% 3.11/1.87 thf(prop2setI,definition,
% 3.11/1.87 ( prop2setI
% 3.11/1.87 = ( ! [Xphi: $o] :
% 3.11/1.87 ( Xphi
% 3.11/1.87 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(set2prop_type,type,
% 3.11/1.87 set2prop: $i > $o ).
% 3.11/1.87
% 3.11/1.87 thf(prop2set2propI_type,type,
% 3.11/1.87 prop2set2propI: $o ).
% 3.11/1.87
% 3.11/1.87 thf(prop2set2propI,definition,
% 3.11/1.87 ( prop2set2propI
% 3.11/1.87 = ( ! [Xphi: $o] :
% 3.11/1.87 ( Xphi
% 3.11/1.87 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(notdexE_type,type,
% 3.11/1.87 notdexE: $o ).
% 3.11/1.87
% 3.11/1.87 thf(notdexE,definition,
% 3.11/1.87 ( notdexE
% 3.11/1.87 = ( ! [A: $i,Xphi: $i > $o] :
% 3.11/1.87 ( ~ ? [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 & ( Xphi @ Xx ) )
% 3.11/1.87 => ! [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(notdallE_type,type,
% 3.11/1.87 notdallE: $o ).
% 3.11/1.87
% 3.11/1.87 thf(notdallE,definition,
% 3.11/1.87 ( notdallE
% 3.11/1.87 = ( ! [A: $i,Xphi: $i > $o] :
% 3.11/1.87 ( ~ ! [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 => ( Xphi @ Xx ) )
% 3.11/1.87 => ? [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(exuI1_type,type,
% 3.11/1.87 exuI1: $o ).
% 3.11/1.87
% 3.11/1.87 thf(exuI1,definition,
% 3.11/1.87 ( exuI1
% 3.11/1.87 = ( ! [Xphi: $i > $o] :
% 3.11/1.87 ( ? [Xx: $i] :
% 3.11/1.87 ( ( Xphi @ Xx )
% 3.11/1.87 & ! [Xy: $i] :
% 3.11/1.87 ( ( Xphi @ Xy )
% 3.11/1.87 => ( Xx = Xy ) ) )
% 3.11/1.87 => ( exu
% 3.11/1.87 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(exuI3_type,type,
% 3.11/1.87 exuI3: $o ).
% 3.11/1.87
% 3.11/1.87 thf(exuI3,definition,
% 3.11/1.87 ( exuI3
% 3.11/1.87 = ( ! [Xphi: $i > $o] :
% 3.11/1.87 ( ? [Xx: $i] : ( Xphi @ Xx )
% 3.11/1.87 => ( ! [Xx: $i,Xy: $i] :
% 3.11/1.87 ( ( Xphi @ Xx )
% 3.11/1.87 => ( ( Xphi @ Xy )
% 3.11/1.87 => ( Xx = Xy ) ) )
% 3.11/1.87 => ( exu
% 3.11/1.87 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(exuI2_type,type,
% 3.11/1.87 exuI2: $o ).
% 3.11/1.87
% 3.11/1.87 thf(exuI2,definition,
% 3.11/1.87 ( exuI2
% 3.11/1.87 = ( ! [Xphi: $i > $o] :
% 3.11/1.87 ( ? [Xx: $i] :
% 3.11/1.87 ! [Xy: $i] :
% 3.11/1.87 ( ( Xphi @ Xy )
% 3.11/1.87 <=> ( Xy = Xx ) )
% 3.11/1.87 => ( exu
% 3.11/1.87 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(inCongP_type,type,
% 3.11/1.87 inCongP: $o ).
% 3.11/1.87
% 3.11/1.87 thf(inCongP,definition,
% 3.11/1.87 ( inCongP
% 3.11/1.87 = ( ! [A: $i,B: $i] :
% 3.11/1.87 ( ( A = B )
% 3.11/1.87 => ! [Xx: $i,Xy: $i] :
% 3.11/1.87 ( ( Xx = Xy )
% 3.11/1.87 => ( ( in @ Xx @ A )
% 3.11/1.87 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(in__Cong_type,type,
% 3.11/1.87 in__Cong: $o ).
% 3.11/1.87
% 3.11/1.87 thf(in__Cong,definition,
% 3.11/1.87 ( in__Cong
% 3.11/1.87 = ( ! [A: $i,B: $i] :
% 3.11/1.87 ( ( A = B )
% 3.11/1.87 => ! [Xx: $i,Xy: $i] :
% 3.11/1.87 ( ( Xx = Xy )
% 3.11/1.87 => ( ( in @ Xx @ A )
% 3.11/1.87 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(exuE3u_type,type,
% 3.11/1.87 exuE3u: $o ).
% 3.11/1.87
% 3.11/1.87 thf(exuE3u,definition,
% 3.11/1.87 ( exuE3u
% 3.11/1.87 = ( ! [Xphi: $i > $o] :
% 3.11/1.87 ( ( exu
% 3.11/1.87 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.11/1.87 => ! [Xx: $i,Xy: $i] :
% 3.11/1.87 ( ( Xphi @ Xx )
% 3.11/1.87 => ( ( Xphi @ Xy )
% 3.11/1.87 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(exu__Cong_type,type,
% 3.11/1.87 exu__Cong: $o ).
% 3.11/1.87
% 3.11/1.87 thf(exu__Cong,definition,
% 3.11/1.87 ( exu__Cong
% 3.11/1.87 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.11/1.87 ( ! [Xx: $i,Xy: $i] :
% 3.11/1.87 ( ( Xx = Xy )
% 3.11/1.87 => ( ( Xphi @ Xx )
% 3.11/1.87 <=> ( Xpsi @ Xy ) ) )
% 3.11/1.87 => ( ( exu
% 3.11/1.87 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.11/1.87 <=> ( exu
% 3.11/1.87 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(emptyset__Cong_type,type,
% 3.11/1.87 emptyset__Cong: $o ).
% 3.11/1.87
% 3.11/1.87 thf(emptyset__Cong,definition,
% 3.11/1.87 ( emptyset__Cong
% 3.11/1.87 = ( emptyset = emptyset ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setadjoin__Cong_type,type,
% 3.11/1.87 setadjoin__Cong: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setadjoin__Cong,definition,
% 3.11/1.87 ( setadjoin__Cong
% 3.11/1.87 = ( ! [Xx: $i,Xy: $i] :
% 3.11/1.87 ( ( Xx = Xy )
% 3.11/1.87 => ! [Xz: $i,Xu: $i] :
% 3.11/1.87 ( ( Xz = Xu )
% 3.11/1.87 => ( ( setadjoin @ Xx @ Xz )
% 3.11/1.87 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(powerset__Cong_type,type,
% 3.11/1.87 powerset__Cong: $o ).
% 3.11/1.87
% 3.11/1.87 thf(powerset__Cong,definition,
% 3.11/1.87 ( powerset__Cong
% 3.11/1.87 = ( ! [A: $i,B: $i] :
% 3.11/1.87 ( ( A = B )
% 3.11/1.87 => ( ( powerset @ A )
% 3.11/1.87 = ( powerset @ B ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setunion__Cong_type,type,
% 3.11/1.87 setunion__Cong: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setunion__Cong,definition,
% 3.11/1.87 ( setunion__Cong
% 3.11/1.87 = ( ! [A: $i,B: $i] :
% 3.11/1.87 ( ( A = B )
% 3.11/1.87 => ( ( setunion @ A )
% 3.11/1.87 = ( setunion @ B ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(omega__Cong_type,type,
% 3.11/1.87 omega__Cong: $o ).
% 3.11/1.87
% 3.11/1.87 thf(omega__Cong,definition,
% 3.11/1.87 ( omega__Cong
% 3.11/1.87 = ( omega = omega ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(exuEu_type,type,
% 3.11/1.87 exuEu: $o ).
% 3.11/1.87
% 3.11/1.87 thf(exuEu,definition,
% 3.11/1.87 ( exuEu
% 3.11/1.87 = ( ! [Xphi: $i > $o] :
% 3.11/1.87 ( ( exu
% 3.11/1.87 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.11/1.87 => ! [Xx: $i,Xy: $i] :
% 3.11/1.87 ( ( Xphi @ Xx )
% 3.11/1.87 => ( ( Xphi @ Xy )
% 3.11/1.87 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(descr__Cong_type,type,
% 3.11/1.87 descr__Cong: $o ).
% 3.11/1.87
% 3.11/1.87 thf(descr__Cong,definition,
% 3.11/1.87 ( descr__Cong
% 3.11/1.87 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.11/1.87 ( ! [Xx: $i,Xy: $i] :
% 3.11/1.87 ( ( Xx = Xy )
% 3.11/1.87 => ( ( Xphi @ Xx )
% 3.11/1.87 <=> ( Xpsi @ Xy ) ) )
% 3.11/1.87 => ( ( exu
% 3.11/1.87 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.11/1.87 => ( ( exu
% 3.11/1.87 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 3.11/1.87 => ( ( descr
% 3.11/1.87 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.11/1.87 = ( descr
% 3.11/1.87 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(dsetconstr__Cong_type,type,
% 3.11/1.87 dsetconstr__Cong: $o ).
% 3.11/1.87
% 3.11/1.87 thf(dsetconstr__Cong,definition,
% 3.11/1.87 ( dsetconstr__Cong
% 3.11/1.87 = ( ! [A: $i,B: $i] :
% 3.11/1.87 ( ( A = B )
% 3.11/1.87 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.11/1.87 ( ! [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 => ! [Xy: $i] :
% 3.11/1.87 ( ( in @ Xy @ B )
% 3.11/1.87 => ( ( Xx = Xy )
% 3.11/1.87 => ( ( Xphi @ Xx )
% 3.11/1.87 <=> ( Xpsi @ Xy ) ) ) ) )
% 3.11/1.87 => ( ( dsetconstr @ A
% 3.11/1.87 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.11/1.87 = ( dsetconstr @ B
% 3.11/1.87 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(subset_type,type,
% 3.11/1.87 subset: $i > $i > $o ).
% 3.11/1.87
% 3.11/1.87 thf(disjoint_type,type,
% 3.11/1.87 disjoint: $i > $i > $o ).
% 3.11/1.87
% 3.11/1.87 thf(setsmeet_type,type,
% 3.11/1.87 setsmeet: $i > $i > $o ).
% 3.11/1.87
% 3.11/1.87 thf(subsetI1_type,type,
% 3.11/1.87 subsetI1: $o ).
% 3.11/1.87
% 3.11/1.87 thf(subsetI1,definition,
% 3.11/1.87 ( subsetI1
% 3.11/1.87 = ( ! [A: $i,B: $i] :
% 3.11/1.87 ( ! [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 => ( in @ Xx @ B ) )
% 3.11/1.87 => ( subset @ A @ B ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(eqimpsubset2_type,type,
% 3.11/1.87 eqimpsubset2: $o ).
% 3.11/1.87
% 3.11/1.87 thf(eqimpsubset2,definition,
% 3.11/1.87 ( eqimpsubset2
% 3.11/1.87 = ( ! [A: $i,B: $i] :
% 3.11/1.87 ( ( A = B )
% 3.11/1.87 => ( subset @ B @ A ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(eqimpsubset1_type,type,
% 3.11/1.87 eqimpsubset1: $o ).
% 3.11/1.87
% 3.11/1.87 thf(eqimpsubset1,definition,
% 3.11/1.87 ( eqimpsubset1
% 3.11/1.87 = ( ! [A: $i,B: $i] :
% 3.11/1.87 ( ( A = B )
% 3.11/1.87 => ( subset @ A @ B ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(subsetI2_type,type,
% 3.11/1.87 subsetI2: $o ).
% 3.11/1.87
% 3.11/1.87 thf(subsetI2,definition,
% 3.11/1.87 ( subsetI2
% 3.11/1.87 = ( ! [A: $i,B: $i] :
% 3.11/1.87 ( ! [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 => ( in @ Xx @ B ) )
% 3.11/1.87 => ( subset @ A @ B ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(emptysetsubset_type,type,
% 3.11/1.87 emptysetsubset: $o ).
% 3.11/1.87
% 3.11/1.87 thf(emptysetsubset,definition,
% 3.11/1.87 ( emptysetsubset
% 3.11/1.87 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(subsetE_type,type,
% 3.11/1.87 subsetE: $o ).
% 3.11/1.87
% 3.11/1.87 thf(subsetE,definition,
% 3.11/1.87 ( subsetE
% 3.11/1.87 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.87 ( ( subset @ A @ B )
% 3.11/1.87 => ( ( in @ Xx @ A )
% 3.11/1.87 => ( in @ Xx @ B ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(subsetE2_type,type,
% 3.11/1.87 subsetE2: $o ).
% 3.11/1.87
% 3.11/1.87 thf(subsetE2,definition,
% 3.11/1.87 ( subsetE2
% 3.11/1.87 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.87 ( ( subset @ A @ B )
% 3.11/1.87 => ( ~ ( in @ Xx @ B )
% 3.11/1.87 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(notsubsetI_type,type,
% 3.11/1.87 notsubsetI: $o ).
% 3.11/1.87
% 3.11/1.87 thf(notsubsetI,definition,
% 3.11/1.87 ( notsubsetI
% 3.11/1.87 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 => ( ~ ( in @ Xx @ B )
% 3.11/1.87 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(notequalI1_type,type,
% 3.11/1.87 notequalI1: $o ).
% 3.11/1.87
% 3.11/1.87 thf(notequalI1,definition,
% 3.11/1.87 ( notequalI1
% 3.11/1.87 = ( ! [A: $i,B: $i] :
% 3.11/1.87 ( ~ ( subset @ A @ B )
% 3.11/1.87 => ( A != B ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(notequalI2_type,type,
% 3.11/1.87 notequalI2: $o ).
% 3.11/1.87
% 3.11/1.87 thf(notequalI2,definition,
% 3.11/1.87 ( notequalI2
% 3.11/1.87 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 => ( ~ ( in @ Xx @ B )
% 3.11/1.87 => ( A != B ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(subsetRefl_type,type,
% 3.11/1.87 subsetRefl: $o ).
% 3.11/1.87
% 3.11/1.87 thf(subsetRefl,definition,
% 3.11/1.87 ( subsetRefl
% 3.11/1.87 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(subsetTrans_type,type,
% 3.11/1.87 subsetTrans: $o ).
% 3.11/1.87
% 3.11/1.87 thf(subsetTrans,definition,
% 3.11/1.87 ( subsetTrans
% 3.11/1.87 = ( ! [A: $i,B: $i,C: $i] :
% 3.11/1.87 ( ( subset @ A @ B )
% 3.11/1.87 => ( ( subset @ B @ C )
% 3.11/1.87 => ( subset @ A @ C ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setadjoinSub_type,type,
% 3.11/1.87 setadjoinSub: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setadjoinSub,definition,
% 3.11/1.87 ( setadjoinSub
% 3.11/1.87 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setadjoinSub2_type,type,
% 3.11/1.87 setadjoinSub2: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setadjoinSub2,definition,
% 3.11/1.87 ( setadjoinSub2
% 3.11/1.87 = ( ! [A: $i,Xx: $i,B: $i] :
% 3.11/1.87 ( ( subset @ A @ B )
% 3.11/1.87 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(subset2powerset_type,type,
% 3.11/1.87 subset2powerset: $o ).
% 3.11/1.87
% 3.11/1.87 thf(subset2powerset,definition,
% 3.11/1.87 ( subset2powerset
% 3.11/1.87 = ( ! [A: $i,B: $i] :
% 3.11/1.87 ( ( subset @ A @ B )
% 3.11/1.87 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setextsub_type,type,
% 3.11/1.87 setextsub: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setextsub,definition,
% 3.11/1.87 ( setextsub
% 3.11/1.87 = ( ! [A: $i,B: $i] :
% 3.11/1.87 ( ( subset @ A @ B )
% 3.11/1.87 => ( ( subset @ B @ A )
% 3.11/1.87 => ( A = B ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(subsetemptysetimpeq_type,type,
% 3.11/1.87 subsetemptysetimpeq: $o ).
% 3.11/1.87
% 3.11/1.87 thf(subsetemptysetimpeq,definition,
% 3.11/1.87 ( subsetemptysetimpeq
% 3.11/1.87 = ( ! [A: $i] :
% 3.11/1.87 ( ( subset @ A @ emptyset )
% 3.11/1.87 => ( A = emptyset ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(powersetI1_type,type,
% 3.11/1.87 powersetI1: $o ).
% 3.11/1.87
% 3.11/1.87 thf(powersetI1,definition,
% 3.11/1.87 ( powersetI1
% 3.11/1.87 = ( ! [A: $i,B: $i] :
% 3.11/1.87 ( ( subset @ B @ A )
% 3.11/1.87 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(powersetE1_type,type,
% 3.11/1.87 powersetE1: $o ).
% 3.11/1.87
% 3.11/1.87 thf(powersetE1,definition,
% 3.11/1.87 ( powersetE1
% 3.11/1.87 = ( ! [A: $i,B: $i] :
% 3.11/1.87 ( ( in @ B @ ( powerset @ A ) )
% 3.11/1.87 => ( subset @ B @ A ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(inPowerset_type,type,
% 3.11/1.87 inPowerset: $o ).
% 3.11/1.87
% 3.11/1.87 thf(inPowerset,definition,
% 3.11/1.87 ( inPowerset
% 3.11/1.87 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(powersetsubset_type,type,
% 3.11/1.87 powersetsubset: $o ).
% 3.11/1.87
% 3.11/1.87 thf(powersetsubset,definition,
% 3.11/1.87 ( powersetsubset
% 3.11/1.87 = ( ! [A: $i,B: $i] :
% 3.11/1.87 ( ( subset @ A @ B )
% 3.11/1.87 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(sepInPowerset_type,type,
% 3.11/1.87 sepInPowerset: $o ).
% 3.11/1.87
% 3.11/1.87 thf(sepInPowerset,definition,
% 3.11/1.87 ( sepInPowerset
% 3.11/1.87 = ( ! [A: $i,Xphi: $i > $o] :
% 3.11/1.87 ( in
% 3.11/1.87 @ ( dsetconstr @ A
% 3.11/1.87 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.11/1.87 @ ( powerset @ A ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(sepSubset_type,type,
% 3.11/1.87 sepSubset: $o ).
% 3.11/1.87
% 3.11/1.87 thf(sepSubset,definition,
% 3.11/1.87 ( sepSubset
% 3.11/1.87 = ( ! [A: $i,Xphi: $i > $o] :
% 3.11/1.87 ( subset
% 3.11/1.87 @ ( dsetconstr @ A
% 3.11/1.87 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.11/1.87 @ A ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(binunion_type,type,
% 3.11/1.87 binunion: $i > $i > $i ).
% 3.11/1.87
% 3.11/1.87 thf(binunionIL_type,type,
% 3.11/1.87 binunionIL: $o ).
% 3.11/1.87
% 3.11/1.87 thf(binunionIL,definition,
% 3.11/1.87 ( binunionIL
% 3.11/1.87 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(upairset2IR_type,type,
% 3.11/1.87 upairset2IR: $o ).
% 3.11/1.87
% 3.11/1.87 thf(upairset2IR,definition,
% 3.11/1.87 ( upairset2IR
% 3.11/1.87 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(binunionIR_type,type,
% 3.11/1.87 binunionIR: $o ).
% 3.11/1.87
% 3.11/1.87 thf(binunionIR,definition,
% 3.11/1.87 ( binunionIR
% 3.11/1.87 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ B )
% 3.11/1.87 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(binunionEcases_type,type,
% 3.11/1.87 binunionEcases: $o ).
% 3.11/1.87
% 3.11/1.87 thf(binunionEcases,definition,
% 3.11/1.87 ( binunionEcases
% 3.11/1.87 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 3.11/1.87 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 3.11/1.87 => ( ( ( in @ Xx @ A )
% 3.11/1.87 => Xphi )
% 3.11/1.87 => ( ( ( in @ Xx @ B )
% 3.11/1.87 => Xphi )
% 3.11/1.87 => Xphi ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(binunionE_type,type,
% 3.11/1.87 binunionE: $o ).
% 3.11/1.87
% 3.11/1.87 thf(binunionE,definition,
% 3.11/1.87 ( binunionE
% 3.11/1.87 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 3.11/1.87 => ( ( in @ Xx @ A )
% 3.11/1.87 | ( in @ Xx @ B ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(binunionLsub_type,type,
% 3.11/1.87 binunionLsub: $o ).
% 3.11/1.87
% 3.11/1.87 thf(binunionLsub,definition,
% 3.11/1.87 ( binunionLsub
% 3.11/1.87 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(binunionRsub_type,type,
% 3.11/1.87 binunionRsub: $o ).
% 3.11/1.87
% 3.11/1.87 thf(binunionRsub,definition,
% 3.11/1.87 ( binunionRsub
% 3.11/1.87 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(binintersect_type,type,
% 3.11/1.87 binintersect: $i > $i > $i ).
% 3.11/1.87
% 3.11/1.87 thf(binintersectI_type,type,
% 3.11/1.87 binintersectI: $o ).
% 3.11/1.87
% 3.11/1.87 thf(binintersectI,definition,
% 3.11/1.87 ( binintersectI
% 3.11/1.87 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 => ( ( in @ Xx @ B )
% 3.11/1.87 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(binintersectSubset5_type,type,
% 3.11/1.87 binintersectSubset5: $o ).
% 3.11/1.87
% 3.11/1.87 thf(binintersectSubset5,definition,
% 3.11/1.87 ( binintersectSubset5
% 3.11/1.87 = ( ! [A: $i,B: $i,C: $i] :
% 3.11/1.87 ( ( subset @ C @ A )
% 3.11/1.87 => ( ( subset @ C @ B )
% 3.11/1.87 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(binintersectEL_type,type,
% 3.11/1.87 binintersectEL: $o ).
% 3.11/1.87
% 3.11/1.87 thf(binintersectEL,definition,
% 3.11/1.87 ( binintersectEL
% 3.11/1.87 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 3.11/1.87 => ( in @ Xx @ A ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(binintersectLsub_type,type,
% 3.11/1.87 binintersectLsub: $o ).
% 3.11/1.87
% 3.11/1.87 thf(binintersectLsub,definition,
% 3.11/1.87 ( binintersectLsub
% 3.11/1.87 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(binintersectSubset2_type,type,
% 3.11/1.87 binintersectSubset2: $o ).
% 3.11/1.87
% 3.11/1.87 thf(binintersectSubset2,definition,
% 3.11/1.87 ( binintersectSubset2
% 3.11/1.87 = ( ! [A: $i,B: $i] :
% 3.11/1.87 ( ( subset @ A @ B )
% 3.11/1.87 => ( ( binintersect @ A @ B )
% 3.11/1.87 = A ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(binintersectSubset3_type,type,
% 3.11/1.87 binintersectSubset3: $o ).
% 3.11/1.87
% 3.11/1.87 thf(binintersectSubset3,definition,
% 3.11/1.87 ( binintersectSubset3
% 3.11/1.87 = ( ! [A: $i,B: $i] :
% 3.11/1.87 ( ( ( binintersect @ A @ B )
% 3.11/1.87 = B )
% 3.11/1.87 => ( subset @ B @ A ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(binintersectER_type,type,
% 3.11/1.87 binintersectER: $o ).
% 3.11/1.87
% 3.11/1.87 thf(binintersectER,definition,
% 3.11/1.87 ( binintersectER
% 3.11/1.87 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 3.11/1.87 => ( in @ Xx @ B ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(disjointsetsI1_type,type,
% 3.11/1.87 disjointsetsI1: $o ).
% 3.11/1.87
% 3.11/1.87 thf(disjointsetsI1,definition,
% 3.11/1.87 ( disjointsetsI1
% 3.11/1.87 = ( ! [A: $i,B: $i] :
% 3.11/1.87 ( ~ ? [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 & ( in @ Xx @ B ) )
% 3.11/1.87 => ( ( binintersect @ A @ B )
% 3.11/1.87 = emptyset ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(binintersectRsub_type,type,
% 3.11/1.87 binintersectRsub: $o ).
% 3.11/1.87
% 3.11/1.87 thf(binintersectRsub,definition,
% 3.11/1.87 ( binintersectRsub
% 3.11/1.87 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(binintersectSubset4_type,type,
% 3.11/1.87 binintersectSubset4: $o ).
% 3.11/1.87
% 3.11/1.87 thf(binintersectSubset4,definition,
% 3.11/1.87 ( binintersectSubset4
% 3.11/1.87 = ( ! [A: $i,B: $i] :
% 3.11/1.87 ( ( subset @ B @ A )
% 3.11/1.87 => ( ( binintersect @ A @ B )
% 3.11/1.87 = B ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(binintersectSubset1_type,type,
% 3.11/1.87 binintersectSubset1: $o ).
% 3.11/1.87
% 3.11/1.87 thf(binintersectSubset1,definition,
% 3.11/1.87 ( binintersectSubset1
% 3.11/1.87 = ( ! [A: $i,B: $i] :
% 3.11/1.87 ( ( ( binintersect @ A @ B )
% 3.11/1.87 = A )
% 3.11/1.87 => ( subset @ A @ B ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(bs114d_type,type,
% 3.11/1.87 bs114d: $o ).
% 3.11/1.87
% 3.11/1.87 thf(bs114d,definition,
% 3.11/1.87 ( bs114d
% 3.11/1.87 = ( ! [A: $i,B: $i,C: $i] :
% 3.11/1.87 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 3.11/1.87 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(regular_type,type,
% 3.11/1.87 regular: $i > $o ).
% 3.11/1.87
% 3.11/1.87 thf(setminus_type,type,
% 3.11/1.87 setminus: $i > $i > $i ).
% 3.11/1.87
% 3.11/1.87 thf(setminusI_type,type,
% 3.11/1.87 setminusI: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setminusI,definition,
% 3.11/1.87 ( setminusI
% 3.11/1.87 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 => ( ~ ( in @ Xx @ B )
% 3.11/1.87 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setminusEL_type,type,
% 3.11/1.87 setminusEL: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setminusEL,definition,
% 3.11/1.87 ( setminusEL
% 3.11/1.87 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 3.11/1.87 => ( in @ Xx @ A ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setminusER_type,type,
% 3.11/1.87 setminusER: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setminusER,definition,
% 3.11/1.87 ( setminusER
% 3.11/1.87 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 3.11/1.87 => ~ ( in @ Xx @ B ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setminusSubset2_type,type,
% 3.11/1.87 setminusSubset2: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setminusSubset2,definition,
% 3.11/1.87 ( setminusSubset2
% 3.11/1.87 = ( ! [A: $i,B: $i] :
% 3.11/1.87 ( ( subset @ A @ B )
% 3.11/1.87 => ( ( setminus @ A @ B )
% 3.11/1.87 = emptyset ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setminusERneg_type,type,
% 3.11/1.87 setminusERneg: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setminusERneg,definition,
% 3.11/1.87 ( setminusERneg
% 3.11/1.87 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.87 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 3.11/1.87 => ( ( in @ Xx @ A )
% 3.11/1.87 => ( in @ Xx @ B ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setminusELneg_type,type,
% 3.11/1.87 setminusELneg: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setminusELneg,definition,
% 3.11/1.87 ( setminusELneg
% 3.11/1.87 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.87 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 3.11/1.87 => ( ~ ( in @ Xx @ B )
% 3.11/1.87 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setminusILneg_type,type,
% 3.11/1.87 setminusILneg: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setminusILneg,definition,
% 3.11/1.87 ( setminusILneg
% 3.11/1.87 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.87 ( ~ ( in @ Xx @ A )
% 3.11/1.87 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setminusIRneg_type,type,
% 3.11/1.87 setminusIRneg: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setminusIRneg,definition,
% 3.11/1.87 ( setminusIRneg
% 3.11/1.87 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ B )
% 3.11/1.87 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setminusLsub_type,type,
% 3.11/1.87 setminusLsub: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setminusLsub,definition,
% 3.11/1.87 ( setminusLsub
% 3.11/1.87 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setminusSubset1_type,type,
% 3.11/1.87 setminusSubset1: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setminusSubset1,definition,
% 3.11/1.87 ( setminusSubset1
% 3.11/1.87 = ( ! [A: $i,B: $i] :
% 3.11/1.87 ( ( ( setminus @ A @ B )
% 3.11/1.87 = emptyset )
% 3.11/1.87 => ( subset @ A @ B ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(symdiff_type,type,
% 3.11/1.87 symdiff: $i > $i > $i ).
% 3.11/1.87
% 3.11/1.87 thf(symdiffE_type,type,
% 3.11/1.87 symdiffE: $o ).
% 3.11/1.87
% 3.11/1.87 thf(symdiffE,definition,
% 3.11/1.87 ( symdiffE
% 3.11/1.87 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 3.11/1.87 => ! [Xphi: $o] :
% 3.11/1.87 ( ( ( in @ Xx @ A )
% 3.11/1.87 => ( ~ ( in @ Xx @ B )
% 3.11/1.87 => Xphi ) )
% 3.11/1.87 => ( ( ~ ( in @ Xx @ A )
% 3.11/1.87 => ( ( in @ Xx @ B )
% 3.11/1.87 => Xphi ) )
% 3.11/1.87 => Xphi ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(symdiffI1_type,type,
% 3.11/1.87 symdiffI1: $o ).
% 3.11/1.87
% 3.11/1.87 thf(symdiffI1,definition,
% 3.11/1.87 ( symdiffI1
% 3.11/1.87 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 => ( ~ ( in @ Xx @ B )
% 3.11/1.87 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(symdiffI2_type,type,
% 3.11/1.87 symdiffI2: $o ).
% 3.11/1.87
% 3.11/1.87 thf(symdiffI2,definition,
% 3.11/1.87 ( symdiffI2
% 3.11/1.87 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.87 ( ~ ( in @ Xx @ A )
% 3.11/1.87 => ( ( in @ Xx @ B )
% 3.11/1.87 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(symdiffIneg1_type,type,
% 3.11/1.87 symdiffIneg1: $o ).
% 3.11/1.87
% 3.11/1.87 thf(symdiffIneg1,definition,
% 3.11/1.87 ( symdiffIneg1
% 3.11/1.87 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 => ( ( in @ Xx @ B )
% 3.11/1.87 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(symdiffIneg2_type,type,
% 3.11/1.87 symdiffIneg2: $o ).
% 3.11/1.87
% 3.11/1.87 thf(symdiffIneg2,definition,
% 3.11/1.87 ( symdiffIneg2
% 3.11/1.87 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.87 ( ~ ( in @ Xx @ A )
% 3.11/1.87 => ( ~ ( in @ Xx @ B )
% 3.11/1.87 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(iskpair_type,type,
% 3.11/1.87 iskpair: $i > $o ).
% 3.11/1.87
% 3.11/1.87 thf(iskpair,definition,
% 3.11/1.87 ( iskpair
% 3.11/1.87 = ( ^ [A: $i] :
% 3.11/1.87 ? [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ ( setunion @ A ) )
% 3.11/1.87 & ? [Xy: $i] :
% 3.11/1.87 ( ( in @ Xy @ ( setunion @ A ) )
% 3.11/1.87 & ( A
% 3.11/1.87 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(secondinupair_type,type,
% 3.11/1.87 secondinupair: $o ).
% 3.11/1.87
% 3.11/1.87 thf(secondinupair,definition,
% 3.11/1.87 ( secondinupair
% 3.11/1.87 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setukpairIL_type,type,
% 3.11/1.87 setukpairIL: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setukpairIL,definition,
% 3.11/1.87 ( setukpairIL
% 3.11/1.87 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setukpairIR_type,type,
% 3.11/1.87 setukpairIR: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setukpairIR,definition,
% 3.11/1.87 ( setukpairIR
% 3.11/1.87 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(kpairiskpair_type,type,
% 3.11/1.87 kpairiskpair: $o ).
% 3.11/1.87
% 3.11/1.87 thf(kpairiskpair,definition,
% 3.11/1.87 ( kpairiskpair
% 3.11/1.87 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(kpair_type,type,
% 3.11/1.87 kpair: $i > $i > $i ).
% 3.11/1.87
% 3.11/1.87 thf(kpair,definition,
% 3.11/1.87 ( kpair
% 3.11/1.87 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(kpairp_type,type,
% 3.11/1.87 kpairp: $o ).
% 3.11/1.87
% 3.11/1.87 thf(kpairp,definition,
% 3.11/1.87 ( kpairp
% 3.11/1.87 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(cartprod_type,type,
% 3.11/1.87 cartprod: $i > $i > $i ).
% 3.11/1.87
% 3.11/1.87 thf(singletonsubset_type,type,
% 3.11/1.87 singletonsubset: $o ).
% 3.11/1.87
% 3.11/1.87 thf(singletonsubset,definition,
% 3.11/1.87 ( singletonsubset
% 3.11/1.87 = ( ! [A: $i,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(singletoninpowerset_type,type,
% 3.11/1.87 singletoninpowerset: $o ).
% 3.11/1.87
% 3.11/1.87 thf(singletoninpowerset,definition,
% 3.11/1.87 ( singletoninpowerset
% 3.11/1.87 = ( ! [A: $i,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(singletoninpowunion_type,type,
% 3.11/1.87 singletoninpowunion: $o ).
% 3.11/1.87
% 3.11/1.87 thf(singletoninpowunion,definition,
% 3.11/1.87 ( singletoninpowunion
% 3.11/1.87 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(upairset2E_type,type,
% 3.11/1.87 upairset2E: $o ).
% 3.11/1.87
% 3.11/1.87 thf(upairset2E,definition,
% 3.11/1.87 ( upairset2E
% 3.11/1.87 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.11/1.87 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 3.11/1.87 => ( ( Xz = Xx )
% 3.11/1.87 | ( Xz = Xy ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(upairsubunion_type,type,
% 3.11/1.87 upairsubunion: $o ).
% 3.11/1.87
% 3.11/1.87 thf(upairsubunion,definition,
% 3.11/1.87 ( upairsubunion
% 3.11/1.87 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 => ! [Xy: $i] :
% 3.11/1.87 ( ( in @ Xy @ B )
% 3.11/1.87 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(upairinpowunion_type,type,
% 3.11/1.87 upairinpowunion: $o ).
% 3.11/1.87
% 3.11/1.87 thf(upairinpowunion,definition,
% 3.11/1.87 ( upairinpowunion
% 3.11/1.87 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 => ! [Xy: $i] :
% 3.11/1.87 ( ( in @ Xy @ B )
% 3.11/1.87 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(ubforcartprodlem1_type,type,
% 3.11/1.87 ubforcartprodlem1: $o ).
% 3.11/1.87
% 3.11/1.87 thf(ubforcartprodlem1,definition,
% 3.11/1.87 ( ubforcartprodlem1
% 3.11/1.87 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 => ! [Xy: $i] :
% 3.11/1.87 ( ( in @ Xy @ B )
% 3.11/1.87 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(ubforcartprodlem2_type,type,
% 3.11/1.87 ubforcartprodlem2: $o ).
% 3.11/1.87
% 3.11/1.87 thf(ubforcartprodlem2,definition,
% 3.11/1.87 ( ubforcartprodlem2
% 3.11/1.87 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 => ! [Xy: $i] :
% 3.11/1.87 ( ( in @ Xy @ B )
% 3.11/1.87 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(ubforcartprodlem3_type,type,
% 3.11/1.87 ubforcartprodlem3: $o ).
% 3.11/1.87
% 3.11/1.87 thf(ubforcartprodlem3,definition,
% 3.11/1.87 ( ubforcartprodlem3
% 3.11/1.87 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 => ! [Xy: $i] :
% 3.11/1.87 ( ( in @ Xy @ B )
% 3.11/1.87 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(cartprodpairin_type,type,
% 3.11/1.87 cartprodpairin: $o ).
% 3.11/1.87
% 3.11/1.87 thf(cartprodpairin,definition,
% 3.11/1.87 ( cartprodpairin
% 3.11/1.87 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 => ! [Xy: $i] :
% 3.11/1.87 ( ( in @ Xy @ B )
% 3.11/1.87 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(cartprodmempair1_type,type,
% 3.11/1.87 cartprodmempair1: $o ).
% 3.11/1.87
% 3.11/1.87 thf(cartprodmempair1,definition,
% 3.11/1.87 ( cartprodmempair1
% 3.11/1.87 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.11/1.87 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.11/1.87 => ? [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 & ? [Xy: $i] :
% 3.11/1.87 ( ( in @ Xy @ B )
% 3.11/1.87 & ( Xu
% 3.11/1.87 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(cartprodmempair_type,type,
% 3.11/1.87 cartprodmempair: $o ).
% 3.11/1.87
% 3.11/1.87 thf(cartprodmempair,definition,
% 3.11/1.87 ( cartprodmempair
% 3.11/1.87 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.11/1.87 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.11/1.87 => ( iskpair @ Xu ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setunionE2_type,type,
% 3.11/1.87 setunionE2: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setunionE2,definition,
% 3.11/1.87 ( setunionE2
% 3.11/1.87 = ( ! [A: $i,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ ( setunion @ A ) )
% 3.11/1.87 => ? [X: $i] :
% 3.11/1.87 ( ( in @ X @ A )
% 3.11/1.87 & ( in @ Xx @ X ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setunionsingleton1_type,type,
% 3.11/1.87 setunionsingleton1: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setunionsingleton1,definition,
% 3.11/1.87 ( setunionsingleton1
% 3.11/1.87 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setunionsingleton2_type,type,
% 3.11/1.87 setunionsingleton2: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setunionsingleton2,definition,
% 3.11/1.87 ( setunionsingleton2
% 3.11/1.87 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setunionsingleton_type,type,
% 3.11/1.87 setunionsingleton: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setunionsingleton,definition,
% 3.11/1.87 ( setunionsingleton
% 3.11/1.87 = ( ! [Xx: $i] :
% 3.11/1.87 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 3.11/1.87 = Xx ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(singleton_type,type,
% 3.11/1.87 singleton: $i > $o ).
