%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU803^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n031.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 09:37:20 AM UTC 2026
% Result : Theorem 19.91s 4.04s
% Output : Refutation 19.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 5148 (1366 equ; 0 cnn)
% Maximal formula atoms : 325 ( 151 avg)
% Number of connectives : 2713 ( 31 ~; 19 |; 987 &; 359 @)
% ( 0 <=>;1306 =>; 0 <=; 0 <~>)
% Maximal formula depth : 332 ( 69 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 516 ( 511 usr; 327 con; 0-6 aty)
% ( 4 !!; 7 ??; 0 @@+; 0 @@-)
% Number of variables : 88 ( 28 ^; 44 !; 16 ?; 88 :)
% 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_203,type,
ksnd: $i > $i ).
thf(func_def_213,type,
breln: $i > $i > $i > $o ).
thf(func_def_214,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_222,type,
func: $i > $i > $i > $o ).
thf(func_def_223,type,
funcSet: $i > $i > $i ).
thf(func_def_226,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_232,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(func_def_259,type,
if: $i > $o > $i > $i > $i ).
thf(func_def_323,type,
breln1: $i > $i > $o ).
thf(func_def_325,type,
breln1Set: $i > $i ).
thf(func_def_327,type,
transitive: $i > $i > $o ).
thf(func_def_328,type,
antisymmetric: $i > $i > $o ).
thf(func_def_329,type,
reflexive: $i > $i > $o ).
thf(func_def_330,type,
refltransitive: $i > $i > $o ).
thf(func_def_331,type,
refllinearorder: $i > $i > $o ).
thf(func_def_332,type,
reflwellordering: $i > $i > $o ).
thf(func_def_338,type,
breln1invset: $i > $i > $i ).
thf(func_def_342,type,
breln1compset: $i > $i > $i > $i ).
thf(func_def_360,type,
image1: $i > ( $i > $i ) > $i ).
thf(func_def_364,type,
injective: $i > $i > $i > $o ).
thf(func_def_365,type,
injFuncSet: $i > $i > $i ).
thf(func_def_369,type,
surjective: $i > $i > $i > $o ).
thf(func_def_370,type,
surjFuncSet: $i > $i > $i ).
thf(func_def_393,type,
sK2: $i > $i ).
thf(func_def_396,type,
sK5: $i > $i > ( $i > $o ) > $i > $i ).
thf(func_def_397,type,
sK6: $i > $i > $i > ( $i > $o ) > $i ).
thf(func_def_398,type,
sK7: $i > $i > $i > ( $i > $o ) > $i ).
thf(func_def_399,type,
sK8: $i > $i > $i > ( $i > $o ) > $i ).
thf(func_def_400,type,
sK9: ( $i > $o ) > $i ).
thf(func_def_401,type,
sK10: ( $i > $o ) > $i > $i ).
thf(func_def_402,type,
sK11: $i > $i > $o > $i > $i > $i > $i ).
thf(func_def_403,type,
sK12: ( $i > $o ) > $i > $i ).
thf(func_def_404,type,
sK13: $i > $i > $i > $i > $i ).
thf(func_def_405,type,
sK14: $i > $i > $i ).
thf(func_def_406,type,
sK15: $i > $i > $i ).
thf(func_def_407,type,
sK16: $i > $i > $i ).
thf(func_def_408,type,
sK17: $i > $i ).
thf(func_def_409,type,
sK18: $i > $i > $i ).
thf(func_def_410,type,
sK19: $i > $i > $i ).
thf(func_def_411,type,
sK20: $i > $i ).
thf(func_def_412,type,
sK21: $i > $i > $i > $i > $i ).
thf(func_def_413,type,
sK22: $i > $i > $i > $i > $i ).
thf(func_def_414,type,
sK23: $i > ( $i > $o ) > $i ).
thf(func_def_415,type,
sK24: ( $i > $o ) > $i > $i ).
thf(func_def_416,type,
sK25: $i > ( $i > $i ) > $i > $i ).
thf(func_def_417,type,
sK26: $i > ( $i > $i ) > $i ).
thf(func_def_418,type,
sK27: $i > ( $i > $i ) > $i > $i ).
thf(func_def_419,type,
sK28: $i > ( $i > $i ) > $i > $i ).
thf(func_def_420,type,
sK29: $i > ( $i > $i ) > $i > $i ).
thf(func_def_421,type,
sK30: ( $i > $o ) > $i ).
thf(func_def_422,type,
sK31: ( $i > $o ) > $i > $i ).
thf(func_def_423,type,
sK32: $i > $i > $i > $i ).
thf(func_def_424,type,
sK33: $i > $i > $i > $i ).
thf(func_def_425,type,
sK34: $i > ( $i > $i ) > $i > $i ).
thf(func_def_426,type,
sK35: $i > ( $i > $o ) > $i > $i ).
thf(func_def_427,type,
sK36: $i > ( $i > $o ) > $i > $i ).
thf(func_def_428,type,
sK37: $i > $i > $i > $i ).
thf(func_def_429,type,
sK38: $i > $i > $i > $i ).
thf(func_def_430,type,
sK39: $i > $i ).
thf(func_def_431,type,
sK40: ( $i > $o ) > $i > $i ).
thf(func_def_432,type,
sK41: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_433,type,
sK42: ( $i > $i > $o ) > $i > $i ).
thf(func_def_434,type,
sK43: ( $i > $i > $o ) > $i > $i ).
thf(func_def_435,type,
sK44: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_436,type,
sK45: ( $i > $i > $o ) > $i > $i ).
thf(func_def_437,type,
sK46: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_438,type,
sK47: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_439,type,
sK48: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_440,type,
sK49: $i > $i > ( $i > $i ) > $i ).
thf(func_def_441,type,
sK50: $i > $i > $o > $i ).
thf(func_def_442,type,
sK51: $i > $i > $i > $i ).
thf(func_def_443,type,
sK52: $i > $i > $i > $i ).
thf(func_def_444,type,
sK53: $i > $i > $i > $i ).
thf(func_def_445,type,
sK54: $i > $i > $i > $i ).
thf(func_def_446,type,
sK55: ( $i > $i ) > $i > $i ).
thf(func_def_447,type,
sK56: ( $i > $i ) > $i > $i > $i ).
thf(func_def_448,type,
sK57: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_449,type,
sK58: ( $i > $o ) > $i > $i ).
thf(func_def_450,type,
sK59: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_451,type,
sK60: ( $i > $o ) > $i > $i ).
thf(func_def_452,type,
sK61: ( $i > $o ) > $i > $i ).
thf(func_def_453,type,
sK62: ( $i > $o ) > $i > $i ).
thf(func_def_454,type,
sK63: ( $i > $o ) > $i > $i ).
thf(func_def_455,type,
sK64: ( $i > $o ) > $i > $i ).
thf(func_def_456,type,
sK65: ( $i > $o ) > $i > $i ).
thf(func_def_457,type,
sK66: ( $i > $o ) > $i ).
thf(func_def_458,type,
sK67: ( $i > $o ) > $i ).
thf(func_def_459,type,
sK68: ( $i > $o ) > $i ).
thf(func_def_460,type,
sK69: ( $i > $o ) > $i ).
thf(func_def_461,type,
sK70: ( $i > $o ) > $i ).
thf(func_def_462,type,
sK71: $i > $i > $i > $i ).
thf(func_def_464,type,
sK73: $i > $i > $i > $i > $i ).
thf(func_def_465,type,
sK74: ( $i > $i ) > $i > $i > $i ).
thf(func_def_466,type,
sK75: ( $i > $o ) > $i > $i ).
thf(func_def_467,type,
sK76: $i > $i > $i ).
thf(func_def_468,type,
sK77: $i > $i ).
thf(func_def_469,type,
sK78: $i > $i > $i > $i > $i ).
thf(func_def_470,type,
sK79: ( $i > $o ) > $i ).
thf(func_def_471,type,
sK80: ( $i > $o ) > $i > $i ).
thf(func_def_472,type,
sK81: ( $i > $o ) > $i > $i ).
thf(func_def_473,type,
sK82: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_474,type,
sK83: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_475,type,
sK84: ( $i > $o ) > $i ).
thf(func_def_476,type,
sK85: ( $i > $o ) > $i > $i ).
thf(func_def_477,type,
sK86: ( $i > $o ) > $i > $i ).
thf(func_def_478,type,
sK87: ( $i > $o ) > $i ).
thf(func_def_479,type,
sK88: ( $i > $o ) > $i > $i ).
thf(func_def_480,type,
sK89: ( $i > $o ) > $i > $i ).
thf(func_def_481,type,
sK90: ( $i > $o ) > $i ).
thf(func_def_482,type,
sK91: ( $i > $o ) > $i > $i ).
thf(func_def_483,type,
sK92: ( $i > $o ) > $i > $i ).
thf(func_def_484,type,
sK93: ( $i > $o ) > $i > $i ).
thf(func_def_485,type,
sK94: ( $i > $o ) > $i ).
thf(func_def_486,type,
sK95: ( $i > $o ) > $i ).
thf(func_def_487,type,
sK96: $i > $i > $i > $i > $i ).
thf(func_def_488,type,
sK97: $i > $i > $i > $i > $i ).
thf(func_def_489,type,
sK98: $i > $i > $i > $i > $i ).
thf(func_def_490,type,
sK99: $i > $i > $i > $i > $i ).
thf(func_def_491,type,
sK100: $i > $i > $i > $i > $i ).
thf(func_def_492,type,
sK101: $i > $i > $i > $i > $i ).
thf(func_def_493,type,
sK102: $i > $i ).
thf(func_def_494,type,
sK103: $i > $i > $i > $i ).
thf(func_def_495,type,
sK104: $i > $i > $i ).
thf(func_def_496,type,
sK105: $i > $i > $i ).
thf(func_def_497,type,
sK106: $i > $i > $i ).
thf(func_def_498,type,
sK107: $i > ( $i > $o ) > $i ).
thf(func_def_499,type,
sK108: ( $i > $i ) > $i > $i > $i ).
thf(func_def_500,type,
sK109: $i > $i ).
thf(func_def_501,type,
sK110: $i > $i > $i ).
thf(func_def_502,type,
sK111: ( $i > $o ) > $i > $i ).
thf(func_def_503,type,
sK112: ( $i > $o ) > $i > $i ).
thf(func_def_504,type,
sK113: $i > ( $i > $o ) > $i > $i ).
thf(func_def_505,type,
sK114: $i > ( $i > $o ) > $i > $i ).
thf(func_def_506,type,
sK115: $i > ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(func_def_507,type,
sK116: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_508,type,
sK117: $i > $i > $i ).
thf(func_def_509,type,
sK118: ( $i > $o ) > $i > $i ).
thf(func_def_510,type,
sK119: $i > $i > $i ).
thf(func_def_511,type,
sK120: ( $i > $o ) > $i > $i ).
thf(func_def_512,type,
sK121: $i > $i ).
thf(func_def_513,type,
sK122: $i > $i > ( $i > $o ) > $i ).
thf(func_def_514,type,
sK123: $i > $i > $i > $i ).
thf(func_def_515,type,
sK124: $i > $i > $i > $i ).
thf(func_def_516,type,
sK125: $i > $i > $i > $i ).
thf(func_def_517,type,
sK126: $i > $i > $i > $i ).
thf(func_def_518,type,
sK127: $i > $i > $i > $i ).
thf(func_def_519,type,
sK128: $i > $i > $i > $i ).
thf(func_def_520,type,
sK129: $i > $i > $i > $i ).
thf(func_def_521,type,
sK130: $i > $i > $i > $i ).
thf(func_def_522,type,
sK131: ( $i > $o ) > $i > $i ).
thf(func_def_523,type,
sK132: ( $i > $i ) > $i > $i > $i ).
thf(func_def_524,type,
sK133: ( $i > $i ) > $i > $i > $i ).
thf(func_def_525,type,
sK134: ( $i > $o ) > $i > $i ).
thf(func_def_526,type,
sK135: $i > $i > $i > $i > $i > $i ).
thf(func_def_527,type,
sK136: $i > $i > $i > $i ).
thf(func_def_528,type,
sK137: $i > $i > $i ).
thf(func_def_529,type,
sK138: ( $i > $o ) > $i > $i ).
thf(func_def_530,type,
sK139: ( $i > $o ) > $i > $i ).
thf(func_def_531,type,
sK140: $i > $i > $i > $i > $i ).
thf(func_def_532,type,
ph141:
!>[X0: $tType] : X0 ).
thf(f5889,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f5887]) ).
thf(f5887,plain,
$false = $true,
inference(backward_demodulation,[status(thm)],[f5874,f5886]) ).
thf(f5886,plain,
( ( in @ ( sK2 @ sK72 ) @ sK0 )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f5885]) ).
thf(f5885,plain,
( ( ( in @ ( sK2 @ sK72 ) @ sK0 )
= $false )
| ( sK72 != sK72 ) ),
inference(superposition,[status(thm)],[f3833,f5884]) ).
thf(f5884,plain,
( sK72
= ( ap @ sK0 @ sK1 @ sK3 @ ( sK2 @ sK72 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f5881]) ).
thf(f5881,plain,
( ( sK72
= ( ap @ sK0 @ sK1 @ sK3 @ ( sK2 @ sK72 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1356,f3829]) ).
thf(f3829,plain,
( $true
= ( in @ sK72 @ sK1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f3827]) ).
thf(f3827,plain,
( $false
= ( ( in @ sK72 @ sK1 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
& ( ( ap @ sK0 @ sK1 @ sK3 @ Y0 )
= sK72 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f3826]) ).
thf(f3826,plain,
( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
& ( ( ap @ sK0 @ sK1 @ sK3 @ Y1 )
= Y0 ) ) ) )
@ sK72 ) ),
inference(sigma_clausification,[status(thm)],[f3825]) ).
thf(f3825,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
& ( ( ap @ sK0 @ sK1 @ sK3 @ Y1 )
= Y0 ) ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f1626]) ).
thf(f1626,plain,
( ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( ( ap @ Y0 @ Y1 @ Y2 @ Y4 )
= Y3 ) ) ) ) )
@ sK0
@ sK1
@ sK3 )
!= $true ),
inference(definition_unfolding,[status(thm)],[f1357,f1035]) ).
thf(f1035,plain,
( surjective
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( ( ap @ Y0 @ Y1 @ Y2 @ Y4 )
= Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f889]) ).
thf(f889,plain,
( surjective
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( ( ap @ Y0 @ Y1 @ Y2 @ Y4 )
= Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f888]) ).
thf(f888,plain,
( surjective
= ( ^ [X0: $i,X1: $i,X2: $i] :
! [X3: $i] :
( ( in @ X3 @ X1 )
=> ? [X4: $i] :
( ( ( ap @ X0 @ X1 @ X2 @ X4 )
= X3 )
& ( in @ X4 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f320]) ).
thf(f320,axiom,
( surjective
= ( ^ [X3: $i,X4: $i,X12: $i] :
! [X1: $i] :
( ( in @ X1 @ X4 )
=> ? [X2: $i] :
( ( ( ap @ X3 @ X4 @ X12 @ X2 )
= X1 )
& ( in @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.gzAOYGIDe7/DTF2THF_7160.p',surjective) ).
thf(f1357,plain,
( $true
!= ( surjective @ sK0 @ sK1 @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f970]) ).
thf(f970,plain,
( ( woz1_4 = $true )
& ( upairsetIL = $true )
& ( foundationAx = $true )
& ( ubforcartprodlem2 = $true )
& ( notsubsetI = $true )
& ( lam2p = $true )
& ( upairsetIR = $true )
& ( iftrueProp1 = $true )
& ( demorgan2b2 = $true )
& ( binintersectRsub = $true )
& ( subsetemptysetimpeq = $true )
& ( omegaIndAx = $true )
& ( app = $true )
& ( ex1I2 = $true )
& ( descr__Cong = $true )
& ( cartprodsndin = $true )
& ( dpsetconstrI = $true )
& ( setukpairinjR1 = $true )
& ! [X3: $i] :
( ( $true
!= ( in @ X3 @ sK1 ) )
| ( $true
= ( in @ ( sK2 @ X3 ) @ sK0 ) ) )
& ( $true
= ( in @ sK3 @ ( funcSet @ sK0 @ sK1 ) ) )
& ( $true
!= ( surjective @ sK0 @ sK1 @ sK3 ) )
& ! [X5: $i] :
( ( ( ap @ sK0 @ sK1 @ sK3 @ ( sK2 @ X5 ) )
= X5 )
| ( $true
!= ( in @ X5 @ sK1 ) ) )
& ( binunionTE = $true )
& ( exuI3 = $true )
& ( upairequniteq = $true )
& ( woz13rule4 = $true )
& ( cartprodfstin = $true )
& ( setadjoinOr = $true )
& ( image1Equiv = $true )
& ( breln1unionprop = $true )
& ( doubleComplementSub1 = $true )
& ( funcext = $true )
& ( woz13rule1 = $true )
& ( dpsetconstrSub = $true )
& ( exuE3u = $true )
& ( upairset2E = $true )
& ( setadjoinIL = $true )
& ( dsetconstrEL = $true )
& ( emptyset__Cong = $true )
& ( ap2apEq1 = $true )
& ( injFuncSetFuncInj = $true )
& ( contrasubsetT2 = $true )
& ( surjFuncSetFuncSurj = $true )
& ( emptyInPowerset = $true )
& ( binintersectTERcontra = $true )
& ( binunionT_lem = $true )
& ( setadjoin__Cong = $true )
& ( setunionI = $true )
& ( binunionTIRcontra = $true )
& ( binunionIL = $true )
& ( notdexE = $true )
& ( lam2lamEq = $true )
& ( lamProp = $true )
& ( binintersectSubset3 = $true )
& ( subbreln1 = $true )
& ( setminusI = $true )
& ( breln1unionEcases = $true )
& ( powersetI1 = $true )
& ( ubforcartprodlem3 = $true )
& ( setunionsingleton2 = $true )
& ( cartprodpairsurjEq = $true )
& ( lamp = $true )
& ( woz1_3 = $true )
& ( in__Cong = $true )
& ( powersetE = $true )
& ( setext = $true )
& ( inIntersectImpInUnion2 = $true )
& ( eqbreln = $true )
& ( beta2 = $true )
& ( setminusT_lem = $true )
& ( setukpairIR = $true )
& ( eqinunit = $true )
& ( setminusER = $true )
& ( demorgan2a2 = $true )
& ( ex1I = $true )
& ( setunionE = $true )
& ( binintersectER = $true )
& ( complementTcontraSubset = $true )
& ( vacuousDall = $true )
& ( ifp = $true )
& ( emptyE1 = $true )
& ( surjFuncSetFuncIn = $true )
& ( binintersectSubset4 = $true )
& ( quantDeMorgan4 = $true )
& ( powersetTE1 = $true )
& ( cartprodpairmemER = $true )
& ( complementTI1 = $true )
& ( exuE2 = $true )
& ( setadjoinAx = $true )
& ( setukpairinjL1 = $true )
& ( dsetconstrER = $true )
& ( subsetE = $true )
& ( cartprodpairin = $true )
& ( dsetconstrI = $true )
& ( setadjoinE = $true )
& ( ex1E2 = $true )
& ( quantDeMorgan1 = $true )
& ( eqimpsubset2 = $true )
& ( kfstpairEq = $true )
& ( brelnall1 = $true )
& ( kpairsurjEq = $true )
& ( subsetTI = $true )
& ( nonemptyI1 = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( ap2apEq2 = $true )
& ( funcGraphProp3 = $true )
& ( setminusELneg = $true )
& ( setunionAx = $true )
& ( breln1invI = $true )
& ( powerset__Cong = $true )
& ( setukpairIL = $true )
& ( ksndpairEq = $true )
& ( wellorderingAx = $true )
& ( symdiffIneg1 = $true )
& ( upairinpowunion = $true )
& ( singletonsswitch = $true )
& ( quantDeMorgan3 = $true )
& ( iffalseProp2 = $true )
& ( woz1_1 = $true )
& ( notequalI1 = $true )
& ( woz2B = $true )
& ( binintersectT_lem = $true )
& ( woz1_2 = $true )
& ( emptysetsubset = $true )
& ( injFuncSetFuncIn = $true )
& ( breln1SetBreln1 = $true )
& ( symdiffE = $true )
& ( binintersectI = $true )
& ( emptysetimpfalse = $true )
& ( setminusEL = $true )
& ( kfstsingleton = $true )
& ( demorgan1a = $true )
& ( powersetI = $true )
& ( omega__Cong = $true )
& ( setextT = $true )
& ( nonemptyImpWitness = $true )
& ( complementUnionInPowersetComplement = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( setminusILneg = $true )
& ( dpsetconstrERa = $true )
& ( sepSubset = $true )
& ( setminusSubset2 = $true )
& ( demorgan2b = $true )
& ( eqimpsubset1 = $true )
& ( prop2set2propI = $true )
& ( breln1compI = $true )
& ( subsetI2 = $true )
& ( disjointsetsI1 = $true )
& ( cartprodmempair1 = $true )
& ( powersetE1 = $true )
& ( subsetE2 = $true )
& ( upairsetE = $true )
& ( breln1invprop = $true )
& ( setukpairinjL2 = $true )
& ( exuE3e = $true )
& ( binunionLsub = $true )
& ( cartprodpairmemEL = $true )
& ( setOfPairsIsBReln = $true )
& ( secondinupair = $true )
& ( subset2powerset = $true )
& ( setunion__Cong = $true )
& ( image1E = $true )
& ( ex1E1 = $true )
& ( replAx = $true )
& ( emptysetAx = $true )
& ( cartprodmempaircEq = $true )
& ( dpsetconstrEL1 = $true )
& ( nonemptyI = $true )
& ( iftrueorfalse = $true )
& ( funcGraphProp2 = $true )
& ( demorgan1b = $true )
& ( nonemptyE1 = $true )
& ( setadjoinIR = $true )
& ( setukpairinjR11 = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( brelnall2 = $true )
& ( noeltsimpempty = $true )
& ( breln1compEex = $true )
& ( theprop = $true )
& ( setminusERneg = $true )
& ( apProp = $true )
& ( notinemptyset = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( kpairp = $true )
& ( emptyinPowerset = $true )
& ( demorgan2a = $true )
& ( descrp = $true )
& ( symdiffI1 = $true )
& ( notequalI2 = $true )
& ( notinsingleton = $true )
& ( setunionE2 = $true )
& ( funcGraphProp1 = $true )
& ( ksndsingleton = $true )
& ( powersetsubset = $true )
& ( upairset2IR = $true )
& ( binunionRsub = $true )
& ( setOfPairsIsBReln1 = $true )
& ( funcinfuncset = $true )
& ( setukpairinjR = $true )
& ( woz2A = $true )
& ( kpairiskpair = $true )
& ( exu__Cong = $true )
& ( subPowSU = $true )
& ( beta1 = $true )
& ( upairsubunion = $true )
& ( eqbreln1 = $true )
& ( powersetT_lem = $true )
& ( woz2Ex = $true )
& ( image1Ex = $true )
& ( prop2setE = $true )
& ( quantDeMorgan2 = $true )
& ( symdiffIneg2 = $true )
& ( iftrueProp2 = $true )
& ( ubforcartprodlem1 = $true )
& ( setadjoinSub2 = $true )
& ( ifSingleton = $true )
& ( prop2setI = $true )
& ( breln1unionI = $true )
& ( binintersectEL = $true )
& ( infuncsetfunc = $true )
& ( inPowerset = $true )
& ( powersetAx = $true )
& ( breln1unionIR = $true )
& ( complementTnotintersectT = $true )
& ( choice2fnsingleton = $true )
& ( setbeta = $true )
& ( notdallE = $true )
& ( binintersectTELcontra = $true )
& ( eta2 = $true )
& ( dpsetconstrEL2 = $true )
& ( sepInPowerset = $true )
& ( woz1_5 = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset5 = $true )
& ( setextAx = $true )
& ( omegaSAx = $true )
& ( setextsub = $true )
& ( dpsetconstrER = $true )
& ( setminusIRneg = $true )
& ( setoftrueEq = $true )
& ( binintersectLsub = $true )
& ( exuE1 = $true )
& ( complementImpComplementIntersect = $true )
& ( woz2W = $true )
& ( woz13rule2 = $true )
& ( breln1unionE = $true )
& ( cartprodfstpairEq = $true )
& ( doubleComplementE1 = $true )
& ( setunionsingleton1 = $true )
& ( setukpairinjR12 = $true )
& ( setunionsingleton = $true )
& ( doubleComplementEq = $true )
& ( doubleComplementSub2 = $true )
& ( breln1unionIL = $true )
& ( cartprodmempair = $true )
& ( iffalse = $true )
& ( woz13rule0 = $true )
& ( complementTE1 = $true )
& ( powersetTI1 = $true )
& ( funcGraphProp4 = $true )
& ( binunionE = $true )
& ( subsetTrans = $true )
& ( injFuncInInjFuncSet = $true )
& ( breln1compprop = $true )
& ( image1Ex1 = $true )
& ( setminusLsub = $true )
& ( doubleComplementI1 = $true )
& ( emptyinunitempty = $true )
& ( funcImageSingleton = $true )
& ( demorgan1 = $true )
& ( funcextLem = $true )
& ( singletoninpowerset = $true )
& ( contrasubsetT1 = $true )
& ( binunionTILcontra = $true )
& ( eta1 = $true )
& ( binunionEcases = $true )
& ( binunionTEcontra = $true )
& ( demorgan2 = $true )
& ( emptyI = $true )
& ( dsetconstr__Cong = $true )
& ( funcext2 = $true )
& ( symdiffI2 = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( binunionIR = $true )
& ( omega0Ax = $true )
& ( contrasubsetT3 = $true )
& ( demorgan2a1 = $true )
& ( cartprodsndpairEq = $true )
& ( breln1unionCommutes = $true )
& ( contrasubsetT = $true )
& ( uniqinunit = $true )
& ( emptysetE = $true )
& ( complementT_lem = $true )
& ( inCongP = $true )
& ( theeq = $true )
& ( singletoninpowunion = $true )
& ( breln1all1 = $true )
& ( singletonprop = $true )
& ( woz13rule3 = $true )
& ( subbreln = $true )
& ( setminusSubset1 = $true )
& ( inIntersectImpInUnion = $true )
& ( singletonsuniq = $true )
& ( exuI2 = $true )
& ( setukpairinjR2 = $true )
& ( subsetRefl = $true )
& ( contraSubsetComplement = $true )
& ( exuEu = $true )
& ( bs114d = $true )
& ( singletonsubset = $true )
& ( ap2p = $true )
& ( setadjoinSub = $true )
& ( iftrue = $true )
& ( breln1compE = $true )
& ( image1I = $true )
& ( binintersectSubset2 = $true )
& ( complementSubsetComplementIntersect = $true )
& ( setukpairinjL = $true )
& ( breln1all2 = $true )
& ( iffalseProp1 = $true )
& ( exuI1 = $true )
& ( subsetI1 = $true )
& ( breln1invE = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f967,f969,f968]) ).
thf(f968,plain,
( ? [X0: $i,X1: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ ( X2 @ X3 ) @ X0 )
= $true ) )
& ? [X4: $i] :
( ( ( in @ X4 @ ( funcSet @ X0 @ X1 ) )
= $true )
& ( $true
!= ( surjective @ X0 @ X1 @ X4 ) )
& ! [X5: $i] :
( ( ( ap @ X0 @ X1 @ X4 @ ( X2 @ X5 ) )
= X5 )
| ( $true
!= ( in @ X5 @ X1 ) ) ) ) )
=> ( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ sK1 ) )
| ( $true
= ( in @ ( sK2 @ X3 ) @ sK0 ) ) )
& ? [X4: $i] :
( ( ( in @ X4 @ ( funcSet @ sK0 @ sK1 ) )
= $true )
& ( $true
!= ( surjective @ sK0 @ sK1 @ X4 ) )
& ! [X5: $i] :
( ( ( ap @ sK0 @ sK1 @ X4 @ ( sK2 @ X5 ) )
= X5 )
| ( $true
!= ( in @ X5 @ sK1 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f969,plain,
( ? [X4: $i] :
( ( ( in @ X4 @ ( funcSet @ sK0 @ sK1 ) )
= $true )
& ( $true
!= ( surjective @ sK0 @ sK1 @ X4 ) )
& ! [X5: $i] :
( ( ( ap @ sK0 @ sK1 @ X4 @ ( sK2 @ X5 ) )
= X5 )
| ( $true
!= ( in @ X5 @ sK1 ) ) ) )
=> ( ( $true
= ( in @ sK3 @ ( funcSet @ sK0 @ sK1 ) ) )
& ( $true
!= ( surjective @ sK0 @ sK1 @ sK3 ) )
& ! [X5: $i] :
( ( ( ap @ sK0 @ sK1 @ sK3 @ ( sK2 @ X5 ) )
= X5 )
| ( $true
!= ( in @ X5 @ sK1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f967,plain,
( ( woz1_4 = $true )
& ( upairsetIL = $true )
& ( foundationAx = $true )
& ( ubforcartprodlem2 = $true )
& ( notsubsetI = $true )
& ( lam2p = $true )
& ( upairsetIR = $true )
& ( iftrueProp1 = $true )
& ( demorgan2b2 = $true )
& ( binintersectRsub = $true )
& ( subsetemptysetimpeq = $true )
& ( omegaIndAx = $true )
& ( app = $true )
& ( ex1I2 = $true )
& ( descr__Cong = $true )
& ( cartprodsndin = $true )
& ( dpsetconstrI = $true )
& ( setukpairinjR1 = $true )
& ? [X0: $i,X1: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ ( X2 @ X3 ) @ X0 )
= $true ) )
& ? [X4: $i] :
( ( ( in @ X4 @ ( funcSet @ X0 @ X1 ) )
= $true )
& ( $true
!= ( surjective @ X0 @ X1 @ X4 ) )
& ! [X5: $i] :
( ( ( ap @ X0 @ X1 @ X4 @ ( X2 @ X5 ) )
= X5 )
| ( $true
!= ( in @ X5 @ X1 ) ) ) ) )
& ( binunionTE = $true )
& ( exuI3 = $true )
& ( upairequniteq = $true )
& ( woz13rule4 = $true )
& ( cartprodfstin = $true )
& ( setadjoinOr = $true )
& ( image1Equiv = $true )
& ( breln1unionprop = $true )
& ( doubleComplementSub1 = $true )
& ( funcext = $true )
& ( woz13rule1 = $true )
& ( dpsetconstrSub = $true )
& ( exuE3u = $true )
& ( upairset2E = $true )
& ( setadjoinIL = $true )
& ( dsetconstrEL = $true )
& ( emptyset__Cong = $true )
& ( ap2apEq1 = $true )
& ( injFuncSetFuncInj = $true )
& ( contrasubsetT2 = $true )
& ( surjFuncSetFuncSurj = $true )
& ( emptyInPowerset = $true )
& ( binintersectTERcontra = $true )
& ( binunionT_lem = $true )
& ( setadjoin__Cong = $true )
& ( setunionI = $true )
& ( binunionTIRcontra = $true )
& ( binunionIL = $true )
& ( notdexE = $true )
& ( lam2lamEq = $true )
& ( lamProp = $true )
& ( binintersectSubset3 = $true )
& ( subbreln1 = $true )
& ( setminusI = $true )
& ( breln1unionEcases = $true )
& ( powersetI1 = $true )
& ( ubforcartprodlem3 = $true )
& ( setunionsingleton2 = $true )
& ( cartprodpairsurjEq = $true )
& ( lamp = $true )
& ( woz1_3 = $true )
& ( in__Cong = $true )
& ( powersetE = $true )
& ( setext = $true )
& ( inIntersectImpInUnion2 = $true )
& ( eqbreln = $true )
& ( beta2 = $true )
& ( setminusT_lem = $true )
& ( setukpairIR = $true )
& ( eqinunit = $true )
& ( setminusER = $true )
& ( demorgan2a2 = $true )
& ( ex1I = $true )
& ( setunionE = $true )
& ( binintersectER = $true )
& ( complementTcontraSubset = $true )
& ( vacuousDall = $true )
& ( ifp = $true )
& ( emptyE1 = $true )
& ( surjFuncSetFuncIn = $true )
& ( binintersectSubset4 = $true )
& ( quantDeMorgan4 = $true )
& ( powersetTE1 = $true )
& ( cartprodpairmemER = $true )
& ( complementTI1 = $true )
& ( exuE2 = $true )
& ( setadjoinAx = $true )
& ( setukpairinjL1 = $true )
& ( dsetconstrER = $true )
& ( subsetE = $true )
& ( cartprodpairin = $true )
& ( dsetconstrI = $true )
& ( setadjoinE = $true )
& ( ex1E2 = $true )
& ( quantDeMorgan1 = $true )
& ( eqimpsubset2 = $true )
& ( kfstpairEq = $true )
& ( brelnall1 = $true )
& ( kpairsurjEq = $true )
& ( subsetTI = $true )
& ( nonemptyI1 = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( ap2apEq2 = $true )
& ( funcGraphProp3 = $true )
& ( setminusELneg = $true )
& ( setunionAx = $true )
& ( breln1invI = $true )
& ( powerset__Cong = $true )
& ( setukpairIL = $true )
& ( ksndpairEq = $true )
& ( wellorderingAx = $true )
& ( symdiffIneg1 = $true )
& ( upairinpowunion = $true )
& ( singletonsswitch = $true )
& ( quantDeMorgan3 = $true )
& ( iffalseProp2 = $true )
& ( woz1_1 = $true )
& ( notequalI1 = $true )
& ( woz2B = $true )
& ( binintersectT_lem = $true )
& ( woz1_2 = $true )
& ( emptysetsubset = $true )
& ( injFuncSetFuncIn = $true )
& ( breln1SetBreln1 = $true )
& ( symdiffE = $true )
& ( binintersectI = $true )
& ( emptysetimpfalse = $true )
& ( setminusEL = $true )
& ( kfstsingleton = $true )
& ( demorgan1a = $true )
& ( powersetI = $true )
& ( omega__Cong = $true )
& ( setextT = $true )
& ( nonemptyImpWitness = $true )
& ( complementUnionInPowersetComplement = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( setminusILneg = $true )
& ( dpsetconstrERa = $true )
& ( sepSubset = $true )
& ( setminusSubset2 = $true )
& ( demorgan2b = $true )
& ( eqimpsubset1 = $true )
& ( prop2set2propI = $true )
& ( breln1compI = $true )
& ( subsetI2 = $true )
& ( disjointsetsI1 = $true )
& ( cartprodmempair1 = $true )
& ( powersetE1 = $true )
& ( subsetE2 = $true )
& ( upairsetE = $true )
& ( breln1invprop = $true )
& ( setukpairinjL2 = $true )
& ( exuE3e = $true )
& ( binunionLsub = $true )
& ( cartprodpairmemEL = $true )
& ( setOfPairsIsBReln = $true )
& ( secondinupair = $true )
& ( subset2powerset = $true )
& ( setunion__Cong = $true )
& ( image1E = $true )
& ( ex1E1 = $true )
& ( replAx = $true )
& ( emptysetAx = $true )
& ( cartprodmempaircEq = $true )
& ( dpsetconstrEL1 = $true )
& ( nonemptyI = $true )
& ( iftrueorfalse = $true )
& ( funcGraphProp2 = $true )
& ( demorgan1b = $true )
& ( nonemptyE1 = $true )
& ( setadjoinIR = $true )
& ( setukpairinjR11 = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( brelnall2 = $true )
& ( noeltsimpempty = $true )
& ( breln1compEex = $true )
& ( theprop = $true )
& ( setminusERneg = $true )
& ( apProp = $true )
& ( notinemptyset = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( kpairp = $true )
& ( emptyinPowerset = $true )
& ( demorgan2a = $true )
& ( descrp = $true )
& ( symdiffI1 = $true )
& ( notequalI2 = $true )
& ( notinsingleton = $true )
& ( setunionE2 = $true )
& ( funcGraphProp1 = $true )
& ( ksndsingleton = $true )
& ( powersetsubset = $true )
& ( upairset2IR = $true )
& ( binunionRsub = $true )
& ( setOfPairsIsBReln1 = $true )
& ( funcinfuncset = $true )
& ( setukpairinjR = $true )
& ( woz2A = $true )
& ( kpairiskpair = $true )
& ( exu__Cong = $true )
& ( subPowSU = $true )
& ( beta1 = $true )
& ( upairsubunion = $true )
& ( eqbreln1 = $true )
& ( powersetT_lem = $true )
& ( woz2Ex = $true )
& ( image1Ex = $true )
& ( prop2setE = $true )
& ( quantDeMorgan2 = $true )
& ( symdiffIneg2 = $true )
& ( iftrueProp2 = $true )
& ( ubforcartprodlem1 = $true )
& ( setadjoinSub2 = $true )
& ( ifSingleton = $true )
& ( prop2setI = $true )
& ( breln1unionI = $true )
& ( binintersectEL = $true )
& ( infuncsetfunc = $true )
& ( inPowerset = $true )
& ( powersetAx = $true )
& ( breln1unionIR = $true )
& ( complementTnotintersectT = $true )
& ( choice2fnsingleton = $true )
& ( setbeta = $true )
& ( notdallE = $true )
& ( binintersectTELcontra = $true )
& ( eta2 = $true )
& ( dpsetconstrEL2 = $true )
& ( sepInPowerset = $true )
& ( woz1_5 = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset5 = $true )
& ( setextAx = $true )
& ( omegaSAx = $true )
& ( setextsub = $true )
& ( dpsetconstrER = $true )
& ( setminusIRneg = $true )
& ( setoftrueEq = $true )
& ( binintersectLsub = $true )
& ( exuE1 = $true )
& ( complementImpComplementIntersect = $true )
& ( woz2W = $true )
& ( woz13rule2 = $true )
& ( breln1unionE = $true )
& ( cartprodfstpairEq = $true )
& ( doubleComplementE1 = $true )
& ( setunionsingleton1 = $true )
& ( setukpairinjR12 = $true )
& ( setunionsingleton = $true )
& ( doubleComplementEq = $true )
& ( doubleComplementSub2 = $true )
& ( breln1unionIL = $true )
& ( cartprodmempair = $true )
& ( iffalse = $true )
& ( woz13rule0 = $true )
& ( complementTE1 = $true )
& ( powersetTI1 = $true )
& ( funcGraphProp4 = $true )
& ( binunionE = $true )
& ( subsetTrans = $true )
& ( injFuncInInjFuncSet = $true )
& ( breln1compprop = $true )
& ( image1Ex1 = $true )
& ( setminusLsub = $true )
& ( doubleComplementI1 = $true )
& ( emptyinunitempty = $true )
& ( funcImageSingleton = $true )
& ( demorgan1 = $true )
& ( funcextLem = $true )
& ( singletoninpowerset = $true )
& ( contrasubsetT1 = $true )
& ( binunionTILcontra = $true )
& ( eta1 = $true )
& ( binunionEcases = $true )
& ( binunionTEcontra = $true )
& ( demorgan2 = $true )
& ( emptyI = $true )
& ( dsetconstr__Cong = $true )
& ( funcext2 = $true )
& ( symdiffI2 = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( binunionIR = $true )
& ( omega0Ax = $true )
& ( contrasubsetT3 = $true )
& ( demorgan2a1 = $true )
& ( cartprodsndpairEq = $true )
& ( breln1unionCommutes = $true )
& ( contrasubsetT = $true )
& ( uniqinunit = $true )
& ( emptysetE = $true )
& ( complementT_lem = $true )
& ( inCongP = $true )
& ( theeq = $true )
& ( singletoninpowunion = $true )
& ( breln1all1 = $true )
& ( singletonprop = $true )
& ( woz13rule3 = $true )
& ( subbreln = $true )
& ( setminusSubset1 = $true )
& ( inIntersectImpInUnion = $true )
& ( singletonsuniq = $true )
& ( exuI2 = $true )
& ( setukpairinjR2 = $true )
& ( subsetRefl = $true )
& ( contraSubsetComplement = $true )
& ( exuEu = $true )
& ( bs114d = $true )
& ( singletonsubset = $true )
& ( ap2p = $true )
& ( setadjoinSub = $true )
& ( iftrue = $true )
& ( breln1compE = $true )
& ( image1I = $true )
& ( binintersectSubset2 = $true )
& ( complementSubsetComplementIntersect = $true )
& ( setukpairinjL = $true )
& ( breln1all2 = $true )
& ( iffalseProp1 = $true )
& ( exuI1 = $true )
& ( subsetI1 = $true )
& ( breln1invE = $true ) ),
inference(flattening,[status(thm)],[f966]) ).
thf(f966,plain,
( ? [X0: $i,X1: $i,X2: $i > $i] :
( ? [X4: $i] :
( ( $true
!= ( surjective @ X0 @ X1 @ X4 ) )
& ! [X5: $i] :
( ( ( ap @ X0 @ X1 @ X4 @ ( X2 @ X5 ) )
= X5 )
| ( $true
!= ( in @ X5 @ X1 ) ) )
& ( ( in @ X4 @ ( funcSet @ X0 @ X1 ) )
= $true ) )
& ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ ( X2 @ X3 ) @ X0 )
= $true ) ) )
& ( surjFuncSetFuncSurj = $true )
& ( surjFuncSetFuncIn = $true )
& ( injFuncSetFuncInj = $true )
& ( injFuncSetFuncIn = $true )
& ( injFuncInInjFuncSet = $true )
& ( image1I = $true )
& ( image1E = $true )
& ( image1Equiv = $true )
& ( image1Ex1 = $true )
& ( image1Ex = $true )
& ( woz2B = $true )
& ( woz2A = $true )
& ( woz2W = $true )
& ( woz2Ex = $true )
& ( breln1unionCommutes = $true )
& ( breln1unionEcases = $true )
& ( breln1unionE = $true )
& ( breln1unionI = $true )
& ( breln1unionIR = $true )
& ( breln1unionIL = $true )
& ( breln1unionprop = $true )
& ( breln1compEex = $true )
& ( breln1compE = $true )
& ( breln1compI = $true )
& ( breln1compprop = $true )
& ( breln1invE = $true )
& ( breln1invI = $true )
& ( breln1invprop = $true )
& ( eqbreln1 = $true )
& ( subbreln1 = $true )
& ( breln1all1 = $true )
& ( setOfPairsIsBReln1 = $true )
& ( choice2fnsingleton = $true )
& ( breln1SetBreln1 = $true )
& ( breln1all2 = $true )
& ( woz1_5 = $true )
& ( woz1_4 = $true )
& ( woz1_3 = $true )
& ( woz1_2 = $true )
& ( woz1_1 = $true )
& ( woz13rule4 = $true )
& ( woz13rule3 = $true )
& ( woz13rule2 = $true )
& ( woz13rule1 = $true )
& ( woz13rule0 = $true )
& ( demorgan2 = $true )
& ( demorgan2b = $true )
& ( demorgan2b2 = $true )
& ( demorgan2a = $true )
& ( demorgan1 = $true )
& ( demorgan1b = $true )
& ( demorgan1a = $true )
& ( demorgan2a2 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( demorgan2a1 = $true )
& ( binunionTEcontra = $true )
& ( binunionTE = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( inIntersectImpInUnion2 = $true )
& ( inIntersectImpInUnion = $true )
& ( binunionTIRcontra = $true )
& ( binunionTILcontra = $true )
& ( complementTcontraSubset = $true )
& ( contraSubsetComplement = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( complementSubsetComplementIntersect = $true )
& ( complementImpComplementIntersect = $true )
& ( complementTnotintersectT = $true )
& ( doubleComplementEq = $true )
& ( doubleComplementSub2 = $true )
& ( doubleComplementSub1 = $true )
& ( doubleComplementE1 = $true )
& ( doubleComplementI1 = $true )
& ( contrasubsetT3 = $true )
& ( contrasubsetT2 = $true )
& ( contrasubsetT1 = $true )
& ( contrasubsetT = $true )
& ( binintersectTERcontra = $true )
& ( binintersectTELcontra = $true )
& ( complementTE1 = $true )
& ( complementTI1 = $true )
& ( powersetTE1 = $true )
& ( powersetTI1 = $true )
& ( subsetTI = $true )
& ( setextT = $true )
& ( complementT_lem = $true )
& ( setminusT_lem = $true )
& ( powersetT_lem = $true )
& ( binunionT_lem = $true )
& ( binintersectT_lem = $true )
& ( iftrueorfalse = $true )
& ( iffalse = $true )
& ( iftrue = $true )
& ( theeq = $true )
& ( ifp = $true )
& ( ifSingleton = $true )
& ( iftrueProp2 = $true )
& ( iftrueProp1 = $true )
& ( iffalseProp2 = $true )
& ( iffalseProp1 = $true )
& ( eta2 = $true )
& ( beta2 = $true )
& ( lam2lamEq = $true )
& ( eta1 = $true )
& ( beta1 = $true )
& ( ap2apEq2 = $true )
& ( ap2apEq1 = $true )
& ( funcext2 = $true )
& ( funcext = $true )
& ( eqbreln = $true )
& ( subbreln = $true )
& ( funcGraphProp4 = $true )
& ( funcextLem = $true )
& ( funcGraphProp2 = $true )
& ( funcGraphProp3 = $true )
& ( funcGraphProp1 = $true )
& ( ex1E2 = $true )
& ( brelnall2 = $true )
& ( brelnall1 = $true )
& ( lam2p = $true )
& ( lamp = $true )
& ( lamProp = $true )
& ( funcinfuncset = $true )
& ( ap2p = $true )
& ( infuncsetfunc = $true )
& ( app = $true )
& ( apProp = $true )
& ( funcImageSingleton = $true )
& ( dpsetconstrER = $true )
& ( dpsetconstrEL2 = $true )
& ( dpsetconstrEL1 = $true )
& ( dpsetconstrERa = $true )
& ( setOfPairsIsBReln = $true )
& ( dpsetconstrSub = $true )
& ( dpsetconstrI = $true )
& ( cartprodpairsurjEq = $true )
& ( cartprodsndpairEq = $true )
& ( cartprodfstpairEq = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodpairmemER = $true )
& ( cartprodpairmemEL = $true )
& ( cartprodsndin = $true )
& ( kpairsurjEq = $true )
& ( ksndpairEq = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR = $true )
& ( setukpairinjR2 = $true )
& ( upairequniteq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjR12 = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjL = $true )
& ( setukpairinjL2 = $true )
& ( cartprodfstin = $true )
& ( kfstpairEq = $true )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( singletonsuniq = $true )
& ( ex1I2 = $true )
& ( ex1I = $true )
& ( ex1E1 = $true )
& ( singletonprop = $true )
& ( setunionsingleton = $true )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( setunionE2 = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( cartprodpairin = $true )
& ( ubforcartprodlem3 = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( upairsubunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f463]) ).
thf(f463,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ( ( setukpairinjR2 = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ( ( ksndpairEq = $true )
=> ( ( kpairsurjEq = $true )
=> ( ( cartprodsndin = $true )
=> ( ( cartprodpairmemEL = $true )
=> ( ( cartprodpairmemER = $true )
=> ( ( cartprodmempaircEq = $true )
=> ( ( cartprodfstpairEq = $true )
=> ( ( cartprodsndpairEq = $true )
=> ( ( cartprodpairsurjEq = $true )
=> ( ( dpsetconstrI = $true )
=> ( ( dpsetconstrSub = $true )
=> ( ( setOfPairsIsBReln = $true )
=> ( ( dpsetconstrERa = $true )
=> ( ( dpsetconstrEL1 = $true )
=> ( ( dpsetconstrEL2 = $true )
=> ( ( dpsetconstrER = $true )
=> ( ( funcImageSingleton = $true )
=> ( ( apProp = $true )
=> ( ( app = $true )
=> ( ( infuncsetfunc = $true )
=> ( ( ap2p = $true )
=> ( ( funcinfuncset = $true )
=> ( ( lamProp = $true )
=> ( ( lamp = $true )
=> ( ( lam2p = $true )
=> ( ( brelnall1 = $true )
=> ( ( brelnall2 = $true )
=> ( ( ex1E2 = $true )
=> ( ( funcGraphProp1 = $true )
=> ( ( funcGraphProp3 = $true )
=> ( ( funcGraphProp2 = $true )
=> ( ( funcextLem = $true )
=> ( ( funcGraphProp4 = $true )
=> ( ( subbreln = $true )
=> ( ( eqbreln = $true )
=> ( ( funcext = $true )
=> ( ( funcext2 = $true )
=> ( ( ap2apEq1 = $true )
=> ( ( ap2apEq2 = $true )
=> ( ( beta1 = $true )
=> ( ( eta1 = $true )
=> ( ( lam2lamEq = $true )
=> ( ( beta2 = $true )
=> ( ( eta2 = $true )
=> ( ( iffalseProp1 = $true )
=> ( ( iffalseProp2 = $true )
=> ( ( iftrueProp1 = $true )
=> ( ( iftrueProp2 = $true )
=> ( ( ifSingleton = $true )
=> ( ( ifp = $true )
=> ( ( theeq = $true )
=> ( ( iftrue = $true )
=> ( ( iffalse = $true )
=> ( ( iftrueorfalse = $true )
=> ( ( binintersectT_lem = $true )
=> ( ( binunionT_lem = $true )
=> ( ( powersetT_lem = $true )
=> ( ( setminusT_lem = $true )
=> ( ( complementT_lem = $true )
=> ( ( setextT = $true )
=> ( ( subsetTI = $true )
=> ( ( powersetTI1 = $true )
=> ( ( powersetTE1 = $true )
=> ( ( complementTI1 = $true )
=> ( ( complementTE1 = $true )
=> ( ( binintersectTELcontra = $true )
=> ( ( binintersectTERcontra = $true )
=> ( ( contrasubsetT = $true )
=> ( ( contrasubsetT1 = $true )
=> ( ( contrasubsetT2 = $true )
=> ( ( contrasubsetT3 = $true )
=> ( ( doubleComplementI1 = $true )
=> ( ( doubleComplementE1 = $true )
=> ( ( doubleComplementSub1 = $true )
=> ( ( doubleComplementSub2 = $true )
=> ( ( doubleComplementEq = $true )
=> ( ( complementTnotintersectT = $true )
=> ( ( complementImpComplementIntersect = $true )
=> ( ( complementSubsetComplementIntersect = $true )
=> ( ( complementInPowersetComplementIntersect = $true )
=> ( ( contraSubsetComplement = $true )
=> ( ( complementTcontraSubset = $true )
=> ( ( binunionTILcontra = $true )
=> ( ( binunionTIRcontra = $true )
=> ( ( inIntersectImpInUnion = $true )
=> ( ( inIntersectImpInUnion2 = $true )
=> ( ( inIntersectImpInIntersectUnions = $true )
=> ( ( intersectInPowersetIntersectUnions = $true )
=> ( ( inComplementUnionImpNotIn1 = $true )
=> ( ( inComplementUnionImpInComplement1 = $true )
=> ( ( binunionTE = $true )
=> ( ( binunionTEcontra = $true )
=> ( ( demorgan2a1 = $true )
=> ( ( complementUnionInPowersetComplement = $true )
=> ( ( demorgan2a2 = $true )
=> ( ( demorgan1a = $true )
=> ( ( demorgan1b = $true )
=> ( ( demorgan1 = $true )
=> ( ( demorgan2a = $true )
=> ( ( demorgan2b2 = $true )
=> ( ( demorgan2b = $true )
=> ( ( demorgan2 = $true )
=> ( ( woz13rule0 = $true )
=> ( ( woz13rule1 = $true )
=> ( ( woz13rule2 = $true )
=> ( ( woz13rule3 = $true )
=> ( ( woz13rule4 = $true )
=> ( ( woz1_1 = $true )
=> ( ( woz1_2 = $true )
=> ( ( woz1_3 = $true )
=> ( ( woz1_4 = $true )
=> ( ( woz1_5 = $true )
=> ( ( breln1all2 = $true )
=> ( ( breln1SetBreln1 = $true )
=> ( ( choice2fnsingleton = $true )
=> ( ( setOfPairsIsBReln1 = $true )
=> ( ( breln1all1 = $true )
=> ( ( subbreln1 = $true )
=> ( ( eqbreln1 = $true )
=> ( ( breln1invprop = $true )
=> ( ( breln1invI = $true )
=> ( ( breln1invE = $true )
=> ( ( breln1compprop = $true )
=> ( ( breln1compI = $true )
=> ( ( breln1compE = $true )
=> ( ( breln1compEex = $true )
=> ( ( breln1unionprop = $true )
=> ( ( breln1unionIL = $true )
=> ( ( breln1unionIR = $true )
=> ( ( breln1unionI = $true )
=> ( ( breln1unionE = $true )
=> ( ( breln1unionEcases = $true )
=> ( ( breln1unionCommutes = $true )
=> ( ( woz2Ex = $true )
=> ( ( woz2W = $true )
=> ( ( woz2A = $true )
=> ( ( woz2B = $true )
=> ( ( image1Ex = $true )
=> ( ( image1Ex1 = $true )
=> ( ( image1Equiv = $true )
=> ( ( image1E = $true )
=> ( ( image1I = $true )
=> ( ( injFuncInInjFuncSet = $true )
=> ( ( injFuncSetFuncIn = $true )
=> ( ( injFuncSetFuncInj = $true )
=> ( ( surjFuncSetFuncIn = $true )
=> ( ( surjFuncSetFuncSurj = $true )
=> ! [X0: $i,X1: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( in @ ( X2 @ X3 ) @ X0 )
= $true ) )
=> ! [X4: $i] :
( ( ( in @ X4 @ ( funcSet @ X0 @ X1 ) )
= $true )
=> ( ! [X5: $i] :
( ( $true
= ( in @ X5 @ X1 ) )
=> ( ( ap @ X0 @ X1 @ X4 @ ( X2 @ X5 ) )
= X5 ) )
=> ( $true
= ( surjective @ X0 @ X1 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f462]) ).
thf(f462,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ( breln1compprop
=> ( breln1compI
=> ( breln1compE
=> ( breln1compEex
=> ( breln1unionprop
=> ( breln1unionIL
=> ( breln1unionIR
=> ( breln1unionI
=> ( breln1unionE
=> ( breln1unionEcases
=> ( breln1unionCommutes
=> ( woz2Ex
=> ( woz2W
=> ( woz2A
=> ( woz2B
=> ( image1Ex
=> ( image1Ex1
=> ( image1Equiv
=> ( image1E
=> ( image1I
=> ( injFuncInInjFuncSet
=> ( injFuncSetFuncIn
=> ( injFuncSetFuncInj
=> ( surjFuncSetFuncIn
=> ( surjFuncSetFuncSurj
=> ! [X0: $i,X1: $i,X2: $i > $i] :
( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( X2 @ X3 ) @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( funcSet @ X0 @ X1 ) )
=> ( ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( ap @ X0 @ X1 @ X4 @ ( X2 @ X5 ) )
= X5 ) )
=> ( surjective @ X0 @ X1 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f324]) ).
thf(f324,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ( breln1compprop
=> ( breln1compI
=> ( breln1compE
=> ( breln1compEex
=> ( breln1unionprop
=> ( breln1unionIL
=> ( breln1unionIR
=> ( breln1unionI
=> ( breln1unionE
=> ( breln1unionEcases
=> ( breln1unionCommutes
=> ( woz2Ex
=> ( woz2W
=> ( woz2A
=> ( woz2B
=> ( image1Ex
=> ( image1Ex1
=> ( image1Equiv
=> ( image1E
=> ( image1I
=> ( injFuncInInjFuncSet
=> ( injFuncSetFuncIn
=> ( injFuncSetFuncInj
=> ( surjFuncSetFuncIn
=> ( surjFuncSetFuncSurj
=> ! [X4: $i,X3: $i,X12: $i > $i] :
( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( in @ ( X12 @ X1 ) @ X4 ) )
=> ! [X14: $i] :
( ( in @ X14 @ ( funcSet @ X4 @ X3 ) )
=> ( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( ( ap @ X4 @ X3 @ X14 @ ( X12 @ X1 ) )
= X1 ) )
=> ( surjective @ X4 @ X3 @ X14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f323]) ).
thf(f323,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ( breln1compprop
=> ( breln1compI
=> ( breln1compE
=> ( breln1compEex
=> ( breln1unionprop
=> ( breln1unionIL
=> ( breln1unionIR
=> ( breln1unionI
=> ( breln1unionE
=> ( breln1unionEcases
=> ( breln1unionCommutes
=> ( woz2Ex
=> ( woz2W
=> ( woz2A
=> ( woz2B
=> ( image1Ex
=> ( image1Ex1
=> ( image1Equiv
=> ( image1E
=> ( image1I
=> ( injFuncInInjFuncSet
=> ( injFuncSetFuncIn
=> ( injFuncSetFuncInj
=> ( surjFuncSetFuncIn
=> ( surjFuncSetFuncSurj
=> ! [X4: $i,X3: $i,X12: $i > $i] :
( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( in @ ( X12 @ X1 ) @ X4 ) )
=> ! [X14: $i] :
( ( in @ X14 @ ( funcSet @ X4 @ X3 ) )
=> ( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( ( ap @ X4 @ X3 @ X14 @ ( X12 @ X1 ) )
= X1 ) )
=> ( surjective @ X4 @ X3 @ X14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.gzAOYGIDe7/DTF2THF_7160.p',leftInvIsSurj) ).
thf(f1356,plain,
! [X5: $i] :
( ( $true
!= ( in @ X5 @ sK1 ) )
| ( ( ap @ sK0 @ sK1 @ sK3 @ ( sK2 @ X5 ) )
= X5 ) ),
inference(cnf_transformation,[status(thm)],[f970]) ).
thf(f3833,plain,
! [X1: $i] :
( ( sK72
!= ( ap @ sK0 @ sK1 @ sK3 @ X1 ) )
| ( ( in @ X1 @ sK0 )
= $false ) ),
inference(equality_proxy_clausification,[status(thm)],[f3832]) ).
thf(f3832,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK0 )
= $false )
| ( $false
= ( ( ap @ sK0 @ sK1 @ sK3 @ X1 )
= sK72 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f3831]) ).
thf(f3831,plain,
! [X1: $i] :
( ( ( in @ X1 @ sK0 )
& ( ( ap @ sK0 @ sK1 @ sK3 @ X1 )
= sK72 ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f3830]) ).
thf(f3830,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
& ( ( ap @ sK0 @ sK1 @ sK3 @ Y0 )
= sK72 ) )
@ X1 )
= $false ),
inference(pi_clausification,[status(thm)],[f3828]) ).
thf(f3828,plain,
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
& ( ( ap @ sK0 @ sK1 @ sK3 @ Y0 )
= sK72 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f3827]) ).
thf(f5874,plain,
( ( in @ ( sK2 @ sK72 ) @ sK0 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f5871]) ).
thf(f5871,plain,
( ( $true != $true )
| ( ( in @ ( sK2 @ sK72 ) @ sK0 )
= $true ) ),
inference(superposition,[status(thm)],[f1359,f3829]) ).
thf(f1359,plain,
! [X3: $i] :
( ( $true
!= ( in @ X3 @ sK1 ) )
| ( $true
= ( in @ ( sK2 @ X3 ) @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f970]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU803^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n031.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 12:35:33 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : SEU803^1 : TPTP v9.2.1. Released v3.7.0.
% 0.28/0.46 % Domain : Set Theory
% 0.28/0.46 % Problem : More about Functions - Surjective Functions
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English : (! A:i.! B:i.! f:i>i.(! x:i.in x A -> in (f x) B) ->
% 0.28/0.46 % (! g:i.in g (funcSet B A) -> (! x:i.in x A ->
% 0.28/0.46 % ap B A g (f x) = x) -> surjective B A g))
% 0.28/0.46
% 0.28/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.28/0.46 % Source : [Bro08]
% 0.28/0.46 % Names : ZFC305g [Bro08]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.40 v8.2.0, 0.38 v8.1.0, 0.27 v7.5.0, 0.29 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v6.1.0, 0.71 v6.0.0, 0.57 v5.5.0, 0.67 v5.4.0, 0.80 v5.2.0, 1.00 v3.7.0
% 0.28/0.46 % Syntax : Number of formulae : 695 ( 322 unt; 372 typ; 322 def)
% 0.28/0.46 % Number of atoms : 1988 ( 464 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 325 ( 6 avg)
% 0.28/0.46 % Number of connectives : 4373 ( 73 ~; 14 |; 54 &;3186 @)
% 0.28/0.46 % ( 17 <=>;1029 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 331 ( 2 avg)
% 0.28/0.46 % Number of types : 2 ( 0 usr)
% 0.28/0.46 % Number of type conns : 176 ( 176 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 375 ( 372 usr; 323 con; 0-4 aty)
% 0.28/0.46 % Number of variables : 1144 ( 78 ^;1022 !; 44 ?;1144 :)
% 0.28/0.46 % SPC : TH0_THM_EQU_NAR
% 0.28/0.46
% 0.28/0.46 % Comments : http://mathgate.info/detsetitem.php?id=486
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(in_type,type,
% 0.28/0.46 in: $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(exu_type,type,
% 0.28/0.46 exu: ( $i > $o ) > $o ).
% 0.28/0.46
% 0.28/0.46 thf(exu,definition,
% 0.28/0.46 ( exu
% 0.28/0.46 = ( ^ [Xphi: $i > $o] :
% 0.28/0.46 ? [Xx: $i] :
% 0.28/0.46 ( ( Xphi @ Xx )
% 0.28/0.46 & ! [Xy: $i] :
% 0.28/0.46 ( ( Xphi @ Xy )
% 0.28/0.46 => ( Xx = Xy ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setextAx_type,type,
% 0.28/0.46 setextAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setextAx,definition,
% 0.28/0.46 ( setextAx
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 <=> ( in @ Xx @ B ) )
% 0.28/0.46 => ( A = B ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(emptyset_type,type,
% 0.28/0.46 emptyset: $i ).
% 0.28/0.46
% 0.28/0.46 thf(emptysetAx_type,type,
% 0.28/0.46 emptysetAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptysetAx,definition,
% 0.28/0.46 ( emptysetAx
% 0.28/0.46 = ( ! [Xx: $i] :
% 0.28/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoin_type,type,
% 0.28/0.46 setadjoin: $i > $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinAx_type,type,
% 0.28/0.46 setadjoinAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinAx,definition,
% 0.28/0.46 ( setadjoinAx
% 0.28/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.46 <=> ( ( Xy = Xx )
% 0.28/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(powerset_type,type,
% 0.28/0.46 powerset: $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(powersetAx_type,type,
% 0.28/0.46 powersetAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(powersetAx,definition,
% 0.28/0.46 ( powersetAx
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.28/0.46 <=> ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setunion_type,type,
% 0.28/0.46 setunion: $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(setunionAx_type,type,
% 0.28/0.46 setunionAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setunionAx,definition,
% 0.28/0.46 ( setunionAx
% 0.28/0.46 = ( ! [A: $i,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.28/0.46 <=> ? [B: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 & ( in @ B @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(omega_type,type,
% 0.28/0.46 omega: $i ).
% 0.28/0.46
% 0.28/0.46 thf(omega0Ax_type,type,
% 0.28/0.46 omega0Ax: $o ).
% 0.28/0.46
% 0.28/0.46 thf(omega0Ax,definition,
% 0.28/0.46 ( omega0Ax
% 0.28/0.46 = ( in @ emptyset @ omega ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(omegaSAx_type,type,
% 0.28/0.46 omegaSAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(omegaSAx,definition,
% 0.28/0.46 ( omegaSAx
% 0.28/0.46 = ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ omega )
% 0.28/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(omegaIndAx_type,type,
% 0.28/0.46 omegaIndAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(omegaIndAx,definition,
% 0.28/0.46 ( omegaIndAx
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ( ( ( in @ emptyset @ A )
% 0.28/0.46 & ! [Xx: $i] :
% 0.28/0.46 ( ( ( in @ Xx @ omega )
% 0.28/0.46 & ( in @ Xx @ A ) )
% 0.28/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.28/0.46 => ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ omega )
% 0.28/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(replAx_type,type,
% 0.28/0.46 replAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(replAx,definition,
% 0.28/0.46 ( replAx
% 0.28/0.46 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( exu
% 0.28/0.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.28/0.46 => ? [B: $i] :
% 0.28/0.46 ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 <=> ? [Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ A )
% 0.28/0.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(foundationAx_type,type,
% 0.28/0.46 foundationAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(foundationAx,definition,
% 0.28/0.46 ( foundationAx
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.28/0.46 => ? [B: $i] :
% 0.28/0.46 ( ( in @ B @ A )
% 0.28/0.46 & ~ ? [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(wellorderingAx_type,type,
% 0.28/0.46 wellorderingAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(wellorderingAx,definition,
% 0.28/0.46 ( wellorderingAx
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ? [B: $i] :
% 0.28/0.46 ( ! [C: $i] :
% 0.28/0.46 ( ( in @ C @ B )
% 0.28/0.46 => ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ C )
% 0.28/0.46 => ( in @ Xx @ A ) ) )
% 0.28/0.46 & ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( ( in @ Xx @ A )
% 0.28/0.46 & ( in @ Xy @ A ) )
% 0.28/0.46 => ( ! [C: $i] :
% 0.28/0.46 ( ( in @ C @ B )
% 0.28/0.46 => ( ( in @ Xx @ C )
% 0.28/0.46 <=> ( in @ Xy @ C ) ) )
% 0.28/0.46 => ( Xx = Xy ) ) )
% 0.28/0.46 & ! [C: $i,D: $i] :
% 0.28/0.46 ( ( ( in @ C @ B )
% 0.28/0.46 & ( in @ D @ B ) )
% 0.28/0.46 => ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ C )
% 0.28/0.46 => ( in @ Xx @ D ) )
% 0.28/0.46 | ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ D )
% 0.28/0.46 => ( in @ Xx @ C ) ) ) )
% 0.28/0.46 & ! [C: $i] :
% 0.28/0.46 ( ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ C )
% 0.28/0.46 => ( in @ Xx @ A ) )
% 0.28/0.46 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.28/0.46 => ? [D: $i,Xx: $i] :
% 0.28/0.46 ( ( in @ D @ B )
% 0.28/0.46 & ( in @ Xx @ C )
% 0.28/0.46 & ~ ? [Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ D )
% 0.28/0.46 & ( in @ Xy @ C ) )
% 0.28/0.46 & ! [E: $i] :
% 0.28/0.46 ( ( in @ E @ B )
% 0.28/0.46 => ( ! [Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ E )
% 0.28/0.46 => ( in @ Xy @ D ) )
% 0.28/0.46 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(descr_type,type,
% 0.28/0.46 descr: ( $i > $o ) > $i ).
% 0.28/0.46
% 0.28/0.46 thf(descrp_type,type,
% 0.28/0.46 descrp: $o ).
% 0.28/0.46
% 0.28/0.46 thf(descrp,definition,
% 0.28/0.46 ( descrp
% 0.28/0.46 = ( ! [Xphi: $i > $o] :
% 0.28/0.46 ( ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 => ( Xphi
% 0.28/0.46 @ ( descr
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstr_type,type,
% 0.28/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrI_type,type,
% 0.28/0.46 dsetconstrI: $o ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrI,definition,
% 0.28/0.46 ( dsetconstrI
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( ( Xphi @ Xx )
% 0.28/0.46 => ( in @ Xx
% 0.28/0.46 @ ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrEL_type,type,
% 0.28/0.46 dsetconstrEL: $o ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrEL,definition,
% 0.28/0.46 ( dsetconstrEL
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx
% 0.28/0.46 @ ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrER_type,type,
% 0.28/0.46 dsetconstrER: $o ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrER,definition,
% 0.28/0.46 ( dsetconstrER
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx
% 0.28/0.46 @ ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(exuE1_type,type,
% 0.28/0.46 exuE1: $o ).
% 0.28/0.46
% 0.28/0.46 thf(exuE1,definition,
% 0.28/0.46 ( exuE1
% 0.28/0.46 = ( ! [Xphi: $i > $o] :
% 0.28/0.46 ( ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 => ? [Xx: $i] :
% 0.28/0.46 ( ( Xphi @ Xx )
% 0.28/0.46 & ! [Xy: $i] :
% 0.28/0.46 ( ( Xphi @ Xy )
% 0.28/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(prop2set_type,type,
% 0.28/0.46 prop2set: $o > $i ).
% 0.28/0.46
% 0.28/0.46 thf(prop2setE_type,type,
% 0.28/0.46 prop2setE: $o ).
% 0.28/0.46
% 0.28/0.46 thf(prop2setE,definition,
% 0.28/0.46 ( prop2setE
% 0.28/0.46 = ( ! [Xphi: $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.28/0.46 => Xphi ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(emptysetE_type,type,
% 0.28/0.46 emptysetE: $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptysetE,definition,
% 0.28/0.46 ( emptysetE
% 0.28/0.46 = ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ emptyset )
% 0.28/0.46 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(emptysetimpfalse_type,type,
% 0.28/0.46 emptysetimpfalse: $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptysetimpfalse,definition,
% 0.28/0.46 ( emptysetimpfalse
% 0.28/0.46 = ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ emptyset )
% 0.28/0.46 => $false ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(notinemptyset_type,type,
% 0.28/0.46 notinemptyset: $o ).
% 0.28/0.46
% 0.28/0.46 thf(notinemptyset,definition,
% 0.28/0.46 ( notinemptyset
% 0.28/0.46 = ( ! [Xx: $i] :
% 0.28/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(exuE3e_type,type,
% 0.28/0.46 exuE3e: $o ).
% 0.28/0.46
% 0.28/0.46 thf(exuE3e,definition,
% 0.28/0.46 ( exuE3e
% 0.28/0.46 = ( ! [Xphi: $i > $o] :
% 0.28/0.46 ( ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setext_type,type,
% 0.28/0.46 setext: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setext,definition,
% 0.28/0.46 ( setext
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( in @ Xx @ B ) )
% 0.28/0.46 => ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 => ( in @ Xx @ A ) )
% 0.28/0.46 => ( A = B ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(emptyI_type,type,
% 0.28/0.46 emptyI: $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptyI,definition,
% 0.28/0.46 ( emptyI
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ~ ( in @ Xx @ A )
% 0.28/0.46 => ( A = emptyset ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(noeltsimpempty_type,type,
% 0.28/0.46 noeltsimpempty: $o ).
% 0.28/0.46
% 0.28/0.46 thf(noeltsimpempty,definition,
% 0.28/0.46 ( noeltsimpempty
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ~ ( in @ Xx @ A )
% 0.28/0.46 => ( A = emptyset ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setbeta_type,type,
% 0.28/0.46 setbeta: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setbeta,definition,
% 0.28/0.46 ( setbeta
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( ( in @ Xx
% 0.28/0.46 @ ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.46 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(nonempty_type,type,
% 0.28/0.46 nonempty: $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(nonempty,definition,
% 0.28/0.46 ( nonempty
% 0.28/0.46 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(nonemptyE1_type,type,
% 0.28/0.46 nonemptyE1: $o ).
% 0.28/0.46
% 0.28/0.46 thf(nonemptyE1,definition,
% 0.28/0.46 ( nonemptyE1
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ( ( nonempty @ A )
% 0.28/0.46 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(nonemptyI_type,type,
% 0.28/0.46 nonemptyI: $o ).
% 0.28/0.46
% 0.28/0.46 thf(nonemptyI,definition,
% 0.28/0.46 ( nonemptyI
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( ( Xphi @ Xx )
% 0.28/0.46 => ( nonempty
% 0.28/0.46 @ ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(nonemptyI1_type,type,
% 0.28/0.46 nonemptyI1: $o ).
% 0.28/0.46
% 0.28/0.46 thf(nonemptyI1,definition,
% 0.28/0.46 ( nonemptyI1
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.28/0.46 => ( nonempty @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinIL_type,type,
% 0.28/0.46 setadjoinIL: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinIL,definition,
% 0.28/0.46 ( setadjoinIL
% 0.28/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(emptyinunitempty_type,type,
% 0.28/0.46 emptyinunitempty: $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptyinunitempty,definition,
% 0.28/0.46 ( emptyinunitempty
% 0.28/0.46 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinIR_type,type,
% 0.28/0.46 setadjoinIR: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinIR,definition,
% 0.28/0.46 ( setadjoinIR
% 0.28/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ A )
% 0.28/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinE_type,type,
% 0.28/0.46 setadjoinE: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinE,definition,
% 0.28/0.46 ( setadjoinE
% 0.28/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.46 => ! [Xphi: $o] :
% 0.28/0.46 ( ( ( Xy = Xx )
% 0.28/0.46 => Xphi )
% 0.28/0.46 => ( ( ( in @ Xy @ A )
% 0.28/0.46 => Xphi )
% 0.28/0.46 => Xphi ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinOr_type,type,
% 0.28/0.46 setadjoinOr: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinOr,definition,
% 0.28/0.46 ( setadjoinOr
% 0.28/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.46 => ( ( Xy = Xx )
% 0.28/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setoftrueEq_type,type,
% 0.28/0.46 setoftrueEq: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setoftrueEq,definition,
% 0.28/0.46 ( setoftrueEq
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ( ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xx: $i] : $true )
% 0.28/0.47 = A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powersetI_type,type,
% 0.28/0.47 powersetI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powersetI,definition,
% 0.28/0.47 ( powersetI
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ A ) )
% 0.28/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyinPowerset_type,type,
% 0.28/0.47 emptyinPowerset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptyinPowerset,definition,
% 0.28/0.47 ( emptyinPowerset
% 0.28/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyInPowerset_type,type,
% 0.28/0.47 emptyInPowerset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptyInPowerset,definition,
% 0.28/0.47 ( emptyInPowerset
% 0.28/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powersetE_type,type,
% 0.28/0.47 powersetE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powersetE,definition,
% 0.28/0.47 ( powersetE
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.28/0.47 => ( ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunionI_type,type,
% 0.28/0.47 setunionI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunionI,definition,
% 0.28/0.47 ( setunionI
% 0.28/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ( ( in @ B @ A )
% 0.28/0.47 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunionE_type,type,
% 0.28/0.47 setunionE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunionE,definition,
% 0.28/0.47 ( setunionE
% 0.28/0.47 = ( ! [A: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.28/0.47 => ! [Xphi: $o] :
% 0.28/0.47 ( ! [B: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ( ( in @ B @ A )
% 0.28/0.47 => Xphi ) )
% 0.28/0.47 => Xphi ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subPowSU_type,type,
% 0.28/0.47 subPowSU: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subPowSU,definition,
% 0.28/0.47 ( subPowSU
% 0.28/0.47 = ( ! [A: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuE2_type,type,
% 0.28/0.47 exuE2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuE2,definition,
% 0.28/0.47 ( exuE2
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ? [Xx: $i] :
% 0.28/0.47 ! [Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xy )
% 0.28/0.47 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyImpWitness_type,type,
% 0.28/0.47 nonemptyImpWitness: $o ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyImpWitness,definition,
% 0.28/0.47 ( nonemptyImpWitness
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ( nonempty @ A )
% 0.28/0.47 => ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & $true ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(uniqinunit_type,type,
% 0.28/0.47 uniqinunit: $o ).
% 0.28/0.47
% 0.28/0.47 thf(uniqinunit,definition,
% 0.28/0.47 ( uniqinunit
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(notinsingleton_type,type,
% 0.28/0.47 notinsingleton: $o ).
% 0.28/0.47
% 0.28/0.47 thf(notinsingleton,definition,
% 0.28/0.47 ( notinsingleton
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx != Xy )
% 0.28/0.47 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(eqinunit_type,type,
% 0.28/0.47 eqinunit: $o ).
% 0.28/0.47
% 0.28/0.47 thf(eqinunit,definition,
% 0.28/0.47 ( eqinunit
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(singletonsswitch_type,type,
% 0.28/0.47 singletonsswitch: $o ).
% 0.28/0.47
% 0.28/0.47 thf(singletonsswitch,definition,
% 0.28/0.47 ( singletonsswitch
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(upairsetE_type,type,
% 0.28/0.47 upairsetE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(upairsetE,definition,
% 0.28/0.47 ( upairsetE
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.28/0.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.28/0.47 => ( ( Xz = Xx )
% 0.28/0.47 | ( Xz = Xy ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(upairsetIL_type,type,
% 0.28/0.47 upairsetIL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(upairsetIL,definition,
% 0.28/0.47 ( upairsetIL
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(upairsetIR_type,type,
% 0.28/0.47 upairsetIR: $o ).
% 0.28/0.47
% 0.28/0.47 thf(upairsetIR,definition,
% 0.28/0.47 ( upairsetIR
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyE1_type,type,
% 0.28/0.47 emptyE1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptyE1,definition,
% 0.28/0.47 ( emptyE1
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( Xphi @ Xx ) )
% 0.28/0.47 => ( ( ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 = emptyset )
% 0.28/0.47 => $false ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(vacuousDall_type,type,
% 0.28/0.47 vacuousDall: $o ).
% 0.28/0.47
% 0.28/0.47 thf(vacuousDall,definition,
% 0.28/0.47 ( vacuousDall
% 0.28/0.47 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ emptyset )
% 0.28/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(quantDeMorgan1_type,type,
% 0.28/0.47 quantDeMorgan1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(quantDeMorgan1,definition,
% 0.28/0.47 ( quantDeMorgan1
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ~ ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( Xphi @ Xx ) )
% 0.28/0.47 => ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(quantDeMorgan2_type,type,
% 0.28/0.47 quantDeMorgan2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(quantDeMorgan2,definition,
% 0.28/0.47 ( quantDeMorgan2
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ~ ( Xphi @ Xx ) )
% 0.28/0.47 => ~ ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(quantDeMorgan3_type,type,
% 0.28/0.47 quantDeMorgan3: $o ).
% 0.28/0.47
% 0.28/0.47 thf(quantDeMorgan3,definition,
% 0.28/0.47 ( quantDeMorgan3
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ~ ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( Xphi @ Xx ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(quantDeMorgan4_type,type,
% 0.28/0.47 quantDeMorgan4: $o ).
% 0.28/0.47
% 0.28/0.47 thf(quantDeMorgan4,definition,
% 0.28/0.47 ( quantDeMorgan4
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ~ ( Xphi @ Xx ) )
% 0.28/0.47 => ~ ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(prop2setI_type,type,
% 0.28/0.47 prop2setI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(prop2setI,definition,
% 0.28/0.47 ( prop2setI
% 0.28/0.47 = ( ! [Xphi: $o] :
% 0.28/0.47 ( Xphi
% 0.28/0.47 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(set2prop_type,type,
% 0.28/0.47 set2prop: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(prop2set2propI_type,type,
% 0.28/0.47 prop2set2propI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(prop2set2propI,definition,
% 0.28/0.47 ( prop2set2propI
% 0.28/0.47 = ( ! [Xphi: $o] :
% 0.28/0.47 ( Xphi
% 0.28/0.47 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(notdexE_type,type,
% 0.28/0.47 notdexE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(notdexE,definition,
% 0.28/0.47 ( notdexE
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ~ ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( Xphi @ Xx ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(notdallE_type,type,
% 0.28/0.47 notdallE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(notdallE,definition,
% 0.28/0.47 ( notdallE
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ~ ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( Xphi @ Xx ) )
% 0.28/0.47 => ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuI1_type,type,
% 0.28/0.47 exuI1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuI1,definition,
% 0.28/0.47 ( exuI1
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ? [Xx: $i] :
% 0.28/0.47 ( ( Xphi @ Xx )
% 0.28/0.47 & ! [Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) )
% 0.28/0.47 => ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuI3_type,type,
% 0.28/0.47 exuI3: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuI3,definition,
% 0.28/0.47 ( exuI3
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.28/0.47 => ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xx )
% 0.28/0.47 => ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) )
% 0.28/0.47 => ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuI2_type,type,
% 0.28/0.47 exuI2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuI2,definition,
% 0.28/0.47 ( exuI2
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ? [Xx: $i] :
% 0.28/0.47 ! [Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xy )
% 0.28/0.47 <=> ( Xy = Xx ) )
% 0.28/0.47 => ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(inCongP_type,type,
% 0.28/0.47 inCongP: $o ).
% 0.28/0.47
% 0.28/0.47 thf(inCongP,definition,
% 0.28/0.47 ( inCongP
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(in__Cong_type,type,
% 0.28/0.47 in__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(in__Cong,definition,
% 0.28/0.47 ( in__Cong
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ( ( in @ Xx @ A )
% 0.28/0.47 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuE3u_type,type,
% 0.28/0.47 exuE3u: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuE3u,definition,
% 0.28/0.47 ( exuE3u
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xx )
% 0.28/0.47 => ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exu__Cong_type,type,
% 0.28/0.47 exu__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exu__Cong,definition,
% 0.28/0.47 ( exu__Cong
% 0.28/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.28/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ( ( Xphi @ Xx )
% 0.28/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.28/0.47 => ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 <=> ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyset__Cong_type,type,
% 0.28/0.47 emptyset__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptyset__Cong,definition,
% 0.28/0.47 ( emptyset__Cong
% 0.28/0.47 = ( emptyset = emptyset ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoin__Cong_type,type,
% 0.28/0.47 setadjoin__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoin__Cong,definition,
% 0.28/0.47 ( setadjoin__Cong
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ! [Xz: $i,Xu: $i] :
% 0.28/0.47 ( ( Xz = Xu )
% 0.28/0.47 => ( ( setadjoin @ Xx @ Xz )
% 0.28/0.47 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powerset__Cong_type,type,
% 0.28/0.47 powerset__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powerset__Cong,definition,
% 0.28/0.47 ( powerset__Cong
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ( ( powerset @ A )
% 0.28/0.47 = ( powerset @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunion__Cong_type,type,
% 0.28/0.47 setunion__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunion__Cong,definition,
% 0.28/0.47 ( setunion__Cong
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ( ( setunion @ A )
% 0.28/0.47 = ( setunion @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(omega__Cong_type,type,
% 0.28/0.47 omega__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(omega__Cong,definition,
% 0.28/0.47 ( omega__Cong
% 0.28/0.47 = ( omega = omega ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuEu_type,type,
% 0.28/0.47 exuEu: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuEu,definition,
% 0.28/0.47 ( exuEu
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xx )
% 0.28/0.47 => ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(descr__Cong_type,type,
% 0.28/0.47 descr__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(descr__Cong,definition,
% 0.28/0.47 ( descr__Cong
% 0.28/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.28/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ( ( Xphi @ Xx )
% 0.28/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.28/0.47 => ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.28/0.47 => ( ( descr
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 = ( descr
% 0.28/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstr__Cong_type,type,
% 0.28/0.47 dsetconstr__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstr__Cong,definition,
% 0.28/0.47 ( dsetconstr__Cong
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( ( Xx = Xy )
% 0.28/0.47 => ( ( Xphi @ Xx )
% 0.28/0.47 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.28/0.47 => ( ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 = ( dsetconstr @ B
% 0.28/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subset_type,type,
% 0.28/0.47 subset: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(disjoint_type,type,
% 0.28/0.47 disjoint: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(setsmeet_type,type,
% 0.28/0.47 setsmeet: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(subsetI1_type,type,
% 0.28/0.47 subsetI1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subsetI1,definition,
% 0.28/0.47 ( subsetI1
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xx @ B ) )
% 0.28/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(eqimpsubset2_type,type,
% 0.28/0.47 eqimpsubset2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(eqimpsubset2,definition,
% 0.28/0.47 ( eqimpsubset2
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(eqimpsubset1_type,type,
% 0.28/0.47 eqimpsubset1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(eqimpsubset1,definition,
% 0.28/0.47 ( eqimpsubset1
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subsetI2_type,type,
% 0.28/0.47 subsetI2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subsetI2,definition,
% 0.28/0.47 ( subsetI2
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xx @ B ) )
% 0.28/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetsubset_type,type,
% 0.28/0.47 emptysetsubset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetsubset,definition,
% 0.28/0.47 ( emptysetsubset
% 0.28/0.47 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subsetE_type,type,
% 0.28/0.47 subsetE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subsetE,definition,
% 0.28/0.47 ( subsetE
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subsetE2_type,type,
% 0.28/0.47 subsetE2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subsetE2,definition,
% 0.28/0.47 ( subsetE2
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( ~ ( in @ Xx @ B )
% 0.28/0.47 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(notsubsetI_type,type,
% 0.28/0.47 notsubsetI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(notsubsetI,definition,
% 0.28/0.47 ( notsubsetI
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ~ ( in @ Xx @ B )
% 0.28/0.47 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(notequalI1_type,type,
% 0.28/0.47 notequalI1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(notequalI1,definition,
% 0.28/0.47 ( notequalI1
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ~ ( subset @ A @ B )
% 0.28/0.47 => ( A != B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(notequalI2_type,type,
% 0.28/0.47 notequalI2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(notequalI2,definition,
% 0.28/0.47 ( notequalI2
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ~ ( in @ Xx @ B )
% 0.28/0.47 => ( A != B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subsetRefl_type,type,
% 0.28/0.47 subsetRefl: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subsetRefl,definition,
% 0.28/0.47 ( subsetRefl
% 0.28/0.47 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subsetTrans_type,type,
% 0.28/0.47 subsetTrans: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subsetTrans,definition,
% 0.28/0.47 ( subsetTrans
% 0.28/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( ( subset @ B @ C )
% 0.28/0.47 => ( subset @ A @ C ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinSub_type,type,
% 0.28/0.47 setadjoinSub: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinSub,definition,
% 0.28/0.47 ( setadjoinSub
% 0.28/0.47 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinSub2_type,type,
% 0.28/0.47 setadjoinSub2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinSub2,definition,
% 0.28/0.47 ( setadjoinSub2
% 0.28/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subset2powerset_type,type,
% 0.28/0.47 subset2powerset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subset2powerset,definition,
% 0.28/0.47 ( subset2powerset
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setextsub_type,type,
% 0.28/0.47 setextsub: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setextsub,definition,
% 0.28/0.47 ( setextsub
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( ( subset @ B @ A )
% 0.28/0.47 => ( A = B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subsetemptysetimpeq_type,type,
% 0.28/0.47 subsetemptysetimpeq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subsetemptysetimpeq,definition,
% 0.28/0.47 ( subsetemptysetimpeq
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ( subset @ A @ emptyset )
% 0.28/0.47 => ( A = emptyset ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powersetI1_type,type,
% 0.28/0.47 powersetI1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powersetI1,definition,
% 0.28/0.47 ( powersetI1
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( subset @ B @ A )
% 0.28/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powersetE1_type,type,
% 0.28/0.47 powersetE1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powersetE1,definition,
% 0.28/0.47 ( powersetE1
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.28/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(inPowerset_type,type,
% 0.28/0.47 inPowerset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(inPowerset,definition,
% 0.28/0.47 ( inPowerset
% 0.28/0.47 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powersetsubset_type,type,
% 0.28/0.47 powersetsubset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powersetsubset,definition,
% 0.28/0.47 ( powersetsubset
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(sepInPowerset_type,type,
% 0.28/0.47 sepInPowerset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(sepInPowerset,definition,
% 0.28/0.47 ( sepInPowerset
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( in
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 @ ( powerset @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(sepSubset_type,type,
% 0.28/0.47 sepSubset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(sepSubset,definition,
% 0.28/0.47 ( sepSubset
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( subset
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binunion_type,type,
% 0.28/0.47 binunion: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(binunionIL_type,type,
% 0.28/0.47 binunionIL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binunionIL,definition,
% 0.28/0.47 ( binunionIL
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(upairset2IR_type,type,
% 0.28/0.47 upairset2IR: $o ).
% 0.28/0.47
% 0.28/0.47 thf(upairset2IR,definition,
% 0.28/0.47 ( upairset2IR
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binunionIR_type,type,
% 0.28/0.47 binunionIR: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binunionIR,definition,
% 0.28/0.47 ( binunionIR
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binunionEcases_type,type,
% 0.28/0.47 binunionEcases: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binunionEcases,definition,
% 0.28/0.47 ( binunionEcases
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.28/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.28/0.47 => ( ( ( in @ Xx @ A )
% 0.28/0.47 => Xphi )
% 0.28/0.47 => ( ( ( in @ Xx @ B )
% 0.28/0.47 => Xphi )
% 0.28/0.47 => Xphi ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binunionE_type,type,
% 0.28/0.47 binunionE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binunionE,definition,
% 0.28/0.47 ( binunionE
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.28/0.47 => ( ( in @ Xx @ A )
% 0.28/0.47 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binunionLsub_type,type,
% 0.28/0.47 binunionLsub: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binunionLsub,definition,
% 0.28/0.47 ( binunionLsub
% 0.28/0.47 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binunionRsub_type,type,
% 0.28/0.47 binunionRsub: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binunionRsub,definition,
% 0.28/0.47 ( binunionRsub
% 0.28/0.47 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersect_type,type,
% 0.28/0.47 binintersect: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectI_type,type,
% 0.28/0.47 binintersectI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectI,definition,
% 0.28/0.47 ( binintersectI
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset5_type,type,
% 0.28/0.47 binintersectSubset5: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset5,definition,
% 0.28/0.47 ( binintersectSubset5
% 0.28/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.28/0.47 ( ( subset @ C @ A )
% 0.28/0.47 => ( ( subset @ C @ B )
% 0.28/0.47 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectEL_type,type,
% 0.28/0.47 binintersectEL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectEL,definition,
% 0.28/0.47 ( binintersectEL
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.28/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectLsub_type,type,
% 0.28/0.47 binintersectLsub: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectLsub,definition,
% 0.28/0.47 ( binintersectLsub
% 0.28/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset2_type,type,
% 0.28/0.47 binintersectSubset2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset2,definition,
% 0.28/0.47 ( binintersectSubset2
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( ( binintersect @ A @ B )
% 0.28/0.47 = A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset3_type,type,
% 0.28/0.47 binintersectSubset3: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset3,definition,
% 0.28/0.47 ( binintersectSubset3
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( ( binintersect @ A @ B )
% 0.28/0.47 = B )
% 0.28/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectER_type,type,
% 0.28/0.47 binintersectER: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectER,definition,
% 0.28/0.47 ( binintersectER
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.28/0.47 => ( in @ Xx @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(disjointsetsI1_type,type,
% 0.28/0.47 disjointsetsI1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(disjointsetsI1,definition,
% 0.28/0.47 ( disjointsetsI1
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ~ ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( in @ Xx @ B ) )
% 0.28/0.47 => ( ( binintersect @ A @ B )
% 0.28/0.47 = emptyset ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectRsub_type,type,
% 0.28/0.47 binintersectRsub: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectRsub,definition,
% 0.28/0.47 ( binintersectRsub
% 0.28/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset4_type,type,
% 0.28/0.47 binintersectSubset4: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset4,definition,
% 0.28/0.47 ( binintersectSubset4
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( subset @ B @ A )
% 0.28/0.47 => ( ( binintersect @ A @ B )
% 0.28/0.47 = B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset1_type,type,
% 0.28/0.47 binintersectSubset1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset1,definition,
% 0.28/0.47 ( binintersectSubset1
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( ( binintersect @ A @ B )
% 0.28/0.47 = A )
% 0.28/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(bs114d_type,type,
% 0.28/0.47 bs114d: $o ).
% 0.28/0.47
% 0.28/0.47 thf(bs114d,definition,
% 0.28/0.47 ( bs114d
% 0.28/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.28/0.47 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.28/0.47 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(regular_type,type,
% 0.28/0.47 regular: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminus_type,type,
% 0.28/0.47 setminus: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(setminusI_type,type,
% 0.28/0.47 setminusI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusI,definition,
% 0.28/0.47 ( setminusI
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ~ ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusEL_type,type,
% 0.28/0.47 setminusEL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusEL,definition,
% 0.28/0.47 ( setminusEL
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.28/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusER_type,type,
% 0.28/0.47 setminusER: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusER,definition,
% 0.28/0.47 ( setminusER
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.28/0.47 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusSubset2_type,type,
% 0.28/0.47 setminusSubset2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusSubset2,definition,
% 0.28/0.47 ( setminusSubset2
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( ( setminus @ A @ B )
% 0.28/0.47 = emptyset ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusERneg_type,type,
% 0.28/0.47 setminusERneg: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusERneg,definition,
% 0.28/0.47 ( setminusERneg
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.28/0.47 => ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusELneg_type,type,
% 0.28/0.47 setminusELneg: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusELneg,definition,
% 0.28/0.47 ( setminusELneg
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.28/0.47 => ( ~ ( in @ Xx @ B )
% 0.28/0.47 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusILneg_type,type,
% 0.28/0.47 setminusILneg: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusILneg,definition,
% 0.28/0.47 ( setminusILneg
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ~ ( in @ Xx @ A )
% 0.28/0.47 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusIRneg_type,type,
% 0.28/0.47 setminusIRneg: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusIRneg,definition,
% 0.28/0.47 ( setminusIRneg
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusLsub_type,type,
% 0.28/0.47 setminusLsub: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusLsub,definition,
% 0.28/0.47 ( setminusLsub
% 0.28/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusSubset1_type,type,
% 0.28/0.47 setminusSubset1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusSubset1,definition,
% 0.28/0.47 ( setminusSubset1
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( ( setminus @ A @ B )
% 0.28/0.47 = emptyset )
% 0.28/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(symdiff_type,type,
% 0.28/0.47 symdiff: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffE_type,type,
% 0.28/0.47 symdiffE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffE,definition,
% 0.28/0.47 ( symdiffE
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.28/0.47 => ! [Xphi: $o] :
% 0.28/0.47 ( ( ( in @ Xx @ A )
% 0.28/0.47 => ( ~ ( in @ Xx @ B )
% 0.28/0.47 => Xphi ) )
% 0.28/0.47 => ( ( ~ ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ B )
% 0.28/0.47 => Xphi ) )
% 0.28/0.47 => Xphi ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffI1_type,type,
% 0.28/0.47 symdiffI1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffI1,definition,
% 0.28/0.47 ( symdiffI1
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ~ ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffI2_type,type,
% 0.28/0.47 symdiffI2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffI2,definition,
% 0.28/0.47 ( symdiffI2
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ~ ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffIneg1_type,type,
% 0.28/0.47 symdiffIneg1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffIneg1,definition,
% 0.28/0.47 ( symdiffIneg1
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ B )
% 0.28/0.47 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffIneg2_type,type,
% 0.28/0.47 symdiffIneg2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffIneg2,definition,
% 0.28/0.47 ( symdiffIneg2
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ~ ( in @ Xx @ A )
% 0.28/0.47 => ( ~ ( in @ Xx @ B )
% 0.28/0.47 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(iskpair_type,type,
% 0.28/0.47 iskpair: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(secondinupair_type,type,
% 0.28/0.47 secondinupair: $o ).
% 0.28/0.47
% 0.28/0.47 thf(secondinupair,definition,
% 0.28/0.47 ( secondinupair
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairIL_type,type,
% 0.28/0.47 setukpairIL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairIL,definition,
% 0.28/0.47 ( setukpairIL
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairIR_type,type,
% 0.28/0.47 setukpairIR: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairIR,definition,
% 0.28/0.47 ( setukpairIR
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(kpairiskpair_type,type,
% 0.28/0.47 kpairiskpair: $o ).
% 0.28/0.47
% 0.28/0.47 thf(kpairiskpair,definition,
% 0.28/0.47 ( kpairiskpair
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(kpair_type,type,
% 0.28/0.47 kpair: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(kpairp_type,type,
% 0.28/0.47 kpairp: $o ).
% 0.28/0.47
% 0.28/0.47 thf(kpairp,definition,
% 0.28/0.47 ( kpairp
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(cartprod_type,type,
% 0.28/0.47 cartprod: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(singletonsubset_type,type,
% 0.28/0.47 singletonsubset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(singletonsubset,definition,
% 0.28/0.47 ( singletonsubset
% 0.28/0.47 = ( ! [A: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(singletoninpowerset_type,type,
% 0.28/0.47 singletoninpowerset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(singletoninpowerset,definition,
% 0.28/0.47 ( singletoninpowerset
% 0.28/0.47 = ( ! [A: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(singletoninpowunion_type,type,
% 0.28/0.47 singletoninpowunion: $o ).
% 0.28/0.47
% 0.28/0.47 thf(singletoninpowunion,definition,
% 0.28/0.47 ( singletoninpowunion
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(upairset2E_type,type,
% 0.28/0.47 upairset2E: $o ).
% 0.28/0.47
% 0.28/0.47 thf(upairset2E,definition,
% 0.28/0.47 ( upairset2E
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.28/0.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.28/0.47 => ( ( Xz = Xx )
% 0.28/0.47 | ( Xz = Xy ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(upairsubunion_type,type,
% 0.28/0.47 upairsubunion: $o ).
% 0.28/0.47
% 0.28/0.47 thf(upairsubunion,definition,
% 0.28/0.47 ( upairsubunion
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(upairinpowunion_type,type,
% 0.28/0.47 upairinpowunion: $o ).
% 0.28/0.47
% 0.28/0.47 thf(upairinpowunion,definition,
% 0.28/0.47 ( upairinpowunion
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ubforcartprodlem1_type,type,
% 0.28/0.47 ubforcartprodlem1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ubforcartprodlem1,definition,
% 0.28/0.47 ( ubforcartprodlem1
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ubforcartprodlem2_type,type,
% 0.28/0.47 ubforcartprodlem2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ubforcartprodlem2,definition,
% 0.28/0.47 ( ubforcartprodlem2
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ubforcartprodlem3_type,type,
% 0.28/0.47 ubforcartprodlem3: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ubforcartprodlem3,definition,
% 0.28/0.47 ( ubforcartprodlem3
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodpairin_type,type,
% 0.28/0.47 cartprodpairin: $o ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodpairin,definition,
% 0.28/0.47 ( cartprodpairin
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodmempair1_type,type,
% 0.28/0.47 cartprodmempair1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodmempair1,definition,
% 0.28/0.47 ( cartprodmempair1
% 0.28/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.28/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.28/0.47 => ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ? [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 & ( Xu
% 0.28/0.47 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodmempair_type,type,
% 0.28/0.47 cartprodmempair: $o ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodmempair,definition,
% 0.28/0.47 ( cartprodmempair
% 0.28/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.28/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.28/0.47 => ( iskpair @ Xu ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunionE2_type,type,
% 0.28/0.47 setunionE2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunionE2,definition,
% 0.28/0.47 ( setunionE2
% 0.28/0.47 = ( ! [A: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.28/0.47 => ? [X: $i] :
% 0.28/0.47 ( ( in @ X @ A )
% 0.28/0.47 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunionsingleton1_type,type,
% 0.28/0.47 setunionsingleton1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunionsingleton1,definition,
% 0.28/0.47 ( setunionsingleton1
% 0.28/0.47 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunionsingleton2_type,type,
% 0.28/0.47 setunionsingleton2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunionsingleton2,definition,
% 0.28/0.47 ( setunionsingleton2
% 0.28/0.47 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunionsingleton_type,type,
% 0.28/0.47 setunionsingleton: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunionsingleton,definition,
% 0.28/0.47 ( setunionsingleton
% 0.28/0.47 = ( ! [Xx: $i] :
% 0.28/0.47 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.28/0.47 = Xx ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(singleton_type,type,
% 0.28/0.47 singleton: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(singletonprop_type,type,
% 0.28/0.47 singletonprop: $o ).
% 0.28/0.47
% 0.28/0.47 thf(singletonprop,definition,
% 0.28/0.47 ( singletonprop
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( ( Xphi @ Xx )
% 0.28/0.47 => ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) )
% 0.28/0.47 => ( ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( Xphi @ Xx ) )
% 0.28/0.47 => ( singleton
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ex1_type,type,
% 0.28/0.47 ex1: $i > ( $i > $o ) > $o ).
% 0.28/0.47
% 0.28/0.47 thf(ex1E1_type,type,
% 0.28/0.47 ex1E1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ex1E1,definition,
% 0.28/0.47 ( ex1E1
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ( ex1 @ A
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ex1I_type,type,
% 0.28/0.47 ex1I: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ex1I,definition,
% 0.28/0.47 ( ex1I
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( Xphi @ Xx )
% 0.28/0.47 => ( ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xy = Xx ) ) )
% 0.28/0.47 => ( ex1 @ A
% 0.28/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ex1I2_type,type,
% 0.28/0.47 ex1I2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ex1I2,definition,
% 0.28/0.47 ( ex1I2
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( ( Xphi @ Xx )
% 0.28/0.47 => ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) )
% 0.28/0.47 => ( ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( Xphi @ Xx ) )
% 0.28/0.47 => ( ex1 @ A
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(singletonsuniq_type,type,
% 0.28/0.47 singletonsuniq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(singletonsuniq,definition,
% 0.28/0.47 ( singletonsuniq
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( ( setadjoin @ Xx @ emptyset )
% 0.28/0.47 = ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(atmost1p_type,type,
% 0.28/0.47 atmost1p: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(atleast2p_type,type,
% 0.28/0.47 atleast2p: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(atmost2p_type,type,
% 0.28/0.47 atmost2p: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(upairsetp_type,type,
% 0.28/0.47 upairsetp: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjL1_type,type,
% 0.28/0.47 setukpairinjL1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjL1,definition,
% 0.28/0.47 ( setukpairinjL1
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.28/0.47 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.28/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(kfstsingleton_type,type,
% 0.28/0.47 kfstsingleton: $o ).
% 0.28/0.47
% 0.28/0.47 thf(kfstsingleton,definition,
% 0.28/0.47 ( kfstsingleton
% 0.28/0.47 = ( ! [Xu: $i] :
% 0.28/0.47 ( ( iskpair @ Xu )
% 0.28/0.47 => ( singleton
% 0.28/0.47 @ ( dsetconstr @ ( setunion @ Xu )
% 0.28/0.47 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(theprop_type,type,
% 0.28/0.47 theprop: $o ).
% 0.28/0.47
% 0.28/0.47 thf(theprop,definition,
% 0.28/0.47 ( theprop
% 0.28/0.47 = ( ! [X: $i] :
% 0.28/0.47 ( ( singleton @ X )
% 0.28/0.47 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(kfst_type,type,
% 0.28/0.47 kfst: $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(kfstpairEq_type,type,
% 0.28/0.47 kfstpairEq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(kfstpairEq,definition,
% 0.28/0.47 ( kfstpairEq
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.28/0.47 = Xx ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodfstin_type,type,
% 0.28/0.47 cartprodfstin: $o ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodfstin,definition,
% 0.28/0.47 ( cartprodfstin
% 0.28/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.28/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.28/0.47 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjL2_type,type,
% 0.28/0.47 setukpairinjL2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjL2,definition,
% 0.28/0.47 ( setukpairinjL2
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.28/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.28/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.28/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjL_type,type,
% 0.28/0.47 setukpairinjL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjL,definition,
% 0.28/0.47 ( setukpairinjL
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.28/0.47 ( ( ( kpair @ Xx @ Xy )
% 0.28/0.47 = ( kpair @ Xz @ Xu ) )
% 0.28/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjR11_type,type,
% 0.28/0.47 setukpairinjR11: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjR11,definition,
% 0.28/0.47 ( setukpairinjR11
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.47 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjR12_type,type,
% 0.28/0.47 setukpairinjR12: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjR12,definition,
% 0.28/0.47 ( setukpairinjR12
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.28/0.47 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjR1_type,type,
% 0.28/0.47 setukpairinjR1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjR1,definition,
% 0.28/0.47 ( setukpairinjR1
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.28/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.28/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.28/0.47 => ( ( Xz = Xu )
% 0.28/0.47 => ( Xy = Xu ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(upairequniteq_type,type,
% 0.28/0.47 upairequniteq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(upairequniteq,definition,
% 0.28/0.47 ( upairequniteq
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.28/0.47 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.47 = ( setadjoin @ Xz @ emptyset ) )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjR2_type,type,
% 0.28/0.47 setukpairinjR2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjR2,definition,
% 0.28/0.47 ( setukpairinjR2
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.28/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.28/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.28/0.47 => ( Xy = Xu ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjR_type,type,
% 0.28/0.47 setukpairinjR: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjR,definition,
% 0.28/0.47 ( setukpairinjR
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.28/0.47 ( ( ( kpair @ Xx @ Xy )
% 0.28/0.47 = ( kpair @ Xz @ Xu ) )
% 0.28/0.47 => ( Xy = Xu ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ksndsingleton_type,type,
% 0.28/0.47 ksndsingleton: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ksndsingleton,definition,
% 0.28/0.47 ( ksndsingleton
% 0.28/0.47 = ( ! [Xu: $i] :
% 0.28/0.47 ( ( iskpair @ Xu )
% 0.28/0.47 => ( singleton
% 0.28/0.47 @ ( dsetconstr @ ( setunion @ Xu )
% 0.28/0.47 @ ^ [Xx: $i] :
% 0.28/0.47 ( Xu
% 0.28/0.47 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ksnd_type,type,
% 0.28/0.47 ksnd: $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(ksndpairEq_type,type,
% 0.28/0.47 ksndpairEq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ksndpairEq,definition,
% 0.28/0.47 ( ksndpairEq
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.28/0.47 = Xy ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(kpairsurjEq_type,type,
% 0.28/0.47 kpairsurjEq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(kpairsurjEq,definition,
% 0.28/0.47 ( kpairsurjEq
% 0.28/0.47 = ( ! [Xu: $i] :
% 0.28/0.47 ( ( iskpair @ Xu )
% 0.28/0.47 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.28/0.47 = Xu ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodsndin_type,type,
% 0.28/0.47 cartprodsndin: $o ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodsndin,definition,
% 0.28/0.47 ( cartprodsndin
% 0.28/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.28/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.28/0.47 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodpairmemEL_type,type,
% 0.28/0.47 cartprodpairmemEL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodpairmemEL,definition,
% 0.28/0.47 ( cartprodpairmemEL
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.28/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodpairmemER_type,type,
% 0.28/0.47 cartprodpairmemER: $o ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodpairmemER,definition,
% 0.28/0.47 ( cartprodpairmemER
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.28/0.47 => ( in @ Xy @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodmempaircEq_type,type,
% 0.28/0.47 cartprodmempaircEq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodmempaircEq,definition,
% 0.28/0.47 ( cartprodmempaircEq
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( ( kpair @ Xx @ Xy )
% 0.28/0.47 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodfstpairEq_type,type,
% 0.28/0.47 cartprodfstpairEq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodfstpairEq,definition,
% 0.28/0.47 ( cartprodfstpairEq
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.28/0.47 = Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodsndpairEq_type,type,
% 0.28/0.47 cartprodsndpairEq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodsndpairEq,definition,
% 0.28/0.47 ( cartprodsndpairEq
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.28/0.47 = Xy ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodpairsurjEq_type,type,
% 0.28/0.47 cartprodpairsurjEq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodpairsurjEq,definition,
% 0.28/0.47 ( cartprodpairsurjEq
% 0.28/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.28/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.28/0.47 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.28/0.47 = Xu ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(breln_type,type,
% 0.28/0.47 breln: $i > $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(dpsetconstr_type,type,
% 0.28/0.47 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.28/0.47
% 0.28/0.47 thf(dpsetconstrI_type,type,
% 0.28/0.47 dpsetconstrI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(dpsetconstrI,definition,
% 0.28/0.47 ( dpsetconstrI
% 0.28/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( ( Xphi @ Xx @ Xy )
% 0.28/0.47 => ( in @ ( kpair @ Xx @ Xy )
% 0.28/0.47 @ ( dpsetconstr @ A @ B
% 0.28/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(dpsetconstrSub_type,type,
% 0.28/0.47 dpsetconstrSub: $o ).
% 0.28/0.47
% 0.28/0.47 thf(dpsetconstrSub,definition,
% 0.28/0.47 ( dpsetconstrSub
% 0.28/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.28/0.47 ( subset
% 0.28/0.47 @ ( dpsetconstr @ A @ B
% 0.28/0.47 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.28/0.47 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setOfPairsIsBReln_type,type,
% 0.28/0.47 setOfPairsIsBReln: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setOfPairsIsBReln,definition,
% 0.28/0.47 ( setOfPairsIsBReln
% 0.28/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.28/0.47 ( breln @ A @ B
% 0.28/0.47 @ ( dpsetconstr @ A @ B
% 0.28/0.47 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(dpsetconstrERa_type,type,
% 0.28/0.47 dpsetconstrERa: $o ).