% 3.11/1.87
% 3.11/1.87 thf(singleton,definition,
% 3.11/1.87 ( singleton
% 3.11/1.87 = ( ^ [A: $i] :
% 3.11/1.87 ? [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 & ( A
% 3.11/1.87 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(singletonprop_type,type,
% 3.11/1.87 singletonprop: $o ).
% 3.11/1.87
% 3.11/1.87 thf(singletonprop,definition,
% 3.11/1.87 ( singletonprop
% 3.11/1.87 = ( ! [A: $i,Xphi: $i > $o] :
% 3.11/1.87 ( ! [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 => ! [Xy: $i] :
% 3.11/1.87 ( ( in @ Xy @ A )
% 3.11/1.87 => ( ( Xphi @ Xx )
% 3.11/1.87 => ( ( Xphi @ Xy )
% 3.11/1.87 => ( Xx = Xy ) ) ) ) )
% 3.11/1.87 => ( ? [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 & ( Xphi @ Xx ) )
% 3.11/1.87 => ( singleton
% 3.11/1.87 @ ( dsetconstr @ A
% 3.11/1.87 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(ex1_type,type,
% 3.11/1.87 ex1: $i > ( $i > $o ) > $o ).
% 3.11/1.87
% 3.11/1.87 thf(ex1,definition,
% 3.11/1.87 ( ex1
% 3.11/1.87 = ( ^ [A: $i,Xphi: $i > $o] :
% 3.11/1.87 ( singleton
% 3.11/1.87 @ ( dsetconstr @ A
% 3.11/1.87 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(ex1E1_type,type,
% 3.11/1.87 ex1E1: $o ).
% 3.11/1.87
% 3.11/1.87 thf(ex1E1,definition,
% 3.11/1.87 ( ex1E1
% 3.11/1.87 = ( ! [A: $i,Xphi: $i > $o] :
% 3.11/1.87 ( ( ex1 @ A
% 3.11/1.87 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.11/1.87 => ? [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 & ( Xphi @ Xx ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(ex1I_type,type,
% 3.11/1.87 ex1I: $o ).
% 3.11/1.87
% 3.11/1.87 thf(ex1I,definition,
% 3.11/1.87 ( ex1I
% 3.11/1.87 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 => ( ( Xphi @ Xx )
% 3.11/1.87 => ( ! [Xy: $i] :
% 3.11/1.87 ( ( in @ Xy @ A )
% 3.11/1.87 => ( ( Xphi @ Xy )
% 3.11/1.87 => ( Xy = Xx ) ) )
% 3.11/1.87 => ( ex1 @ A
% 3.11/1.87 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(ex1I2_type,type,
% 3.11/1.87 ex1I2: $o ).
% 3.11/1.87
% 3.11/1.87 thf(ex1I2,definition,
% 3.11/1.87 ( ex1I2
% 3.11/1.87 = ( ! [A: $i,Xphi: $i > $o] :
% 3.11/1.87 ( ! [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 => ! [Xy: $i] :
% 3.11/1.87 ( ( in @ Xy @ A )
% 3.11/1.87 => ( ( Xphi @ Xx )
% 3.11/1.87 => ( ( Xphi @ Xy )
% 3.11/1.87 => ( Xx = Xy ) ) ) ) )
% 3.11/1.87 => ( ? [Xx: $i] :
% 3.11/1.87 ( ( in @ Xx @ A )
% 3.11/1.87 & ( Xphi @ Xx ) )
% 3.11/1.87 => ( ex1 @ A
% 3.11/1.87 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(singletonsuniq_type,type,
% 3.11/1.87 singletonsuniq: $o ).
% 3.11/1.87
% 3.11/1.87 thf(singletonsuniq,definition,
% 3.11/1.87 ( singletonsuniq
% 3.11/1.87 = ( ! [Xx: $i,Xy: $i] :
% 3.11/1.87 ( ( ( setadjoin @ Xx @ emptyset )
% 3.11/1.87 = ( setadjoin @ Xy @ emptyset ) )
% 3.11/1.87 => ( Xx = Xy ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(atmost1p_type,type,
% 3.11/1.87 atmost1p: $i > $o ).
% 3.11/1.87
% 3.11/1.87 thf(atleast2p_type,type,
% 3.11/1.87 atleast2p: $i > $o ).
% 3.11/1.87
% 3.11/1.87 thf(atmost2p_type,type,
% 3.11/1.87 atmost2p: $i > $o ).
% 3.11/1.87
% 3.11/1.87 thf(upairsetp_type,type,
% 3.11/1.87 upairsetp: $i > $o ).
% 3.11/1.87
% 3.11/1.87 thf(setukpairinjL1_type,type,
% 3.11/1.87 setukpairinjL1: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setukpairinjL1,definition,
% 3.11/1.87 ( setukpairinjL1
% 3.11/1.87 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.11/1.87 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 3.11/1.87 => ( Xx = Xz ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(kfstsingleton_type,type,
% 3.11/1.87 kfstsingleton: $o ).
% 3.11/1.87
% 3.11/1.87 thf(kfstsingleton,definition,
% 3.11/1.87 ( kfstsingleton
% 3.11/1.87 = ( ! [Xu: $i] :
% 3.11/1.87 ( ( iskpair @ Xu )
% 3.11/1.87 => ( singleton
% 3.11/1.87 @ ( dsetconstr @ ( setunion @ Xu )
% 3.11/1.87 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(theprop_type,type,
% 3.11/1.87 theprop: $o ).
% 3.11/1.87
% 3.11/1.87 thf(theprop,definition,
% 3.11/1.87 ( theprop
% 3.11/1.87 = ( ! [X: $i] :
% 3.11/1.87 ( ( singleton @ X )
% 3.11/1.87 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(kfst_type,type,
% 3.11/1.87 kfst: $i > $i ).
% 3.11/1.87
% 3.11/1.87 thf(kfstpairEq_type,type,
% 3.11/1.87 kfstpairEq: $o ).
% 3.11/1.87
% 3.11/1.87 thf(kfstpairEq,definition,
% 3.11/1.87 ( kfstpairEq
% 3.11/1.87 = ( ! [Xx: $i,Xy: $i] :
% 3.11/1.87 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 3.11/1.87 = Xx ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(cartprodfstin_type,type,
% 3.11/1.87 cartprodfstin: $o ).
% 3.11/1.87
% 3.11/1.87 thf(cartprodfstin,definition,
% 3.11/1.87 ( cartprodfstin
% 3.11/1.87 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.11/1.87 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.11/1.87 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setukpairinjL2_type,type,
% 3.11/1.87 setukpairinjL2: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setukpairinjL2,definition,
% 3.11/1.87 ( setukpairinjL2
% 3.11/1.87 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.11/1.87 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.11/1.87 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.11/1.87 => ( Xx = Xz ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setukpairinjL_type,type,
% 3.11/1.87 setukpairinjL: $o ).
% 3.11/1.87
% 3.11/1.87 thf(setukpairinjL,definition,
% 3.11/1.87 ( setukpairinjL
% 3.11/1.87 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.11/1.87 ( ( ( kpair @ Xx @ Xy )
% 3.11/1.87 = ( kpair @ Xz @ Xu ) )
% 3.11/1.87 => ( Xx = Xz ) ) ) ) ).
% 3.11/1.87
% 3.11/1.87 thf(setukpairinjR11,conjecture,
% 3.11/1.87 ( setextAx
% 3.11/1.87 => ( emptysetAx
% 3.11/1.87 => ( setadjoinAx
% 3.11/1.87 => ( powersetAx
% 3.11/1.87 => ( setunionAx
% 3.11/1.87 => ( omega0Ax
% 3.11/1.87 => ( omegaSAx
% 3.11/1.87 => ( omegaIndAx
% 3.11/1.87 => ( replAx
% 3.11/1.87 => ( foundationAx
% 3.11/1.87 => ( wellorderingAx
% 3.11/1.87 => ( descrp
% 3.11/1.87 => ( dsetconstrI
% 3.11/1.87 => ( dsetconstrEL
% 3.11/1.87 => ( dsetconstrER
% 3.11/1.87 => ( exuE1
% 3.11/1.87 => ( prop2setE
% 3.11/1.87 => ( emptysetE
% 3.11/1.87 => ( emptysetimpfalse
% 3.11/1.87 => ( notinemptyset
% 3.11/1.87 => ( exuE3e
% 3.11/1.87 => ( setext
% 3.11/1.87 => ( emptyI
% 3.11/1.87 => ( noeltsimpempty
% 3.11/1.87 => ( setbeta
% 3.11/1.87 => ( nonemptyE1
% 3.11/1.87 => ( nonemptyI
% 3.11/1.87 => ( nonemptyI1
% 3.11/1.87 => ( setadjoinIL
% 3.11/1.87 => ( emptyinunitempty
% 3.11/1.87 => ( setadjoinIR
% 3.11/1.87 => ( setadjoinE
% 3.11/1.87 => ( setadjoinOr
% 3.11/1.87 => ( setoftrueEq
% 3.11/1.87 => ( powersetI
% 3.11/1.87 => ( emptyinPowerset
% 3.11/1.87 => ( emptyInPowerset
% 3.11/1.87 => ( powersetE
% 3.11/1.87 => ( setunionI
% 3.11/1.87 => ( setunionE
% 3.11/1.87 => ( subPowSU
% 3.11/1.87 => ( exuE2
% 3.11/1.87 => ( nonemptyImpWitness
% 3.11/1.87 => ( uniqinunit
% 3.11/1.87 => ( notinsingleton
% 3.11/1.87 => ( eqinunit
% 3.11/1.87 => ( singletonsswitch
% 3.11/1.87 => ( upairsetE
% 3.11/1.87 => ( upairsetIL
% 3.11/1.87 => ( upairsetIR
% 3.11/1.87 => ( emptyE1
% 3.11/1.87 => ( vacuousDall
% 3.11/1.87 => ( quantDeMorgan1
% 3.11/1.87 => ( quantDeMorgan2
% 3.11/1.87 => ( quantDeMorgan3
% 3.11/1.87 => ( quantDeMorgan4
% 3.11/1.87 => ( prop2setI
% 3.11/1.87 => ( prop2set2propI
% 3.11/1.87 => ( notdexE
% 3.11/1.87 => ( notdallE
% 3.11/1.87 => ( exuI1
% 3.11/1.87 => ( exuI3
% 3.11/1.87 => ( exuI2
% 3.11/1.87 => ( inCongP
% 3.11/1.87 => ( in__Cong
% 3.11/1.87 => ( exuE3u
% 3.11/1.87 => ( exu__Cong
% 3.11/1.87 => ( emptyset__Cong
% 3.11/1.87 => ( setadjoin__Cong
% 3.11/1.87 => ( powerset__Cong
% 3.11/1.87 => ( setunion__Cong
% 3.11/1.87 => ( omega__Cong
% 3.11/1.87 => ( exuEu
% 3.11/1.87 => ( descr__Cong
% 3.11/1.87 => ( dsetconstr__Cong
% 3.11/1.87 => ( subsetI1
% 3.11/1.87 => ( eqimpsubset2
% 3.11/1.87 => ( eqimpsubset1
% 3.11/1.87 => ( subsetI2
% 3.11/1.87 => ( emptysetsubset
% 3.11/1.87 => ( subsetE
% 3.11/1.87 => ( subsetE2
% 3.11/1.87 => ( notsubsetI
% 3.11/1.87 => ( notequalI1
% 3.11/1.87 => ( notequalI2
% 3.11/1.87 => ( subsetRefl
% 3.11/1.87 => ( subsetTrans
% 3.11/1.87 => ( setadjoinSub
% 3.11/1.87 => ( setadjoinSub2
% 3.11/1.87 => ( subset2powerset
% 3.11/1.87 => ( setextsub
% 3.11/1.87 => ( subsetemptysetimpeq
% 3.11/1.87 => ( powersetI1
% 3.11/1.87 => ( powersetE1
% 3.11/1.87 => ( inPowerset
% 3.11/1.87 => ( powersetsubset
% 3.11/1.87 => ( sepInPowerset
% 3.11/1.87 => ( sepSubset
% 3.11/1.87 => ( binunionIL
% 3.11/1.87 => ( upairset2IR
% 3.11/1.87 => ( binunionIR
% 3.11/1.87 => ( binunionEcases
% 3.11/1.87 => ( binunionE
% 3.11/1.87 => ( binunionLsub
% 3.11/1.87 => ( binunionRsub
% 3.11/1.87 => ( binintersectI
% 3.11/1.87 => ( binintersectSubset5
% 3.11/1.87 => ( binintersectEL
% 3.11/1.87 => ( binintersectLsub
% 3.11/1.87 => ( binintersectSubset2
% 3.11/1.87 => ( binintersectSubset3
% 3.11/1.87 => ( binintersectER
% 3.11/1.87 => ( disjointsetsI1
% 3.11/1.87 => ( binintersectRsub
% 3.11/1.87 => ( binintersectSubset4
% 3.11/1.87 => ( binintersectSubset1
% 3.11/1.87 => ( bs114d
% 3.11/1.87 => ( setminusI
% 3.11/1.87 => ( setminusEL
% 3.11/1.87 => ( setminusER
% 3.11/1.87 => ( setminusSubset2
% 3.11/1.87 => ( setminusERneg
% 3.11/1.87 => ( setminusELneg
% 3.11/1.87 => ( setminusILneg
% 3.11/1.87 => ( setminusIRneg
% 3.11/1.87 => ( setminusLsub
% 3.11/1.87 => ( setminusSubset1
% 3.11/1.87 => ( symdiffE
% 3.11/1.87 => ( symdiffI1
% 3.11/1.87 => ( symdiffI2
% 3.11/1.87 => ( symdiffIneg1
% 3.11/1.87 => ( symdiffIneg2
% 3.11/1.87 => ( secondinupair
% 3.11/1.87 => ( setukpairIL
% 3.11/1.87 => ( setukpairIR
% 3.11/1.87 => ( kpairiskpair
% 3.11/1.87 => ( kpairp
% 3.11/1.87 => ( singletonsubset
% 3.11/1.87 => ( singletoninpowerset
% 3.11/1.87 => ( singletoninpowunion
% 3.11/1.87 => ( upairset2E
% 3.11/1.87 => ( upairsubunion
% 3.11/1.87 => ( upairinpowunion
% 3.11/1.87 => ( ubforcartprodlem1
% 3.11/1.87 => ( ubforcartprodlem2
% 3.11/1.87 => ( ubforcartprodlem3
% 3.11/1.87 => ( cartprodpairin
% 3.11/1.87 => ( cartprodmempair1
% 3.11/1.87 => ( cartprodmempair
% 3.11/1.87 => ( setunionE2
% 3.11/1.87 => ( setunionsingleton1
% 3.11/1.87 => ( setunionsingleton2
% 3.11/1.87 => ( setunionsingleton
% 3.11/1.87 => ( singletonprop
% 3.11/1.87 => ( ex1E1
% 3.11/1.87 => ( ex1I
% 3.11/1.87 => ( ex1I2
% 3.11/1.87 => ( singletonsuniq
% 3.11/1.87 => ( setukpairinjL1
% 3.11/1.87 => ( kfstsingleton
% 3.11/1.87 => ( theprop
% 3.11/1.87 => ( kfstpairEq
% 3.11/1.87 => ( cartprodfstin
% 3.11/1.87 => ( setukpairinjL2
% 3.11/1.87 => ( setukpairinjL
% 3.11/1.87 => ! [Xx: $i,Xy: $i] :
% 3.11/1.87 ( ( Xx = Xy )
% 3.11/1.87 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.11/1.87 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.11/1.87 ------------------------
% 3.19/1.90 % (23399)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23265 for (2999ds/18Mi)
% 3.19/1.90 % (23395)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_23265 for (2999ds/27Mi)
% 3.19/1.90 % (23394)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_23265 for (2999ds/4Mi)
% 3.19/1.90 % (23393)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23265 for (2999ds/183Mi)
% 3.19/1.90 % (23396)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23265 for (2999ds/2Mi)
% 3.19/1.90 % (23398)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_23265 for (2999ds/275Mi)
% 3.19/1.90 % (23397)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_23265 for (2999ds/2Mi)
% 3.19/1.90 % (23396)Instruction limit reached!
% 3.19/1.90 % (23396)------------------------------
% 3.19/1.90 % (23396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.90 % (23396)Termination reason: Unknown
% 3.19/1.90 % (23397)Instruction limit reached!
% 3.19/1.90 % (23397)------------------------------
% 3.19/1.90 % (23397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.90 % (23397)Termination reason: Unknown
% 3.19/1.90 % (23397)Termination phase: shuffling
% 3.19/1.90
% 3.19/1.90 % (23397)Memory used [KB]: 1279
% 3.19/1.90 % (23397)Time elapsed: 0.004 s
% 3.19/1.90 % (23397)Instructions burned: 3 (million)
% 3.19/1.90 % (23397)------------------------------
% 3.19/1.90 % (23397)------------------------------
% 3.19/1.90 % (23396)Termination phase: shuffling
% 3.19/1.90
% 3.19/1.90 % (23396)Memory used [KB]: 1279
% 3.19/1.90 % (23396)Time elapsed: 0.004 s
% 3.19/1.90 % (23396)Instructions burned: 3 (million)
% 3.19/1.90 % (23396)------------------------------
% 3.19/1.90 % (23396)------------------------------
% 3.19/1.91 % (23394)Instruction limit reached!
% 3.19/1.91 % (23394)------------------------------
% 3.19/1.91 % (23394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.91 % (23394)Termination reason: Unknown
% 3.19/1.91 % (23394)Termination phase: shuffling
% 3.19/1.91
% 3.19/1.91 % (23394)Memory used [KB]: 1407
% 3.19/1.91 % (23394)Time elapsed: 0.004 s
% 3.19/1.91 % (23394)Instructions burned: 5 (million)
% 3.19/1.91 % (23394)------------------------------
% 3.19/1.91 % (23394)------------------------------
% 3.19/1.91 % (23399)Instruction limit reached!
% 3.19/1.91 % (23399)------------------------------
% 3.19/1.91 % (23399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.91 % (23399)Termination reason: Unknown
% 3.19/1.91 % (23399)Termination phase: Property scanning
% 3.19/1.91
% 3.19/1.91 % (23399)Memory used [KB]: 1535
% 3.19/1.91 % (23399)Time elapsed: 0.012 s
% 3.19/1.91 % (23399)Instructions burned: 19 (million)
% 3.19/1.91 % (23399)------------------------------
% 3.19/1.91 % (23399)------------------------------
% 3.19/1.92 % (23395)Instruction limit reached!
% 3.19/1.92 % (23395)------------------------------
% 3.19/1.92 % (23395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.92 % (23395)Termination reason: Unknown
% 3.19/1.92 % (23395)Termination phase: Property scanning
% 3.19/1.92
% 3.19/1.92 % (23395)Memory used [KB]: 1791
% 3.19/1.92 % (23395)Time elapsed: 0.014 s
% 3.19/1.92 % (23395)Instructions burned: 27 (million)
% 3.19/1.92 % (23395)------------------------------
% 3.19/1.92 % (23395)------------------------------
% 3.19/1.92 % (23402)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_23265 for (2999ds/15Mi)
% 3.19/1.92 % (23401)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_23265 for (2999ds/37Mi)
% 3.19/1.92 % (23400)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_23265 for (2999ds/3Mi)
% 3.19/1.92 % (23400)Instruction limit reached!
% 3.19/1.92 % (23400)------------------------------
% 3.19/1.92 % (23400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.92 % (23400)Termination reason: Unknown
% 3.19/1.92 % (23400)Termination phase: shuffling
% 3.19/1.92
% 3.19/1.92 % (23400)Memory used [KB]: 1279
% 3.19/1.92 % (23400)Time elapsed: 0.004 s
% 3.19/1.92 % (23400)Instructions burned: 4 (million)
% 3.19/1.92 % (23400)------------------------------
% 3.19/1.92 % (23400)------------------------------
% 3.19/1.93 % (23402)Instruction limit reached!
% 3.19/1.93 % (23402)------------------------------
% 3.19/1.93 % (23402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.93 % (23402)Termination reason: Unknown
% 3.19/1.93 % (23402)Termination phase: Property scanning
% 3.19/1.93
% 3.19/1.93 % (23402)Memory used [KB]: 1535
% 3.19/1.93 % (23402)Time elapsed: 0.009 s
% 3.19/1.93 % (23402)Instructions burned: 15 (million)
% 3.19/1.93 % (23402)------------------------------
% 3.19/1.93 % (23402)------------------------------
% 3.19/1.93 % (23403)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_23265 for (2999ds/3Mi)
% 3.19/1.93 % (23403)Instruction limit reached!
% 3.19/1.93 % (23403)------------------------------
% 3.19/1.93 % (23403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.93 % (23403)Termination reason: Unknown
% 3.19/1.93 % (23403)Termination phase: shuffling
% 3.19/1.93
% 3.19/1.93 % (23403)Memory used [KB]: 1279
% 3.19/1.93 % (23403)Time elapsed: 0.004 s
% 3.19/1.93 % (23403)Instructions burned: 3 (million)
% 3.19/1.93 % (23403)------------------------------
% 3.19/1.93 % (23403)------------------------------
% 3.19/1.93 % (23404)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_23265 for (2999ds/1041Mi)
% 3.19/1.94 % (23401)Instruction limit reached!
% 3.19/1.94 % (23401)------------------------------
% 3.19/1.94 % (23401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.94 % (23401)Termination reason: Unknown
% 3.19/1.94 % (23401)Termination phase: Property scanning
% 3.19/1.94
% 3.19/1.94 % (23401)Memory used [KB]: 1791
% 3.19/1.94 % (23401)Time elapsed: 0.019 s
% 3.19/1.94 % (23401)Instructions burned: 38 (million)
% 3.19/1.94 % (23401)------------------------------
% 3.19/1.94 % (23401)------------------------------
% 3.19/1.94 % (23405)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_23265 for (2999ds/7Mi)
% 3.19/1.94 % (23405)Instruction limit reached!
% 3.19/1.94 % (23405)------------------------------
% 3.19/1.94 % (23405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.94 % (23405)Termination reason: Unknown
% 3.19/1.94 % (23405)Termination phase: shuffling
% 3.19/1.94
% 3.19/1.94 % (23405)Memory used [KB]: 1407
% 3.19/1.94 % (23405)Time elapsed: 0.006 s
% 3.19/1.94 % (23405)Instructions burned: 8 (million)
% 3.19/1.94 % (23405)------------------------------
% 3.19/1.94 % (23405)------------------------------
% 3.19/1.95 % (23406)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_23265 for (2999ds/16Mi)
% 3.19/1.95 % (23407)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_23265 for (2999ds/3Mi)
% 3.19/1.95 % (23407)Instruction limit reached!
% 3.19/1.95 % (23407)------------------------------
% 3.19/1.95 % (23407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.95 % (23407)Termination reason: Unknown
% 3.19/1.95 % (23407)Termination phase: shuffling
% 3.19/1.95
% 3.19/1.95 % (23407)Memory used [KB]: 1279
% 3.19/1.95 % (23407)Time elapsed: 0.004 s
% 3.19/1.95 % (23407)Instructions burned: 4 (million)
% 3.19/1.95 % (23407)------------------------------
% 3.19/1.95 % (23407)------------------------------
% 3.19/1.95 % (23406)Instruction limit reached!
% 3.19/1.95 % (23406)------------------------------
% 3.19/1.95 % (23406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.95 % (23406)Termination reason: Unknown
% 3.19/1.95 % (23406)Termination phase: shuffling
% 3.19/1.95
% 3.19/1.95 % (23406)Memory used [KB]: 1535
% 3.19/1.95 % (23406)Time elapsed: 0.009 s
% 3.19/1.95 % (23406)Instructions burned: 16 (million)
% 3.19/1.95 % (23406)------------------------------
% 3.19/1.95 % (23406)------------------------------
% 3.19/1.95 % (23408)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_23265 for (2999ds/3Mi)
% 3.19/1.96 % (23408)Instruction limit reached!
% 3.19/1.96 % (23408)------------------------------
% 3.19/1.96 % (23408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.96 % (23408)Termination reason: Unknown
% 3.19/1.96 % (23408)Termination phase: shuffling
% 3.19/1.96
% 3.19/1.96 % (23408)Memory used [KB]: 1279
% 3.19/1.96 % (23408)Time elapsed: 0.004 s
% 3.19/1.96 % (23408)Instructions burned: 5 (million)
% 3.19/1.96 % (23408)------------------------------
% 3.19/1.96 % (23408)------------------------------
% 3.19/1.96 % (23409)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_23265 for (2999ds/7Mi)
% 3.19/1.96 % (23409)Instruction limit reached!
% 3.19/1.96 % (23409)------------------------------
% 3.19/1.96 % (23409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.96 % (23409)Termination reason: Unknown
% 3.19/1.96 % (23409)Termination phase: shuffling
% 3.19/1.96
% 3.19/1.96 % (23409)Memory used [KB]: 1407
% 3.19/1.96 % (23409)Time elapsed: 0.006 s
% 3.19/1.96 % (23409)Instructions burned: 8 (million)
% 3.19/1.96 % (23409)------------------------------
% 3.19/1.96 % (23409)------------------------------
% 3.19/1.97 % (23410)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_23265 for (2999ds/3Mi)
% 3.19/1.97 % (23410)Instruction limit reached!
% 3.19/1.97 % (23410)------------------------------
% 3.19/1.97 % (23410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.97 % (23410)Termination reason: Unknown
% 3.19/1.97 % (23410)Termination phase: shuffling
% 3.19/1.97
% 3.19/1.97 % (23410)Memory used [KB]: 1279
% 3.19/1.97 % (23410)Time elapsed: 0.004 s
% 3.19/1.97 % (23410)Instructions burned: 3 (million)
% 3.19/1.97 % (23410)------------------------------
% 3.19/1.97 % (23410)------------------------------
% 3.19/1.97 % (23411)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_23265 for (2999ds/4Mi)
% 3.19/1.97 % (23411)Instruction limit reached!
% 3.19/1.97 % (23411)------------------------------
% 3.19/1.97 % (23411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.97 % (23411)Termination reason: Unknown
% 3.19/1.97 % (23411)Termination phase: shuffling
% 3.19/1.97
% 3.19/1.97 % (23411)Memory used [KB]: 1279
% 3.19/1.97 % (23411)Time elapsed: 0.004 s
% 3.19/1.97 % (23411)Instructions burned: 4 (million)
% 3.19/1.97 % (23411)------------------------------
% 3.19/1.97 % (23411)------------------------------
% 3.19/1.97 % (23412)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_23265 for (2999ds/18Mi)
% 3.19/1.98 % (23413)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_23265 for (2999ds/710Mi)
% 3.19/1.98 % (23412)Instruction limit reached!
% 3.19/1.98 % (23412)------------------------------
% 3.19/1.98 % (23412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.98 % (23412)Termination reason: Unknown
% 3.19/1.98 % (23412)Termination phase: shuffling
% 3.19/1.98
% 3.19/1.98 % (23412)Memory used [KB]: 1663
% 3.19/1.98 % (23412)Time elapsed: 0.011 s
% 3.19/1.98 % (23412)Instructions burned: 19 (million)
% 3.19/1.98 % (23412)------------------------------
% 3.19/1.98 % (23412)------------------------------
% 3.19/1.99 % (23414)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_23265 for (2999ds/6Mi)
% 3.19/1.99 % (23415)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_23265 for (2999ds/902Mi)
% 3.19/1.99 % (23414)Instruction limit reached!
% 3.19/1.99 % (23414)------------------------------
% 3.19/1.99 % (23414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.99 % (23414)Termination reason: Unknown
% 3.19/1.99 % (23414)Termination phase: shuffling
% 3.19/1.99
% 3.19/1.99 % (23414)Memory used [KB]: 1407
% 3.19/1.99 % (23414)Time elapsed: 0.005 s
% 3.19/1.99 % (23414)Instructions burned: 7 (million)
% 3.19/1.99 % (23414)------------------------------
% 3.19/1.99 % (23414)------------------------------
% 3.19/1.99 % (23393)Instruction limit reached!
% 3.19/1.99 % (23393)------------------------------
% 3.19/1.99 % (23393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.99 % (23393)Termination reason: Unknown
% 3.19/1.99 % (23393)Termination phase: Saturation
% 3.19/1.99
% 3.19/1.99 % (23393)Memory used [KB]: 7419
% 3.19/1.99 % (23393)Time elapsed: 0.089 s
% 3.19/1.99 % (23393)Instructions burned: 183 (million)
% 3.19/1.99 % (23393)------------------------------
% 3.19/1.99 % (23393)------------------------------
% 3.19/2.00 % (23416)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_23265 for (2999ds/21Mi)
% 3.19/2.01 % (23417)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_23265 for (2998ds/5Mi)
% 3.19/2.01 % (23418)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_23265 for (2998ds/6Mi)
% 3.19/2.01 % (23417)Instruction limit reached!
% 3.19/2.01 % (23417)------------------------------
% 3.19/2.01 % (23417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/2.01 % (23417)Termination reason: Unknown
% 3.19/2.01 % (23417)Termination phase: shuffling
% 3.19/2.01
% 3.19/2.01 % (23417)Memory used [KB]: 1407
% 3.19/2.01 % (23417)Time elapsed: 0.005 s
% 3.19/2.01 % (23417)Instructions burned: 6 (million)
% 3.19/2.01 % (23417)------------------------------
% 3.19/2.01 % (23417)------------------------------
% 3.19/2.01 % (23418)Instruction limit reached!
% 3.19/2.01 % (23418)------------------------------
% 3.19/2.01 % (23418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/2.01 % (23418)Termination reason: Unknown
% 3.19/2.01 % (23418)Termination phase: shuffling
% 3.19/2.01
% 3.19/2.01 % (23418)Memory used [KB]: 1407
% 3.19/2.01 % (23418)Time elapsed: 0.006 s
% 3.19/2.01 % (23418)Instructions burned: 7 (million)
% 3.19/2.01 % (23418)------------------------------
% 3.19/2.01 % (23418)------------------------------
% 3.19/2.01 % (23416)Instruction limit reached!
% 3.19/2.01 % (23416)------------------------------
% 3.19/2.01 % (23416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/2.01 % (23416)Termination reason: Unknown
% 3.19/2.01 % (23416)Termination phase: shuffling
% 3.19/2.01
% 3.19/2.01 % (23416)Memory used [KB]: 1791
% 3.19/2.01 % (23416)Time elapsed: 0.012 s
% 3.19/2.01 % (23416)Instructions burned: 22 (million)
% 3.19/2.01 % (23416)------------------------------
% 3.19/2.01 % (23416)------------------------------
% 4.07/2.03 % (23419)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_23265 for (2998ds/377Mi)
% 4.07/2.03 % (23420)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_23265 for (2998ds/779Mi)
% 4.07/2.03 % (23421)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_23265 for (2998ds/19Mi)
% 4.07/2.04 % (23421)Instruction limit reached!
% 4.07/2.04 % (23421)------------------------------
% 4.07/2.04 % (23421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.07/2.04 % (23421)Termination reason: Unknown
% 4.07/2.04 % (23421)Termination phase: shuffling
% 4.07/2.04
% 4.07/2.04 % (23421)Memory used [KB]: 1791
% 4.07/2.04 % (23421)Time elapsed: 0.011 s
% 4.07/2.04 % (23421)Instructions burned: 19 (million)
% 4.07/2.04 % (23421)------------------------------
% 4.07/2.04 % (23421)------------------------------
% 4.07/2.04 % (23398)Instruction limit reached!
% 4.07/2.04 % (23398)------------------------------
% 4.07/2.04 % (23398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.07/2.04 % (23398)Termination reason: Unknown
% 4.07/2.04 % (23398)Termination phase: Saturation
% 4.07/2.04
% 4.07/2.04 % (23398)Memory used [KB]: 8187
% 4.07/2.04 % (23398)Time elapsed: 0.143 s
% 4.07/2.04 % (23398)Instructions burned: 275 (million)
% 4.07/2.04 % (23398)------------------------------
% 4.07/2.04 % (23398)------------------------------
% 4.07/2.06 % (23422)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_23265 for (2998ds/879Mi)
% 4.07/2.06 % (23423)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_23265 for (2998ds/17Mi)
% 4.07/2.07 % (23423)Instruction limit reached!
% 4.07/2.07 % (23423)------------------------------
% 4.07/2.07 % (23423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.07/2.07 % (23423)Termination reason: Unknown
% 4.07/2.07 % (23423)Termination phase: shuffling
% 4.07/2.07
% 4.07/2.07 % (23423)Memory used [KB]: 1663
% 4.07/2.07 % (23423)Time elapsed: 0.010 s
% 4.07/2.07 % (23423)Instructions burned: 17 (million)
% 4.07/2.07 % (23423)------------------------------
% 4.07/2.07 % (23423)------------------------------
% 4.07/2.08 % (23415)Refutation not found, incomplete strategy
% 4.07/2.08 % (23415)------------------------------
% 4.07/2.08 % (23415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.07/2.08 % (23415)Termination reason: Refutation not found, incomplete strategy
% 4.07/2.08
% 4.07/2.08
% 4.07/2.08 % (23415)Memory used [KB]: 7931
% 4.07/2.08 % (23415)Time elapsed: 0.093 s
% 4.07/2.08 % (23415)Instructions burned: 182 (million)
% 4.07/2.08 % (23415)------------------------------
% 4.07/2.08 % (23415)------------------------------
% 4.07/2.09 % (23424)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_23265 for (2998ds/3Mi)
% 4.07/2.09 % (23424)Instruction limit reached!
% 4.07/2.09 % (23424)------------------------------
% 4.07/2.09 % (23424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.07/2.09 % (23424)Termination reason: Unknown
% 4.07/2.09 % (23424)Termination phase: shuffling
% 4.07/2.09
% 4.07/2.09 % (23424)Memory used [KB]: 1279
% 4.07/2.09 % (23424)Time elapsed: 0.004 s
% 4.07/2.09 % (23424)Instructions burned: 3 (million)
% 4.07/2.09 % (23424)------------------------------
% 4.07/2.09 % (23424)------------------------------
% 4.07/2.10 % (23425)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_23265 for (2998ds/30Mi)
% 4.07/2.11 % (23426)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_23265 for (2998ds/127Mi)
% 4.07/2.11 % (23425)Instruction limit reached!
% 4.07/2.11 % (23425)------------------------------
% 4.07/2.11 % (23425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.07/2.11 % (23425)Termination reason: Unknown
% 4.07/2.11 % (23425)Termination phase: Property scanning
% 4.07/2.11
% 4.07/2.11 % (23425)Memory used [KB]: 1791
% 4.07/2.11 % (23425)Time elapsed: 0.016 s
% 4.07/2.11 % (23425)Instructions burned: 31 (million)
% 4.07/2.11 % (23425)------------------------------
% 4.07/2.11 % (23425)------------------------------
% 4.48/2.13 % (23427)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_23265 for (2997ds/100Mi)
% 4.48/2.16 % (23426)Instruction limit reached!
% 4.48/2.16 % (23426)------------------------------
% 4.48/2.16 % (23426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.48/2.16 % (23426)Termination reason: Unknown
% 4.48/2.16 % (23426)Termination phase: Saturation
% 4.48/2.16
% 4.48/2.16 % (23426)Memory used [KB]: 6908
% 4.48/2.16 % (23426)Time elapsed: 0.060 s
% 4.48/2.16 % (23426)Instructions burned: 128 (million)
% 4.48/2.16 % (23426)------------------------------
% 4.48/2.16 % (23426)------------------------------
% 4.48/2.18 % (23427)Instruction limit reached!
% 4.48/2.18 % (23427)------------------------------
% 4.48/2.18 % (23427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.48/2.18 % (23427)Termination reason: Unknown
% 4.48/2.18 % (23427)Termination phase: Saturation
% 4.48/2.18
% 4.48/2.18 % (23427)Memory used [KB]: 6652
% 4.48/2.18 % (23427)Time elapsed: 0.048 s
% 4.48/2.18 % (23427)Instructions burned: 101 (million)
% 4.48/2.18 % (23427)------------------------------
% 4.48/2.18 % (23427)------------------------------
% 4.48/2.18 % (23428)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_23265 for (2997ds/3Mi)
% 4.48/2.18 % (23428)Instruction limit reached!
% 4.48/2.18 % (23428)------------------------------
% 4.48/2.18 % (23428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.48/2.18 % (23428)Termination reason: Unknown
% 4.48/2.18 % (23428)Termination phase: shuffling
% 4.48/2.18
% 4.48/2.18 % (23428)Memory used [KB]: 1279
% 4.48/2.18 % (23428)Time elapsed: 0.003 s
% 4.48/2.18 % (23428)Instructions burned: 3 (million)
% 4.48/2.18 % (23428)------------------------------
% 4.48/2.18 % (23428)------------------------------
% 4.48/2.20 % (23429)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_23265 for (2997ds/20Mi)
% 4.77/2.20 % (23430)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_23265 for (2997ds/86Mi)
% 4.77/2.21 % (23429)Instruction limit reached!
% 4.77/2.21 % (23429)------------------------------
% 4.77/2.21 % (23429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.77/2.21 % (23429)Termination reason: Unknown
% 4.77/2.21 % (23429)Termination phase: Property scanning
% 4.77/2.21
% 4.77/2.21 % (23429)Memory used [KB]: 1535
% 4.77/2.21 % (23429)Time elapsed: 0.013 s
% 4.77/2.21 % (23429)Instructions burned: 21 (million)
% 4.77/2.21 % (23429)------------------------------
% 4.77/2.21 % (23429)------------------------------
% 4.77/2.21 % (23419)Instruction limit reached!