% 0.28/0.47
% 0.28/0.47 thf(dpsetconstrERa,definition,
% 0.28/0.47 ( dpsetconstrERa
% 0.28/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.28/0.47 @ ( dpsetconstr @ A @ B
% 0.28/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.28/0.47 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(dpsetconstrEL1_type,type,
% 0.28/0.47 dpsetconstrEL1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(dpsetconstrEL1,definition,
% 0.28/0.47 ( dpsetconstrEL1
% 0.28/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ ( kpair @ Xx @ Xy )
% 0.28/0.47 @ ( dpsetconstr @ A @ B
% 0.28/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.28/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(dpsetconstrEL2_type,type,
% 0.28/0.47 dpsetconstrEL2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(dpsetconstrEL2,definition,
% 0.28/0.47 ( dpsetconstrEL2
% 0.28/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ ( kpair @ Xx @ Xy )
% 0.28/0.47 @ ( dpsetconstr @ A @ B
% 0.28/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.28/0.47 => ( in @ Xy @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(dpsetconstrER_type,type,
% 0.28/0.47 dpsetconstrER: $o ).
% 0.28/0.47
% 0.28/0.47 thf(dpsetconstrER,definition,
% 0.28/0.47 ( dpsetconstrER
% 0.28/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ ( kpair @ Xx @ Xy )
% 0.28/0.47 @ ( dpsetconstr @ A @ B
% 0.28/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.28/0.47 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(func_type,type,
% 0.28/0.47 func: $i > $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(funcSet_type,type,
% 0.28/0.47 funcSet: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(funcImageSingleton_type,type,
% 0.28/0.47 funcImageSingleton: $o ).
% 0.28/0.47
% 0.28/0.47 thf(funcImageSingleton,definition,
% 0.28/0.47 ( funcImageSingleton
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( func @ A @ B @ Xf )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( singleton
% 0.28/0.47 @ ( dsetconstr @ B
% 0.28/0.47 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(apProp_type,type,
% 0.28/0.47 apProp: $o ).
% 0.28/0.47
% 0.28/0.47 thf(apProp,definition,
% 0.28/0.47 ( apProp
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( func @ A @ B @ Xf )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in
% 0.28/0.47 @ ( setunion
% 0.28/0.47 @ ( dsetconstr @ B
% 0.28/0.47 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.28/0.47 @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ap_type,type,
% 0.28/0.47 ap: $i > $i > $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(app_type,type,
% 0.28/0.47 app: $o ).
% 0.28/0.47
% 0.28/0.47 thf(app,definition,
% 0.28/0.47 ( app
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( func @ A @ B @ Xf )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(infuncsetfunc_type,type,
% 0.28/0.47 infuncsetfunc: $o ).
% 0.28/0.47
% 0.28/0.47 thf(infuncsetfunc,definition,
% 0.28/0.47 ( infuncsetfunc
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.28/0.47 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ap2p_type,type,
% 0.28/0.47 ap2p: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ap2p,definition,
% 0.28/0.47 ( ap2p
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(funcinfuncset_type,type,
% 0.28/0.47 funcinfuncset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(funcinfuncset,definition,
% 0.28/0.47 ( funcinfuncset
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( func @ A @ B @ Xf )
% 0.28/0.47 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(lamProp_type,type,
% 0.28/0.47 lamProp: $o ).
% 0.28/0.47
% 0.28/0.47 thf(lamProp,definition,
% 0.28/0.47 ( lamProp
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.28/0.47 => ( func @ A @ B
% 0.28/0.47 @ ( dpsetconstr @ A @ B
% 0.28/0.47 @ ^ [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xf @ Xx )
% 0.28/0.47 = Xy ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(lam_type,type,
% 0.28/0.47 lam: $i > $i > ( $i > $i ) > $i ).
% 0.28/0.47
% 0.28/0.47 thf(lamp_type,type,
% 0.28/0.47 lamp: $o ).
% 0.28/0.47
% 0.28/0.47 thf(lamp,definition,
% 0.28/0.47 ( lamp
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.28/0.47 => ( func @ A @ B
% 0.28/0.47 @ ( lam @ A @ B
% 0.28/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(lam2p_type,type,
% 0.28/0.47 lam2p: $o ).
% 0.28/0.47
% 0.28/0.47 thf(lam2p,definition,
% 0.28/0.47 ( lam2p
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.28/0.47 => ( in
% 0.28/0.47 @ ( lam @ A @ B
% 0.28/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.28/0.47 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(brelnall1_type,type,
% 0.28/0.47 brelnall1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(brelnall1,definition,
% 0.28/0.47 ( brelnall1
% 0.28/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.28/0.47 ( ( breln @ A @ B @ R )
% 0.28/0.47 => ! [Xphi: $i > $o] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.28/0.47 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ R )
% 0.28/0.47 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(brelnall2_type,type,
% 0.28/0.47 brelnall2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(brelnall2,definition,
% 0.28/0.47 ( brelnall2
% 0.28/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.28/0.47 ( ( breln @ A @ B @ R )
% 0.28/0.47 => ! [Xphi: $i > $o] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.28/0.47 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ R )
% 0.28/0.47 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ex1E2_type,type,
% 0.28/0.47 ex1E2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ex1E2,definition,
% 0.28/0.47 ( ex1E2
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ( ex1 @ A
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( ( Xphi @ Xx )
% 0.28/0.47 => ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(funcGraphProp1_type,type,
% 0.28/0.47 funcGraphProp1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(funcGraphProp1,definition,
% 0.28/0.47 ( funcGraphProp1
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( func @ A @ B @ Xf )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(funcGraphProp3_type,type,
% 0.28/0.47 funcGraphProp3: $o ).
% 0.28/0.47
% 0.28/0.47 thf(funcGraphProp3,definition,
% 0.28/0.47 ( funcGraphProp3
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(funcGraphProp2_type,type,
% 0.28/0.47 funcGraphProp2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(funcGraphProp2,definition,
% 0.28/0.47 ( funcGraphProp2
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( func @ A @ B @ Xf )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.28/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.28/0.47 = Xy ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(funcextLem_type,type,
% 0.28/0.47 funcextLem: $o ).
% 0.28/0.47
% 0.28/0.47 thf(funcextLem,definition,
% 0.28/0.47 ( funcextLem
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( func @ A @ B @ Xf )
% 0.28/0.47 => ! [Xg: $i] :
% 0.28/0.47 ( ( func @ A @ B @ Xg )
% 0.28/0.47 => ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.28/0.47 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 0.28/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(funcGraphProp4_type,type,
% 0.28/0.47 funcGraphProp4: $o ).
% 0.28/0.47
% 0.28/0.47 thf(funcGraphProp4,definition,
% 0.28/0.47 ( funcGraphProp4
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.28/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.28/0.47 = Xy ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subbreln_type,type,
% 0.28/0.47 subbreln: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subbreln,definition,
% 0.28/0.47 ( subbreln
% 0.28/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.28/0.47 ( ( breln @ A @ B @ R )
% 0.28/0.47 => ! [S: $i] :
% 0.28/0.47 ( ( breln @ A @ B @ S )
% 0.28/0.47 => ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.28/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.28/0.47 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(eqbreln_type,type,
% 0.28/0.47 eqbreln: $o ).
% 0.28/0.47
% 0.28/0.47 thf(eqbreln,definition,
% 0.28/0.47 ( eqbreln
% 0.28/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.28/0.47 ( ( breln @ A @ B @ R )
% 0.28/0.47 => ! [S: $i] :
% 0.28/0.47 ( ( breln @ A @ B @ S )
% 0.28/0.47 => ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.28/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.28/0.47 => ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.28/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.28/0.47 => ( R = S ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(funcext_type,type,
% 0.28/0.47 funcext: $o ).
% 0.28/0.47
% 0.28/0.47 thf(funcext,definition,
% 0.28/0.47 ( funcext
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( func @ A @ B @ Xf )
% 0.28/0.47 => ! [Xg: $i] :
% 0.28/0.47 ( ( func @ A @ B @ Xg )
% 0.28/0.47 => ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.28/0.47 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.28/0.47 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(funcext2_type,type,
% 0.28/0.47 funcext2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(funcext2,definition,
% 0.28/0.47 ( funcext2
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.28/0.47 => ! [Xg: $i] :
% 0.28/0.47 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 0.28/0.47 => ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.28/0.47 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.28/0.47 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ap2apEq1_type,type,
% 0.28/0.47 ap2apEq1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ap2apEq1,definition,
% 0.28/0.47 ( ap2apEq1
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.28/0.47 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ap2apEq2_type,type,
% 0.28/0.47 ap2apEq2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ap2apEq2,definition,
% 0.28/0.47 ( ap2apEq2
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( func @ A @ B @ Xf )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.28/0.47 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(beta1_type,type,
% 0.28/0.47 beta1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(beta1,definition,
% 0.28/0.47 ( beta1
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( ap @ A @ B
% 0.28/0.47 @ ( lam @ A @ B
% 0.28/0.47 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.28/0.47 @ Xx )
% 0.28/0.47 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(eta1_type,type,
% 0.28/0.47 eta1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(eta1,definition,
% 0.28/0.47 ( eta1
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( func @ A @ B @ Xf )
% 0.28/0.47 => ( ( lam @ A @ B
% 0.28/0.47 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.28/0.47 = Xf ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(lam2lamEq_type,type,
% 0.28/0.47 lam2lamEq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(lam2lamEq,definition,
% 0.28/0.47 ( lam2lamEq
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.28/0.47 => ( ( lam @ A @ B
% 0.28/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.28/0.47 = ( lam @ A @ B
% 0.28/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(beta2_type,type,
% 0.28/0.47 beta2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(beta2,definition,
% 0.28/0.47 ( beta2
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( ap @ A @ B
% 0.28/0.47 @ ( lam @ A @ B
% 0.28/0.47 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.28/0.47 @ Xx )
% 0.28/0.47 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(eta2_type,type,
% 0.28/0.47 eta2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(eta2,definition,
% 0.28/0.47 ( eta2
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.28/0.47 => ( ( lam @ A @ B
% 0.28/0.47 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.28/0.47 = Xf ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(iffalseProp1_type,type,
% 0.28/0.47 iffalseProp1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(iffalseProp1,definition,
% 0.28/0.47 ( iffalseProp1
% 0.28/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( ~ Xphi
% 0.28/0.47 => ( in @ Xy
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xz: $i] :
% 0.28/0.47 ( ( Xphi
% 0.28/0.47 & ( Xz = Xx ) )
% 0.28/0.47 | ( ~ Xphi
% 0.28/0.47 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(iffalseProp2_type,type,
% 0.28/0.47 iffalseProp2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(iffalseProp2,definition,
% 0.28/0.47 ( iffalseProp2
% 0.28/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( ~ Xphi
% 0.28/0.47 => ( ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xz: $i] :
% 0.28/0.47 ( ( Xphi
% 0.28/0.47 & ( Xz = Xx ) )
% 0.28/0.47 | ( ~ Xphi
% 0.28/0.47 & ( Xz = Xy ) ) ) )
% 0.28/0.47 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(iftrueProp1_type,type,
% 0.28/0.47 iftrueProp1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(iftrueProp1,definition,
% 0.28/0.47 ( iftrueProp1
% 0.28/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( Xphi
% 0.28/0.47 => ( in @ Xx
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xz: $i] :
% 0.28/0.47 ( ( Xphi
% 0.28/0.47 & ( Xz = Xx ) )
% 0.28/0.47 | ( ~ Xphi
% 0.28/0.47 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(iftrueProp2_type,type,
% 0.28/0.47 iftrueProp2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(iftrueProp2,definition,
% 0.28/0.47 ( iftrueProp2
% 0.28/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( Xphi
% 0.28/0.47 => ( ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xz: $i] :
% 0.28/0.47 ( ( Xphi
% 0.28/0.47 & ( Xz = Xx ) )
% 0.28/0.47 | ( ~ Xphi
% 0.28/0.47 & ( Xz = Xy ) ) ) )
% 0.28/0.47 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ifSingleton_type,type,
% 0.28/0.47 ifSingleton: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ifSingleton,definition,
% 0.28/0.47 ( ifSingleton
% 0.28/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( singleton
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xz: $i] :
% 0.28/0.47 ( ( Xphi
% 0.28/0.47 & ( Xz = Xx ) )
% 0.28/0.47 | ( ~ Xphi
% 0.28/0.47 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(if_type,type,
% 0.28/0.47 if: $i > $o > $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(ifp_type,type,
% 0.28/0.47 ifp: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ifp,definition,
% 0.28/0.47 ( ifp
% 0.28/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(theeq_type,type,
% 0.28/0.47 theeq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(theeq,definition,
% 0.28/0.47 ( theeq
% 0.28/0.47 = ( ! [X: $i] :
% 0.28/0.47 ( ( singleton @ X )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ X )
% 0.28/0.47 => ( ( setunion @ X )
% 0.28/0.47 = Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(iftrue_type,type,
% 0.28/0.47 iftrue: $o ).
% 0.28/0.47
% 0.28/0.47 thf(iftrue,definition,
% 0.28/0.47 ( iftrue
% 0.28/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( Xphi
% 0.28/0.47 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.28/0.47 = Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(iffalse_type,type,
% 0.28/0.47 iffalse: $o ).
% 0.28/0.47
% 0.28/0.47 thf(iffalse,definition,
% 0.28/0.47 ( iffalse
% 0.28/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( ~ Xphi
% 0.28/0.47 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.28/0.47 = Xy ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(iftrueorfalse_type,type,
% 0.28/0.47 iftrueorfalse: $o ).
% 0.28/0.47
% 0.28/0.47 thf(iftrueorfalse,definition,
% 0.28/0.47 ( iftrueorfalse
% 0.28/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectT_lem_type,type,
% 0.28/0.47 binintersectT_lem: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectT_lem,definition,
% 0.28/0.47 ( binintersectT_lem
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binunionT_lem_type,type,
% 0.28/0.47 binunionT_lem: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binunionT_lem,definition,
% 0.28/0.47 ( binunionT_lem
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powersetT_lem_type,type,
% 0.28/0.47 powersetT_lem: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powersetT_lem,definition,
% 0.28/0.47 ( powersetT_lem
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusT_lem_type,type,
% 0.28/0.47 setminusT_lem: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusT_lem,definition,
% 0.28/0.47 ( setminusT_lem
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(complementT_lem_type,type,
% 0.28/0.47 complementT_lem: $o ).
% 0.28/0.47
% 0.28/0.47 thf(complementT_lem,definition,
% 0.28/0.47 ( complementT_lem
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setextT_type,type,
% 0.28/0.47 setextT: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setextT,definition,
% 0.28/0.47 ( setextT
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ X )
% 0.28/0.47 => ( in @ Xx @ Y ) ) )
% 0.28/0.47 => ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ Y )
% 0.28/0.47 => ( in @ Xx @ X ) ) )
% 0.28/0.47 => ( X = Y ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subsetTI_type,type,
% 0.28/0.47 subsetTI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subsetTI,definition,
% 0.28/0.47 ( subsetTI
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ X )
% 0.28/0.47 => ( in @ Xx @ Y ) ) )
% 0.28/0.47 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powersetTI1_type,type,
% 0.28/0.47 powersetTI1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powersetTI1,definition,
% 0.28/0.47 ( powersetTI1
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ X )
% 0.28/0.47 => ( in @ Xx @ Y ) ) )
% 0.28/0.47 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powersetTE1_type,type,
% 0.28/0.47 powersetTE1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powersetTE1,definition,
% 0.28/0.47 ( powersetTE1
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ X @ ( powerset @ Y ) )
% 0.28/0.47 => ( ( in @ Xx @ X )
% 0.28/0.47 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(complementTI1_type,type,
% 0.28/0.47 complementTI1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(complementTI1,definition,
% 0.28/0.47 ( complementTI1
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ X )
% 0.28/0.47 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(complementTE1_type,type,
% 0.28/0.47 complementTE1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(complementTE1,definition,
% 0.28/0.47 ( complementTE1
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 0.28/0.47 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectTELcontra_type,type,
% 0.28/0.47 binintersectTELcontra: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectTELcontra,definition,
% 0.28/0.47 ( binintersectTELcontra
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ~ ( in @ Xx @ X )
% 0.28/0.47 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectTERcontra_type,type,
% 0.28/0.47 binintersectTERcontra: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectTERcontra,definition,
% 0.28/0.47 ( binintersectTERcontra
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ~ ( in @ Xx @ Y )
% 0.28/0.47 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(contrasubsetT_type,type,
% 0.28/0.47 contrasubsetT: $o ).
% 0.28/0.47
% 0.28/0.47 thf(contrasubsetT,definition,
% 0.28/0.47 ( contrasubsetT
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.28/0.47 => ( ( in @ Xx @ Y )
% 0.28/0.47 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(contrasubsetT1_type,type,
% 0.28/0.47 contrasubsetT1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(contrasubsetT1,definition,
% 0.28/0.47 ( contrasubsetT1
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( subset @ X @ Y )
% 0.28/0.47 => ( ~ ( in @ Xx @ Y )
% 0.28/0.47 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(contrasubsetT2_type,type,
% 0.28/0.47 contrasubsetT2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(contrasubsetT2,definition,
% 0.28/0.47 ( contrasubsetT2
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ( ( subset @ X @ Y )
% 0.28/0.47 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(contrasubsetT3_type,type,
% 0.28/0.47 contrasubsetT3: $o ).
% 0.28/0.47
% 0.28/0.47 thf(contrasubsetT3,definition,
% 0.28/0.47 ( contrasubsetT3
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 0.28/0.47 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(doubleComplementI1_type,type,
% 0.28/0.47 doubleComplementI1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(doubleComplementI1,definition,
% 0.28/0.47 ( doubleComplementI1
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ X )
% 0.28/0.47 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(doubleComplementE1_type,type,
% 0.28/0.47 doubleComplementE1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(doubleComplementE1,definition,
% 0.28/0.47 ( doubleComplementE1
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 0.28/0.47 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(doubleComplementSub1_type,type,
% 0.28/0.47 doubleComplementSub1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(doubleComplementSub1,definition,
% 0.28/0.47 ( doubleComplementSub1
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(doubleComplementSub2_type,type,
% 0.28/0.47 doubleComplementSub2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(doubleComplementSub2,definition,
% 0.28/0.47 ( doubleComplementSub2
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(doubleComplementEq_type,type,
% 0.28/0.47 doubleComplementEq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(doubleComplementEq,definition,
% 0.28/0.47 ( doubleComplementEq
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ( X
% 0.28/0.47 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(complementTnotintersectT_type,type,
% 0.28/0.47 complementTnotintersectT: $o ).
% 0.28/0.47
% 0.28/0.47 thf(complementTnotintersectT,definition,
% 0.28/0.47 ( complementTnotintersectT
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.28/0.47 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(complementImpComplementIntersect_type,type,
% 0.28/0.47 complementImpComplementIntersect: $o ).
% 0.28/0.47
% 0.28/0.47 thf(complementImpComplementIntersect,definition,
% 0.28/0.47 ( complementImpComplementIntersect
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.28/0.47 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(complementSubsetComplementIntersect_type,type,
% 0.28/0.47 complementSubsetComplementIntersect: $o ).
% 0.28/0.47
% 0.28/0.47 thf(complementSubsetComplementIntersect,definition,
% 0.28/0.47 ( complementSubsetComplementIntersect
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(complementInPowersetComplementIntersect_type,type,
% 0.28/0.47 complementInPowersetComplementIntersect: $o ).
% 0.28/0.47
% 0.28/0.47 thf(complementInPowersetComplementIntersect,definition,
% 0.28/0.47 ( complementInPowersetComplementIntersect
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(contraSubsetComplement_type,type,
% 0.28/0.47 contraSubsetComplement: $o ).
% 0.28/0.47
% 0.28/0.47 thf(contraSubsetComplement,definition,
% 0.28/0.47 ( contraSubsetComplement
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ Y )
% 0.28/0.47 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(complementTcontraSubset_type,type,
% 0.28/0.47 complementTcontraSubset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(complementTcontraSubset,definition,
% 0.28/0.47 ( complementTcontraSubset
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.28/0.47 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binunionTILcontra_type,type,
% 0.28/0.47 binunionTILcontra: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binunionTILcontra,definition,
% 0.28/0.47 ( binunionTILcontra
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.28/0.47 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binunionTIRcontra_type,type,
% 0.28/0.47 binunionTIRcontra: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binunionTIRcontra,definition,
% 0.28/0.47 ( binunionTIRcontra
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.28/0.47 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(inIntersectImpInUnion_type,type,
% 0.28/0.47 inIntersectImpInUnion: $o ).
% 0.28/0.47
% 0.28/0.47 thf(inIntersectImpInUnion,definition,
% 0.28/0.47 ( inIntersectImpInUnion
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ! [Z: $i] :
% 0.28/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.28/0.47 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(inIntersectImpInUnion2_type,type,
% 0.28/0.47 inIntersectImpInUnion2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(inIntersectImpInUnion2,definition,
% 0.28/0.47 ( inIntersectImpInUnion2
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ! [Z: $i] :
% 0.28/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.28/0.47 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(inIntersectImpInIntersectUnions_type,type,
% 0.28/0.47 inIntersectImpInIntersectUnions: $o ).
% 0.28/0.47
% 0.28/0.47 thf(inIntersectImpInIntersectUnions,definition,
% 0.28/0.47 ( inIntersectImpInIntersectUnions
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ! [Z: $i] :
% 0.28/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.28/0.47 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(intersectInPowersetIntersectUnions_type,type,
% 0.28/0.47 intersectInPowersetIntersectUnions: $o ).
% 0.28/0.47
% 0.28/0.47 thf(intersectInPowersetIntersectUnions,definition,
% 0.28/0.47 ( intersectInPowersetIntersectUnions
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ! [Z: $i] :
% 0.28/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.28/0.47 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(inComplementUnionImpNotIn1_type,type,
% 0.28/0.47 inComplementUnionImpNotIn1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(inComplementUnionImpNotIn1,definition,
% 0.28/0.47 ( inComplementUnionImpNotIn1
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.28/0.47 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(inComplementUnionImpInComplement1_type,type,
% 0.28/0.47 inComplementUnionImpInComplement1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(inComplementUnionImpInComplement1,definition,
% 0.28/0.47 ( inComplementUnionImpInComplement1
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.28/0.47 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binunionTE_type,type,
% 0.28/0.47 binunionTE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binunionTE,definition,
% 0.28/0.47 ( binunionTE
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ! [Xphi: $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.28/0.47 => ( ( ( in @ Xx @ X )
% 0.28/0.47 => Xphi )
% 0.28/0.47 => ( ( ( in @ Xx @ Y )
% 0.28/0.47 => Xphi )
% 0.28/0.47 => Xphi ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binunionTEcontra_type,type,
% 0.28/0.47 binunionTEcontra: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binunionTEcontra,definition,
% 0.28/0.47 ( binunionTEcontra
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ~ ( in @ Xx @ X )
% 0.28/0.47 => ( ~ ( in @ Xx @ Y )
% 0.28/0.47 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(demorgan2a1_type,type,
% 0.28/0.47 demorgan2a1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(demorgan2a1,definition,
% 0.28/0.47 ( demorgan2a1
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.28/0.47 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(complementUnionInPowersetComplement_type,type,
% 0.28/0.47 complementUnionInPowersetComplement: $o ).
% 0.28/0.47
% 0.28/0.47 thf(complementUnionInPowersetComplement,definition,
% 0.28/0.47 ( complementUnionInPowersetComplement
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(demorgan2a2_type,type,
% 0.28/0.47 demorgan2a2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(demorgan2a2,definition,
% 0.28/0.47 ( demorgan2a2
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.28/0.47 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(demorgan1a_type,type,
% 0.28/0.47 demorgan1a: $o ).
% 0.28/0.47
% 0.28/0.47 thf(demorgan1a,definition,
% 0.28/0.47 ( demorgan1a
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 0.28/0.47 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(demorgan1b_type,type,
% 0.28/0.47 demorgan1b: $o ).
% 0.28/0.47
% 0.28/0.47 thf(demorgan1b,definition,
% 0.28/0.47 ( demorgan1b
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.28/0.47 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(demorgan1_type,type,
% 0.28/0.47 demorgan1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(demorgan1,definition,
% 0.28/0.47 ( demorgan1
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 0.28/0.47 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(demorgan2a_type,type,
% 0.28/0.47 demorgan2a: $o ).
% 0.28/0.47
% 0.28/0.47 thf(demorgan2a,definition,
% 0.28/0.47 ( demorgan2a
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.28/0.47 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(demorgan2b2_type,type,
% 0.28/0.47 demorgan2b2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(demorgan2b2,definition,
% 0.28/0.47 ( demorgan2b2
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.28/0.47 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 0.28/0.47 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(demorgan2b_type,type,
% 0.28/0.47 demorgan2b: $o ).
% 0.28/0.47
% 0.28/0.47 thf(demorgan2b,definition,
% 0.28/0.47 ( demorgan2b
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.28/0.47 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(demorgan2_type,type,
% 0.28/0.47 demorgan2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(demorgan2,definition,
% 0.28/0.47 ( demorgan2
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 0.28/0.47 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(woz13rule0_type,type,
% 0.28/0.47 woz13rule0: $o ).
% 0.28/0.47
% 0.28/0.47 thf(woz13rule0,definition,
% 0.28/0.47 ( woz13rule0
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.28/0.47 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(woz13rule1_type,type,
% 0.28/0.47 woz13rule1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(woz13rule1,definition,
% 0.28/0.47 ( woz13rule1
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ! [Z: $i] :
% 0.28/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.28/0.47 => ( ( subset @ X @ Z )
% 0.28/0.47 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(woz13rule2_type,type,
% 0.28/0.47 woz13rule2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(woz13rule2,definition,
% 0.28/0.47 ( woz13rule2
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ! [Z: $i] :
% 0.28/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.28/0.47 => ( ( subset @ Y @ Z )
% 0.28/0.47 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(woz13rule3_type,type,
% 0.28/0.47 woz13rule3: $o ).
% 0.28/0.47
% 0.28/0.47 thf(woz13rule3,definition,
% 0.28/0.47 ( woz13rule3
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ! [Z: $i] :
% 0.28/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.28/0.47 => ( ( subset @ X @ Y )
% 0.28/0.47 => ( ( subset @ X @ Z )
% 0.28/0.47 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(woz13rule4_type,type,
% 0.28/0.47 woz13rule4: $o ).
% 0.28/0.47
% 0.28/0.47 thf(woz13rule4,definition,
% 0.28/0.47 ( woz13rule4
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ! [Z: $i] :
% 0.28/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.28/0.47 => ! [W: $i] :
% 0.28/0.47 ( ( in @ W @ ( powerset @ A ) )
% 0.28/0.47 => ( ( subset @ X @ Z )
% 0.28/0.47 => ( ( subset @ Y @ W )
% 0.28/0.47 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(woz1_1_type,type,
% 0.28/0.47 woz1_1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(woz1_1,definition,
% 0.28/0.47 ( woz1_1
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(woz1_2_type,type,
% 0.28/0.47 woz1_2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(woz1_2,definition,
% 0.28/0.47 ( woz1_2
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ! [Z: $i] :
% 0.28/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.28/0.47 => ! [W: $i] :
% 0.28/0.47 ( ( in @ W @ ( powerset @ A ) )
% 0.28/0.47 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 0.28/0.47 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(woz1_3_type,type,
% 0.28/0.47 woz1_3: $o ).
% 0.28/0.47
% 0.28/0.47 thf(woz1_3,definition,
% 0.28/0.47 ( woz1_3
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ! [Z: $i] :
% 0.28/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.28/0.47 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(woz1_4_type,type,
% 0.28/0.47 woz1_4: $o ).
% 0.28/0.47
% 0.28/0.47 thf(woz1_4,definition,
% 0.28/0.47 ( woz1_4
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.28/0.47 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(woz1_5_type,type,
% 0.28/0.47 woz1_5: $o ).
% 0.28/0.47
% 0.28/0.47 thf(woz1_5,definition,
% 0.28/0.47 ( woz1_5
% 0.28/0.47 = ( ! [A: $i,X: $i] :
% 0.28/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.28/0.47 => ! [Y: $i] :
% 0.28/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.28/0.47 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(breln1_type,type,
% 0.28/0.47 breln1: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(breln1all2_type,type,
% 0.28/0.47 breln1all2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(breln1all2,definition,
% 0.28/0.47 ( breln1all2
% 0.28/0.47 = ( ! [A: $i,R: $i] :
% 0.28/0.47 ( ( breln1 @ A @ R )
% 0.28/0.47 => ! [Xphi: $i > $o] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.28/0.47 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ R )
% 0.28/0.47 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(breln1Set_type,type,
% 0.28/0.47 breln1Set: $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(breln1SetBreln1_type,type,
% 0.28/0.47 breln1SetBreln1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(breln1SetBreln1,definition,
% 0.28/0.47 ( breln1SetBreln1
% 0.28/0.47 = ( ! [A: $i,R: $i] :
% 0.28/0.47 ( ( in @ R @ ( breln1Set @ A ) )
% 0.28/0.47 => ( breln1 @ A @ R ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(transitive_type,type,
% 0.28/0.47 transitive: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(antisymmetric_type,type,
% 0.28/0.47 antisymmetric: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(reflexive_type,type,
% 0.28/0.47 reflexive: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(refltransitive_type,type,
% 0.28/0.47 refltransitive: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(refllinearorder_type,type,
% 0.28/0.47 refllinearorder: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(reflwellordering_type,type,
% 0.28/0.47 reflwellordering: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(choice2fnsingleton_type,type,
% 0.28/0.47 choice2fnsingleton: $o ).
% 0.28/0.47
% 0.28/0.47 thf(choice2fnsingleton,definition,
% 0.28/0.47 ( choice2fnsingleton
% 0.28/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ? [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 & ( Xphi @ Xx @ Xy ) ) )
% 0.28/0.47 => ! [R: $i] :
% 0.28/0.47 ( ( in @ R @ ( breln1Set @ B ) )
% 0.28/0.47 => ( ( reflwellordering @ B @ R )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( singleton
% 0.28/0.47 @ ( dsetconstr @ B
% 0.28/0.47 @ ^ [Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xx @ Xy )
% 0.28/0.47 & ! [Xz: $i] :
% 0.28/0.47 ( ( in @ Xz @ B )
% 0.28/0.47 => ( ( Xphi @ Xx @ Xz )
% 0.28/0.47 => ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setOfPairsIsBReln1_type,type,
% 0.28/0.47 setOfPairsIsBReln1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setOfPairsIsBReln1,definition,
% 0.28/0.47 ( setOfPairsIsBReln1
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $i > $o] :
% 0.28/0.47 ( breln1 @ A
% 0.28/0.47 @ ( dpsetconstr @ A @ A
% 0.28/0.47 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(breln1all1_type,type,
% 0.28/0.47 breln1all1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(breln1all1,definition,
% 0.28/0.47 ( breln1all1
% 0.28/0.47 = ( ! [A: $i,R: $i] :
% 0.28/0.47 ( ( breln1 @ A @ R )
% 0.28/0.47 => ! [Xphi: $i > $o] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.28/0.47 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ R )
% 0.28/0.47 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subbreln1_type,type,
% 0.28/0.47 subbreln1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subbreln1,definition,
% 0.28/0.47 ( subbreln1
% 0.28/0.47 = ( ! [A: $i,R: $i] :
% 0.28/0.47 ( ( breln1 @ A @ R )
% 0.28/0.47 => ! [S: $i] :
% 0.28/0.47 ( ( breln1 @ A @ S )
% 0.28/0.47 => ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.28/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.28/0.47 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(eqbreln1_type,type,
% 0.28/0.47 eqbreln1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(eqbreln1,definition,
% 0.28/0.47 ( eqbreln1
% 0.28/0.47 = ( ! [A: $i,R: $i] :
% 0.28/0.47 ( ( breln1 @ A @ R )
% 0.28/0.47 => ! [S: $i] :
% 0.28/0.47 ( ( breln1 @ A @ S )
% 0.28/0.47 => ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.28/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.28/0.47 => ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.28/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.28/0.47 => ( R = S ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(breln1invset_type,type,
% 0.28/0.47 breln1invset: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(breln1invprop_type,type,
% 0.28/0.47 breln1invprop: $o ).
% 0.28/0.47
% 0.28/0.47 thf(breln1invprop,definition,
% 0.28/0.47 ( breln1invprop
% 0.28/0.47 = ( ! [A: $i,R: $i] :
% 0.28/0.47 ( ( breln1 @ A @ R )
% 0.28/0.47 => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(breln1invI_type,type,
% 0.28/0.47 breln1invI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(breln1invI,definition,
% 0.28/0.47 ( breln1invI
% 0.28/0.47 = ( ! [A: $i,R: $i] :
% 0.28/0.47 ( ( breln1 @ A @ R )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.28/0.47 => ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(breln1invE_type,type,
% 0.28/0.47 breln1invE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(breln1invE,definition,
% 0.28/0.47 ( breln1invE
% 0.28/0.47 = ( ! [A: $i,R: $i] :
% 0.28/0.47 ( ( breln1 @ A @ R )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
% 0.28/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(breln1compset_type,type,
% 0.28/0.47 breln1compset: $i > $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(breln1compprop_type,type,
% 0.28/0.47 breln1compprop: $o ).
% 0.28/0.47
% 0.28/0.47 thf(breln1compprop,definition,
% 0.28/0.47 ( breln1compprop
% 0.28/0.47 = ( ! [A: $i,R: $i] :
% 0.28/0.47 ( ( breln1 @ A @ R )
% 0.28/0.47 => ! [S: $i] :
% 0.28/0.47 ( ( breln1 @ A @ S )
% 0.28/0.47 => ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(breln1compI_type,type,
% 0.28/0.47 breln1compI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(breln1compI,definition,
% 0.28/0.47 ( breln1compI
% 0.28/0.47 = ( ! [A: $i,R: $i] :
% 0.28/0.47 ( ( breln1 @ A @ R )
% 0.28/0.47 => ! [S: $i] :
% 0.28/0.47 ( ( breln1 @ A @ S )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ! [Xz: $i] :
% 0.28/0.47 ( ( in @ Xz @ A )
% 0.28/0.47 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.28/0.47 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 0.28/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(breln1compE_type,type,
% 0.28/0.47 breln1compE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(breln1compE,definition,
% 0.28/0.47 ( breln1compE
% 0.28/0.47 = ( ! [A: $i,R: $i] :
% 0.28/0.47 ( ( breln1 @ A @ R )
% 0.28/0.47 => ! [S: $i] :
% 0.28/0.47 ( ( breln1 @ A @ S )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 0.28/0.47 => ? [Xz: $i] :
% 0.28/0.47 ( ( in @ Xz @ A )
% 0.28/0.47 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.28/0.47 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(breln1compEex_type,type,
% 0.28/0.47 breln1compEex: $o ).
% 0.28/0.47
% 0.28/0.47 thf(breln1compEex,definition,
% 0.28/0.47 ( breln1compEex
% 0.28/0.47 = ( ! [A: $i,R: $i] :
% 0.28/0.47 ( ( breln1 @ A @ R )
% 0.28/0.47 => ! [S: $i] :
% 0.28/0.47 ( ( breln1 @ A @ S )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 0.28/0.47 => ! [Xphi: $o] :
% 0.28/0.47 ( ! [Xz: $i] :
% 0.28/0.47 ( ( in @ Xz @ A )
% 0.28/0.47 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.28/0.47 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 0.28/0.47 => Xphi ) ) )
% 0.28/0.47 => Xphi ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(breln1unionprop_type,type,
% 0.28/0.47 breln1unionprop: $o ).
% 0.28/0.47
% 0.28/0.47 thf(breln1unionprop,definition,
% 0.28/0.47 ( breln1unionprop
% 0.28/0.47 = ( ! [A: $i,R: $i] :
% 0.28/0.47 ( ( breln1 @ A @ R )
% 0.28/0.47 => ! [S: $i] :
% 0.28/0.47 ( ( breln1 @ A @ S )
% 0.28/0.47 => ( breln1 @ A @ ( binunion @ R @ S ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(breln1unionIL_type,type,
% 0.28/0.47 breln1unionIL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(breln1unionIL,definition,
% 0.28/0.47 ( breln1unionIL
% 0.28/0.47 = ( ! [A: $i,R: $i] :
% 0.28/0.47 ( ( breln1 @ A @ R )
% 0.28/0.47 => ! [S: $i] :
% 0.28/0.47 ( ( breln1 @ A @ S )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.28/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(breln1unionIR_type,type,
% 0.28/0.47 breln1unionIR: $o ).
% 0.28/0.47
% 0.28/0.47 thf(breln1unionIR,definition,
% 0.28/0.47 ( breln1unionIR
% 0.28/0.47 = ( ! [A: $i,R: $i] :
% 0.28/0.47 ( ( breln1 @ A @ R )
% 0.28/0.47 => ! [S: $i] :
% 0.28/0.47 ( ( breln1 @ A @ S )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.28/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(breln1unionI_type,type,
% 0.28/0.47 breln1unionI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(breln1unionI,definition,
% 0.28/0.47 ( breln1unionI
% 0.28/0.47 = ( ! [A: $i,R: $i] :
% 0.28/0.47 ( ( breln1 @ A @ R )
% 0.28/0.47 => ! [S: $i] :
% 0.28/0.47 ( ( breln1 @ A @ S )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.28/0.47 | ( in @ ( kpair @ Xx @ Xy ) @ S ) )
% 0.28/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(breln1unionE_type,type,
% 0.28/0.47 breln1unionE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(breln1unionE,definition,
% 0.28/0.47 ( breln1unionE
% 0.28/0.47 = ( ! [A: $i,R: $i] :
% 0.28/0.47 ( ( breln1 @ A @ R )
% 0.28/0.47 => ! [S: $i] :
% 0.28/0.47 ( ( breln1 @ A @ S )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 0.28/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.28/0.47 | ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(breln1unionEcases_type,type,
% 0.28/0.47 breln1unionEcases: $o ).
% 0.28/0.47
% 0.28/0.47 thf(breln1unionEcases,definition,
% 0.28/0.47 ( breln1unionEcases
% 0.28/0.47 = ( ! [A: $i,R: $i] :
% 0.28/0.47 ( ( breln1 @ A @ R )
% 0.28/0.47 => ! [S: $i] :
% 0.28/0.47 ( ( breln1 @ A @ S )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 0.28/0.47 => ! [Xphi: $o] :
% 0.28/0.47 ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.28/0.47 => Xphi )
% 0.28/0.47 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.28/0.47 => Xphi )
% 0.28/0.47 => Xphi ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(breln1unionCommutes_type,type,
% 0.28/0.47 breln1unionCommutes: $o ).
% 0.28/0.47
% 0.28/0.47 thf(breln1unionCommutes,definition,
% 0.28/0.47 ( breln1unionCommutes
% 0.28/0.47 = ( ! [A: $i,R: $i] :
% 0.28/0.47 ( ( breln1 @ A @ R )
% 0.28/0.47 => ! [S: $i] :
% 0.28/0.47 ( ( breln1 @ A @ S )
% 0.28/0.47 => ( ( binunion @ R @ S )
% 0.28/0.47 = ( binunion @ S @ R ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(woz2Ex_type,type,
% 0.28/0.47 woz2Ex: $o ).
% 0.28/0.47
% 0.28/0.47 thf(woz2Ex,definition,
% 0.28/0.47 ( woz2Ex
% 0.28/0.47 = ( ! [A: $i,R: $i] :
% 0.28/0.47 ( ( breln1 @ A @ R )
% 0.28/0.47 => ( R
% 0.28/0.47 = ( breln1invset @ A @ ( breln1invset @ A @ R ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(woz2W_type,type,
% 0.28/0.47 woz2W: $o ).
% 0.28/0.47
% 0.28/0.47 thf(woz2W,definition,
% 0.28/0.47 ( woz2W
% 0.28/0.47 = ( ! [A: $i,R: $i] :
% 0.28/0.47 ( ( breln1 @ A @ R )
% 0.28/0.47 => ! [S: $i] :
% 0.28/0.47 ( ( breln1 @ A @ S )
% 0.28/0.47 => ( ( breln1invset @ A @ ( breln1compset @ A @ R @ S ) )
% 0.28/0.47 = ( breln1compset @ A @ ( breln1invset @ A @ S ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(woz2A_type,type,
% 0.28/0.47 woz2A: $o ).
% 0.28/0.47
% 0.28/0.47 thf(woz2A,definition,
% 0.28/0.47 ( woz2A
% 0.28/0.47 = ( ! [A: $i,R: $i] :
% 0.28/0.47 ( ( breln1 @ A @ R )
% 0.28/0.47 => ! [S: $i] :
% 0.28/0.47 ( ( breln1 @ A @ S )
% 0.28/0.47 => ! [T: $i] :
% 0.28/0.47 ( ( breln1 @ A @ T )
% 0.28/0.47 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 0.28/0.47 = ( binunion @ ( breln1compset @ A @ R @ T ) @ ( breln1compset @ A @ S @ T ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(woz2B_type,type,
% 0.28/0.47 woz2B: $o ).
% 0.28/0.47
% 0.28/0.47 thf(woz2B,definition,
% 0.28/0.47 ( woz2B
% 0.28/0.47 = ( ! [A: $i,R: $i] :
% 0.28/0.47 ( ( breln1 @ A @ R )
% 0.28/0.47 => ! [S: $i] :
% 0.28/0.47 ( ( breln1 @ A @ S )
% 0.28/0.47 => ! [T: $i] :
% 0.28/0.47 ( ( breln1 @ A @ T )
% 0.28/0.47 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 0.28/0.47 = ( binunion @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ S ) ) ) @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(image1Ex_type,type,
% 0.28/0.47 image1Ex: $o ).
% 0.28/0.47
% 0.28/0.47 thf(image1Ex,definition,
% 0.28/0.47 ( image1Ex
% 0.28/0.47 = ( ! [A: $i,Xf: $i > $i] :
% 0.28/0.47 ? [B: $i] :
% 0.28/0.47 ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 <=> ? [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 & ( Xx
% 0.28/0.47 = ( Xf @ Xy ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(image1Ex1_type,type,
% 0.28/0.47 image1Ex1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(image1Ex1,definition,
% 0.28/0.47 ( image1Ex1
% 0.28/0.47 = ( ! [A: $i,Xf: $i > $i] :
% 0.28/0.47 ( exu
% 0.28/0.47 @ ^ [B: $i] :
% 0.28/0.47 ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 <=> ? [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 & ( Xx
% 0.28/0.47 = ( Xf @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(image1_type,type,
% 0.28/0.47 image1: $i > ( $i > $i ) > $i ).
% 0.28/0.47
% 0.28/0.47 thf(image1Equiv_type,type,
% 0.28/0.47 image1Equiv: $o ).
% 0.28/0.47
% 0.28/0.47 thf(image1Equiv,definition,
% 0.28/0.47 ( image1Equiv
% 0.28/0.47 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx
% 0.28/0.47 @ ( image1 @ A
% 0.28/0.47 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 0.28/0.47 <=> ? [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 & ( Xx
% 0.28/0.47 = ( Xf @ Xy ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(image1E_type,type,
% 0.28/0.47 image1E: $o ).
% 0.28/0.47
% 0.28/0.47 thf(image1E,definition,
% 0.28/0.47 ( image1E
% 0.28/0.47 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx
% 0.28/0.47 @ ( image1 @ A
% 0.28/0.47 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 0.28/0.47 => ? [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 & ( Xx
% 0.28/0.47 = ( Xf @ Xy ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(image1I_type,type,
% 0.28/0.47 image1I: $o ).
% 0.28/0.47
% 0.28/0.47 thf(image1I,definition,
% 0.28/0.47 ( image1I
% 0.28/0.47 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 0.28/0.47 ( ? [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 & ( Xx
% 0.28/0.47 = ( Xf @ Xy ) ) )
% 0.28/0.47 => ( in @ Xx
% 0.28/0.47 @ ( image1 @ A
% 0.28/0.47 @ ^ [Xy: $i] : ( Xf @ Xy ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(injective_type,type,
% 0.28/0.47 injective: $i > $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(injFuncSet_type,type,
% 0.28/0.47 injFuncSet: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(injFuncInInjFuncSet_type,type,
% 0.28/0.47 injFuncInInjFuncSet: $o ).
% 0.28/0.47
% 0.28/0.47 thf(injFuncInInjFuncSet,definition,
% 0.28/0.47 ( injFuncInInjFuncSet
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.28/0.47 => ( ( injective @ A @ B @ Xf )
% 0.28/0.47 => ( in @ Xf @ ( injFuncSet @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(injFuncSetFuncIn_type,type,
% 0.28/0.47 injFuncSetFuncIn: $o ).
% 0.28/0.47
% 0.28/0.47 thf(injFuncSetFuncIn,definition,
% 0.28/0.47 ( injFuncSetFuncIn
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( in @ Xf @ ( injFuncSet @ A @ B ) )
% 0.28/0.47 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(injFuncSetFuncInj_type,type,
% 0.28/0.47 injFuncSetFuncInj: $o ).
% 0.28/0.47
% 0.28/0.47 thf(injFuncSetFuncInj,definition,
% 0.28/0.47 ( injFuncSetFuncInj
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i,Xf: $i] :
% 0.28/0.47 ( ( in @ Xf @ ( injFuncSet @ Xx @ Xy ) )
% 0.28/0.47 => ( injective @ Xx @ Xy @ Xf ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(surjective_type,type,
% 0.28/0.47 surjective: $i > $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(surjective,definition,
% 0.28/0.47 ( surjective
% 0.28/0.47 = ( ^ [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ? [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 & ( ( ap @ A @ B @ Xf @ Xy )
% 0.28/0.47 = Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(surjFuncSet_type,type,
% 0.28/0.47 surjFuncSet: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(surjFuncSetFuncIn_type,type,
% 0.28/0.47 surjFuncSetFuncIn: $o ).
% 0.28/0.47
% 0.28/0.47 thf(surjFuncSetFuncIn,definition,
% 0.28/0.47 ( surjFuncSetFuncIn
% 0.28/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.28/0.47 ( ( in @ Xf @ ( surjFuncSet @ A @ B ) )
% 0.28/0.47 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(surjFuncSetFuncSurj_type,type,
% 0.28/0.47 surjFuncSetFuncSurj: $o ).