% 4.77/2.21 % (23419)------------------------------
% 4.77/2.21 % (23419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.77/2.21 % (23419)Termination reason: Unknown
% 4.77/2.21 % (23419)Termination phase: Saturation
% 4.77/2.21
% 4.77/2.21 % (23419)Memory used [KB]: 7931
% 4.77/2.21 % (23419)Time elapsed: 0.187 s
% 4.77/2.21 % (23419)Instructions burned: 377 (million)
% 4.77/2.21 % (23419)------------------------------
% 4.77/2.21 % (23419)------------------------------
% 4.77/2.23 % (23431)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_23265 for (2996ds/107Mi)
% 4.77/2.23 % (23432)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_23265 for (2996ds/39Mi)
% 4.77/2.24 % (23430)Instruction limit reached!
% 4.77/2.24 % (23430)------------------------------
% 4.77/2.24 % (23430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.77/2.24 % (23430)Termination reason: Unknown
% 4.77/2.24 % (23430)Termination phase: Saturation
% 4.77/2.24
% 4.77/2.24 % (23430)Memory used [KB]: 6524
% 4.77/2.24 % (23430)Time elapsed: 0.040 s
% 4.77/2.24 % (23430)Instructions burned: 86 (million)
% 4.77/2.24 % (23430)------------------------------
% 4.77/2.24 % (23430)------------------------------
% 4.77/2.25 % (23432)Instruction limit reached!
% 4.77/2.25 % (23432)------------------------------
% 4.77/2.25 % (23432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.77/2.25 % (23432)Termination reason: Unknown
% 4.77/2.25 % (23432)Termination phase: Property scanning
% 4.77/2.25
% 4.77/2.25 % (23432)Memory used [KB]: 1791
% 4.77/2.25 % (23432)Time elapsed: 0.019 s
% 4.77/2.25 % (23432)Instructions burned: 39 (million)
% 4.77/2.25 % (23432)------------------------------
% 4.77/2.25 % (23432)------------------------------
% 4.77/2.26 % (23433)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_23265 for (2996ds/448Mi)
% 4.77/2.26 % (23434)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_23265 for (2996ds/46Mi)
% 4.77/2.28 % (23431)Instruction limit reached!
% 4.77/2.28 % (23431)------------------------------
% 4.77/2.28 % (23431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.77/2.28 % (23431)Termination reason: Unknown
% 4.77/2.28 % (23431)Termination phase: Saturation
% 4.77/2.28
% 4.77/2.28 % (23431)Memory used [KB]: 6780
% 4.77/2.28 % (23431)Time elapsed: 0.053 s
% 4.77/2.28 % (23431)Instructions burned: 108 (million)
% 4.77/2.28 % (23431)------------------------------
% 4.77/2.28 % (23431)------------------------------
% 4.77/2.28 % (23434)Instruction limit reached!
% 4.77/2.28 % (23434)------------------------------
% 4.77/2.28 % (23434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.77/2.28 % (23434)Termination reason: Unknown
% 4.77/2.28 % (23434)Termination phase: SInE selection
% 4.77/2.28
% 4.77/2.28 % (23434)Memory used [KB]: 1791
% 4.77/2.28 % (23434)Time elapsed: 0.023 s
% 4.77/2.28 % (23434)Instructions burned: 47 (million)
% 4.77/2.28 % (23434)------------------------------
% 4.77/2.28 % (23434)------------------------------
% 5.41/2.30 % (23435)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_23265 for (2995ds/98Mi)
% 5.41/2.30 % (23436)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_23265 for (2995ds/507Mi)
% 5.41/2.34 % (23435)Instruction limit reached!
% 5.41/2.34 % (23435)------------------------------
% 5.41/2.34 % (23435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.41/2.34 % (23435)Termination reason: Unknown
% 5.41/2.34 % (23435)Termination phase: Saturation
% 5.41/2.34
% 5.41/2.34 % (23435)Memory used [KB]: 2174
% 5.41/2.34 % (23435)Time elapsed: 0.047 s
% 5.41/2.34 % (23435)Instructions burned: 99 (million)
% 5.41/2.34 % (23435)------------------------------
% 5.41/2.34 % (23435)------------------------------
% 5.41/2.35 % (23420)Instruction limit reached!
% 5.41/2.35 % (23420)------------------------------
% 5.41/2.35 % (23420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.41/2.36 % (23420)Termination reason: Unknown
% 5.41/2.36 % (23420)Termination phase: Saturation
% 5.41/2.36
% 5.41/2.36 % (23420)Memory used [KB]: 6780
% 5.41/2.36 % (23420)Time elapsed: 0.327 s
% 5.41/2.36 % (23420)Instructions burned: 779 (million)
% 5.41/2.36 % (23420)------------------------------
% 5.41/2.36 % (23420)------------------------------
% 5.41/2.36 % (23437)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_23265 for (2995ds/149Mi)
% 5.41/2.37 % (23404)Instruction limit reached!
% 5.41/2.37 % (23404)------------------------------
% 5.41/2.37 % (23404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.41/2.37 % (23404)Termination reason: Unknown
% 5.41/2.37 % (23404)Termination phase: Saturation
% 5.41/2.37
% 5.41/2.37 % (23404)Memory used [KB]: 10106
% 5.41/2.37 % (23404)Time elapsed: 0.436 s
% 5.41/2.37 % (23404)Instructions burned: 1043 (million)
% 5.41/2.37 % (23404)------------------------------
% 5.41/2.37 % (23404)------------------------------
% 5.41/2.37 % (23413)Instruction limit reached!
% 5.41/2.37 % (23413)------------------------------
% 5.41/2.37 % (23413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.41/2.37 % (23413)Termination reason: Unknown
% 5.41/2.37 % (23413)Termination phase: Saturation
% 5.41/2.37
% 5.41/2.37 % (23413)Memory used [KB]: 9210
% 5.41/2.37 % (23413)Time elapsed: 0.389 s
% 5.41/2.37 % (23413)Instructions burned: 711 (million)
% 5.41/2.37 % (23413)------------------------------
% 5.41/2.37 % (23413)------------------------------
% 5.41/2.38 % (23438)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_23265 for (2995ds/39Mi)
% 5.41/2.39 % (23439)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_23265 for (2995ds/6Mi)
% 5.41/2.39 % (23440)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_23265 for (2995ds/1087Mi)
% 5.41/2.39 % (23439)Instruction limit reached!
% 5.41/2.39 % (23439)------------------------------
% 5.41/2.39 % (23439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.41/2.39 % (23439)Termination reason: Unknown
% 5.41/2.39 % (23439)Termination phase: shuffling
% 5.41/2.39
% 5.41/2.39 % (23439)Memory used [KB]: 1407
% 5.41/2.39 % (23439)Time elapsed: 0.005 s
% 5.41/2.39 % (23439)Instructions burned: 8 (million)
% 5.41/2.39 % (23439)------------------------------
% 5.41/2.39 % (23439)------------------------------
% 5.41/2.39 % (23438)Instruction limit reached!
% 5.41/2.39 % (23438)------------------------------
% 5.41/2.39 % (23438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.41/2.39 % (23438)Termination reason: Unknown
% 5.41/2.39 % (23438)Termination phase: Property scanning
% 5.41/2.39
% 5.41/2.39 % (23438)Memory used [KB]: 1918
% 5.41/2.39 % (23438)Time elapsed: 0.021 s
% 5.41/2.39 % (23438)Instructions burned: 40 (million)
% 5.41/2.39 % (23438)------------------------------
% 5.41/2.39 % (23438)------------------------------
% 6.05/2.41 % (23441)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_23265 for (2994ds/47Mi)
% 6.05/2.41 % (23442)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_23265 for (2994ds/44Mi)
% 6.05/2.43 % (23441)Instruction limit reached!
% 6.05/2.43 % (23441)------------------------------
% 6.05/2.43 % (23441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.05/2.43 % (23441)Termination reason: Unknown
% 6.05/2.43 % (23441)Termination phase: Property scanning
% 6.05/2.43
% 6.05/2.43 % (23441)Memory used [KB]: 1918
% 6.05/2.43 % (23441)Time elapsed: 0.025 s
% 6.05/2.43 % (23441)Instructions burned: 49 (million)
% 6.05/2.43 % (23441)------------------------------
% 6.05/2.43 % (23441)------------------------------
% 6.05/2.43 % (23442)Instruction limit reached!
% 6.05/2.43 % (23442)------------------------------
% 6.05/2.43 % (23442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.05/2.43 % (23442)Termination reason: Unknown
% 6.05/2.43 % (23442)Termination phase: SInE selection
% 6.05/2.43
% 6.05/2.43 % (23442)Memory used [KB]: 1791
% 6.05/2.43 % (23442)Time elapsed: 0.023 s
% 6.05/2.43 % (23442)Instructions burned: 45 (million)
% 6.05/2.43 % (23442)------------------------------
% 6.05/2.43 % (23442)------------------------------
% 6.05/2.44 % (23437)Instruction limit reached!
% 6.05/2.44 % (23437)------------------------------
% 6.05/2.44 % (23437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.05/2.44 % (23437)Termination reason: Unknown
% 6.05/2.44 % (23437)Termination phase: Saturation
% 6.05/2.44
% 6.05/2.44 % (23437)Memory used [KB]: 7164
% 6.05/2.44 % (23437)Time elapsed: 0.077 s
% 6.05/2.44 % (23437)Instructions burned: 150 (million)
% 6.05/2.44 % (23437)------------------------------
% 6.05/2.44 % (23437)------------------------------
% 6.05/2.44 % (23433)Instruction limit reached!
% 6.05/2.44 % (23433)------------------------------
% 6.05/2.44 % (23433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.05/2.44 % (23433)Termination reason: Unknown
% 6.05/2.44 % (23433)Termination phase: Saturation
% 6.05/2.44
% 6.05/2.44 % (23433)Memory used [KB]: 6780
% 6.05/2.44 % (23433)Time elapsed: 0.184 s
% 6.05/2.44 % (23433)Instructions burned: 448 (million)
% 6.05/2.44 % (23433)------------------------------
% 6.05/2.44 % (23433)------------------------------
% 6.05/2.45 % (23443)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_23265 for (2994ds/432Mi)
% 6.05/2.45 % (23444)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_23265 for (2994ds/62Mi)
% 6.05/2.46 % (23445)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_23265 for (2994ds/31Mi)
% 6.05/2.46 % (23446)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_23265 for (2994ds/96Mi)
% 6.05/2.47 % (23445)Instruction limit reached!
% 6.05/2.47 % (23445)------------------------------
% 6.05/2.47 % (23445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.05/2.47 % (23445)Termination reason: Unknown
% 6.05/2.47 % (23445)Termination phase: Property scanning
% 6.05/2.47
% 6.05/2.47 % (23445)Memory used [KB]: 1791
% 6.05/2.47 % (23445)Time elapsed: 0.017 s
% 6.05/2.47 % (23445)Instructions burned: 31 (million)
% 6.05/2.47 % (23445)------------------------------
% 6.05/2.47 % (23445)------------------------------
% 6.05/2.48 % (23444)Instruction limit reached!
% 6.05/2.48 % (23444)------------------------------
% 6.05/2.48 % (23444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.05/2.48 % (23444)Termination reason: Unknown
% 6.05/2.48 % (23444)Termination phase: Function definition elimination
% 6.05/2.48
% 6.05/2.48 % (23444)Memory used [KB]: 1918
% 6.05/2.48 % (23444)Time elapsed: 0.032 s
% 6.05/2.48 % (23444)Instructions burned: 64 (million)
% 6.05/2.48 % (23444)------------------------------
% 6.05/2.48 % (23444)------------------------------
% 6.05/2.49 % (23447)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_23265 for (2994ds/453Mi)
% 6.50/2.50 % (23448)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_23265 for (2993ds/71Mi)
% 6.50/2.50 % (23422)Refutation not found, non-redundant clauses discarded% (23422)------------------------------
% 6.50/2.50 % (23422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.50/2.50 % (23422)Termination reason: Refutation not found, non-redundant clauses discarded
% 6.50/2.50
% 6.50/2.50 % (23422)Memory used [KB]: 8187
% 6.50/2.50 % (23422)Time elapsed: 0.446 s
% 6.50/2.50 % (23422)Instructions burned: 867 (million)
% 6.50/2.50 % (23422)------------------------------
% 6.50/2.50 % (23422)------------------------------
% 6.50/2.51 % (23446)Instruction limit reached!
% 6.50/2.51 % (23446)------------------------------
% 6.50/2.51 % (23446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.50/2.51 % (23446)Termination reason: Unknown
% 6.50/2.51 % (23446)Termination phase: Saturation
% 6.50/2.51
% 6.50/2.51 % (23446)Memory used [KB]: 6780
% 6.50/2.51 % (23446)Time elapsed: 0.048 s
% 6.50/2.51 % (23446)Instructions burned: 97 (million)
% 6.50/2.51 % (23446)------------------------------
% 6.50/2.51 % (23446)------------------------------
% 6.50/2.52 % (23449)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_23265 for (2993ds/83Mi)
% 6.50/2.53 % (23450)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_23265 for (2993ds/11Mi)
% 6.50/2.53 % (23450)Instruction limit reached!
% 6.50/2.53 % (23450)------------------------------
% 6.50/2.53 % (23450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.50/2.53 % (23450)Termination reason: Unknown
% 6.50/2.53 % (23450)Termination phase: shuffling
% 6.50/2.53
% 6.50/2.53 % (23450)Memory used [KB]: 1535
% 6.50/2.53 % (23450)Time elapsed: 0.008 s
% 6.50/2.53 % (23450)Instructions burned: 12 (million)
% 6.50/2.53 % (23450)------------------------------
% 6.50/2.53 % (23450)------------------------------
% 6.50/2.53 % (23448)Instruction limit reached!
% 6.50/2.53 % (23448)------------------------------
% 6.50/2.53 % (23448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.50/2.53 % (23448)Termination reason: Unknown
% 6.50/2.53 % (23448)Termination phase: Property scanning
% 6.50/2.53
% 6.50/2.53 % (23448)Memory used [KB]: 2046
% 6.50/2.53 % (23448)Time elapsed: 0.035 s
% 6.50/2.53 % (23448)Instructions burned: 72 (million)
% 6.50/2.53 % (23448)------------------------------
% 6.50/2.53 % (23448)------------------------------
% 6.50/2.55 % (23451)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_23265 for (2993ds/41Mi)
% 6.50/2.56 % (23436)Instruction limit reached!
% 6.50/2.56 % (23436)------------------------------
% 6.50/2.56 % (23436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.50/2.56 % (23436)Termination reason: Unknown
% 6.50/2.56 % (23436)Termination phase: Saturation
% 6.50/2.56
% 6.50/2.56 % (23436)Memory used [KB]: 7547
% 6.50/2.56 % (23436)Time elapsed: 0.255 s
% 6.50/2.56 % (23436)Instructions burned: 508 (million)
% 6.50/2.56 % (23436)------------------------------
% 6.50/2.56 % (23436)------------------------------
% 6.50/2.56 % (23452)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_23265 for (2993ds/6Mi)
% 6.50/2.56 % (23452)Instruction limit reached!
% 6.50/2.56 % (23452)------------------------------
% 6.50/2.56 % (23452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.50/2.56 % (23449)Instruction limit reached!
% 6.50/2.56 % (23449)------------------------------
% 6.50/2.56 % (23449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.50/2.56 % (23452)Termination reason: Unknown
% 6.50/2.56 % (23449)Termination reason: Unknown
% 6.50/2.56 % (23452)Termination phase: shuffling
% 6.50/2.56
% 6.50/2.56 % (23449)Termination phase: Property scanning
% 6.50/2.56
% 6.50/2.56 % (23452)Memory used [KB]: 1407
% 6.50/2.56 % (23449)Memory used [KB]: 2046
% 6.50/2.56 % (23449)Time elapsed: 0.040 s
% 6.50/2.56 % (23452)Time elapsed: 0.005 s
% 6.50/2.56 % (23449)Instructions burned: 84 (million)
% 6.50/2.56 % (23452)Instructions burned: 7 (million)
% 6.50/2.56 % (23449)------------------------------
% 6.50/2.56 % (23449)------------------------------
% 6.50/2.56 % (23452)------------------------------
% 6.50/2.56 % (23452)------------------------------
% 6.50/2.57 % (23451)Instruction limit reached!
% 6.50/2.57 % (23451)------------------------------
% 6.50/2.57 % (23451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.50/2.57 % (23451)Termination reason: Unknown
% 6.50/2.57 % (23451)Termination phase: Property scanning
% 6.50/2.57
% 6.50/2.57 % (23451)Memory used [KB]: 1791
% 6.50/2.57 % (23451)Time elapsed: 0.022 s
% 6.50/2.57 % (23451)Instructions burned: 42 (million)
% 6.50/2.57 % (23451)------------------------------
% 6.50/2.57 % (23451)------------------------------
% 6.50/2.57 % (23453)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_23265 for (2993ds/150Mi)
% 6.50/2.58 % (23454)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_23265 for (2993ds/343Mi)
% 6.50/2.58 % (23455)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_23265 for (2993ds/109Mi)
% 6.50/2.59 % (23456)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_23265 for (2993ds/253Mi)
% 7.50/2.63 % (23455)Instruction limit reached!
% 7.50/2.63 % (23455)------------------------------
% 7.50/2.63 % (23455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.50/2.63 % (23455)Termination reason: Unknown
% 7.50/2.63 % (23455)Termination phase: Saturation
% 7.50/2.63
% 7.50/2.63 % (23455)Memory used [KB]: 6780
% 7.50/2.63 % (23455)Time elapsed: 0.053 s
% 7.50/2.63 % (23455)Instructions burned: 109 (million)
% 7.50/2.63 % (23455)------------------------------
% 7.50/2.63 % (23455)------------------------------
% 7.50/2.63 % (23443)Instruction limit reached!
% 7.50/2.63 % (23443)------------------------------
% 7.50/2.63 % (23443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.50/2.63 % (23443)Termination reason: Unknown
% 7.50/2.63 % (23443)Termination phase: Saturation
% 7.50/2.63
% 7.50/2.63 % (23443)Memory used [KB]: 2942
% 7.50/2.63 % (23443)Time elapsed: 0.185 s
% 7.50/2.63 % (23443)Instructions burned: 433 (million)
% 7.50/2.63 % (23443)------------------------------
% 7.50/2.63 % (23443)------------------------------
% 7.50/2.65 % (23457)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_23265 for (2992ds/140Mi)
% 7.50/2.65 % (23458)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_23265 for (2992ds/614Mi)
% 7.50/2.65 % (23453)Instruction limit reached!
% 7.50/2.65 % (23453)------------------------------
% 7.50/2.65 % (23453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.50/2.65 % (23453)Termination reason: Unknown
% 7.50/2.65 % (23453)Termination phase: Saturation
% 7.50/2.65
% 7.50/2.65 % (23453)Memory used [KB]: 7931
% 7.50/2.65 % (23453)Time elapsed: 0.081 s
% 7.50/2.65 % (23453)Instructions burned: 150 (million)
% 7.50/2.65 % (23453)------------------------------
% 7.50/2.65 % (23453)------------------------------
% 7.50/2.67 % (23459)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_23265 for (2992ds/202Mi)
% 7.50/2.68 % (23447)Instruction limit reached!
% 7.50/2.68 % (23447)------------------------------
% 7.50/2.68 % (23447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.50/2.68 % (23447)Termination reason: Unknown
% 7.50/2.68 % (23447)Termination phase: Saturation
% 7.50/2.68
% 7.50/2.68 % (23447)Memory used [KB]: 6652
% 7.50/2.68 % (23447)Time elapsed: 0.192 s
% 7.50/2.68 % (23447)Instructions burned: 453 (million)
% 7.50/2.68 % (23447)------------------------------
% 7.50/2.68 % (23447)------------------------------
% 8.07/2.70 % (23460)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_23265 for (2992ds/339Mi)
% 8.07/2.71 % (23457)Instruction limit reached!
% 8.07/2.71 % (23457)------------------------------
% 8.07/2.71 % (23457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.07/2.71 % (23457)Termination reason: Unknown
% 8.07/2.71 % (23457)Termination phase: Saturation
% 8.07/2.71
% 8.07/2.71 % (23457)Memory used [KB]: 6652
% 8.07/2.71 % (23457)Time elapsed: 0.068 s
% 8.07/2.71 % (23457)Instructions burned: 141 (million)
% 8.07/2.71 % (23457)------------------------------
% 8.07/2.71 % (23457)------------------------------
% 8.07/2.72 % (23456)Instruction limit reached!
% 8.07/2.72 % (23456)------------------------------
% 8.07/2.72 % (23456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.07/2.72 % (23456)Termination reason: Unknown
% 8.07/2.72 % (23456)Termination phase: Saturation
% 8.07/2.72
% 8.07/2.72 % (23456)Memory used [KB]: 8187
% 8.07/2.72 % (23456)Time elapsed: 0.132 s
% 8.07/2.72 % (23456)Instructions burned: 254 (million)
% 8.07/2.72 % (23456)------------------------------
% 8.07/2.72 % (23456)------------------------------
% 8.07/2.73 % (23461)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_23265 for (2991ds/283Mi)
% 8.07/2.73 % (23462)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_23265 for (2991ds/134Mi)
% 8.07/2.74 % (23454)Instruction limit reached!
% 8.07/2.74 % (23454)------------------------------
% 8.07/2.74 % (23454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.07/2.74 % (23454)Termination reason: Unknown
% 8.07/2.74 % (23454)Termination phase: Saturation
% 8.07/2.74
% 8.07/2.74 % (23454)Memory used [KB]: 7931
% 8.07/2.74 % (23454)Time elapsed: 0.169 s
% 8.07/2.74 % (23454)Instructions burned: 343 (million)
% 8.07/2.74 % (23454)------------------------------
% 8.07/2.74 % (23454)------------------------------
% 8.07/2.76 % (23463)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_23265 for (2991ds/298Mi)
% 8.07/2.78 % (23459)Instruction limit reached!
% 8.07/2.78 % (23459)------------------------------
% 8.07/2.78 % (23459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.07/2.78 % (23459)Termination reason: Unknown
% 8.07/2.78 % (23459)Termination phase: Saturation
% 8.07/2.78
% 8.07/2.78 % (23459)Memory used [KB]: 8571
% 8.07/2.78 % (23459)Time elapsed: 0.108 s
% 8.07/2.78 % (23459)Instructions burned: 202 (million)
% 8.07/2.78 % (23459)------------------------------
% 8.07/2.78 % (23459)------------------------------
% 8.62/2.80 % (23464)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_23265 for (2991ds/192Mi)
% 8.62/2.80 % (23462)Instruction limit reached!
% 8.62/2.80 % (23462)------------------------------
% 8.62/2.80 % (23462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.62/2.80 % (23462)Termination reason: Unknown
% 8.62/2.80 % (23462)Termination phase: Saturation
% 8.62/2.80
% 8.62/2.80 % (23462)Memory used [KB]: 6908
% 8.62/2.80 % (23462)Time elapsed: 0.067 s
% 8.62/2.80 % (23462)Instructions burned: 134 (million)
% 8.62/2.80 % (23462)------------------------------
% 8.62/2.80 % (23462)------------------------------
% 8.62/2.82 % (23465)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_23265 for (2990ds/258Mi)
% 8.62/2.85 % (23461)Instruction limit reached!
% 8.62/2.85 % (23461)------------------------------
% 8.62/2.85 % (23461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.62/2.85 % (23461)Termination reason: Unknown
% 8.62/2.85 % (23461)Termination phase: Saturation
% 8.62/2.85
% 8.62/2.85 % (23461)Memory used [KB]: 9210
% 8.62/2.85 % (23461)Time elapsed: 0.123 s
% 8.62/2.85 % (23461)Instructions burned: 284 (million)
% 8.62/2.85 % (23461)------------------------------
% 8.62/2.85 % (23461)------------------------------
% 8.62/2.86 % (23460)Instruction limit reached!
% 8.62/2.86 % (23460)------------------------------
% 8.62/2.86 % (23460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.62/2.86 % (23460)Termination reason: Unknown
% 8.62/2.86 % (23460)Termination phase: Saturation
% 8.62/2.86
% 8.62/2.86 % (23460)Memory used [KB]: 7547
% 8.62/2.86 % (23460)Time elapsed: 0.168 s
% 8.62/2.86 % (23460)Instructions burned: 339 (million)
% 8.62/2.86 % (23460)------------------------------
% 8.62/2.86 % (23460)------------------------------
% 8.62/2.87 % (23466)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_23265 for (2990ds/90Mi)
% 8.62/2.88 % (23467)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_23265 for (2990ds/231Mi)
% 8.62/2.89 % (23464)Instruction limit reached!
% 8.62/2.89 % (23464)------------------------------
% 8.62/2.89 % (23464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.62/2.89 % (23464)Termination reason: Unknown
% 8.62/2.89 % (23464)Termination phase: Saturation
% 8.62/2.89
% 8.62/2.89 % (23464)Memory used [KB]: 7419
% 8.62/2.89 % (23464)Time elapsed: 0.090 s
% 8.62/2.89 % (23464)Instructions burned: 192 (million)
% 8.62/2.89 % (23464)------------------------------
% 8.62/2.89 % (23464)------------------------------
% 8.62/2.89 % (23463)Instruction limit reached!
% 8.62/2.89 % (23463)------------------------------
% 8.62/2.89 % (23463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.62/2.89 % (23463)Termination reason: Unknown
% 8.62/2.89 % (23463)Termination phase: Saturation
% 8.62/2.89
% 8.62/2.89 % (23463)Memory used [KB]: 6652
% 8.62/2.89 % (23463)Time elapsed: 0.131 s
% 8.62/2.89 % (23463)Instructions burned: 299 (million)
% 8.62/2.89 % (23463)------------------------------
% 8.62/2.89 % (23463)------------------------------
% 9.27/2.90 % (23468)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_23265 for (2990ds/458Mi)
% 9.27/2.91 % (23469)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_23265 for (2990ds/31Mi)
% 9.27/2.91 % (23466)Instruction limit reached!
% 9.27/2.91 % (23466)------------------------------
% 9.27/2.91 % (23466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.27/2.91 % (23466)Termination reason: Unknown
% 9.27/2.91 % (23466)Termination phase: Property scanning
% 9.27/2.91
% 9.27/2.91 % (23466)Memory used [KB]: 2430
% 9.27/2.91 % (23466)Time elapsed: 0.045 s
% 9.27/2.91 % (23466)Instructions burned: 92 (million)
% 9.27/2.91 % (23466)------------------------------
% 9.27/2.91 % (23466)------------------------------
% 9.27/2.92 % (23469)Instruction limit reached!
% 9.27/2.92 % (23469)------------------------------
% 9.27/2.92 % (23469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.27/2.92 % (23469)Termination reason: Unknown
% 9.27/2.92 % (23469)Termination phase: Property scanning
% 9.27/2.92
% 9.27/2.92 % (23469)Memory used [KB]: 1791
% 9.27/2.92 % (23469)Time elapsed: 0.017 s
% 9.27/2.92 % (23469)Instructions burned: 33 (million)
% 9.27/2.92 % (23469)------------------------------
% 9.27/2.92 % (23469)------------------------------
% 9.27/2.93 % (23470)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_23265 for (2989ds/297Mi)
% 9.27/2.94 % (23465)Instruction limit reached!
% 9.27/2.94 % (23465)------------------------------
% 9.27/2.94 % (23465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.27/2.94 % (23465)Termination reason: Unknown
% 9.27/2.94 % (23465)Termination phase: Saturation
% 9.27/2.94
% 9.27/2.94 % (23465)Memory used [KB]: 7547
% 9.27/2.94 % (23465)Time elapsed: 0.127 s
% 9.27/2.94 % (23465)Instructions burned: 259 (million)
% 9.27/2.94 % (23465)------------------------------
% 9.27/2.94 % (23465)------------------------------
% 9.27/2.94 % (23471)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_23265 for (2989ds/987Mi)
% 9.27/2.96 % (23472)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_23265 for (2989ds/182Mi)
% 9.27/2.97 % (23440)Instruction limit reached!
% 9.27/2.97 % (23440)------------------------------
% 9.27/2.97 % (23440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.27/2.97 % (23440)Termination reason: Unknown
% 9.27/2.97 % (23440)Termination phase: Saturation
% 9.27/2.97
% 9.27/2.97 % (23440)Memory used [KB]: 10362
% 9.27/2.97 % (23440)Time elapsed: 0.586 s
% 9.27/2.97 % (23440)Instructions burned: 1087 (million)
% 9.27/2.97 % (23440)------------------------------
% 9.27/2.97 % (23440)------------------------------
% 9.27/2.99 % (23458)Instruction limit reached!
% 9.27/2.99 % (23458)------------------------------
% 9.27/2.99 % (23458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.27/2.99 % (23458)Termination reason: Unknown
% 9.27/2.99 % (23458)Termination phase: Saturation
% 9.27/2.99
% 9.27/2.99 % (23458)Memory used [KB]: 8187
% 9.27/2.99 % (23458)Time elapsed: 0.337 s
% 9.27/2.99 % (23458)Instructions burned: 615 (million)
% 9.27/2.99 % (23458)------------------------------
% 9.27/2.99 % (23458)------------------------------
% 9.27/2.99 % (23473)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_23265 for (2989ds/182Mi)
% 9.27/3.01 % (23474)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_23265 for (2988ds/154Mi)
% 9.27/3.01 % (23467)Instruction limit reached!
% 9.27/3.01 % (23467)------------------------------
% 9.27/3.01 % (23467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.27/3.01 % (23467)Termination reason: Unknown
% 9.27/3.01 % (23467)Termination phase: Saturation
% 9.27/3.01
% 9.27/3.01 % (23467)Memory used [KB]: 11001
% 9.27/3.01 % (23467)Time elapsed: 0.150 s
% 9.27/3.01 % (23467)Instructions burned: 231 (million)
% 9.27/3.01 % (23467)------------------------------
% 9.27/3.01 % (23467)------------------------------
% 11.10/3.03 % (23475)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_23265 for (2988ds/79Mi)
% 11.10/3.05 % (23472)Instruction limit reached!
% 11.10/3.05 % (23472)------------------------------
% 11.10/3.05 % (23472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.10/3.05 % (23472)Termination reason: Unknown
% 11.10/3.05 % (23472)Termination phase: Saturation
% 11.10/3.05
% 11.10/3.05 % (23472)Memory used [KB]: 7419
% 11.10/3.05 % (23472)Time elapsed: 0.093 s
% 11.10/3.05 % (23472)Instructions burned: 182 (million)
% 11.10/3.05 % (23472)------------------------------
% 11.10/3.05 % (23472)------------------------------
% 11.10/3.06 % (23470)Instruction limit reached!
% 11.10/3.06 % (23470)------------------------------
% 11.10/3.06 % (23470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.10/3.06 % (23470)Termination reason: Unknown
% 11.10/3.06 % (23470)Termination phase: Saturation
% 11.10/3.06
% 11.10/3.06 % (23470)Memory used [KB]: 8699
% 11.10/3.06 % (23470)Time elapsed: 0.128 s
% 11.10/3.06 % (23470)Instructions burned: 298 (million)
% 11.10/3.06 % (23470)------------------------------
% 11.10/3.06 % (23470)------------------------------
% 11.10/3.07 % (23476)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_23265 for (2988ds/216Mi)
% 11.10/3.08 % (23474)Instruction limit reached!
% 11.10/3.08 % (23474)------------------------------
% 11.10/3.08 % (23474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.10/3.08 % (23474)Termination reason: Unknown
% 11.10/3.08 % (23474)Termination phase: Saturation
% 11.10/3.08
% 11.10/3.08 % (23474)Memory used [KB]: 6652
% 11.10/3.08 % (23474)Time elapsed: 0.071 s
% 11.10/3.08 % (23474)Instructions burned: 154 (million)
% 11.10/3.08 % (23474)------------------------------
% 11.10/3.08 % (23474)------------------------------
% 11.10/3.08 % (23475)Instruction limit reached!
% 11.10/3.08 % (23475)------------------------------
% 11.10/3.08 % (23475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.10/3.08 % (23475)Termination reason: Unknown
% 11.10/3.08 % (23475)Termination phase: Saturation
% 11.10/3.08
% 11.10/3.08 % (23475)Memory used [KB]: 2046
% 11.10/3.08 % (23475)Time elapsed: 0.046 s
% 11.10/3.08 % (23475)Instructions burned: 79 (million)
% 11.10/3.08 % (23475)------------------------------
% 11.10/3.08 % (23475)------------------------------
% 11.10/3.08 % (23477)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_23265 for (2988ds/114Mi)
% 11.10/3.08 % (23473)Instruction limit reached!
% 11.10/3.08 % (23473)------------------------------
% 11.10/3.08 % (23473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.10/3.08 % (23473)Termination reason: Unknown
% 11.10/3.08 % (23473)Termination phase: Saturation
% 11.10/3.08
% 11.10/3.08 % (23473)Memory used [KB]: 9850
% 11.10/3.08 % (23473)Time elapsed: 0.092 s
% 11.10/3.08 % (23473)Instructions burned: 182 (million)
% 11.10/3.08 % (23473)------------------------------
% 11.10/3.08 % (23473)------------------------------
% 11.10/3.09 % (23478)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_23265 for (2988ds/922Mi)
% 11.10/3.09 % (23479)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_23265 for (2988ds/182Mi)
% 11.10/3.10 % (23480)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_23265 for (2988ds/164Mi)
% 11.57/3.13 % (23477)Instruction limit reached!
% 11.57/3.13 % (23477)------------------------------
% 11.57/3.13 % (23477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.57/3.13 % (23477)Termination reason: Unknown
% 11.57/3.13 % (23477)Termination phase: Saturation
% 11.57/3.13
% 11.57/3.13 % (23477)Memory used [KB]: 6780
% 11.57/3.13 % (23477)Time elapsed: 0.054 s
% 11.57/3.13 % (23477)Instructions burned: 114 (million)
% 11.57/3.13 % (23477)------------------------------
% 11.57/3.13 % (23477)------------------------------
% 11.57/3.14 % (23468)Instruction limit reached!
% 11.57/3.14 % (23468)------------------------------
% 11.57/3.14 % (23468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.57/3.14 % (23468)Termination reason: Unknown
% 11.57/3.14 % (23468)Termination phase: Saturation
% 11.57/3.14
% 11.57/3.14 % (23468)Memory used [KB]: 7931
% 11.57/3.14 % (23468)Time elapsed: 0.236 s
% 11.57/3.14 % (23468)Instructions burned: 458 (million)
% 11.57/3.14 % (23468)------------------------------
% 11.57/3.14 % (23468)------------------------------
% 11.57/3.15 % (23481)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_23265 for (2987ds/50Mi)
% 11.57/3.16 % (23482)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_23265 for (2987ds/368Mi)
% 11.57/3.17 % (23476)Instruction limit reached!
% 11.57/3.17 % (23476)------------------------------
% 11.57/3.17 % (23476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.57/3.17 % (23476)Termination reason: Unknown
% 11.57/3.17 % (23476)Termination phase: Saturation
% 11.57/3.17
% 11.57/3.17 % (23476)Memory used [KB]: 6652
% 11.57/3.17 % (23476)Time elapsed: 0.096 s
% 11.57/3.17 % (23476)Instructions burned: 218 (million)
% 11.57/3.17 % (23476)------------------------------
% 11.57/3.17 % (23476)------------------------------
% 11.57/3.17 % (23481)Instruction limit reached!
% 11.57/3.17 % (23481)------------------------------
% 11.57/3.17 % (23481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.57/3.17 % (23481)Termination reason: Unknown
% 11.57/3.17 % (23481)Termination phase: Property scanning
% 11.57/3.17
% 11.57/3.17 % (23481)Memory used [KB]: 1791
% 11.57/3.17 % (23481)Time elapsed: 0.026 s
% 11.57/3.17 % (23481)Instructions burned: 51 (million)
% 11.57/3.17 % (23481)------------------------------
% 11.57/3.17 % (23481)------------------------------
% 11.57/3.17 % (23479)Instruction limit reached!
% 11.57/3.17 % (23479)------------------------------
% 11.57/3.17 % (23479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.57/3.17 % (23479)Termination reason: Unknown
% 11.57/3.17 % (23479)Termination phase: Saturation
% 11.57/3.17
% 11.57/3.17 % (23479)Memory used [KB]: 6652
% 11.57/3.17 % (23479)Time elapsed: 0.083 s
% 11.57/3.17 % (23479)Instructions burned: 184 (million)
% 11.57/3.17 % (23479)------------------------------
% 11.57/3.17 % (23479)------------------------------
% 11.57/3.18 % (23480)Instruction limit reached!
% 11.57/3.18 % (23480)------------------------------
% 11.57/3.18 % (23480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.57/3.18 % (23480)Termination reason: Unknown
% 11.57/3.18 % (23480)Termination phase: Saturation
% 11.57/3.18
% 11.57/3.18 % (23480)Memory used [KB]: 2302
% 11.57/3.18 % (23480)Time elapsed: 0.083 s
% 11.57/3.18 % (23480)Instructions burned: 165 (million)
% 11.57/3.18 % (23480)------------------------------
% 11.57/3.18 % (23480)------------------------------
% 11.57/3.18 % (23483)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_23265 for (2987ds/1021Mi)
% 11.57/3.19 % (23484)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_23265 for (2987ds/267Mi)
% 11.57/3.19 % (23485)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_23265 for (2987ds/204Mi)
% 12.07/3.20 % (23486)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_23265 for (2987ds/26Mi)
% 12.07/3.21 % (23486)Instruction limit reached!
% 12.07/3.21 % (23486)------------------------------
% 12.07/3.21 % (23486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.07/3.21 % (23486)Termination reason: Unknown
% 12.07/3.21 % (23486)Termination phase: shuffling
% 12.07/3.21
% 12.07/3.21 % (23486)Memory used [KB]: 1791
% 12.07/3.21 % (23486)Time elapsed: 0.014 s
% 12.07/3.21 % (23486)Instructions burned: 26 (million)
% 12.07/3.21 % (23486)------------------------------
% 12.07/3.21 % (23486)------------------------------
% 12.07/3.23 % (23487)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_23265 for (2986ds/53Mi)
% 12.07/3.26 % (23487)Instruction limit reached!
% 12.07/3.26 % (23487)------------------------------
% 12.07/3.26 % (23487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.07/3.26 % (23487)Termination reason: Unknown
% 12.07/3.26 % (23487)Termination phase: Property scanning
% 12.07/3.26
% 12.07/3.26 % (23487)Memory used [KB]: 1791
% 12.07/3.26 % (23487)Time elapsed: 0.028 s
% 12.07/3.26 % (23487)Instructions burned: 54 (million)
% 12.07/3.26 % (23487)------------------------------
% 12.07/3.26 % (23487)------------------------------
% 12.07/3.28 % (23488)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_23265 for (2986ds/4436Mi)
% 12.07/3.29 % (23485)Instruction limit reached!
% 12.07/3.29 % (23485)------------------------------
% 12.07/3.29 % (23485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.07/3.29 % (23485)Termination reason: Unknown
% 12.07/3.29 % (23485)Termination phase: Saturation
% 12.07/3.29
% 12.07/3.29 % (23485)Memory used [KB]: 7419
% 12.07/3.29 % (23485)Time elapsed: 0.096 s
% 12.07/3.29 % (23485)Instructions burned: 205 (million)
% 12.07/3.29 % (23485)------------------------------
% 12.07/3.29 % (23485)------------------------------
% 12.36/3.30 % (23484)Instruction limit reached!
% 12.36/3.30 % (23484)------------------------------
% 12.36/3.30 % (23484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.36/3.30 % (23484)Termination reason: Unknown
% 12.36/3.30 % (23484)Termination phase: Saturation
% 12.36/3.30
% 12.36/3.30 % (23484)Memory used [KB]: 8699
% 12.36/3.30 % (23484)Time elapsed: 0.111 s
% 12.36/3.30 % (23484)Instructions burned: 270 (million)
% 12.36/3.30 % (23484)------------------------------
% 12.36/3.30 % (23484)------------------------------
% 12.36/3.31 % (23489)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_23265 for (2986ds/1539Mi)
% 12.36/3.31 % (23471)Instruction limit reached!
% 12.36/3.31 % (23471)------------------------------
% 12.36/3.31 % (23471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.36/3.31 % (23471)Termination reason: Unknown
% 12.36/3.31 % (23471)Termination phase: Saturation
% 12.36/3.31
% 12.36/3.31 % (23471)Memory used [KB]: 10106
% 12.36/3.31 % (23471)Time elapsed: 0.372 s
% 12.36/3.31 % (23471)Instructions burned: 989 (million)
% 12.36/3.31 % (23471)------------------------------
% 12.36/3.31 % (23471)------------------------------
% 12.36/3.32 % (23490)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_23265 for (2985ds/408Mi)
% 12.36/3.33 % (23491)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_23265 for (2985ds/5205Mi)
% 12.36/3.34 % (23482)Instruction limit reached!
% 12.36/3.34 % (23482)------------------------------
% 12.36/3.34 % (23482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.36/3.34 % (23482)Termination reason: Unknown
% 12.36/3.34 % (23482)Termination phase: Saturation
% 12.36/3.34
% 12.36/3.34 % (23482)Memory used [KB]: 7931
% 12.36/3.34 % (23482)Time elapsed: 0.186 s
% 12.36/3.34 % (23482)Instructions burned: 369 (million)
% 12.36/3.34 % (23482)------------------------------
% 12.36/3.34 % (23482)------------------------------
% 12.36/3.36 % (23492)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_23265 for (2985ds/1913Mi)
% 12.72/3.54 % (23490)Instruction limit reached!
% 12.72/3.54 % (23490)------------------------------
% 12.72/3.54 % (23490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.72/3.54 % (23490)Termination reason: Unknown
% 12.72/3.54 % (23490)Termination phase: Saturation
% 12.72/3.54
% 12.72/3.55 % (23490)Memory used [KB]: 9338
% 12.72/3.55 % (23490)Time elapsed: 0.250 s
% 12.72/3.55 % (23490)Instructions burned: 408 (million)
% 12.72/3.55 % (23490)------------------------------
% 12.72/3.55 % (23490)------------------------------
% 12.72/3.56 % (23493)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_23265 for (2983ds/4350Mi)
% 12.72/3.58 % (23478)Instruction limit reached!
% 12.72/3.58 % (23478)------------------------------
% 12.72/3.58 % (23478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.72/3.58 % (23478)Termination reason: Unknown
% 12.72/3.58 % (23478)Termination phase: Saturation
% 12.72/3.58
% 12.72/3.58 % (23478)Memory used [KB]: 9594
% 12.72/3.58 % (23478)Time elapsed: 0.489 s
% 12.72/3.58 % (23478)Instructions burned: 923 (million)
% 12.72/3.58 % (23478)------------------------------
% 12.72/3.58 % (23478)------------------------------
% 13.47/3.60 % (23494)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_23265 for (2982ds/68Mi)
% 13.47/3.63 % (23494)Instruction limit reached!
% 13.47/3.63 % (23494)------------------------------
% 13.47/3.63 % (23494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.47/3.63 % (23494)Termination reason: Unknown
% 13.47/3.63 % (23494)Termination phase: Function definition elimination
% 13.47/3.63
% 13.47/3.63 % (23494)Memory used [KB]: 2046
% 13.47/3.63 % (23494)Time elapsed: 0.032 s
% 13.47/3.63 % (23494)Instructions burned: 68 (million)
% 13.47/3.63 % (23494)------------------------------
% 13.47/3.63 % (23494)------------------------------
% 13.47/3.65 % (23495)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_23265 for (2982ds/358Mi)
% 13.53/3.72 % (23483)Instruction limit reached!
% 13.53/3.72 % (23483)------------------------------
% 13.53/3.72 % (23483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.53/3.72 % (23483)Termination reason: Unknown
% 13.53/3.72 % (23483)Termination phase: Saturation
% 13.53/3.72
% 13.53/3.72 % (23483)Memory used [KB]: 10106
% 13.53/3.72 % (23483)Time elapsed: 0.541 s
% 13.53/3.72 % (23483)Instructions burned: 1022 (million)
% 13.53/3.72 % (23483)------------------------------
% 13.53/3.72 % (23483)------------------------------
% 13.53/3.74 % (23496)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_23265 for (2981ds/31Mi)
% 13.53/3.76 % (23496)Instruction limit reached!
% 13.53/3.76 % (23496)------------------------------
% 13.53/3.76 % (23496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.53/3.76 % (23496)Termination reason: Unknown
% 13.53/3.76 % (23496)Termination phase: Property scanning
% 13.53/3.76
% 13.53/3.76 % (23496)Memory used [KB]: 1791
% 13.53/3.76 % (23496)Time elapsed: 0.017 s
% 13.53/3.76 % (23496)Instructions burned: 32 (million)
% 13.53/3.76 % (23496)------------------------------
% 13.53/3.76 % (23496)------------------------------
% 13.53/3.78 % (23497)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_23265 for (2981ds/279Mi)
% 14.12/3.82 % (23495)Instruction limit reached!
% 14.12/3.82 % (23495)------------------------------
% 14.12/3.82 % (23495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.12/3.82 % (23495)Termination reason: Unknown
% 14.12/3.82 % (23495)Termination phase: Saturation
% 14.12/3.82
% 14.12/3.82 % (23495)Memory used [KB]: 7803
% 14.12/3.82 % (23495)Time elapsed: 0.171 s
% 14.12/3.82 % (23495)Instructions burned: 358 (million)
% 14.12/3.82 % (23495)------------------------------
% 14.12/3.82 % (23495)------------------------------
% 14.12/3.83 % (23498)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_23265 for (2980ds/258Mi)
% 14.12/3.89 % (23497)Instruction limit reached!
% 14.12/3.89 % (23497)------------------------------
% 14.12/3.89 % (23497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.12/3.89 % (23497)Termination reason: Unknown
% 14.12/3.89 % (23497)Termination phase: Saturation
% 14.12/3.89
% 14.12/3.89 % (23497)Memory used [KB]: 6780
% 14.12/3.89 % (23497)Time elapsed: 0.119 s
% 14.12/3.89 % (23497)Instructions burned: 280 (million)
% 14.12/3.89 % (23497)------------------------------
% 14.12/3.89 % (23497)------------------------------
% 14.44/3.91 % (23499)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_23265 for (2979ds/26Mi)
% 14.44/3.92 % (23499)Instruction limit reached!
% 14.44/3.92 % (23499)------------------------------
% 14.44/3.92 % (23499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.44/3.92 % (23499)Termination reason: Unknown
% 14.44/3.92 % (23499)Termination phase: Property scanning
% 14.44/3.92
% 14.44/3.92 % (23499)Memory used [KB]: 1791
% 14.44/3.92 % (23499)Time elapsed: 0.014 s
% 14.44/3.92 % (23499)Instructions burned: 26 (million)
% 14.44/3.92 % (23499)------------------------------
% 14.44/3.92 % (23499)------------------------------
% 14.44/3.94 % (23500)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_23265 for (2979ds/995Mi)
% 14.44/3.95 % (23498)Instruction limit reached!
% 14.44/3.95 % (23498)------------------------------
% 14.44/3.95 % (23498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.44/3.95 % (23498)Termination reason: Unknown
% 14.44/3.95 % (23498)Termination phase: Saturation
% 14.44/3.95
% 14.44/3.95 % (23498)Memory used [KB]: 7675
% 14.44/3.95 % (23498)Time elapsed: 0.116 s
% 14.44/3.95 % (23498)Instructions burned: 259 (million)
% 14.44/3.95 % (23498)------------------------------
% 14.44/3.95 % (23498)------------------------------
% 14.44/3.97 % (23501)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_23265 for (2979ds/373Mi)
% 18.09/4.06 % (23489)Instruction limit reached!
% 18.09/4.06 % (23489)------------------------------
% 18.09/4.06 % (23489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.09/4.06 % (23489)Termination reason: Unknown
% 18.09/4.06 % (23489)Termination phase: Saturation
% 18.09/4.06
% 18.09/4.06 % (23489)Memory used [KB]: 8827
% 18.09/4.06 % (23489)Time elapsed: 0.777 s
% 18.09/4.06 % (23489)Instructions burned: 1539 (million)
% 18.09/4.06 % (23489)------------------------------
% 18.09/4.06 % (23489)------------------------------
% 18.09/4.08 % (23502)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_23265 for (2978ds/253Mi)
% 18.75/4.16 % (23501)Instruction limit reached!
% 18.75/4.16 % (23501)------------------------------
% 18.75/4.16 % (23501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.75/4.16 % (23501)Termination reason: Unknown
% 18.75/4.16 % (23501)Termination phase: Saturation
% 18.75/4.16
% 18.75/4.16 % (23501)Memory used [KB]: 7803
% 18.75/4.16 % (23501)Time elapsed: 0.192 s
% 18.75/4.16 % (23501)Instructions burned: 373 (million)
% 18.75/4.16 % (23501)------------------------------
% 18.75/4.16 % (23501)------------------------------
% 18.75/4.18 % (23503)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_23265 for (2977ds/832Mi)
% 18.75/4.18 % (23502)Instruction limit reached!
% 18.75/4.18 % (23502)------------------------------
% 18.75/4.18 % (23502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.75/4.18 % (23502)Termination reason: Unknown
% 18.75/4.18 % (23502)Termination phase: Saturation
% 18.75/4.18
% 18.75/4.18 % (23502)Memory used [KB]: 6908
% 18.75/4.18 % (23502)Time elapsed: 0.103 s
% 18.75/4.18 % (23502)Instructions burned: 253 (million)
% 18.75/4.18 % (23502)------------------------------
% 18.75/4.18 % (23502)------------------------------
% 18.75/4.20 % (23504)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_23265 for (2976ds/668Mi)
% 19.24/4.27 % (23503)Refutation not found, incomplete strategy
% 19.24/4.27 % (23503)------------------------------
% 19.24/4.27 % (23503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.24/4.27 % (23503)Termination reason: Refutation not found, incomplete strategy
% 19.24/4.27
% 19.24/4.27
% 19.24/4.27 % (23503)Memory used [KB]: 8187
% 19.24/4.27 % (23503)Time elapsed: 0.098 s
% 19.24/4.27 % (23503)Instructions burned: 194 (million)
% 19.24/4.27 % (23503)------------------------------
% 19.24/4.27 % (23503)------------------------------
% 19.24/4.29 % (23505)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_23265 for (2976ds/40Mi)
% 19.86/4.31 % (23492)Instruction limit reached!
% 19.86/4.31 % (23492)------------------------------
% 19.86/4.31 % (23492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.86/4.31 % (23492)Termination reason: Unknown
% 19.86/4.31 % (23492)Termination phase: Saturation
% 19.86/4.31
% 19.86/4.31 % (23492)Memory used [KB]: 4221
% 19.86/4.31 % (23492)Time elapsed: 0.972 s
% 19.86/4.31 % (23492)Instructions burned: 1913 (million)
% 19.86/4.31 % (23492)------------------------------
% 19.86/4.31 % (23492)------------------------------
% 19.86/4.31 % (23505)Instruction limit reached!
% 19.86/4.31 % (23505)------------------------------
% 19.86/4.31 % (23505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.86/4.31 % (23505)Termination reason: Unknown
% 19.86/4.31 % (23505)Termination phase: Property scanning
% 19.86/4.31
% 19.86/4.31 % (23505)Memory used [KB]: 1791
% 19.86/4.31 % (23505)Time elapsed: 0.020 s
% 19.86/4.31 % (23505)Instructions burned: 40 (million)
% 19.86/4.31 % (23505)------------------------------
% 19.86/4.31 % (23505)------------------------------
% 19.86/4.32 % (23506)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_23265 for (2975ds/294Mi)
% 19.86/4.33 % (23507)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_23265 for (2975ds/187Mi)
% 19.86/4.33 % (23500)Instruction limit reached!
% 19.86/4.33 % (23500)------------------------------
% 19.86/4.33 % (23500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.86/4.33 % (23500)Termination reason: Unknown
% 19.86/4.33 % (23500)Termination phase: Saturation
% 19.86/4.33
% 19.86/4.33 % (23500)Memory used [KB]: 9594
% 19.86/4.33 % (23500)Time elapsed: 0.388 s
% 19.86/4.33 % (23500)Instructions burned: 996 (million)
% 19.86/4.33 % (23500)------------------------------
% 19.86/4.33 % (23500)------------------------------
% 19.86/4.36 % (23508)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_23265 for (2975ds/371Mi)
% 20.27/4.41 % (23507)Instruction limit reached!
% 20.27/4.41 % (23507)------------------------------
% 20.27/4.41 % (23507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.27/4.41 % (23507)Termination reason: Unknown
% 20.27/4.41 % (23507)Termination phase: Saturation
% 20.27/4.41
% 20.27/4.41 % (23507)Memory used [KB]: 7419
% 20.27/4.41 % (23507)Time elapsed: 0.086 s
% 20.27/4.41 % (23507)Instructions burned: 189 (million)
% 20.27/4.41 % (23507)------------------------------
% 20.27/4.41 % (23507)------------------------------
% 20.27/4.43 % (23509)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_23265 for (2974ds/1827Mi)
% 20.27/4.45 % (23506)Instruction limit reached!
% 20.27/4.45 % (23506)------------------------------
% 20.27/4.45 % (23506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.27/4.45 % (23506)Termination reason: Unknown
% 20.27/4.45 % (23506)Termination phase: Saturation
% 20.27/4.45
% 20.27/4.45 % (23506)Memory used [KB]: 6652
% 20.27/4.45 % (23506)Time elapsed: 0.123 s
% 20.27/4.45 % (23506)Instructions burned: 294 (million)
% 20.27/4.45 % (23506)------------------------------
% 20.27/4.45 % (23506)------------------------------
% 20.27/4.45 % (23504)Instruction limit reached!
% 20.27/4.45 % (23504)------------------------------
% 20.27/4.45 % (23504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.27/4.45 % (23504)Termination reason: Unknown
% 20.27/4.45 % (23504)Termination phase: Saturation
% 20.27/4.45
% 20.27/4.45 % (23504)Memory used [KB]: 14200
% 20.27/4.45 % (23504)Time elapsed: 0.258 s
% 20.27/4.45 % (23504)Instructions burned: 668 (million)
% 20.27/4.45 % (23504)------------------------------
% 20.27/4.45 % (23504)------------------------------
% 20.27/4.46 % (23510)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_23265 for (2974ds/70Mi)
% 20.27/4.47 % (23511)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_23265 for (2974ds/316Mi)
% 20.27/4.49 % (23510)Instruction limit reached!
% 20.27/4.49 % (23510)------------------------------
% 20.27/4.49 % (23510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.27/4.49 % (23510)Termination reason: Unknown
% 20.27/4.49 % (23510)Termination phase: Property scanning
% 20.27/4.49
% 20.27/4.49 % (23510)Memory used [KB]: 1918
% 20.27/4.49 % (23510)Time elapsed: 0.033 s
% 20.27/4.49 % (23510)Instructions burned: 72 (million)
% 20.27/4.49 % (23510)------------------------------
% 20.27/4.49 % (23510)------------------------------
% 21.12/4.51 % (23512)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_23265 for (2973ds/932Mi)
% 21.12/4.54 % (23508)Instruction limit reached!
% 21.12/4.54 % (23508)------------------------------
% 21.12/4.54 % (23508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.12/4.54 % (23508)Termination reason: Unknown
% 21.12/4.54 % (23508)Termination phase: Saturation
% 21.12/4.54
% 21.12/4.54 % (23508)Memory used [KB]: 8059
% 21.12/4.54 % (23508)Time elapsed: 0.180 s
% 21.12/4.54 % (23508)Instructions burned: 371 (million)
% 21.12/4.54 % (23508)------------------------------
% 21.12/4.54 % (23508)------------------------------
% 21.12/4.56 % (23513)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_23265 for (2973ds/4714Mi)
% 21.62/4.60 % (23511)Instruction limit reached!
% 21.62/4.60 % (23511)------------------------------
% 21.62/4.60 % (23511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.62/4.60 % (23511)Termination reason: Unknown
% 21.62/4.60 % (23511)Termination phase: Saturation
% 21.62/4.60
% 21.62/4.60 % (23511)Memory used [KB]: 7419
% 21.62/4.60 % (23511)Time elapsed: 0.130 s
% 21.62/4.60 % (23511)Instructions burned: 317 (million)
% 21.62/4.60 % (23511)------------------------------
% 21.62/4.60 % (23511)------------------------------
% 21.62/4.62 % (23514)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_23265 for (2972ds/8250Mi)
% 22.36/4.88 % (23512)Instruction limit reached!
% 22.36/4.88 % (23512)------------------------------
% 22.36/4.88 % (23512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.36/4.88 % (23512)Termination reason: Unknown
% 22.36/4.88 % (23512)Termination phase: Saturation
% 22.36/4.88
% 22.36/4.88 % (23512)Memory used [KB]: 10618
% 22.36/4.88 % (23512)Time elapsed: 0.368 s
% 22.36/4.88 % (23512)Instructions burned: 932 (million)
% 22.36/4.88 % (23512)------------------------------
% 22.36/4.88 % (23512)------------------------------
% 22.36/4.90 % (23515)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_23265 for (2970ds/770Mi)
% 26.28/5.24 % (23515)Instruction limit reached!
% 26.28/5.24 % (23515)------------------------------
% 26.28/5.24 % (23515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.28/5.24 % (23515)Termination reason: Unknown
% 26.28/5.24 % (23515)Termination phase: Saturation
% 26.28/5.24
% 26.28/5.24 % (23515)Memory used [KB]: 6908
% 26.28/5.24 % (23515)Time elapsed: 0.350 s
% 26.28/5.24 % (23515)Instructions burned: 770 (million)
% 26.28/5.24 % (23515)------------------------------
% 26.28/5.24 % (23515)------------------------------
% 26.28/5.26 % (23516)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_23265 for (2966ds/794Mi)
% 26.93/5.30 % (23509)Instruction limit reached!
% 26.93/5.30 % (23509)------------------------------
% 26.93/5.30 % (23509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.93/5.30 % (23509)Termination reason: Unknown
% 26.93/5.30 % (23509)Termination phase: Saturation
% 26.93/5.30
% 26.93/5.30 % (23509)Memory used [KB]: 16247
% 26.93/5.30 % (23509)Time elapsed: 0.878 s
% 26.93/5.30 % (23509)Instructions burned: 1827 (million)
% 26.93/5.30 % (23509)------------------------------
% 26.93/5.30 % (23509)------------------------------
% 26.93/5.32 % (23517)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_23265 for (2965ds/464Mi)
% 26.93/5.39 % (23491)Instruction limit reached!
% 26.93/5.39 % (23491)------------------------------
% 26.93/5.39 % (23491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.93/5.39 % (23491)Termination reason: Unknown
% 26.93/5.39 % (23491)Termination phase: Saturation
% 26.93/5.39
% 26.93/5.39 % (23491)Memory used [KB]: 10618
% 26.93/5.39 % (23491)Time elapsed: 2.084 s
% 26.93/5.39 % (23491)Instructions burned: 5207 (million)
% 26.93/5.39 % (23491)------------------------------
% 26.93/5.39 % (23491)------------------------------
% 27.46/5.41 % (23518)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_23265 for (2964ds/1376Mi)
% 27.86/5.55 % (23517)Instruction limit reached!
% 27.86/5.55 % (23517)------------------------------
% 27.86/5.55 % (23517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.86/5.55 % (23517)Termination reason: Unknown
% 27.86/5.55 % (23517)Termination phase: Saturation
% 27.86/5.55
% 27.86/5.55 % (23517)Memory used [KB]: 8059
% 27.86/5.55 % (23517)Time elapsed: 0.226 s
% 27.86/5.55 % (23517)Instructions burned: 464 (million)
% 27.86/5.55 % (23517)------------------------------
% 27.86/5.55 % (23517)------------------------------
% 27.86/5.57 % (23519)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_23265 for (2963ds/906Mi)
% 27.86/5.57 % (23488)Instruction limit reached!
% 27.86/5.57 % (23488)------------------------------
% 27.86/5.57 % (23488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.86/5.57 % (23488)Termination reason: Unknown
% 27.86/5.57 % (23488)Termination phase: Saturation
% 27.86/5.57
% 27.86/5.57 % (23488)Memory used [KB]: 17014
% 27.86/5.57 % (23488)Time elapsed: 2.315 s
% 27.86/5.57 % (23488)Instructions burned: 4437 (million)
% 27.86/5.57 % (23488)------------------------------
% 27.86/5.57 % (23488)------------------------------
% 27.86/5.59 % (23520)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_23265 for (2963ds/434Mi)
% 28.48/5.66 % (23516)Instruction limit reached!
% 28.48/5.66 % (23516)------------------------------
% 28.48/5.66 % (23516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.48/5.66 % (23516)Termination reason: Unknown
% 28.48/5.66 % (23516)Termination phase: Saturation
% 28.48/5.66
% 28.48/5.66 % (23516)Memory used [KB]: 4221
% 28.48/5.66 % (23516)Time elapsed: 0.396 s
% 28.48/5.66 % (23516)Instructions burned: 794 (million)
% 28.48/5.66 % (23516)------------------------------
% 28.48/5.66 % (23516)------------------------------
% 28.48/5.67 % (23521)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_23265 for (2962ds/865Mi)
% 29.49/5.80 % (23493)Instruction limit reached!
% 29.49/5.80 % (23493)------------------------------
% 29.49/5.80 % (23493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.49/5.80 % (23493)Termination reason: Unknown
% 29.49/5.80 % (23493)Termination phase: Saturation
% 29.49/5.80
% 29.49/5.80 % (23493)Memory used [KB]: 11129
% 29.49/5.80 % (23493)Time elapsed: 2.265 s
% 29.49/5.80 % (23493)Instructions burned: 4351 (million)
% 29.49/5.80 % (23493)------------------------------
% 29.49/5.80 % (23493)------------------------------
% 29.49/5.80 % (23520)Instruction limit reached!
% 29.49/5.80 % (23520)------------------------------
% 29.49/5.80 % (23520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.49/5.80 % (23520)Termination reason: Unknown
% 29.49/5.80 % (23520)Termination phase: Saturation
% 29.49/5.80
% 29.49/5.80 % (23520)Memory used [KB]: 9083
% 29.49/5.80 % (23520)Time elapsed: 0.217 s
% 29.49/5.80 % (23520)Instructions burned: 434 (million)
% 29.49/5.80 % (23520)------------------------------
% 29.49/5.80 % (23520)------------------------------
% 29.49/5.82 % (23522)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_23265 for (2960ds/593Mi)
% 29.49/5.82 % (23523)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_23265 for (2960ds/443Mi)
% 29.95/5.98 % (23521)Instruction limit reached!
% 29.95/5.98 % (23521)------------------------------
% 29.95/5.98 % (23521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.95/5.98 % (23521)Termination reason: Unknown
% 29.95/5.98 % (23521)Termination phase: Saturation
% 29.95/5.98
% 29.95/5.98 % (23521)Memory used [KB]: 8187
% 29.95/5.98 % (23521)Time elapsed: 0.310 s
% 29.95/5.98 % (23521)Instructions burned: 866 (million)
% 29.95/5.98 % (23521)------------------------------
% 29.95/5.98 % (23521)------------------------------
% 29.95/5.99 % (23524)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_23265 for (2959ds/594Mi)
% 29.95/6.01 % (23519)Instruction limit reached!
% 29.95/6.01 % (23519)------------------------------
% 29.95/6.01 % (23519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.95/6.01 % (23519)Termination reason: Unknown
% 29.95/6.01 % (23519)Termination phase: Saturation
% 29.95/6.01
% 29.95/6.01 % (23519)Memory used [KB]: 9722
% 29.95/6.01 % (23519)Time elapsed: 0.444 s
% 29.95/6.01 % (23519)Instructions burned: 907 (million)
% 29.95/6.01 % (23519)------------------------------
% 29.95/6.01 % (23519)------------------------------
% 29.95/6.01 % (23518)Instruction limit reached!
% 29.95/6.01 % (23518)------------------------------
% 29.95/6.01 % (23518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.95/6.01 % (23518)Termination reason: Unknown
% 29.95/6.01 % (23518)Termination phase: Saturation
% 29.95/6.01
% 29.95/6.01 % (23518)Memory used [KB]: 8187
% 29.95/6.01 % (23518)Time elapsed: 0.604 s
% 29.95/6.01 % (23518)Instructions burned: 1378 (million)
% 29.95/6.01 % (23518)------------------------------
% 29.95/6.01 % (23518)------------------------------
% 31.36/6.03 % (23525)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_23265 for (2958ds/327Mi)
% 31.36/6.03 % (23526)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_23265 for (2958ds/5411Mi)
% 31.36/6.04 % (23523)Instruction limit reached!
% 31.36/6.04 % (23523)------------------------------
% 31.36/6.04 % (23523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.36/6.04 % (23523)Termination reason: Unknown
% 31.36/6.04 % (23523)Termination phase: Saturation
% 31.36/6.04
% 31.36/6.04 % (23523)Memory used [KB]: 8059
% 31.36/6.04 % (23523)Time elapsed: 0.218 s
% 31.36/6.04 % (23523)Instructions burned: 444 (million)
% 31.36/6.04 % (23523)------------------------------
% 31.36/6.04 % (23523)------------------------------
% 31.36/6.05 % (23522)Instruction limit reached!
% 31.36/6.05 % (23522)------------------------------
% 31.36/6.05 % (23522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.36/6.05 % (23522)Termination reason: Unknown
% 31.36/6.05 % (23522)Termination phase: Saturation
% 31.36/6.05
% 31.36/6.05 % (23522)Memory used [KB]: 6780
% 31.36/6.05 % (23522)Time elapsed: 0.227 s
% 31.36/6.05 % (23522)Instructions burned: 594 (million)
% 31.36/6.05 % (23522)------------------------------
% 31.36/6.05 % (23522)------------------------------
% 31.36/6.06 % (23527)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_23265 for (2958ds/1762Mi)
% 31.36/6.07 % (23528)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_23265 for (2958ds/96Mi)
% 31.36/6.11 % (23528)Instruction limit reached!
% 31.36/6.11 % (23528)------------------------------
% 31.36/6.11 % (23528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.36/6.11 % (23528)Termination reason: Unknown
% 31.36/6.11 % (23528)Termination phase: Saturation
% 31.36/6.11
% 31.36/6.11 % (23528)Memory used [KB]: 6652
% 31.36/6.11 % (23528)Time elapsed: 0.045 s
% 31.36/6.11 % (23528)Instructions burned: 98 (million)
% 31.36/6.11 % (23528)------------------------------
% 31.36/6.11 % (23528)------------------------------
% 32.43/6.13 % (23529)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_23265 for (2957ds/503Mi)
% 32.43/6.20 % (23525)Instruction limit reached!
% 32.43/6.20 % (23525)------------------------------
% 32.43/6.20 % (23525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.43/6.20 % (23525)Termination reason: Unknown
% 32.43/6.20 % (23525)Termination phase: Saturation
% 32.43/6.20
% 32.43/6.20 % (23525)Memory used [KB]: 9594
% 32.43/6.20 % (23525)Time elapsed: 0.195 s
% 32.43/6.20 % (23525)Instructions burned: 327 (million)
% 32.43/6.20 % (23525)------------------------------
% 32.43/6.20 % (23525)------------------------------
% 32.87/6.21 % (23530)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_23265 for (2956ds/90Mi)
% 32.87/6.25 % (23530)Instruction limit reached!
% 32.87/6.25 % (23530)------------------------------
% 32.87/6.25 % (23530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.87/6.25 % (23530)Termination reason: Unknown
% 32.87/6.25 % (23530)Termination phase: Property scanning
% 32.87/6.25
% 32.87/6.25 % (23530)Memory used [KB]: 2430
% 32.87/6.25 % (23530)Time elapsed: 0.042 s
% 32.87/6.25 % (23530)Instructions burned: 90 (million)
% 32.87/6.25 % (23530)------------------------------
% 32.87/6.25 % (23530)------------------------------
% 32.87/6.27 % (23524)Instruction limit reached!
% 32.87/6.27 % (23524)------------------------------
% 32.87/6.27 % (23524)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.87/6.27 % (23524)Termination reason: Unknown
% 32.87/6.27 % (23524)Termination phase: Saturation
% 32.87/6.27
% 32.87/6.27 % (23524)Memory used [KB]: 8059
% 32.87/6.27 % (23524)Time elapsed: 0.285 s
% 32.87/6.27 % (23524)Instructions burned: 594 (million)
% 32.87/6.27 % (23524)------------------------------
% 32.87/6.27 % (23524)------------------------------
% 32.87/6.27 % (23531)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_23265 for (2956ds/593Mi)
% 32.87/6.29 % (23532)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_23265 for (2956ds/1512Mi)
% 33.21/6.34 % (23513)Instruction limit reached!
% 33.21/6.34 % (23513)------------------------------
% 33.21/6.34 % (23513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.21/6.34 % (23513)Termination reason: Unknown
% 33.21/6.34 % (23513)Termination phase: Saturation
% 33.21/6.34
% 33.21/6.34 % (23513)Memory used [KB]: 7291
% 33.21/6.34 % (23513)Time elapsed: 1.783 s
% 33.21/6.34 % (23513)Instructions burned: 4714 (million)
% 33.21/6.34 % (23513)------------------------------
% 33.21/6.34 % (23513)------------------------------
% 33.21/6.36 % (23533)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_23265 for (2955ds/569Mi)
% 33.21/6.39 % (23532)Refutation not found, incomplete strategy
% 33.21/6.39 % (23532)------------------------------
% 33.21/6.39 % (23532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.21/6.39 % (23532)Termination reason: Refutation not found, incomplete strategy
% 33.21/6.39
% 33.21/6.39
% 33.21/6.39 % (23532)Memory used [KB]: 8315
% 33.21/6.39 % (23532)Time elapsed: 0.108 s
% 33.21/6.39 % (23532)Instructions burned: 213 (million)
% 33.21/6.39 % (23532)------------------------------
% 33.21/6.39 % (23532)------------------------------
% 33.48/6.40 % (23529)Instruction limit reached!
% 33.48/6.40 % (23529)------------------------------
% 33.48/6.40 % (23529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.48/6.40 % (23529)Termination reason: Unknown
% 33.48/6.40 % (23529)Termination phase: Saturation
% 33.48/6.40
% 33.48/6.40 % (23529)Memory used [KB]: 8187
% 33.48/6.40 % (23529)Time elapsed: 0.270 s
% 33.48/6.40 % (23529)Instructions burned: 503 (million)
% 33.48/6.40 % (23529)------------------------------
% 33.48/6.40 % (23529)------------------------------
% 33.48/6.41 % (23534)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_23265 for (2954ds/501Mi)
% 33.48/6.42 % (23535)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_23265 for (2954ds/562Mi)
% 33.87/6.58 % (23531)Instruction limit reached!
% 33.87/6.58 % (23531)------------------------------
% 33.87/6.58 % (23531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.87/6.58 % (23531)Termination reason: Unknown
% 33.87/6.58 % (23531)Termination phase: Saturation
% 33.87/6.58
% 33.87/6.58 % (23531)Memory used [KB]: 7931
% 33.87/6.58 % (23531)Time elapsed: 0.305 s
% 33.87/6.58 % (23531)Instructions burned: 594 (million)
% 33.87/6.58 % (23531)------------------------------
% 33.87/6.58 % (23531)------------------------------
% 33.87/6.59 % (23533)Instruction limit reached!
% 33.87/6.59 % (23533)------------------------------
% 33.87/6.59 % (23533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.87/6.59 % (23533)Termination reason: Unknown
% 33.87/6.59 % (23533)Termination phase: Saturation
% 33.87/6.59
% 33.87/6.59 % (23533)Memory used [KB]: 9594
% 33.87/6.59 % (23533)Time elapsed: 0.239 s
% 33.87/6.59 % (23533)Instructions burned: 569 (million)
% 33.87/6.59 % (23533)------------------------------
% 33.87/6.59 % (23533)------------------------------
% 33.87/6.60 % (23536)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_23265 for (2953ds/406Mi)
% 34.54/6.61 % (23537)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_23265 for (2952ds/582Mi)
% 34.54/6.66 % (23534)Instruction limit reached!
% 34.54/6.66 % (23534)------------------------------
% 34.54/6.66 % (23534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.54/6.66 % (23534)Termination reason: Unknown
% 34.54/6.66 % (23534)Termination phase: Saturation
% 34.54/6.66
% 34.54/6.66 % (23534)Memory used [KB]: 8955
% 34.54/6.66 % (23534)Time elapsed: 0.252 s
% 34.54/6.66 % (23534)Instructions burned: 502 (million)
% 34.54/6.66 % (23534)------------------------------
% 34.54/6.66 % (23534)------------------------------
% 34.54/6.68 % (23538)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_23265 for (2952ds/456Mi)
% 34.54/6.68 % (23535)Instruction limit reached!
% 34.54/6.68 % (23535)------------------------------
% 34.54/6.68 % (23535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.54/6.68 % (23535)Termination reason: Unknown
% 34.54/6.68 % (23535)Termination phase: Saturation
% 34.54/6.68
% 34.54/6.68 % (23535)Memory used [KB]: 7547
% 34.54/6.68 % (23535)Time elapsed: 0.266 s
% 34.54/6.68 % (23535)Instructions burned: 564 (million)
% 34.54/6.68 % (23535)------------------------------
% 34.54/6.68 % (23535)------------------------------
% 35.19/6.70 % (23539)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_23265 for (2951ds/393Mi)
% 35.19/6.77 % (23527)Instruction limit reached!
% 35.19/6.77 % (23527)------------------------------
% 35.19/6.77 % (23527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.19/6.77 % (23527)Termination reason: Unknown
% 35.19/6.77 % (23527)Termination phase: Saturation
% 35.19/6.77
% 35.19/6.77 % (23527)Memory used [KB]: 13304
% 35.19/6.77 % (23527)Time elapsed: 0.713 s
% 35.19/6.77 % (23527)Instructions burned: 1763 (million)
% 35.19/6.77 % (23527)------------------------------
% 35.19/6.77 % (23527)------------------------------
% 35.19/6.79 % (23540)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_23265 for (2951ds/1335Mi)
% 35.19/6.79 % (23536)Instruction limit reached!
% 35.19/6.79 % (23536)------------------------------
% 35.19/6.79 % (23536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.19/6.79 % (23536)Termination reason: Unknown
% 35.19/6.79 % (23536)Termination phase: Saturation
% 35.19/6.79
% 35.19/6.79 % (23536)Memory used [KB]: 7164
% 35.19/6.79 % (23536)Time elapsed: 0.201 s
% 35.19/6.79 % (23536)Instructions burned: 407 (million)
% 35.19/6.79 % (23536)------------------------------
% 35.19/6.79 % (23536)------------------------------
% 36.25/6.81 % (23541)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_23265 for (2950ds/3373Mi)
% 36.25/6.89 % (23539)Instruction limit reached!