% 0.28/0.47
% 0.28/0.47 thf(surjFuncSetFuncSurj,definition,
% 0.28/0.47 ( surjFuncSetFuncSurj
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i,Xf: $i] :
% 0.28/0.47 ( ( in @ Xf @ ( surjFuncSet @ Xx @ Xy ) )
% 0.28/0.47 => ( surjective @ Xx @ Xy @ Xf ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(leftInvIsSurj,conjecture,
% 0.28/0.47 ( setextAx
% 0.28/0.47 => ( emptysetAx
% 0.28/0.47 => ( setadjoinAx
% 0.28/0.47 => ( powersetAx
% 0.28/0.47 => ( setunionAx
% 0.28/0.47 => ( omega0Ax
% 0.28/0.47 => ( omegaSAx
% 0.28/0.47 => ( omegaIndAx
% 0.28/0.47 => ( replAx
% 0.28/0.47 => ( foundationAx
% 0.28/0.47 => ( wellorderingAx
% 0.28/0.47 => ( descrp
% 0.28/0.47 => ( dsetconstrI
% 0.28/0.47 => ( dsetconstrEL
% 0.28/0.47 => ( dsetconstrER
% 0.28/0.47 => ( exuE1
% 0.28/0.47 => ( prop2setE
% 0.28/0.47 => ( emptysetE
% 0.28/0.47 => ( emptysetimpfalse
% 0.28/0.47 => ( notinemptyset
% 0.28/0.47 => ( exuE3e
% 0.28/0.47 => ( setext
% 0.28/0.47 => ( emptyI
% 0.28/0.47 => ( noeltsimpempty
% 0.28/0.47 => ( setbeta
% 0.28/0.47 => ( nonemptyE1
% 0.28/0.47 => ( nonemptyI
% 0.28/0.47 => ( nonemptyI1
% 0.28/0.47 => ( setadjoinIL
% 0.28/0.47 => ( emptyinunitempty
% 0.28/0.47 => ( setadjoinIR
% 0.28/0.47 => ( setadjoinE
% 0.28/0.47 => ( setadjoinOr
% 0.28/0.47 => ( setoftrueEq
% 0.28/0.47 => ( powersetI
% 0.28/0.47 => ( emptyinPowerset
% 0.28/0.47 => ( emptyInPowerset
% 0.28/0.47 => ( powersetE
% 0.28/0.47 => ( setunionI
% 0.28/0.47 => ( setunionE
% 0.28/0.47 => ( subPowSU
% 0.28/0.47 => ( exuE2
% 0.28/0.47 => ( nonemptyImpWitness
% 0.28/0.47 => ( uniqinunit
% 0.28/0.47 => ( notinsingleton
% 0.28/0.47 => ( eqinunit
% 0.28/0.47 => ( singletonsswitch
% 0.28/0.47 => ( upairsetE
% 0.28/0.47 => ( upairsetIL
% 0.28/0.47 => ( upairsetIR
% 0.28/0.47 => ( emptyE1
% 0.28/0.47 => ( vacuousDall
% 0.28/0.47 => ( quantDeMorgan1
% 0.28/0.47 => ( quantDeMorgan2
% 0.28/0.47 => ( quantDeMorgan3
% 0.28/0.47 => ( quantDeMorgan4
% 0.28/0.47 => ( prop2setI
% 0.28/0.47 => ( prop2set2propI
% 0.28/0.47 => ( notdexE
% 0.28/0.47 => ( notdallE
% 0.28/0.47 => ( exuI1
% 0.28/0.47 => ( exuI3
% 0.28/0.47 => ( exuI2
% 0.28/0.47 => ( inCongP
% 0.28/0.47 => ( in__Cong
% 0.28/0.47 => ( exuE3u
% 0.28/0.47 => ( exu__Cong
% 0.28/0.47 => ( emptyset__Cong
% 0.28/0.47 => ( setadjoin__Cong
% 0.28/0.47 => ( powerset__Cong
% 0.28/0.47 => ( setunion__Cong
% 0.28/0.47 => ( omega__Cong
% 0.28/0.47 => ( exuEu
% 0.28/0.47 => ( descr__Cong
% 0.28/0.47 => ( dsetconstr__Cong
% 0.28/0.47 => ( subsetI1
% 0.28/0.47 => ( eqimpsubset2
% 0.28/0.47 => ( eqimpsubset1
% 0.28/0.47 => ( subsetI2
% 0.28/0.47 => ( emptysetsubset
% 0.28/0.47 => ( subsetE
% 0.28/0.47 => ( subsetE2
% 0.28/0.47 => ( notsubsetI
% 0.28/0.47 => ( notequalI1
% 0.28/0.47 => ( notequalI2
% 0.28/0.47 => ( subsetRefl
% 0.28/0.47 => ( subsetTrans
% 0.28/0.47 => ( setadjoinSub
% 0.28/0.47 => ( setadjoinSub2
% 0.28/0.47 => ( subset2powerset
% 0.28/0.47 => ( setextsub
% 0.28/0.47 => ( subsetemptysetimpeq
% 0.28/0.47 => ( powersetI1
% 0.28/0.47 => ( powersetE1
% 0.28/0.47 => ( inPowerset
% 0.28/0.47 => ( powersetsubset
% 0.28/0.47 => ( sepInPowerset
% 0.28/0.47 => ( sepSubset
% 0.28/0.47 => ( binunionIL
% 0.28/0.47 => ( upairset2IR
% 0.28/0.47 => ( binunionIR
% 0.28/0.47 => ( binunionEcases
% 0.28/0.47 => ( binunionE
% 0.28/0.47 => ( binunionLsub
% 0.28/0.47 => ( binunionRsub
% 0.28/0.47 => ( binintersectI
% 0.28/0.47 => ( binintersectSubset5
% 0.28/0.47 => ( binintersectEL
% 0.28/0.47 => ( binintersectLsub
% 0.28/0.47 => ( binintersectSubset2
% 0.28/0.47 => ( binintersectSubset3
% 0.28/0.47 => ( binintersectER
% 0.28/0.47 => ( disjointsetsI1
% 0.28/0.47 => ( binintersectRsub
% 0.28/0.47 => ( binintersectSubset4
% 0.28/0.47 => ( binintersectSubset1
% 0.28/0.47 => ( bs114d
% 0.28/0.47 => ( setminusI
% 0.28/0.47 => ( setminusEL
% 0.28/0.47 => ( setminusER
% 0.28/0.47 => ( setminusSubset2
% 0.28/0.47 => ( setminusERneg
% 0.28/0.47 => ( setminusELneg
% 0.28/0.47 => ( setminusILneg
% 0.28/0.47 => ( setminusIRneg
% 0.28/0.47 => ( setminusLsub
% 0.28/0.47 => ( setminusSubset1
% 0.28/0.47 => ( symdiffE
% 0.28/0.47 => ( symdiffI1
% 0.28/0.47 => ( symdiffI2
% 0.28/0.47 => ( symdiffIneg1
% 0.28/0.47 => ( symdiffIneg2
% 0.28/0.47 => ( secondinupair
% 0.28/0.47 => ( setukpairIL
% 0.28/0.47 => ( setukpairIR
% 0.28/0.47 => ( kpairiskpair
% 0.28/0.47 => ( kpairp
% 0.28/0.47 => ( singletonsubset
% 0.28/0.47 => ( singletoninpowerset
% 0.28/0.47 => ( singletoninpowunion
% 0.28/0.47 => ( upairset2E
% 0.28/0.47 => ( upairsubunion
% 0.28/0.47 => ( upairinpowunion
% 0.28/0.48 => ( ubforcartprodlem1
% 0.28/0.48 => ( ubforcartprodlem2
% 0.28/0.48 => ( ubforcartprodlem3
% 0.28/0.48 => ( cartprodpairin
% 0.28/0.48 => ( cartprodmempair1
% 0.28/0.48 => ( cartprodmempair
% 0.28/0.48 => ( setunionE2
% 0.28/0.48 => ( setunionsingleton1
% 0.28/0.48 => ( setunionsingleton2
% 0.28/0.48 => ( setunionsingleton
% 0.28/0.48 => ( singletonprop
% 0.28/0.48 => ( ex1E1
% 0.28/0.48 => ( ex1I
% 0.28/0.48 => ( ex1I2
% 0.28/0.48 => ( singletonsuniq
% 0.28/0.48 => ( setukpairinjL1
% 0.28/0.48 => ( kfstsingleton
% 0.28/0.48 => ( theprop
% 0.28/0.48 => ( kfstpairEq
% 0.28/0.48 => ( cartprodfstin
% 0.28/0.48 => ( setukpairinjL2
% 0.28/0.48 => ( setukpairinjL
% 0.28/0.48 => ( setukpairinjR11
% 0.28/0.48 => ( setukpairinjR12
% 0.28/0.48 => ( setukpairinjR1
% 0.28/0.48 => ( upairequniteq
% 0.28/0.48 => ( setukpairinjR2
% 0.28/0.48 => ( setukpairinjR
% 0.28/0.48 => ( ksndsingleton
% 0.28/0.48 => ( ksndpairEq
% 0.28/0.48 => ( kpairsurjEq
% 0.28/0.48 => ( cartprodsndin
% 0.28/0.48 => ( cartprodpairmemEL
% 0.28/0.48 => ( cartprodpairmemER
% 0.28/0.48 => ( cartprodmempaircEq
% 0.28/0.48 => ( cartprodfstpairEq
% 0.28/0.48 => ( cartprodsndpairEq
% 0.28/0.48 => ( cartprodpairsurjEq
% 0.28/0.48 => ( dpsetconstrI
% 0.28/0.48 => ( dpsetconstrSub
% 0.28/0.48 => ( setOfPairsIsBReln
% 0.28/0.48 => ( dpsetconstrERa
% 0.28/0.48 => ( dpsetconstrEL1
% 0.28/0.48 => ( dpsetconstrEL2
% 0.28/0.48 => ( dpsetconstrER
% 0.28/0.48 => ( funcImageSingleton
% 0.28/0.48 => ( apProp
% 0.28/0.48 => ( app
% 0.28/0.48 => ( infuncsetfunc
% 0.28/0.48 => ( ap2p
% 0.28/0.48 => ( funcinfuncset
% 0.28/0.48 => ( lamProp
% 0.28/0.48 => ( lamp
% 0.28/0.48 => ( lam2p
% 0.28/0.48 => ( brelnall1
% 0.28/0.48 => ( brelnall2
% 0.28/0.48 => ( ex1E2
% 0.28/0.48 => ( funcGraphProp1
% 0.28/0.48 => ( funcGraphProp3
% 0.28/0.48 => ( funcGraphProp2
% 0.28/0.48 => ( funcextLem
% 0.28/0.48 => ( funcGraphProp4
% 0.28/0.48 => ( subbreln
% 0.28/0.48 => ( eqbreln
% 0.28/0.48 => ( funcext
% 0.28/0.48 => ( funcext2
% 0.28/0.48 => ( ap2apEq1
% 0.28/0.48 => ( ap2apEq2
% 0.28/0.48 => ( beta1
% 0.28/0.48 => ( eta1
% 0.28/0.48 => ( lam2lamEq
% 0.28/0.48 => ( beta2
% 0.28/0.48 => ( eta2
% 0.28/0.48 => ( iffalseProp1
% 0.28/0.48 => ( iffalseProp2
% 0.28/0.48 => ( iftrueProp1
% 0.28/0.48 => ( iftrueProp2
% 0.28/0.48 => ( ifSingleton
% 0.28/0.48 => ( ifp
% 0.28/0.48 => ( theeq
% 0.28/0.48 => ( iftrue
% 0.28/0.48 => ( iffalse
% 0.28/0.48 => ( iftrueorfalse
% 0.28/0.48 => ( binintersectT_lem
% 0.28/0.48 => ( binunionT_lem
% 0.28/0.48 => ( powersetT_lem
% 0.28/0.48 => ( setminusT_lem
% 0.28/0.48 => ( complementT_lem
% 0.28/0.48 => ( setextT
% 0.28/0.48 => ( subsetTI
% 0.28/0.48 => ( powersetTI1
% 0.28/0.48 => ( powersetTE1
% 0.28/0.48 => ( complementTI1
% 0.28/0.48 => ( complementTE1
% 0.28/0.48 => ( binintersectTELcontra
% 0.28/0.48 => ( binintersectTERcontra
% 0.28/0.48 => ( contrasubsetT
% 0.28/0.48 => ( contrasubsetT1
% 0.28/0.48 => ( contrasubsetT2
% 0.28/0.48 => ( contrasubsetT3
% 0.28/0.48 => ( doubleComplementI1
% 0.28/0.48 => ( doubleComplementE1
% 0.28/0.48 => ( doubleComplementSub1
% 0.28/0.48 => ( doubleComplementSub2
% 0.28/0.48 => ( doubleComplementEq
% 0.28/0.48 => ( complementTnotintersectT
% 0.28/0.48 => ( complementImpComplementIntersect
% 0.28/0.48 => ( complementSubsetComplementIntersect
% 0.28/0.48 => ( complementInPowersetComplementIntersect
% 0.28/0.48 => ( contraSubsetComplement
% 0.28/0.48 => ( complementTcontraSubset
% 0.28/0.48 => ( binunionTILcontra
% 0.28/0.48 => ( binunionTIRcontra
% 0.28/0.48 => ( inIntersectImpInUnion
% 0.28/0.48 => ( inIntersectImpInUnion2
% 0.28/0.48 => ( inIntersectImpInIntersectUnions
% 0.28/0.48 => ( intersectInPowersetIntersectUnions
% 0.28/0.48 => ( inComplementUnionImpNotIn1
% 0.28/0.48 => ( inComplementUnionImpInComplement1
% 0.28/0.48 => ( binunionTE
% 0.28/0.48 => ( binunionTEcontra
% 0.28/0.48 => ( demorgan2a1
% 0.28/0.48 => ( complementUnionInPowersetComplement
% 0.28/0.48 => ( demorgan2a2
% 0.28/0.48 => ( demorgan1a
% 0.28/0.48 => ( demorgan1b
% 0.28/0.48 => ( demorgan1
% 0.28/0.48 => ( demorgan2a
% 0.28/0.48 => ( demorgan2b2
% 0.28/0.48 => ( demorgan2b
% 0.28/0.48 => ( demorgan2
% 0.28/0.48 => ( woz13rule0
% 0.28/0.48 => ( woz13rule1
% 0.28/0.48 => ( woz13rule2
% 0.28/0.48 => ( woz13rule3
% 0.28/0.48 => ( woz13rule4
% 0.28/0.48 => ( woz1_1
% 0.28/0.48 => ( woz1_2
% 0.28/0.48 => ( woz1_3
% 0.28/0.48 => ( woz1_4
% 0.28/0.48 => ( woz1_5
% 0.28/0.48 => ( breln1all2
% 0.28/0.48 => ( breln1SetBreln1
% 0.28/0.48 => ( choice2fnsingleton
% 0.28/0.48 => ( setOfPairsIsBReln1
% 0.28/0.48 => ( breln1all1
% 0.28/0.48 => ( subbreln1
% 0.28/0.48 => ( eqbreln1
% 0.28/0.48 => ( breln1invprop
% 0.28/0.48 => ( breln1invI
% 0.28/0.48 => ( breln1invE
% 0.28/0.48 => ( breln1compprop
% 0.28/0.48 => ( breln1compI
% 0.28/0.48 => ( breln1compE
% 0.28/0.48 => ( breln1compEex
% 0.28/0.48 => ( breln1unionprop
% 0.28/0.48 => ( breln1unionIL
% 0.28/0.48 => ( breln1unionIR
% 0.28/0.48 => ( breln1unionI
% 0.28/0.48 => ( breln1unionE
% 0.28/0.48 => ( breln1unionEcases
% 0.28/0.48 => ( breln1unionCommutes
% 0.28/0.48 => ( woz2Ex
% 0.28/0.48 => ( woz2W
% 0.28/0.48 => ( woz2A
% 0.28/0.48 => ( woz2B
% 0.28/0.48 => ( image1Ex
% 0.28/0.48 => ( image1Ex1
% 0.28/0.48 => ( image1Equiv
% 0.28/0.48 => ( image1E
% 0.28/0.48 => ( image1I
% 0.28/0.48 => ( injFuncInInjFuncSet
% 0.28/0.48 => ( injFuncSetFuncIn
% 0.28/0.48 => ( injFuncSetFuncInj
% 0.28/0.48 => ( surjFuncSetFuncIn
% 0.28/0.48 => ( surjFuncSetFuncSurj
% 0.28/0.48 => ! [A: $i,B: $i,Xf: $i > $i] :
% 0.28/0.48 ( ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.28/0.48 => ! [Xg: $i] :
% 0.28/0.48 ( ( in @ Xg @ ( funcSet @ B @ A ) )
% 0.28/0.48 => ( ! [Xx: $i] :
% 0.28/0.48 ( ( in @ Xx @ A )
% 0.28/0.48 => ( ( ap @ B @ A @ Xg @ ( Xf @ Xx ) )
% 0.28/0.48 = Xx ) )
% 0.28/0.48 => ( surjective @ B @ A @ Xg ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 %------------------------------------------------------------------------------
% 0.28/0.48 ------------------------
% 3.03/1.53 ---- Embedded in THF ---
% 3.03/1.53 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.03/1.53 %%% Generated on Tue Feb 24 12:35:34 EST 2026
% 3.03/1.53 %%% using '$$dhol' embedding, version 1.3.0.
% 3.03/1.53 %%% Logic specification used:
% 3.03/1.53 %%% thf(spec, logic, $$dhol).
% 3.03/1.53
% 3.03/1.53 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.gzAOYGIDe7/DTF2DTF7160.p
% See solution above
% 3.03/1.53 ------------------------
% 3.03/1.58 ---- Cleaned THF ---
% 3.03/1.58 thf(in_type,type,
% 3.03/1.58 in: $i > $i > $o ).
% 3.03/1.58
% 3.03/1.58 thf(exu_type,type,
% 3.03/1.58 exu: ( $i > $o ) > $o ).
% 3.03/1.58
% 3.03/1.58 thf(exu,definition,
% 3.03/1.58 ( exu
% 3.03/1.58 = ( ^ [Xphi: $i > $o] :
% 3.03/1.58 ? [Xx: $i] :
% 3.03/1.58 ( ( Xphi @ Xx )
% 3.03/1.58 & ! [Xy: $i] :
% 3.03/1.58 ( ( Xphi @ Xy )
% 3.03/1.58 => ( Xx = Xy ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setextAx_type,type,
% 3.03/1.58 setextAx: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setextAx,definition,
% 3.03/1.58 ( setextAx
% 3.03/1.58 = ( ! [A: $i,B: $i] :
% 3.03/1.58 ( ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 <=> ( in @ Xx @ B ) )
% 3.03/1.58 => ( A = B ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(emptyset_type,type,
% 3.03/1.58 emptyset: $i ).
% 3.03/1.58
% 3.03/1.58 thf(emptysetAx_type,type,
% 3.03/1.58 emptysetAx: $o ).
% 3.03/1.58
% 3.03/1.58 thf(emptysetAx,definition,
% 3.03/1.58 ( emptysetAx
% 3.03/1.58 = ( ! [Xx: $i] :
% 3.03/1.58 ~ ( in @ Xx @ emptyset ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setadjoin_type,type,
% 3.03/1.58 setadjoin: $i > $i > $i ).
% 3.03/1.58
% 3.03/1.58 thf(setadjoinAx_type,type,
% 3.03/1.58 setadjoinAx: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setadjoinAx,definition,
% 3.03/1.58 ( setadjoinAx
% 3.03/1.58 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.03/1.58 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.03/1.58 <=> ( ( Xy = Xx )
% 3.03/1.58 | ( in @ Xy @ A ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(powerset_type,type,
% 3.03/1.58 powerset: $i > $i ).
% 3.03/1.58
% 3.03/1.58 thf(powersetAx_type,type,
% 3.03/1.58 powersetAx: $o ).
% 3.03/1.58
% 3.03/1.58 thf(powersetAx,definition,
% 3.03/1.58 ( powersetAx
% 3.03/1.58 = ( ! [A: $i,B: $i] :
% 3.03/1.58 ( ( in @ B @ ( powerset @ A ) )
% 3.03/1.58 <=> ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ B )
% 3.03/1.58 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setunion_type,type,
% 3.03/1.58 setunion: $i > $i ).
% 3.03/1.58
% 3.03/1.58 thf(setunionAx_type,type,
% 3.03/1.58 setunionAx: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setunionAx,definition,
% 3.03/1.58 ( setunionAx
% 3.03/1.58 = ( ! [A: $i,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ ( setunion @ A ) )
% 3.03/1.58 <=> ? [B: $i] :
% 3.03/1.58 ( ( in @ Xx @ B )
% 3.03/1.58 & ( in @ B @ A ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(omega_type,type,
% 3.03/1.58 omega: $i ).
% 3.03/1.58
% 3.03/1.58 thf(omega0Ax_type,type,
% 3.03/1.58 omega0Ax: $o ).
% 3.03/1.58
% 3.03/1.58 thf(omega0Ax,definition,
% 3.03/1.58 ( omega0Ax
% 3.03/1.58 = ( in @ emptyset @ omega ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(omegaSAx_type,type,
% 3.03/1.58 omegaSAx: $o ).
% 3.03/1.58
% 3.03/1.58 thf(omegaSAx,definition,
% 3.03/1.58 ( omegaSAx
% 3.03/1.58 = ( ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ omega )
% 3.03/1.58 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(omegaIndAx_type,type,
% 3.03/1.58 omegaIndAx: $o ).
% 3.03/1.58
% 3.03/1.58 thf(omegaIndAx,definition,
% 3.03/1.58 ( omegaIndAx
% 3.03/1.58 = ( ! [A: $i] :
% 3.03/1.58 ( ( ( in @ emptyset @ A )
% 3.03/1.58 & ! [Xx: $i] :
% 3.03/1.58 ( ( ( in @ Xx @ omega )
% 3.03/1.58 & ( in @ Xx @ A ) )
% 3.03/1.58 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 3.03/1.58 => ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ omega )
% 3.03/1.58 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(replAx_type,type,
% 3.03/1.58 replAx: $o ).
% 3.03/1.58
% 3.03/1.58 thf(replAx,definition,
% 3.03/1.58 ( replAx
% 3.03/1.58 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 3.03/1.58 ( ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ( exu
% 3.03/1.58 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 3.03/1.58 => ? [B: $i] :
% 3.03/1.58 ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ B )
% 3.03/1.58 <=> ? [Xy: $i] :
% 3.03/1.58 ( ( in @ Xy @ A )
% 3.03/1.58 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(foundationAx_type,type,
% 3.03/1.58 foundationAx: $o ).
% 3.03/1.58
% 3.03/1.58 thf(foundationAx,definition,
% 3.03/1.58 ( foundationAx
% 3.03/1.58 = ( ! [A: $i] :
% 3.03/1.58 ( ? [Xx: $i] : ( in @ Xx @ A )
% 3.03/1.58 => ? [B: $i] :
% 3.03/1.58 ( ( in @ B @ A )
% 3.03/1.58 & ~ ? [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ B )
% 3.03/1.58 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(wellorderingAx_type,type,
% 3.03/1.58 wellorderingAx: $o ).
% 3.03/1.58
% 3.03/1.58 thf(wellorderingAx,definition,
% 3.03/1.58 ( wellorderingAx
% 3.03/1.58 = ( ! [A: $i] :
% 3.03/1.58 ? [B: $i] :
% 3.03/1.58 ( ! [C: $i] :
% 3.03/1.58 ( ( in @ C @ B )
% 3.03/1.58 => ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ C )
% 3.03/1.58 => ( in @ Xx @ A ) ) )
% 3.03/1.58 & ! [Xx: $i,Xy: $i] :
% 3.03/1.58 ( ( ( in @ Xx @ A )
% 3.03/1.58 & ( in @ Xy @ A ) )
% 3.03/1.58 => ( ! [C: $i] :
% 3.03/1.58 ( ( in @ C @ B )
% 3.03/1.58 => ( ( in @ Xx @ C )
% 3.03/1.58 <=> ( in @ Xy @ C ) ) )
% 3.03/1.58 => ( Xx = Xy ) ) )
% 3.03/1.58 & ! [C: $i,D: $i] :
% 3.03/1.58 ( ( ( in @ C @ B )
% 3.03/1.58 & ( in @ D @ B ) )
% 3.03/1.58 => ( ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ C )
% 3.03/1.58 => ( in @ Xx @ D ) )
% 3.03/1.58 | ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ D )
% 3.03/1.58 => ( in @ Xx @ C ) ) ) )
% 3.03/1.58 & ! [C: $i] :
% 3.03/1.58 ( ( ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ C )
% 3.03/1.58 => ( in @ Xx @ A ) )
% 3.03/1.58 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 3.03/1.58 => ? [D: $i,Xx: $i] :
% 3.03/1.58 ( ( in @ D @ B )
% 3.03/1.58 & ( in @ Xx @ C )
% 3.03/1.58 & ~ ? [Xy: $i] :
% 3.03/1.58 ( ( in @ Xy @ D )
% 3.03/1.58 & ( in @ Xy @ C ) )
% 3.03/1.58 & ! [E: $i] :
% 3.03/1.58 ( ( in @ E @ B )
% 3.03/1.58 => ( ! [Xy: $i] :
% 3.03/1.58 ( ( in @ Xy @ E )
% 3.03/1.58 => ( in @ Xy @ D ) )
% 3.03/1.58 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(descr_type,type,
% 3.03/1.58 descr: ( $i > $o ) > $i ).
% 3.03/1.58
% 3.03/1.58 thf(descrp_type,type,
% 3.03/1.58 descrp: $o ).
% 3.03/1.58
% 3.03/1.58 thf(descrp,definition,
% 3.03/1.58 ( descrp
% 3.03/1.58 = ( ! [Xphi: $i > $o] :
% 3.03/1.58 ( ( exu
% 3.03/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.03/1.58 => ( Xphi
% 3.03/1.58 @ ( descr
% 3.03/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(dsetconstr_type,type,
% 3.03/1.58 dsetconstr: $i > ( $i > $o ) > $i ).
% 3.03/1.58
% 3.03/1.58 thf(dsetconstrI_type,type,
% 3.03/1.58 dsetconstrI: $o ).
% 3.03/1.58
% 3.03/1.58 thf(dsetconstrI,definition,
% 3.03/1.58 ( dsetconstrI
% 3.03/1.58 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ( ( Xphi @ Xx )
% 3.03/1.58 => ( in @ Xx
% 3.03/1.58 @ ( dsetconstr @ A
% 3.03/1.58 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(dsetconstrEL_type,type,
% 3.03/1.58 dsetconstrEL: $o ).
% 3.03/1.58
% 3.03/1.58 thf(dsetconstrEL,definition,
% 3.03/1.58 ( dsetconstrEL
% 3.03/1.58 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx
% 3.03/1.58 @ ( dsetconstr @ A
% 3.03/1.58 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.03/1.58 => ( in @ Xx @ A ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(dsetconstrER_type,type,
% 3.03/1.58 dsetconstrER: $o ).
% 3.03/1.58
% 3.03/1.58 thf(dsetconstrER,definition,
% 3.03/1.58 ( dsetconstrER
% 3.03/1.58 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx
% 3.03/1.58 @ ( dsetconstr @ A
% 3.03/1.58 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.03/1.58 => ( Xphi @ Xx ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(exuE1_type,type,
% 3.03/1.58 exuE1: $o ).
% 3.03/1.58
% 3.03/1.58 thf(exuE1,definition,
% 3.03/1.58 ( exuE1
% 3.03/1.58 = ( ! [Xphi: $i > $o] :
% 3.03/1.58 ( ( exu
% 3.03/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.03/1.58 => ? [Xx: $i] :
% 3.03/1.58 ( ( Xphi @ Xx )
% 3.03/1.58 & ! [Xy: $i] :
% 3.03/1.58 ( ( Xphi @ Xy )
% 3.03/1.58 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(prop2set_type,type,
% 3.03/1.58 prop2set: $o > $i ).
% 3.03/1.58
% 3.03/1.58 thf(prop2setE_type,type,
% 3.03/1.58 prop2setE: $o ).
% 3.03/1.58
% 3.03/1.58 thf(prop2setE,definition,
% 3.03/1.58 ( prop2setE
% 3.03/1.58 = ( ! [Xphi: $o,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 3.03/1.58 => Xphi ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(emptysetE_type,type,
% 3.03/1.58 emptysetE: $o ).
% 3.03/1.58
% 3.03/1.58 thf(emptysetE,definition,
% 3.03/1.58 ( emptysetE
% 3.03/1.58 = ( ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ emptyset )
% 3.03/1.58 => ! [Xphi: $o] : Xphi ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(emptysetimpfalse_type,type,
% 3.03/1.58 emptysetimpfalse: $o ).
% 3.03/1.58
% 3.03/1.58 thf(emptysetimpfalse,definition,
% 3.03/1.58 ( emptysetimpfalse
% 3.03/1.58 = ( ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ emptyset )
% 3.03/1.58 => $false ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(notinemptyset_type,type,
% 3.03/1.58 notinemptyset: $o ).
% 3.03/1.58
% 3.03/1.58 thf(notinemptyset,definition,
% 3.03/1.58 ( notinemptyset
% 3.03/1.58 = ( ! [Xx: $i] :
% 3.03/1.58 ~ ( in @ Xx @ emptyset ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(exuE3e_type,type,
% 3.03/1.58 exuE3e: $o ).
% 3.03/1.58
% 3.03/1.58 thf(exuE3e,definition,
% 3.03/1.58 ( exuE3e
% 3.03/1.58 = ( ! [Xphi: $i > $o] :
% 3.03/1.58 ( ( exu
% 3.03/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.03/1.58 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setext_type,type,
% 3.03/1.58 setext: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setext,definition,
% 3.03/1.58 ( setext
% 3.03/1.58 = ( ! [A: $i,B: $i] :
% 3.03/1.58 ( ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ( in @ Xx @ B ) )
% 3.03/1.58 => ( ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ B )
% 3.03/1.58 => ( in @ Xx @ A ) )
% 3.03/1.58 => ( A = B ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(emptyI_type,type,
% 3.03/1.58 emptyI: $o ).
% 3.03/1.58
% 3.03/1.58 thf(emptyI,definition,
% 3.03/1.58 ( emptyI
% 3.03/1.58 = ( ! [A: $i] :
% 3.03/1.58 ( ! [Xx: $i] :
% 3.03/1.58 ~ ( in @ Xx @ A )
% 3.03/1.58 => ( A = emptyset ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(noeltsimpempty_type,type,
% 3.03/1.58 noeltsimpempty: $o ).
% 3.03/1.58
% 3.03/1.58 thf(noeltsimpempty,definition,
% 3.03/1.58 ( noeltsimpempty
% 3.03/1.58 = ( ! [A: $i] :
% 3.03/1.58 ( ! [Xx: $i] :
% 3.03/1.58 ~ ( in @ Xx @ A )
% 3.03/1.58 => ( A = emptyset ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setbeta_type,type,
% 3.03/1.58 setbeta: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setbeta,definition,
% 3.03/1.58 ( setbeta
% 3.03/1.58 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ( ( in @ Xx
% 3.03/1.58 @ ( dsetconstr @ A
% 3.03/1.58 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.03/1.58 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(nonempty_type,type,
% 3.03/1.58 nonempty: $i > $o ).
% 3.03/1.58
% 3.03/1.58 thf(nonempty,definition,
% 3.03/1.58 ( nonempty
% 3.03/1.58 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(nonemptyE1_type,type,
% 3.03/1.58 nonemptyE1: $o ).
% 3.03/1.58
% 3.03/1.58 thf(nonemptyE1,definition,
% 3.03/1.58 ( nonemptyE1
% 3.03/1.58 = ( ! [A: $i] :
% 3.03/1.58 ( ( nonempty @ A )
% 3.03/1.58 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(nonemptyI_type,type,
% 3.03/1.58 nonemptyI: $o ).
% 3.03/1.58
% 3.03/1.58 thf(nonemptyI,definition,
% 3.03/1.58 ( nonemptyI
% 3.03/1.58 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ( ( Xphi @ Xx )
% 3.03/1.58 => ( nonempty
% 3.03/1.58 @ ( dsetconstr @ A
% 3.03/1.58 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(nonemptyI1_type,type,
% 3.03/1.58 nonemptyI1: $o ).
% 3.03/1.58
% 3.03/1.58 thf(nonemptyI1,definition,
% 3.03/1.58 ( nonemptyI1
% 3.03/1.58 = ( ! [A: $i] :
% 3.03/1.58 ( ? [Xx: $i] : ( in @ Xx @ A )
% 3.03/1.58 => ( nonempty @ A ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setadjoinIL_type,type,
% 3.03/1.58 setadjoinIL: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setadjoinIL,definition,
% 3.03/1.58 ( setadjoinIL
% 3.03/1.58 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(emptyinunitempty_type,type,
% 3.03/1.58 emptyinunitempty: $o ).
% 3.03/1.58
% 3.03/1.58 thf(emptyinunitempty,definition,
% 3.03/1.58 ( emptyinunitempty
% 3.03/1.58 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setadjoinIR_type,type,
% 3.03/1.58 setadjoinIR: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setadjoinIR,definition,
% 3.03/1.58 ( setadjoinIR
% 3.03/1.58 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.03/1.58 ( ( in @ Xy @ A )
% 3.03/1.58 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setadjoinE_type,type,
% 3.03/1.58 setadjoinE: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setadjoinE,definition,
% 3.03/1.58 ( setadjoinE
% 3.03/1.58 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.03/1.58 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.03/1.58 => ! [Xphi: $o] :
% 3.03/1.58 ( ( ( Xy = Xx )
% 3.03/1.58 => Xphi )
% 3.03/1.58 => ( ( ( in @ Xy @ A )
% 3.03/1.58 => Xphi )
% 3.03/1.58 => Xphi ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setadjoinOr_type,type,
% 3.03/1.58 setadjoinOr: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setadjoinOr,definition,
% 3.03/1.58 ( setadjoinOr
% 3.03/1.58 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.03/1.58 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.03/1.58 => ( ( Xy = Xx )
% 3.03/1.58 | ( in @ Xy @ A ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setoftrueEq_type,type,
% 3.03/1.58 setoftrueEq: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setoftrueEq,definition,
% 3.03/1.58 ( setoftrueEq
% 3.03/1.58 = ( ! [A: $i] :
% 3.03/1.58 ( ( dsetconstr @ A
% 3.03/1.58 @ ^ [Xx: $i] : $true )
% 3.03/1.58 = A ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(powersetI_type,type,
% 3.03/1.58 powersetI: $o ).
% 3.03/1.58
% 3.03/1.58 thf(powersetI,definition,
% 3.03/1.58 ( powersetI
% 3.03/1.58 = ( ! [A: $i,B: $i] :
% 3.03/1.58 ( ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ B )
% 3.03/1.58 => ( in @ Xx @ A ) )
% 3.03/1.58 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(emptyinPowerset_type,type,
% 3.03/1.58 emptyinPowerset: $o ).
% 3.03/1.58
% 3.03/1.58 thf(emptyinPowerset,definition,
% 3.03/1.58 ( emptyinPowerset
% 3.03/1.58 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(emptyInPowerset_type,type,
% 3.03/1.58 emptyInPowerset: $o ).
% 3.03/1.58
% 3.03/1.58 thf(emptyInPowerset,definition,
% 3.03/1.58 ( emptyInPowerset
% 3.03/1.58 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(powersetE_type,type,
% 3.03/1.58 powersetE: $o ).
% 3.03/1.58
% 3.03/1.58 thf(powersetE,definition,
% 3.03/1.58 ( powersetE
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.03/1.58 ( ( in @ B @ ( powerset @ A ) )
% 3.03/1.58 => ( ( in @ Xx @ B )
% 3.03/1.58 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setunionI_type,type,
% 3.03/1.58 setunionI: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setunionI,definition,
% 3.03/1.58 ( setunionI
% 3.03/1.58 = ( ! [A: $i,Xx: $i,B: $i] :
% 3.03/1.58 ( ( in @ Xx @ B )
% 3.03/1.58 => ( ( in @ B @ A )
% 3.03/1.58 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setunionE_type,type,
% 3.03/1.58 setunionE: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setunionE,definition,
% 3.03/1.58 ( setunionE
% 3.03/1.58 = ( ! [A: $i,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ ( setunion @ A ) )
% 3.03/1.58 => ! [Xphi: $o] :
% 3.03/1.58 ( ! [B: $i] :
% 3.03/1.58 ( ( in @ Xx @ B )
% 3.03/1.58 => ( ( in @ B @ A )
% 3.03/1.58 => Xphi ) )
% 3.03/1.58 => Xphi ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(subPowSU_type,type,
% 3.03/1.58 subPowSU: $o ).
% 3.03/1.58
% 3.03/1.58 thf(subPowSU,definition,
% 3.03/1.58 ( subPowSU
% 3.03/1.58 = ( ! [A: $i,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(exuE2_type,type,
% 3.03/1.58 exuE2: $o ).
% 3.03/1.58
% 3.03/1.58 thf(exuE2,definition,
% 3.03/1.58 ( exuE2
% 3.03/1.58 = ( ! [Xphi: $i > $o] :
% 3.03/1.58 ( ( exu
% 3.03/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.03/1.58 => ? [Xx: $i] :
% 3.03/1.58 ! [Xy: $i] :
% 3.03/1.58 ( ( Xphi @ Xy )
% 3.03/1.58 <=> ( Xy = Xx ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(nonemptyImpWitness_type,type,
% 3.03/1.58 nonemptyImpWitness: $o ).
% 3.03/1.58
% 3.03/1.58 thf(nonemptyImpWitness,definition,
% 3.03/1.58 ( nonemptyImpWitness
% 3.03/1.58 = ( ! [A: $i] :
% 3.03/1.58 ( ( nonempty @ A )
% 3.03/1.58 => ? [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 & $true ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(uniqinunit_type,type,
% 3.03/1.58 uniqinunit: $o ).
% 3.03/1.58
% 3.03/1.58 thf(uniqinunit,definition,
% 3.03/1.58 ( uniqinunit
% 3.03/1.58 = ( ! [Xx: $i,Xy: $i] :
% 3.03/1.58 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.03/1.58 => ( Xx = Xy ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(notinsingleton_type,type,
% 3.03/1.58 notinsingleton: $o ).
% 3.03/1.58
% 3.03/1.58 thf(notinsingleton,definition,
% 3.03/1.58 ( notinsingleton
% 3.03/1.58 = ( ! [Xx: $i,Xy: $i] :
% 3.03/1.58 ( ( Xx != Xy )
% 3.03/1.58 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(eqinunit_type,type,
% 3.03/1.58 eqinunit: $o ).
% 3.03/1.58
% 3.03/1.58 thf(eqinunit,definition,
% 3.03/1.58 ( eqinunit
% 3.03/1.58 = ( ! [Xx: $i,Xy: $i] :
% 3.03/1.58 ( ( Xx = Xy )
% 3.03/1.58 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(singletonsswitch_type,type,
% 3.03/1.58 singletonsswitch: $o ).
% 3.03/1.58
% 3.03/1.58 thf(singletonsswitch,definition,
% 3.03/1.58 ( singletonsswitch
% 3.03/1.58 = ( ! [Xx: $i,Xy: $i] :
% 3.03/1.58 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.03/1.58 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(upairsetE_type,type,
% 3.03/1.58 upairsetE: $o ).
% 3.03/1.58
% 3.03/1.58 thf(upairsetE,definition,
% 3.03/1.58 ( upairsetE
% 3.03/1.58 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.03/1.58 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 3.03/1.58 => ( ( Xz = Xx )
% 3.03/1.58 | ( Xz = Xy ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(upairsetIL_type,type,
% 3.03/1.58 upairsetIL: $o ).
% 3.03/1.58
% 3.03/1.58 thf(upairsetIL,definition,
% 3.03/1.58 ( upairsetIL
% 3.03/1.58 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(upairsetIR_type,type,
% 3.03/1.58 upairsetIR: $o ).
% 3.03/1.58
% 3.03/1.58 thf(upairsetIR,definition,
% 3.03/1.58 ( upairsetIR
% 3.03/1.58 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(emptyE1_type,type,
% 3.03/1.58 emptyE1: $o ).
% 3.03/1.58
% 3.03/1.58 thf(emptyE1,definition,
% 3.03/1.58 ( emptyE1
% 3.03/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 3.03/1.58 ( ? [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 & ( Xphi @ Xx ) )
% 3.03/1.58 => ( ( ( dsetconstr @ A
% 3.03/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.03/1.58 = emptyset )
% 3.03/1.58 => $false ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(vacuousDall_type,type,
% 3.03/1.58 vacuousDall: $o ).
% 3.03/1.58
% 3.03/1.58 thf(vacuousDall,definition,
% 3.03/1.58 ( vacuousDall
% 3.03/1.58 = ( ! [Xphi: $i > $o,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ emptyset )
% 3.03/1.58 => ( Xphi @ Xx ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(quantDeMorgan1_type,type,
% 3.03/1.58 quantDeMorgan1: $o ).
% 3.03/1.58
% 3.03/1.58 thf(quantDeMorgan1,definition,
% 3.03/1.58 ( quantDeMorgan1
% 3.03/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 3.03/1.58 ( ~ ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ( Xphi @ Xx ) )
% 3.03/1.58 => ? [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(quantDeMorgan2_type,type,
% 3.03/1.58 quantDeMorgan2: $o ).
% 3.03/1.58
% 3.03/1.58 thf(quantDeMorgan2,definition,
% 3.03/1.58 ( quantDeMorgan2
% 3.03/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 3.03/1.58 ( ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ~ ( Xphi @ Xx ) )
% 3.03/1.58 => ~ ? [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 & ( Xphi @ Xx ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(quantDeMorgan3_type,type,
% 3.03/1.58 quantDeMorgan3: $o ).
% 3.03/1.58
% 3.03/1.58 thf(quantDeMorgan3,definition,
% 3.03/1.58 ( quantDeMorgan3
% 3.03/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 3.03/1.58 ( ~ ? [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 & ( Xphi @ Xx ) )
% 3.03/1.58 => ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(quantDeMorgan4_type,type,
% 3.03/1.58 quantDeMorgan4: $o ).
% 3.03/1.58
% 3.03/1.58 thf(quantDeMorgan4,definition,
% 3.03/1.58 ( quantDeMorgan4
% 3.03/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 3.03/1.58 ( ? [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 & ~ ( Xphi @ Xx ) )
% 3.03/1.58 => ~ ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ( Xphi @ Xx ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(prop2setI_type,type,
% 3.03/1.58 prop2setI: $o ).
% 3.03/1.58
% 3.03/1.58 thf(prop2setI,definition,
% 3.03/1.58 ( prop2setI
% 3.03/1.58 = ( ! [Xphi: $o] :
% 3.03/1.58 ( Xphi
% 3.03/1.58 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(set2prop_type,type,
% 3.03/1.58 set2prop: $i > $o ).
% 3.03/1.58
% 3.03/1.58 thf(prop2set2propI_type,type,
% 3.03/1.58 prop2set2propI: $o ).
% 3.03/1.58
% 3.03/1.58 thf(prop2set2propI,definition,
% 3.03/1.58 ( prop2set2propI
% 3.03/1.58 = ( ! [Xphi: $o] :
% 3.03/1.58 ( Xphi
% 3.03/1.58 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(notdexE_type,type,
% 3.03/1.58 notdexE: $o ).
% 3.03/1.58
% 3.03/1.58 thf(notdexE,definition,
% 3.03/1.58 ( notdexE
% 3.03/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 3.03/1.58 ( ~ ? [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 & ( Xphi @ Xx ) )
% 3.03/1.58 => ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(notdallE_type,type,
% 3.03/1.58 notdallE: $o ).
% 3.03/1.58
% 3.03/1.58 thf(notdallE,definition,
% 3.03/1.58 ( notdallE
% 3.03/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 3.03/1.58 ( ~ ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ( Xphi @ Xx ) )
% 3.03/1.58 => ? [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(exuI1_type,type,
% 3.03/1.58 exuI1: $o ).
% 3.03/1.58
% 3.03/1.58 thf(exuI1,definition,
% 3.03/1.58 ( exuI1
% 3.03/1.58 = ( ! [Xphi: $i > $o] :
% 3.03/1.58 ( ? [Xx: $i] :
% 3.03/1.58 ( ( Xphi @ Xx )
% 3.03/1.58 & ! [Xy: $i] :
% 3.03/1.58 ( ( Xphi @ Xy )
% 3.03/1.58 => ( Xx = Xy ) ) )
% 3.03/1.58 => ( exu
% 3.03/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(exuI3_type,type,
% 3.03/1.58 exuI3: $o ).
% 3.03/1.58
% 3.03/1.58 thf(exuI3,definition,
% 3.03/1.58 ( exuI3
% 3.03/1.58 = ( ! [Xphi: $i > $o] :
% 3.03/1.58 ( ? [Xx: $i] : ( Xphi @ Xx )
% 3.03/1.58 => ( ! [Xx: $i,Xy: $i] :
% 3.03/1.58 ( ( Xphi @ Xx )
% 3.03/1.58 => ( ( Xphi @ Xy )
% 3.03/1.58 => ( Xx = Xy ) ) )
% 3.03/1.58 => ( exu
% 3.03/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(exuI2_type,type,
% 3.03/1.58 exuI2: $o ).
% 3.03/1.58
% 3.03/1.58 thf(exuI2,definition,
% 3.03/1.58 ( exuI2
% 3.03/1.58 = ( ! [Xphi: $i > $o] :
% 3.03/1.58 ( ? [Xx: $i] :
% 3.03/1.58 ! [Xy: $i] :
% 3.03/1.58 ( ( Xphi @ Xy )
% 3.03/1.58 <=> ( Xy = Xx ) )
% 3.03/1.58 => ( exu
% 3.03/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(inCongP_type,type,
% 3.03/1.58 inCongP: $o ).
% 3.03/1.58
% 3.03/1.58 thf(inCongP,definition,
% 3.03/1.58 ( inCongP
% 3.03/1.58 = ( ! [A: $i,B: $i] :
% 3.03/1.58 ( ( A = B )
% 3.03/1.58 => ! [Xx: $i,Xy: $i] :
% 3.03/1.58 ( ( Xx = Xy )
% 3.03/1.58 => ( ( in @ Xx @ A )
% 3.03/1.58 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(in__Cong_type,type,
% 3.03/1.58 in__Cong: $o ).
% 3.03/1.58
% 3.03/1.58 thf(in__Cong,definition,
% 3.03/1.58 ( in__Cong
% 3.03/1.58 = ( ! [A: $i,B: $i] :
% 3.03/1.58 ( ( A = B )
% 3.03/1.58 => ! [Xx: $i,Xy: $i] :
% 3.03/1.58 ( ( Xx = Xy )
% 3.03/1.58 => ( ( in @ Xx @ A )
% 3.03/1.58 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(exuE3u_type,type,
% 3.03/1.58 exuE3u: $o ).
% 3.03/1.58
% 3.03/1.58 thf(exuE3u,definition,
% 3.03/1.58 ( exuE3u
% 3.03/1.58 = ( ! [Xphi: $i > $o] :
% 3.03/1.58 ( ( exu
% 3.03/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.03/1.58 => ! [Xx: $i,Xy: $i] :
% 3.03/1.58 ( ( Xphi @ Xx )
% 3.03/1.58 => ( ( Xphi @ Xy )
% 3.03/1.58 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(exu__Cong_type,type,
% 3.03/1.58 exu__Cong: $o ).
% 3.03/1.58
% 3.03/1.58 thf(exu__Cong,definition,
% 3.03/1.58 ( exu__Cong
% 3.03/1.58 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.03/1.58 ( ! [Xx: $i,Xy: $i] :
% 3.03/1.58 ( ( Xx = Xy )
% 3.03/1.58 => ( ( Xphi @ Xx )
% 3.03/1.58 <=> ( Xpsi @ Xy ) ) )
% 3.03/1.58 => ( ( exu
% 3.03/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.03/1.58 <=> ( exu
% 3.03/1.58 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(emptyset__Cong_type,type,
% 3.03/1.58 emptyset__Cong: $o ).
% 3.03/1.58
% 3.03/1.58 thf(emptyset__Cong,definition,
% 3.03/1.58 ( emptyset__Cong
% 3.03/1.58 = ( emptyset = emptyset ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setadjoin__Cong_type,type,
% 3.03/1.58 setadjoin__Cong: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setadjoin__Cong,definition,
% 3.03/1.58 ( setadjoin__Cong
% 3.03/1.58 = ( ! [Xx: $i,Xy: $i] :
% 3.03/1.58 ( ( Xx = Xy )
% 3.03/1.58 => ! [Xz: $i,Xu: $i] :
% 3.03/1.58 ( ( Xz = Xu )
% 3.03/1.58 => ( ( setadjoin @ Xx @ Xz )
% 3.03/1.58 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(powerset__Cong_type,type,
% 3.03/1.58 powerset__Cong: $o ).
% 3.03/1.58
% 3.03/1.58 thf(powerset__Cong,definition,
% 3.03/1.58 ( powerset__Cong
% 3.03/1.58 = ( ! [A: $i,B: $i] :
% 3.03/1.58 ( ( A = B )
% 3.03/1.58 => ( ( powerset @ A )
% 3.03/1.58 = ( powerset @ B ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setunion__Cong_type,type,
% 3.03/1.58 setunion__Cong: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setunion__Cong,definition,
% 3.03/1.58 ( setunion__Cong
% 3.03/1.58 = ( ! [A: $i,B: $i] :
% 3.03/1.58 ( ( A = B )
% 3.03/1.58 => ( ( setunion @ A )
% 3.03/1.58 = ( setunion @ B ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(omega__Cong_type,type,
% 3.03/1.58 omega__Cong: $o ).
% 3.03/1.58
% 3.03/1.58 thf(omega__Cong,definition,
% 3.03/1.58 ( omega__Cong
% 3.03/1.58 = ( omega = omega ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(exuEu_type,type,
% 3.03/1.58 exuEu: $o ).
% 3.03/1.58
% 3.03/1.58 thf(exuEu,definition,
% 3.03/1.58 ( exuEu
% 3.03/1.58 = ( ! [Xphi: $i > $o] :
% 3.03/1.58 ( ( exu
% 3.03/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.03/1.58 => ! [Xx: $i,Xy: $i] :
% 3.03/1.58 ( ( Xphi @ Xx )
% 3.03/1.58 => ( ( Xphi @ Xy )
% 3.03/1.58 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(descr__Cong_type,type,
% 3.03/1.58 descr__Cong: $o ).
% 3.03/1.58
% 3.03/1.58 thf(descr__Cong,definition,
% 3.03/1.58 ( descr__Cong
% 3.03/1.58 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.03/1.58 ( ! [Xx: $i,Xy: $i] :
% 3.03/1.58 ( ( Xx = Xy )
% 3.03/1.58 => ( ( Xphi @ Xx )
% 3.03/1.58 <=> ( Xpsi @ Xy ) ) )
% 3.03/1.58 => ( ( exu
% 3.03/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.03/1.58 => ( ( exu
% 3.03/1.58 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 3.03/1.58 => ( ( descr
% 3.03/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.03/1.58 = ( descr
% 3.03/1.58 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(dsetconstr__Cong_type,type,
% 3.03/1.58 dsetconstr__Cong: $o ).
% 3.03/1.58
% 3.03/1.58 thf(dsetconstr__Cong,definition,
% 3.03/1.58 ( dsetconstr__Cong
% 3.03/1.58 = ( ! [A: $i,B: $i] :
% 3.03/1.58 ( ( A = B )
% 3.03/1.58 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.03/1.58 ( ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ! [Xy: $i] :
% 3.03/1.58 ( ( in @ Xy @ B )
% 3.03/1.58 => ( ( Xx = Xy )
% 3.03/1.58 => ( ( Xphi @ Xx )
% 3.03/1.58 <=> ( Xpsi @ Xy ) ) ) ) )
% 3.03/1.58 => ( ( dsetconstr @ A
% 3.03/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.03/1.58 = ( dsetconstr @ B
% 3.03/1.58 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(subset_type,type,
% 3.03/1.58 subset: $i > $i > $o ).
% 3.03/1.58
% 3.03/1.58 thf(disjoint_type,type,
% 3.03/1.58 disjoint: $i > $i > $o ).
% 3.03/1.58
% 3.03/1.58 thf(setsmeet_type,type,
% 3.03/1.58 setsmeet: $i > $i > $o ).
% 3.03/1.58
% 3.03/1.58 thf(subsetI1_type,type,
% 3.03/1.58 subsetI1: $o ).
% 3.03/1.58
% 3.03/1.58 thf(subsetI1,definition,
% 3.03/1.58 ( subsetI1
% 3.03/1.58 = ( ! [A: $i,B: $i] :
% 3.03/1.58 ( ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ( in @ Xx @ B ) )
% 3.03/1.58 => ( subset @ A @ B ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(eqimpsubset2_type,type,
% 3.03/1.58 eqimpsubset2: $o ).
% 3.03/1.58
% 3.03/1.58 thf(eqimpsubset2,definition,
% 3.03/1.58 ( eqimpsubset2
% 3.03/1.58 = ( ! [A: $i,B: $i] :
% 3.03/1.58 ( ( A = B )
% 3.03/1.58 => ( subset @ B @ A ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(eqimpsubset1_type,type,
% 3.03/1.58 eqimpsubset1: $o ).
% 3.03/1.58
% 3.03/1.58 thf(eqimpsubset1,definition,
% 3.03/1.58 ( eqimpsubset1
% 3.03/1.58 = ( ! [A: $i,B: $i] :
% 3.03/1.58 ( ( A = B )
% 3.03/1.58 => ( subset @ A @ B ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(subsetI2_type,type,
% 3.03/1.58 subsetI2: $o ).
% 3.03/1.58
% 3.03/1.58 thf(subsetI2,definition,
% 3.03/1.58 ( subsetI2
% 3.03/1.58 = ( ! [A: $i,B: $i] :
% 3.03/1.58 ( ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ( in @ Xx @ B ) )
% 3.03/1.58 => ( subset @ A @ B ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(emptysetsubset_type,type,
% 3.03/1.58 emptysetsubset: $o ).
% 3.03/1.58
% 3.03/1.58 thf(emptysetsubset,definition,
% 3.03/1.58 ( emptysetsubset
% 3.03/1.58 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(subsetE_type,type,
% 3.03/1.58 subsetE: $o ).
% 3.03/1.58
% 3.03/1.58 thf(subsetE,definition,
% 3.03/1.58 ( subsetE
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.03/1.58 ( ( subset @ A @ B )
% 3.03/1.58 => ( ( in @ Xx @ A )
% 3.03/1.58 => ( in @ Xx @ B ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(subsetE2_type,type,
% 3.03/1.58 subsetE2: $o ).
% 3.03/1.58
% 3.03/1.58 thf(subsetE2,definition,
% 3.03/1.58 ( subsetE2
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.03/1.58 ( ( subset @ A @ B )
% 3.03/1.58 => ( ~ ( in @ Xx @ B )
% 3.03/1.58 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(notsubsetI_type,type,
% 3.03/1.58 notsubsetI: $o ).
% 3.03/1.58
% 3.03/1.58 thf(notsubsetI,definition,
% 3.03/1.58 ( notsubsetI
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ( ~ ( in @ Xx @ B )
% 3.03/1.58 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(notequalI1_type,type,
% 3.03/1.58 notequalI1: $o ).
% 3.03/1.58
% 3.03/1.58 thf(notequalI1,definition,
% 3.03/1.58 ( notequalI1
% 3.03/1.58 = ( ! [A: $i,B: $i] :
% 3.03/1.58 ( ~ ( subset @ A @ B )
% 3.03/1.58 => ( A != B ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(notequalI2_type,type,
% 3.03/1.58 notequalI2: $o ).
% 3.03/1.58
% 3.03/1.58 thf(notequalI2,definition,
% 3.03/1.58 ( notequalI2
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ( ~ ( in @ Xx @ B )
% 3.03/1.58 => ( A != B ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(subsetRefl_type,type,
% 3.03/1.58 subsetRefl: $o ).
% 3.03/1.58
% 3.03/1.58 thf(subsetRefl,definition,
% 3.03/1.58 ( subsetRefl
% 3.03/1.58 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(subsetTrans_type,type,
% 3.03/1.58 subsetTrans: $o ).
% 3.03/1.58
% 3.03/1.58 thf(subsetTrans,definition,
% 3.03/1.58 ( subsetTrans
% 3.03/1.58 = ( ! [A: $i,B: $i,C: $i] :
% 3.03/1.58 ( ( subset @ A @ B )
% 3.03/1.58 => ( ( subset @ B @ C )
% 3.03/1.58 => ( subset @ A @ C ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setadjoinSub_type,type,
% 3.03/1.58 setadjoinSub: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setadjoinSub,definition,
% 3.03/1.58 ( setadjoinSub
% 3.03/1.58 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setadjoinSub2_type,type,
% 3.03/1.58 setadjoinSub2: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setadjoinSub2,definition,
% 3.03/1.58 ( setadjoinSub2
% 3.03/1.58 = ( ! [A: $i,Xx: $i,B: $i] :
% 3.03/1.58 ( ( subset @ A @ B )
% 3.03/1.58 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(subset2powerset_type,type,
% 3.03/1.58 subset2powerset: $o ).
% 3.03/1.58
% 3.03/1.58 thf(subset2powerset,definition,
% 3.03/1.58 ( subset2powerset
% 3.03/1.58 = ( ! [A: $i,B: $i] :
% 3.03/1.58 ( ( subset @ A @ B )
% 3.03/1.58 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setextsub_type,type,
% 3.03/1.58 setextsub: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setextsub,definition,
% 3.03/1.58 ( setextsub
% 3.03/1.58 = ( ! [A: $i,B: $i] :
% 3.03/1.58 ( ( subset @ A @ B )
% 3.03/1.58 => ( ( subset @ B @ A )
% 3.03/1.58 => ( A = B ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(subsetemptysetimpeq_type,type,
% 3.03/1.58 subsetemptysetimpeq: $o ).
% 3.03/1.58
% 3.03/1.58 thf(subsetemptysetimpeq,definition,
% 3.03/1.58 ( subsetemptysetimpeq
% 3.03/1.58 = ( ! [A: $i] :
% 3.03/1.58 ( ( subset @ A @ emptyset )
% 3.03/1.58 => ( A = emptyset ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(powersetI1_type,type,
% 3.03/1.58 powersetI1: $o ).
% 3.03/1.58
% 3.03/1.58 thf(powersetI1,definition,
% 3.03/1.58 ( powersetI1
% 3.03/1.58 = ( ! [A: $i,B: $i] :
% 3.03/1.58 ( ( subset @ B @ A )
% 3.03/1.58 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(powersetE1_type,type,
% 3.03/1.58 powersetE1: $o ).
% 3.03/1.58
% 3.03/1.58 thf(powersetE1,definition,
% 3.03/1.58 ( powersetE1
% 3.03/1.58 = ( ! [A: $i,B: $i] :
% 3.03/1.58 ( ( in @ B @ ( powerset @ A ) )
% 3.03/1.58 => ( subset @ B @ A ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(inPowerset_type,type,
% 3.03/1.58 inPowerset: $o ).
% 3.03/1.58
% 3.03/1.58 thf(inPowerset,definition,
% 3.03/1.58 ( inPowerset
% 3.03/1.58 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(powersetsubset_type,type,
% 3.03/1.58 powersetsubset: $o ).
% 3.03/1.58
% 3.03/1.58 thf(powersetsubset,definition,
% 3.03/1.58 ( powersetsubset
% 3.03/1.58 = ( ! [A: $i,B: $i] :
% 3.03/1.58 ( ( subset @ A @ B )
% 3.03/1.58 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(sepInPowerset_type,type,
% 3.03/1.58 sepInPowerset: $o ).
% 3.03/1.58
% 3.03/1.58 thf(sepInPowerset,definition,
% 3.03/1.58 ( sepInPowerset
% 3.03/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 3.03/1.58 ( in
% 3.03/1.58 @ ( dsetconstr @ A
% 3.03/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.03/1.58 @ ( powerset @ A ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(sepSubset_type,type,
% 3.03/1.58 sepSubset: $o ).
% 3.03/1.58
% 3.03/1.58 thf(sepSubset,definition,
% 3.03/1.58 ( sepSubset
% 3.03/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 3.03/1.58 ( subset
% 3.03/1.58 @ ( dsetconstr @ A
% 3.03/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.03/1.58 @ A ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(binunion_type,type,
% 3.03/1.58 binunion: $i > $i > $i ).
% 3.03/1.58
% 3.03/1.58 thf(binunionIL_type,type,
% 3.03/1.58 binunionIL: $o ).
% 3.03/1.58
% 3.03/1.58 thf(binunionIL,definition,
% 3.03/1.58 ( binunionIL
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(upairset2IR_type,type,
% 3.03/1.58 upairset2IR: $o ).
% 3.03/1.58
% 3.03/1.58 thf(upairset2IR,definition,
% 3.03/1.58 ( upairset2IR
% 3.03/1.58 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(binunionIR_type,type,
% 3.03/1.58 binunionIR: $o ).
% 3.03/1.58
% 3.03/1.58 thf(binunionIR,definition,
% 3.03/1.58 ( binunionIR
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ B )
% 3.03/1.58 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(binunionEcases_type,type,
% 3.03/1.58 binunionEcases: $o ).
% 3.03/1.58
% 3.03/1.58 thf(binunionEcases,definition,
% 3.03/1.58 ( binunionEcases
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 3.03/1.58 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 3.03/1.58 => ( ( ( in @ Xx @ A )
% 3.03/1.58 => Xphi )
% 3.03/1.58 => ( ( ( in @ Xx @ B )
% 3.03/1.58 => Xphi )
% 3.03/1.58 => Xphi ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(binunionE_type,type,
% 3.03/1.58 binunionE: $o ).