% 36.25/6.89 % (23539)------------------------------
% 36.25/6.89 % (23539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.25/6.89 % (23539)Termination reason: Unknown
% 36.25/6.89 % (23539)Termination phase: Saturation
% 36.25/6.89
% 36.25/6.89 % (23539)Memory used [KB]: 8315
% 36.25/6.89 % (23539)Time elapsed: 0.193 s
% 36.25/6.89 % (23539)Instructions burned: 394 (million)
% 36.25/6.89 % (23539)------------------------------
% 36.25/6.89 % (23539)------------------------------
% 36.57/6.90 % (23538)Instruction limit reached!
% 36.57/6.90 % (23538)------------------------------
% 36.57/6.90 % (23538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.57/6.90 % (23538)Termination reason: Unknown
% 36.57/6.90 % (23538)Termination phase: Saturation
% 36.57/6.90
% 36.57/6.90 % (23538)Memory used [KB]: 8059
% 36.57/6.90 % (23538)Time elapsed: 0.221 s
% 36.57/6.90 % (23538)Instructions burned: 457 (million)
% 36.57/6.90 % (23538)------------------------------
% 36.57/6.90 % (23538)------------------------------
% 36.57/6.91 % (23537)Instruction limit reached!
% 36.57/6.91 % (23537)------------------------------
% 36.57/6.91 % (23537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.57/6.91 % (23537)Termination reason: Unknown
% 36.57/6.91 % (23537)Termination phase: Saturation
% 36.57/6.91
% 36.57/6.91 % (23537)Memory used [KB]: 9083
% 36.57/6.91 % (23537)Time elapsed: 0.298 s
% 36.57/6.91 % (23537)Instructions burned: 583 (million)
% 36.57/6.91 % (23537)------------------------------
% 36.57/6.91 % (23537)------------------------------
% 36.57/6.91 % (23542)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_23265 for (2949ds/474Mi)
% 36.57/6.91 % (23543)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_23265 for (2949ds/157Mi)
% 36.57/6.93 % (23544)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_23265 for (2949ds/590Mi)
% 36.57/6.98 % (23543)Instruction limit reached!
% 36.57/6.98 % (23543)------------------------------
% 36.57/6.98 % (23543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.57/6.98 % (23543)Termination reason: Unknown
% 36.57/6.98 % (23543)Termination phase: Saturation
% 36.57/6.98
% 36.57/6.98 % (23543)Memory used [KB]: 6652
% 36.57/6.98 % (23543)Time elapsed: 0.068 s
% 36.57/6.98 % (23543)Instructions burned: 157 (million)
% 36.57/6.98 % (23543)------------------------------
% 36.57/6.98 % (23543)------------------------------
% 36.57/7.00 % (23545)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_23265 for (2949ds/104Mi)
% 39.06/7.04 % (23545)Instruction limit reached!
% 39.06/7.04 % (23545)------------------------------
% 39.06/7.04 % (23545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.06/7.04 % (23545)Termination reason: Unknown
% 39.06/7.04 % (23545)Termination phase: Saturation
% 39.06/7.04
% 39.06/7.04 % (23545)Memory used [KB]: 6780
% 39.06/7.04 % (23545)Time elapsed: 0.047 s
% 39.06/7.04 % (23545)Instructions burned: 104 (million)
% 39.06/7.04 % (23545)------------------------------
% 39.06/7.04 % (23545)------------------------------
% 39.06/7.06 % (23546)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_23265 for (2948ds/414Mi)
% 39.06/7.11 % (23542)Instruction limit reached!
% 39.06/7.11 % (23542)------------------------------
% 39.06/7.11 % (23542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.06/7.11 % (23542)Termination reason: Unknown
% 39.06/7.11 % (23542)Termination phase: Saturation
% 39.06/7.11
% 39.06/7.11 % (23542)Memory used [KB]: 9722
% 39.06/7.11 % (23542)Time elapsed: 0.199 s
% 39.06/7.11 % (23542)Instructions burned: 475 (million)
% 39.06/7.11 % (23542)------------------------------
% 39.06/7.11 % (23542)------------------------------
% 39.68/7.13 % (23547)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_23265 for (2947ds/715Mi)
% 39.68/7.20 % (23544)Instruction limit reached!
% 39.68/7.20 % (23544)------------------------------
% 39.68/7.20 % (23544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.68/7.20 % (23544)Termination reason: Unknown
% 39.68/7.20 % (23544)Termination phase: Saturation
% 39.68/7.20
% 39.68/7.20 % (23544)Memory used [KB]: 8443
% 39.68/7.20 % (23544)Time elapsed: 0.272 s
% 39.68/7.20 % (23544)Instructions burned: 590 (million)
% 39.68/7.20 % (23544)------------------------------
% 39.68/7.20 % (23544)------------------------------
% 39.75/7.22 % (23548)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_23265 for (2946ds/961Mi)
% 39.75/7.22 % (23546)Instruction limit reached!
% 39.75/7.22 % (23546)------------------------------
% 39.75/7.22 % (23546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.75/7.22 % (23546)Termination reason: Unknown
% 39.75/7.22 % (23546)Termination phase: Saturation
% 39.75/7.22
% 39.75/7.22 % (23546)Memory used [KB]: 6652
% 39.75/7.22 % (23546)Time elapsed: 0.161 s
% 39.75/7.22 % (23546)Instructions burned: 415 (million)
% 39.75/7.22 % (23546)------------------------------
% 39.75/7.22 % (23546)------------------------------
% 39.75/7.24 % (23549)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_23265 for (2946ds/1213Mi)
% 41.01/7.45 % (23540)Instruction limit reached!
% 41.01/7.45 % (23540)------------------------------
% 41.01/7.45 % (23540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.01/7.45 % (23540)Termination reason: Unknown
% 41.01/7.45 % (23540)Termination phase: Saturation
% 41.01/7.45
% 41.01/7.45 % (23540)Memory used [KB]: 8443
% 41.01/7.45 % (23540)Time elapsed: 0.665 s
% 41.01/7.45 % (23540)Instructions burned: 1337 (million)
% 41.01/7.45 % (23540)------------------------------
% 41.01/7.45 % (23540)------------------------------
% 41.01/7.47 % (23550)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_23265 for (2944ds/1979Mi)
% 41.01/7.48 % (23547)Instruction limit reached!
% 41.01/7.48 % (23547)------------------------------
% 41.01/7.48 % (23547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.01/7.48 % (23547)Termination reason: Unknown
% 41.01/7.48 % (23547)Termination phase: Saturation
% 41.01/7.48
% 41.01/7.48 % (23547)Memory used [KB]: 3837
% 41.01/7.48 % (23547)Time elapsed: 0.352 s
% 41.01/7.48 % (23547)Instructions burned: 715 (million)
% 41.01/7.48 % (23547)------------------------------
% 41.01/7.48 % (23547)------------------------------
% 41.01/7.50 % (23551)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_23265 for (2943ds/481Mi)
% 42.06/7.68 % (23548)Instruction limit reached!
% 42.06/7.68 % (23548)------------------------------
% 42.06/7.68 % (23548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.06/7.68 % (23551)Instruction limit reached!
% 42.06/7.68 % (23551)------------------------------
% 42.06/7.68 % (23551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.06/7.68 % (23548)Termination reason: Unknown
% 42.06/7.68 % (23548)Termination phase: Saturation
% 42.06/7.68
% 42.06/7.68 % (23548)Memory used [KB]: 8443
% 42.06/7.68 % (23548)Time elapsed: 0.491 s
% 42.06/7.68 % (23548)Instructions burned: 962 (million)
% 42.06/7.68 % (23548)------------------------------
% 42.06/7.68 % (23548)------------------------------
% 42.06/7.68 % (23551)Termination reason: Unknown
% 42.06/7.68 % (23551)Termination phase: Saturation
% 42.06/7.68
% 42.06/7.68 % (23551)Memory used [KB]: 9722
% 42.06/7.68 % (23551)Time elapsed: 0.190 s
% 42.06/7.68 % (23551)Instructions burned: 483 (million)
% 42.06/7.68 % (23551)------------------------------
% 42.06/7.68 % (23551)------------------------------
% 43.05/7.70 % (23553)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_23265 for (2941ds/432Mi)
% 43.05/7.70 % (23552)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_23265 for (2941ds/783Mi)
% 43.35/7.87 % (23549)Instruction limit reached!
% 43.35/7.87 % (23549)------------------------------
% 43.35/7.87 % (23549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.35/7.87 % (23549)Termination reason: Unknown
% 43.35/7.87 % (23549)Termination phase: Saturation
% 43.35/7.87
% 43.35/7.87 % (23549)Memory used [KB]: 11385
% 43.35/7.87 % (23549)Time elapsed: 0.651 s
% 43.35/7.87 % (23549)Instructions burned: 1214 (million)
% 43.35/7.87 % (23549)------------------------------
% 43.35/7.87 % (23549)------------------------------
% 43.35/7.89 % (23554)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_23265 for (2940ds/1670Mi)
% 44.29/7.92 % (23553)Instruction limit reached!
% 44.29/7.92 % (23553)------------------------------
% 44.29/7.92 % (23553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.29/7.92 % (23553)Termination reason: Unknown
% 44.29/7.92 % (23553)Termination phase: Saturation
% 44.29/7.92
% 44.29/7.92 % (23553)Memory used [KB]: 7803
% 44.29/7.92 % (23553)Time elapsed: 0.218 s
% 44.29/7.92 % (23553)Instructions burned: 433 (million)
% 44.29/7.92 % (23553)------------------------------
% 44.29/7.92 % (23553)------------------------------
% 44.29/7.94 % (23555)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_23265 for (2939ds/90Mi)
% 44.29/7.98 % (23555)Instruction limit reached!
% 44.29/7.98 % (23555)------------------------------
% 44.29/7.98 % (23555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.29/7.98 % (23555)Termination reason: Unknown
% 44.29/7.98 % (23555)Termination phase: Saturation
% 44.29/7.98
% 44.29/7.98 % (23555)Memory used [KB]: 6524
% 44.29/7.98 % (23555)Time elapsed: 0.044 s
% 44.29/7.98 % (23555)Instructions burned: 90 (million)
% 44.29/7.98 % (23555)------------------------------
% 44.29/7.98 % (23555)------------------------------
% 44.29/8.00 % (23556)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_23265 for (2938ds/346Mi)
% 46.03/8.10 % (23552)Instruction limit reached!
% 46.03/8.10 % (23552)------------------------------
% 46.03/8.10 % (23552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 46.03/8.10 % (23552)Termination reason: Unknown
% 46.03/8.10 % (23552)Termination phase: Saturation
% 46.03/8.10
% 46.03/8.10 % (23552)Memory used [KB]: 10106
% 46.03/8.10 % (23552)Time elapsed: 0.399 s
% 46.03/8.10 % (23552)Instructions burned: 784 (million)
% 46.03/8.10 % (23552)------------------------------
% 46.03/8.10 % (23552)------------------------------
% 46.03/8.12 % (23557)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_23265 for (2937ds/401Mi)
% 46.75/8.14 % (23556)Instruction limit reached!
% 46.75/8.14 % (23556)------------------------------
% 46.75/8.14 % (23556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 46.75/8.14 % (23556)Termination reason: Unknown
% 46.75/8.14 % (23556)Termination phase: Saturation
% 46.75/8.14
% 46.75/8.14 % (23556)Memory used [KB]: 9594
% 46.75/8.14 % (23556)Time elapsed: 0.141 s
% 46.75/8.14 % (23556)Instructions burned: 347 (million)
% 46.75/8.14 % (23556)------------------------------
% 46.75/8.14 % (23556)------------------------------
% 46.75/8.16 % (23558)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_23265 for (2937ds/6454Mi)
% 47.12/8.27 % (23557)Instruction limit reached!
% 47.12/8.27 % (23557)------------------------------
% 47.12/8.27 % (23557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.12/8.27 % (23557)Termination reason: Unknown
% 47.12/8.27 % (23557)Termination phase: Saturation
% 47.12/8.27
% 47.12/8.27 % (23557)Memory used [KB]: 6652
% 47.12/8.27 % (23557)Time elapsed: 0.158 s
% 47.12/8.27 % (23557)Instructions burned: 403 (million)
% 47.12/8.27 % (23557)------------------------------
% 47.12/8.27 % (23557)------------------------------
% 47.12/8.29 % (23559)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_23265 for (2936ds/283Mi)
% 48.29/8.42 % (23559)Instruction limit reached!
% 48.29/8.42 % (23559)------------------------------
% 48.29/8.42 % (23559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.29/8.42 % (23559)Termination reason: Unknown
% 48.29/8.42 % (23559)Termination phase: Saturation
% 48.29/8.42
% 48.29/8.42 % (23559)Memory used [KB]: 7803
% 48.29/8.42 % (23559)Time elapsed: 0.135 s
% 48.29/8.42 % (23559)Instructions burned: 283 (million)
% 48.29/8.42 % (23559)------------------------------
% 48.29/8.42 % (23559)------------------------------
% 48.29/8.43 % (23550)Instruction limit reached!
% 48.29/8.43 % (23550)------------------------------
% 48.29/8.43 % (23550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.29/8.43 % (23550)Termination reason: Unknown
% 48.29/8.43 % (23550)Termination phase: Saturation
% 48.29/8.43
% 48.29/8.43 % (23550)Memory used [KB]: 8955
% 48.29/8.43 % (23550)Time elapsed: 0.963 s
% 48.29/8.43 % (23550)Instructions burned: 1980 (million)
% 48.29/8.43 % (23550)------------------------------
% 48.29/8.43 % (23550)------------------------------
% 48.29/8.44 % (23560)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_23265 for (2934ds/865Mi)
% 48.29/8.45 % (23561)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_23265 for (2934ds/4528Mi)
% 48.90/8.52 % (23554)Instruction limit reached!
% 48.90/8.52 % (23554)------------------------------
% 48.90/8.52 % (23554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.90/8.52 % (23554)Termination reason: Unknown
% 48.90/8.52 % (23554)Termination phase: Saturation
% 48.90/8.52
% 48.90/8.52 % (23554)Memory used [KB]: 10490
% 48.90/8.52 % (23554)Time elapsed: 0.637 s
% 48.90/8.52 % (23554)Instructions burned: 1672 (million)
% 48.90/8.52 % (23554)------------------------------
% 48.90/8.52 % (23554)------------------------------
% 48.90/8.54 % (23562)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_23265 for (2933ds/1001Mi)
% 48.90/8.56 % (23541)Instruction limit reached!
% 48.90/8.56 % (23541)------------------------------
% 48.90/8.56 % (23541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.90/8.56 % (23541)Termination reason: Unknown
% 48.90/8.56 % (23541)Termination phase: Saturation
% 48.90/8.56
% 48.90/8.56 % (23541)Memory used [KB]: 11513
% 48.90/8.56 % (23541)Time elapsed: 1.745 s
% 48.90/8.56 % (23541)Instructions burned: 3374 (million)
% 48.90/8.56 % (23541)------------------------------
% 48.90/8.56 % (23541)------------------------------
% 48.90/8.56 % (23561)Refutation not found, incomplete strategy
% 48.90/8.56 % (23561)------------------------------
% 48.90/8.56 % (23561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.90/8.56 % (23561)Termination reason: Refutation not found, incomplete strategy
% 48.90/8.56
% 48.90/8.56
% 48.90/8.56 % (23561)Memory used [KB]: 2174
% 48.90/8.56 % (23561)Time elapsed: 0.116 s
% 48.90/8.56 % (23561)Instructions burned: 266 (million)
% 48.90/8.56 % (23561)------------------------------
% 48.90/8.56 % (23561)------------------------------
% 48.90/8.57 % (23563)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_23265 for (2933ds/102Mi)
% 48.90/8.58 % (23564)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_23265 for (2933ds/952Mi)
% 49.33/8.62 % (23563)Instruction limit reached!
% 49.33/8.62 % (23563)------------------------------
% 49.33/8.62 % (23563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.33/8.62 % (23563)Termination reason: Unknown
% 49.33/8.62 % (23563)Termination phase: Saturation
% 49.33/8.62
% 49.33/8.62 % (23563)Memory used [KB]: 6652
% 49.33/8.62 % (23563)Time elapsed: 0.047 s
% 49.33/8.62 % (23563)Instructions burned: 102 (million)
% 49.33/8.62 % (23563)------------------------------
% 49.33/8.62 % (23563)------------------------------
% 49.33/8.64 % (23565)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_23265 for (2932ds/578Mi)
% 49.59/8.74 % (23526)Instruction limit reached!
% 49.59/8.74 % (23526)------------------------------
% 49.59/8.74 % (23526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.59/8.74 % (23526)Termination reason: Unknown
% 49.59/8.74 % (23526)Termination phase: Saturation
% 49.59/8.74
% 49.59/8.74 % (23526)Memory used [KB]: 13688
% 49.59/8.74 % (23526)Time elapsed: 2.715 s
% 49.59/8.74 % (23526)Instructions burned: 5412 (million)
% 49.59/8.74 % (23526)------------------------------
% 49.59/8.74 % (23526)------------------------------
% 49.59/8.76 % (23566)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_23265 for (2931ds/643Mi)
% 49.76/8.85 % (23560)Instruction limit reached!
% 49.76/8.85 % (23560)------------------------------
% 49.76/8.85 % (23560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.76/8.85 % (23560)Termination reason: Unknown
% 49.76/8.85 % (23560)Termination phase: Saturation
% 49.76/8.85
% 49.76/8.85 % (23560)Memory used [KB]: 7931
% 49.76/8.85 % (23560)Time elapsed: 0.409 s
% 49.76/8.85 % (23560)Instructions burned: 865 (million)
% 49.76/8.85 % (23560)------------------------------
% 49.76/8.85 % (23560)------------------------------
% 49.76/8.87 % (23567)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_23265 for (2930ds/865Mi)
% 49.76/8.88 % (23565)Instruction limit reached!
% 49.76/8.88 % (23565)------------------------------
% 49.76/8.88 % (23565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.76/8.88 % (23565)Termination reason: Unknown
% 49.76/8.88 % (23565)Termination phase: Saturation
% 49.76/8.88
% 49.76/8.88 % (23565)Memory used [KB]: 7803
% 49.76/8.88 % (23565)Time elapsed: 0.248 s
% 49.76/8.88 % (23565)Instructions burned: 580 (million)
% 49.76/8.88 % (23565)------------------------------
% 49.76/8.88 % (23565)------------------------------
% 50.55/8.90 % (23568)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_23265 for (2930ds/1174Mi)
% 50.55/9.00 % (23514)Instruction limit reached!
% 50.55/9.00 % (23514)------------------------------
% 50.55/9.00 % (23514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.55/9.00 % (23514)Termination reason: Unknown
% 50.55/9.00 % (23514)Termination phase: Saturation
% 50.55/9.00
% 50.55/9.00 % (23514)Memory used [KB]: 25330
% 50.55/9.00 % (23514)Time elapsed: 4.390 s
% 50.55/9.00 % (23514)Instructions burned: 8251 (million)
% 50.55/9.00 % (23514)------------------------------
% 50.55/9.00 % (23514)------------------------------
% 50.55/9.02 % (23569)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_23265 for (2928ds/644Mi)
% 53.02/9.03 % (23562)Instruction limit reached!
% 53.02/9.03 % (23562)------------------------------
% 53.02/9.03 % (23562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.02/9.03 % (23562)Termination reason: Unknown
% 53.02/9.03 % (23562)Termination phase: Saturation
% 53.02/9.03
% 53.02/9.03 % (23562)Memory used [KB]: 8571
% 53.02/9.03 % (23562)Time elapsed: 0.514 s
% 53.02/9.03 % (23562)Instructions burned: 1001 (million)
% 53.02/9.03 % (23562)------------------------------
% 53.02/9.03 % (23562)------------------------------
% 53.02/9.05 % (23566)Instruction limit reached!
% 53.02/9.05 % (23566)------------------------------
% 53.02/9.05 % (23566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.02/9.05 % (23566)Termination reason: Unknown
% 53.02/9.05 % (23566)Termination phase: Saturation
% 53.02/9.05
% 53.02/9.05 % (23566)Memory used [KB]: 9466
% 53.02/9.05 % (23566)Time elapsed: 0.286 s
% 53.02/9.05 % (23566)Instructions burned: 644 (million)
% 53.02/9.05 % (23566)------------------------------
% 53.02/9.05 % (23566)------------------------------
% 53.02/9.05 % (23570)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_23265 for (2928ds/1201Mi)
% 53.02/9.07 % (23571)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_23265 for (2928ds/1046Mi)
% 53.02/9.07 % (23564)Instruction limit reached!
% 53.02/9.07 % (23564)------------------------------
% 53.02/9.07 % (23564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.02/9.07 % (23564)Termination reason: Unknown
% 53.02/9.07 % (23564)Termination phase: Saturation
% 53.02/9.07
% 53.02/9.07 % (23564)Memory used [KB]: 8699
% 53.02/9.07 % (23564)Time elapsed: 0.492 s
% 53.02/9.07 % (23564)Instructions burned: 952 (million)
% 53.02/9.07 % (23564)------------------------------
% 53.02/9.07 % (23564)------------------------------
% 53.02/9.09 % (23572)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_23265 for (2928ds/222Mi)
% 53.45/9.18 % (23572)Instruction limit reached!
% 53.45/9.18 % (23572)------------------------------
% 53.45/9.18 % (23572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.45/9.18 % (23572)Termination reason: Unknown
% 53.45/9.18 % (23572)Termination phase: Saturation
% 53.45/9.18
% 53.45/9.18 % (23572)Memory used [KB]: 6652
% 53.45/9.18 % (23572)Time elapsed: 0.091 s
% 53.45/9.18 % (23572)Instructions burned: 224 (million)
% 53.45/9.18 % (23572)------------------------------
% 53.45/9.18 % (23572)------------------------------
% 53.76/9.20 % (23573)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_23265 for (2926ds/68Mi)
% 53.76/9.23 % (23573)Instruction limit reached!
% 53.76/9.23 % (23573)------------------------------
% 53.76/9.23 % (23573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.76/9.23 % (23573)Termination reason: Unknown
% 53.76/9.23 % (23573)Termination phase: Function definition elimination
% 53.76/9.23
% 53.76/9.23 % (23573)Memory used [KB]: 1918
% 53.76/9.23 % (23573)Time elapsed: 0.032 s
% 53.76/9.23 % (23573)Instructions burned: 69 (million)
% 53.76/9.23 % (23573)------------------------------
% 53.76/9.23 % (23573)------------------------------
% 53.76/9.25 % (23574)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_23265 for (2926ds/454Mi)
% 53.76/9.25 % (23567)Instruction limit reached!
% 53.76/9.25 % (23567)------------------------------
% 53.76/9.25 % (23567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.76/9.25 % (23567)Termination reason: Unknown
% 53.76/9.25 % (23567)Termination phase: Saturation
% 53.76/9.25
% 53.76/9.25 % (23567)Memory used [KB]: 7036
% 53.76/9.25 % (23567)Time elapsed: 0.408 s
% 53.76/9.25 % (23567)Instructions burned: 865 (million)
% 53.76/9.25 % (23567)------------------------------
% 53.76/9.25 % (23567)------------------------------
% 53.76/9.27 % (23575)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_23265 for (2926ds/360Mi)
% 54.08/9.33 % (23569)Instruction limit reached!
% 54.08/9.33 % (23569)------------------------------
% 54.08/9.33 % (23569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.08/9.33 % (23569)Termination reason: Unknown
% 54.08/9.33 % (23569)Termination phase: Saturation
% 54.08/9.33
% 54.08/9.33 % (23569)Memory used [KB]: 7164
% 54.08/9.33 % (23569)Time elapsed: 0.328 s
% 54.08/9.33 % (23569)Instructions burned: 645 (million)
% 54.08/9.33 % (23569)------------------------------
% 54.08/9.33 % (23569)------------------------------
% 54.08/9.35 % (23576)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_23265 for (2925ds/157Mi)
% 54.60/9.41 % (23575)Instruction limit reached!
% 54.60/9.41 % (23575)------------------------------
% 54.60/9.41 % (23575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.60/9.41 % (23575)Termination reason: Unknown
% 54.60/9.41 % (23575)Termination phase: Saturation
% 54.60/9.41
% 54.60/9.41 % (23575)Memory used [KB]: 6652
% 54.60/9.41 % (23575)Time elapsed: 0.142 s
% 54.60/9.41 % (23575)Instructions burned: 362 (million)
% 54.60/9.41 % (23575)------------------------------
% 54.60/9.41 % (23575)------------------------------
% 54.60/9.41 % (23576)Instruction limit reached!
% 54.60/9.41 % (23576)------------------------------
% 54.60/9.41 % (23576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.60/9.41 % (23576)Termination reason: Unknown
% 54.60/9.41 % (23576)Termination phase: Saturation
% 54.60/9.41
% 54.60/9.41 % (23576)Memory used [KB]: 6652
% 54.60/9.41 % (23576)Time elapsed: 0.068 s
% 54.60/9.41 % (23576)Instructions burned: 157 (million)
% 54.60/9.41 % (23576)------------------------------
% 54.60/9.41 % (23576)------------------------------
% 54.60/9.43 % (23574)Instruction limit reached!
% 54.60/9.43 % (23574)------------------------------
% 54.60/9.43 % (23574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.60/9.43 % (23574)Termination reason: Unknown
% 54.60/9.43 % (23574)Termination phase: Saturation
% 54.60/9.43
% 54.60/9.43 % (23574)Memory used [KB]: 14328
% 54.60/9.43 % (23574)Time elapsed: 0.181 s
% 54.60/9.43 % (23574)Instructions burned: 455 (million)
% 54.60/9.43 % (23574)------------------------------
% 54.60/9.43 % (23574)------------------------------
% 54.60/9.43 % (23578)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_23265 for (2924ds/2401Mi)
% 54.60/9.43 % (23577)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_23265 for (2924ds/5061Mi)
% 54.60/9.44 % (23579)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_23265 for (2924ds/5798Mi)
% 54.60/9.49 % (23568)Instruction limit reached!
% 54.60/9.49 % (23568)------------------------------
% 54.60/9.49 % (23568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.60/9.49 % (23568)Termination reason: Unknown
% 54.60/9.49 % (23568)Termination phase: Saturation
% 54.60/9.49
% 54.60/9.49 % (23568)Memory used [KB]: 8571
% 54.60/9.49 % (23568)Time elapsed: 0.611 s
% 54.60/9.49 % (23568)Instructions burned: 1174 (million)
% 54.60/9.49 % (23568)------------------------------
% 54.60/9.49 % (23568)------------------------------
% 55.25/9.51 % (23571)Instruction limit reached!
% 55.25/9.51 % (23571)------------------------------
% 55.25/9.51 % (23571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.25/9.51 % (23571)Termination reason: Unknown
% 55.25/9.51 % (23571)Termination phase: Saturation
% 55.25/9.51
% 55.25/9.51 % (23571)Memory used [KB]: 6780
% 55.25/9.51 % (23571)Time elapsed: 0.442 s
% 55.25/9.51 % (23571)Instructions burned: 1047 (million)
% 55.25/9.51 % (23571)------------------------------
% 55.25/9.51 % (23571)------------------------------
% 55.25/9.51 % (23580)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_23265 for (2923ds/346Mi)
% 55.25/9.52 % (23581)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_23265 for (2923ds/1321Mi)
% 55.81/9.62 % (23570)Instruction limit reached!
% 55.81/9.62 % (23570)------------------------------
% 55.81/9.62 % (23570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.81/9.62 % (23570)Termination reason: Unknown
% 55.81/9.62 % (23570)Termination phase: Saturation
% 55.81/9.62
% 55.81/9.62 % (23570)Memory used [KB]: 9466
% 55.81/9.62 % (23570)Time elapsed: 0.589 s
% 55.81/9.62 % (23570)Instructions burned: 1201 (million)
% 55.81/9.62 % (23570)------------------------------
% 55.81/9.62 % (23570)------------------------------
% 55.81/9.63 % (23582)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_23265 for (2922ds/1312Mi)
% 55.81/9.64 % (23580)Instruction limit reached!
% 55.81/9.64 % (23580)------------------------------
% 55.81/9.64 % (23580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.81/9.64 % (23580)Termination reason: Unknown
% 55.81/9.64 % (23580)Termination phase: Saturation
% 55.81/9.64
% 55.81/9.64 % (23580)Memory used [KB]: 9594
% 55.81/9.64 % (23580)Time elapsed: 0.135 s
% 55.81/9.64 % (23580)Instructions burned: 348 (million)
% 55.81/9.64 % (23580)------------------------------
% 55.81/9.64 % (23580)------------------------------
% 55.81/9.68 % (23583)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_23265 for (2922ds/672Mi)
% 56.74/9.84 % (23581)Refutation not found, incomplete strategy
% 56.74/9.84 % (23581)------------------------------
% 56.74/9.84 % (23581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.74/9.84 % (23581)Termination reason: Refutation not found, incomplete strategy
% 56.74/9.84
% 56.74/9.84
% 56.74/9.84 % (23581)Memory used [KB]: 4989
% 56.74/9.84 % (23581)Time elapsed: 0.320 s
% 56.74/9.84 % (23581)Instructions burned: 709 (million)
% 56.74/9.84 % (23581)------------------------------
% 56.74/9.84 % (23581)------------------------------
% 56.74/9.86 % (23584)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_23265 for (2920ds/1897Mi)
% 57.18/10.02 % (23583)Instruction limit reached!
% 57.18/10.02 % (23583)------------------------------
% 57.18/10.02 % (23583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.18/10.02 % (23583)Termination reason: Unknown
% 57.18/10.02 % (23583)Termination phase: Saturation
% 57.18/10.02
% 57.18/10.02 % (23583)Memory used [KB]: 9466
% 57.18/10.02 % (23583)Time elapsed: 0.371 s
% 57.18/10.02 % (23583)Instructions burned: 672 (million)
% 57.18/10.02 % (23583)------------------------------
% 57.18/10.02 % (23583)------------------------------
% 60.08/10.04 % (23585)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_23265 for (2918ds/1202Mi)
% 60.69/10.15 % (23582)Instruction limit reached!
% 60.69/10.15 % (23582)------------------------------
% 60.69/10.15 % (23582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 60.69/10.15 % (23582)Termination reason: Unknown
% 60.69/10.15 % (23582)Termination phase: Saturation
% 60.69/10.15
% 60.69/10.15 % (23582)Memory used [KB]: 10234
% 60.69/10.15 % (23582)Time elapsed: 0.525 s
% 60.69/10.15 % (23582)Instructions burned: 1313 (million)
% 60.69/10.15 % (23582)------------------------------
% 60.69/10.15 % (23582)------------------------------
% 60.69/10.17 % (23586)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_23265 for (2917ds/1493Mi)
% 62.50/10.59 % (23578)Instruction limit reached!
% 62.50/10.59 % (23578)------------------------------
% 62.50/10.59 % (23578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.50/10.59 % (23578)Termination reason: Unknown
% 62.50/10.59 % (23578)Termination phase: Saturation
% 62.50/10.59
% 62.50/10.59 % (23578)Memory used [KB]: 8443
% 62.50/10.59 % (23578)Time elapsed: 1.167 s
% 62.50/10.59 % (23578)Instructions burned: 2401 (million)
% 62.50/10.59 % (23578)------------------------------
% 62.50/10.59 % (23578)------------------------------
% 63.01/10.61 % (23587)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_23265 for (2912ds/7679Mi)
% 63.01/10.62 % (23585)Instruction limit reached!
% 63.01/10.62 % (23585)------------------------------
% 63.01/10.62 % (23585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.01/10.62 % (23585)Termination reason: Unknown
% 63.01/10.62 % (23585)Termination phase: Saturation
% 63.01/10.62
% 63.01/10.62 % (23585)Memory used [KB]: 6652
% 63.01/10.62 % (23585)Time elapsed: 0.579 s
% 63.01/10.62 % (23585)Instructions burned: 1203 (million)
% 63.01/10.62 % (23585)------------------------------
% 63.01/10.62 % (23585)------------------------------
% 63.01/10.64 % (23588)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_23265 for (2912ds/340Mi)
% 64.01/10.70 % (23586)Instruction limit reached!
% 64.01/10.70 % (23586)------------------------------
% 64.01/10.70 % (23586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.01/10.70 % (23586)Termination reason: Unknown
% 64.01/10.70 % (23586)Termination phase: Saturation
% 64.01/10.70
% 64.01/10.70 % (23586)Memory used [KB]: 6908
% 64.01/10.70 % (23586)Time elapsed: 0.534 s
% 64.01/10.70 % (23586)Instructions burned: 1494 (million)
% 64.01/10.70 % (23586)------------------------------
% 64.01/10.70 % (23586)------------------------------
% 64.01/10.72 % (23589)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_23265 for (2911ds/3672Mi)
% 64.96/10.81 % (23588)Instruction limit reached!
% 64.96/10.81 % (23588)------------------------------
% 64.96/10.81 % (23588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.96/10.81 % (23588)Termination reason: Unknown
% 64.96/10.81 % (23588)Termination phase: Saturation
% 64.96/10.81
% 64.96/10.81 % (23588)Memory used [KB]: 8955
% 64.96/10.81 % (23588)Time elapsed: 0.173 s
% 64.96/10.81 % (23588)Instructions burned: 341 (million)
% 64.96/10.81 % (23588)------------------------------
% 64.96/10.81 % (23588)------------------------------
% 64.96/10.83 % (23590)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_23265 for (2910ds/1535Mi)
% 64.96/10.84 % (23584)Instruction limit reached!
% 64.96/10.84 % (23584)------------------------------
% 64.96/10.84 % (23584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.96/10.84 % (23584)Termination reason: Unknown
% 64.96/10.84 % (23584)Termination phase: Saturation
% 64.96/10.84
% 64.96/10.84 % (23584)Memory used [KB]: 11897
% 64.96/10.84 % (23584)Time elapsed: 0.993 s
% 64.96/10.84 % (23584)Instructions burned: 1897 (million)
% 64.96/10.84 % (23584)------------------------------
% 64.96/10.84 % (23584)------------------------------
% 64.96/10.86 % (23591)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on DTF2THF_23265 for (2910ds/4637Mi)
% 69.60/11.46 % (23558)Instruction limit reached!
% 69.60/11.46 % (23558)------------------------------
% 69.60/11.46 % (23558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.60/11.46 % (23558)Termination reason: Unknown
% 69.60/11.46 % (23558)Termination phase: Saturation
% 69.60/11.46
% 69.60/11.46 % (23558)Memory used [KB]: 11897
% 69.60/11.46 % (23558)Time elapsed: 3.311 s
% 69.60/11.46 % (23558)Instructions burned: 6455 (million)
% 69.60/11.46 % (23558)------------------------------
% 69.60/11.46 % (23558)------------------------------
% 69.60/11.48 % (23590)Instruction limit reached!
% 69.60/11.48 % (23590)------------------------------
% 69.60/11.48 % (23590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.60/11.48 % (23590)Termination reason: Unknown
% 69.60/11.48 % (23590)Termination phase: Saturation
% 69.60/11.48
% 69.60/11.48 % (23590)Memory used [KB]: 11001
% 69.60/11.48 % (23590)Time elapsed: 0.657 s
% 69.60/11.48 % (23590)Instructions burned: 1535 (million)
% 69.60/11.48 % (23590)------------------------------
% 69.60/11.48 % (23590)------------------------------
% 69.60/11.49 % (23592)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_23265 for (2904ds/3174Mi)
% 70.27/11.50 % (23593)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_23265 for (2904ds/307Mi)
% 70.27/11.59 % (23577)Instruction limit reached!
% 70.27/11.59 % (23577)------------------------------
% 70.27/11.59 % (23577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.27/11.59 % (23577)Termination reason: Unknown
% 70.27/11.59 % (23577)Termination phase: Saturation
% 70.27/11.59
% 70.27/11.59 % (23577)Memory used [KB]: 9594
% 70.27/11.59 % (23577)Time elapsed: 2.165 s
% 70.27/11.59 % (23577)Instructions burned: 5062 (million)
% 70.27/11.59 % (23577)------------------------------
% 70.27/11.59 % (23577)------------------------------
% 70.77/11.61 % (23594)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on DTF2THF_23265 for (2902ds/3619Mi)
% 70.77/11.62 % (23593)Instruction limit reached!
% 70.77/11.62 % (23593)------------------------------
% 70.77/11.62 % (23593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.77/11.62 % (23593)Termination reason: Unknown
% 70.77/11.62 % (23593)Termination phase: Saturation
% 70.77/11.62
% 70.77/11.62 % (23593)Memory used [KB]: 6652
% 70.77/11.62 % (23593)Time elapsed: 0.122 s
% 70.77/11.62 % (23593)Instructions burned: 308 (million)
% 70.77/11.62 % (23593)------------------------------
% 70.77/11.62 % (23593)------------------------------
% 70.77/11.64 % (23595)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_23265 for (2902ds/2325Mi)
% 71.30/11.70 % (23594)Refutation not found, incomplete strategy
% 71.30/11.70 % (23594)------------------------------
% 71.30/11.70 % (23594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.30/11.70 % (23594)Termination reason: Refutation not found, incomplete strategy
% 71.30/11.70
% 71.30/11.70
% 71.30/11.70 % (23594)Memory used [KB]: 8059
% 71.30/11.70 % (23594)Time elapsed: 0.091 s
% 71.30/11.70 % (23594)Instructions burned: 183 (million)
% 71.30/11.70 % (23594)------------------------------
% 71.30/11.70 % (23594)------------------------------
% 71.30/11.72 % (23596)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on DTF2THF_23265 for (2901ds/2341Mi)
% 76.60/12.41 % (23579)Instruction limit reached!
% 76.60/12.41 % (23579)------------------------------
% 76.60/12.41 % (23579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.60/12.41 % (23579)Termination reason: Unknown
% 76.60/12.41 % (23579)Termination phase: Saturation
% 76.60/12.41
% 76.60/12.41 % (23579)Memory used [KB]: 12409
% 76.60/12.41 % (23579)Time elapsed: 2.966 s
% 76.60/12.41 % (23579)Instructions burned: 5799 (million)
% 76.60/12.41 % (23579)------------------------------
% 76.60/12.41 % (23579)------------------------------
% 76.60/12.43 % (23597)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on DTF2THF_23265 for (2894ds/7257Mi)
% 77.21/12.58 % (23589)Instruction limit reached!
% 77.21/12.58 % (23589)------------------------------
% 77.21/12.58 % (23589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.21/12.58 % (23589)Termination reason: Unknown
% 77.21/12.58 % (23589)Termination phase: Saturation
% 77.21/12.58
% 77.21/12.58 % (23589)Memory used [KB]: 11001
% 77.21/12.58 % (23589)Time elapsed: 1.861 s
% 77.21/12.58 % (23589)Instructions burned: 3674 (million)
% 77.21/12.58 % (23589)------------------------------
% 77.21/12.58 % (23589)------------------------------
% 77.82/12.60 % (23598)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on DTF2THF_23265 for (2893ds/3710Mi)
% 78.81/12.85 % (23595)Instruction limit reached!
% 78.81/12.85 % (23595)------------------------------
% 78.81/12.85 % (23595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.81/12.85 % (23595)Termination reason: Unknown
% 78.81/12.85 % (23595)Termination phase: Saturation
% 78.81/12.85
% 78.81/12.85 % (23595)Memory used [KB]: 13176
% 78.81/12.85 % (23595)Time elapsed: 1.209 s
% 78.81/12.85 % (23595)Instructions burned: 2325 (million)
% 78.81/12.85 % (23595)------------------------------
% 78.81/12.85 % (23595)------------------------------
% 78.81/12.86 % (23599)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on DTF2THF_23265 for (2890ds/326Mi)
% 79.26/12.93 % (23596)Instruction limit reached!
% 79.26/12.93 % (23596)------------------------------
% 79.26/12.93 % (23596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 79.26/12.93 % (23596)Termination reason: Unknown
% 79.26/12.93 % (23596)Termination phase: Saturation
% 79.26/12.93
% 79.26/12.93 % (23596)Memory used [KB]: 9466
% 79.26/12.93 % (23596)Time elapsed: 1.225 s
% 79.26/12.93 % (23596)Instructions burned: 2341 (million)
% 79.26/12.93 % (23596)------------------------------
% 79.26/12.93 % (23596)------------------------------
% 79.26/12.95 % (23600)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on DTF2THF_23265 for (2889ds/1100Mi)
% 79.26/13.02 % (23599)Instruction limit reached!
% 79.26/13.02 % (23599)------------------------------
% 79.26/13.02 % (23599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 79.26/13.02 % (23599)Termination reason: Unknown
% 79.26/13.02 % (23599)Termination phase: Saturation
% 79.26/13.02
% 79.26/13.02 % (23599)Memory used [KB]: 7675
% 79.26/13.02 % (23599)Time elapsed: 0.159 s
% 79.26/13.02 % (23599)Instructions burned: 326 (million)
% 79.26/13.02 % (23599)------------------------------
% 79.26/13.02 % (23599)------------------------------
% 80.81/13.04 % (23601)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_23265 for (2888ds/406Mi)
% 80.81/13.07 % (23591)Instruction limit reached!
% 80.81/13.07 % (23591)------------------------------
% 80.81/13.07 % (23591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 80.81/13.07 % (23591)Termination reason: Unknown
% 80.81/13.07 % (23591)Termination phase: Saturation
% 80.81/13.07
% 80.81/13.07 % (23591)Memory used [KB]: 9722
% 80.81/13.07 % (23591)Time elapsed: 2.204 s
% 80.81/13.07 % (23591)Instructions burned: 4638 (million)
% 80.81/13.07 % (23591)------------------------------
% 80.81/13.07 % (23591)------------------------------
% 80.81/13.08 % (23602)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1871:si=on:rtra=on_0 on DTF2THF_23265 for (2888ds/1871Mi)
% 80.81/13.09 % (23592)Instruction limit reached!
% 80.81/13.09 % (23592)------------------------------
% 80.81/13.09 % (23592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 80.81/13.09 % (23592)Termination reason: Unknown
% 80.81/13.09 % (23592)Termination phase: Saturation
% 80.81/13.09
% 80.81/13.09 % (23592)Memory used [KB]: 19189
% 80.81/13.09 % (23592)Time elapsed: 1.604 s
% 80.81/13.09 % (23592)Instructions burned: 3174 (million)
% 80.81/13.09 % (23592)------------------------------
% 80.81/13.09 % (23592)------------------------------
% 80.81/13.11 % (23603)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1194:si=on:rtra=on_0 on DTF2THF_23265 for (2888ds/1194Mi)
% 81.80/13.23 % (23601)Instruction limit reached!
% 81.80/13.23 % (23601)------------------------------
% 81.80/13.23 % (23601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 81.80/13.23 % (23601)Termination reason: Unknown
% 81.80/13.23 % (23601)Termination phase: Saturation
% 81.80/13.23
% 81.80/13.23 % (23601)Memory used [KB]: 7164
% 81.80/13.23 % (23601)Time elapsed: 0.210 s
% 81.80/13.23 % (23601)Instructions burned: 407 (million)
% 81.80/13.23 % (23601)------------------------------
% 81.80/13.23 % (23601)------------------------------
% 81.80/13.25 % (23604)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_23265 for (2886ds/474Mi)
% 82.79/13.43 % (23604)Instruction limit reached!
% 82.79/13.43 % (23604)------------------------------
% 82.79/13.43 % (23604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 82.79/13.43 % (23604)Termination reason: Unknown
% 82.79/13.43 % (23604)Termination phase: Saturation
% 82.79/13.43
% 82.79/13.43 % (23604)Memory used [KB]: 9850
% 82.79/13.43 % (23604)Time elapsed: 0.185 s
% 82.79/13.43 % (23604)Instructions burned: 475 (million)
% 82.79/13.43 % (23604)------------------------------
% 82.79/13.43 % (23604)------------------------------
% 82.79/13.45 % (23605)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3115:si=on:rtra=on_0 on DTF2THF_23265 for (2884ds/3115Mi)
% 83.40/13.54 % (23600)Instruction limit reached!
% 83.40/13.54 % (23600)------------------------------
% 83.40/13.54 % (23600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.40/13.54 % (23600)Termination reason: Unknown
% 83.40/13.54 % (23600)Termination phase: Saturation
% 83.40/13.54
% 83.40/13.54 % (23600)Memory used [KB]: 11897
% 83.40/13.54 % (23600)Time elapsed: 0.598 s
% 83.40/13.54 % (23600)Instructions burned: 1101 (million)
% 83.40/13.54 % (23600)------------------------------
% 83.40/13.54 % (23600)------------------------------
% 83.40/13.56 % (23606)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_23265 for (2883ds/831Mi)
% 84.05/13.72 % (23603)Instruction limit reached!
% 84.05/13.72 % (23603)------------------------------
% 84.05/13.72 % (23603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 84.05/13.72 % (23603)Termination reason: Unknown
% 84.05/13.72 % (23603)Termination phase: Saturation
% 84.05/13.72
% 84.05/13.72 % (23603)Memory used [KB]: 10362
% 84.05/13.72 % (23603)Time elapsed: 0.637 s
% 84.05/13.72 % (23603)Instructions burned: 1195 (million)
% 84.05/13.72 % (23603)------------------------------
% 84.05/13.72 % (23603)------------------------------
% 84.05/13.74 % (23607)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_23265 for (2881ds/1188Mi)
% 85.28/13.97 % (23606)Instruction limit reached!
% 85.28/13.97 % (23606)------------------------------
% 85.28/13.97 % (23606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 85.28/13.97 % (23606)Termination reason: Unknown
% 85.28/13.97 % (23606)Termination phase: Saturation
% 85.28/13.97
% 85.28/13.97 % (23606)Memory used [KB]: 8315
% 85.28/13.97 % (23606)Time elapsed: 0.414 s
% 85.28/13.97 % (23606)Instructions burned: 832 (million)
% 85.28/13.97 % (23606)------------------------------
% 85.28/13.97 % (23606)------------------------------
% 85.28/13.99 % (23608)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=2868:si=on:rtra=on_0 on DTF2THF_23265 for (2879ds/2868Mi)
% 87.95/14.09 % (23602)Instruction limit reached!
% 87.95/14.09 % (23602)------------------------------
% 87.95/14.09 % (23602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 87.95/14.09 % (23602)Termination reason: Unknown
% 87.95/14.09 % (23602)Termination phase: Saturation
% 87.95/14.09
% 87.95/14.09 % (23602)Memory used [KB]: 14328
% 87.95/14.09 % (23602)Time elapsed: 1.030 s
% 87.95/14.09 % (23602)Instructions burned: 1871 (million)
% 87.95/14.09 % (23602)------------------------------
% 87.95/14.09 % (23602)------------------------------
% 87.95/14.11 % (23609)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on DTF2THF_23265 for (2877ds/1516Mi)
% 88.64/14.13 % (23598)Instruction limit reached!
% 88.64/14.13 % (23598)------------------------------
% 88.64/14.13 % (23598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 88.64/14.13 % (23598)Termination reason: Unknown
% 88.64/14.13 % (23598)Termination phase: Saturation
% 88.64/14.13
% 88.64/14.13 % (23598)Memory used [KB]: 11001
% 88.64/14.13 % (23598)Time elapsed: 1.532 s
% 88.64/14.13 % (23598)Instructions burned: 3710 (million)
% 88.64/14.13 % (23598)------------------------------
% 88.64/14.13 % (23598)------------------------------
% 88.64/14.14 % (23610)lrs+1002_1:20_afp=1000:au=on:bsd=on:cnfonf=lazy_not_gen_be_off:sos=all:sp=const_max:i=2321:si=on:rtra=on_0 on DTF2THF_23265 for (2877ds/2321Mi)
% 89.01/14.22 % (23607)Instruction limit reached!
% 89.01/14.22 % (23607)------------------------------
% 89.01/14.22 % (23607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 89.01/14.22 % (23607)Termination reason: Unknown
% 89.01/14.22 % (23607)Termination phase: Saturation
% 89.01/14.22
% 89.01/14.22 % (23607)Memory used [KB]: 10618
% 89.01/14.22 % (23607)Time elapsed: 0.488 s
% 89.01/14.22 % (23607)Instructions burned: 1189 (million)
% 89.01/14.22 % (23607)------------------------------
% 89.01/14.22 % (23607)------------------------------
% 89.01/14.24 % (23611)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_23265 for (2876ds/2812Mi)
% 89.84/14.46 % (23587)Instruction limit reached!
% 89.84/14.46 % (23587)------------------------------
% 89.84/14.46 % (23587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 89.84/14.46 % (23587)Termination reason: Unknown
% 89.84/14.46 % (23587)Termination phase: Saturation
% 89.84/14.46
% 89.84/14.46 % (23587)Memory used [KB]: 15607
% 89.84/14.46 % (23587)Time elapsed: 3.835 s
% 89.84/14.46 % (23587)Instructions burned: 7680 (million)
% 89.84/14.46 % (23587)------------------------------
% 89.84/14.46 % (23587)------------------------------
% 89.84/14.48 % (23612)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_23265 for (2874ds/4604Mi)
% 90.52/14.64 % (23605)Instruction limit reached!
% 90.52/14.64 % (23605)------------------------------
% 90.52/14.64 % (23605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 90.52/14.64 % (23605)Termination reason: Unknown
% 90.52/14.64 % (23605)Termination phase: Saturation
% 90.52/14.64
% 90.52/14.64 % (23605)Memory used [KB]: 10106
% 90.52/14.64 % (23605)Time elapsed: 1.213 s
% 90.52/14.64 % (23605)Instructions burned: 3116 (million)
% 90.52/14.64 % (23605)------------------------------
% 90.52/14.64 % (23605)------------------------------
% 90.52/14.66 % (23613)ott+1002_1:4_c=on:chr=on:cnfonf=lazy_not_be_gen:hud=10:nm=10:piset=all_but_not_eq:rp=on:spb=goal:uhcvi=on:i=2678:si=on:rtra=on_0 on DTF2THF_23265 for (2872ds/2678Mi)
% 90.97/14.87 % (23609)Instruction limit reached!
% 90.97/14.87 % (23609)------------------------------
% 90.97/14.87 % (23609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 90.97/14.87 % (23609)Termination reason: Unknown
% 90.97/14.87 % (23609)Termination phase: Saturation
% 90.97/14.87
% 90.97/14.87 % (23609)Memory used [KB]: 11129
% 90.97/14.87 % (23609)Time elapsed: 0.757 s
% 90.97/14.87 % (23609)Instructions burned: 1517 (million)
% 90.97/14.87 % (23609)------------------------------
% 90.97/14.87 % (23609)------------------------------
% 90.97/14.88 % (23614)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_23265 for (2870ds/643Mi)
% 94.96/15.06 % (23610)Instruction limit reached!
% 94.96/15.06 % (23610)------------------------------
% 94.96/15.06 % (23610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 94.96/15.06 % (23610)Termination reason: Unknown
% 94.96/15.06 % (23610)Termination phase: Saturation
% 94.96/15.06
% 94.96/15.06 % (23610)Memory used [KB]: 10106
% 94.96/15.06 % (23610)Time elapsed: 0.914 s
% 94.96/15.06 % (23610)Instructions burned: 2322 (million)
% 94.96/15.06 % (23610)------------------------------
% 94.96/15.06 % (23610)------------------------------
% 94.96/15.08 % (23615)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=458:si=on:rtra=on_0 on DTF2THF_23265 for (2868ds/458Mi)
% 94.96/15.09 % (23608)Instruction limit reached!
% 94.96/15.09 % (23608)------------------------------
% 94.96/15.09 % (23608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 94.96/15.09 % (23608)Termination reason: Unknown
% 94.96/15.09 % (23608)Termination phase: Saturation
% 94.96/15.09
% 94.96/15.09 % (23608)Memory used [KB]: 7164
% 94.96/15.09 % (23608)Time elapsed: 1.105 s
% 94.96/15.09 % (23608)Instructions burned: 2869 (million)
% 94.96/15.09 % (23608)------------------------------
% 94.96/15.09 % (23608)------------------------------
% 94.96/15.11 % (23616)lrs+1010_1:1_anc=all_dependent:apa=on:au=on:bd=off:c=on:cnfonf=off:ntd=on:i=2546:si=on:rtra=on_0 on DTF2THF_23265 for (2867ds/2546Mi)
% 95.58/15.13 % (23614)Instruction limit reached!
% 95.58/15.13 % (23614)------------------------------
% 95.58/15.13 % (23614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 95.58/15.13 % (23614)Termination reason: Unknown
% 95.58/15.13 % (23614)Termination phase: Saturation
% 95.58/15.13
% 95.58/15.13 % (23614)Memory used [KB]: 9594
% 95.58/15.13 % (23614)Time elapsed: 0.247 s
% 95.58/15.13 % (23614)Instructions burned: 644 (million)
% 95.58/15.13 % (23614)------------------------------
% 95.58/15.13 % (23614)------------------------------
% 95.58/15.15 % (23617)dis+21_1:1_acc=model:au=on:cnfonf=lazy_gen:ins=2:plsq=on:plsqc=1:plsqr=32,1:i=1432:si=on:rtra=on_0 on DTF2THF_23265 for (2867ds/1432Mi)
% 95.88/15.26 % (23615)Instruction limit reached!
% 95.88/15.26 % (23615)------------------------------
% 95.88/15.26 % (23615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 95.88/15.26 % (23615)Termination reason: Unknown
% 95.88/15.26 % (23615)Termination phase: Saturation
% 95.88/15.26
% 95.88/15.26 % (23615)Memory used [KB]: 9466
% 95.88/15.26 % (23615)Time elapsed: 0.185 s
% 95.88/15.26 % (23615)Instructions burned: 458 (million)
% 95.88/15.26 % (23615)------------------------------
% 95.88/15.26 % (23615)------------------------------
% 95.88/15.28 % (23618)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=386:si=on:rtra=on_0 on DTF2THF_23265 for (2866ds/386Mi)
% 96.87/15.43 % (23618)Instruction limit reached!
% 96.87/15.43 % (23618)------------------------------
% 96.87/15.43 % (23618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 96.87/15.43 % (23618)Termination reason: Unknown
% 96.87/15.43 % (23618)Termination phase: Saturation
% 96.87/15.43
% 96.87/15.43 % (23618)Memory used [KB]: 6652
% 96.87/15.43 % (23618)Time elapsed: 0.150 s
% 96.87/15.43 % (23618)Instructions burned: 388 (million)
% 96.87/15.43 % (23618)------------------------------
% 96.87/15.43 % (23618)------------------------------
% 96.87/15.44 % (23619)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_23265 for (2864ds/360Mi)
% 97.44/15.58 % (23619)Instruction limit reached!
% 97.44/15.58 % (23619)------------------------------
% 97.44/15.58 % (23619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 97.44/15.58 % (23619)Termination reason: Unknown
% 97.44/15.58 % (23619)Termination phase: Saturation
% 97.44/15.58
% 97.44/15.58 % (23619)Memory used [KB]: 6652
% 97.44/15.58 % (23619)Time elapsed: 0.136 s
% 97.44/15.58 % (23619)Instructions burned: 361 (million)
% 97.44/15.58 % (23619)------------------------------
% 97.44/15.58 % (23619)------------------------------
% 98.00/15.61 % (23620)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=5446:si=on:rtra=on_0 on DTF2THF_23265 for (2863ds/5446Mi)
% 98.00/15.67 % (23611)Instruction limit reached!
% 98.00/15.67 % (23611)------------------------------
% 98.00/15.67 % (23611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 98.00/15.67 % (23611)Termination reason: Unknown
% 98.00/15.67 % (23611)Termination phase: Saturation
% 98.00/15.67
% 98.00/15.67 % (23611)Memory used [KB]: 10362
% 98.00/15.67 % (23611)Time elapsed: 1.423 s
% 98.00/15.67 % (23611)Instructions burned: 2813 (million)
% 98.00/15.67 % (23611)------------------------------
% 98.00/15.67 % (23611)------------------------------
% 98.00/15.69 % (23621)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=2573:si=on:rtra=on_0 on DTF2THF_23265 for (2862ds/2573Mi)
% 98.37/15.71 % (23617)Instruction limit reached!
% 98.37/15.71 % (23617)------------------------------
% 98.37/15.71 % (23617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 98.37/15.71 % (23617)Termination reason: Unknown
% 98.37/15.71 % (23617)Termination phase: Saturation
% 98.37/15.71
% 98.37/15.71 % (23617)Memory used [KB]: 13304
% 98.37/15.71 % (23617)Time elapsed: 0.567 s
% 98.37/15.71 % (23617)Instructions burned: 1434 (million)
% 98.37/15.71 % (23617)------------------------------
% 98.37/15.71 % (23617)------------------------------
% 98.37/15.73 % (23622)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=2655:si=on:rtra=on_0 on DTF2THF_23265 for (2861ds/2655Mi)
% 98.37/15.75 % (23613)Instruction limit reached!
% 98.37/15.75 % (23613)------------------------------
% 98.37/15.75 % (23613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 98.37/15.75 % (23613)Termination reason: Unknown
% 98.37/15.75 % (23613)Termination phase: Saturation
% 98.37/15.75
% 98.37/15.75 % (23613)Memory used [KB]: 13432
% 98.37/15.75 % (23613)Time elapsed: 1.096 s
% 98.37/15.75 % (23613)Instructions burned: 2679 (million)
% 98.37/15.75 % (23613)------------------------------
% 98.37/15.75 % (23613)------------------------------
% 98.37/15.77 % (23623)dis+1002_16:1_apa=on:au=on:av=off:cnfonf=off:e2e=on:nm=0:nwc=10.0:i=2781:si=on:rtra=on_0 on DTF2THF_23265 for (2861ds/2781Mi)
% 99.43/15.99 % (23597)Instruction limit reached!
% 99.43/15.99 % (23597)------------------------------
% 99.43/15.99 % (23597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 99.43/15.99 % (23597)Termination reason: Unknown
% 99.43/15.99 % (23597)Termination phase: Saturation
% 99.43/15.99
% 99.43/15.99 % (23597)Memory used [KB]: 10106
% 99.43/15.99 % (23597)Time elapsed: 3.567 s
% 99.43/15.99 % (23597)Instructions burned: 7257 (million)
% 99.43/15.99 % (23597)------------------------------
% 99.43/15.99 % (23597)------------------------------
% 101.70/16.04 % (23624)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_23265 for (2858ds/307Mi)
% 102.38/16.17 % (23624)Instruction limit reached!
% 102.38/16.17 % (23624)------------------------------
% 102.38/16.17 % (23624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 102.38/16.17 % (23624)Termination reason: Unknown
% 102.38/16.17 % (23624)Termination phase: Saturation
% 102.38/16.17
% 102.38/16.17 % (23624)Memory used [KB]: 6780
% 102.38/16.17 % (23624)Time elapsed: 0.132 s
% 102.38/16.17 % (23624)Instructions burned: 307 (million)
% 102.38/16.17 % (23624)------------------------------
% 102.38/16.17 % (23624)------------------------------
% 102.38/16.19 % (23625)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=1548:si=on:rtra=on_0 on DTF2THF_23265 for (2857ds/1548Mi)
% 104.16/16.41 % (23616)Instruction limit reached!
% 104.16/16.41 % (23616)------------------------------
% 104.16/16.41 % (23616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 104.16/16.41 % (23616)Termination reason: Unknown
% 104.16/16.41 % (23616)Termination phase: Saturation
% 104.16/16.41
% 104.16/16.41 % (23616)Memory used [KB]: 10618
% 104.16/16.41 % (23616)Time elapsed: 1.289 s
% 104.16/16.41 % (23616)Instructions burned: 2547 (million)
% 104.16/16.41 % (23616)------------------------------
% 104.16/16.41 % (23616)------------------------------
% 104.16/16.43 % (23626)lrs+10_1:3_alpa=true:hud=3:ins=1:ntd=on:plsq=on:plsqc=1:plsqr=32,1:prag=on:s2a=on:s2agt=10:i=5214:si=on:rtra=on_0 on DTF2THF_23265 for (2854ds/5214Mi)
% 106.17/16.81 % (23612)Instruction limit reached!
% 106.17/16.81 % (23612)------------------------------
% 106.17/16.81 % (23612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 106.17/16.81 % (23612)Termination reason: Unknown
% 106.17/16.81 % (23612)Termination phase: Saturation
% 106.17/16.81
% 106.17/16.81 % (23612)Memory used [KB]: 13304
% 106.17/16.81 % (23612)Time elapsed: 2.328 s
% 106.17/16.81 % (23612)Instructions burned: 4604 (million)
% 106.17/16.81 % (23612)------------------------------
% 106.17/16.81 % (23612)------------------------------
% 106.17/16.82 % (23621)Instruction limit reached!
% 106.17/16.82 % (23621)------------------------------
% 106.17/16.82 % (23621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 106.17/16.82 % (23621)Termination reason: Unknown
% 106.17/16.82 % (23621)Termination phase: Saturation
% 106.17/16.82
% 106.17/16.82 % (23621)Memory used [KB]: 10618
% 106.17/16.82 % (23621)Time elapsed: 1.135 s
% 106.17/16.82 % (23621)Instructions burned: 2574 (million)
% 106.17/16.82 % (23621)------------------------------
% 106.17/16.82 % (23621)------------------------------
% 106.17/16.83 % (23627)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_23265 for (2850ds/3201Mi)
% 106.17/16.83 % (23622)Instruction limit reached!
% 106.17/16.83 % (23622)------------------------------
% 106.17/16.83 % (23622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 106.17/16.83 % (23622)Termination reason: Unknown
% 106.17/16.83 % (23622)Termination phase: Saturation
% 106.17/16.83
% 106.17/16.83 % (23622)Memory used [KB]: 3965
% 106.17/16.83 % (23622)Time elapsed: 1.105 s
% 106.17/16.83 % (23622)Instructions burned: 2656 (million)
% 106.17/16.83 % (23622)------------------------------
% 106.17/16.83 % (23622)------------------------------
% 106.17/16.84 % (23628)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_23265 for (2850ds/454Mi)
% 106.17/16.85 % (23629)lrs+1002_1:32_au=on:ins=2:nm=16:ntd=on:piset=all_but_not_eq:sp=occurrence:i=3049:si=on:rtra=on_0 on DTF2THF_23265 for (2850ds/3049Mi)
% 106.48/17.01 % (23625)Instruction limit reached!
% 106.48/17.01 % (23625)------------------------------
% 106.48/17.01 % (23625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 106.48/17.01 % (23625)Termination reason: Unknown
% 106.48/17.01 % (23625)Termination phase: Saturation
% 106.48/17.01
% 106.48/17.01 % (23625)Memory used [KB]: 10234
% 106.48/17.01 % (23625)Time elapsed: 0.818 s
% 106.48/17.01 % (23625)Instructions burned: 1549 (million)
% 106.48/17.01 % (23625)------------------------------
% 106.48/17.01 % (23625)------------------------------
% 106.48/17.02 % (23628)Instruction limit reached!
% 106.48/17.02 % (23628)------------------------------
% 106.48/17.02 % (23628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 106.48/17.02 % (23628)Termination reason: Unknown
% 106.48/17.02 % (23628)Termination phase: Saturation
% 106.48/17.02
% 106.48/17.02 % (23628)Memory used [KB]: 14328
% 106.48/17.02 % (23628)Time elapsed: 0.185 s
% 106.48/17.02 % (23628)Instructions burned: 455 (million)
% 106.48/17.02 % (23628)------------------------------
% 106.48/17.02 % (23628)------------------------------
% 108.57/17.03 % (23630)lrs+1010_1:1_bd=preordered:cnfonf=off:e2e=on:kws=inv_precedence:lwlo=on:sd=2:ss=axioms:i=7311:si=on:rtra=on_0 on DTF2THF_23265 for (2848ds/7311Mi)
% 108.57/17.04 % (23631)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=6804:si=on:rtra=on_0 on DTF2THF_23265 for (2848ds/6804Mi)
% 109.28/17.14 % (23631)Refutation not found, incomplete strategy
% 109.28/17.14 % (23631)------------------------------
% 109.28/17.14 % (23631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 109.28/17.14 % (23631)Termination reason: Refutation not found, incomplete strategy
% 109.28/17.14
% 109.28/17.14
% 109.28/17.14 % (23631)Memory used [KB]: 8315
% 109.28/17.14 % (23631)Time elapsed: 0.102 s
% 109.28/17.14 % (23631)Instructions burned: 195 (million)
% 109.28/17.14 % (23631)------------------------------
% 109.28/17.14 % (23631)------------------------------
% 109.28/17.15 % (23623)Instruction limit reached!
% 109.28/17.15 % (23623)------------------------------
% 109.28/17.15 % (23623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 109.28/17.15 % (23623)Termination reason: Unknown
% 109.28/17.15 % (23623)Termination phase: Saturation
% 109.28/17.15
% 109.28/17.15 % (23623)Memory used [KB]: 7419
% 109.28/17.15 % (23623)Time elapsed: 1.375 s
% 109.28/17.15 % (23623)Instructions burned: 2782 (million)
% 109.28/17.15 % (23623)------------------------------
% 109.28/17.15 % (23623)------------------------------
% 109.28/17.16 % (23632)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_23265 for (2847ds/1683Mi)
% 109.28/17.16 % (23633)lrs+10_8:1_au=on:av=off:bd=off:cs=on:e2e=on:hfsq=on:hfsqc=50:hfsql=off:nm=0:i=4688:si=on:rtra=on_0 on DTF2THF_23265 for (2847ds/4688Mi)
% 112.51/17.99 % (23632)Instruction limit reached!
% 112.51/17.99 % (23632)------------------------------
% 112.51/17.99 % (23632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 112.51/17.99 % (23632)Termination reason: Unknown
% 112.51/17.99 % (23632)Termination phase: Saturation
% 112.51/17.99
% 112.51/17.99 % (23632)Memory used [KB]: 15863
% 112.51/17.99 % (23632)Time elapsed: 0.830 s
% 112.51/17.99 % (23632)Instructions burned: 1683 (million)
% 112.51/17.99 % (23632)------------------------------
% 112.51/17.99 % (23632)------------------------------
% 112.51/18.01 % (23634)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_23265 for (2838ds/2207Mi)
% 115.70/18.07 % (23620)Instruction limit reached!
% 115.70/18.07 % (23620)------------------------------
% 115.70/18.07 % (23620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 115.70/18.07 % (23620)Termination reason: Unknown
% 115.70/18.07 % (23620)Termination phase: Saturation
% 115.70/18.07
% 115.70/18.07 % (23620)Memory used [KB]: 14967
% 115.70/18.07 % (23620)Time elapsed: 2.470 s
% 115.70/18.07 % (23620)Instructions burned: 5447 (million)
% 115.70/18.07 % (23620)------------------------------
% 115.70/18.07 % (23620)------------------------------
% 115.70/18.09 % (23635)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=8216:si=on:rtra=on_0 on DTF2THF_23265 for (2838ds/8216Mi)
% 117.43/18.39 % (23629)Instruction limit reached!
% 117.43/18.39 % (23629)------------------------------
% 117.43/18.39 % (23629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 117.43/18.39 % (23629)Termination reason: Unknown
% 117.43/18.39 % (23629)Termination phase: Saturation
% 117.43/18.39
% 117.43/18.39 % (23629)Memory used [KB]: 9083
% 117.43/18.39 % (23629)Time elapsed: 1.536 s
% 117.43/18.39 % (23629)Instructions burned: 3050 (million)
% 117.43/18.39 % (23629)------------------------------
% 117.43/18.39 % (23629)------------------------------
% 118.03/18.41 % (23636)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=430:si=on:rtra=on_0 on DTF2THF_23265 for (2835ds/430Mi)
% 118.03/18.48 % (23627)Instruction limit reached!
% 118.03/18.48 % (23627)------------------------------
% 118.03/18.48 % (23627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 118.03/18.48 % (23627)Termination reason: Unknown
% 118.03/18.48 % (23627)Termination phase: Saturation
% 118.03/18.48
% 118.03/18.48 % (23627)Memory used [KB]: 10362
% 118.03/18.48 % (23627)Time elapsed: 1.653 s
% 118.03/18.48 % (23627)Instructions burned: 3201 (million)
% 118.03/18.48 % (23627)------------------------------
% 118.03/18.48 % (23627)------------------------------
% 118.52/18.50 % (23637)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=2012:si=on:rtra=on_0 on DTF2THF_23265 for (2834ds/2012Mi)
% 118.93/18.63 % (23636)Instruction limit reached!
% 118.93/18.63 % (23636)------------------------------
% 118.93/18.63 % (23636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 118.93/18.63 % (23636)Termination reason: Unknown
% 118.93/18.63 % (23636)Termination phase: Saturation
% 118.93/18.63
% 118.93/18.63 % (23636)Memory used [KB]: 10362
% 118.93/18.63 % (23636)Time elapsed: 0.222 s
% 118.93/18.63 % (23636)Instructions burned: 430 (million)
% 118.93/18.63 % (23636)------------------------------
% 118.93/18.63 % (23636)------------------------------
% 118.93/18.65 % (23638)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=631:si=on:rtra=on_0 on DTF2THF_23265 for (2832ds/631Mi)
% 119.98/18.87 % (23626)Instruction limit reached!
% 119.98/18.87 % (23626)------------------------------
% 119.98/18.87 % (23626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 119.98/18.87 % (23626)Termination reason: Unknown
% 119.98/18.87 % (23626)Termination phase: Saturation
% 119.98/18.87
% 119.98/18.87 % (23626)Memory used [KB]: 9210
% 119.98/18.87 % (23626)Time elapsed: 2.446 s
% 119.98/18.87 % (23626)Instructions burned: 5216 (million)
% 119.98/18.87 % (23626)------------------------------
% 119.98/18.87 % (23626)------------------------------
% 119.98/18.89 % (23639)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=8785:si=on:rtra=on_0 on DTF2THF_23265 for (2830ds/8785Mi)
% 120.34/18.97 % (23638)Instruction limit reached!
% 120.34/18.97 % (23638)------------------------------
% 120.34/18.97 % (23638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 120.34/18.97 % (23638)Termination reason: Unknown
% 120.34/18.97 % (23638)Termination phase: Saturation
% 120.34/18.97
% 120.34/18.97 % (23638)Memory used [KB]: 7164
% 120.34/18.97 % (23638)Time elapsed: 0.346 s
% 120.34/18.97 % (23638)Instructions burned: 631 (million)
% 120.34/18.97 % (23638)------------------------------
% 120.34/18.97 % (23638)------------------------------
% 120.34/18.99 % (23640)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=739:si=on:rtra=on_0 on DTF2THF_23265 for (2829ds/739Mi)
% 122.76/19.10 % (23634)Instruction limit reached!
% 122.76/19.10 % (23634)------------------------------
% 122.76/19.10 % (23634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 122.76/19.10 % (23634)Termination reason: Unknown
% 122.76/19.10 % (23634)Termination phase: Saturation
% 122.76/19.10
% 122.76/19.10 % (23634)Memory used [KB]: 9850
% 122.76/19.10 % (23634)Time elapsed: 1.094 s
% 122.76/19.10 % (23634)Instructions burned: 2207 (million)
% 122.76/19.10 % (23634)------------------------------
% 122.76/19.10 % (23634)------------------------------
% 122.76/19.12 % (23641)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on DTF2THF_23265 for (2827ds/5473Mi)
% 124.45/19.33 % (23637)Instruction limit reached!
% 124.45/19.33 % (23637)------------------------------
% 124.45/19.33 % (23637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 124.45/19.33 % (23637)Termination reason: Unknown
% 124.45/19.33 % (23637)Termination phase: Saturation
% 124.45/19.33
% 124.45/19.33 % (23637)Memory used [KB]: 11257
% 124.45/19.33 % (23637)Time elapsed: 0.837 s
% 124.45/19.33 % (23637)Instructions burned: 2013 (million)
% 124.45/19.33 % (23637)------------------------------
% 124.45/19.33 % (23637)------------------------------
% 124.45/19.35 % (23642)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=43570:si=on:rtra=on_0 on DTF2THF_23265 for (2825ds/43570Mi)
% 124.45/19.38 % (23640)Instruction limit reached!
% 124.45/19.38 % (23640)------------------------------
% 124.45/19.38 % (23640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 124.45/19.38 % (23640)Termination reason: Unknown
% 124.45/19.38 % (23640)Termination phase: Saturation
% 124.45/19.38
% 124.45/19.38 % (23640)Memory used [KB]: 10490
% 124.45/19.38 % (23640)Time elapsed: 0.412 s
% 124.45/19.38 % (23640)Instructions burned: 739 (million)
% 124.45/19.38 % (23640)------------------------------
% 124.45/19.38 % (23640)------------------------------
% 124.45/19.39 % (23643)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=8382:si=on:rtra=on_0 on DTF2THF_23265 for (2824ds/8382Mi)
% 125.00/19.47 % (23633)Instruction limit reached!
% 125.00/19.47 % (23633)------------------------------
% 125.00/19.47 % (23633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 125.00/19.47 % (23633)Termination reason: Unknown
% 125.00/19.47 % (23633)Termination phase: Saturation
% 125.00/19.47
% 125.00/19.47 % (23633)Memory used [KB]: 13176
% 125.00/19.47 % (23633)Time elapsed: 2.311 s
% 125.00/19.47 % (23633)Instructions burned: 4689 (million)
% 125.00/19.47 % (23633)------------------------------
% 125.00/19.47 % (23633)------------------------------
% 125.00/19.49 % (23644)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on DTF2THF_23265 for (2823ds/407Mi)
% 125.69/19.69 % (23644)Instruction limit reached!
% 125.69/19.69 % (23644)------------------------------
% 125.69/19.69 % (23644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 125.69/19.69 % (23644)Termination reason: Unknown
% 125.69/19.69 % (23644)Termination phase: Saturation
% 125.69/19.69
% 125.69/19.69 % (23644)Memory used [KB]: 7931
% 125.69/19.69 % (23644)Time elapsed: 0.198 s
% 125.69/19.69 % (23644)Instructions burned: 407 (million)
% 125.69/19.69 % (23644)------------------------------
% 125.69/19.69 % (23644)------------------------------
% 126.19/19.71 % (23645)lrs+10_1:50_cbe=off:cnfonf=lazy_pi_sigma_gen:fe=off:hud=5:plsq=on:plsqr=1,32:sos=all:i=2971:si=on:rtra=on_0 on DTF2THF_23265 for (2821ds/2971Mi)
% 135.13/20.83 % (23645)Refutation not found, non-redundant clauses discarded% (23645)------------------------------
% 135.13/20.83 % (23645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 135.13/20.83 % (23645)Termination reason: Refutation not found, non-redundant clauses discarded
% 135.13/20.83
% 135.13/20.83 % (23645)Memory used [KB]: 7164
% 135.13/20.83 % (23645)Time elapsed: 1.124 s
% 135.13/20.83 % (23645)Instructions burned: 2911 (million)
% 135.13/20.83 % (23645)------------------------------
% 135.13/20.83 % (23645)------------------------------
% 135.13/20.85 % (23646)lrs+1002_1:1_aac=none:bd=off:e2e=on:fde=none:fe=off:piset=or:prag=on:rawr=on:sos=on:updr=off:i=9822:si=on:rtra=on_0 on DTF2THF_23265 for (2810ds/9822Mi)
% 135.79/21.00 % (23630)Instruction limit reached!