% 3.03/1.58
% 3.03/1.58 thf(binunionE,definition,
% 3.03/1.58 ( binunionE
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 3.03/1.58 => ( ( in @ Xx @ A )
% 3.03/1.58 | ( in @ Xx @ B ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(binunionLsub_type,type,
% 3.03/1.58 binunionLsub: $o ).
% 3.03/1.58
% 3.03/1.58 thf(binunionLsub,definition,
% 3.03/1.58 ( binunionLsub
% 3.03/1.58 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(binunionRsub_type,type,
% 3.03/1.58 binunionRsub: $o ).
% 3.03/1.58
% 3.03/1.58 thf(binunionRsub,definition,
% 3.03/1.58 ( binunionRsub
% 3.03/1.58 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(binintersect_type,type,
% 3.03/1.58 binintersect: $i > $i > $i ).
% 3.03/1.58
% 3.03/1.58 thf(binintersectI_type,type,
% 3.03/1.58 binintersectI: $o ).
% 3.03/1.58
% 3.03/1.58 thf(binintersectI,definition,
% 3.03/1.58 ( binintersectI
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ( ( in @ Xx @ B )
% 3.03/1.58 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(binintersectSubset5_type,type,
% 3.03/1.58 binintersectSubset5: $o ).
% 3.03/1.58
% 3.03/1.58 thf(binintersectSubset5,definition,
% 3.03/1.58 ( binintersectSubset5
% 3.03/1.58 = ( ! [A: $i,B: $i,C: $i] :
% 3.03/1.58 ( ( subset @ C @ A )
% 3.03/1.58 => ( ( subset @ C @ B )
% 3.03/1.58 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(binintersectEL_type,type,
% 3.03/1.58 binintersectEL: $o ).
% 3.03/1.58
% 3.03/1.58 thf(binintersectEL,definition,
% 3.03/1.58 ( binintersectEL
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 3.03/1.58 => ( in @ Xx @ A ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(binintersectLsub_type,type,
% 3.03/1.58 binintersectLsub: $o ).
% 3.03/1.58
% 3.03/1.58 thf(binintersectLsub,definition,
% 3.03/1.58 ( binintersectLsub
% 3.03/1.58 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(binintersectSubset2_type,type,
% 3.03/1.58 binintersectSubset2: $o ).
% 3.03/1.58
% 3.03/1.58 thf(binintersectSubset2,definition,
% 3.03/1.58 ( binintersectSubset2
% 3.03/1.58 = ( ! [A: $i,B: $i] :
% 3.03/1.58 ( ( subset @ A @ B )
% 3.03/1.58 => ( ( binintersect @ A @ B )
% 3.03/1.58 = A ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(binintersectSubset3_type,type,
% 3.03/1.58 binintersectSubset3: $o ).
% 3.03/1.58
% 3.03/1.58 thf(binintersectSubset3,definition,
% 3.03/1.58 ( binintersectSubset3
% 3.03/1.58 = ( ! [A: $i,B: $i] :
% 3.03/1.58 ( ( ( binintersect @ A @ B )
% 3.03/1.58 = B )
% 3.03/1.58 => ( subset @ B @ A ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(binintersectER_type,type,
% 3.03/1.58 binintersectER: $o ).
% 3.03/1.58
% 3.03/1.58 thf(binintersectER,definition,
% 3.03/1.58 ( binintersectER
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 3.03/1.58 => ( in @ Xx @ B ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(disjointsetsI1_type,type,
% 3.03/1.58 disjointsetsI1: $o ).
% 3.03/1.58
% 3.03/1.58 thf(disjointsetsI1,definition,
% 3.03/1.58 ( disjointsetsI1
% 3.03/1.58 = ( ! [A: $i,B: $i] :
% 3.03/1.58 ( ~ ? [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 & ( in @ Xx @ B ) )
% 3.03/1.58 => ( ( binintersect @ A @ B )
% 3.03/1.58 = emptyset ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(binintersectRsub_type,type,
% 3.03/1.58 binintersectRsub: $o ).
% 3.03/1.58
% 3.03/1.58 thf(binintersectRsub,definition,
% 3.03/1.58 ( binintersectRsub
% 3.03/1.58 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(binintersectSubset4_type,type,
% 3.03/1.58 binintersectSubset4: $o ).
% 3.03/1.58
% 3.03/1.58 thf(binintersectSubset4,definition,
% 3.03/1.58 ( binintersectSubset4
% 3.03/1.58 = ( ! [A: $i,B: $i] :
% 3.03/1.58 ( ( subset @ B @ A )
% 3.03/1.58 => ( ( binintersect @ A @ B )
% 3.03/1.58 = B ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(binintersectSubset1_type,type,
% 3.03/1.58 binintersectSubset1: $o ).
% 3.03/1.58
% 3.03/1.58 thf(binintersectSubset1,definition,
% 3.03/1.58 ( binintersectSubset1
% 3.03/1.58 = ( ! [A: $i,B: $i] :
% 3.03/1.58 ( ( ( binintersect @ A @ B )
% 3.03/1.58 = A )
% 3.03/1.58 => ( subset @ A @ B ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(bs114d_type,type,
% 3.03/1.58 bs114d: $o ).
% 3.03/1.58
% 3.03/1.58 thf(bs114d,definition,
% 3.03/1.58 ( bs114d
% 3.03/1.58 = ( ! [A: $i,B: $i,C: $i] :
% 3.03/1.58 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 3.03/1.58 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(regular_type,type,
% 3.03/1.58 regular: $i > $o ).
% 3.03/1.58
% 3.03/1.58 thf(setminus_type,type,
% 3.03/1.58 setminus: $i > $i > $i ).
% 3.03/1.58
% 3.03/1.58 thf(setminusI_type,type,
% 3.03/1.58 setminusI: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setminusI,definition,
% 3.03/1.58 ( setminusI
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ( ~ ( in @ Xx @ B )
% 3.03/1.58 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setminusEL_type,type,
% 3.03/1.58 setminusEL: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setminusEL,definition,
% 3.03/1.58 ( setminusEL
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 3.03/1.58 => ( in @ Xx @ A ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setminusER_type,type,
% 3.03/1.58 setminusER: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setminusER,definition,
% 3.03/1.58 ( setminusER
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 3.03/1.58 => ~ ( in @ Xx @ B ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setminusSubset2_type,type,
% 3.03/1.58 setminusSubset2: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setminusSubset2,definition,
% 3.03/1.58 ( setminusSubset2
% 3.03/1.58 = ( ! [A: $i,B: $i] :
% 3.03/1.58 ( ( subset @ A @ B )
% 3.03/1.58 => ( ( setminus @ A @ B )
% 3.03/1.58 = emptyset ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setminusERneg_type,type,
% 3.03/1.58 setminusERneg: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setminusERneg,definition,
% 3.03/1.58 ( setminusERneg
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.03/1.58 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 3.03/1.58 => ( ( in @ Xx @ A )
% 3.03/1.58 => ( in @ Xx @ B ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setminusELneg_type,type,
% 3.03/1.58 setminusELneg: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setminusELneg,definition,
% 3.03/1.58 ( setminusELneg
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.03/1.58 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 3.03/1.58 => ( ~ ( in @ Xx @ B )
% 3.03/1.58 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setminusILneg_type,type,
% 3.03/1.58 setminusILneg: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setminusILneg,definition,
% 3.03/1.58 ( setminusILneg
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.03/1.58 ( ~ ( in @ Xx @ A )
% 3.03/1.58 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setminusIRneg_type,type,
% 3.03/1.58 setminusIRneg: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setminusIRneg,definition,
% 3.03/1.58 ( setminusIRneg
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ B )
% 3.03/1.58 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setminusLsub_type,type,
% 3.03/1.58 setminusLsub: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setminusLsub,definition,
% 3.03/1.58 ( setminusLsub
% 3.03/1.58 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setminusSubset1_type,type,
% 3.03/1.58 setminusSubset1: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setminusSubset1,definition,
% 3.03/1.58 ( setminusSubset1
% 3.03/1.58 = ( ! [A: $i,B: $i] :
% 3.03/1.58 ( ( ( setminus @ A @ B )
% 3.03/1.58 = emptyset )
% 3.03/1.58 => ( subset @ A @ B ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(symdiff_type,type,
% 3.03/1.58 symdiff: $i > $i > $i ).
% 3.03/1.58
% 3.03/1.58 thf(symdiffE_type,type,
% 3.03/1.58 symdiffE: $o ).
% 3.03/1.58
% 3.03/1.58 thf(symdiffE,definition,
% 3.03/1.58 ( symdiffE
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 3.03/1.58 => ! [Xphi: $o] :
% 3.03/1.58 ( ( ( in @ Xx @ A )
% 3.03/1.58 => ( ~ ( in @ Xx @ B )
% 3.03/1.58 => Xphi ) )
% 3.03/1.58 => ( ( ~ ( in @ Xx @ A )
% 3.03/1.58 => ( ( in @ Xx @ B )
% 3.03/1.58 => Xphi ) )
% 3.03/1.58 => Xphi ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(symdiffI1_type,type,
% 3.03/1.58 symdiffI1: $o ).
% 3.03/1.58
% 3.03/1.58 thf(symdiffI1,definition,
% 3.03/1.58 ( symdiffI1
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ( ~ ( in @ Xx @ B )
% 3.03/1.58 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(symdiffI2_type,type,
% 3.03/1.58 symdiffI2: $o ).
% 3.03/1.58
% 3.03/1.58 thf(symdiffI2,definition,
% 3.03/1.58 ( symdiffI2
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.03/1.58 ( ~ ( in @ Xx @ A )
% 3.03/1.58 => ( ( in @ Xx @ B )
% 3.03/1.58 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(symdiffIneg1_type,type,
% 3.03/1.58 symdiffIneg1: $o ).
% 3.03/1.58
% 3.03/1.58 thf(symdiffIneg1,definition,
% 3.03/1.58 ( symdiffIneg1
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ( ( in @ Xx @ B )
% 3.03/1.58 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(symdiffIneg2_type,type,
% 3.03/1.58 symdiffIneg2: $o ).
% 3.03/1.58
% 3.03/1.58 thf(symdiffIneg2,definition,
% 3.03/1.58 ( symdiffIneg2
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.03/1.58 ( ~ ( in @ Xx @ A )
% 3.03/1.58 => ( ~ ( in @ Xx @ B )
% 3.03/1.58 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(iskpair_type,type,
% 3.03/1.58 iskpair: $i > $o ).
% 3.03/1.58
% 3.03/1.58 thf(secondinupair_type,type,
% 3.03/1.58 secondinupair: $o ).
% 3.03/1.58
% 3.03/1.58 thf(secondinupair,definition,
% 3.03/1.58 ( secondinupair
% 3.03/1.58 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setukpairIL_type,type,
% 3.03/1.58 setukpairIL: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setukpairIL,definition,
% 3.03/1.58 ( setukpairIL
% 3.03/1.58 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setukpairIR_type,type,
% 3.03/1.58 setukpairIR: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setukpairIR,definition,
% 3.03/1.58 ( setukpairIR
% 3.03/1.58 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(kpairiskpair_type,type,
% 3.03/1.58 kpairiskpair: $o ).
% 3.03/1.58
% 3.03/1.58 thf(kpairiskpair,definition,
% 3.03/1.58 ( kpairiskpair
% 3.03/1.58 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(kpair_type,type,
% 3.03/1.58 kpair: $i > $i > $i ).
% 3.03/1.58
% 3.03/1.58 thf(kpairp_type,type,
% 3.03/1.58 kpairp: $o ).
% 3.03/1.58
% 3.03/1.58 thf(kpairp,definition,
% 3.03/1.58 ( kpairp
% 3.03/1.58 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(cartprod_type,type,
% 3.03/1.58 cartprod: $i > $i > $i ).
% 3.03/1.58
% 3.03/1.58 thf(singletonsubset_type,type,
% 3.03/1.58 singletonsubset: $o ).
% 3.03/1.58
% 3.03/1.58 thf(singletonsubset,definition,
% 3.03/1.58 ( singletonsubset
% 3.03/1.58 = ( ! [A: $i,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(singletoninpowerset_type,type,
% 3.03/1.58 singletoninpowerset: $o ).
% 3.03/1.58
% 3.03/1.58 thf(singletoninpowerset,definition,
% 3.03/1.58 ( singletoninpowerset
% 3.03/1.58 = ( ! [A: $i,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(singletoninpowunion_type,type,
% 3.03/1.58 singletoninpowunion: $o ).
% 3.03/1.58
% 3.03/1.58 thf(singletoninpowunion,definition,
% 3.03/1.58 ( singletoninpowunion
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(upairset2E_type,type,
% 3.03/1.58 upairset2E: $o ).
% 3.03/1.58
% 3.03/1.58 thf(upairset2E,definition,
% 3.03/1.58 ( upairset2E
% 3.03/1.58 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.03/1.58 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 3.03/1.58 => ( ( Xz = Xx )
% 3.03/1.58 | ( Xz = Xy ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(upairsubunion_type,type,
% 3.03/1.58 upairsubunion: $o ).
% 3.03/1.58
% 3.03/1.58 thf(upairsubunion,definition,
% 3.03/1.58 ( upairsubunion
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ! [Xy: $i] :
% 3.03/1.58 ( ( in @ Xy @ B )
% 3.03/1.58 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(upairinpowunion_type,type,
% 3.03/1.58 upairinpowunion: $o ).
% 3.03/1.58
% 3.03/1.58 thf(upairinpowunion,definition,
% 3.03/1.58 ( upairinpowunion
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ! [Xy: $i] :
% 3.03/1.58 ( ( in @ Xy @ B )
% 3.03/1.58 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(ubforcartprodlem1_type,type,
% 3.03/1.58 ubforcartprodlem1: $o ).
% 3.03/1.58
% 3.03/1.58 thf(ubforcartprodlem1,definition,
% 3.03/1.58 ( ubforcartprodlem1
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ! [Xy: $i] :
% 3.03/1.58 ( ( in @ Xy @ B )
% 3.03/1.58 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(ubforcartprodlem2_type,type,
% 3.03/1.58 ubforcartprodlem2: $o ).
% 3.03/1.58
% 3.03/1.58 thf(ubforcartprodlem2,definition,
% 3.03/1.58 ( ubforcartprodlem2
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ! [Xy: $i] :
% 3.03/1.58 ( ( in @ Xy @ B )
% 3.03/1.58 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(ubforcartprodlem3_type,type,
% 3.03/1.58 ubforcartprodlem3: $o ).
% 3.03/1.58
% 3.03/1.58 thf(ubforcartprodlem3,definition,
% 3.03/1.58 ( ubforcartprodlem3
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ! [Xy: $i] :
% 3.03/1.58 ( ( in @ Xy @ B )
% 3.03/1.58 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(cartprodpairin_type,type,
% 3.03/1.58 cartprodpairin: $o ).
% 3.03/1.58
% 3.03/1.58 thf(cartprodpairin,definition,
% 3.03/1.58 ( cartprodpairin
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ! [Xy: $i] :
% 3.03/1.58 ( ( in @ Xy @ B )
% 3.03/1.58 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(cartprodmempair1_type,type,
% 3.03/1.58 cartprodmempair1: $o ).
% 3.03/1.58
% 3.03/1.58 thf(cartprodmempair1,definition,
% 3.03/1.58 ( cartprodmempair1
% 3.03/1.58 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.03/1.58 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.03/1.58 => ? [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 & ? [Xy: $i] :
% 3.03/1.58 ( ( in @ Xy @ B )
% 3.03/1.58 & ( Xu
% 3.03/1.58 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(cartprodmempair_type,type,
% 3.03/1.58 cartprodmempair: $o ).
% 3.03/1.58
% 3.03/1.58 thf(cartprodmempair,definition,
% 3.03/1.58 ( cartprodmempair
% 3.03/1.58 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.03/1.58 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.03/1.58 => ( iskpair @ Xu ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setunionE2_type,type,
% 3.03/1.58 setunionE2: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setunionE2,definition,
% 3.03/1.58 ( setunionE2
% 3.03/1.58 = ( ! [A: $i,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ ( setunion @ A ) )
% 3.03/1.58 => ? [X: $i] :
% 3.03/1.58 ( ( in @ X @ A )
% 3.03/1.58 & ( in @ Xx @ X ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setunionsingleton1_type,type,
% 3.03/1.58 setunionsingleton1: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setunionsingleton1,definition,
% 3.03/1.58 ( setunionsingleton1
% 3.03/1.58 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setunionsingleton2_type,type,
% 3.03/1.58 setunionsingleton2: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setunionsingleton2,definition,
% 3.03/1.58 ( setunionsingleton2
% 3.03/1.58 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setunionsingleton_type,type,
% 3.03/1.58 setunionsingleton: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setunionsingleton,definition,
% 3.03/1.58 ( setunionsingleton
% 3.03/1.58 = ( ! [Xx: $i] :
% 3.03/1.58 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 3.03/1.58 = Xx ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(singleton_type,type,
% 3.03/1.58 singleton: $i > $o ).
% 3.03/1.58
% 3.03/1.58 thf(singletonprop_type,type,
% 3.03/1.58 singletonprop: $o ).
% 3.03/1.58
% 3.03/1.58 thf(singletonprop,definition,
% 3.03/1.58 ( singletonprop
% 3.03/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 3.03/1.58 ( ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ! [Xy: $i] :
% 3.03/1.58 ( ( in @ Xy @ A )
% 3.03/1.58 => ( ( Xphi @ Xx )
% 3.03/1.58 => ( ( Xphi @ Xy )
% 3.03/1.58 => ( Xx = Xy ) ) ) ) )
% 3.03/1.58 => ( ? [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 & ( Xphi @ Xx ) )
% 3.03/1.58 => ( singleton
% 3.03/1.58 @ ( dsetconstr @ A
% 3.03/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(ex1_type,type,
% 3.03/1.58 ex1: $i > ( $i > $o ) > $o ).
% 3.03/1.58
% 3.03/1.58 thf(ex1E1_type,type,
% 3.03/1.58 ex1E1: $o ).
% 3.03/1.58
% 3.03/1.58 thf(ex1E1,definition,
% 3.03/1.58 ( ex1E1
% 3.03/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 3.03/1.58 ( ( ex1 @ A
% 3.03/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.03/1.58 => ? [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 & ( Xphi @ Xx ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(ex1I_type,type,
% 3.03/1.58 ex1I: $o ).
% 3.03/1.58
% 3.03/1.58 thf(ex1I,definition,
% 3.03/1.58 ( ex1I
% 3.03/1.58 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ( ( Xphi @ Xx )
% 3.03/1.58 => ( ! [Xy: $i] :
% 3.03/1.58 ( ( in @ Xy @ A )
% 3.03/1.58 => ( ( Xphi @ Xy )
% 3.03/1.58 => ( Xy = Xx ) ) )
% 3.03/1.58 => ( ex1 @ A
% 3.03/1.58 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(ex1I2_type,type,
% 3.03/1.58 ex1I2: $o ).
% 3.03/1.58
% 3.03/1.58 thf(ex1I2,definition,
% 3.03/1.58 ( ex1I2
% 3.03/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 3.03/1.58 ( ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ! [Xy: $i] :
% 3.03/1.58 ( ( in @ Xy @ A )
% 3.03/1.58 => ( ( Xphi @ Xx )
% 3.03/1.58 => ( ( Xphi @ Xy )
% 3.03/1.58 => ( Xx = Xy ) ) ) ) )
% 3.03/1.58 => ( ? [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 & ( Xphi @ Xx ) )
% 3.03/1.58 => ( ex1 @ A
% 3.03/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(singletonsuniq_type,type,
% 3.03/1.58 singletonsuniq: $o ).
% 3.03/1.58
% 3.03/1.58 thf(singletonsuniq,definition,
% 3.03/1.58 ( singletonsuniq
% 3.03/1.58 = ( ! [Xx: $i,Xy: $i] :
% 3.03/1.58 ( ( ( setadjoin @ Xx @ emptyset )
% 3.03/1.58 = ( setadjoin @ Xy @ emptyset ) )
% 3.03/1.58 => ( Xx = Xy ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(atmost1p_type,type,
% 3.03/1.58 atmost1p: $i > $o ).
% 3.03/1.58
% 3.03/1.58 thf(atleast2p_type,type,
% 3.03/1.58 atleast2p: $i > $o ).
% 3.03/1.58
% 3.03/1.58 thf(atmost2p_type,type,
% 3.03/1.58 atmost2p: $i > $o ).
% 3.03/1.58
% 3.03/1.58 thf(upairsetp_type,type,
% 3.03/1.58 upairsetp: $i > $o ).
% 3.03/1.58
% 3.03/1.58 thf(setukpairinjL1_type,type,
% 3.03/1.58 setukpairinjL1: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setukpairinjL1,definition,
% 3.03/1.58 ( setukpairinjL1
% 3.03/1.58 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.03/1.58 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 3.03/1.58 => ( Xx = Xz ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(kfstsingleton_type,type,
% 3.03/1.58 kfstsingleton: $o ).
% 3.03/1.58
% 3.03/1.58 thf(kfstsingleton,definition,
% 3.03/1.58 ( kfstsingleton
% 3.03/1.58 = ( ! [Xu: $i] :
% 3.03/1.58 ( ( iskpair @ Xu )
% 3.03/1.58 => ( singleton
% 3.03/1.58 @ ( dsetconstr @ ( setunion @ Xu )
% 3.03/1.58 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(theprop_type,type,
% 3.03/1.58 theprop: $o ).
% 3.03/1.58
% 3.03/1.58 thf(theprop,definition,
% 3.03/1.58 ( theprop
% 3.03/1.58 = ( ! [X: $i] :
% 3.03/1.58 ( ( singleton @ X )
% 3.03/1.58 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(kfst_type,type,
% 3.03/1.58 kfst: $i > $i ).
% 3.03/1.58
% 3.03/1.58 thf(kfstpairEq_type,type,
% 3.03/1.58 kfstpairEq: $o ).
% 3.03/1.58
% 3.03/1.58 thf(kfstpairEq,definition,
% 3.03/1.58 ( kfstpairEq
% 3.03/1.58 = ( ! [Xx: $i,Xy: $i] :
% 3.03/1.58 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 3.03/1.58 = Xx ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(cartprodfstin_type,type,
% 3.03/1.58 cartprodfstin: $o ).
% 3.03/1.58
% 3.03/1.58 thf(cartprodfstin,definition,
% 3.03/1.58 ( cartprodfstin
% 3.03/1.58 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.03/1.58 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.03/1.58 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setukpairinjL2_type,type,
% 3.03/1.58 setukpairinjL2: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setukpairinjL2,definition,
% 3.03/1.58 ( setukpairinjL2
% 3.03/1.58 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.03/1.58 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.03/1.58 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.03/1.58 => ( Xx = Xz ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setukpairinjL_type,type,
% 3.03/1.58 setukpairinjL: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setukpairinjL,definition,
% 3.03/1.58 ( setukpairinjL
% 3.03/1.58 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.03/1.58 ( ( ( kpair @ Xx @ Xy )
% 3.03/1.58 = ( kpair @ Xz @ Xu ) )
% 3.03/1.58 => ( Xx = Xz ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setukpairinjR11_type,type,
% 3.03/1.58 setukpairinjR11: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setukpairinjR11,definition,
% 3.03/1.58 ( setukpairinjR11
% 3.03/1.58 = ( ! [Xx: $i,Xy: $i] :
% 3.03/1.58 ( ( Xx = Xy )
% 3.03/1.58 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.03/1.58 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setukpairinjR12_type,type,
% 3.03/1.58 setukpairinjR12: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setukpairinjR12,definition,
% 3.03/1.58 ( setukpairinjR12
% 3.03/1.58 = ( ! [Xx: $i,Xy: $i] :
% 3.03/1.58 ( ( Xx = Xy )
% 3.03/1.58 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.03/1.58 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setukpairinjR1_type,type,
% 3.03/1.58 setukpairinjR1: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setukpairinjR1,definition,
% 3.03/1.58 ( setukpairinjR1
% 3.03/1.58 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.03/1.58 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.03/1.58 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.03/1.58 => ( ( Xz = Xu )
% 3.03/1.58 => ( Xy = Xu ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(upairequniteq_type,type,
% 3.03/1.58 upairequniteq: $o ).
% 3.03/1.58
% 3.03/1.58 thf(upairequniteq,definition,
% 3.03/1.58 ( upairequniteq
% 3.03/1.58 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.03/1.58 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.03/1.58 = ( setadjoin @ Xz @ emptyset ) )
% 3.03/1.58 => ( Xx = Xy ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setukpairinjR2_type,type,
% 3.03/1.58 setukpairinjR2: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setukpairinjR2,definition,
% 3.03/1.58 ( setukpairinjR2
% 3.03/1.58 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.03/1.58 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.03/1.58 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.03/1.58 => ( Xy = Xu ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setukpairinjR_type,type,
% 3.03/1.58 setukpairinjR: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setukpairinjR,definition,
% 3.03/1.58 ( setukpairinjR
% 3.03/1.58 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.03/1.58 ( ( ( kpair @ Xx @ Xy )
% 3.03/1.58 = ( kpair @ Xz @ Xu ) )
% 3.03/1.58 => ( Xy = Xu ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(ksndsingleton_type,type,
% 3.03/1.58 ksndsingleton: $o ).
% 3.03/1.58
% 3.03/1.58 thf(ksndsingleton,definition,
% 3.03/1.58 ( ksndsingleton
% 3.03/1.58 = ( ! [Xu: $i] :
% 3.03/1.58 ( ( iskpair @ Xu )
% 3.03/1.58 => ( singleton
% 3.03/1.58 @ ( dsetconstr @ ( setunion @ Xu )
% 3.03/1.58 @ ^ [Xx: $i] :
% 3.03/1.58 ( Xu
% 3.03/1.58 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(ksnd_type,type,
% 3.03/1.58 ksnd: $i > $i ).
% 3.03/1.58
% 3.03/1.58 thf(ksndpairEq_type,type,
% 3.03/1.58 ksndpairEq: $o ).
% 3.03/1.58
% 3.03/1.58 thf(ksndpairEq,definition,
% 3.03/1.58 ( ksndpairEq
% 3.03/1.58 = ( ! [Xx: $i,Xy: $i] :
% 3.03/1.58 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 3.03/1.58 = Xy ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(kpairsurjEq_type,type,
% 3.03/1.58 kpairsurjEq: $o ).
% 3.03/1.58
% 3.03/1.58 thf(kpairsurjEq,definition,
% 3.03/1.58 ( kpairsurjEq
% 3.03/1.58 = ( ! [Xu: $i] :
% 3.03/1.58 ( ( iskpair @ Xu )
% 3.03/1.58 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 3.03/1.58 = Xu ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(cartprodsndin_type,type,
% 3.03/1.58 cartprodsndin: $o ).
% 3.03/1.58
% 3.03/1.58 thf(cartprodsndin,definition,
% 3.03/1.58 ( cartprodsndin
% 3.03/1.58 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.03/1.58 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.03/1.58 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(cartprodpairmemEL_type,type,
% 3.03/1.58 cartprodpairmemEL: $o ).
% 3.03/1.58
% 3.03/1.58 thf(cartprodpairmemEL,definition,
% 3.03/1.58 ( cartprodpairmemEL
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 3.03/1.58 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 3.03/1.58 => ( in @ Xx @ A ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(cartprodpairmemER_type,type,
% 3.03/1.58 cartprodpairmemER: $o ).
% 3.03/1.58
% 3.03/1.58 thf(cartprodpairmemER,definition,
% 3.03/1.58 ( cartprodpairmemER
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 3.03/1.58 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 3.03/1.58 => ( in @ Xy @ B ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(cartprodmempaircEq_type,type,
% 3.03/1.58 cartprodmempaircEq: $o ).
% 3.03/1.58
% 3.03/1.58 thf(cartprodmempaircEq,definition,
% 3.03/1.58 ( cartprodmempaircEq
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ! [Xy: $i] :
% 3.03/1.58 ( ( in @ Xy @ B )
% 3.03/1.58 => ( ( kpair @ Xx @ Xy )
% 3.03/1.58 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(cartprodfstpairEq_type,type,
% 3.03/1.58 cartprodfstpairEq: $o ).
% 3.03/1.58
% 3.03/1.58 thf(cartprodfstpairEq,definition,
% 3.03/1.58 ( cartprodfstpairEq
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ! [Xy: $i] :
% 3.03/1.58 ( ( in @ Xy @ B )
% 3.03/1.58 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 3.03/1.58 = Xx ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(cartprodsndpairEq_type,type,
% 3.03/1.58 cartprodsndpairEq: $o ).
% 3.03/1.58
% 3.03/1.58 thf(cartprodsndpairEq,definition,
% 3.03/1.58 ( cartprodsndpairEq
% 3.03/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ! [Xy: $i] :
% 3.03/1.58 ( ( in @ Xy @ B )
% 3.03/1.58 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 3.03/1.58 = Xy ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(cartprodpairsurjEq_type,type,
% 3.03/1.58 cartprodpairsurjEq: $o ).
% 3.03/1.58
% 3.03/1.58 thf(cartprodpairsurjEq,definition,
% 3.03/1.58 ( cartprodpairsurjEq
% 3.03/1.58 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.03/1.58 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.03/1.58 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 3.03/1.58 = Xu ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(breln_type,type,
% 3.03/1.58 breln: $i > $i > $i > $o ).
% 3.03/1.58
% 3.03/1.58 thf(dpsetconstr_type,type,
% 3.03/1.58 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 3.03/1.58
% 3.03/1.58 thf(dpsetconstrI_type,type,
% 3.03/1.58 dpsetconstrI: $o ).
% 3.03/1.58
% 3.03/1.58 thf(dpsetconstrI,definition,
% 3.03/1.58 ( dpsetconstrI
% 3.03/1.58 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ! [Xy: $i] :
% 3.03/1.58 ( ( in @ Xy @ B )
% 3.03/1.58 => ( ( Xphi @ Xx @ Xy )
% 3.03/1.58 => ( in @ ( kpair @ Xx @ Xy )
% 3.03/1.58 @ ( dpsetconstr @ A @ B
% 3.03/1.58 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(dpsetconstrSub_type,type,
% 3.03/1.58 dpsetconstrSub: $o ).
% 3.03/1.58
% 3.03/1.58 thf(dpsetconstrSub,definition,
% 3.03/1.58 ( dpsetconstrSub
% 3.03/1.58 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.03/1.58 ( subset
% 3.03/1.58 @ ( dpsetconstr @ A @ B
% 3.03/1.58 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 3.03/1.58 @ ( cartprod @ A @ B ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(setOfPairsIsBReln_type,type,
% 3.03/1.58 setOfPairsIsBReln: $o ).
% 3.03/1.58
% 3.03/1.58 thf(setOfPairsIsBReln,definition,
% 3.03/1.58 ( setOfPairsIsBReln
% 3.03/1.58 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.03/1.58 ( breln @ A @ B
% 3.03/1.58 @ ( dpsetconstr @ A @ B
% 3.03/1.58 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(dpsetconstrERa_type,type,
% 3.03/1.58 dpsetconstrERa: $o ).
% 3.03/1.58
% 3.03/1.58 thf(dpsetconstrERa,definition,
% 3.03/1.58 ( dpsetconstrERa
% 3.03/1.58 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ! [Xy: $i] :
% 3.03/1.58 ( ( in @ Xy @ B )
% 3.03/1.58 => ( ( in @ ( kpair @ Xx @ Xy )
% 3.03/1.58 @ ( dpsetconstr @ A @ B
% 3.03/1.58 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.03/1.58 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(dpsetconstrEL1_type,type,
% 3.03/1.58 dpsetconstrEL1: $o ).
% 3.03/1.58
% 3.03/1.58 thf(dpsetconstrEL1,definition,
% 3.03/1.58 ( dpsetconstrEL1
% 3.03/1.58 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.03/1.58 ( ( in @ ( kpair @ Xx @ Xy )
% 3.03/1.58 @ ( dpsetconstr @ A @ B
% 3.03/1.58 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.03/1.58 => ( in @ Xx @ A ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(dpsetconstrEL2_type,type,
% 3.03/1.58 dpsetconstrEL2: $o ).
% 3.03/1.58
% 3.03/1.58 thf(dpsetconstrEL2,definition,
% 3.03/1.58 ( dpsetconstrEL2
% 3.03/1.58 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.03/1.58 ( ( in @ ( kpair @ Xx @ Xy )
% 3.03/1.58 @ ( dpsetconstr @ A @ B
% 3.03/1.58 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.03/1.58 => ( in @ Xy @ B ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(dpsetconstrER_type,type,
% 3.03/1.58 dpsetconstrER: $o ).
% 3.03/1.58
% 3.03/1.58 thf(dpsetconstrER,definition,
% 3.03/1.58 ( dpsetconstrER
% 3.03/1.58 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.03/1.58 ( ( in @ ( kpair @ Xx @ Xy )
% 3.03/1.58 @ ( dpsetconstr @ A @ B
% 3.03/1.58 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.03/1.58 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(func_type,type,
% 3.03/1.58 func: $i > $i > $i > $o ).
% 3.03/1.58
% 3.03/1.58 thf(funcSet_type,type,
% 3.03/1.58 funcSet: $i > $i > $i ).
% 3.03/1.58
% 3.03/1.58 thf(funcImageSingleton_type,type,
% 3.03/1.58 funcImageSingleton: $o ).
% 3.03/1.58
% 3.03/1.58 thf(funcImageSingleton,definition,
% 3.03/1.58 ( funcImageSingleton
% 3.03/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.03/1.58 ( ( func @ A @ B @ Xf )
% 3.03/1.58 => ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ( singleton
% 3.03/1.58 @ ( dsetconstr @ B
% 3.03/1.58 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(apProp_type,type,
% 3.03/1.58 apProp: $o ).
% 3.03/1.58
% 3.03/1.58 thf(apProp,definition,
% 3.03/1.58 ( apProp
% 3.03/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.03/1.58 ( ( func @ A @ B @ Xf )
% 3.03/1.58 => ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ( in
% 3.03/1.58 @ ( setunion
% 3.03/1.58 @ ( dsetconstr @ B
% 3.03/1.58 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 3.03/1.58 @ B ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(ap_type,type,
% 3.03/1.58 ap: $i > $i > $i > $i > $i ).
% 3.03/1.58
% 3.03/1.58 thf(app_type,type,
% 3.03/1.58 app: $o ).
% 3.03/1.58
% 3.03/1.58 thf(app,definition,
% 3.03/1.58 ( app
% 3.03/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.03/1.58 ( ( func @ A @ B @ Xf )
% 3.03/1.58 => ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(infuncsetfunc_type,type,
% 3.03/1.58 infuncsetfunc: $o ).
% 3.03/1.58
% 3.03/1.58 thf(infuncsetfunc,definition,
% 3.03/1.58 ( infuncsetfunc
% 3.03/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.03/1.58 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.03/1.58 => ( func @ A @ B @ Xf ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(ap2p_type,type,
% 3.03/1.58 ap2p: $o ).
% 3.03/1.58
% 3.03/1.58 thf(ap2p,definition,
% 3.03/1.58 ( ap2p
% 3.03/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.03/1.58 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.03/1.58 => ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(funcinfuncset_type,type,
% 3.03/1.58 funcinfuncset: $o ).
% 3.03/1.58
% 3.03/1.58 thf(funcinfuncset,definition,
% 3.03/1.58 ( funcinfuncset
% 3.03/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.03/1.58 ( ( func @ A @ B @ Xf )
% 3.03/1.58 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(lamProp_type,type,
% 3.03/1.58 lamProp: $o ).
% 3.03/1.58
% 3.03/1.58 thf(lamProp,definition,
% 3.03/1.58 ( lamProp
% 3.03/1.58 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.03/1.58 ( ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.03/1.58 => ( func @ A @ B
% 3.03/1.58 @ ( dpsetconstr @ A @ B
% 3.03/1.58 @ ^ [Xx: $i,Xy: $i] :
% 3.03/1.58 ( ( Xf @ Xx )
% 3.03/1.58 = Xy ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(lam_type,type,
% 3.03/1.58 lam: $i > $i > ( $i > $i ) > $i ).
% 3.03/1.58
% 3.03/1.58 thf(lamp_type,type,
% 3.03/1.58 lamp: $o ).
% 3.03/1.58
% 3.03/1.58 thf(lamp,definition,
% 3.03/1.58 ( lamp
% 3.03/1.58 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.03/1.58 ( ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.03/1.58 => ( func @ A @ B
% 3.03/1.58 @ ( lam @ A @ B
% 3.03/1.58 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(lam2p_type,type,
% 3.03/1.58 lam2p: $o ).
% 3.03/1.58
% 3.03/1.58 thf(lam2p,definition,
% 3.03/1.58 ( lam2p
% 3.03/1.58 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.03/1.58 ( ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.03/1.58 => ( in
% 3.03/1.58 @ ( lam @ A @ B
% 3.03/1.58 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 3.03/1.58 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(brelnall1_type,type,
% 3.03/1.58 brelnall1: $o ).
% 3.03/1.58
% 3.03/1.58 thf(brelnall1,definition,
% 3.03/1.58 ( brelnall1
% 3.03/1.58 = ( ! [A: $i,B: $i,R: $i] :
% 3.03/1.58 ( ( breln @ A @ B @ R )
% 3.03/1.58 => ! [Xphi: $i > $o] :
% 3.03/1.58 ( ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ! [Xy: $i] :
% 3.03/1.58 ( ( in @ Xy @ B )
% 3.03/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.03/1.58 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.03/1.58 => ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ R )
% 3.03/1.58 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(brelnall2_type,type,
% 3.03/1.58 brelnall2: $o ).
% 3.03/1.58
% 3.03/1.58 thf(brelnall2,definition,
% 3.03/1.58 ( brelnall2
% 3.03/1.58 = ( ! [A: $i,B: $i,R: $i] :
% 3.03/1.58 ( ( breln @ A @ B @ R )
% 3.03/1.58 => ! [Xphi: $i > $o] :
% 3.03/1.58 ( ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ! [Xy: $i] :
% 3.03/1.58 ( ( in @ Xy @ B )
% 3.03/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.03/1.58 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.03/1.58 => ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ R )
% 3.03/1.58 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(ex1E2_type,type,
% 3.03/1.58 ex1E2: $o ).
% 3.03/1.58
% 3.03/1.58 thf(ex1E2,definition,
% 3.03/1.58 ( ex1E2
% 3.03/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 3.03/1.58 ( ( ex1 @ A
% 3.03/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.03/1.58 => ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ! [Xy: $i] :
% 3.03/1.58 ( ( in @ Xy @ A )
% 3.03/1.58 => ( ( Xphi @ Xx )
% 3.03/1.58 => ( ( Xphi @ Xy )
% 3.03/1.58 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(funcGraphProp1_type,type,
% 3.03/1.58 funcGraphProp1: $o ).
% 3.03/1.58
% 3.03/1.58 thf(funcGraphProp1,definition,
% 3.03/1.58 ( funcGraphProp1
% 3.03/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.03/1.58 ( ( func @ A @ B @ Xf )
% 3.03/1.58 => ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(funcGraphProp3_type,type,
% 3.03/1.58 funcGraphProp3: $o ).
% 3.03/1.58
% 3.03/1.58 thf(funcGraphProp3,definition,
% 3.03/1.58 ( funcGraphProp3
% 3.03/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.03/1.58 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.03/1.58 => ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(funcGraphProp2_type,type,
% 3.03/1.58 funcGraphProp2: $o ).
% 3.03/1.58
% 3.03/1.58 thf(funcGraphProp2,definition,
% 3.03/1.58 ( funcGraphProp2
% 3.03/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.03/1.58 ( ( func @ A @ B @ Xf )
% 3.03/1.58 => ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ! [Xy: $i] :
% 3.03/1.58 ( ( in @ Xy @ B )
% 3.03/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 3.03/1.58 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.03/1.58 = Xy ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(funcextLem_type,type,
% 3.03/1.58 funcextLem: $o ).
% 3.03/1.58
% 3.03/1.58 thf(funcextLem,definition,
% 3.03/1.58 ( funcextLem
% 3.03/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.03/1.58 ( ( func @ A @ B @ Xf )
% 3.03/1.58 => ! [Xg: $i] :
% 3.03/1.58 ( ( func @ A @ B @ Xg )
% 3.03/1.58 => ( ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.03/1.58 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.03/1.58 => ! [Xx: $i] :
% 3.03/1.58 ( ( in @ Xx @ A )
% 3.03/1.58 => ! [Xy: $i] :
% 3.03/1.58 ( ( in @ Xy @ B )
% 3.03/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 3.03/1.58 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 3.03/1.58
% 3.03/1.58 thf(funcGraphProp4_type,type,
% 3.03/1.58 funcGraphProp4: $o ).
% 3.03/1.58
% 3.03/1.58 thf(funcGraphProp4,definition,
% 3.03/1.59 ( funcGraphProp4
% 3.03/1.59 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.03/1.59 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ! [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ B )
% 3.03/1.59 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 3.03/1.59 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.03/1.59 = Xy ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(subbreln_type,type,
% 3.03/1.59 subbreln: $o ).
% 3.03/1.59
% 3.03/1.59 thf(subbreln,definition,
% 3.03/1.59 ( subbreln
% 3.03/1.59 = ( ! [A: $i,B: $i,R: $i] :
% 3.03/1.59 ( ( breln @ A @ B @ R )
% 3.03/1.59 => ! [S: $i] :
% 3.03/1.59 ( ( breln @ A @ B @ S )
% 3.03/1.59 => ( ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ! [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ B )
% 3.03/1.59 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.03/1.59 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.03/1.59 => ( subset @ R @ S ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(eqbreln_type,type,
% 3.03/1.59 eqbreln: $o ).
% 3.03/1.59
% 3.03/1.59 thf(eqbreln,definition,
% 3.03/1.59 ( eqbreln
% 3.03/1.59 = ( ! [A: $i,B: $i,R: $i] :
% 3.03/1.59 ( ( breln @ A @ B @ R )
% 3.03/1.59 => ! [S: $i] :
% 3.03/1.59 ( ( breln @ A @ B @ S )
% 3.03/1.59 => ( ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ! [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ B )
% 3.03/1.59 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.03/1.59 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.03/1.59 => ( ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ! [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ B )
% 3.03/1.59 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.03/1.59 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 3.03/1.59 => ( R = S ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(funcext_type,type,
% 3.03/1.59 funcext: $o ).
% 3.03/1.59
% 3.03/1.59 thf(funcext,definition,
% 3.03/1.59 ( funcext
% 3.03/1.59 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.03/1.59 ( ( func @ A @ B @ Xf )
% 3.03/1.59 => ! [Xg: $i] :
% 3.03/1.59 ( ( func @ A @ B @ Xg )
% 3.03/1.59 => ( ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.03/1.59 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.03/1.59 => ( Xf = Xg ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(funcext2_type,type,
% 3.03/1.59 funcext2: $o ).
% 3.03/1.59
% 3.03/1.59 thf(funcext2,definition,
% 3.03/1.59 ( funcext2
% 3.03/1.59 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.03/1.59 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.03/1.59 => ! [Xg: $i] :
% 3.03/1.59 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 3.03/1.59 => ( ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.03/1.59 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.03/1.59 => ( Xf = Xg ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(ap2apEq1_type,type,
% 3.03/1.59 ap2apEq1: $o ).
% 3.03/1.59
% 3.03/1.59 thf(ap2apEq1,definition,
% 3.03/1.59 ( ap2apEq1
% 3.03/1.59 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.03/1.59 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.03/1.59 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(ap2apEq2_type,type,
% 3.03/1.59 ap2apEq2: $o ).
% 3.03/1.59
% 3.03/1.59 thf(ap2apEq2,definition,
% 3.03/1.59 ( ap2apEq2
% 3.03/1.59 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.03/1.59 ( ( func @ A @ B @ Xf )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.03/1.59 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(beta1_type,type,
% 3.03/1.59 beta1: $o ).
% 3.03/1.59
% 3.03/1.59 thf(beta1,definition,
% 3.03/1.59 ( beta1
% 3.03/1.59 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.03/1.59 ( ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ( ap @ A @ B
% 3.03/1.59 @ ( lam @ A @ B
% 3.03/1.59 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 3.03/1.59 @ Xx )
% 3.03/1.59 = ( Xf @ Xx ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(eta1_type,type,
% 3.03/1.59 eta1: $o ).
% 3.03/1.59
% 3.03/1.59 thf(eta1,definition,
% 3.03/1.59 ( eta1
% 3.03/1.59 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.03/1.59 ( ( func @ A @ B @ Xf )
% 3.03/1.59 => ( ( lam @ A @ B
% 3.03/1.59 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 3.03/1.59 = Xf ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(lam2lamEq_type,type,
% 3.03/1.59 lam2lamEq: $o ).
% 3.03/1.59
% 3.03/1.59 thf(lam2lamEq,definition,
% 3.03/1.59 ( lam2lamEq
% 3.03/1.59 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.03/1.59 ( ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.03/1.59 => ( ( lam @ A @ B
% 3.03/1.59 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 3.03/1.59 = ( lam @ A @ B
% 3.03/1.59 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(beta2_type,type,
% 3.03/1.59 beta2: $o ).
% 3.03/1.59
% 3.03/1.59 thf(beta2,definition,
% 3.03/1.59 ( beta2
% 3.03/1.59 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.03/1.59 ( ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ( ap @ A @ B
% 3.03/1.59 @ ( lam @ A @ B
% 3.03/1.59 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 3.03/1.59 @ Xx )
% 3.03/1.59 = ( Xf @ Xx ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(eta2_type,type,
% 3.03/1.59 eta2: $o ).
% 3.03/1.59
% 3.03/1.59 thf(eta2,definition,
% 3.03/1.59 ( eta2
% 3.03/1.59 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.03/1.59 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.03/1.59 => ( ( lam @ A @ B
% 3.03/1.59 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 3.03/1.59 = Xf ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(iffalseProp1_type,type,
% 3.03/1.59 iffalseProp1: $o ).
% 3.03/1.59
% 3.03/1.59 thf(iffalseProp1,definition,
% 3.03/1.59 ( iffalseProp1
% 3.03/1.59 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ! [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ A )
% 3.03/1.59 => ( ~ Xphi
% 3.03/1.59 => ( in @ Xy
% 3.03/1.59 @ ( dsetconstr @ A
% 3.03/1.59 @ ^ [Xz: $i] :
% 3.03/1.59 ( ( Xphi
% 3.03/1.59 & ( Xz = Xx ) )
% 3.03/1.59 | ( ~ Xphi
% 3.03/1.59 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(iffalseProp2_type,type,
% 3.03/1.59 iffalseProp2: $o ).
% 3.03/1.59
% 3.03/1.59 thf(iffalseProp2,definition,
% 3.03/1.59 ( iffalseProp2
% 3.03/1.59 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ! [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ A )
% 3.03/1.59 => ( ~ Xphi
% 3.03/1.59 => ( ( dsetconstr @ A
% 3.03/1.59 @ ^ [Xz: $i] :
% 3.03/1.59 ( ( Xphi
% 3.03/1.59 & ( Xz = Xx ) )
% 3.03/1.59 | ( ~ Xphi
% 3.03/1.59 & ( Xz = Xy ) ) ) )
% 3.03/1.59 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(iftrueProp1_type,type,
% 3.03/1.59 iftrueProp1: $o ).
% 3.03/1.59
% 3.03/1.59 thf(iftrueProp1,definition,
% 3.03/1.59 ( iftrueProp1
% 3.03/1.59 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ! [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ A )
% 3.03/1.59 => ( Xphi
% 3.03/1.59 => ( in @ Xx
% 3.03/1.59 @ ( dsetconstr @ A
% 3.03/1.59 @ ^ [Xz: $i] :
% 3.03/1.59 ( ( Xphi
% 3.03/1.59 & ( Xz = Xx ) )
% 3.03/1.59 | ( ~ Xphi
% 3.03/1.59 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(iftrueProp2_type,type,
% 3.03/1.59 iftrueProp2: $o ).
% 3.03/1.59
% 3.03/1.59 thf(iftrueProp2,definition,
% 3.03/1.59 ( iftrueProp2
% 3.03/1.59 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ! [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ A )
% 3.03/1.59 => ( Xphi
% 3.03/1.59 => ( ( dsetconstr @ A
% 3.03/1.59 @ ^ [Xz: $i] :
% 3.03/1.59 ( ( Xphi
% 3.03/1.59 & ( Xz = Xx ) )
% 3.03/1.59 | ( ~ Xphi
% 3.03/1.59 & ( Xz = Xy ) ) ) )
% 3.03/1.59 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(ifSingleton_type,type,
% 3.03/1.59 ifSingleton: $o ).
% 3.03/1.59
% 3.03/1.59 thf(ifSingleton,definition,
% 3.03/1.59 ( ifSingleton
% 3.03/1.59 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ! [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ A )
% 3.03/1.59 => ( singleton
% 3.03/1.59 @ ( dsetconstr @ A
% 3.03/1.59 @ ^ [Xz: $i] :
% 3.03/1.59 ( ( Xphi
% 3.03/1.59 & ( Xz = Xx ) )
% 3.03/1.59 | ( ~ Xphi
% 3.03/1.59 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(if_type,type,
% 3.03/1.59 if: $i > $o > $i > $i > $i ).
% 3.03/1.59
% 3.03/1.59 thf(ifp_type,type,
% 3.03/1.59 ifp: $o ).
% 3.03/1.59
% 3.03/1.59 thf(ifp,definition,
% 3.03/1.59 ( ifp
% 3.03/1.59 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ! [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ A )
% 3.03/1.59 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(theeq_type,type,
% 3.03/1.59 theeq: $o ).
% 3.03/1.59
% 3.03/1.59 thf(theeq,definition,
% 3.03/1.59 ( theeq
% 3.03/1.59 = ( ! [X: $i] :
% 3.03/1.59 ( ( singleton @ X )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ X )
% 3.03/1.59 => ( ( setunion @ X )
% 3.03/1.59 = Xx ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(iftrue_type,type,
% 3.03/1.59 iftrue: $o ).
% 3.03/1.59
% 3.03/1.59 thf(iftrue,definition,
% 3.03/1.59 ( iftrue
% 3.03/1.59 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ! [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ A )
% 3.03/1.59 => ( Xphi
% 3.03/1.59 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 3.03/1.59 = Xx ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(iffalse_type,type,
% 3.03/1.59 iffalse: $o ).
% 3.03/1.59
% 3.03/1.59 thf(iffalse,definition,
% 3.03/1.59 ( iffalse
% 3.03/1.59 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ! [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ A )
% 3.03/1.59 => ( ~ Xphi
% 3.03/1.59 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 3.03/1.59 = Xy ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(iftrueorfalse_type,type,
% 3.03/1.59 iftrueorfalse: $o ).
% 3.03/1.59
% 3.03/1.59 thf(iftrueorfalse,definition,
% 3.03/1.59 ( iftrueorfalse
% 3.03/1.59 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ! [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ A )
% 3.03/1.59 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(binintersectT_lem_type,type,
% 3.03/1.59 binintersectT_lem: $o ).
% 3.03/1.59
% 3.03/1.59 thf(binintersectT_lem,definition,
% 3.03/1.59 ( binintersectT_lem
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(binunionT_lem_type,type,
% 3.03/1.59 binunionT_lem: $o ).
% 3.03/1.59
% 3.03/1.59 thf(binunionT_lem,definition,
% 3.03/1.59 ( binunionT_lem
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(powersetT_lem_type,type,
% 3.03/1.59 powersetT_lem: $o ).
% 3.03/1.59
% 3.03/1.59 thf(powersetT_lem,definition,
% 3.03/1.59 ( powersetT_lem
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(setminusT_lem_type,type,
% 3.03/1.59 setminusT_lem: $o ).
% 3.03/1.59
% 3.03/1.59 thf(setminusT_lem,definition,
% 3.03/1.59 ( setminusT_lem
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(complementT_lem_type,type,
% 3.03/1.59 complementT_lem: $o ).
% 3.03/1.59
% 3.03/1.59 thf(complementT_lem,definition,
% 3.03/1.59 ( complementT_lem
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(setextT_type,type,
% 3.03/1.59 setextT: $o ).
% 3.03/1.59
% 3.03/1.59 thf(setextT,definition,
% 3.03/1.59 ( setextT
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ( ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ( in @ Xx @ X )
% 3.03/1.59 => ( in @ Xx @ Y ) ) )
% 3.03/1.59 => ( ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ( in @ Xx @ Y )
% 3.03/1.59 => ( in @ Xx @ X ) ) )
% 3.03/1.59 => ( X = Y ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(subsetTI_type,type,
% 3.03/1.59 subsetTI: $o ).
% 3.03/1.59
% 3.03/1.59 thf(subsetTI,definition,
% 3.03/1.59 ( subsetTI
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ( ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ( in @ Xx @ X )
% 3.03/1.59 => ( in @ Xx @ Y ) ) )
% 3.03/1.59 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(powersetTI1_type,type,
% 3.03/1.59 powersetTI1: $o ).
% 3.03/1.59
% 3.03/1.59 thf(powersetTI1,definition,
% 3.03/1.59 ( powersetTI1
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ( ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ( in @ Xx @ X )
% 3.03/1.59 => ( in @ Xx @ Y ) ) )
% 3.03/1.59 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(powersetTE1_type,type,
% 3.03/1.59 powersetTE1: $o ).
% 3.03/1.59
% 3.03/1.59 thf(powersetTE1,definition,
% 3.03/1.59 ( powersetTE1
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ( in @ X @ ( powerset @ Y ) )
% 3.03/1.59 => ( ( in @ Xx @ X )
% 3.03/1.59 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(complementTI1_type,type,
% 3.03/1.59 complementTI1: $o ).
% 3.03/1.59
% 3.03/1.59 thf(complementTI1,definition,
% 3.03/1.59 ( complementTI1
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ( in @ Xx @ X )
% 3.03/1.59 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(complementTE1_type,type,
% 3.03/1.59 complementTE1: $o ).
% 3.03/1.59
% 3.03/1.59 thf(complementTE1,definition,
% 3.03/1.59 ( complementTE1
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 3.03/1.59 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(binintersectTELcontra_type,type,
% 3.03/1.59 binintersectTELcontra: $o ).
% 3.03/1.59
% 3.03/1.59 thf(binintersectTELcontra,definition,
% 3.03/1.59 ( binintersectTELcontra
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ~ ( in @ Xx @ X )
% 3.03/1.59 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(binintersectTERcontra_type,type,
% 3.03/1.59 binintersectTERcontra: $o ).