% 135.79/21.00 % (23630)------------------------------
% 135.79/21.00 % (23630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 135.79/21.00 % (23630)Termination reason: Unknown
% 135.79/21.00 % (23630)Termination phase: Saturation
% 135.79/21.00
% 135.79/21.00 % (23630)Memory used [KB]: 17398
% 135.79/21.00 % (23630)Time elapsed: 3.975 s
% 135.79/21.00 % (23630)Instructions burned: 7311 (million)
% 135.79/21.00 % (23630)------------------------------
% 135.79/21.00 % (23630)------------------------------
% 135.79/21.02 % (23647)dis+10_5:1_av=off:ntd=on:s2a=on:s2at=3.0:sgt=16:sp=unary_frequency:ss=axioms:i=8425:si=on:rtra=on_0 on DTF2THF_23265 for (2808ds/8425Mi)
% 140.76/21.77 % (23646)Refutation not found, incomplete strategy
% 140.76/21.77 % (23646)------------------------------
% 140.76/21.77 % (23646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 140.76/21.77 % (23646)Termination reason: Refutation not found, incomplete strategy
% 140.76/21.77
% 140.76/21.77
% 140.76/21.77 % (23646)Memory used [KB]: 12537
% 140.76/21.77 % (23646)Time elapsed: 0.920 s
% 140.76/21.77 % (23646)Instructions burned: 1928 (million)
% 140.76/21.77 % (23646)------------------------------
% 140.76/21.77 % (23646)------------------------------
% 140.76/21.79 % (23635)Instruction limit reached!
% 140.76/21.79 % (23635)------------------------------
% 140.76/21.79 % (23635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 140.76/21.79 % (23635)Termination reason: Unknown
% 140.76/21.79 % (23635)Termination phase: Saturation
% 140.76/21.79
% 140.76/21.79 % (23635)Memory used [KB]: 11385
% 140.76/21.79 % (23635)Time elapsed: 3.722 s
% 140.76/21.79 % (23635)Instructions burned: 8216 (million)
% 140.76/21.79 % (23635)------------------------------
% 140.76/21.79 % (23635)------------------------------
% 140.76/21.80 % (23648)lrs+30_1:1_aac=none:au=on:cbe=off:cs=on:nm=2:rawr=on:sos=on:i=3107:si=on:rtra=on_0 on DTF2THF_23265 for (2801ds/3107Mi)
% 141.34/21.80 % (23649)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=7967:si=on:rtra=on_0 on DTF2THF_23265 for (2800ds/7967Mi)
% 141.34/21.82 % (23641)Instruction limit reached!
% 141.34/21.82 % (23641)------------------------------
% 141.34/21.82 % (23641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 141.34/21.82 % (23641)Termination reason: Unknown
% 141.34/21.82 % (23641)Termination phase: Saturation
% 141.34/21.82
% 141.34/21.82 % (23641)Memory used [KB]: 11513
% 141.34/21.82 % (23641)Time elapsed: 2.700 s
% 141.34/21.82 % (23641)Instructions burned: 5473 (million)
% 141.34/21.82 % (23641)------------------------------
% 141.34/21.82 % (23641)------------------------------
% 141.34/21.84 % (23650)lrs+1010_10:959_abs=on:acc=on:bd=off:ccuc=small_ones:cha=on:cnfonf=lazy_simp:fd=preordered:fe=off:hud=3:ile=on:kws=inv_frequency:nm=2:piset=and:sd=5:sp=frequency:spb=goal_then_units:ss=axioms:st=4.5:i=3629:si=on:rtra=on_0 on DTF2THF_23265 for (2800ds/3629Mi)
% 147.70/22.68 % (23650)Refutation not found, non-redundant clauses discarded% (23650)------------------------------
% 147.70/22.68 % (23650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 147.70/22.68 % (23650)Termination reason: Refutation not found, non-redundant clauses discarded
% 147.70/22.68
% 147.70/22.68 % (23650)Memory used [KB]: 8187
% 147.70/22.68 % (23650)Time elapsed: 0.849 s
% 147.70/22.68 % (23650)Instructions burned: 3322 (million)
% 147.70/22.68 % (23650)------------------------------
% 147.70/22.68 % (23650)------------------------------
% 147.70/22.69 % (23748)lrs+1010_1:1024_au=on:fe=axiom:lwlo=on:nm=0:ntd=on:nwc=10.0:spb=non_intro:uhcvi=on:i=939:si=on:rtra=on_0 on DTF2THF_23265 for (2791ds/939Mi)
% 148.40/22.71 % (23643)Instruction limit reached!
% 148.40/22.71 % (23643)------------------------------
% 148.40/22.71 % (23643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 148.40/22.71 % (23643)Termination reason: Unknown
% 148.40/22.71 % (23643)Termination phase: Saturation
% 148.40/22.71
% 148.40/22.71 % (23643)Memory used [KB]: 13048
% 148.40/22.71 % (23643)Time elapsed: 3.320 s
% 148.40/22.71 % (23643)Instructions burned: 8385 (million)
% 148.40/22.71 % (23643)------------------------------
% 148.40/22.71 % (23643)------------------------------
% 148.40/22.73 % (23762)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_23265 for (2791ds/1188Mi)
% 148.94/22.80 % (23639)Instruction limit reached!
% 148.94/22.80 % (23639)------------------------------
% 148.94/22.80 % (23639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 148.94/22.80 % (23639)Termination reason: Unknown
% 148.94/22.80 % (23639)Termination phase: Saturation
% 148.94/22.80
% 148.94/22.80 % (23639)Memory used [KB]: 18549
% 148.94/22.80 % (23639)Time elapsed: 3.942 s
% 148.94/22.80 % (23639)Instructions burned: 8786 (million)
% 148.94/22.80 % (23639)------------------------------
% 148.94/22.80 % (23639)------------------------------
% 148.94/22.81 % (23648)Instruction limit reached!
% 148.94/22.81 % (23648)------------------------------
% 148.94/22.81 % (23648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 148.94/22.81 % (23648)Termination reason: Unknown
% 148.94/22.81 % (23648)Termination phase: Saturation
% 148.94/22.81
% 148.94/22.81 % (23648)Memory used [KB]: 18421
% 148.94/22.81 % (23648)Time elapsed: 1.015 s
% 148.94/22.81 % (23648)Instructions burned: 3108 (million)
% 148.94/22.81 % (23648)------------------------------
% 148.94/22.81 % (23648)------------------------------
% 148.94/22.82 % (23804)dis+21_3:2_avsq=on:cbe=off:e2e=on:flr=on:ile=on:nwc=5.0:piset=or:rawr=on:sp=occurrence:i=3205:si=on:rtra=on_0 on DTF2THF_23265 for (2790ds/3205Mi)
% 148.94/22.82 % (23807)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_23265 for (2790ds/865Mi)
% 149.28/22.98 % (23748)Instruction limit reached!
% 149.28/22.98 % (23748)------------------------------
% 149.28/22.98 % (23748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 149.28/22.98 % (23748)Termination reason: Unknown
% 149.28/22.98 % (23748)Termination phase: Saturation
% 149.28/22.98
% 149.28/22.98 % (23748)Memory used [KB]: 8187
% 149.28/22.98 % (23748)Time elapsed: 0.288 s
% 149.28/22.98 % (23748)Instructions burned: 940 (million)
% 149.28/22.98 % (23748)------------------------------
% 149.28/22.98 % (23748)------------------------------
% 149.28/22.99 % (23871)ott+1002_1:1_au=on:bd=off:cbe=off:cha=on:cnfonf=lazy_pi_sigma_gen:fd=off:fe=off:ntd=on:sp=const_frequency:i=7469:si=on:rtra=on_0 on DTF2THF_23265 for (2789ds/7469Mi)
% 150.64/23.02 % (23762)Instruction limit reached!
% 150.64/23.02 % (23762)------------------------------
% 150.64/23.02 % (23762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 150.64/23.02 % (23762)Termination reason: Unknown
% 150.64/23.02 % (23762)Termination phase: Saturation
% 150.64/23.02
% 150.64/23.02 % (23762)Memory used [KB]: 10362
% 150.64/23.02 % (23762)Time elapsed: 0.296 s
% 150.64/23.02 % (23762)Instructions burned: 1188 (million)
% 150.64/23.02 % (23762)------------------------------
% 150.64/23.02 % (23762)------------------------------
% 150.64/23.03 % (23885)dis+10_1:10_bd=preordered:e2e=on:fde=none:fe=axiom:hud=3:kws=precedence:nwc=3.0:prag=on:sp=const_max:tgt=full:i=4165:si=on:rtra=on_0 on DTF2THF_23265 for (2788ds/4165Mi)
% 151.26/23.12 % (23807)Instruction limit reached!
% 151.26/23.12 % (23807)------------------------------
% 151.26/23.12 % (23807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 151.26/23.12 % (23807)Termination reason: Unknown
% 151.26/23.12 % (23807)Termination phase: Saturation
% 151.26/23.12
% 151.26/23.12 % (23807)Memory used [KB]: 6908
% 151.26/23.12 % (23807)Time elapsed: 0.312 s
% 151.26/23.12 % (23807)Instructions burned: 865 (million)
% 151.26/23.12 % (23807)------------------------------
% 151.26/23.12 % (23807)------------------------------
% 151.26/23.13 % (23886)dis+1010_1:1_au=on:avsq=on:cnfonf=lazy_simp:fsr=off:ntd=on:nwc=10.0:sp=reverse_frequency:ss=axioms:st=1.5:i=13468:si=on:rtra=on_0 on DTF2THF_23265 for (2787ds/13468Mi)
% 154.22/23.79 % (23649)Instruction limit reached!
% 154.22/23.79 % (23649)------------------------------
% 154.22/23.79 % (23649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 154.22/23.79 % (23649)Termination reason: Unknown
% 154.22/23.79 % (23649)Termination phase: Saturation
% 154.22/23.79
% 154.22/23.79 % (23649)Memory used [KB]: 11257
% 154.22/23.79 % (23649)Time elapsed: 1.998 s
% 154.22/23.79 % (23649)Instructions burned: 7967 (million)
% 154.22/23.79 % (23649)------------------------------
% 154.22/23.79 % (23649)------------------------------
% 154.73/23.81 % (23887)dis+1002_1:1_au=on:bsr=unit_only:cbe=off:fe=off:fsr=off:nm=10:nwc=6.0:plsq=on:plsqc=1:plsqr=32,1:sos=all:i=2635:si=on:rtra=on_0 on DTF2THF_23265 for (2780ds/2635Mi)
% 154.73/23.83 % (23804)Instruction limit reached!
% 154.73/23.83 % (23804)------------------------------
% 154.73/23.83 % (23804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 154.73/23.83 % (23804)Termination reason: Unknown
% 154.73/23.83 % (23804)Termination phase: Saturation
% 154.73/23.83
% 154.73/23.83 % (23804)Memory used [KB]: 14583
% 154.73/23.83 % (23804)Time elapsed: 1.015 s
% 154.73/23.83 % (23804)Instructions burned: 3206 (million)
% 154.73/23.83 % (23804)------------------------------
% 154.73/23.83 % (23804)------------------------------
% 154.73/23.84 % (23888)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=631:si=on:rtra=on_0 on DTF2THF_23265 for (2780ds/631Mi)
% 154.73/23.86 % (23647)Instruction limit reached!
% 154.73/23.86 % (23647)------------------------------
% 154.73/23.86 % (23647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 154.73/23.86 % (23647)Termination reason: Unknown
% 154.73/23.86 % (23647)Termination phase: Saturation
% 154.73/23.86
% 154.73/23.86 % (23647)Memory used [KB]: 12025
% 154.73/23.86 % (23647)Time elapsed: 2.836 s
% 154.73/23.86 % (23647)Instructions burned: 8427 (million)
% 154.73/23.86 % (23647)------------------------------
% 154.73/23.86 % (23647)------------------------------
% 154.73/23.87 % (23889)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=15557:si=on:rtra=on_0 on DTF2THF_23265 for (2780ds/15557Mi)
% 155.03/24.00 % (23888)Instruction limit reached!
% 155.03/24.00 % (23888)------------------------------
% 155.03/24.00 % (23888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 155.03/24.00 % (23888)Termination reason: Unknown
% 155.03/24.00 % (23888)Termination phase: Saturation
% 155.03/24.00
% 155.03/24.00 % (23888)Memory used [KB]: 9594
% 155.03/24.00 % (23888)Time elapsed: 0.157 s
% 155.03/24.00 % (23888)Instructions burned: 631 (million)
% 155.03/24.00 % (23888)------------------------------
% 155.03/24.00 % (23888)------------------------------
% 155.03/24.01 % (23890)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2142:si=on:rtra=on_0 on DTF2THF_23265 for (2778ds/2142Mi)
% 155.03/24.01 % (23885)First to succeed.
% 155.03/24.02 % (23885)Refutation found. Thanks to Tanya!
% 155.03/24.02 % SZS status Theorem for DTF2THF_23265
% 155.03/24.02 % SZS output start Proof for DTF2THF_23265
% 155.03/24.02 thf(func_def_0, type, in: $i > $i > $o).
% 155.03/24.02 thf(func_def_1, type, exu: ($i > $o) > $o).
% 155.03/24.02 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 155.03/24.02 thf(func_def_8, type, powerset: $i > $i).
% 155.03/24.02 thf(func_def_10, type, setunion: $i > $i).
% 155.03/24.02 thf(func_def_19, type, descr: ($i > $o) > $i).
% 155.03/24.02 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 155.03/24.02 thf(func_def_26, type, prop2set: $o > $i).
% 155.03/24.02 thf(func_def_36, type, nonempty: $i > $o).
% 155.03/24.02 thf(func_def_69, type, set2prop: $i > $o).
% 155.03/24.02 thf(func_def_88, type, subset: $i > $i > $o).
% 155.03/24.02 thf(func_def_89, type, disjoint: $i > $i > $o).
% 155.03/24.02 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 155.03/24.02 thf(func_def_114, type, binunion: $i > $i > $i).
% 155.03/24.02 thf(func_def_122, type, binintersect: $i > $i > $i).
% 155.03/24.02 thf(func_def_135, type, regular: $i > $o).
% 155.03/24.02 thf(func_def_136, type, setminus: $i > $i > $i).
% 155.03/24.02 thf(func_def_147, type, symdiff: $i > $i > $i).
% 155.03/24.02 thf(func_def_153, type, iskpair: $i > $o).
% 155.03/24.02 thf(func_def_158, type, kpair: $i > $i > $i).
% 155.03/24.02 thf(func_def_160, type, cartprod: $i > $i > $i).
% 155.03/24.02 thf(func_def_177, type, singleton: $i > $o).
% 155.03/24.02 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 155.03/24.02 thf(func_def_184, type, atmost1p: $i > $o).
% 155.03/24.02 thf(func_def_185, type, atleast2p: $i > $o).
% 155.03/24.02 thf(func_def_186, type, atmost2p: $i > $o).
% 155.03/24.02 thf(func_def_187, type, upairsetp: $i > $o).
% 155.03/24.02 thf(func_def_191, type, kfst: $i > $i).
% 155.03/24.02 thf(func_def_208, type, diff: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X0 > X1) > X0)).
% 155.03/24.02 thf(func_def_211, type, sP2: $o > $i > $i > $i > $o).
% 155.03/24.02 thf(func_def_213, type, sP4: $i > $i > $o).
% 155.03/24.02 thf(func_def_214, type, sP5: $i > $o).
% 155.03/24.02 thf(func_def_215, type, sP6: $i > $i > $o).
% 155.03/24.02 thf(func_def_216, type, sP7: $i > $i > $o).
% 155.03/24.02 thf(func_def_226, type, sK17: $i > $i > $i).
% 155.03/24.02 thf(func_def_227, type, sK18: $i > $i > $i).
% 155.03/24.02 thf(func_def_254, type, sK45: $i > $i > $i).
% 155.03/24.02 thf(func_def_256, type, sK47: $i > $i).
% 155.03/24.02 thf(func_def_270, type, sK61: $i > $o).
% 155.03/24.02 thf(func_def_271, type, sK62: $i > $o).
% 155.03/24.02 thf(func_def_272, type, sK63: ($i > $o) > ($i > $o) > $i > $i > $i).
% 155.03/24.02 thf(func_def_273, type, sK64: ($i > $o) > ($i > $o) > $i > $i > $i).
% 155.03/24.02 thf(func_def_277, type, sK68: $i > $i > $o).
% 155.03/24.02 thf(func_def_279, type, sK70: $i > $i).
% 155.03/24.02 thf(func_def_280, type, sK71: $i > $i).
% 155.03/24.02 thf(func_def_281, type, sK72: $i > ($i > $i > $o) > $i).
% 155.03/24.02 thf(func_def_282, type, sK73: $i > $i > ($i > $i > $o) > $i).
% 155.03/24.02 thf(func_def_283, type, sK74: $i > ($i > $i > $o) > $i).
% 155.03/24.02 thf(func_def_292, type, sK83: $i > $i).
% 155.03/24.02 thf(func_def_308, type, sK99: $i > $o).
% 155.03/24.02 thf(func_def_311, type, sK102: $i > ($i > $o) > $i).
% 155.03/24.02 thf(func_def_312, type, sK103: $i > ($i > $o) > $i).
% 155.03/24.02 thf(func_def_321, type, sK112: ($i > $o) > $i).
% 155.03/24.02 thf(func_def_322, type, sK113: $i > $o).
% 155.03/24.02 thf(func_def_323, type, sK114: $i > $i).
% 155.03/24.02 thf(func_def_328, type, sK119: $i > $o).
% 155.03/24.02 thf(func_def_331, type, sK122: $i > ($i > $o) > $i).
% 155.03/24.02 thf(func_def_334, type, sK125: $i > $o).
% 155.03/24.02 thf(func_def_337, type, sK128: $i > ($i > $o) > $i).
% 155.03/24.02 thf(func_def_345, type, sK136: $i > $i > $i).
% 155.03/24.02 thf(func_def_349, type, sK140: $i > $i).
% 155.03/24.02 thf(func_def_366, type, sK157: $i > ($i > $o) > $i).
% 155.03/24.02 thf(func_def_367, type, sK158: $i > $o).
% 155.03/24.02 thf(func_def_370, type, sK161: ($i > $o) > $i > $i).
% 155.03/24.02 thf(func_def_372, type, sK163: $i > $o).
% 155.03/24.02 thf(func_def_376, type, sK167: $i > $o).
% 155.03/24.02 thf(func_def_377, type, sK168: ($i > $o) > $i > $i > $i).
% 155.03/24.02 thf(func_def_380, type, sK171: $i > $o).
% 155.03/24.02 thf(func_def_384, type, sK175: $i > $o).
% 155.03/24.02 thf(func_def_389, type, sK180: $i > $o).
% 155.03/24.02 thf(func_def_391, type, sK182: $i > ($i > $o) > $i).
% 155.03/24.02 thf(func_def_405, type, sK196: $i > $o).
% 155.03/24.02 thf(func_def_411, type, sK202: $i > $o).
% 155.03/24.02 thf(func_def_412, type, sK203: $i > $o).
% 155.03/24.02 thf(func_def_413, type, sK204: ($i > $o) > ($i > $o) > $i).
% 155.03/24.02 thf(func_def_414, type, sK205: ($i > $o) > ($i > $o) > $i).
% 155.03/24.02 thf(func_def_417, type, sK208: ($i > $o) > $i).
% 155.03/24.02 thf(func_def_418, type, sK209: $i > $o).
% 155.03/24.02 thf(func_def_419, type, sK210: $i > $o).
% 155.03/24.02 thf(func_def_424, type, sK215: $i > $o).
% 155.03/24.02 thf(func_def_426, type, sK217: ($i > $o) > $i).
% 155.03/24.02 thf(func_def_427, type, sK218: ($i > $o) > $i).
% 155.03/24.02 thf(func_def_443, type, sK234: $i > $o).
% 155.03/24.02 thf(func_def_446, type, sK237: $i > $o).
% 155.03/24.02 thf(func_def_451, type, sK242: $i > $o).
% 155.03/24.02 thf(func_def_452, type, sK243: $i > $o).
% 155.03/24.02 thf(func_def_453, type, sK244: ($i > $o) > ($i > $o) > $i).
% 155.03/24.02 thf(func_def_454, type, sK245: ($i > $o) > ($i > $o) > $i).
% 155.03/24.02 thf(func_def_458, type, sK249: $i > $o).
% 155.03/24.02 thf(func_def_461, type, sK252: $i > ($i > $o) > $i).
% 155.03/24.02 thf(func_def_471, type, sK262: $i > ($i > $o) > $i).
% 155.03/24.02 thf(func_def_472, type, sK263: $i > $o).
% 155.03/24.02 thf(func_def_475, type, sK266: $i > $i).
% 155.03/24.02 thf(func_def_477, type, sK268: $i > $i).
% 155.03/24.02 thf(func_def_481, type, sK272: $i > $i).
% 155.03/24.02 thf(func_def_492, type, sK283: $i > $o).
% 155.03/24.02 thf(func_def_493, type, sK284: $i > $i).
% 155.03/24.02 thf(func_def_494, type, sK285: ($i > $o) > $i).
% 155.03/24.02 thf(func_def_497, type, sK288: $i > $i > $i).
% 155.03/24.02 thf(func_def_502, type, sK293: $i > $i).
% 155.03/24.02 thf(func_def_505, type, sK296: $i > $i > $i).
% 155.03/24.02 thf(func_def_510, type, sK301: $i > $o).
% 155.03/24.02 thf(func_def_513, type, sK304: $o > $i > $i > $i).
% 155.03/24.02 thf(func_def_520, type, sK311: $i > $i > $i).
% 155.03/24.02 thf(func_def_535, type, sK326: $i > $o).
% 155.03/24.02 thf(func_def_543, type, sK334: $i > $o).
% 155.03/24.02 thf(func_def_544, type, sK335: $i > $o).
% 155.03/24.02 thf(func_def_546, type, sK337: $i > ($i > $o) > $i).
% 155.03/24.02 thf(func_def_553, type, sK344: $i > $o).
% 155.03/24.02 thf(func_def_556, type, sK347: $i > $o).
% 155.03/24.02 thf(func_def_561, type, sK352: $i > $i > $i).
% 155.03/24.02 thf(func_def_576, type, sK367: $i > $o).
% 155.03/24.02 thf(func_def_579, type, sK370: $i > ($i > $o) > $i).
% 155.03/24.02 thf(func_def_580, type, sK371: $i > ($i > $o) > $i).
% 155.03/24.02 thf(func_def_588, type, sK379: $i > $i > $i).
% 155.03/24.02 thf(func_def_591, type, sK382: $i > $i > $i > $i).
% 155.03/24.02 thf(func_def_592, type, sK383: $i > $i > $i > $i).
% 155.03/24.02 thf(func_def_599, type, sK390: $i > $i > $i).
% 155.03/24.02 thf(func_def_600, type, sK391: $i > $i > $i).
% 155.03/24.02 thf(func_def_601, type, sK392: $i > $i > $i).
% 155.03/24.02 thf(func_def_602, type, sK393: $i > $i > $i).
% 155.03/24.02 thf(func_def_603, type, sK394: $i > $i > $i).
% 155.03/24.02 thf(func_def_604, type, sK395: $i > $i > $i > $i).
% 155.03/24.02 thf(func_def_605, type, sK396: $i > $i).
% 155.03/24.02 thf(func_def_606, type, sK397: $i > $i).
% 155.03/24.02 thf(func_def_607, type, sK398: $i > $i).
% 155.03/24.02 thf(func_def_608, type, sK399: $i > $i).
% 155.03/24.02 thf(func_def_609, type, sK400: $i > $i > $i > $i).
% 155.03/24.02 thf(func_def_610, type, sK401: $i > $i > $i > $i).
% 155.03/24.02 thf(func_def_611, type, sK402: $i > $i > $i).
% 155.03/24.02 thf(func_def_612, type, sK403: $i > $i > $i).
% 155.03/24.02 thf(func_def_613, type, sK404: $i > $i > $i).
% 155.03/24.02 thf(func_def_614, type, sK405: $i > $i).
% 155.03/24.02 thf(func_def_616, type, sK407: $i > $i).
% 155.03/24.02 thf(func_def_617, type, sK408: $i > $i).
% 155.03/24.02 thf(func_def_624, type, sK415: $i > $o).
% 155.03/24.02 thf(func_def_663, type, sK454: $i > $i > $i).
% 155.03/24.02 thf(func_def_664, type, sK455: $i > ($i > $o) > $i).
% 155.03/24.02 thf(func_def_665, type, sK456: $i > $o).
% 155.03/24.02 thf(func_def_671, type, sF462: $i > $i).
% 155.03/24.02 thf(func_def_672, type, sF463: $i > $i).
% 155.03/24.02 thf(func_def_677, type, ph468: !>[X0: $tType]:(X0)).
% 155.03/24.02 thf(f19887,plain,(
% 155.03/24.02 $false),
% 155.03/24.02 inference(avatar_sat_refutation,[status(thm)],[f2603,f3149,f4255,f4559,f4590,f5104,f5313,f5535,f5743,f5879,f5965,f19873])).
% 155.03/24.02 thf(f19873,plain,(
% 155.03/24.02 ~spl467_10 | ~spl467_157 | ~spl467_173 | ~spl467_402 | ~spl467_664 | ~spl467_708),
% 155.03/24.02 inference(avatar_contradiction_clause,[status(thm)],[f19872])).
% 155.03/24.02 thf(f19872,plain,(
% 155.03/24.02 $false | (~spl467_10 | ~spl467_157 | ~spl467_173 | ~spl467_402 | ~spl467_664 | ~spl467_708)),
% 155.03/24.02 inference(trivial_inequality_removal,[status(thm)],[f19851])).
% 155.03/24.02 thf(f19851,plain,(
% 155.03/24.02 ($true != $true) | (~spl467_10 | ~spl467_157 | ~spl467_173 | ~spl467_402 | ~spl467_664 | ~spl467_708)),
% 155.03/24.02 inference(superposition,[status(thm)],[f7706,f19499])).
% 155.03/24.02 thf(f19499,plain,(
% 155.03/24.02 ( ! [X0 : $i] : (((subset @ sF465 @ (setadjoin @ sK356 @ X0)) = $true)) ) | (~spl467_10 | ~spl467_173 | ~spl467_664 | ~spl467_708)),
% 155.03/24.02 inference(trivial_inequality_removal,[status(thm)],[f19481])).
% 155.03/24.02 thf(f19481,plain,(
% 155.03/24.02 ( ! [X0 : $i] : (((subset @ sF465 @ (setadjoin @ sK356 @ X0)) = $true) | ($true != $true)) ) | (~spl467_10 | ~spl467_173 | ~spl467_664 | ~spl467_708)),
% 155.03/24.02 inference(superposition,[status(thm)],[f18760,f2507])).
% 155.03/24.02 thf(f2507,plain,(
% 155.03/24.02 ( ! [X2 : $i,X0 : $i] : (((in @ X2 @ (setadjoin @ X2 @ X0)) = $true)) ) | ~spl467_10),
% 155.03/24.02 inference(avatar_component_clause,[status(thm)],[f2506])).
% 155.03/24.02 thf(f2506,definition,(
% 155.03/24.02 spl467_10 <=> ! [X2 : $i,X0 : $i] : ((in @ X2 @ (setadjoin @ X2 @ X0)) = $true)),
% 155.03/24.02 introduced(definition,[new_symbols(naming,[spl467_10])],[avatar_definition])).
% 155.03/24.02 thf(f18760,plain,(
% 155.03/24.02 ( ! [X0 : $i] : (($true != (in @ sK356 @ X0)) | ((subset @ sF465 @ X0) = $true)) ) | (~spl467_173 | ~spl467_664 | ~spl467_708)),
% 155.03/24.02 inference(duplicate_literal_removal,[status(thm)],[f18759])).
% 155.03/24.02 thf(f18759,plain,(
% 155.03/24.02 ( ! [X0 : $i] : (($true != (in @ sK356 @ X0)) | ((subset @ sF465 @ X0) = $true) | ((subset @ sF465 @ X0) = $true)) ) | (~spl467_173 | ~spl467_664 | ~spl467_708)),
% 155.03/24.02 inference(superposition,[status(thm)],[f5534,f16182])).
% 155.03/24.02 thf(f16182,plain,(
% 155.03/24.02 ( ! [X0 : $i] : (((sK45 @ X0 @ sF465) = sK356) | ((subset @ sF465 @ X0) = $true)) ) | (~spl467_173 | ~spl467_708)),
% 155.03/24.02 inference(trivial_inequality_removal,[status(thm)],[f16181])).
% 155.03/24.02 thf(f16181,plain,(
% 155.03/24.02 ( ! [X0 : $i] : (($true != $true) | ((subset @ sF465 @ X0) = $true) | ((sK45 @ X0 @ sF465) = sK356)) ) | (~spl467_173 | ~spl467_708)),
% 155.03/24.02 inference(superposition,[status(thm)],[f16164,f5742])).
% 155.03/24.02 thf(f5742,plain,(
% 155.03/24.02 ( ! [X3 : $i,X4 : $i] : (((in @ (sK45 @ X4 @ X3) @ X3) = $true) | ((subset @ X3 @ X4) = $true)) ) | ~spl467_708),
% 155.03/24.02 inference(avatar_component_clause,[status(thm)],[f5741])).
% 155.03/24.02 thf(f5741,definition,(
% 155.03/24.02 spl467_708 <=> ! [X4 : $i,X3 : $i] : (((in @ (sK45 @ X4 @ X3) @ X3) = $true) | ((subset @ X3 @ X4) = $true))),
% 155.03/24.02 introduced(definition,[new_symbols(naming,[spl467_708])],[avatar_definition])).
% 155.03/24.02 thf(f16164,plain,(
% 155.03/24.02 ( ! [X0 : $i] : (((in @ X0 @ sF465) != $true) | (sK356 = X0)) ) | ~spl467_173),
% 155.03/24.02 inference(duplicate_literal_removal,[status(thm)],[f16155])).
% 155.03/24.02 thf(f16155,plain,(
% 155.03/24.02 ( ! [X0 : $i] : ((sK356 = X0) | (sK356 = X0) | ((in @ X0 @ sF465) != $true)) ) | ~spl467_173),
% 155.03/24.02 inference(superposition,[status(thm)],[f3218,f6020])).
% 155.03/24.02 thf(f6020,plain,(
% 155.03/24.02 ((setadjoin @ sK356 @ (setadjoin @ sK356 @ emptyset)) = sF465)),
% 155.03/24.02 inference(superposition,[status(thm)],[f6000,f6004])).
% 155.03/24.02 thf(f6004,plain,(
% 155.03/24.02 ((sF462 @ (setadjoin @ sK356 @ emptyset)) = sF465)),
% 155.03/24.02 inference(backward_demodulation,[status(thm)],[f2346,f6003])).
% 155.03/24.02 thf(f6003,plain,(
% 155.03/24.02 (sF464 = (setadjoin @ sK356 @ emptyset))),
% 155.03/24.02 inference(backward_demodulation,[status(thm)],[f2345,f6002])).
% 155.03/24.02 thf(f6002,plain,(
% 155.03/24.02 ( ! [X1 : $i] : (((sF463 @ X1) = (setadjoin @ sK356 @ X1))) )),
% 155.03/24.02 inference(argument_congruence,[status(thm)],[f6001])).
% 155.03/24.02 thf(f6001,plain,(
% 155.03/24.02 (sF463 = (setadjoin @ sK356))),
% 155.03/24.02 inference(forward_demodulation,[status(thm)],[f2344,f2020])).
% 155.03/24.02 thf(f2020,plain,(
% 155.03/24.02 (sK357 = sK356)),
% 155.03/24.02 inference(cnf_transformation,[status(thm)],[f1321])).
% 155.03/24.02 thf(f1321,plain,(
% 155.03/24.02 (emptyinPowerset = $true) & (upairsubunion = $true) & (nonemptyE1 = $true) & (wellorderingAx = $true) & (subset2powerset = $true) & (setukpairIR = $true) & (exuE1 = $true) & (exuI2 = $true) & (ex1E1 = $true) & (binintersectEL = $true) & (exuEu = $true) & (inPowerset = $true) & (exu__Cong = $true) & (emptysetE = $true) & (cartprodfstin = $true) & (upairsetIR = $true) & (setminusER = $true) & (dsetconstrEL = $true) & (binintersectSubset5 = $true) & (setadjoinE = $true) & (dsetconstrI = $true) & (ubforcartprodlem3 = $true) & (theprop = $true) & (setminusLsub = $true) & (powersetI1 = $true) & (singletoninpowunion = $true) & (binintersectI = $true) & (symdiffI1 = $true) & (subsetE = $true) & (kpairp = $true) & (foundationAx = $true) & (subsetI2 = $true) & (descrp = $true) & (setunionsingleton1 = $true) & (setadjoinIR = $true) & (emptyInPowerset = $true) & (setunion__Cong = $true) & (omega0Ax = $true) & (powersetAx = $true) & (setadjoinAx = $true) & (powersetE = $true) & (powersetI = $true) & (uniqinunit = $true) & (emptysetimpfalse = $true) & (binunionIL = $true) & (vacuousDall = $true) & (prop2set2propI = $true) & (emptyinunitempty = $true) & (quantDeMorgan2 = $true) & (sepInPowerset = $true) & (setunionsingleton2 = $true) & (emptyE1 = $true) & (symdiffI2 = $true) & (powerset__Cong = $true) & (setunionAx = $true) & (exuE3e = $true) & (setminusILneg = $true) & (setextAx = $true) & (singletonsubset = $true) & (singletonsswitch = $true) & (noeltsimpempty = $true) & (binintersectSubset2 = $true) & (descr__Cong = $true) & (disjointsetsI1 = $true) & (notinsingleton = $true) & (subsetI1 = $true) & (emptyI = $true) & (exuI3 = $true) & (singletonsuniq = $true) & (ex1I2 = $true) & (prop2setI = $true) & (cartprodmempair = $true) & (setunionE2 = $true) & (nonemptyI1 = $true) & (powersetE1 = $true) & (binintersectRsub = $true) & (upairsetE = $true) & (upairset2IR = $true) & (omega__Cong = $true) & (setunionI = $true) & (exuE2 = $true) & (binintersectSubset1 = $true) & (in__Cong = $true) & (emptysetAx = $true) & (setminusELneg = $true) & (kfstsingleton = $true) & (quantDeMorgan1 = $true) & (setext = $true) & (setadjoin__Cong = $true) & (cartprodmempair1 = $true) & (notequalI2 = $true) & (setukpairinjL = $true) & (setadjoinSub2 = $true) & (secondinupair = $true) & (replAx = $true) & (sepSubset = $true) & (singletonprop = $true) & (notsubsetI = $true) & (setukpairIL = $true) & (setadjoinIL = $true) & (ex1I = $true) & (eqinunit = $true) & (cartprodpairin = $true) & (setminusI = $true) & (setunionsingleton = $true) & (prop2setE = $true) & (kfstpairEq = $true) & (setukpairinjL2 = $true) & (ubforcartprodlem2 = $true) & (upairinpowunion = $true) & (nonemptyImpWitness = $true) & (symdiffE = $true) & (binunionE = $true) & (quantDeMorgan3 = $true) & (notequalI1 = $true) & (ubforcartprodlem1 = $true) & (emptysetsubset = $true) & (emptyset__Cong = $true) & (binintersectSubset4 = $true) & (eqimpsubset1 = $true) & (symdiffIneg2 = $true) & (omegaSAx = $true) & (exuI1 = $true) & (setminusSubset1 = $true) & (powersetsubset = $true) & (setukpairinjL1 = $true) & (upairset2E = $true) & (binintersectSubset3 = $true) & (exuE3u = $true) & (dsetconstrER = $true) & (quantDeMorgan4 = $true) & (setextsub = $true) & (setminusEL = $true) & (symdiffIneg1 = $true) & (notdexE = $true) & (subsetE2 = $true) & (subsetRefl = $true) & (setminusERneg = $true) & (subsetemptysetimpeq = $true) & (bs114d = $true) & (((setadjoin @ sK356 @ (setadjoin @ sK357 @ emptyset)) != (setadjoin @ sK356 @ emptyset)) & (sK357 = sK356)) & (notinemptyset = $true) & (upairsetIL = $true) & (singletoninpowerset = $true) & (setoftrueEq = $true) & (setbeta = $true) & (setminusIRneg = $true) & (nonemptyI = $true) & (binunionRsub = $true) & (setminusSubset2 = $true) & (notdallE = $true) & (omegaIndAx = $true) & (setadjoinSub = $true) & (kpairiskpair = $true) & (subsetTrans = $true) & (binunionLsub = $true) & (binintersectLsub = $true) & (setadjoinOr = $true) & (dsetconstr__Cong = $true) & (eqimpsubset2 = $true) & (binunionEcases = $true) & (binintersectER = $true) & (inCongP = $true) & (subPowSU = $true) & (binunionIR = $true) & (setunionE = $true)),
% 155.03/24.02 inference(skolemisation,[status(esa),new_symbols(skolem,[sK356,sK357])],[f589,f1320])).
% 155.03/24.02 thf(f1320,plain,(
% 155.03/24.02 ? [X0 : $i,X1 : $i] : (((setadjoin @ X0 @ emptyset) != (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) & (X0 = X1)) => (((setadjoin @ sK356 @ (setadjoin @ sK357 @ emptyset)) != (setadjoin @ sK356 @ emptyset)) & (sK357 = sK356))),
% 155.03/24.02 introduced(definition,[],[choice_axiom])).
% 155.03/24.02 thf(f589,plain,(
% 155.03/24.02 (emptyinPowerset = $true) & (upairsubunion = $true) & (nonemptyE1 = $true) & (wellorderingAx = $true) & (subset2powerset = $true) & (setukpairIR = $true) & (exuE1 = $true) & (exuI2 = $true) & (ex1E1 = $true) & (binintersectEL = $true) & (exuEu = $true) & (inPowerset = $true) & (exu__Cong = $true) & (emptysetE = $true) & (cartprodfstin = $true) & (upairsetIR = $true) & (setminusER = $true) & (dsetconstrEL = $true) & (binintersectSubset5 = $true) & (setadjoinE = $true) & (dsetconstrI = $true) & (ubforcartprodlem3 = $true) & (theprop = $true) & (setminusLsub = $true) & (powersetI1 = $true) & (singletoninpowunion = $true) & (binintersectI = $true) & (symdiffI1 = $true) & (subsetE = $true) & (kpairp = $true) & (foundationAx = $true) & (subsetI2 = $true) & (descrp = $true) & (setunionsingleton1 = $true) & (setadjoinIR = $true) & (emptyInPowerset = $true) & (setunion__Cong = $true) & (omega0Ax = $true) & (powersetAx = $true) & (setadjoinAx = $true) & (powersetE = $true) & (powersetI = $true) & (uniqinunit = $true) & (emptysetimpfalse = $true) & (binunionIL = $true) & (vacuousDall = $true) & (prop2set2propI = $true) & (emptyinunitempty = $true) & (quantDeMorgan2 = $true) & (sepInPowerset = $true) & (setunionsingleton2 = $true) & (emptyE1 = $true) & (symdiffI2 = $true) & (powerset__Cong = $true) & (setunionAx = $true) & (exuE3e = $true) & (setminusILneg = $true) & (setextAx = $true) & (singletonsubset = $true) & (singletonsswitch = $true) & (noeltsimpempty = $true) & (binintersectSubset2 = $true) & (descr__Cong = $true) & (disjointsetsI1 = $true) & (notinsingleton = $true) & (subsetI1 = $true) & (emptyI = $true) & (exuI3 = $true) & (singletonsuniq = $true) & (ex1I2 = $true) & (prop2setI = $true) & (cartprodmempair = $true) & (setunionE2 = $true) & (nonemptyI1 = $true) & (powersetE1 = $true) & (binintersectRsub = $true) & (upairsetE = $true) & (upairset2IR = $true) & (omega__Cong = $true) & (setunionI = $true) & (exuE2 = $true) & (binintersectSubset1 = $true) & (in__Cong = $true) & (emptysetAx = $true) & (setminusELneg = $true) & (kfstsingleton = $true) & (quantDeMorgan1 = $true) & (setext = $true) & (setadjoin__Cong = $true) & (cartprodmempair1 = $true) & (notequalI2 = $true) & (setukpairinjL = $true) & (setadjoinSub2 = $true) & (secondinupair = $true) & (replAx = $true) & (sepSubset = $true) & (singletonprop = $true) & (notsubsetI = $true) & (setukpairIL = $true) & (setadjoinIL = $true) & (ex1I = $true) & (eqinunit = $true) & (cartprodpairin = $true) & (setminusI = $true) & (setunionsingleton = $true) & (prop2setE = $true) & (kfstpairEq = $true) & (setukpairinjL2 = $true) & (ubforcartprodlem2 = $true) & (upairinpowunion = $true) & (nonemptyImpWitness = $true) & (symdiffE = $true) & (binunionE = $true) & (quantDeMorgan3 = $true) & (notequalI1 = $true) & (ubforcartprodlem1 = $true) & (emptysetsubset = $true) & (emptyset__Cong = $true) & (binintersectSubset4 = $true) & (eqimpsubset1 = $true) & (symdiffIneg2 = $true) & (omegaSAx = $true) & (exuI1 = $true) & (setminusSubset1 = $true) & (powersetsubset = $true) & (setukpairinjL1 = $true) & (upairset2E = $true) & (binintersectSubset3 = $true) & (exuE3u = $true) & (dsetconstrER = $true) & (quantDeMorgan4 = $true) & (setextsub = $true) & (setminusEL = $true) & (symdiffIneg1 = $true) & (notdexE = $true) & (subsetE2 = $true) & (subsetRefl = $true) & (setminusERneg = $true) & (subsetemptysetimpeq = $true) & (bs114d = $true) & ? [X0 : $i,X1 : $i] : (((setadjoin @ X0 @ emptyset) != (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) & (X0 = X1)) & (notinemptyset = $true) & (upairsetIL = $true) & (singletoninpowerset = $true) & (setoftrueEq = $true) & (setbeta = $true) & (setminusIRneg = $true) & (nonemptyI = $true) & (binunionRsub = $true) & (setminusSubset2 = $true) & (notdallE = $true) & (omegaIndAx = $true) & (setadjoinSub = $true) & (kpairiskpair = $true) & (subsetTrans = $true) & (binunionLsub = $true) & (binintersectLsub = $true) & (setadjoinOr = $true) & (dsetconstr__Cong = $true) & (eqimpsubset2 = $true) & (binunionEcases = $true) & (binintersectER = $true) & (inCongP = $true) & (subPowSU = $true) & (binunionIR = $true) & (setunionE = $true)),
% 155.03/24.02 inference(flattening,[status(thm)],[f588])).
% 155.03/24.02 thf(f588,plain,(
% 155.03/24.02 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : (((setadjoin @ X0 @ emptyset) != (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) & (X0 = X1)) & (setukpairinjL = $true)) & (setukpairinjL2 = $true)) & (cartprodfstin = $true)) & (kfstpairEq = $true)) & (theprop = $true)) & (kfstsingleton = $true)) & (setukpairinjL1 = $true)) & (singletonsuniq = $true)) & (ex1I2 = $true)) & (ex1I = $true)) & (ex1E1 = $true)) & (singletonprop = $true)) & (setunionsingleton = $true)) & (setunionsingleton2 = $true)) & (setunionsingleton1 = $true)) & (setunionE2 = $true)) & (cartprodmempair = $true)) & (cartprodmempair1 = $true)) & (cartprodpairin = $true)) & (ubforcartprodlem3 = $true)) & (ubforcartprodlem2 = $true)) & (ubforcartprodlem1 = $true)) & (upairinpowunion = $true)) & (upairsubunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (singletoninpowerset = $true)) & (singletonsubset = $true)) & (kpairp = $true)) & (kpairiskpair = $true)) & (setukpairIR = $true)) & (setukpairIL = $true)) & (secondinupair = $true)) & (symdiffIneg2 = $true)) & (symdiffIneg1 = $true)) & (symdiffI2 = $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 155.03/24.02 inference(ennf_transformation,[status(thm)],[f253])).
% 155.03/24.02 thf(f253,plain,(
% 155.03/24.02 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ((ubforcartprodlem1 = $true) => ((ubforcartprodlem2 = $true) => ((ubforcartprodlem3 = $true) => ((cartprodpairin = $true) => ((cartprodmempair1 = $true) => ((cartprodmempair = $true) => ((setunionE2 = $true) => ((setunionsingleton1 = $true) => ((setunionsingleton2 = $true) => ((setunionsingleton = $true) => ((singletonprop = $true) => ((ex1E1 = $true) => ((ex1I = $true) => ((ex1I2 = $true) => ((singletonsuniq = $true) => ((setukpairinjL1 = $true) => ((kfstsingleton = $true) => ((theprop = $true) => ((kfstpairEq = $true) => ((cartprodfstin = $true) => ((setukpairinjL2 = $true) => ((setukpairinjL = $true) => ! [X0 : $i,X1 : $i] : ((X0 = X1) => ((setadjoin @ X0 @ emptyset) = (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 155.03/24.02 inference(fool_elimination,[status(thm)],[f252])).
% 155.03/24.02 thf(f252,plain,(
% 155.03/24.02 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => ! [X0 : $i,X1 : $i] : ((X0 = X1) => ((setadjoin @ X0 @ emptyset) = (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 155.03/24.02 inference(rectify,[status(thm)],[f173])).
% 155.03/24.02 thf(f173,negated_conjecture,(
% 155.03/24.02 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => ! [X1 : $i,X2 : $i] : ((X1 = X2) => ((setadjoin @ X1 @ emptyset) = (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 155.03/24.02 inference(negated_conjecture,[status(cth)],[f172])).
% 155.03/24.02 thf(f172,conjecture,(
% 155.03/24.02 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => ! [X1 : $i,X2 : $i] : ((X1 = X2) => ((setadjoin @ X1 @ emptyset) = (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 155.03/24.02 file('/export/starexec/sandbox/tmp/tmp.u7Pd4WLIgv/DTF2THF_23265.p',setukpairinjR11)).
% 155.03/24.02 thf(f2344,definition,(
% 155.03/24.02 ((setadjoin @ sK357) = sF463)),
% 155.03/24.02 introduced(definition,[],[function_definition])).
% 155.03/24.02 thf(f2345,definition,(
% 155.03/24.02 ((sF463 @ emptyset) = sF464)),
% 155.03/24.02 introduced(definition,[],[function_definition])).
% 155.03/24.02 thf(f2346,definition,(
% 155.03/24.02 ((sF462 @ sF464) = sF465)),
% 155.03/24.02 introduced(definition,[],[function_definition])).
% 155.03/24.02 thf(f6000,plain,(
% 155.03/24.02 ( ! [X1 : $i] : (((sF462 @ X1) = (setadjoin @ sK356 @ X1))) )),
% 155.03/24.02 inference(argument_congruence,[status(thm)],[f2343])).
% 155.03/24.02 thf(f2343,definition,(
% 155.03/24.02 (sF462 = (setadjoin @ sK356))),
% 155.03/24.02 introduced(definition,[],[function_definition])).
% 155.03/24.02 thf(f3218,plain,(
% 155.03/24.02 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X4 @ (setadjoin @ X5 @ (setadjoin @ X3 @ emptyset)))) | (X4 = X5) | (X3 = X4)) ) | ~spl467_173),
% 155.03/24.02 inference(avatar_component_clause,[status(thm)],[f3217])).
% 155.03/24.02 thf(f3217,definition,(
% 155.03/24.02 spl467_173 <=> ! [X4 : $i,X5 : $i,X3 : $i] : ((X3 = X4) | (X4 = X5) | ($true != (in @ X4 @ (setadjoin @ X5 @ (setadjoin @ X3 @ emptyset)))))),
% 155.03/24.02 introduced(definition,[new_symbols(naming,[spl467_173])],[avatar_definition])).
% 155.03/24.02 thf(f5534,plain,(
% 155.03/24.02 ( ! [X3 : $i,X4 : $i] : (($true != (in @ (sK45 @ X4 @ X3) @ X4)) | ((subset @ X3 @ X4) = $true)) ) | ~spl467_664),
% 155.03/24.02 inference(avatar_component_clause,[status(thm)],[f5533])).
% 155.03/24.02 thf(f5533,definition,(
% 155.03/24.02 spl467_664 <=> ! [X4 : $i,X3 : $i] : (($true != (in @ (sK45 @ X4 @ X3) @ X4)) | ((subset @ X3 @ X4) = $true))),
% 155.03/24.02 introduced(definition,[new_symbols(naming,[spl467_664])],[avatar_definition])).
% 155.03/24.02 thf(f7706,plain,(
% 155.03/24.02 ((subset @ sF465 @ (setadjoin @ sK356 @ emptyset)) != $true) | (~spl467_157 | ~spl467_402)),
% 155.03/24.02 inference(subsumption_resolution,[status(thm)],[f7698,f6022])).
% 155.03/24.02 thf(f6022,plain,(
% 155.03/24.02 (sF465 != (setadjoin @ sK356 @ emptyset))),
% 155.03/24.02 inference(backward_demodulation,[status(thm)],[f2348,f6019])).
% 155.03/24.02 thf(f6019,plain,(
% 155.03/24.02 (sF466 = (setadjoin @ sK356 @ emptyset))),
% 155.03/24.02 inference(backward_demodulation,[status(thm)],[f2347,f6000])).
% 155.03/24.02 thf(f2347,definition,(
% 155.03/24.02 ((sF462 @ emptyset) = sF466)),
% 155.03/24.02 introduced(definition,[],[function_definition])).
% 155.03/24.02 thf(f2348,plain,(
% 155.03/24.02 (sF466 != sF465)),
% 155.03/24.02 inference(definition_folding,[status(thm)],[f2021,f2347,f2343,f2346,f2345,f2344,f2343])).
% 155.03/24.02 thf(f2021,plain,(
% 155.03/24.02 ((setadjoin @ sK356 @ (setadjoin @ sK357 @ emptyset)) != (setadjoin @ sK356 @ emptyset))),
% 155.03/24.02 inference(cnf_transformation,[status(thm)],[f1321])).
% 155.03/24.02 thf(f7698,plain,(
% 155.03/24.02 (sF465 = (setadjoin @ sK356 @ emptyset)) | ((subset @ sF465 @ (setadjoin @ sK356 @ emptyset)) != $true) | (~spl467_157 | ~spl467_402)),
% 155.03/24.02 inference(trivial_inequality_removal,[status(thm)],[f7696])).
% 155.03/24.02 thf(f7696,plain,(
% 155.03/24.02 (sF465 = (setadjoin @ sK356 @ emptyset)) | ((subset @ sF465 @ (setadjoin @ sK356 @ emptyset)) != $true) | ($true != $true) | (~spl467_157 | ~spl467_402)),
% 155.03/24.02 inference(superposition,[status(thm)],[f4254,f6068])).
% 155.03/24.02 thf(f6068,plain,(
% 155.03/24.02 ((subset @ (setadjoin @ sK356 @ emptyset) @ sF465) = $true) | ~spl467_157),
% 155.03/24.02 inference(superposition,[status(thm)],[f3148,f6020])).
% 155.03/24.02 thf(f3148,plain,(
% 155.03/24.02 ( ! [X0 : $i,X1 : $i] : (((subset @ X1 @ (setadjoin @ X0 @ X1)) = $true)) ) | ~spl467_157),
% 155.03/24.02 inference(avatar_component_clause,[status(thm)],[f3147])).
% 155.03/24.02 thf(f3147,definition,(
% 155.03/24.02 spl467_157 <=> ! [X0 : $i,X1 : $i] : ((subset @ X1 @ (setadjoin @ X0 @ X1)) = $true)),
% 155.03/24.02 introduced(definition,[new_symbols(naming,[spl467_157])],[avatar_definition])).
% 155.03/24.02 thf(f4254,plain,(
% 155.03/24.02 ( ! [X2 : $i,X3 : $i] : (($true != (subset @ X2 @ X3)) | ((subset @ X3 @ X2) != $true) | (X2 = X3)) ) | ~spl467_402),
% 155.03/24.02 inference(avatar_component_clause,[status(thm)],[f4253])).
% 155.03/24.02 thf(f4253,definition,(
% 155.03/24.02 spl467_402 <=> ! [X2 : $i,X3 : $i] : (((subset @ X3 @ X2) != $true) | (X2 = X3) | ($true != (subset @ X2 @ X3)))),
% 155.03/24.02 introduced(definition,[new_symbols(naming,[spl467_402])],[avatar_definition])).
% 155.03/24.02 thf(f5965,plain,(
% 155.03/24.02 spl467_483),
% 155.03/24.02 inference(avatar_split_clause,[status(thm)],[f2096,f4647])).
% 155.03/24.02 thf(f4647,definition,(
% 155.03/24.02 spl467_483 <=> (subsetI1 = $true)),
% 155.03/24.02 introduced(definition,[new_symbols(naming,[spl467_483])],[avatar_definition])).
% 155.03/24.02 thf(f2096,plain,(
% 155.03/24.02 (subsetI1 = $true)),
% 155.03/24.02 inference(cnf_transformation,[status(thm)],[f1321])).
% 155.03/24.02 thf(f5879,plain,(
% 155.03/24.02 spl467_310),
% 155.03/24.02 inference(avatar_split_clause,[status(thm)],[f2035,f3824])).
% 155.03/24.02 thf(f3824,definition,(
% 155.03/24.02 spl467_310 <=> (upairset2E = $true)),
% 155.03/24.02 introduced(definition,[new_symbols(naming,[spl467_310])],[avatar_definition])).
% 155.03/24.02 thf(f2035,plain,(
% 155.03/24.02 (upairset2E = $true)),
% 155.03/24.02 inference(cnf_transformation,[status(thm)],[f1321])).
% 155.03/24.02 thf(f5743,plain,(
% 155.03/24.02 spl467_708 | ~spl467_483),
% 155.03/24.02 inference(avatar_split_clause,[status(thm)],[f1549,f4647,f5741])).
% 155.03/24.02 thf(f1549,plain,(
% 155.03/24.02 ( ! [X3 : $i,X4 : $i] : (((in @ (sK45 @ X4 @ X3) @ X3) = $true) | ((subset @ X3 @ X4) = $true) | (subsetI1 != $true)) )),
% 155.03/24.02 inference(cnf_transformation,[status(thm)],[f801])).
% 155.03/24.02 thf(f801,plain,(
% 155.03/24.02 ((subsetI1 = $true) | (((subset @ sK43 @ sK44) != $true) & ! [X2 : $i] : (($true = (in @ X2 @ sK44)) | ((in @ X2 @ sK43) != $true)))) & (! [X3 : $i,X4 : $i] : (((subset @ X3 @ X4) = $true) | (($true != (in @ (sK45 @ X4 @ X3) @ X4)) & ((in @ (sK45 @ X4 @ X3) @ X3) = $true))) | (subsetI1 != $true))),
% 155.03/24.02 inference(skolemisation,[status(esa),new_symbols(skolem,[sK43,sK44,sK45])],[f798,f800,f799])).
% 155.03/24.02 thf(f799,plain,(
% 155.03/24.02 ? [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) & ! [X2 : $i] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true))) => (((subset @ sK43 @ sK44) != $true) & ! [X2 : $i] : (($true = (in @ X2 @ sK44)) | ((in @ X2 @ sK43) != $true)))),
% 155.03/24.02 introduced(definition,[],[choice_axiom])).
% 155.03/24.02 thf(f800,plain,(
% 155.03/24.02 ! [X3 : $i,X4 : $i] : (? [X5 : $i] : (((in @ X5 @ X4) != $true) & ((in @ X5 @ X3) = $true)) => (($true != (in @ (sK45 @ X4 @ X3) @ X4)) & ((in @ (sK45 @ X4 @ X3) @ X3) = $true)))),
% 155.03/24.02 introduced(definition,[],[choice_axiom])).
% 155.03/24.02 thf(f798,plain,(
% 155.03/24.02 ((subsetI1 = $true) | ? [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) & ! [X2 : $i] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true)))) & (! [X3 : $i,X4 : $i] : (((subset @ X3 @ X4) = $true) | ? [X5 : $i] : (((in @ X5 @ X4) != $true) & ((in @ X5 @ X3) = $true))) | (subsetI1 != $true))),
% 155.03/24.02 inference(rectify,[status(thm)],[f797])).
% 155.03/24.02 thf(f797,plain,(
% 155.03/24.02 ((subsetI1 = $true) | ? [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) & ! [X2 : $i] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true)))) & (! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ? [X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true))) | (subsetI1 != $true))),
% 155.03/24.02 inference(nnf_transformation,[status(thm)],[f650])).
% 155.03/24.02 thf(f650,plain,(
% 155.03/24.02 (subsetI1 = $true) <=> ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ? [X2 : $i] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true)))),
% 155.03/24.02 inference(ennf_transformation,[status(thm)],[f460])).
% 155.03/24.02 thf(f460,plain,(
% 155.03/24.02 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (((in @ X2 @ X0) = $true) => ((in @ X2 @ X1) = $true)) => ((subset @ X0 @ X1) = $true)) <=> (subsetI1 = $true)),
% 155.03/24.02 inference(fool_elimination,[status(thm)],[f459])).
% 155.03/24.02 thf(f459,plain,(
% 155.03/24.02 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI1)),
% 155.03/24.02 inference(rectify,[status(thm)],[f78])).
% 155.03/24.02 thf(f78,axiom,(
% 155.03/24.02 (! [X3 : $i,X4 : $i] : (! [X1 : $i] : ((in @ X1 @ X3) => (in @ X1 @ X4)) => (subset @ X3 @ X4)) = subsetI1)),
% 155.03/24.02 file('/export/starexec/sandbox/tmp/tmp.u7Pd4WLIgv/DTF2THF_23265.p',subsetI1)).
% 155.03/24.02 thf(f5535,plain,(
% 155.03/24.02 ~spl467_483 | spl467_664),
% 155.03/24.02 inference(avatar_split_clause,[status(thm)],[f1550,f5533,f4647])).
% 155.03/24.02 thf(f1550,plain,(
% 155.03/24.02 ( ! [X3 : $i,X4 : $i] : (($true != (in @ (sK45 @ X4 @ X3) @ X4)) | (subsetI1 != $true) | ((subset @ X3 @ X4) = $true)) )),
% 155.03/24.02 inference(cnf_transformation,[status(thm)],[f801])).
% 155.03/24.02 thf(f5313,plain,(
% 155.03/24.02 spl467_156),
% 155.03/24.02 inference(avatar_split_clause,[status(thm)],[f2008,f3143])).
% 155.03/24.02 thf(f3143,definition,(
% 155.03/24.02 spl467_156 <=> (setadjoinSub = $true)),
% 155.03/24.02 introduced(definition,[new_symbols(naming,[spl467_156])],[avatar_definition])).
% 155.03/24.02 thf(f2008,plain,(
% 155.03/24.02 (setadjoinSub = $true)),
% 155.03/24.02 inference(cnf_transformation,[status(thm)],[f1321])).
% 155.03/24.02 thf(f5104,plain,(
% 155.03/24.02 ~spl467_310 | spl467_173),
% 155.03/24.02 inference(avatar_split_clause,[status(thm)],[f1621,f3217,f3824])).
% 155.03/24.02 thf(f1621,plain,(
% 155.03/24.02 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((upairset2E != $true) | (X0 = X2) | (X1 = X2) | ((in @ X2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) != $true)) )),
% 155.03/24.02 inference(cnf_transformation,[status(thm)],[f881])).
% 155.03/24.02 thf(f881,plain,(
% 155.03/24.02 (! [X0 : $i,X1 : $i,X2 : $i] : ((X0 = X2) | ((in @ X2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) != $true) | (X1 = X2)) | (upairset2E != $true)) & ((upairset2E = $true) | ((sK96 != sK98) & ((in @ sK98 @ (setadjoin @ sK96 @ (setadjoin @ sK97 @ emptyset))) = $true) & (sK98 != sK97)))),
% 155.03/24.02 inference(skolemisation,[status(esa),new_symbols(skolem,[sK96,sK97,sK98])],[f879,f880])).
% 155.03/24.02 thf(f880,plain,(
% 155.03/24.02 ? [X3 : $i,X4 : $i,X5 : $i] : ((X3 != X5) & ((in @ X5 @ (setadjoin @ X3 @ (setadjoin @ X4 @ emptyset))) = $true) & (X4 != X5)) => ((sK96 != sK98) & ((in @ sK98 @ (setadjoin @ sK96 @ (setadjoin @ sK97 @ emptyset))) = $true) & (sK98 != sK97))),
% 155.03/24.02 introduced(definition,[],[choice_axiom])).
% 155.03/24.02 thf(f879,plain,(
% 155.03/24.02 (! [X0 : $i,X1 : $i,X2 : $i] : ((X0 = X2) | ((in @ X2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) != $true) | (X1 = X2)) | (upairset2E != $true)) & ((upairset2E = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : ((X3 != X5) & ((in @ X5 @ (setadjoin @ X3 @ (setadjoin @ X4 @ emptyset))) = $true) & (X4 != X5)))),
% 155.03/24.02 inference(rectify,[status(thm)],[f878])).
% 155.03/24.02 thf(f878,plain,(
% 155.03/24.02 (! [X0 : $i,X1 : $i,X2 : $i] : ((X0 = X2) | ((in @ X2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) != $true) | (X1 = X2)) | (upairset2E != $true)) & ((upairset2E = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((X0 != X2) & ((in @ X2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = $true) & (X1 != X2)))),
% 155.03/24.02 inference(nnf_transformation,[status(thm)],[f711])).
% 155.03/24.02 thf(f711,plain,(
% 155.03/24.02 ! [X0 : $i,X1 : $i,X2 : $i] : ((X0 = X2) | ((in @ X2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) != $true) | (X1 = X2)) <=> (upairset2E = $true)),
% 155.03/24.02 inference(flattening,[status(thm)],[f710])).
% 155.03/24.02 thf(f710,plain,(
% 155.03/24.02 ! [X0 : $i,X1 : $i,X2 : $i] : (((X0 = X2) | (X1 = X2)) | ((in @ X2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) != $true)) <=> (upairset2E = $true)),
% 155.03/24.02 inference(ennf_transformation,[status(thm)],[f195])).
% 155.03/24.02 thf(f195,plain,(
% 155.03/24.02 ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = $true) => ((X0 = X2) | (X1 = X2))) <=> (upairset2E = $true)),
% 155.03/24.02 inference(fool_elimination,[status(thm)],[f194])).
% 155.03/24.02 thf(f194,plain,(
% 155.03/24.02 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) => ((X0 = X2) | (X1 = X2))) = upairset2E)),
% 155.03/24.02 inference(rectify,[status(thm)],[f145])).
% 155.03/24.02 thf(f145,axiom,(
% 155.03/24.02 (! [X1 : $i,X2 : $i,X8 : $i] : ((in @ X8 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset))) => ((X1 = X8) | (X2 = X8))) = upairset2E)),
% 155.03/24.02 file('/export/starexec/sandbox/tmp/tmp.u7Pd4WLIgv/DTF2THF_23265.p',upairset2E)).
% 155.03/24.02 thf(f4590,plain,(
% 155.03/24.02 spl467_32),
% 155.03/24.02 inference(avatar_split_clause,[status(thm)],[f2062,f2600])).
% 155.03/24.02 thf(f2600,definition,(
% 155.03/24.02 spl467_32 <=> (setadjoinIL = $true)),
% 155.03/24.02 introduced(definition,[new_symbols(naming,[spl467_32])],[avatar_definition])).
% 155.03/24.02 thf(f2062,plain,(
% 155.03/24.02 (setadjoinIL = $true)),
% 155.03/24.02 inference(cnf_transformation,[status(thm)],[f1321])).
% 155.03/24.02 thf(f4559,plain,(
% 155.03/24.02 spl467_141),
% 155.03/24.02 inference(avatar_split_clause,[status(thm)],[f2030,f3077])).
% 155.03/24.02 thf(f3077,definition,(
% 155.03/24.02 spl467_141 <=> (setextsub = $true)),
% 155.03/24.02 introduced(definition,[new_symbols(naming,[spl467_141])],[avatar_definition])).
% 155.03/24.02 thf(f2030,plain,(
% 155.03/24.02 (setextsub = $true)),
% 155.03/24.02 inference(cnf_transformation,[status(thm)],[f1321])).
% 155.03/24.02 thf(f4255,plain,(
% 155.03/24.02 spl467_402 | ~spl467_141),
% 155.03/24.02 inference(avatar_split_clause,[status(thm)],[f2162,f3077,f4253])).
% 155.03/24.02 thf(f2162,plain,(
% 155.03/24.02 ( ! [X2 : $i,X3 : $i] : (((subset @ X3 @ X2) != $true) | ($true != (subset @ X2 @ X3)) | (X2 = X3) | (setextsub != $true)) )),
% 155.03/24.02 inference(cnf_transformation,[status(thm)],[f1325])).
% 155.03/24.02 thf(f1325,plain,(
% 155.03/24.02 ((setextsub = $true) | (((subset @ sK358 @ sK359) = $true) & ((subset @ sK359 @ sK358) = $true) & (sK358 != sK359))) & (! [X2 : $i,X3 : $i] : (($true != (subset @ X2 @ X3)) | ((subset @ X3 @ X2) != $true) | (X2 = X3)) | (setextsub != $true))),
% 155.03/24.02 inference(skolemisation,[status(esa),new_symbols(skolem,[sK358,sK359])],[f1323,f1324])).
% 155.03/24.02 thf(f1324,plain,(
% 155.03/24.02 ? [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) & ((subset @ X1 @ X0) = $true) & (X0 != X1)) => (((subset @ sK358 @ sK359) = $true) & ((subset @ sK359 @ sK358) = $true) & (sK358 != sK359))),
% 155.03/24.02 introduced(definition,[],[choice_axiom])).
% 155.03/24.02 thf(f1323,plain,(
% 155.03/24.02 ((setextsub = $true) | ? [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) & ((subset @ X1 @ X0) = $true) & (X0 != X1))) & (! [X2 : $i,X3 : $i] : (($true != (subset @ X2 @ X3)) | ((subset @ X3 @ X2) != $true) | (X2 = X3)) | (setextsub != $true))),
% 155.03/24.02 inference(rectify,[status(thm)],[f1322])).
% 155.03/24.02 thf(f1322,plain,(
% 155.03/24.02 ((setextsub = $true) | ? [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) & ((subset @ X1 @ X0) = $true) & (X0 != X1))) & (! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) | ((subset @ X1 @ X0) != $true) | (X0 = X1)) | (setextsub != $true))),
% 155.03/24.02 inference(nnf_transformation,[status(thm)],[f662])).
% 155.03/24.02 thf(f662,plain,(
% 155.03/24.02 (setextsub = $true) <=> ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) | ((subset @ X1 @ X0) != $true) | (X0 = X1))),
% 155.03/24.02 inference(flattening,[status(thm)],[f661])).
% 155.03/24.02 thf(f661,plain,(
% 155.03/24.02 ! [X0 : $i,X1 : $i] : (((X0 = X1) | ((subset @ X1 @ X0) != $true)) | ((subset @ X0 @ X1) != $true)) <=> (setextsub = $true)),
% 155.03/24.02 inference(ennf_transformation,[status(thm)],[f379])).
% 155.03/24.02 thf(f379,plain,(
% 155.03/24.02 ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) => (((subset @ X1 @ X0) = $true) => (X0 = X1))) <=> (setextsub = $true)),
% 155.03/24.02 inference(fool_elimination,[status(thm)],[f378])).
% 155.03/24.02 thf(f378,plain,(
% 155.03/24.02 (setextsub = ! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((subset @ X1 @ X0) => (X0 = X1))))),
% 155.03/24.02 inference(rectify,[status(thm)],[f93])).
% 155.03/24.02 thf(f93,axiom,(
% 155.03/24.02 (setextsub = ! [X3 : $i,X4 : $i] : ((subset @ X3 @ X4) => ((subset @ X4 @ X3) => (X3 = X4))))),
% 155.03/24.02 file('/export/starexec/sandbox/tmp/tmp.u7Pd4WLIgv/DTF2THF_23265.p',setextsub)).
% 155.03/24.02 thf(f3149,plain,(
% 155.03/24.02 ~spl467_156 | spl467_157),
% 155.03/24.02 inference(avatar_split_clause,[status(thm)],[f2171,f3147,f3143])).
% 155.03/24.02 thf(f2171,plain,(
% 155.03/24.02 ( ! [X0 : $i,X1 : $i] : ((setadjoinSub != $true) | ((subset @ X1 @ (setadjoin @ X0 @ X1)) = $true)) )),
% 155.03/24.02 inference(cnf_transformation,[status(thm)],[f1337])).
% 155.03/24.02 thf(f1337,plain,(
% 155.03/24.02 (! [X0 : $i,X1 : $i] : ((subset @ X1 @ (setadjoin @ X0 @ X1)) = $true) | (setadjoinSub != $true)) & ((setadjoinSub = $true) | ((subset @ sK366 @ (setadjoin @ sK365 @ sK366)) != $true))),
% 155.03/24.02 inference(skolemisation,[status(esa),new_symbols(skolem,[sK365,sK366])],[f1335,f1336])).
% 155.03/24.02 thf(f1336,plain,(
% 155.03/24.02 ? [X2 : $i,X3 : $i] : ((subset @ X3 @ (setadjoin @ X2 @ X3)) != $true) => ((subset @ sK366 @ (setadjoin @ sK365 @ sK366)) != $true)),
% 155.03/24.02 introduced(definition,[],[choice_axiom])).
% 155.03/24.02 thf(f1335,plain,(
% 155.03/24.02 (! [X0 : $i,X1 : $i] : ((subset @ X1 @ (setadjoin @ X0 @ X1)) = $true) | (setadjoinSub != $true)) & ((setadjoinSub = $true) | ? [X2 : $i,X3 : $i] : ((subset @ X3 @ (setadjoin @ X2 @ X3)) != $true))),
% 155.03/24.02 inference(rectify,[status(thm)],[f1334])).
% 155.03/24.02 thf(f1334,plain,(
% 155.03/24.02 (! [X0 : $i,X1 : $i] : ((subset @ X1 @ (setadjoin @ X0 @ X1)) = $true) | (setadjoinSub != $true)) & ((setadjoinSub = $true) | ? [X0 : $i,X1 : $i] : ((subset @ X1 @ (setadjoin @ X0 @ X1)) != $true))),
% 155.03/24.02 inference(nnf_transformation,[status(thm)],[f458])).
% 155.03/24.02 thf(f458,plain,(
% 155.03/24.02 ! [X0 : $i,X1 : $i] : ((subset @ X1 @ (setadjoin @ X0 @ X1)) = $true) <=> (setadjoinSub = $true)),
% 155.03/24.02 inference(fool_elimination,[status(thm)],[f457])).
% 155.03/24.02 thf(f457,plain,(
% 155.03/24.02 (! [X0 : $i,X1 : $i] : (subset @ X1 @ (setadjoin @ X0 @ X1)) = setadjoinSub)),
% 155.03/24.02 inference(rectify,[status(thm)],[f90])).
% 155.03/24.02 thf(f90,axiom,(
% 155.03/24.02 (! [X1 : $i,X3 : $i] : (subset @ X3 @ (setadjoin @ X1 @ X3)) = setadjoinSub)),
% 155.03/24.02 file('/export/starexec/sandbox/tmp/tmp.u7Pd4WLIgv/DTF2THF_23265.p',setadjoinSub)).
% 155.03/24.02 thf(f2603,plain,(
% 155.03/24.02 spl467_10 | ~spl467_32),
% 155.03/24.02 inference(avatar_split_clause,[status(thm)],[f1522,f2600,f2506])).
% 155.03/24.02 thf(f1522,plain,(
% 155.03/24.02 ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X0 @ X1)) = $true) | (setadjoinIL != $true)) )),
% 155.03/24.02 inference(cnf_transformation,[status(thm)],[f763])).
% 155.03/24.02 thf(f763,plain,(
% 155.03/24.02 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X0 @ X1)) = $true) | (setadjoinIL != $true)) & ((setadjoinIL = $true) | ((in @ sK21 @ (setadjoin @ sK21 @ sK22)) != $true))),
% 155.03/24.02 inference(skolemisation,[status(esa),new_symbols(skolem,[sK21,sK22])],[f761,f762])).
% 155.03/24.02 thf(f762,plain,(
% 155.03/24.02 ? [X2 : $i,X3 : $i] : ($true != (in @ X2 @ (setadjoin @ X2 @ X3))) => ((in @ sK21 @ (setadjoin @ sK21 @ sK22)) != $true)),
% 155.03/24.02 introduced(definition,[],[choice_axiom])).
% 155.03/24.02 thf(f761,plain,(
% 155.03/24.02 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X0 @ X1)) = $true) | (setadjoinIL != $true)) & ((setadjoinIL = $true) | ? [X2 : $i,X3 : $i] : ($true != (in @ X2 @ (setadjoin @ X2 @ X3))))),
% 155.03/24.02 inference(rectify,[status(thm)],[f760])).
% 155.03/24.02 thf(f760,plain,(
% 155.03/24.02 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X0 @ X1)) = $true) | (setadjoinIL != $true)) & ((setadjoinIL = $true) | ? [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X0 @ X1)) != $true))),
% 155.03/24.02 inference(nnf_transformation,[status(thm)],[f367])).
% 155.03/24.02 thf(f367,plain,(
% 155.03/24.02 ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X0 @ X1)) = $true) <=> (setadjoinIL = $true)),
% 155.03/24.02 inference(fool_elimination,[status(thm)],[f366])).
% 155.03/24.02 thf(f366,plain,(
% 155.03/24.02 (setadjoinIL = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)))),
% 155.03/24.02 inference(rectify,[status(thm)],[f31])).
% 155.03/24.02 thf(f31,axiom,(
% 155.03/24.02 (setadjoinIL = ! [X1 : $i,X2 : $i] : (in @ X1 @ (setadjoin @ X1 @ X2)))),
% 155.03/24.02 file('/export/starexec/sandbox/tmp/tmp.u7Pd4WLIgv/DTF2THF_23265.p',setadjoinIL)).
% 155.03/24.02 % SZS output end Proof for DTF2THF_23265
% 155.03/24.02 % (23885)------------------------------
% 155.03/24.02 % (23885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 155.03/24.02 % (23885)Termination reason: Refutation
% 155.03/24.02
% 155.03/24.02 % (23885)Memory used [KB]: 18166
% 155.03/24.02 % (23885)Time elapsed: 0.985 s
% 155.03/24.02 % (23885)Instructions burned: 3003 (million)
% 155.03/24.02 % (23885)------------------------------
% 155.03/24.02 % (23885)------------------------------
% 155.03/24.02 % (23392)Success in time 22.128 s
%------------------------------------------------------------------------------