% 3.03/1.59
% 3.03/1.59 thf(binintersectTERcontra,definition,
% 3.03/1.59 ( binintersectTERcontra
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ~ ( in @ Xx @ Y )
% 3.03/1.59 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(contrasubsetT_type,type,
% 3.03/1.59 contrasubsetT: $o ).
% 3.03/1.59
% 3.03/1.59 thf(contrasubsetT,definition,
% 3.03/1.59 ( contrasubsetT
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.03/1.59 => ( ( in @ Xx @ Y )
% 3.03/1.59 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(contrasubsetT1_type,type,
% 3.03/1.59 contrasubsetT1: $o ).
% 3.03/1.59
% 3.03/1.59 thf(contrasubsetT1,definition,
% 3.03/1.59 ( contrasubsetT1
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ( subset @ X @ Y )
% 3.03/1.59 => ( ~ ( in @ Xx @ Y )
% 3.03/1.59 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(contrasubsetT2_type,type,
% 3.03/1.59 contrasubsetT2: $o ).
% 3.03/1.59
% 3.03/1.59 thf(contrasubsetT2,definition,
% 3.03/1.59 ( contrasubsetT2
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ( ( subset @ X @ Y )
% 3.03/1.59 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(contrasubsetT3_type,type,
% 3.03/1.59 contrasubsetT3: $o ).
% 3.03/1.59
% 3.03/1.59 thf(contrasubsetT3,definition,
% 3.03/1.59 ( contrasubsetT3
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 3.03/1.59 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(doubleComplementI1_type,type,
% 3.03/1.59 doubleComplementI1: $o ).
% 3.03/1.59
% 3.03/1.59 thf(doubleComplementI1,definition,
% 3.03/1.59 ( doubleComplementI1
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ( in @ Xx @ X )
% 3.03/1.59 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(doubleComplementE1_type,type,
% 3.03/1.59 doubleComplementE1: $o ).
% 3.03/1.59
% 3.03/1.59 thf(doubleComplementE1,definition,
% 3.03/1.59 ( doubleComplementE1
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 3.03/1.59 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(doubleComplementSub1_type,type,
% 3.03/1.59 doubleComplementSub1: $o ).
% 3.03/1.59
% 3.03/1.59 thf(doubleComplementSub1,definition,
% 3.03/1.59 ( doubleComplementSub1
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(doubleComplementSub2_type,type,
% 3.03/1.59 doubleComplementSub2: $o ).
% 3.03/1.59
% 3.03/1.59 thf(doubleComplementSub2,definition,
% 3.03/1.59 ( doubleComplementSub2
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(doubleComplementEq_type,type,
% 3.03/1.59 doubleComplementEq: $o ).
% 3.03/1.59
% 3.03/1.59 thf(doubleComplementEq,definition,
% 3.03/1.59 ( doubleComplementEq
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ( X
% 3.03/1.59 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(complementTnotintersectT_type,type,
% 3.03/1.59 complementTnotintersectT: $o ).
% 3.03/1.59
% 3.03/1.59 thf(complementTnotintersectT,definition,
% 3.03/1.59 ( complementTnotintersectT
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.03/1.59 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(complementImpComplementIntersect_type,type,
% 3.03/1.59 complementImpComplementIntersect: $o ).
% 3.03/1.59
% 3.03/1.59 thf(complementImpComplementIntersect,definition,
% 3.03/1.59 ( complementImpComplementIntersect
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.03/1.59 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(complementSubsetComplementIntersect_type,type,
% 3.03/1.59 complementSubsetComplementIntersect: $o ).
% 3.03/1.59
% 3.03/1.59 thf(complementSubsetComplementIntersect,definition,
% 3.03/1.59 ( complementSubsetComplementIntersect
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(complementInPowersetComplementIntersect_type,type,
% 3.03/1.59 complementInPowersetComplementIntersect: $o ).
% 3.03/1.59
% 3.03/1.59 thf(complementInPowersetComplementIntersect,definition,
% 3.03/1.59 ( complementInPowersetComplementIntersect
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(contraSubsetComplement_type,type,
% 3.03/1.59 contraSubsetComplement: $o ).
% 3.03/1.59
% 3.03/1.59 thf(contraSubsetComplement,definition,
% 3.03/1.59 ( contraSubsetComplement
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ( in @ Xx @ Y )
% 3.03/1.59 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(complementTcontraSubset_type,type,
% 3.03/1.59 complementTcontraSubset: $o ).
% 3.03/1.59
% 3.03/1.59 thf(complementTcontraSubset,definition,
% 3.03/1.59 ( complementTcontraSubset
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.03/1.59 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(binunionTILcontra_type,type,
% 3.03/1.59 binunionTILcontra: $o ).
% 3.03/1.59
% 3.03/1.59 thf(binunionTILcontra,definition,
% 3.03/1.59 ( binunionTILcontra
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.03/1.59 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(binunionTIRcontra_type,type,
% 3.03/1.59 binunionTIRcontra: $o ).
% 3.03/1.59
% 3.03/1.59 thf(binunionTIRcontra,definition,
% 3.03/1.59 ( binunionTIRcontra
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.03/1.59 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(inIntersectImpInUnion_type,type,
% 3.03/1.59 inIntersectImpInUnion: $o ).
% 3.03/1.59
% 3.03/1.59 thf(inIntersectImpInUnion,definition,
% 3.03/1.59 ( inIntersectImpInUnion
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ! [Z: $i] :
% 3.03/1.59 ( ( in @ Z @ ( powerset @ A ) )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.03/1.59 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(inIntersectImpInUnion2_type,type,
% 3.03/1.59 inIntersectImpInUnion2: $o ).
% 3.03/1.59
% 3.03/1.59 thf(inIntersectImpInUnion2,definition,
% 3.03/1.59 ( inIntersectImpInUnion2
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ! [Z: $i] :
% 3.03/1.59 ( ( in @ Z @ ( powerset @ A ) )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.03/1.59 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(inIntersectImpInIntersectUnions_type,type,
% 3.03/1.59 inIntersectImpInIntersectUnions: $o ).
% 3.03/1.59
% 3.03/1.59 thf(inIntersectImpInIntersectUnions,definition,
% 3.03/1.59 ( inIntersectImpInIntersectUnions
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ! [Z: $i] :
% 3.03/1.59 ( ( in @ Z @ ( powerset @ A ) )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.03/1.59 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(intersectInPowersetIntersectUnions_type,type,
% 3.03/1.59 intersectInPowersetIntersectUnions: $o ).
% 3.03/1.59
% 3.03/1.59 thf(intersectInPowersetIntersectUnions,definition,
% 3.03/1.59 ( intersectInPowersetIntersectUnions
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ! [Z: $i] :
% 3.03/1.59 ( ( in @ Z @ ( powerset @ A ) )
% 3.03/1.59 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(inComplementUnionImpNotIn1_type,type,
% 3.03/1.59 inComplementUnionImpNotIn1: $o ).
% 3.03/1.59
% 3.03/1.59 thf(inComplementUnionImpNotIn1,definition,
% 3.03/1.59 ( inComplementUnionImpNotIn1
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.03/1.59 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(inComplementUnionImpInComplement1_type,type,
% 3.03/1.59 inComplementUnionImpInComplement1: $o ).
% 3.03/1.59
% 3.03/1.59 thf(inComplementUnionImpInComplement1,definition,
% 3.03/1.59 ( inComplementUnionImpInComplement1
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.03/1.59 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(binunionTE_type,type,
% 3.03/1.59 binunionTE: $o ).
% 3.03/1.59
% 3.03/1.59 thf(binunionTE,definition,
% 3.03/1.59 ( binunionTE
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ! [Xphi: $o,Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.03/1.59 => ( ( ( in @ Xx @ X )
% 3.03/1.59 => Xphi )
% 3.03/1.59 => ( ( ( in @ Xx @ Y )
% 3.03/1.59 => Xphi )
% 3.03/1.59 => Xphi ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(binunionTEcontra_type,type,
% 3.03/1.59 binunionTEcontra: $o ).
% 3.03/1.59
% 3.03/1.59 thf(binunionTEcontra,definition,
% 3.03/1.59 ( binunionTEcontra
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ~ ( in @ Xx @ X )
% 3.03/1.59 => ( ~ ( in @ Xx @ Y )
% 3.03/1.59 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(demorgan2a1_type,type,
% 3.03/1.59 demorgan2a1: $o ).
% 3.03/1.59
% 3.03/1.59 thf(demorgan2a1,definition,
% 3.03/1.59 ( demorgan2a1
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.03/1.59 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(complementUnionInPowersetComplement_type,type,
% 3.03/1.59 complementUnionInPowersetComplement: $o ).
% 3.03/1.59
% 3.03/1.59 thf(complementUnionInPowersetComplement,definition,
% 3.03/1.59 ( complementUnionInPowersetComplement
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(demorgan2a2_type,type,
% 3.03/1.59 demorgan2a2: $o ).
% 3.03/1.59
% 3.03/1.59 thf(demorgan2a2,definition,
% 3.03/1.59 ( demorgan2a2
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.03/1.59 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(demorgan1a_type,type,
% 3.03/1.59 demorgan1a: $o ).
% 3.03/1.59
% 3.03/1.59 thf(demorgan1a,definition,
% 3.03/1.59 ( demorgan1a
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 3.03/1.59 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(demorgan1b_type,type,
% 3.03/1.59 demorgan1b: $o ).
% 3.03/1.59
% 3.03/1.59 thf(demorgan1b,definition,
% 3.03/1.59 ( demorgan1b
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 3.03/1.59 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(demorgan1_type,type,
% 3.03/1.59 demorgan1: $o ).
% 3.03/1.59
% 3.03/1.59 thf(demorgan1,definition,
% 3.03/1.59 ( demorgan1
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 3.03/1.59 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(demorgan2a_type,type,
% 3.03/1.59 demorgan2a: $o ).
% 3.03/1.59
% 3.03/1.59 thf(demorgan2a,definition,
% 3.03/1.59 ( demorgan2a
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.03/1.59 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(demorgan2b2_type,type,
% 3.03/1.59 demorgan2b2: $o ).
% 3.03/1.59
% 3.03/1.59 thf(demorgan2b2,definition,
% 3.03/1.59 ( demorgan2b2
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.03/1.59 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 3.03/1.59 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(demorgan2b_type,type,
% 3.03/1.59 demorgan2b: $o ).
% 3.03/1.59
% 3.03/1.59 thf(demorgan2b,definition,
% 3.03/1.59 ( demorgan2b
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 3.03/1.59 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(demorgan2_type,type,
% 3.03/1.59 demorgan2: $o ).
% 3.03/1.59
% 3.03/1.59 thf(demorgan2,definition,
% 3.03/1.59 ( demorgan2
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 3.03/1.59 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(woz13rule0_type,type,
% 3.03/1.59 woz13rule0: $o ).
% 3.03/1.59
% 3.03/1.59 thf(woz13rule0,definition,
% 3.03/1.59 ( woz13rule0
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.03/1.59 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(woz13rule1_type,type,
% 3.03/1.59 woz13rule1: $o ).
% 3.03/1.59
% 3.03/1.59 thf(woz13rule1,definition,
% 3.03/1.59 ( woz13rule1
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ! [Z: $i] :
% 3.03/1.59 ( ( in @ Z @ ( powerset @ A ) )
% 3.03/1.59 => ( ( subset @ X @ Z )
% 3.03/1.59 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(woz13rule2_type,type,
% 3.03/1.59 woz13rule2: $o ).
% 3.03/1.59
% 3.03/1.59 thf(woz13rule2,definition,
% 3.03/1.59 ( woz13rule2
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ! [Z: $i] :
% 3.03/1.59 ( ( in @ Z @ ( powerset @ A ) )
% 3.03/1.59 => ( ( subset @ Y @ Z )
% 3.03/1.59 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(woz13rule3_type,type,
% 3.03/1.59 woz13rule3: $o ).
% 3.03/1.59
% 3.03/1.59 thf(woz13rule3,definition,
% 3.03/1.59 ( woz13rule3
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ! [Z: $i] :
% 3.03/1.59 ( ( in @ Z @ ( powerset @ A ) )
% 3.03/1.59 => ( ( subset @ X @ Y )
% 3.03/1.59 => ( ( subset @ X @ Z )
% 3.03/1.59 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(woz13rule4_type,type,
% 3.03/1.59 woz13rule4: $o ).
% 3.03/1.59
% 3.03/1.59 thf(woz13rule4,definition,
% 3.03/1.59 ( woz13rule4
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ! [Z: $i] :
% 3.03/1.59 ( ( in @ Z @ ( powerset @ A ) )
% 3.03/1.59 => ! [W: $i] :
% 3.03/1.59 ( ( in @ W @ ( powerset @ A ) )
% 3.03/1.59 => ( ( subset @ X @ Z )
% 3.03/1.59 => ( ( subset @ Y @ W )
% 3.03/1.59 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(woz1_1_type,type,
% 3.03/1.59 woz1_1: $o ).
% 3.03/1.59
% 3.03/1.59 thf(woz1_1,definition,
% 3.03/1.59 ( woz1_1
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(woz1_2_type,type,
% 3.03/1.59 woz1_2: $o ).
% 3.03/1.59
% 3.03/1.59 thf(woz1_2,definition,
% 3.03/1.59 ( woz1_2
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ! [Z: $i] :
% 3.03/1.59 ( ( in @ Z @ ( powerset @ A ) )
% 3.03/1.59 => ! [W: $i] :
% 3.03/1.59 ( ( in @ W @ ( powerset @ A ) )
% 3.03/1.59 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 3.03/1.59 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(woz1_3_type,type,
% 3.03/1.59 woz1_3: $o ).
% 3.03/1.59
% 3.03/1.59 thf(woz1_3,definition,
% 3.03/1.59 ( woz1_3
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ! [Z: $i] :
% 3.03/1.59 ( ( in @ Z @ ( powerset @ A ) )
% 3.03/1.59 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(woz1_4_type,type,
% 3.03/1.59 woz1_4: $o ).
% 3.03/1.59
% 3.03/1.59 thf(woz1_4,definition,
% 3.03/1.59 ( woz1_4
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.03/1.59 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(woz1_5_type,type,
% 3.03/1.59 woz1_5: $o ).
% 3.03/1.59
% 3.03/1.59 thf(woz1_5,definition,
% 3.03/1.59 ( woz1_5
% 3.03/1.59 = ( ! [A: $i,X: $i] :
% 3.03/1.59 ( ( in @ X @ ( powerset @ A ) )
% 3.03/1.59 => ! [Y: $i] :
% 3.03/1.59 ( ( in @ Y @ ( powerset @ A ) )
% 3.03/1.59 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(breln1_type,type,
% 3.03/1.59 breln1: $i > $i > $o ).
% 3.03/1.59
% 3.03/1.59 thf(breln1all2_type,type,
% 3.03/1.59 breln1all2: $o ).
% 3.03/1.59
% 3.03/1.59 thf(breln1all2,definition,
% 3.03/1.59 ( breln1all2
% 3.03/1.59 = ( ! [A: $i,R: $i] :
% 3.03/1.59 ( ( breln1 @ A @ R )
% 3.03/1.59 => ! [Xphi: $i > $o] :
% 3.03/1.59 ( ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ! [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ A )
% 3.03/1.59 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.03/1.59 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ R )
% 3.03/1.59 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(breln1Set_type,type,
% 3.03/1.59 breln1Set: $i > $i ).
% 3.03/1.59
% 3.03/1.59 thf(breln1SetBreln1_type,type,
% 3.03/1.59 breln1SetBreln1: $o ).
% 3.03/1.59
% 3.03/1.59 thf(breln1SetBreln1,definition,
% 3.03/1.59 ( breln1SetBreln1
% 3.03/1.59 = ( ! [A: $i,R: $i] :
% 3.03/1.59 ( ( in @ R @ ( breln1Set @ A ) )
% 3.03/1.59 => ( breln1 @ A @ R ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(transitive_type,type,
% 3.03/1.59 transitive: $i > $i > $o ).
% 3.03/1.59
% 3.03/1.59 thf(antisymmetric_type,type,
% 3.03/1.59 antisymmetric: $i > $i > $o ).
% 3.03/1.59
% 3.03/1.59 thf(reflexive_type,type,
% 3.03/1.59 reflexive: $i > $i > $o ).
% 3.03/1.59
% 3.03/1.59 thf(refltransitive_type,type,
% 3.03/1.59 refltransitive: $i > $i > $o ).
% 3.03/1.59
% 3.03/1.59 thf(refllinearorder_type,type,
% 3.03/1.59 refllinearorder: $i > $i > $o ).
% 3.03/1.59
% 3.03/1.59 thf(reflwellordering_type,type,
% 3.03/1.59 reflwellordering: $i > $i > $o ).
% 3.03/1.59
% 3.03/1.59 thf(choice2fnsingleton_type,type,
% 3.03/1.59 choice2fnsingleton: $o ).
% 3.03/1.59
% 3.03/1.59 thf(choice2fnsingleton,definition,
% 3.03/1.59 ( choice2fnsingleton
% 3.03/1.59 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.03/1.59 ( ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ? [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ B )
% 3.03/1.59 & ( Xphi @ Xx @ Xy ) ) )
% 3.03/1.59 => ! [R: $i] :
% 3.03/1.59 ( ( in @ R @ ( breln1Set @ B ) )
% 3.03/1.59 => ( ( reflwellordering @ B @ R )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( singleton
% 3.03/1.59 @ ( dsetconstr @ B
% 3.03/1.59 @ ^ [Xy: $i] :
% 3.03/1.59 ( ( Xphi @ Xx @ Xy )
% 3.03/1.59 & ! [Xz: $i] :
% 3.03/1.59 ( ( in @ Xz @ B )
% 3.03/1.59 => ( ( Xphi @ Xx @ Xz )
% 3.03/1.59 => ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(setOfPairsIsBReln1_type,type,
% 3.03/1.59 setOfPairsIsBReln1: $o ).
% 3.03/1.59
% 3.03/1.59 thf(setOfPairsIsBReln1,definition,
% 3.03/1.59 ( setOfPairsIsBReln1
% 3.03/1.59 = ( ! [A: $i,Xphi: $i > $i > $o] :
% 3.03/1.59 ( breln1 @ A
% 3.03/1.59 @ ( dpsetconstr @ A @ A
% 3.03/1.59 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(breln1all1_type,type,
% 3.03/1.59 breln1all1: $o ).
% 3.03/1.59
% 3.03/1.59 thf(breln1all1,definition,
% 3.03/1.59 ( breln1all1
% 3.03/1.59 = ( ! [A: $i,R: $i] :
% 3.03/1.59 ( ( breln1 @ A @ R )
% 3.03/1.59 => ! [Xphi: $i > $o] :
% 3.03/1.59 ( ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ! [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ A )
% 3.03/1.59 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.03/1.59 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ R )
% 3.03/1.59 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(subbreln1_type,type,
% 3.03/1.59 subbreln1: $o ).
% 3.03/1.59
% 3.03/1.59 thf(subbreln1,definition,
% 3.03/1.59 ( subbreln1
% 3.03/1.59 = ( ! [A: $i,R: $i] :
% 3.03/1.59 ( ( breln1 @ A @ R )
% 3.03/1.59 => ! [S: $i] :
% 3.03/1.59 ( ( breln1 @ A @ S )
% 3.03/1.59 => ( ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ! [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ A )
% 3.03/1.59 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.03/1.59 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.03/1.59 => ( subset @ R @ S ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(eqbreln1_type,type,
% 3.03/1.59 eqbreln1: $o ).
% 3.03/1.59
% 3.03/1.59 thf(eqbreln1,definition,
% 3.03/1.59 ( eqbreln1
% 3.03/1.59 = ( ! [A: $i,R: $i] :
% 3.03/1.59 ( ( breln1 @ A @ R )
% 3.03/1.59 => ! [S: $i] :
% 3.03/1.59 ( ( breln1 @ A @ S )
% 3.03/1.59 => ( ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ! [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ A )
% 3.03/1.59 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.03/1.59 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.03/1.59 => ( ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ! [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ A )
% 3.03/1.59 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.03/1.59 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 3.03/1.59 => ( R = S ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(breln1invset_type,type,
% 3.03/1.59 breln1invset: $i > $i > $i ).
% 3.03/1.59
% 3.03/1.59 thf(breln1invprop_type,type,
% 3.03/1.59 breln1invprop: $o ).
% 3.03/1.59
% 3.03/1.59 thf(breln1invprop,definition,
% 3.03/1.59 ( breln1invprop
% 3.03/1.59 = ( ! [A: $i,R: $i] :
% 3.03/1.59 ( ( breln1 @ A @ R )
% 3.03/1.59 => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(breln1invI_type,type,
% 3.03/1.59 breln1invI: $o ).
% 3.03/1.59
% 3.03/1.59 thf(breln1invI,definition,
% 3.03/1.59 ( breln1invI
% 3.03/1.59 = ( ! [A: $i,R: $i] :
% 3.03/1.59 ( ( breln1 @ A @ R )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ! [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ A )
% 3.03/1.59 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.03/1.59 => ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(breln1invE_type,type,
% 3.03/1.59 breln1invE: $o ).
% 3.03/1.59
% 3.03/1.59 thf(breln1invE,definition,
% 3.03/1.59 ( breln1invE
% 3.03/1.59 = ( ! [A: $i,R: $i] :
% 3.03/1.59 ( ( breln1 @ A @ R )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ! [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ A )
% 3.03/1.59 => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
% 3.03/1.59 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(breln1compset_type,type,
% 3.03/1.59 breln1compset: $i > $i > $i > $i ).
% 3.03/1.59
% 3.03/1.59 thf(breln1compprop_type,type,
% 3.03/1.59 breln1compprop: $o ).
% 3.03/1.59
% 3.03/1.59 thf(breln1compprop,definition,
% 3.03/1.59 ( breln1compprop
% 3.03/1.59 = ( ! [A: $i,R: $i] :
% 3.03/1.59 ( ( breln1 @ A @ R )
% 3.03/1.59 => ! [S: $i] :
% 3.03/1.59 ( ( breln1 @ A @ S )
% 3.03/1.59 => ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(breln1compI_type,type,
% 3.03/1.59 breln1compI: $o ).
% 3.03/1.59
% 3.03/1.59 thf(breln1compI,definition,
% 3.03/1.59 ( breln1compI
% 3.03/1.59 = ( ! [A: $i,R: $i] :
% 3.03/1.59 ( ( breln1 @ A @ R )
% 3.03/1.59 => ! [S: $i] :
% 3.03/1.59 ( ( breln1 @ A @ S )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ! [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ A )
% 3.03/1.59 => ! [Xz: $i] :
% 3.03/1.59 ( ( in @ Xz @ A )
% 3.03/1.59 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 3.03/1.59 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 3.03/1.59 => ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(breln1compE_type,type,
% 3.03/1.59 breln1compE: $o ).
% 3.03/1.59
% 3.03/1.59 thf(breln1compE,definition,
% 3.03/1.59 ( breln1compE
% 3.03/1.59 = ( ! [A: $i,R: $i] :
% 3.03/1.59 ( ( breln1 @ A @ R )
% 3.03/1.59 => ! [S: $i] :
% 3.03/1.59 ( ( breln1 @ A @ S )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ! [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ A )
% 3.03/1.59 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 3.03/1.59 => ? [Xz: $i] :
% 3.03/1.59 ( ( in @ Xz @ A )
% 3.03/1.59 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 3.03/1.59 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(breln1compEex_type,type,
% 3.03/1.59 breln1compEex: $o ).
% 3.03/1.59
% 3.03/1.59 thf(breln1compEex,definition,
% 3.03/1.59 ( breln1compEex
% 3.03/1.59 = ( ! [A: $i,R: $i] :
% 3.03/1.59 ( ( breln1 @ A @ R )
% 3.03/1.59 => ! [S: $i] :
% 3.03/1.59 ( ( breln1 @ A @ S )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ! [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ A )
% 3.03/1.59 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
% 3.03/1.59 => ! [Xphi: $o] :
% 3.03/1.59 ( ! [Xz: $i] :
% 3.03/1.59 ( ( in @ Xz @ A )
% 3.03/1.59 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 3.03/1.59 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 3.03/1.59 => Xphi ) ) )
% 3.03/1.59 => Xphi ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(breln1unionprop_type,type,
% 3.03/1.59 breln1unionprop: $o ).
% 3.03/1.59
% 3.03/1.59 thf(breln1unionprop,definition,
% 3.03/1.59 ( breln1unionprop
% 3.03/1.59 = ( ! [A: $i,R: $i] :
% 3.03/1.59 ( ( breln1 @ A @ R )
% 3.03/1.59 => ! [S: $i] :
% 3.03/1.59 ( ( breln1 @ A @ S )
% 3.03/1.59 => ( breln1 @ A @ ( binunion @ R @ S ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(breln1unionIL_type,type,
% 3.03/1.59 breln1unionIL: $o ).
% 3.03/1.59
% 3.03/1.59 thf(breln1unionIL,definition,
% 3.03/1.59 ( breln1unionIL
% 3.03/1.59 = ( ! [A: $i,R: $i] :
% 3.03/1.59 ( ( breln1 @ A @ R )
% 3.03/1.59 => ! [S: $i] :
% 3.03/1.59 ( ( breln1 @ A @ S )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ! [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ A )
% 3.03/1.59 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.03/1.59 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(breln1unionIR_type,type,
% 3.03/1.59 breln1unionIR: $o ).
% 3.03/1.59
% 3.03/1.59 thf(breln1unionIR,definition,
% 3.03/1.59 ( breln1unionIR
% 3.03/1.59 = ( ! [A: $i,R: $i] :
% 3.03/1.59 ( ( breln1 @ A @ R )
% 3.03/1.59 => ! [S: $i] :
% 3.03/1.59 ( ( breln1 @ A @ S )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ! [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ A )
% 3.03/1.59 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.03/1.59 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(breln1unionI_type,type,
% 3.03/1.59 breln1unionI: $o ).
% 3.03/1.59
% 3.03/1.59 thf(breln1unionI,definition,
% 3.03/1.59 ( breln1unionI
% 3.03/1.59 = ( ! [A: $i,R: $i] :
% 3.03/1.59 ( ( breln1 @ A @ R )
% 3.03/1.59 => ! [S: $i] :
% 3.03/1.59 ( ( breln1 @ A @ S )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ! [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ A )
% 3.03/1.59 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.03/1.59 | ( in @ ( kpair @ Xx @ Xy ) @ S ) )
% 3.03/1.59 => ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(breln1unionE_type,type,
% 3.03/1.59 breln1unionE: $o ).
% 3.03/1.59
% 3.03/1.59 thf(breln1unionE,definition,
% 3.03/1.59 ( breln1unionE
% 3.03/1.59 = ( ! [A: $i,R: $i] :
% 3.03/1.59 ( ( breln1 @ A @ R )
% 3.03/1.59 => ! [S: $i] :
% 3.03/1.59 ( ( breln1 @ A @ S )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ! [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ A )
% 3.03/1.59 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 3.03/1.59 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.03/1.59 | ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(breln1unionEcases_type,type,
% 3.03/1.59 breln1unionEcases: $o ).
% 3.03/1.59
% 3.03/1.59 thf(breln1unionEcases,definition,
% 3.03/1.59 ( breln1unionEcases
% 3.03/1.59 = ( ! [A: $i,R: $i] :
% 3.03/1.59 ( ( breln1 @ A @ R )
% 3.03/1.59 => ! [S: $i] :
% 3.03/1.59 ( ( breln1 @ A @ S )
% 3.03/1.59 => ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ! [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ A )
% 3.03/1.59 => ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
% 3.03/1.59 => ! [Xphi: $o] :
% 3.03/1.59 ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.03/1.59 => Xphi )
% 3.03/1.59 => ( ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.03/1.59 => Xphi )
% 3.03/1.59 => Xphi ) ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(breln1unionCommutes_type,type,
% 3.03/1.59 breln1unionCommutes: $o ).
% 3.03/1.59
% 3.03/1.59 thf(breln1unionCommutes,definition,
% 3.03/1.59 ( breln1unionCommutes
% 3.03/1.59 = ( ! [A: $i,R: $i] :
% 3.03/1.59 ( ( breln1 @ A @ R )
% 3.03/1.59 => ! [S: $i] :
% 3.03/1.59 ( ( breln1 @ A @ S )
% 3.03/1.59 => ( ( binunion @ R @ S )
% 3.03/1.59 = ( binunion @ S @ R ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(woz2Ex_type,type,
% 3.03/1.59 woz2Ex: $o ).
% 3.03/1.59
% 3.03/1.59 thf(woz2Ex,definition,
% 3.03/1.59 ( woz2Ex
% 3.03/1.59 = ( ! [A: $i,R: $i] :
% 3.03/1.59 ( ( breln1 @ A @ R )
% 3.03/1.59 => ( R
% 3.03/1.59 = ( breln1invset @ A @ ( breln1invset @ A @ R ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(woz2W_type,type,
% 3.03/1.59 woz2W: $o ).
% 3.03/1.59
% 3.03/1.59 thf(woz2W,definition,
% 3.03/1.59 ( woz2W
% 3.03/1.59 = ( ! [A: $i,R: $i] :
% 3.03/1.59 ( ( breln1 @ A @ R )
% 3.03/1.59 => ! [S: $i] :
% 3.03/1.59 ( ( breln1 @ A @ S )
% 3.03/1.59 => ( ( breln1invset @ A @ ( breln1compset @ A @ R @ S ) )
% 3.03/1.59 = ( breln1compset @ A @ ( breln1invset @ A @ S ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(woz2A_type,type,
% 3.03/1.59 woz2A: $o ).
% 3.03/1.59
% 3.03/1.59 thf(woz2A,definition,
% 3.03/1.59 ( woz2A
% 3.03/1.59 = ( ! [A: $i,R: $i] :
% 3.03/1.59 ( ( breln1 @ A @ R )
% 3.03/1.59 => ! [S: $i] :
% 3.03/1.59 ( ( breln1 @ A @ S )
% 3.03/1.59 => ! [T: $i] :
% 3.03/1.59 ( ( breln1 @ A @ T )
% 3.03/1.59 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 3.03/1.59 = ( binunion @ ( breln1compset @ A @ R @ T ) @ ( breln1compset @ A @ S @ T ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(woz2B_type,type,
% 3.03/1.59 woz2B: $o ).
% 3.03/1.59
% 3.03/1.59 thf(woz2B,definition,
% 3.03/1.59 ( woz2B
% 3.03/1.59 = ( ! [A: $i,R: $i] :
% 3.03/1.59 ( ( breln1 @ A @ R )
% 3.03/1.59 => ! [S: $i] :
% 3.03/1.59 ( ( breln1 @ A @ S )
% 3.03/1.59 => ! [T: $i] :
% 3.03/1.59 ( ( breln1 @ A @ T )
% 3.03/1.59 => ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
% 3.03/1.59 = ( binunion @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ S ) ) ) @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(image1Ex_type,type,
% 3.03/1.59 image1Ex: $o ).
% 3.03/1.59
% 3.03/1.59 thf(image1Ex,definition,
% 3.03/1.59 ( image1Ex
% 3.03/1.59 = ( ! [A: $i,Xf: $i > $i] :
% 3.03/1.59 ? [B: $i] :
% 3.03/1.59 ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ B )
% 3.03/1.59 <=> ? [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ A )
% 3.03/1.59 & ( Xx
% 3.03/1.59 = ( Xf @ Xy ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(image1Ex1_type,type,
% 3.03/1.59 image1Ex1: $o ).
% 3.03/1.59
% 3.03/1.59 thf(image1Ex1,definition,
% 3.03/1.59 ( image1Ex1
% 3.03/1.59 = ( ! [A: $i,Xf: $i > $i] :
% 3.03/1.59 ( exu
% 3.03/1.59 @ ^ [B: $i] :
% 3.03/1.59 ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ B )
% 3.03/1.59 <=> ? [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ A )
% 3.03/1.59 & ( Xx
% 3.03/1.59 = ( Xf @ Xy ) ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(image1_type,type,
% 3.03/1.59 image1: $i > ( $i > $i ) > $i ).
% 3.03/1.59
% 3.03/1.59 thf(image1Equiv_type,type,
% 3.03/1.59 image1Equiv: $o ).
% 3.03/1.59
% 3.03/1.59 thf(image1Equiv,definition,
% 3.03/1.59 ( image1Equiv
% 3.03/1.59 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 3.03/1.59 ( ( in @ Xx
% 3.03/1.59 @ ( image1 @ A
% 3.03/1.59 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 3.03/1.59 <=> ? [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ A )
% 3.03/1.59 & ( Xx
% 3.03/1.59 = ( Xf @ Xy ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(image1E_type,type,
% 3.03/1.59 image1E: $o ).
% 3.03/1.59
% 3.03/1.59 thf(image1E,definition,
% 3.03/1.59 ( image1E
% 3.03/1.59 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 3.03/1.59 ( ( in @ Xx
% 3.03/1.59 @ ( image1 @ A
% 3.03/1.59 @ ^ [Xy: $i] : ( Xf @ Xy ) ) )
% 3.03/1.59 => ? [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ A )
% 3.03/1.59 & ( Xx
% 3.03/1.59 = ( Xf @ Xy ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(image1I_type,type,
% 3.03/1.59 image1I: $o ).
% 3.03/1.59
% 3.03/1.59 thf(image1I,definition,
% 3.03/1.59 ( image1I
% 3.03/1.59 = ( ! [A: $i,Xf: $i > $i,Xx: $i] :
% 3.03/1.59 ( ? [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ A )
% 3.03/1.59 & ( Xx
% 3.03/1.59 = ( Xf @ Xy ) ) )
% 3.03/1.59 => ( in @ Xx
% 3.03/1.59 @ ( image1 @ A
% 3.03/1.59 @ ^ [Xy: $i] : ( Xf @ Xy ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(injective_type,type,
% 3.03/1.59 injective: $i > $i > $i > $o ).
% 3.03/1.59
% 3.03/1.59 thf(injFuncSet_type,type,
% 3.03/1.59 injFuncSet: $i > $i > $i ).
% 3.03/1.59
% 3.03/1.59 thf(injFuncInInjFuncSet_type,type,
% 3.03/1.59 injFuncInInjFuncSet: $o ).
% 3.03/1.59
% 3.03/1.59 thf(injFuncInInjFuncSet,definition,
% 3.03/1.59 ( injFuncInInjFuncSet
% 3.03/1.59 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.03/1.59 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.03/1.59 => ( ( injective @ A @ B @ Xf )
% 3.03/1.59 => ( in @ Xf @ ( injFuncSet @ A @ B ) ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(injFuncSetFuncIn_type,type,
% 3.03/1.59 injFuncSetFuncIn: $o ).
% 3.03/1.59
% 3.03/1.59 thf(injFuncSetFuncIn,definition,
% 3.03/1.59 ( injFuncSetFuncIn
% 3.03/1.59 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.03/1.59 ( ( in @ Xf @ ( injFuncSet @ A @ B ) )
% 3.03/1.59 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(injFuncSetFuncInj_type,type,
% 3.03/1.59 injFuncSetFuncInj: $o ).
% 3.03/1.59
% 3.03/1.59 thf(injFuncSetFuncInj,definition,
% 3.03/1.59 ( injFuncSetFuncInj
% 3.03/1.59 = ( ! [Xx: $i,Xy: $i,Xf: $i] :
% 3.03/1.59 ( ( in @ Xf @ ( injFuncSet @ Xx @ Xy ) )
% 3.03/1.59 => ( injective @ Xx @ Xy @ Xf ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(surjective_type,type,
% 3.03/1.59 surjective: $i > $i > $i > $o ).
% 3.03/1.59
% 3.03/1.59 thf(surjective,definition,
% 3.03/1.59 ( surjective
% 3.03/1.59 = ( ^ [A: $i,B: $i,Xf: $i] :
% 3.03/1.59 ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ B )
% 3.03/1.59 => ? [Xy: $i] :
% 3.03/1.59 ( ( in @ Xy @ A )
% 3.03/1.59 & ( ( ap @ A @ B @ Xf @ Xy )
% 3.03/1.59 = Xx ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(surjFuncSet_type,type,
% 3.03/1.59 surjFuncSet: $i > $i > $i ).
% 3.03/1.59
% 3.03/1.59 thf(surjFuncSetFuncIn_type,type,
% 3.03/1.59 surjFuncSetFuncIn: $o ).
% 3.03/1.59
% 3.03/1.59 thf(surjFuncSetFuncIn,definition,
% 3.03/1.59 ( surjFuncSetFuncIn
% 3.03/1.59 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.03/1.59 ( ( in @ Xf @ ( surjFuncSet @ A @ B ) )
% 3.03/1.59 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(surjFuncSetFuncSurj_type,type,
% 3.03/1.59 surjFuncSetFuncSurj: $o ).
% 3.03/1.59
% 3.03/1.59 thf(surjFuncSetFuncSurj,definition,
% 3.03/1.59 ( surjFuncSetFuncSurj
% 3.03/1.59 = ( ! [Xx: $i,Xy: $i,Xf: $i] :
% 3.03/1.59 ( ( in @ Xf @ ( surjFuncSet @ Xx @ Xy ) )
% 3.03/1.59 => ( surjective @ Xx @ Xy @ Xf ) ) ) ) ).
% 3.03/1.59
% 3.03/1.59 thf(leftInvIsSurj,conjecture,
% 3.03/1.59 ( setextAx
% 3.03/1.59 => ( emptysetAx
% 3.03/1.59 => ( setadjoinAx
% 3.03/1.59 => ( powersetAx
% 3.03/1.59 => ( setunionAx
% 3.03/1.59 => ( omega0Ax
% 3.03/1.59 => ( omegaSAx
% 3.03/1.59 => ( omegaIndAx
% 3.03/1.59 => ( replAx
% 3.03/1.59 => ( foundationAx
% 3.03/1.59 => ( wellorderingAx
% 3.03/1.59 => ( descrp
% 3.03/1.59 => ( dsetconstrI
% 3.03/1.59 => ( dsetconstrEL
% 3.03/1.59 => ( dsetconstrER
% 3.03/1.59 => ( exuE1
% 3.03/1.59 => ( prop2setE
% 3.03/1.59 => ( emptysetE
% 3.03/1.59 => ( emptysetimpfalse
% 3.03/1.59 => ( notinemptyset
% 3.03/1.59 => ( exuE3e
% 3.03/1.59 => ( setext
% 3.03/1.59 => ( emptyI
% 3.03/1.59 => ( noeltsimpempty
% 3.03/1.59 => ( setbeta
% 3.03/1.59 => ( nonemptyE1
% 3.03/1.59 => ( nonemptyI
% 3.03/1.59 => ( nonemptyI1
% 3.03/1.59 => ( setadjoinIL
% 3.03/1.59 => ( emptyinunitempty
% 3.03/1.59 => ( setadjoinIR
% 3.03/1.59 => ( setadjoinE
% 3.03/1.59 => ( setadjoinOr
% 3.03/1.59 => ( setoftrueEq
% 3.03/1.59 => ( powersetI
% 3.03/1.59 => ( emptyinPowerset
% 3.03/1.59 => ( emptyInPowerset
% 3.03/1.59 => ( powersetE
% 3.03/1.59 => ( setunionI
% 3.03/1.59 => ( setunionE
% 3.03/1.59 => ( subPowSU
% 3.03/1.59 => ( exuE2
% 3.03/1.59 => ( nonemptyImpWitness
% 3.03/1.59 => ( uniqinunit
% 3.03/1.59 => ( notinsingleton
% 3.03/1.59 => ( eqinunit
% 3.03/1.59 => ( singletonsswitch
% 3.03/1.59 => ( upairsetE
% 3.03/1.59 => ( upairsetIL
% 3.03/1.59 => ( upairsetIR
% 3.03/1.59 => ( emptyE1
% 3.03/1.59 => ( vacuousDall
% 3.03/1.59 => ( quantDeMorgan1
% 3.03/1.59 => ( quantDeMorgan2
% 3.03/1.59 => ( quantDeMorgan3
% 3.03/1.59 => ( quantDeMorgan4
% 3.03/1.59 => ( prop2setI
% 3.03/1.59 => ( prop2set2propI
% 3.03/1.59 => ( notdexE
% 3.03/1.59 => ( notdallE
% 3.03/1.59 => ( exuI1
% 3.03/1.59 => ( exuI3
% 3.03/1.59 => ( exuI2
% 3.03/1.59 => ( inCongP
% 3.03/1.59 => ( in__Cong
% 3.03/1.59 => ( exuE3u
% 3.03/1.59 => ( exu__Cong
% 3.03/1.59 => ( emptyset__Cong
% 3.03/1.59 => ( setadjoin__Cong
% 3.03/1.59 => ( powerset__Cong
% 3.03/1.59 => ( setunion__Cong
% 3.03/1.59 => ( omega__Cong
% 3.03/1.59 => ( exuEu
% 3.03/1.59 => ( descr__Cong
% 3.03/1.59 => ( dsetconstr__Cong
% 3.03/1.59 => ( subsetI1
% 3.03/1.59 => ( eqimpsubset2
% 3.03/1.59 => ( eqimpsubset1
% 3.03/1.59 => ( subsetI2
% 3.03/1.59 => ( emptysetsubset
% 3.03/1.59 => ( subsetE
% 3.03/1.59 => ( subsetE2
% 3.03/1.59 => ( notsubsetI
% 3.03/1.59 => ( notequalI1
% 3.03/1.59 => ( notequalI2
% 3.03/1.59 => ( subsetRefl
% 3.03/1.59 => ( subsetTrans
% 3.03/1.59 => ( setadjoinSub
% 3.03/1.59 => ( setadjoinSub2
% 3.03/1.59 => ( subset2powerset
% 3.03/1.59 => ( setextsub
% 3.03/1.59 => ( subsetemptysetimpeq
% 3.03/1.59 => ( powersetI1
% 3.03/1.59 => ( powersetE1
% 3.03/1.59 => ( inPowerset
% 3.03/1.59 => ( powersetsubset
% 3.03/1.59 => ( sepInPowerset
% 3.03/1.59 => ( sepSubset
% 3.03/1.59 => ( binunionIL
% 3.03/1.59 => ( upairset2IR
% 3.03/1.59 => ( binunionIR
% 3.03/1.59 => ( binunionEcases
% 3.03/1.59 => ( binunionE
% 3.03/1.59 => ( binunionLsub
% 3.03/1.59 => ( binunionRsub
% 3.03/1.59 => ( binintersectI
% 3.03/1.59 => ( binintersectSubset5
% 3.03/1.59 => ( binintersectEL
% 3.03/1.59 => ( binintersectLsub
% 3.03/1.59 => ( binintersectSubset2
% 3.03/1.59 => ( binintersectSubset3
% 3.03/1.59 => ( binintersectER
% 3.03/1.59 => ( disjointsetsI1
% 3.03/1.59 => ( binintersectRsub
% 3.03/1.59 => ( binintersectSubset4
% 3.03/1.59 => ( binintersectSubset1
% 3.03/1.59 => ( bs114d
% 3.03/1.59 => ( setminusI
% 3.03/1.59 => ( setminusEL
% 3.03/1.59 => ( setminusER
% 3.03/1.59 => ( setminusSubset2
% 3.03/1.59 => ( setminusERneg
% 3.03/1.59 => ( setminusELneg
% 3.03/1.59 => ( setminusILneg
% 3.03/1.59 => ( setminusIRneg
% 3.03/1.59 => ( setminusLsub
% 3.03/1.59 => ( setminusSubset1
% 3.03/1.59 => ( symdiffE
% 3.03/1.59 => ( symdiffI1
% 3.03/1.59 => ( symdiffI2
% 3.03/1.59 => ( symdiffIneg1
% 3.03/1.59 => ( symdiffIneg2
% 3.03/1.59 => ( secondinupair
% 3.03/1.59 => ( setukpairIL
% 3.03/1.59 => ( setukpairIR
% 3.03/1.59 => ( kpairiskpair
% 3.03/1.59 => ( kpairp
% 3.03/1.59 => ( singletonsubset
% 3.03/1.59 => ( singletoninpowerset
% 3.03/1.59 => ( singletoninpowunion
% 3.03/1.59 => ( upairset2E
% 3.03/1.59 => ( upairsubunion
% 3.03/1.59 => ( upairinpowunion
% 3.03/1.59 => ( ubforcartprodlem1
% 3.03/1.59 => ( ubforcartprodlem2
% 3.03/1.59 => ( ubforcartprodlem3
% 3.03/1.59 => ( cartprodpairin
% 3.03/1.59 => ( cartprodmempair1
% 3.03/1.59 => ( cartprodmempair
% 3.03/1.59 => ( setunionE2
% 3.03/1.59 => ( setunionsingleton1
% 3.03/1.59 => ( setunionsingleton2
% 3.03/1.59 => ( setunionsingleton
% 3.03/1.59 => ( singletonprop
% 3.03/1.59 => ( ex1E1
% 3.03/1.59 => ( ex1I
% 3.03/1.59 => ( ex1I2
% 3.03/1.59 => ( singletonsuniq
% 3.03/1.59 => ( setukpairinjL1
% 3.03/1.59 => ( kfstsingleton
% 3.03/1.59 => ( theprop
% 3.03/1.59 => ( kfstpairEq
% 3.03/1.59 => ( cartprodfstin
% 3.03/1.59 => ( setukpairinjL2
% 3.03/1.59 => ( setukpairinjL
% 3.03/1.59 => ( setukpairinjR11
% 3.03/1.59 => ( setukpairinjR12
% 3.03/1.59 => ( setukpairinjR1
% 3.03/1.59 => ( upairequniteq
% 3.03/1.59 => ( setukpairinjR2
% 3.03/1.59 => ( setukpairinjR
% 3.03/1.59 => ( ksndsingleton
% 3.03/1.59 => ( ksndpairEq
% 3.03/1.59 => ( kpairsurjEq
% 3.03/1.59 => ( cartprodsndin
% 3.03/1.59 => ( cartprodpairmemEL
% 3.03/1.59 => ( cartprodpairmemER
% 3.03/1.59 => ( cartprodmempaircEq
% 3.03/1.59 => ( cartprodfstpairEq
% 3.03/1.59 => ( cartprodsndpairEq
% 3.03/1.59 => ( cartprodpairsurjEq
% 3.03/1.59 => ( dpsetconstrI
% 3.03/1.59 => ( dpsetconstrSub
% 3.03/1.59 => ( setOfPairsIsBReln
% 3.03/1.59 => ( dpsetconstrERa
% 3.03/1.59 => ( dpsetconstrEL1
% 3.03/1.59 => ( dpsetconstrEL2
% 3.03/1.59 => ( dpsetconstrER
% 3.03/1.59 => ( funcImageSingleton
% 3.03/1.59 => ( apProp
% 3.03/1.59 => ( app
% 3.03/1.59 => ( infuncsetfunc
% 3.03/1.59 => ( ap2p
% 3.03/1.59 => ( funcinfuncset
% 3.03/1.59 => ( lamProp
% 3.03/1.59 => ( lamp
% 3.03/1.59 => ( lam2p
% 3.03/1.59 => ( brelnall1
% 3.03/1.59 => ( brelnall2
% 3.03/1.59 => ( ex1E2
% 3.03/1.59 => ( funcGraphProp1
% 3.03/1.59 => ( funcGraphProp3
% 3.03/1.59 => ( funcGraphProp2
% 3.03/1.59 => ( funcextLem
% 3.03/1.59 => ( funcGraphProp4
% 3.03/1.59 => ( subbreln
% 3.03/1.59 => ( eqbreln
% 3.03/1.59 => ( funcext
% 3.03/1.59 => ( funcext2
% 3.03/1.59 => ( ap2apEq1
% 3.03/1.59 => ( ap2apEq2
% 3.03/1.59 => ( beta1
% 3.03/1.59 => ( eta1
% 3.03/1.59 => ( lam2lamEq
% 3.03/1.59 => ( beta2
% 3.03/1.59 => ( eta2
% 3.03/1.59 => ( iffalseProp1
% 3.03/1.59 => ( iffalseProp2
% 3.03/1.59 => ( iftrueProp1
% 3.03/1.59 => ( iftrueProp2
% 3.03/1.59 => ( ifSingleton
% 3.03/1.59 => ( ifp
% 3.03/1.59 => ( theeq
% 3.03/1.59 => ( iftrue
% 3.03/1.59 => ( iffalse
% 3.03/1.59 => ( iftrueorfalse
% 3.03/1.59 => ( binintersectT_lem
% 3.03/1.59 => ( binunionT_lem
% 3.03/1.59 => ( powersetT_lem
% 3.03/1.59 => ( setminusT_lem
% 3.03/1.59 => ( complementT_lem
% 3.03/1.59 => ( setextT
% 3.03/1.59 => ( subsetTI
% 3.03/1.59 => ( powersetTI1
% 3.03/1.59 => ( powersetTE1
% 3.03/1.59 => ( complementTI1
% 3.03/1.59 => ( complementTE1
% 3.03/1.59 => ( binintersectTELcontra
% 3.03/1.59 => ( binintersectTERcontra
% 3.03/1.59 => ( contrasubsetT
% 3.03/1.59 => ( contrasubsetT1
% 3.03/1.59 => ( contrasubsetT2
% 3.03/1.59 => ( contrasubsetT3
% 3.03/1.59 => ( doubleComplementI1
% 3.03/1.59 => ( doubleComplementE1
% 3.03/1.59 => ( doubleComplementSub1
% 3.03/1.59 => ( doubleComplementSub2
% 3.03/1.59 => ( doubleComplementEq
% 3.03/1.59 => ( complementTnotintersectT
% 3.03/1.59 => ( complementImpComplementIntersect
% 3.03/1.59 => ( complementSubsetComplementIntersect
% 3.03/1.59 => ( complementInPowersetComplementIntersect
% 3.03/1.59 => ( contraSubsetComplement
% 3.03/1.59 => ( complementTcontraSubset
% 3.03/1.59 => ( binunionTILcontra
% 3.03/1.59 => ( binunionTIRcontra
% 3.03/1.59 => ( inIntersectImpInUnion
% 3.03/1.59 => ( inIntersectImpInUnion2
% 3.03/1.59 => ( inIntersectImpInIntersectUnions
% 3.03/1.59 => ( intersectInPowersetIntersectUnions
% 3.03/1.59 => ( inComplementUnionImpNotIn1
% 3.03/1.59 => ( inComplementUnionImpInComplement1
% 3.03/1.59 => ( binunionTE
% 3.03/1.59 => ( binunionTEcontra
% 3.03/1.59 => ( demorgan2a1
% 3.03/1.59 => ( complementUnionInPowersetComplement
% 3.03/1.59 => ( demorgan2a2
% 3.03/1.59 => ( demorgan1a
% 3.03/1.59 => ( demorgan1b
% 3.03/1.59 => ( demorgan1
% 3.03/1.59 => ( demorgan2a
% 3.03/1.59 => ( demorgan2b2
% 3.03/1.59 => ( demorgan2b
% 3.03/1.59 => ( demorgan2
% 3.03/1.59 => ( woz13rule0
% 3.03/1.59 => ( woz13rule1
% 3.03/1.59 => ( woz13rule2
% 3.03/1.59 => ( woz13rule3
% 3.03/1.59 => ( woz13rule4
% 3.03/1.59 => ( woz1_1
% 3.03/1.59 => ( woz1_2
% 3.03/1.59 => ( woz1_3
% 3.03/1.59 => ( woz1_4
% 3.03/1.59 => ( woz1_5
% 3.03/1.59 => ( breln1all2
% 3.03/1.59 => ( breln1SetBreln1
% 3.03/1.59 => ( choice2fnsingleton
% 3.03/1.59 => ( setOfPairsIsBReln1
% 3.03/1.59 => ( breln1all1
% 3.03/1.59 => ( subbreln1
% 3.03/1.59 => ( eqbreln1
% 3.03/1.59 => ( breln1invprop
% 3.03/1.59 => ( breln1invI
% 3.03/1.59 => ( breln1invE
% 3.03/1.59 => ( breln1compprop
% 3.03/1.59 => ( breln1compI
% 3.03/1.59 => ( breln1compE
% 3.03/1.59 => ( breln1compEex
% 3.03/1.59 => ( breln1unionprop
% 3.03/1.59 => ( breln1unionIL
% 3.03/1.59 => ( breln1unionIR
% 3.03/1.59 => ( breln1unionI
% 3.03/1.59 => ( breln1unionE
% 3.03/1.59 => ( breln1unionEcases
% 3.03/1.59 => ( breln1unionCommutes
% 3.03/1.59 => ( woz2Ex
% 3.03/1.59 => ( woz2W
% 3.03/1.59 => ( woz2A
% 3.03/1.59 => ( woz2B
% 3.03/1.59 => ( image1Ex
% 3.03/1.59 => ( image1Ex1
% 3.03/1.59 => ( image1Equiv
% 3.03/1.59 => ( image1E
% 3.03/1.59 => ( image1I
% 3.03/1.59 => ( injFuncInInjFuncSet
% 3.03/1.59 => ( injFuncSetFuncIn
% 3.03/1.59 => ( injFuncSetFuncInj
% 3.03/1.59 => ( surjFuncSetFuncIn
% 3.03/1.59 => ( surjFuncSetFuncSurj
% 3.03/1.59 => ! [A: $i,B: $i,Xf: $i > $i] :
% 3.03/1.59 ( ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.03/1.59 => ! [Xg: $i] :
% 3.03/1.59 ( ( in @ Xg @ ( funcSet @ B @ A ) )
% 3.03/1.59 => ( ! [Xx: $i] :
% 3.03/1.59 ( ( in @ Xx @ A )
% 3.03/1.59 => ( ( ap @ B @ A @ Xg @ ( Xf @ Xx ) )
% 3.03/1.59 = Xx ) )
% 3.03/1.59 => ( surjective @ B @ A @ Xg ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.03/1.59 ------------------------
% 3.17/1.64 % (7426)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_7160 for (2999ds/4Mi)
% 3.17/1.64 % (7429)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_7160 for (2999ds/2Mi)
% 3.17/1.64 % (7429)Instruction limit reached!
% 3.17/1.64 % (7429)------------------------------
% 3.17/1.64 % (7429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.64 % (7429)Termination reason: Unknown
% 3.17/1.64 % (7429)Termination phase: shuffling
% 3.17/1.64
% 3.17/1.64 % (7429)Memory used [KB]: 1663
% 3.17/1.64 % (7429)Time elapsed: 0.002 s
% 3.17/1.64 % (7429)Instructions burned: 3 (million)
% 3.17/1.64 % (7429)------------------------------
% 3.17/1.64 % (7429)------------------------------
% 3.17/1.64 % (7426)Instruction limit reached!
% 3.17/1.64 % (7426)------------------------------
% 3.17/1.64 % (7426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.64 % (7426)Termination reason: Unknown
% 3.17/1.64 % (7426)Termination phase: shuffling
% 3.17/1.64
% 3.17/1.64 % (7426)Memory used [KB]: 1663
% 3.17/1.64 % (7426)Time elapsed: 0.003 s
% 3.17/1.64 % (7426)Instructions burned: 6 (million)
% 3.17/1.64 % (7426)------------------------------
% 3.17/1.64 % (7426)------------------------------
% 3.17/1.64 % (7425)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7160 for (2999ds/183Mi)
% 3.17/1.64 % (7428)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7160 for (2999ds/2Mi)
% 3.17/1.64 % (7427)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_7160 for (2999ds/27Mi)
% 3.17/1.64 % (7430)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_7160 for (2999ds/275Mi)
% 3.17/1.64 % (7431)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7160 for (2999ds/18Mi)
% 3.17/1.65 % (7428)Instruction limit reached!
% 3.17/1.65 % (7428)------------------------------
% 3.17/1.65 % (7428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.65 % (7428)Termination reason: Unknown
% 3.17/1.65 % (7428)Termination phase: shuffling
% 3.17/1.65
% 3.17/1.65 % (7428)Memory used [KB]: 1663
% 3.17/1.65 % (7428)Time elapsed: 0.003 s
% 3.17/1.65 % (7428)Instructions burned: 3 (million)
% 3.17/1.65 % (7428)------------------------------
% 3.17/1.65 % (7428)------------------------------
% 3.17/1.65 % (7432)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7160 for (2999ds/3Mi)
% 3.17/1.65 % (7433)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_7160 for (2999ds/37Mi)
% 3.17/1.65 % (7432)Instruction limit reached!
% 3.17/1.65 % (7432)------------------------------
% 3.17/1.65 % (7432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.65 % (7432)Termination reason: Unknown
% 3.17/1.65 % (7432)Termination phase: shuffling
% 3.17/1.65
% 3.17/1.65 % (7432)Memory used [KB]: 1663
% 3.17/1.65 % (7432)Time elapsed: 0.003 s
% 3.17/1.65 % (7432)Instructions burned: 5 (million)
% 3.17/1.65 % (7432)------------------------------
% 3.17/1.65 % (7432)------------------------------
% 3.17/1.66 % (7431)Instruction limit reached!
% 3.17/1.66 % (7431)------------------------------
% 3.17/1.66 % (7431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.66 % (7431)Termination reason: Unknown
% 3.17/1.66 % (7431)Termination phase: shuffling
% 3.17/1.66
% 3.17/1.66 % (7431)Memory used [KB]: 1918
% 3.17/1.66 % (7431)Time elapsed: 0.013 s
% 3.17/1.66 % (7431)Instructions burned: 19 (million)
% 3.17/1.66 % (7431)------------------------------
% 3.17/1.66 % (7431)------------------------------
% 3.17/1.66 % (7427)Instruction limit reached!
% 3.17/1.66 % (7427)------------------------------
% 3.17/1.66 % (7427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.66 % (7427)Termination reason: Unknown
% 3.17/1.66 % (7427)Termination phase: shuffling
% 3.17/1.66
% 3.17/1.66 % (7427)Memory used [KB]: 2046
% 3.17/1.66 % (7427)Time elapsed: 0.016 s
% 3.17/1.66 % (7427)Instructions burned: 28 (million)
% 3.17/1.66 % (7427)------------------------------
% 3.17/1.66 % (7427)------------------------------
% 3.17/1.66 % (7435)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_7160 for (2999ds/3Mi)
% 3.17/1.66 % (7435)Instruction limit reached!
% 3.17/1.66 % (7435)------------------------------
% 3.17/1.66 % (7435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.66 % (7435)Termination reason: Unknown
% 3.17/1.66 % (7435)Termination phase: shuffling
% 3.17/1.66
% 3.17/1.66 % (7435)Memory used [KB]: 1663
% 3.17/1.66 % (7435)Time elapsed: 0.002 s
% 3.17/1.66 % (7435)Instructions burned: 3 (million)
% 3.17/1.66 % (7435)------------------------------
% 3.17/1.66 % (7435)------------------------------
% 3.17/1.66 % (7433)Instruction limit reached!
% 3.17/1.66 % (7433)------------------------------
% 3.17/1.66 % (7433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.66 % (7433)Termination reason: Unknown
% 3.17/1.66 % (7433)Termination phase: shuffling
% 3.17/1.66
% 3.17/1.66 % (7433)Memory used [KB]: 2430
% 3.17/1.66 % (7433)Time elapsed: 0.012 s
% 3.17/1.66 % (7433)Instructions burned: 39 (million)
% 3.17/1.66 % (7433)------------------------------
% 3.17/1.66 % (7433)------------------------------
% 3.17/1.66 % (7434)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_7160 for (2999ds/15Mi)
% 3.17/1.67 % (7438)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_7160 for (2999ds/16Mi)
% 3.17/1.67 % (7439)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_7160 for (2999ds/3Mi)
% 3.17/1.67 % (7439)Instruction limit reached!
% 3.17/1.67 % (7439)------------------------------
% 3.17/1.67 % (7439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.67 % (7439)Termination reason: Unknown
% 3.17/1.67 % (7439)Termination phase: shuffling
% 3.17/1.67
% 3.17/1.67 % (7439)Memory used [KB]: 1663
% 3.17/1.67 % (7439)Time elapsed: 0.003 s
% 3.17/1.67 % (7439)Instructions burned: 6 (million)
% 3.17/1.67 % (7439)------------------------------
% 3.17/1.67 % (7439)------------------------------
% 3.17/1.67 % (7434)Instruction limit reached!
% 3.17/1.67 % (7434)------------------------------
% 3.17/1.67 % (7434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.67 % (7434)Termination reason: Unknown
% 3.17/1.67 % (7434)Termination phase: shuffling
% 3.17/1.67
% 3.17/1.67 % (7434)Memory used [KB]: 1918
% 3.17/1.67 % (7434)Time elapsed: 0.012 s
% 3.17/1.67 % (7434)Instructions burned: 16 (million)
% 3.17/1.67 % (7434)------------------------------
% 3.17/1.67 % (7434)------------------------------
% 3.17/1.67 % (7438)Instruction limit reached!
% 3.17/1.67 % (7438)------------------------------
% 3.17/1.67 % (7438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.67 % (7438)Termination reason: Unknown
% 3.17/1.67 % (7438)Termination phase: shuffling
% 3.17/1.67
% 3.17/1.67 % (7438)Memory used [KB]: 2046
% 3.17/1.67 % (7438)Time elapsed: 0.006 s
% 3.17/1.67 % (7438)Instructions burned: 17 (million)
% 3.17/1.67 % (7438)------------------------------
% 3.17/1.67 % (7438)------------------------------
% 3.17/1.67 % (7436)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_7160 for (2999ds/1041Mi)
% 3.17/1.68 % (7437)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_7160 for (2999ds/7Mi)
% 3.17/1.68 % (7437)Instruction limit reached!
% 3.17/1.68 % (7437)------------------------------
% 3.17/1.68 % (7437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.68 % (7437)Termination reason: Unknown
% 3.17/1.68 % (7437)Termination phase: shuffling
% 3.17/1.68
% 3.17/1.68 % (7437)Memory used [KB]: 1663
% 3.17/1.68 % (7437)Time elapsed: 0.005 s
% 3.17/1.68 % (7437)Instructions burned: 7 (million)
% 3.17/1.68 % (7437)------------------------------
% 3.17/1.68 % (7437)------------------------------
% 3.17/1.68 % (7440)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_7160 for (2999ds/3Mi)
% 3.17/1.68 % (7440)Instruction limit reached!
% 3.17/1.68 % (7440)------------------------------
% 3.17/1.68 % (7440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.68 % (7440)Termination reason: Unknown
% 3.17/1.68 % (7440)Termination phase: shuffling
% 3.17/1.68
% 3.17/1.68 % (7440)Memory used [KB]: 1663
% 3.17/1.68 % (7440)Time elapsed: 0.002 s
% 3.17/1.68 % (7440)Instructions burned: 3 (million)
% 3.17/1.68 % (7440)------------------------------
% 3.17/1.68 % (7440)------------------------------
% 3.17/1.68 % (7442)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_7160 for (2999ds/3Mi)
% 3.17/1.68 % (7442)Instruction limit reached!
% 3.17/1.68 % (7442)------------------------------
% 3.17/1.68 % (7442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.68 % (7442)Termination reason: Unknown
% 3.17/1.68 % (7442)Termination phase: shuffling
% 3.17/1.68
% 3.17/1.68 % (7442)Memory used [KB]: 1663
% 3.17/1.68 % (7442)Time elapsed: 0.002 s
% 3.17/1.68 % (7442)Instructions burned: 3 (million)
% 3.17/1.68 % (7442)------------------------------
% 3.17/1.68 % (7442)------------------------------
% 3.17/1.69 % (7441)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_7160 for (2999ds/7Mi)
% 3.17/1.69 % (7444)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_7160 for (2999ds/18Mi)
% 3.17/1.69 % (7443)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_7160 for (2999ds/4Mi)
% 3.17/1.69 % (7443)Instruction limit reached!
% 3.17/1.69 % (7443)------------------------------
% 3.17/1.69 % (7443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.69 % (7443)Termination reason: Unknown
% 3.17/1.69 % (7443)Termination phase: shuffling
% 3.17/1.69
% 3.17/1.69 % (7443)Memory used [KB]: 1663
% 3.17/1.69 % (7443)Time elapsed: 0.003 s
% 3.17/1.69 % (7443)Instructions burned: 5 (million)
% 3.17/1.69 % (7443)------------------------------
% 3.17/1.69 % (7443)------------------------------
% 3.17/1.69 % (7445)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_7160 for (2999ds/710Mi)
% 3.17/1.69 % (7441)Instruction limit reached!
% 3.17/1.69 % (7441)------------------------------
% 3.17/1.69 % (7441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.69 % (7441)Termination reason: Unknown
% 3.17/1.69 % (7441)Termination phase: shuffling
% 3.17/1.69
% 3.17/1.69 % (7441)Memory used [KB]: 1663
% 3.17/1.69 % (7441)Time elapsed: 0.006 s
% 3.17/1.69 % (7441)Instructions burned: 9 (million)
% 3.17/1.69 % (7441)------------------------------
% 3.17/1.69 % (7441)------------------------------
% 3.17/1.70 % (7444)Instruction limit reached!
% 3.17/1.70 % (7444)------------------------------
% 3.17/1.70 % (7444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.70 % (7444)Termination reason: Unknown
% 3.17/1.70 % (7444)Termination phase: shuffling
% 3.17/1.70
% 3.17/1.70 % (7444)Memory used [KB]: 1918
% 3.17/1.70 % (7444)Time elapsed: 0.006 s
% 3.17/1.70 % (7444)Instructions burned: 18 (million)
% 3.17/1.70 % (7444)------------------------------
% 3.17/1.70 % (7444)------------------------------
% 3.17/1.70 % (7446)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_7160 for (2999ds/6Mi)
% 3.17/1.71 % (7446)Instruction limit reached!
% 3.17/1.71 % (7446)------------------------------
% 3.17/1.71 % (7446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.71 % (7446)Termination reason: Unknown
% 3.17/1.71 % (7446)Termination phase: shuffling
% 3.17/1.71
% 3.17/1.71 % (7446)Memory used [KB]: 1663
% 3.17/1.71 % (7446)Time elapsed: 0.003 s
% 3.17/1.71 % (7446)Instructions burned: 7 (million)
% 3.17/1.71 % (7446)------------------------------
% 3.17/1.71 % (7446)------------------------------
% 3.17/1.71 % (7447)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_7160 for (2999ds/902Mi)
% 3.17/1.71 % (7448)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_7160 for (2999ds/21Mi)
% 3.17/1.71 % (7425)Instruction limit reached!
% 3.17/1.71 % (7425)------------------------------
% 3.17/1.71 % (7425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.71 % (7425)Termination reason: Unknown
% 3.17/1.71 % (7425)Termination phase: Property scanning
% 3.17/1.71
% 3.17/1.71 % (7425)Memory used [KB]: 3070
% 3.17/1.71 % (7425)Time elapsed: 0.068 s
% 3.17/1.71 % (7425)Instructions burned: 184 (million)
% 3.17/1.71 % (7425)------------------------------
% 3.17/1.71 % (7425)------------------------------
% 3.17/1.71 % (7448)Instruction limit reached!
% 3.17/1.71 % (7448)------------------------------
% 3.17/1.71 % (7448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.71 % (7448)Termination reason: Unknown
% 3.17/1.71 % (7448)Termination phase: shuffling
% 3.17/1.71
% 3.17/1.71 % (7448)Memory used [KB]: 1918
% 3.17/1.71 % (7448)Time elapsed: 0.007 s
% 3.17/1.71 % (7448)Instructions burned: 21 (million)
% 3.17/1.71 % (7448)------------------------------
% 3.17/1.71 % (7448)------------------------------
% 3.17/1.72 % (7449)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_7160 for (2998ds/5Mi)
% 3.17/1.72 % (7449)Instruction limit reached!
% 3.17/1.72 % (7449)------------------------------
% 3.17/1.72 % (7449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.72 % (7449)Termination reason: Unknown
% 3.17/1.72 % (7449)Termination phase: shuffling
% 3.17/1.72
% 3.17/1.72 % (7449)Memory used [KB]: 1663
% 3.17/1.72 % (7449)Time elapsed: 0.003 s
% 3.17/1.72 % (7449)Instructions burned: 7 (million)
% 3.17/1.72 % (7449)------------------------------
% 3.17/1.72 % (7449)------------------------------
% 3.17/1.72 % (7450)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_7160 for (2998ds/6Mi)
% 3.17/1.72 % (7451)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_7160 for (2998ds/377Mi)
% 3.17/1.72 % (7450)Instruction limit reached!
% 3.17/1.72 % (7450)------------------------------
% 3.17/1.72 % (7450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.72 % (7450)Termination reason: Unknown
% 3.17/1.72 % (7450)Termination phase: shuffling
% 3.17/1.72
% 3.17/1.72 % (7450)Memory used [KB]: 1663
% 3.17/1.72 % (7450)Time elapsed: 0.003 s
% 3.17/1.72 % (7450)Instructions burned: 6 (million)
% 3.17/1.72 % (7450)------------------------------
% 3.17/1.72 % (7450)------------------------------
% 3.17/1.73 % (7452)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_7160 for (2998ds/779Mi)
% 3.17/1.73 % (7453)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_7160 for (2998ds/19Mi)
% 3.17/1.74 % (7430)Instruction limit reached!
% 3.17/1.74 % (7430)------------------------------
% 3.17/1.74 % (7430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.74 % (7430)Termination reason: Unknown
% 3.17/1.74 % (7430)Termination phase: Saturation
% 3.17/1.74
% 3.17/1.74 % (7430)Memory used [KB]: 6012
% 3.17/1.74 % (7430)Time elapsed: 0.095 s
% 3.17/1.74 % (7430)Instructions burned: 276 (million)
% 3.17/1.74 % (7430)------------------------------
% 3.17/1.74 % (7430)------------------------------
% 3.17/1.74 % (7453)Instruction limit reached!
% 3.17/1.74 % (7453)------------------------------
% 3.17/1.74 % (7453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.74 % (7453)Termination reason: Unknown
% 3.17/1.74 % (7453)Termination phase: shuffling
% 3.17/1.74
% 3.17/1.74 % (7453)Memory used [KB]: 1918
% 3.17/1.74 % (7453)Time elapsed: 0.007 s
% 3.17/1.74 % (7453)Instructions burned: 20 (million)
% 3.17/1.74 % (7453)------------------------------
% 3.17/1.74 % (7453)------------------------------
% 3.17/1.75 % (7454)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_7160 for (2998ds/879Mi)
% 3.17/1.75 % (7455)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_7160 for (2998ds/17Mi)
% 3.17/1.75 % (7455)Instruction limit reached!
% 3.17/1.75 % (7455)------------------------------
% 3.17/1.75 % (7455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.75 % (7455)Termination reason: Unknown
% 3.17/1.75 % (7455)Termination phase: shuffling
% 3.17/1.75
% 3.17/1.75 % (7455)Memory used [KB]: 2046
% 3.17/1.75 % (7455)Time elapsed: 0.007 s
% 3.17/1.75 % (7455)Instructions burned: 20 (million)
% 3.17/1.75 % (7455)------------------------------
% 3.17/1.75 % (7455)------------------------------
% 3.17/1.77 % (7456)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_7160 for (2998ds/3Mi)
% 3.17/1.77 % (7456)Instruction limit reached!
% 3.17/1.77 % (7456)------------------------------
% 3.17/1.77 % (7456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.77 % (7456)Termination reason: Unknown
% 3.17/1.77 % (7456)Termination phase: shuffling
% 3.17/1.77
% 3.17/1.77 % (7456)Memory used [KB]: 1663
% 3.17/1.77 % (7456)Time elapsed: 0.002 s
% 3.17/1.77 % (7456)Instructions burned: 3 (million)
% 3.17/1.77 % (7456)------------------------------
% 3.17/1.77 % (7456)------------------------------
% 3.17/1.78 % (7457)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_7160 for (2998ds/30Mi)
% 3.17/1.79 % (7457)Instruction limit reached!
% 3.17/1.79 % (7457)------------------------------
% 3.17/1.79 % (7457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.79 % (7457)Termination reason: Unknown
% 3.17/1.79 % (7457)Termination phase: shuffling
% 3.17/1.79
% 3.17/1.79 % (7457)Memory used [KB]: 2302
% 3.17/1.79 % (7457)Time elapsed: 0.010 s
% 3.17/1.79 % (7457)Instructions burned: 31 (million)
% 3.17/1.79 % (7457)------------------------------
% 3.17/1.79 % (7457)------------------------------
% 3.17/1.80 % (7458)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_7160 for (2998ds/127Mi)
% 3.17/1.82 % (7451)Instruction limit reached!
% 3.17/1.82 % (7451)------------------------------
% 3.17/1.82 % (7451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.82 % (7451)Termination reason: Unknown
% 3.17/1.82 % (7451)Termination phase: Saturation
% 3.17/1.82
% 3.17/1.82 % (7451)Memory used [KB]: 9594
% 3.17/1.82 % (7451)Time elapsed: 0.100 s
% 3.17/1.82 % (7451)Instructions burned: 378 (million)
% 3.17/1.82 % (7451)------------------------------
% 3.17/1.82 % (7451)------------------------------
% 3.17/1.83 % (7459)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_7160 for (2997ds/100Mi)
% 3.17/1.83 % (7458)Instruction limit reached!
% 3.17/1.83 % (7458)------------------------------
% 3.17/1.83 % (7458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.83 % (7458)Termination reason: Unknown
% 3.17/1.83 % (7458)Termination phase: Property scanning
% 3.17/1.83
% 3.17/1.83 % (7458)Memory used [KB]: 2942
% 3.17/1.83 % (7458)Time elapsed: 0.037 s
% 3.17/1.83 % (7458)Instructions burned: 129 (million)
% 3.17/1.83 % (7458)------------------------------
% 3.17/1.83 % (7458)------------------------------
% 3.17/1.84 % (7460)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_7160 for (2997ds/3Mi)
% 3.17/1.84 % (7460)Instruction limit reached!
% 3.17/1.84 % (7460)------------------------------
% 3.17/1.84 % (7460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.84 % (7460)Termination reason: Unknown
% 3.17/1.84 % (7460)Termination phase: shuffling
% 3.17/1.84
% 3.17/1.84 % (7460)Memory used [KB]: 1663
% 3.17/1.84 % (7460)Time elapsed: 0.003 s
% 3.17/1.84 % (7460)Instructions burned: 5 (million)
% 3.17/1.84 % (7460)------------------------------
% 3.17/1.84 % (7460)------------------------------
% 3.17/1.85 % (7461)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_7160 for (2997ds/20Mi)
% 3.17/1.86 % (7459)Instruction limit reached!
% 3.17/1.86 % (7459)------------------------------
% 3.17/1.86 % (7459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.86 % (7459)Termination reason: Unknown
% 3.17/1.86 % (7459)Termination phase: Preprocessing 3
% 3.17/1.86
% 3.17/1.86 % (7459)Memory used [KB]: 2814
% 3.17/1.86 % (7459)Time elapsed: 0.027 s
% 3.17/1.86 % (7459)Instructions burned: 100 (million)
% 3.17/1.86 % (7459)------------------------------
% 3.17/1.86 % (7459)------------------------------
% 3.17/1.86 % (7461)Instruction limit reached!
% 3.17/1.86 % (7461)------------------------------
% 3.17/1.86 % (7461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.86 % (7461)Termination reason: Unknown
% 3.17/1.86 % (7461)Termination phase: shuffling
% 3.17/1.86
% 3.17/1.86 % (7461)Memory used [KB]: 1918
% 3.17/1.86 % (7461)Time elapsed: 0.008 s
% 3.17/1.86 % (7461)Instructions burned: 22 (million)
% 3.17/1.86 % (7461)------------------------------
% 3.17/1.86 % (7461)------------------------------
% 3.17/1.87 % (7462)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_7160 for (2997ds/86Mi)
% 3.17/1.87 % (7463)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_7160 for (2997ds/107Mi)
% 3.17/1.89 % (7462)Instruction limit reached!
% 3.17/1.89 % (7462)------------------------------
% 3.17/1.89 % (7462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.89 % (7462)Termination reason: Unknown
% 3.17/1.89 % (7462)Termination phase: Property scanning
% 3.17/1.89
% 3.17/1.89 % (7462)Memory used [KB]: 2814
% 3.17/1.89 % (7462)Time elapsed: 0.025 s
% 3.17/1.89 % (7462)Instructions burned: 89 (million)
% 3.17/1.89 % (7462)------------------------------
% 3.17/1.89 % (7462)------------------------------
% 3.17/1.90 % (7463)Instruction limit reached!
% 3.17/1.90 % (7463)------------------------------
% 3.17/1.90 % (7463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.90 % (7463)Termination reason: Unknown
% 3.17/1.90 % (7463)Termination phase: SInE selection
% 3.17/1.90
% 3.17/1.90 % (7463)Memory used [KB]: 2814
% 3.17/1.90 % (7463)Time elapsed: 0.030 s
% 3.17/1.90 % (7463)Instructions burned: 107 (million)
% 3.17/1.90 % (7463)------------------------------
% 3.17/1.90 % (7463)------------------------------
% 3.17/1.90 % (7464)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_7160 for (2997ds/39Mi)
% 3.17/1.91 % (7465)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_7160 for (2996ds/448Mi)
% 3.17/1.91 % (7464)Instruction limit reached!
% 3.17/1.91 % (7464)------------------------------
% 3.17/1.91 % (7464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.91 % (7464)Termination reason: Unknown
% 3.17/1.91 % (7464)Termination phase: shuffling
% 3.17/1.91
% 3.17/1.91 % (7464)Memory used [KB]: 2430
% 3.17/1.91 % (7464)Time elapsed: 0.012 s
% 3.17/1.91 % (7464)Instructions burned: 41 (million)
% 3.17/1.91 % (7464)------------------------------
% 3.17/1.91 % (7464)------------------------------
% 3.17/1.91 % (7445)Instruction limit reached!
% 3.17/1.91 % (7445)------------------------------
% 3.17/1.91 % (7445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.91 % (7445)Termination reason: Unknown
% 3.17/1.91 % (7445)Termination phase: Saturation
% 3.17/1.91
% 3.17/1.91 % (7445)Memory used [KB]: 12409
% 3.17/1.91 % (7445)Time elapsed: 0.219 s
% 3.17/1.91 % (7445)Instructions burned: 711 (million)
% 3.17/1.91 % (7445)------------------------------
% 3.17/1.91 % (7445)------------------------------
% 3.17/1.92 % (7466)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_7160 for (2996ds/46Mi)
% 3.17/1.92 % (7467)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_7160 for (2996ds/98Mi)
% 3.17/1.93 % (7466)Instruction limit reached!
% 3.17/1.93 % (7466)------------------------------
% 3.17/1.93 % (7466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.93 % (7466)Termination reason: Unknown
% 3.17/1.93 % (7466)Termination phase: shuffling
% 3.17/1.93
% 3.17/1.93 % (7466)Memory used [KB]: 2558
% 3.17/1.93 % (7466)Time elapsed: 0.014 s
% 3.17/1.93 % (7466)Instructions burned: 48 (million)
% 3.17/1.93 % (7466)------------------------------
% 3.17/1.93 % (7466)------------------------------
% 3.17/1.94 % (7452)Instruction limit reached!
% 3.17/1.94 % (7452)------------------------------
% 3.17/1.94 % (7452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.94 % (7452)Termination reason: Unknown
% 3.17/1.94 % (7452)Termination phase: Saturation
% 3.17/1.94
% 3.17/1.94 % (7452)Memory used [KB]: 7931
% 3.17/1.94 % (7452)Time elapsed: 0.209 s
% 3.17/1.94 % (7452)Instructions burned: 780 (million)
% 3.17/1.94 % (7452)------------------------------
% 3.17/1.94 % (7452)------------------------------
% 3.17/1.94 % (7468)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_7160 for (2996ds/507Mi)
% 3.17/1.95 % (7469)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_7160 for (2996ds/149Mi)
% 3.17/1.95 % (7467)Instruction limit reached!
% 3.17/1.95 % (7467)------------------------------
% 3.17/1.95 % (7467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.95 % (7467)Termination reason: Unknown
% 3.17/1.95 % (7467)Termination phase: Property scanning
% 3.17/1.95
% 3.17/1.95 % (7467)Memory used [KB]: 2814
% 3.17/1.95 % (7467)Time elapsed: 0.027 s
% 3.17/1.95 % (7467)Instructions burned: 101 (million)
% 3.17/1.95 % (7467)------------------------------
% 3.17/1.95 % (7467)------------------------------
% 3.17/1.96 % (7470)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_7160 for (2996ds/39Mi)
% 3.17/1.97 % (7447)Instruction limit reached!
% 3.17/1.97 % (7447)------------------------------
% 3.17/1.97 % (7447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.97 % (7447)Termination reason: Unknown
% 3.17/1.97 % (7447)Termination phase: Saturation
% 3.17/1.97
% 3.17/1.97 % (7447)Memory used [KB]: 13048
% 3.17/1.97 % (7447)Time elapsed: 0.264 s
% 3.17/1.97 % (7447)Instructions burned: 903 (million)
% 3.17/1.97 % (7447)------------------------------
% 3.17/1.97 % (7447)------------------------------
% 3.17/1.97 % (7470)Instruction limit reached!
% 3.17/1.97 % (7470)------------------------------
% 3.17/1.97 % (7470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.97 % (7470)Termination reason: Unknown
% 3.17/1.97 % (7470)Termination phase: shuffling
% 3.17/1.97
% 3.17/1.97 % (7470)Memory used [KB]: 2430
% 3.17/1.97 % (7470)Time elapsed: 0.013 s
% 3.17/1.97 % (7470)Instructions burned: 42 (million)
% 3.17/1.97 % (7470)------------------------------
% 3.17/1.97 % (7470)------------------------------
% 3.17/1.98 % (7471)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_7160 for (2996ds/6Mi)
% 3.17/1.98 % (7472)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_7160 for (2996ds/1087Mi)
% 3.17/1.98 % (7471)Instruction limit reached!
% 3.17/1.98 % (7471)------------------------------
% 3.17/1.98 % (7471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.98 % (7471)Termination reason: Unknown
% 3.17/1.98 % (7471)Termination phase: shuffling
% 3.17/1.98
% 3.17/1.98 % (7471)Memory used [KB]: 1663
% 3.17/1.98 % (7471)Time elapsed: 0.003 s
% 3.17/1.98 % (7471)Instructions burned: 6 (million)
% 3.17/1.98 % (7471)------------------------------
% 3.17/1.98 % (7471)------------------------------
% 3.17/1.99 % (7469)Instruction limit reached!
% 3.17/1.99 % (7469)------------------------------
% 3.17/1.99 % (7469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.99 % (7469)Termination reason: Unknown
% 3.17/1.99 % (7469)Termination phase: Function definition elimination
% 3.17/1.99
% 3.17/1.99 % (7469)Memory used [KB]: 3070
% 3.17/1.99 % (7469)Time elapsed: 0.041 s
% 3.17/1.99 % (7469)Instructions burned: 153 (million)
% 3.17/1.99 % (7469)------------------------------
% 3.17/1.99 % (7469)------------------------------
% 3.17/1.99 % (7436)Instruction limit reached!
% 3.17/1.99 % (7436)------------------------------
% 3.17/1.99 % (7436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/1.99 % (7436)Termination reason: Unknown
% 3.17/1.99 % (7436)Termination phase: Saturation
% 3.17/1.99
% 3.17/1.99 % (7436)Memory used [KB]: 18166
% 3.17/1.99 % (7436)Time elapsed: 0.317 s
% 3.17/1.99 % (7436)Instructions burned: 1043 (million)
% 3.17/1.99 % (7436)------------------------------
% 3.17/1.99 % (7436)------------------------------
% 3.17/1.99 % (7473)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_7160 for (2996ds/47Mi)
% 3.17/2.00 % (7474)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_7160 for (2996ds/44Mi)
% 3.17/2.00 % (7475)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_7160 for (2996ds/432Mi)
% 3.17/2.00 % (7473)Instruction limit reached!
% 3.17/2.00 % (7473)------------------------------
% 3.17/2.00 % (7473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/2.00 % (7473)Termination reason: Unknown
% 3.17/2.00 % (7473)Termination phase: shuffling
% 3.17/2.00
% 3.17/2.00 % (7473)Memory used [KB]: 2558
% 3.17/2.00 % (7473)Time elapsed: 0.014 s
% 3.17/2.00 % (7473)Instructions burned: 48 (million)
% 3.17/2.00 % (7473)------------------------------
% 3.17/2.00 % (7473)------------------------------
% 3.17/2.01 % (7474)Instruction limit reached!
% 3.17/2.01 % (7474)------------------------------
% 3.17/2.01 % (7474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.17/2.01 % (7474)Termination reason: Unknown
% 3.17/2.01 % (7474)Termination phase: shuffling
% 3.17/2.01
% 3.17/2.01 % (7474)Memory used [KB]: 2430
% 3.17/2.01 % (7474)Time elapsed: 0.013 s
% 3.17/2.01 % (7474)Instructions burned: 44 (million)
% 3.17/2.01 % (7474)------------------------------
% 3.17/2.01 % (7474)------------------------------
% 3.17/2.01 % (7476)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_7160 for (2995ds/62Mi)
% 5.84/2.02 % (7477)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_7160 for (2995ds/31Mi)
% 5.84/2.02 % (7454)Instruction limit reached!
% 5.84/2.02 % (7454)------------------------------
% 5.84/2.02 % (7454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.84/2.02 % (7454)Termination reason: Unknown
% 5.84/2.02 % (7454)Termination phase: Saturation
% 5.84/2.02
% 5.84/2.02 % (7454)Memory used [KB]: 10746
% 5.84/2.02 % (7454)Time elapsed: 0.274 s
% 5.84/2.02 % (7454)Instructions burned: 880 (million)
% 5.84/2.02 % (7454)------------------------------
% 5.84/2.02 % (7454)------------------------------
% 5.84/2.03 % (7477)Instruction limit reached!
% 5.84/2.03 % (7477)------------------------------
% 5.84/2.03 % (7477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.84/2.03 % (7477)Termination reason: Unknown
% 5.84/2.03 % (7477)Termination phase: shuffling
% 5.84/2.03
% 5.84/2.03 % (7477)Memory used [KB]: 2302
% 5.84/2.03 % (7477)Time elapsed: 0.010 s
% 5.84/2.03 % (7477)Instructions burned: 33 (million)
% 5.84/2.03 % (7477)------------------------------
% 5.84/2.03 % (7477)------------------------------
% 5.84/2.03 % (7476)Instruction limit reached!
% 5.84/2.03 % (7476)------------------------------
% 5.84/2.03 % (7476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.84/2.03 % (7476)Termination reason: Unknown
% 5.84/2.03 % (7476)Termination phase: Property scanning
% 5.84/2.03
% 5.84/2.03 % (7476)Memory used [KB]: 2814
% 5.84/2.03 % (7476)Time elapsed: 0.018 s
% 5.84/2.03 % (7476)Instructions burned: 64 (million)
% 5.84/2.03 % (7476)------------------------------
% 5.84/2.03 % (7476)------------------------------
% 5.84/2.03 % (7478)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_7160 for (2995ds/96Mi)
% 5.84/2.03 % (7465)Instruction limit reached!
% 5.84/2.03 % (7465)------------------------------
% 5.84/2.03 % (7465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.84/2.03 % (7465)Termination reason: Unknown
% 5.84/2.03 % (7465)Termination phase: Saturation
% 5.84/2.03
% 5.84/2.03 % (7465)Memory used [KB]: 7803
% 5.84/2.03 % (7465)Time elapsed: 0.112 s
% 5.84/2.03 % (7465)Instructions burned: 449 (million)
% 5.84/2.03 % (7465)------------------------------
% 5.84/2.03 % (7465)------------------------------
% 5.84/2.04 % (7479)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_7160 for (2995ds/453Mi)
% 5.84/2.04 % (7480)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_7160 for (2995ds/71Mi)
% 5.84/2.04 % (7481)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_7160 for (2995ds/83Mi)
% 5.84/2.06 % (7478)Instruction limit reached!
% 5.84/2.06 % (7478)------------------------------
% 5.84/2.06 % (7478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.84/2.06 % (7478)Termination reason: Unknown
% 5.84/2.06 % (7478)Termination phase: Property scanning
% 5.84/2.06
% 5.84/2.06 % (7478)Memory used [KB]: 2814
% 5.84/2.06 % (7478)Time elapsed: 0.028 s
% 5.84/2.06 % (7478)Instructions burned: 99 (million)
% 5.84/2.06 % (7478)------------------------------
% 5.84/2.06 % (7478)------------------------------
% 5.84/2.06 % (7480)Instruction limit reached!
% 5.84/2.06 % (7480)------------------------------
% 5.84/2.06 % (7480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.84/2.06 % (7480)Termination reason: Unknown
% 5.84/2.06 % (7480)Termination phase: Property scanning
% 5.84/2.06
% 5.84/2.06 % (7480)Memory used [KB]: 2814
% 5.84/2.06 % (7480)Time elapsed: 0.021 s
% 5.84/2.06 % (7480)Instructions burned: 73 (million)
% 5.84/2.06 % (7480)------------------------------
% 5.84/2.06 % (7480)------------------------------
% 5.84/2.07 % (7481)Instruction limit reached!
% 5.84/2.07 % (7481)------------------------------
% 5.84/2.07 % (7481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.84/2.07 % (7481)Termination reason: Unknown
% 5.84/2.07 % (7481)Termination phase: Property scanning
% 5.84/2.07
% 5.84/2.07 % (7481)Memory used [KB]: 2814
% 5.84/2.07 % (7481)Time elapsed: 0.025 s
% 5.84/2.07 % (7481)Instructions burned: 85 (million)
% 5.84/2.07 % (7481)------------------------------
% 5.84/2.07 % (7481)------------------------------
% 5.84/2.07 % (7482)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_7160 for (2995ds/11Mi)
% 5.84/2.07 % (7483)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_7160 for (2995ds/41Mi)
% 5.84/2.07 % (7482)Instruction limit reached!
% 5.84/2.07 % (7482)------------------------------
% 5.84/2.07 % (7482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.84/2.07 % (7482)Termination reason: Unknown
% 5.84/2.07 % (7482)Termination phase: shuffling
% 5.84/2.07
% 5.84/2.07 % (7482)Memory used [KB]: 1918
% 5.84/2.07 % (7482)Time elapsed: 0.005 s
% 5.84/2.07 % (7482)Instructions burned: 13 (million)
% 5.84/2.07 % (7482)------------------------------
% 5.84/2.07 % (7482)------------------------------
% 5.84/2.08 % (7483)Instruction limit reached!
% 5.84/2.08 % (7483)------------------------------
% 5.84/2.08 % (7483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.84/2.08 % (7483)Termination reason: Unknown
% 5.84/2.08 % (7483)Termination phase: shuffling
% 5.84/2.08
% 5.84/2.08 % (7483)Memory used [KB]: 2430
% 5.84/2.08 % (7483)Time elapsed: 0.012 s
% 5.84/2.08 % (7483)Instructions burned: 41 (million)
% 5.84/2.08 % (7483)------------------------------
% 5.84/2.08 % (7483)------------------------------
% 5.84/2.08 % (7485)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_7160 for (2995ds/150Mi)
% 5.84/2.09 % (7468)Instruction limit reached!
% 5.84/2.09 % (7468)------------------------------
% 5.84/2.09 % (7468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.84/2.09 % (7468)Termination reason: Unknown
% 5.84/2.09 % (7468)Termination phase: Saturation
% 5.84/2.09
% 5.84/2.09 % (7468)Memory used [KB]: 8315
% 5.84/2.09 % (7468)Time elapsed: 0.145 s
% 5.84/2.09 % (7468)Instructions burned: 509 (million)
% 5.84/2.09 % (7468)------------------------------
% 5.84/2.09 % (7468)------------------------------
% 5.84/2.09 % (7484)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_7160 for (2995ds/6Mi)
% 5.84/2.09 % (7486)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_7160 for (2995ds/343Mi)
% 5.84/2.09 % (7484)Instruction limit reached!
% 5.84/2.09 % (7484)------------------------------
% 5.84/2.09 % (7484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.84/2.09 % (7484)Termination reason: Unknown
% 5.84/2.09 % (7484)Termination phase: shuffling
% 5.84/2.09
% 5.84/2.09 % (7484)Memory used [KB]: 1663
% 5.84/2.09 % (7484)Time elapsed: 0.006 s
% 5.84/2.09 % (7484)Instructions burned: 7 (million)
% 5.84/2.09 % (7484)------------------------------
% 5.84/2.09 % (7484)------------------------------
% 5.84/2.10 % (7487)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_7160 for (2995ds/109Mi)
% 5.84/2.11 % (7488)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_7160 for (2995ds/253Mi)
% 6.37/2.12 % (7475)Instruction limit reached!
% 6.37/2.12 % (7475)------------------------------
% 6.37/2.12 % (7475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.37/2.12 % (7475)Termination reason: Unknown
% 6.37/2.12 % (7475)Termination phase: Saturation
% 6.37/2.12
% 6.37/2.12 % (7475)Memory used [KB]: 3326
% 6.37/2.12 % (7475)Time elapsed: 0.118 s
% 6.37/2.12 % (7475)Instructions burned: 435 (million)
% 6.37/2.12 % (7475)------------------------------
% 6.37/2.12 % (7475)------------------------------
% 6.37/2.12 % (7487)Instruction limit reached!
% 6.37/2.12 % (7487)------------------------------
% 6.37/2.12 % (7487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.37/2.12 % (7487)Termination reason: Unknown
% 6.37/2.12 % (7487)Termination phase: SInE selection
% 6.37/2.12
% 6.37/2.12 % (7487)Memory used [KB]: 2814
% 6.37/2.12 % (7487)Time elapsed: 0.031 s
% 6.37/2.12 % (7487)Instructions burned: 111 (million)
% 6.37/2.12 % (7487)------------------------------
% 6.37/2.12 % (7487)------------------------------
% 6.37/2.13 % (7485)Instruction limit reached!
% 6.37/2.13 % (7485)------------------------------
% 6.37/2.13 % (7485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.37/2.13 % (7485)Termination reason: Unknown
% 6.37/2.13 % (7485)Termination phase: Preprocessing 3
% 6.37/2.13
% 6.37/2.13 % (7485)Memory used [KB]: 5245
% 6.37/2.13 % (7485)Time elapsed: 0.046 s
% 6.37/2.13 % (7485)Instructions burned: 150 (million)
% 6.37/2.13 % (7485)------------------------------
% 6.37/2.13 % (7485)------------------------------
% 6.37/2.13 % (7489)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_7160 for (2994ds/140Mi)
% 6.37/2.13 % (7490)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_7160 for (2994ds/614Mi)
% 6.37/2.14 % (7491)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_7160 for (2994ds/202Mi)
% 6.37/2.15 % (7479)Instruction limit reached!
% 6.37/2.15 % (7479)------------------------------
% 6.37/2.15 % (7479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.37/2.15 % (7479)Termination reason: Unknown
% 6.37/2.15 % (7479)Termination phase: Saturation
% 6.37/2.15
% 6.37/2.15 % (7479)Memory used [KB]: 7803
% 6.37/2.15 % (7479)Time elapsed: 0.115 s
% 6.37/2.15 % (7479)Instructions burned: 453 (million)
% 6.37/2.15 % (7479)------------------------------
% 6.37/2.15 % (7479)------------------------------
% 6.37/2.16 % (7492)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_7160 for (2994ds/339Mi)
% 6.37/2.16 % (7489)Instruction limit reached!
% 6.37/2.16 % (7489)------------------------------
% 6.37/2.16 % (7489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.37/2.16 % (7489)Termination reason: Unknown
% 6.37/2.16 % (7489)Termination phase: Property scanning
% 6.37/2.16
% 6.37/2.16 % (7489)Memory used [KB]: 2942
% 6.37/2.16 % (7489)Time elapsed: 0.039 s
% 6.37/2.16 % (7489)Instructions burned: 141 (million)
% 6.37/2.16 % (7489)------------------------------
% 6.37/2.16 % (7489)------------------------------
% 6.37/2.17 % (7493)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_7160 for (2994ds/283Mi)
% 6.37/2.18 % (7486)Instruction limit reached!
% 6.37/2.18 % (7486)------------------------------
% 6.37/2.18 % (7486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.37/2.18 % (7486)Termination reason: Unknown
% 6.37/2.18 % (7486)Termination phase: Saturation
% 6.37/2.18
% 6.37/2.18 % (7486)Memory used [KB]: 8443
% 6.37/2.18 % (7486)Time elapsed: 0.092 s
% 6.37/2.18 % (7486)Instructions burned: 346 (million)
% 6.37/2.18 % (7486)------------------------------
% 6.37/2.18 % (7486)------------------------------
% 6.37/2.19 % (7494)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_7160 for (2994ds/134Mi)
% 6.82/2.20 % (7491)Instruction limit reached!
% 6.82/2.20 % (7491)------------------------------
% 6.82/2.20 % (7491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.82/2.20 % (7491)Termination reason: Unknown
% 6.82/2.20 % (7491)Termination phase: Property scanning
% 6.82/2.20
% 6.82/2.20 % (7491)Memory used [KB]: 5628
% 6.82/2.20 % (7491)Time elapsed: 0.061 s
% 6.82/2.20 % (7491)Instructions burned: 202 (million)
% 6.82/2.20 % (7491)------------------------------
% 6.82/2.20 % (7491)------------------------------
% 6.82/2.21 % (7495)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_7160 for (2994ds/298Mi)
% 6.82/2.22 % (7494)Instruction limit reached!
% 6.82/2.22 % (7494)------------------------------
% 6.82/2.22 % (7494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.82/2.22 % (7494)Termination reason: Unknown
% 6.82/2.22 % (7494)Termination phase: Property scanning
% 6.82/2.22
% 6.82/2.22 % (7494)Memory used [KB]: 2942
% 6.82/2.22 % (7494)Time elapsed: 0.036 s
% 6.82/2.22 % (7494)Instructions burned: 134 (million)
% 6.82/2.22 % (7494)------------------------------
% 6.82/2.22 % (7494)------------------------------
% 6.82/2.22 % (7488)Instruction limit reached!
% 6.82/2.22 % (7488)------------------------------
% 6.82/2.22 % (7488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.82/2.22 % (7488)Termination reason: Unknown
% 6.82/2.22 % (7488)Termination phase: Property scanning
% 6.82/2.22
% 6.82/2.22 % (7488)Memory used [KB]: 5884
% 6.82/2.22 % (7488)Time elapsed: 0.119 s
% 6.82/2.22 % (7488)Instructions burned: 256 (million)
% 6.82/2.22 % (7488)------------------------------
% 6.82/2.22 % (7488)------------------------------
% 6.82/2.23 % (7496)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_7160 for (2993ds/192Mi)
% 6.82/2.24 % (7497)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_7160 for (2993ds/258Mi)
% 6.82/2.25 % (7493)Instruction limit reached!
% 6.82/2.25 % (7493)------------------------------
% 6.82/2.25 % (7493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.82/2.25 % (7493)Termination reason: Unknown
% 6.82/2.25 % (7493)Termination phase: Saturation
% 6.82/2.25
% 6.82/2.25 % (7493)Memory used [KB]: 7675
% 6.82/2.25 % (7493)Time elapsed: 0.074 s
% 6.82/2.25 % (7493)Instructions burned: 286 (million)
% 6.82/2.25 % (7493)------------------------------
% 6.82/2.25 % (7493)------------------------------
% 6.82/2.25 % (7492)Instruction limit reached!
% 6.82/2.25 % (7492)------------------------------
% 6.82/2.25 % (7492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.82/2.25 % (7492)Termination reason: Unknown
% 6.82/2.25 % (7492)Termination phase: Saturation
% 6.82/2.25
% 6.82/2.25 % (7492)Memory used [KB]: 8315
% 6.82/2.25 % (7492)Time elapsed: 0.095 s
% 6.82/2.25 % (7492)Instructions burned: 342 (million)
% 6.82/2.25 % (7492)------------------------------
% 6.82/2.25 % (7492)------------------------------
% 6.82/2.26 % (7498)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_7160 for (2993ds/90Mi)
% 6.82/2.26 % (7499)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_7160 for (2993ds/231Mi)
% 6.82/2.28 % (7498)Instruction limit reached!
% 6.82/2.28 % (7498)------------------------------
% 6.82/2.28 % (7498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.82/2.28 % (7498)Termination reason: Unknown
% 6.82/2.28 % (7498)Termination phase: Property scanning
% 6.82/2.28
% 6.82/2.28 % (7498)Memory used [KB]: 2814
% 6.82/2.28 % (7498)Time elapsed: 0.025 s
% 6.82/2.28 % (7498)Instructions burned: 91 (million)
% 6.82/2.28 % (7498)------------------------------
% 6.82/2.28 % (7498)------------------------------
% 6.82/2.28 % (7495)Instruction limit reached!
% 6.82/2.28 % (7495)------------------------------
% 6.82/2.28 % (7495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.82/2.28 % (7495)Termination reason: Unknown
% 6.82/2.28 % (7495)Termination phase: Saturation
% 6.82/2.28
% 6.82/2.28 % (7495)Memory used [KB]: 7675
% 6.82/2.28 % (7495)Time elapsed: 0.076 s
% 6.82/2.28 % (7495)Instructions burned: 301 (million)
% 6.82/2.28 % (7495)------------------------------
% 6.82/2.28 % (7495)------------------------------
% 6.82/2.28 % (7496)Instruction limit reached!
% 6.82/2.28 % (7496)------------------------------
% 6.82/2.28 % (7496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.82/2.28 % (7496)Termination reason: Unknown
% 6.82/2.28 % (7496)Termination phase: Saturation
% 6.82/2.28
% 6.82/2.28 % (7496)Memory used [KB]: 3070
% 6.82/2.28 % (7496)Time elapsed: 0.050 s
% 6.82/2.28 % (7496)Instructions burned: 192 (million)
% 6.82/2.28 % (7496)------------------------------
% 6.82/2.28 % (7496)------------------------------
% 6.82/2.29 % (7500)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_7160 for (2993ds/458Mi)
% 6.82/2.29 % (7501)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_7160 for (2993ds/31Mi)
% 6.82/2.29 % (7502)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_7160 for (2993ds/297Mi)
% 7.54/2.30 % (7501)Instruction limit reached!
% 7.54/2.30 % (7501)------------------------------
% 7.54/2.30 % (7501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.30 % (7501)Termination reason: Unknown
% 7.54/2.30 % (7501)Termination phase: shuffling
% 7.54/2.30
% 7.54/2.30 % (7501)Memory used [KB]: 2174
% 7.54/2.30 % (7501)Time elapsed: 0.010 s
% 7.54/2.30 % (7501)Instructions burned: 31 (million)
% 7.54/2.30 % (7501)------------------------------
% 7.54/2.30 % (7501)------------------------------
% 7.54/2.31 % (7497)Instruction limit reached!
% 7.54/2.31 % (7497)------------------------------
% 7.54/2.31 % (7497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.31 % (7497)Termination reason: Unknown
% 7.54/2.31 % (7497)Termination phase: Saturation
% 7.54/2.31
% 7.54/2.31 % (7497)Memory used [KB]: 8059
% 7.54/2.31 % (7497)Time elapsed: 0.072 s
% 7.54/2.31 % (7497)Instructions burned: 258 (million)
% 7.54/2.31 % (7497)------------------------------
% 7.54/2.31 % (7497)------------------------------
% 7.54/2.31 % (7503)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_7160 for (2993ds/987Mi)
% 7.54/2.31 % (7490)Instruction limit reached!
% 7.54/2.31 % (7490)------------------------------
% 7.54/2.31 % (7490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.31 % (7490)Termination reason: Unknown
% 7.54/2.31 % (7490)Termination phase: Saturation
% 7.54/2.31
% 7.54/2.31 % (7490)Memory used [KB]: 10362
% 7.54/2.31 % (7490)Time elapsed: 0.176 s
% 7.54/2.31 % (7490)Instructions burned: 614 (million)
% 7.54/2.31 % (7490)------------------------------
% 7.54/2.31 % (7490)------------------------------
% 7.54/2.32 % (7504)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_7160 for (2993ds/182Mi)
% 7.54/2.32 % (7505)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_7160 for (2993ds/182Mi)
% 7.54/2.32 % (7472)Instruction limit reached!
% 7.54/2.32 % (7472)------------------------------
% 7.54/2.32 % (7472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.32 % (7472)Termination reason: Unknown
% 7.54/2.32 % (7472)Termination phase: Saturation
% 7.54/2.32
% 7.54/2.32 % (7472)Memory used [KB]: 13176
% 7.54/2.32 % (7472)Time elapsed: 0.345 s
% 7.54/2.32 % (7472)Instructions burned: 1087 (million)
% 7.54/2.32 % (7472)------------------------------
% 7.54/2.32 % (7472)------------------------------
% 7.54/2.32 % (7499)Instruction limit reached!
% 7.54/2.32 % (7499)------------------------------
% 7.54/2.32 % (7499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.32 % (7499)Termination reason: Unknown
% 7.54/2.32 % (7499)Termination phase: Property scanning
% 7.54/2.32
% 7.54/2.32 % (7499)Memory used [KB]: 4349
% 7.54/2.32 % (7499)Time elapsed: 0.061 s
% 7.54/2.32 % (7499)Instructions burned: 232 (million)
% 7.54/2.32 % (7499)------------------------------
% 7.54/2.32 % (7499)------------------------------
% 7.54/2.33 % (7506)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_7160 for (2992ds/154Mi)
% 7.54/2.33 % (7507)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_7160 for (2992ds/79Mi)
% 7.54/2.35 % (7507)Instruction limit reached!
% 7.54/2.35 % (7507)------------------------------
% 7.54/2.35 % (7507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.35 % (7507)Termination reason: Unknown
% 7.54/2.35 % (7507)Termination phase: Property scanning
% 7.54/2.35
% 7.54/2.35 % (7507)Memory used [KB]: 2814
% 7.54/2.35 % (7507)Time elapsed: 0.022 s
% 7.54/2.35 % (7507)Instructions burned: 80 (million)
% 7.54/2.35 % (7507)------------------------------
% 7.54/2.35 % (7507)------------------------------
% 7.54/2.36 % (7508)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_7160 for (2992ds/216Mi)
% 7.54/2.37 % (7502)Instruction limit reached!
% 7.54/2.37 % (7502)------------------------------
% 7.54/2.37 % (7502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.37 % (7502)Termination reason: Unknown
% 7.54/2.37 % (7502)Termination phase: Saturation
% 7.54/2.37
% 7.54/2.37 % (7502)Memory used [KB]: 7675
% 7.54/2.37 % (7502)Time elapsed: 0.075 s
% 7.54/2.37 % (7502)Instructions burned: 299 (million)
% 7.54/2.37 % (7502)------------------------------
% 7.54/2.37 % (7502)------------------------------
% 7.54/2.37 % (7504)Instruction limit reached!
% 7.54/2.37 % (7504)------------------------------
% 7.54/2.37 % (7504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.37 % (7504)Termination reason: Unknown
% 7.54/2.37 % (7504)Termination phase: Property scanning
% 7.54/2.37
% 7.54/2.37 % (7504)Memory used [KB]: 3070
% 7.54/2.37 % (7504)Time elapsed: 0.051 s
% 7.54/2.37 % (7504)Instructions burned: 182 (million)
% 7.54/2.37 % (7504)------------------------------
% 7.54/2.37 % (7504)------------------------------
% 7.54/2.37 % (7506)Instruction limit reached!
% 7.54/2.37 % (7506)------------------------------
% 7.54/2.37 % (7506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.37 % (7506)Termination reason: Unknown
% 7.54/2.37 % (7506)Termination phase: Function definition elimination
% 7.54/2.37
% 7.54/2.37 % (7506)Memory used [KB]: 2942
% 7.54/2.37 % (7506)Time elapsed: 0.040 s
% 7.54/2.37 % (7506)Instructions burned: 155 (million)
% 7.54/2.37 % (7506)------------------------------
% 7.54/2.37 % (7506)------------------------------
% 7.54/2.37 % (7505)Instruction limit reached!
% 7.54/2.37 % (7505)------------------------------
% 7.54/2.37 % (7505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.37 % (7505)Termination reason: Unknown
% 7.54/2.37 % (7505)Termination phase: Property scanning
% 7.54/2.37
% 7.54/2.37 % (7505)Memory used [KB]: 5756
% 7.54/2.37 % (7505)Time elapsed: 0.054 s
% 7.54/2.37 % (7505)Instructions burned: 184 (million)
% 7.54/2.37 % (7505)------------------------------
% 7.54/2.37 % (7505)------------------------------
% 7.54/2.38 % (7509)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_7160 for (2992ds/114Mi)
% 7.54/2.38 % (7510)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_7160 for (2992ds/922Mi)
% 7.54/2.38 % (7512)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_7160 for (2992ds/164Mi)
% 7.54/2.39 % (7511)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_7160 for (2992ds/182Mi)
% 8.22/2.41 % (7509)Instruction limit reached!
% 8.22/2.41 % (7509)------------------------------
% 8.22/2.41 % (7509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.22/2.41 % (7509)Termination reason: Unknown
% 8.22/2.41 % (7509)Termination phase: Property scanning
% 8.22/2.41
% 8.22/2.41 % (7509)Memory used [KB]: 2942
% 8.22/2.41 % (7509)Time elapsed: 0.031 s
% 8.22/2.41 % (7509)Instructions burned: 115 (million)
% 8.22/2.41 % (7509)------------------------------
% 8.22/2.41 % (7509)------------------------------
% 8.22/2.41 % (7500)Instruction limit reached!
% 8.22/2.41 % (7500)------------------------------
% 8.22/2.41 % (7500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.22/2.41 % (7500)Termination reason: Unknown
% 8.22/2.41 % (7500)Termination phase: Saturation
% 8.22/2.41
% 8.22/2.41 % (7500)Memory used [KB]: 9722
% 8.22/2.41 % (7500)Time elapsed: 0.122 s
% 8.22/2.41 % (7500)Instructions burned: 459 (million)
% 8.22/2.41 % (7500)------------------------------
% 8.22/2.41 % (7500)------------------------------
% 8.22/2.42 % (7513)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_7160 for (2991ds/50Mi)
% 8.22/2.42 % (7508)Instruction limit reached!
% 8.22/2.42 % (7508)------------------------------
% 8.22/2.42 % (7508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.22/2.42 % (7508)Termination reason: Unknown
% 8.22/2.42 % (7508)Termination phase: Property scanning
% 8.22/2.42
% 8.22/2.42 % (7508)Memory used [KB]: 3198
% 8.22/2.42 % (7508)Time elapsed: 0.055 s
% 8.22/2.42 % (7508)Instructions burned: 219 (million)
% 8.22/2.42 % (7508)------------------------------
% 8.22/2.42 % (7508)------------------------------
% 8.22/2.42 % (7514)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_7160 for (2991ds/368Mi)
% 8.22/2.42 % (7512)Instruction limit reached!
% 8.22/2.42 % (7512)------------------------------
% 8.22/2.42 % (7512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.22/2.42 % (7512)Termination reason: Unknown
% 8.22/2.42 % (7512)Termination phase: Property scanning
% 8.22/2.42
% 8.22/2.42 % (7512)Memory used [KB]: 2942
% 8.22/2.42 % (7512)Time elapsed: 0.042 s
% 8.22/2.42 % (7512)Instructions burned: 164 (million)
% 8.22/2.42 % (7512)------------------------------
% 8.22/2.42 % (7512)------------------------------
% 8.22/2.43 % (7515)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_7160 for (2991ds/1021Mi)
% 8.22/2.43 % (7513)Instruction limit reached!
% 8.22/2.43 % (7513)------------------------------
% 8.22/2.43 % (7513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.22/2.43 % (7513)Termination reason: Unknown
% 8.22/2.43 % (7513)Termination phase: shuffling
% 8.22/2.43
% 8.22/2.43 % (7513)Memory used [KB]: 2558
% 8.22/2.43 % (7513)Time elapsed: 0.015 s
% 8.22/2.43 % (7513)Instructions burned: 51 (million)
% 8.22/2.43 % (7513)------------------------------
% 8.22/2.43 % (7513)------------------------------
% 8.22/2.43 % (7516)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_7160 for (2991ds/267Mi)
% 8.22/2.44 % (7517)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_7160 for (2991ds/204Mi)
% 8.22/2.46 % (7511)Instruction limit reached!
% 8.22/2.46 % (7511)------------------------------
% 8.22/2.46 % (7511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.22/2.46 % (7511)Termination reason: Unknown
% 8.22/2.46 % (7511)Termination phase: Property scanning
% 8.22/2.46
% 8.22/2.46 % (7511)Memory used [KB]: 3198
% 8.22/2.46 % (7511)Time elapsed: 0.076 s
% 8.22/2.46 % (7511)Instructions burned: 183 (million)
% 8.22/2.46 % (7511)------------------------------
% 8.22/2.46 % (7511)------------------------------
% 8.22/2.47 % (7518)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_7160 for (2991ds/26Mi)
% 8.22/2.48 % (7518)Instruction limit reached!
% 8.22/2.48 % (7518)------------------------------
% 8.22/2.48 % (7518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.22/2.48 % (7518)Termination reason: Unknown
% 8.22/2.48 % (7518)Termination phase: shuffling
% 8.22/2.48
% 8.22/2.48 % (7518)Memory used [KB]: 2046
% 8.22/2.48 % (7518)Time elapsed: 0.008 s
% 8.22/2.48 % (7518)Instructions burned: 26 (million)
% 8.22/2.48 % (7518)------------------------------
% 8.22/2.48 % (7518)------------------------------
% 8.22/2.49 % (7519)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_7160 for (2991ds/53Mi)
% 8.22/2.49 % (7517)Instruction limit reached!
% 8.22/2.49 % (7517)------------------------------
% 8.22/2.49 % (7517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.22/2.49 % (7517)Termination reason: Unknown
% 8.22/2.49 % (7517)Termination phase: Property scanning
% 8.22/2.49
% 8.22/2.49 % (7517)Memory used [KB]: 3070
% 8.22/2.49 % (7517)Time elapsed: 0.052 s
% 8.22/2.49 % (7517)Instructions burned: 204 (million)
% 8.22/2.49 % (7517)------------------------------
% 8.22/2.49 % (7517)------------------------------
% 8.68/2.50 % (7516)Instruction limit reached!
% 8.68/2.50 % (7516)------------------------------
% 8.68/2.50 % (7516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.68/2.50 % (7516)Termination reason: Unknown
% 8.68/2.50 % (7516)Termination phase: Saturation
% 8.68/2.50
% 8.68/2.50 % (7516)Memory used [KB]: 7675
% 8.68/2.50 % (7516)Time elapsed: 0.068 s
% 8.68/2.50 % (7516)Instructions burned: 269 (million)
% 8.68/2.50 % (7516)------------------------------
% 8.68/2.50 % (7516)------------------------------
% 8.68/2.50 % (7520)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_7160 for (2991ds/4436Mi)
% 8.68/2.50 % (7519)Instruction limit reached!
% 8.68/2.50 % (7519)------------------------------
% 8.68/2.50 % (7519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.68/2.50 % (7519)Termination reason: Unknown
% 8.68/2.50 % (7519)Termination phase: shuffling
% 8.68/2.50
% 8.68/2.50 % (7519)Memory used [KB]: 2558
% 8.68/2.50 % (7519)Time elapsed: 0.016 s
% 8.68/2.50 % (7519)Instructions burned: 53 (million)
% 8.68/2.50 % (7519)------------------------------
% 8.68/2.50 % (7519)------------------------------
% 8.68/2.51 % (7521)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_7160 for (2990ds/1539Mi)
% 8.68/2.51 % (7522)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_7160 for (2990ds/408Mi)
% 8.68/2.52 % (7514)Instruction limit reached!
% 8.68/2.52 % (7514)------------------------------
% 8.68/2.52 % (7514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.68/2.52 % (7514)Termination reason: Unknown
% 8.68/2.52 % (7514)Termination phase: Saturation
% 8.68/2.52
% 8.68/2.52 % (7514)Memory used [KB]: 9466
% 8.68/2.52 % (7514)Time elapsed: 0.099 s
% 8.68/2.52 % (7514)Instructions burned: 370 (million)
% 8.68/2.52 % (7514)------------------------------
% 8.68/2.52 % (7514)------------------------------
% 8.68/2.53 % (7523)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_7160 for (2990ds/5205Mi)
% 8.68/2.56 % (7503)Instruction limit reached!
% 8.68/2.56 % (7503)------------------------------
% 8.68/2.56 % (7503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.68/2.56 % (7503)Termination reason: Unknown
% 8.68/2.56 % (7503)Termination phase: Saturation
% 8.68/2.56
% 8.68/2.56 % (7503)Memory used [KB]: 14200
% 8.68/2.56 % (7503)Time elapsed: 0.272 s
% 8.68/2.56 % (7503)Instructions burned: 989 (million)
% 8.68/2.56 % (7503)------------------------------
% 8.68/2.56 % (7503)------------------------------
% 8.68/2.57 % (7524)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_7160 for (2990ds/1913Mi)
% 9.15/2.63 % (7522)Instruction limit reached!
% 9.15/2.63 % (7522)------------------------------
% 9.15/2.63 % (7522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.15/2.63 % (7522)Termination reason: Unknown
% 9.15/2.63 % (7522)Termination phase: Saturation
% 9.15/2.63
% 9.15/2.63 % (7522)Memory used [KB]: 11897
% 9.15/2.63 % (7522)Time elapsed: 0.119 s
% 9.15/2.63 % (7522)Instructions burned: 410 (million)
% 9.15/2.63 % (7522)------------------------------
% 9.15/2.63 % (7522)------------------------------
% 9.15/2.64 % (7525)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_7160 for (2989ds/4350Mi)
% 9.15/2.67 % (7510)Instruction limit reached!
% 9.15/2.67 % (7510)------------------------------
% 9.15/2.67 % (7510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.15/2.67 % (7510)Termination reason: Unknown
% 9.15/2.67 % (7510)Termination phase: Saturation
% 9.15/2.67
% 9.15/2.67 % (7510)Memory used [KB]: 12792
% 9.15/2.67 % (7510)Time elapsed: 0.295 s
% 9.15/2.67 % (7510)Instructions burned: 924 (million)
% 9.15/2.67 % (7510)------------------------------
% 9.15/2.67 % (7510)------------------------------
% 9.15/2.68 % (7526)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_7160 for (2989ds/68Mi)
% 9.60/2.70 % (7526)Instruction limit reached!
% 9.60/2.70 % (7526)------------------------------
% 9.60/2.70 % (7526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.60/2.70 % (7526)Termination reason: Unknown
% 9.60/2.70 % (7526)Termination phase: Property scanning
% 9.60/2.70
% 9.60/2.70 % (7526)Memory used [KB]: 2814
% 9.60/2.70 % (7526)Time elapsed: 0.020 s
% 9.60/2.70 % (7526)Instructions burned: 71 (million)
% 9.60/2.70 % (7526)------------------------------
% 9.60/2.70 % (7526)------------------------------
% 9.60/2.71 % (7527)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_7160 for (2988ds/358Mi)
% 9.60/2.74 % (7515)Instruction limit reached!
% 9.60/2.74 % (7515)------------------------------
% 9.60/2.74 % (7515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.60/2.74 % (7515)Termination reason: Unknown
% 9.60/2.74 % (7515)Termination phase: Saturation
% 9.60/2.74
% 9.60/2.74 % (7515)Memory used [KB]: 13176
% 9.60/2.74 % (7515)Time elapsed: 0.313 s
% 9.60/2.74 % (7515)Instructions burned: 1021 (million)
% 9.60/2.74 % (7515)------------------------------
% 9.60/2.74 % (7515)------------------------------
% 9.60/2.75 % (7528)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_7160 for (2988ds/31Mi)
% 9.60/2.76 % (7528)Instruction limit reached!
% 9.60/2.76 % (7528)------------------------------
% 9.60/2.76 % (7528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.60/2.76 % (7528)Termination reason: Unknown
% 9.60/2.76 % (7528)Termination phase: shuffling
% 9.60/2.76
% 9.60/2.76 % (7528)Memory used [KB]: 2302
% 9.60/2.76 % (7528)Time elapsed: 0.010 s
% 9.60/2.76 % (7528)Instructions burned: 31 (million)
% 9.60/2.76 % (7528)------------------------------
% 9.60/2.76 % (7528)------------------------------
% 9.60/2.77 % (7529)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_7160 for (2988ds/279Mi)
% 9.97/2.80 % (7527)Instruction limit reached!
% 9.97/2.80 % (7527)------------------------------
% 9.97/2.80 % (7527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.97/2.80 % (7527)Termination reason: Unknown
% 9.97/2.80 % (7527)Termination phase: Saturation
% 9.97/2.80
% 9.97/2.80 % (7527)Memory used [KB]: 8443
% 9.97/2.80 % (7527)Time elapsed: 0.093 s
% 9.97/2.80 % (7527)Instructions burned: 360 (million)
% 9.97/2.80 % (7527)------------------------------
% 9.97/2.80 % (7527)------------------------------
% 9.97/2.81 % (7530)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_7160 for (2987ds/258Mi)
% 9.97/2.84 % (7529)Instruction limit reached!
% 9.97/2.84 % (7529)------------------------------
% 9.97/2.84 % (7529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.97/2.84 % (7529)Termination reason: Unknown
% 9.97/2.84 % (7529)Termination phase: Saturation
% 9.97/2.84
% 9.97/2.84 % (7529)Memory used [KB]: 7675
% 9.97/2.84 % (7529)Time elapsed: 0.070 s
% 9.97/2.84 % (7529)Instructions burned: 279 (million)
% 9.97/2.84 % (7529)------------------------------
% 9.97/2.84 % (7529)------------------------------
% 9.97/2.85 % (7531)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_7160 for (2987ds/26Mi)
% 9.97/2.85 % (7531)Instruction limit reached!
% 9.97/2.85 % (7531)------------------------------
% 9.97/2.85 % (7531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.97/2.85 % (7531)Termination reason: Unknown
% 9.97/2.85 % (7531)Termination phase: shuffling
% 9.97/2.85
% 9.97/2.85 % (7531)Memory used [KB]: 2046
% 9.97/2.85 % (7531)Time elapsed: 0.008 s
% 9.97/2.85 % (7531)Instructions burned: 27 (million)
% 9.97/2.85 % (7531)------------------------------
% 9.97/2.85 % (7531)------------------------------
% 9.97/2.86 % (7532)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_7160 for (2987ds/995Mi)
% 9.97/2.88 % (7530)Instruction limit reached!
% 9.97/2.88 % (7530)------------------------------
% 9.97/2.88 % (7530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.97/2.88 % (7530)Termination reason: Unknown
% 9.97/2.88 % (7530)Termination phase: Saturation
% 9.97/2.88
% 9.97/2.88 % (7530)Memory used [KB]: 8315
% 9.97/2.88 % (7530)Time elapsed: 0.069 s
% 9.97/2.88 % (7530)Instructions burned: 261 (million)
% 9.97/2.88 % (7530)------------------------------
% 9.97/2.88 % (7530)------------------------------
% 9.97/2.89 % (7533)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_7160 for (2987ds/373Mi)
% 10.24/2.98 % (7521)Instruction limit reached!
% 10.24/2.98 % (7521)------------------------------
% 10.24/2.98 % (7521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.24/2.98 % (7521)Termination reason: Unknown
% 10.24/2.98 % (7521)Termination phase: Saturation
% 10.24/2.98
% 10.24/2.98 % (7521)Memory used [KB]: 11257
% 10.24/2.98 % (7521)Time elapsed: 0.470 s
% 10.24/2.98 % (7521)Instructions burned: 1540 (million)
% 10.24/2.98 % (7521)------------------------------
% 10.24/2.98 % (7521)------------------------------
% 10.24/2.99 % (7534)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_7160 for (2986ds/253Mi)
% 10.24/2.99 % (7533)Instruction limit reached!
% 10.24/2.99 % (7533)------------------------------
% 10.24/2.99 % (7533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.24/2.99 % (7533)Termination reason: Unknown
% 10.24/2.99 % (7533)Termination phase: Saturation
% 10.24/2.99
% 10.24/2.99 % (7533)Memory used [KB]: 9466
% 10.24/2.99 % (7533)Time elapsed: 0.102 s
% 10.24/2.99 % (7533)Instructions burned: 376 (million)
% 10.24/2.99 % (7533)------------------------------
% 10.24/2.99 % (7533)------------------------------
% 10.24/3.00 % (7535)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_7160 for (2986ds/832Mi)
% 12.82/3.05 % (7534)Instruction limit reached!
% 12.82/3.05 % (7534)------------------------------
% 12.82/3.05 % (7534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.82/3.05 % (7534)Termination reason: Unknown
% 12.82/3.05 % (7534)Termination phase: Saturation
% 12.82/3.05
% 12.82/3.05 % (7534)Memory used [KB]: 7675
% 12.82/3.05 % (7534)Time elapsed: 0.064 s
% 12.82/3.05 % (7534)Instructions burned: 254 (million)
% 12.82/3.05 % (7534)------------------------------
% 12.82/3.05 % (7534)------------------------------
% 12.82/3.06 % (7536)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_7160 for (2985ds/668Mi)
% 13.47/3.14 % (7524)Instruction limit reached!
% 13.47/3.14 % (7524)------------------------------
% 13.47/3.14 % (7524)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.47/3.14 % (7524)Termination reason: Unknown
% 13.47/3.14 % (7524)Termination phase: Saturation
% 13.47/3.14
% 13.47/3.14 % (7524)Memory used [KB]: 6524
% 13.47/3.14 % (7524)Time elapsed: 0.575 s
% 13.47/3.14 % (7524)Instructions burned: 1914 (million)
% 13.47/3.14 % (7524)------------------------------
% 13.47/3.14 % (7524)------------------------------
% 13.47/3.15 % (7537)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_7160 for (2984ds/40Mi)
% 13.47/3.16 % (7537)Instruction limit reached!
% 13.47/3.16 % (7537)------------------------------
% 13.47/3.16 % (7537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.47/3.16 % (7537)Termination reason: Unknown
% 13.47/3.16 % (7537)Termination phase: shuffling
% 13.47/3.16
% 13.47/3.16 % (7537)Memory used [KB]: 2430
% 13.47/3.16 % (7537)Time elapsed: 0.012 s
% 13.47/3.16 % (7537)Instructions burned: 40 (million)
% 13.47/3.16 % (7537)------------------------------
% 13.47/3.16 % (7537)------------------------------
% 13.47/3.17 % (7538)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_7160 for (2984ds/294Mi)
% 13.47/3.18 % (7532)Instruction limit reached!
% 13.47/3.18 % (7532)------------------------------
% 13.47/3.18 % (7532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.47/3.18 % (7532)Termination reason: Unknown
% 13.47/3.18 % (7532)Termination phase: Saturation
% 13.47/3.18
% 13.47/3.18 % (7532)Memory used [KB]: 18293
% 13.47/3.18 % (7532)Time elapsed: 0.320 s
% 13.47/3.18 % (7532)Instructions burned: 995 (million)
% 13.47/3.18 % (7532)------------------------------
% 13.47/3.18 % (7532)------------------------------
% 13.47/3.19 % (7539)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_7160 for (2984ds/187Mi)
% 13.96/3.23 % (7536)Instruction limit reached!
% 13.96/3.23 % (7536)------------------------------
% 13.96/3.23 % (7536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.96/3.23 % (7536)Termination reason: Unknown
% 13.96/3.23 % (7536)Termination phase: Saturation
% 13.96/3.23
% 13.96/3.23 % (7536)Memory used [KB]: 12409
% 13.96/3.23 % (7536)Time elapsed: 0.167 s
% 13.96/3.23 % (7536)Instructions burned: 670 (million)
% 13.96/3.23 % (7536)------------------------------
% 13.96/3.23 % (7536)------------------------------
% 13.96/3.24 % (7540)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_7160 for (2983ds/371Mi)
% 13.96/3.24 % (7539)Instruction limit reached!
% 13.96/3.24 % (7539)------------------------------
% 13.96/3.24 % (7539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.96/3.24 % (7539)Termination reason: Unknown
% 13.96/3.24 % (7539)Termination phase: Property scanning
% 13.96/3.24
% 13.96/3.24 % (7539)Memory used [KB]: 3070
% 13.96/3.24 % (7539)Time elapsed: 0.052 s
% 13.96/3.24 % (7539)Instructions burned: 187 (million)
% 13.96/3.24 % (7539)------------------------------
% 13.96/3.24 % (7539)------------------------------
% 13.96/3.25 % (7538)Instruction limit reached!
% 13.96/3.25 % (7538)------------------------------
% 13.96/3.25 % (7538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.96/3.25 % (7538)Termination reason: Unknown
% 13.96/3.25 % (7538)Termination phase: Saturation
% 13.96/3.25
% 13.96/3.25 % (7538)Memory used [KB]: 7675
% 13.96/3.25 % (7538)Time elapsed: 0.075 s
% 13.96/3.25 % (7538)Instructions burned: 296 (million)
% 13.96/3.25 % (7538)------------------------------
% 13.96/3.25 % (7538)------------------------------
% 13.96/3.25 % (7535)Instruction limit reached!
% 13.96/3.25 % (7535)------------------------------
% 13.96/3.25 % (7535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.96/3.25 % (7535)Termination reason: Unknown
% 13.96/3.25 % (7535)Termination phase: Saturation
% 13.96/3.25
% 13.96/3.25 % (7535)Memory used [KB]: 12920
% 13.96/3.25 % (7535)Time elapsed: 0.252 s
% 13.96/3.25 % (7535)Instructions burned: 832 (million)
% 13.96/3.25 % (7535)------------------------------
% 13.96/3.25 % (7535)------------------------------
% 13.96/3.25 % (7541)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_7160 for (2983ds/1827Mi)
% 13.96/3.26 % (7542)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_7160 for (2983ds/70Mi)
% 13.96/3.26 % (7543)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_7160 for (2983ds/316Mi)
% 13.96/3.27 % (7542)Instruction limit reached!
% 13.96/3.27 % (7542)------------------------------
% 13.96/3.27 % (7542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.96/3.27 % (7542)Termination reason: Unknown
% 13.96/3.27 % (7542)Termination phase: Property scanning
% 13.96/3.27
% 13.96/3.27 % (7542)Memory used [KB]: 2814
% 13.96/3.27 % (7542)Time elapsed: 0.020 s
% 13.96/3.27 % (7542)Instructions burned: 72 (million)
% 13.96/3.27 % (7542)------------------------------
% 13.96/3.27 % (7542)------------------------------
% 13.96/3.28 % (7544)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_7160 for (2983ds/932Mi)
% 14.66/3.33 % (7540)Instruction limit reached!
% 14.66/3.33 % (7540)------------------------------
% 14.66/3.33 % (7540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.66/3.33 % (7540)Termination reason: Unknown
% 14.66/3.33 % (7540)Termination phase: Saturation
% 14.66/3.33
% 14.66/3.33 % (7540)Memory used [KB]: 8827
% 14.66/3.33 % (7540)Time elapsed: 0.098 s
% 14.66/3.33 % (7540)Instructions burned: 373 (million)
% 14.66/3.33 % (7540)------------------------------
% 14.66/3.33 % (7540)------------------------------
% 14.66/3.34 % (7543)Instruction limit reached!
% 14.66/3.34 % (7543)------------------------------
% 14.66/3.34 % (7543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.66/3.34 % (7543)Termination reason: Unknown
% 14.66/3.34 % (7543)Termination phase: Saturation
% 14.66/3.34
% 14.66/3.34 % (7543)Memory used [KB]: 7803
% 14.66/3.34 % (7543)Time elapsed: 0.080 s
% 14.66/3.34 % (7543)Instructions burned: 318 (million)
% 14.66/3.34 % (7543)------------------------------
% 14.66/3.34 % (7543)------------------------------
% 14.66/3.34 % (7545)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_7160 for (2982ds/4714Mi)
% 14.66/3.35 % (7546)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_7160 for (2982ds/8250Mi)
% 15.46/3.52 % (7544)Instruction limit reached!
% 15.46/3.52 % (7544)------------------------------
% 15.46/3.52 % (7544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.46/3.52 % (7544)Termination reason: Unknown
% 15.46/3.52 % (7544)Termination phase: Saturation
% 15.46/3.52
% 15.46/3.52 % (7544)Memory used [KB]: 16247
% 15.46/3.52 % (7544)Time elapsed: 0.234 s
% 15.46/3.52 % (7544)Instructions burned: 932 (million)
% 15.46/3.52 % (7544)------------------------------
% 15.46/3.52 % (7544)------------------------------
% 15.46/3.53 % (7547)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_7160 for (2980ds/770Mi)
% 16.30/3.73 % (7547)Instruction limit reached!
% 16.30/3.73 % (7547)------------------------------
% 16.30/3.73 % (7547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.30/3.73 % (7547)Termination reason: Unknown
% 16.30/3.73 % (7547)Termination phase: Saturation
% 16.30/3.73
% 16.30/3.73 % (7547)Memory used [KB]: 7931
% 16.30/3.73 % (7547)Time elapsed: 0.207 s
% 16.30/3.73 % (7547)Instructions burned: 771 (million)
% 16.30/3.73 % (7547)------------------------------
% 16.30/3.73 % (7547)------------------------------
% 16.30/3.74 % (7548)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_7160 for (2978ds/794Mi)
% 16.30/3.75 % (7541)Instruction limit reached!
% 16.30/3.75 % (7541)------------------------------
% 16.30/3.75 % (7541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.30/3.75 % (7541)Termination reason: Unknown
% 16.30/3.75 % (7541)Termination phase: Saturation
% 16.30/3.75
% 16.30/3.75 % (7541)Memory used [KB]: 22259
% 16.30/3.75 % (7541)Time elapsed: 0.500 s
% 16.30/3.75 % (7541)Instructions burned: 1827 (million)
% 16.30/3.75 % (7541)------------------------------
% 16.30/3.75 % (7541)------------------------------
% 16.30/3.76 % (7549)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_7160 for (2978ds/464Mi)
% 17.34/3.84 % (7523)Instruction limit reached!
% 17.34/3.84 % (7523)------------------------------
% 17.34/3.84 % (7523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.34/3.84 % (7523)Termination reason: Unknown
% 17.34/3.84 % (7523)Termination phase: Saturation
% 17.34/3.84
% 17.34/3.84 % (7523)Memory used [KB]: 19189
% 17.34/3.84 % (7523)Time elapsed: 1.309 s
% 17.34/3.84 % (7523)Instructions burned: 5208 (million)
% 17.34/3.84 % (7523)------------------------------
% 17.34/3.84 % (7523)------------------------------
% 17.34/3.85 % (7550)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_7160 for (2977ds/1376Mi)
% 17.34/3.89 % (7549)Instruction limit reached!
% 17.34/3.89 % (7549)------------------------------
% 17.34/3.89 % (7549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.34/3.89 % (7549)Termination reason: Unknown
% 17.34/3.89 % (7549)Termination phase: Saturation
% 17.34/3.89
% 17.34/3.89 % (7549)Memory used [KB]: 9722
% 17.34/3.89 % (7549)Time elapsed: 0.127 s
% 17.34/3.89 % (7549)Instructions burned: 465 (million)
% 17.34/3.89 % (7549)------------------------------
% 17.34/3.89 % (7549)------------------------------
% 17.34/3.90 % (7520)Instruction limit reached!
% 17.34/3.90 % (7520)------------------------------
% 17.34/3.90 % (7520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.34/3.90 % (7520)Termination reason: Unknown
% 17.34/3.90 % (7520)Termination phase: Saturation
% 17.34/3.90
% 17.34/3.90 % (7520)Memory used [KB]: 15735
% 17.34/3.90 % (7520)Time elapsed: 1.398 s
% 17.34/3.90 % (7520)Instructions burned: 4437 (million)
% 17.34/3.90 % (7520)------------------------------
% 17.34/3.90 % (7520)------------------------------
% 16.34/3.90 % (7551)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_7160 for (2977ds/906Mi)
% 16.34/3.91 % (7552)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_7160 for (2977ds/434Mi)
% 16.34/3.97 % (7525)Instruction limit reached!
% 16.34/3.97 % (7525)------------------------------
% 16.34/3.97 % (7525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.34/3.97 % (7525)Termination reason: Unknown
% 16.34/3.97 % (7525)Termination phase: Saturation
% 16.34/3.97
% 16.34/3.97 % (7525)Memory used [KB]: 14200
% 16.34/3.97 % (7525)Time elapsed: 1.329 s
% 16.34/3.97 % (7525)Instructions burned: 4352 (million)
% 16.34/3.97 % (7525)------------------------------
% 16.34/3.97 % (7525)------------------------------
% 16.34/3.97 % (7548)Instruction limit reached!
% 16.34/3.97 % (7548)------------------------------
% 16.34/3.97 % (7548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.34/3.97 % (7548)Termination reason: Unknown
% 16.34/3.97 % (7548)Termination phase: Saturation
% 16.34/3.97
% 16.34/3.97 % (7548)Memory used [KB]: 6396
% 16.34/3.97 % (7548)Time elapsed: 0.231 s
% 16.34/3.97 % (7548)Instructions burned: 794 (million)
% 16.34/3.97 % (7548)------------------------------
% 16.34/3.97 % (7548)------------------------------
% 16.34/3.98 % (7553)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_7160 for (2976ds/865Mi)
% 16.34/3.98 % (7554)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_7160 for (2976ds/593Mi)
% 19.91/4.03 % (7552)Instruction limit reached!
% 19.91/4.03 % (7552)------------------------------
% 19.91/4.03 % (7552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.91/4.03 % (7552)Termination reason: Unknown
% 19.91/4.03 % (7552)Termination phase: Saturation
% 19.91/4.03
% 19.91/4.03 % (7552)Memory used [KB]: 11897
% 19.91/4.03 % (7552)Time elapsed: 0.125 s
% 19.91/4.03 % (7552)Instructions burned: 435 (million)
% 19.91/4.03 % (7552)------------------------------
% 19.91/4.03 % (7552)------------------------------
% 19.91/4.03 % (7551)First to succeed.
% 19.91/4.04 % (7551)Refutation found. Thanks to Tanya!
% 19.91/4.04 % SZS status Theorem for DTF2THF_7160
% 19.91/4.04 % SZS output start Proof for DTF2THF_7160
% 19.91/4.04 thf(func_def_0, type, in: $i > $i > $o).
% 19.91/4.04 thf(func_def_1, type, exu: ($i > $o) > $o).
% 19.91/4.04 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 19.91/4.04 thf(func_def_8, type, powerset: $i > $i).
% 19.91/4.04 thf(func_def_10, type, setunion: $i > $i).
% 19.91/4.04 thf(func_def_19, type, descr: ($i > $o) > $i).
% 19.91/4.04 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 19.91/4.04 thf(func_def_26, type, prop2set: $o > $i).
% 19.91/4.04 thf(func_def_36, type, nonempty: $i > $o).
% 19.91/4.04 thf(func_def_69, type, set2prop: $i > $o).
% 19.91/4.04 thf(func_def_88, type, subset: $i > $i > $o).
% 19.91/4.04 thf(func_def_89, type, disjoint: $i > $i > $o).
% 19.91/4.04 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 19.91/4.04 thf(func_def_114, type, binunion: $i > $i > $i).
% 19.91/4.04 thf(func_def_122, type, binintersect: $i > $i > $i).
% 19.91/4.04 thf(func_def_135, type, regular: $i > $o).
% 19.91/4.04 thf(func_def_136, type, setminus: $i > $i > $i).
% 19.91/4.04 thf(func_def_147, type, symdiff: $i > $i > $i).
% 19.91/4.04 thf(func_def_153, type, iskpair: $i > $o).
% 19.91/4.04 thf(func_def_158, type, kpair: $i > $i > $i).
% 19.91/4.04 thf(func_def_160, type, cartprod: $i > $i > $i).
% 19.91/4.04 thf(func_def_177, type, singleton: $i > $o).
% 19.91/4.04 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 19.91/4.04 thf(func_def_184, type, atmost1p: $i > $o).
% 19.91/4.04 thf(func_def_185, type, atleast2p: $i > $o).
% 19.91/4.04 thf(func_def_186, type, atmost2p: $i > $o).
% 19.91/4.04 thf(func_def_187, type, upairsetp: $i > $o).
% 19.91/4.04 thf(func_def_191, type, kfst: $i > $i).
% 19.91/4.04 thf(func_def_203, type, ksnd: $i > $i).
% 19.91/4.04 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 19.91/4.04 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 19.91/4.04 thf(func_def_222, type, func: $i > $i > $i > $o).
% 19.91/4.04 thf(func_def_223, type, funcSet: $i > $i > $i).
% 19.91/4.04 thf(func_def_226, type, ap: $i > $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_232, type, lam: $i > $i > ($i > $i) > $i).
% 19.91/4.04 thf(func_def_259, type, if: $i > $o > $i > $i > $i).
% 19.91/4.04 thf(func_def_323, type, breln1: $i > $i > $o).
% 19.91/4.04 thf(func_def_325, type, breln1Set: $i > $i).
% 19.91/4.04 thf(func_def_327, type, transitive: $i > $i > $o).
% 19.91/4.04 thf(func_def_328, type, antisymmetric: $i > $i > $o).
% 19.91/4.04 thf(func_def_329, type, reflexive: $i > $i > $o).
% 19.91/4.04 thf(func_def_330, type, refltransitive: $i > $i > $o).
% 19.91/4.04 thf(func_def_331, type, refllinearorder: $i > $i > $o).
% 19.91/4.04 thf(func_def_332, type, reflwellordering: $i > $i > $o).
% 19.91/4.04 thf(func_def_338, type, breln1invset: $i > $i > $i).
% 19.91/4.04 thf(func_def_342, type, breln1compset: $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_360, type, image1: $i > ($i > $i) > $i).
% 19.91/4.04 thf(func_def_364, type, injective: $i > $i > $i > $o).
% 19.91/4.04 thf(func_def_365, type, injFuncSet: $i > $i > $i).
% 19.91/4.04 thf(func_def_369, type, surjective: $i > $i > $i > $o).
% 19.91/4.04 thf(func_def_370, type, surjFuncSet: $i > $i > $i).
% 19.91/4.04 thf(func_def_393, type, sK2: $i > $i).
% 19.91/4.04 thf(func_def_396, type, sK5: $i > $i > ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_397, type, sK6: $i > $i > $i > ($i > $o) > $i).
% 19.91/4.04 thf(func_def_398, type, sK7: $i > $i > $i > ($i > $o) > $i).
% 19.91/4.04 thf(func_def_399, type, sK8: $i > $i > $i > ($i > $o) > $i).
% 19.91/4.04 thf(func_def_400, type, sK9: ($i > $o) > $i).
% 19.91/4.04 thf(func_def_401, type, sK10: ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_402, type, sK11: $i > $i > $o > $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_403, type, sK12: ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_404, type, sK13: $i > $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_405, type, sK14: $i > $i > $i).
% 19.91/4.04 thf(func_def_406, type, sK15: $i > $i > $i).
% 19.91/4.04 thf(func_def_407, type, sK16: $i > $i > $i).
% 19.91/4.04 thf(func_def_408, type, sK17: $i > $i).
% 19.91/4.04 thf(func_def_409, type, sK18: $i > $i > $i).
% 19.91/4.04 thf(func_def_410, type, sK19: $i > $i > $i).
% 19.91/4.04 thf(func_def_411, type, sK20: $i > $i).
% 19.91/4.04 thf(func_def_412, type, sK21: $i > $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_413, type, sK22: $i > $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_414, type, sK23: $i > ($i > $o) > $i).
% 19.91/4.04 thf(func_def_415, type, sK24: ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_416, type, sK25: $i > ($i > $i) > $i > $i).
% 19.91/4.04 thf(func_def_417, type, sK26: $i > ($i > $i) > $i).
% 19.91/4.04 thf(func_def_418, type, sK27: $i > ($i > $i) > $i > $i).
% 19.91/4.04 thf(func_def_419, type, sK28: $i > ($i > $i) > $i > $i).
% 19.91/4.04 thf(func_def_420, type, sK29: $i > ($i > $i) > $i > $i).
% 19.91/4.04 thf(func_def_421, type, sK30: ($i > $o) > $i).
% 19.91/4.04 thf(func_def_422, type, sK31: ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_423, type, sK32: $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_424, type, sK33: $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_425, type, sK34: $i > ($i > $i) > $i > $i).
% 19.91/4.04 thf(func_def_426, type, sK35: $i > ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_427, type, sK36: $i > ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_428, type, sK37: $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_429, type, sK38: $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_430, type, sK39: $i > $i).
% 19.91/4.04 thf(func_def_431, type, sK40: ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_432, type, sK41: ($i > $i > $o) > $i > $i > $i).
% 19.91/4.04 thf(func_def_433, type, sK42: ($i > $i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_434, type, sK43: ($i > $i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_435, type, sK44: ($i > $i > $o) > $i > $i > $i).
% 19.91/4.04 thf(func_def_436, type, sK45: ($i > $i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_437, type, sK46: ($i > $i > $o) > $i > $i > $i).
% 19.91/4.04 thf(func_def_438, type, sK47: ($i > $i > $o) > $i > $i > $i).
% 19.91/4.04 thf(func_def_439, type, sK48: ($i > $i > $o) > $i > $i > $i).
% 19.91/4.04 thf(func_def_440, type, sK49: $i > $i > ($i > $i) > $i).
% 19.91/4.04 thf(func_def_441, type, sK50: $i > $i > $o > $i).
% 19.91/4.04 thf(func_def_442, type, sK51: $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_443, type, sK52: $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_444, type, sK53: $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_445, type, sK54: $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_446, type, sK55: ($i > $i) > $i > $i).
% 19.91/4.04 thf(func_def_447, type, sK56: ($i > $i) > $i > $i > $i).
% 19.91/4.04 thf(func_def_448, type, sK57: ($i > $o) > ($i > $o) > $i).
% 19.91/4.04 thf(func_def_449, type, sK58: ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_450, type, sK59: ($i > $o) > ($i > $o) > $i).
% 19.91/4.04 thf(func_def_451, type, sK60: ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_452, type, sK61: ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_453, type, sK62: ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_454, type, sK63: ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_455, type, sK64: ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_456, type, sK65: ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_457, type, sK66: ($i > $o) > $i).
% 19.91/4.04 thf(func_def_458, type, sK67: ($i > $o) > $i).
% 19.91/4.04 thf(func_def_459, type, sK68: ($i > $o) > $i).
% 19.91/4.04 thf(func_def_460, type, sK69: ($i > $o) > $i).
% 19.91/4.04 thf(func_def_461, type, sK70: ($i > $o) > $i).
% 19.91/4.04 thf(func_def_462, type, sK71: $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_464, type, sK73: $i > $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_465, type, sK74: ($i > $i) > $i > $i > $i).
% 19.91/4.04 thf(func_def_466, type, sK75: ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_467, type, sK76: $i > $i > $i).
% 19.91/4.04 thf(func_def_468, type, sK77: $i > $i).
% 19.91/4.04 thf(func_def_469, type, sK78: $i > $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_470, type, sK79: ($i > $o) > $i).
% 19.91/4.04 thf(func_def_471, type, sK80: ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_472, type, sK81: ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_473, type, sK82: ($i > $o) > ($i > $o) > $i).
% 19.91/4.04 thf(func_def_474, type, sK83: ($i > $o) > ($i > $o) > $i).
% 19.91/4.04 thf(func_def_475, type, sK84: ($i > $o) > $i).
% 19.91/4.04 thf(func_def_476, type, sK85: ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_477, type, sK86: ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_478, type, sK87: ($i > $o) > $i).
% 19.91/4.04 thf(func_def_479, type, sK88: ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_480, type, sK89: ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_481, type, sK90: ($i > $o) > $i).
% 19.91/4.04 thf(func_def_482, type, sK91: ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_483, type, sK92: ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_484, type, sK93: ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_485, type, sK94: ($i > $o) > $i).
% 19.91/4.04 thf(func_def_486, type, sK95: ($i > $o) > $i).
% 19.91/4.04 thf(func_def_487, type, sK96: $i > $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_488, type, sK97: $i > $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_489, type, sK98: $i > $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_490, type, sK99: $i > $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_491, type, sK100: $i > $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_492, type, sK101: $i > $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_493, type, sK102: $i > $i).
% 19.91/4.04 thf(func_def_494, type, sK103: $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_495, type, sK104: $i > $i > $i).
% 19.91/4.04 thf(func_def_496, type, sK105: $i > $i > $i).
% 19.91/4.04 thf(func_def_497, type, sK106: $i > $i > $i).
% 19.91/4.04 thf(func_def_498, type, sK107: $i > ($i > $o) > $i).
% 19.91/4.04 thf(func_def_499, type, sK108: ($i > $i) > $i > $i > $i).
% 19.91/4.04 thf(func_def_500, type, sK109: $i > $i).
% 19.91/4.04 thf(func_def_501, type, sK110: $i > $i > $i).
% 19.91/4.04 thf(func_def_502, type, sK111: ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_503, type, sK112: ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_504, type, sK113: $i > ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_505, type, sK114: $i > ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_506, type, sK115: $i > ($i > $o) > ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_507, type, sK116: $i > $i > ($i > $o) > ($i > $o) > $i).
% 19.91/4.04 thf(func_def_508, type, sK117: $i > $i > $i).
% 19.91/4.04 thf(func_def_509, type, sK118: ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_510, type, sK119: $i > $i > $i).
% 19.91/4.04 thf(func_def_511, type, sK120: ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_512, type, sK121: $i > $i).
% 19.91/4.04 thf(func_def_513, type, sK122: $i > $i > ($i > $o) > $i).
% 19.91/4.04 thf(func_def_514, type, sK123: $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_515, type, sK124: $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_516, type, sK125: $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_517, type, sK126: $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_518, type, sK127: $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_519, type, sK128: $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_520, type, sK129: $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_521, type, sK130: $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_522, type, sK131: ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_523, type, sK132: ($i > $i) > $i > $i > $i).
% 19.91/4.04 thf(func_def_524, type, sK133: ($i > $i) > $i > $i > $i).
% 19.91/4.04 thf(func_def_525, type, sK134: ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_526, type, sK135: $i > $i > $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_527, type, sK136: $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_528, type, sK137: $i > $i > $i).
% 19.91/4.04 thf(func_def_529, type, sK138: ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_530, type, sK139: ($i > $o) > $i > $i).
% 19.91/4.04 thf(func_def_531, type, sK140: $i > $i > $i > $i > $i).
% 19.91/4.04 thf(func_def_532, type, ph141: !>[X0: $tType]:(X0)).
% 19.91/4.04 thf(f5889,plain,(
% 19.91/4.04 $false),
% 19.91/4.04 inference(trivial_inequality_removal,[status(thm)],[f5887])).
% 19.91/4.04 thf(f5887,plain,(
% 19.91/4.04 ($false = $true)),
% 19.91/4.04 inference(backward_demodulation,[status(thm)],[f5874,f5886])).
% 19.91/4.04 thf(f5886,plain,(
% 19.91/4.04 ((in @ (sK2 @ sK72) @ sK0) = $false)),
% 19.91/4.04 inference(trivial_inequality_removal,[status(thm)],[f5885])).
% 19.91/4.04 thf(f5885,plain,(
% 19.91/4.04 ((in @ (sK2 @ sK72) @ sK0) = $false) | (sK72 != sK72)),
% 19.91/4.04 inference(superposition,[status(thm)],[f3833,f5884])).
% 19.91/4.04 thf(f5884,plain,(
% 19.91/4.04 (sK72 = (ap @ sK0 @ sK1 @ sK3 @ (sK2 @ sK72)))),
% 19.91/4.04 inference(trivial_inequality_removal,[status(thm)],[f5881])).
% 19.91/4.04 thf(f5881,plain,(
% 19.91/4.04 (sK72 = (ap @ sK0 @ sK1 @ sK3 @ (sK2 @ sK72))) | ($true != $true)),
% 19.91/4.04 inference(superposition,[status(thm)],[f1356,f3829])).
% 19.91/4.04 thf(f3829,plain,(
% 19.91/4.04 ($true = (in @ sK72 @ sK1))),
% 19.91/4.04 inference(binary_proxy_clausification,[status(thm)],[f3827])).
% 19.91/4.04 thf(f3827,plain,(
% 19.91/4.04 ($false = ((in @ sK72 @ sK1) => (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK0) & ((ap @ sK0 @ sK1 @ sK3 @ Y0) = sK72))))))),
% 19.91/4.04 inference(beta_eta_normalization,[status(thm)],[f3826])).
% 19.91/4.04 thf(f3826,plain,(
% 19.91/4.04 ($false = ((^[Y0 : $i]: ((in @ Y0 @ sK1) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK0) & ((ap @ sK0 @ sK1 @ sK3 @ Y1) = Y0)))))) @ sK72))),
% 19.91/4.04 inference(sigma_clausification,[status(thm)],[f3825])).
% 19.91/4.04 thf(f3825,plain,(
% 19.91/4.04 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK1) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK0) & ((ap @ sK0 @ sK1 @ sK3 @ Y1) = Y0))))))) != $true)),
% 19.91/4.04 inference(beta_eta_normalization,[status(thm)],[f1626])).
% 19.91/4.04 thf(f1626,plain,(
% 19.91/4.04 (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((ap @ Y0 @ Y1 @ Y2 @ Y4) = Y3)))))))))))) @ sK0 @ sK1 @ sK3) != $true)),
% 19.91/4.04 inference(definition_unfolding,[status(thm)],[f1357,f1035])).
% 19.91/4.04 thf(f1035,plain,(
% 19.91/4.04 (surjective = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((ap @ Y0 @ Y1 @ Y2 @ Y4) = Y3)))))))))))))),
% 19.91/4.04 inference(cnf_transformation,[status(thm)],[f889])).
% 19.91/4.04 thf(f889,plain,(
% 19.91/4.04 (surjective = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((ap @ Y0 @ Y1 @ Y2 @ Y4) = Y3)))))))))))))),
% 19.91/4.04 inference(fool_elimination,[status(thm)],[f888])).
% 19.91/4.04 thf(f888,plain,(
% 19.91/4.04 (surjective = (^[X0 : $i, X1 : $i, X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X1) => ? [X4 : $i] : (((ap @ X0 @ X1 @ X2 @ X4) = X3) & (in @ X4 @ X0))))))),
% 19.91/4.04 inference(rectify,[status(thm)],[f320])).
% 19.91/4.04 thf(f320,axiom,(
% 19.91/4.04 (surjective = (^[X3 : $i, X4 : $i, X12 : $i] : (! [X1 : $i] : ((in @ X1 @ X4) => ? [X2 : $i] : (((ap @ X3 @ X4 @ X12 @ X2) = X1) & (in @ X2 @ X3))))))),
% 19.91/4.04 file('/export/starexec/sandbox2/tmp/tmp.gzAOYGIDe7/DTF2THF_7160.p',surjective)).
% 19.91/4.04 thf(f1357,plain,(
% 19.91/4.04 ($true != (surjective @ sK0 @ sK1 @ sK3))),
% 19.91/4.04 inference(cnf_transformation,[status(thm)],[f970])).
% 19.91/4.04 thf(f970,plain,(
% 19.91/4.04 (woz1_4 = $true) & (upairsetIL = $true) & (foundationAx = $true) & (ubforcartprodlem2 = $true) & (notsubsetI = $true) & (lam2p = $true) & (upairsetIR = $true) & (iftrueProp1 = $true) & (demorgan2b2 = $true) & (binintersectRsub = $true) & (subsetemptysetimpeq = $true) & (omegaIndAx = $true) & (app = $true) & (ex1I2 = $true) & (descr__Cong = $true) & (cartprodsndin = $true) & (dpsetconstrI = $true) & (setukpairinjR1 = $true) & (! [X3 : $i] : (($true != (in @ X3 @ sK1)) | ($true = (in @ (sK2 @ X3) @ sK0))) & (($true = (in @ sK3 @ (funcSet @ sK0 @ sK1))) & ($true != (surjective @ sK0 @ sK1 @ sK3)) & ! [X5 : $i] : (((ap @ sK0 @ sK1 @ sK3 @ (sK2 @ X5)) = X5) | ($true != (in @ X5 @ sK1))))) & (binunionTE = $true) & (exuI3 = $true) & (upairequniteq = $true) & (woz13rule4 = $true) & (cartprodfstin = $true) & (setadjoinOr = $true) & (image1Equiv = $true) & (breln1unionprop = $true) & (doubleComplementSub1 = $true) & (funcext = $true) & (woz13rule1 = $true) & (dpsetconstrSub = $true) & (exuE3u = $true) & (upairset2E = $true) & (setadjoinIL = $true) & (dsetconstrEL = $true) & (emptyset__Cong = $true) & (ap2apEq1 = $true) & (injFuncSetFuncInj = $true) & (contrasubsetT2 = $true) & (surjFuncSetFuncSurj = $true) & (emptyInPowerset = $true) & (binintersectTERcontra = $true) & (binunionT_lem = $true) & (setadjoin__Cong = $true) & (setunionI = $true) & (binunionTIRcontra = $true) & (binunionIL = $true) & (notdexE = $true) & (lam2lamEq = $true) & (lamProp = $true) & (binintersectSubset3 = $true) & (subbreln1 = $true) & (setminusI = $true) & (breln1unionEcases = $true) & (powersetI1 = $true) & (ubforcartprodlem3 = $true) & (setunionsingleton2 = $true) & (cartprodpairsurjEq = $true) & (lamp = $true) & (woz1_3 = $true) & (in__Cong = $true) & (powersetE = $true) & (setext = $true) & (inIntersectImpInUnion2 = $true) & (eqbreln = $true) & (beta2 = $true) & (setminusT_lem = $true) & (setukpairIR = $true) & (eqinunit = $true) & (setminusER = $true) & (demorgan2a2 = $true) & (ex1I = $true) & (setunionE = $true) & (binintersectER = $true) & (complementTcontraSubset = $true) & (vacuousDall = $true) & (ifp = $true) & (emptyE1 = $true) & (surjFuncSetFuncIn = $true) & (binintersectSubset4 = $true) & (quantDeMorgan4 = $true) & (powersetTE1 = $true) & (cartprodpairmemER = $true) & (complementTI1 = $true) & (exuE2 = $true) & (setadjoinAx = $true) & (setukpairinjL1 = $true) & (dsetconstrER = $true) & (subsetE = $true) & (cartprodpairin = $true) & (dsetconstrI = $true) & (setadjoinE = $true) & (ex1E2 = $true) & (quantDeMorgan1 = $true) & (eqimpsubset2 = $true) & (kfstpairEq = $true) & (brelnall1 = $true) & (kpairsurjEq = $true) & (subsetTI = $true) & (nonemptyI1 = $true) & (inComplementUnionImpInComplement1 = $true) & (ap2apEq2 = $true) & (funcGraphProp3 = $true) & (setminusELneg = $true) & (setunionAx = $true) & (breln1invI = $true) & (powerset__Cong = $true) & (setukpairIL = $true) & (ksndpairEq = $true) & (wellorderingAx = $true) & (symdiffIneg1 = $true) & (upairinpowunion = $true) & (singletonsswitch = $true) & (quantDeMorgan3 = $true) & (iffalseProp2 = $true) & (woz1_1 = $true) & (notequalI1 = $true) & (woz2B = $true) & (binintersectT_lem = $true) & (woz1_2 = $true) & (emptysetsubset = $true) & (injFuncSetFuncIn = $true) & (breln1SetBreln1 = $true) & (symdiffE = $true) & (binintersectI = $true) & (emptysetimpfalse = $true) & (setminusEL = $true) & (kfstsingleton = $true) & (demorgan1a = $true) & (powersetI = $true) & (omega__Cong = $true) & (setextT = $true) & (nonemptyImpWitness = $true) & (complementUnionInPowersetComplement = $true) & (intersectInPowersetIntersectUnions = $true) & (setminusILneg = $true) & (dpsetconstrERa = $true) & (sepSubset = $true) & (setminusSubset2 = $true) & (demorgan2b = $true) & (eqimpsubset1 = $true) & (prop2set2propI = $true) & (breln1compI = $true) & (subsetI2 = $true) & (disjointsetsI1 = $true) & (cartprodmempair1 = $true) & (powersetE1 = $true) & (subsetE2 = $true) & (upairsetE = $true) & (breln1invprop = $true) & (setukpairinjL2 = $true) & (exuE3e = $true) & (binunionLsub = $true) & (cartprodpairmemEL = $true) & (setOfPairsIsBReln = $true) & (secondinupair = $true) & (subset2powerset = $true) & (setunion__Cong = $true) & (image1E = $true) & (ex1E1 = $true) & (replAx = $true) & (emptysetAx = $true) & (cartprodmempaircEq = $true) & (dpsetconstrEL1 = $true) & (nonemptyI = $true) & (iftrueorfalse = $true) & (funcGraphProp2 = $true) & (demorgan1b = $true) & (nonemptyE1 = $true) & (setadjoinIR = $true) & (setukpairinjR11 = $true) & (inComplementUnionImpNotIn1 = $true) & (brelnall2 = $true) & (noeltsimpempty = $true) & (breln1compEex = $true) & (theprop = $true) & (setminusERneg = $true) & (apProp = $true) & (notinemptyset = $true) & (complementInPowersetComplementIntersect = $true) & (kpairp = $true) & (emptyinPowerset = $true) & (demorgan2a = $true) & (descrp = $true) & (symdiffI1 = $true) & (notequalI2 = $true) & (notinsingleton = $true) & (setunionE2 = $true) & (funcGraphProp1 = $true) & (ksndsingleton = $true) & (powersetsubset = $true) & (upairset2IR = $true) & (binunionRsub = $true) & (setOfPairsIsBReln1 = $true) & (funcinfuncset = $true) & (setukpairinjR = $true) & (woz2A = $true) & (kpairiskpair = $true) & (exu__Cong = $true) & (subPowSU = $true) & (beta1 = $true) & (upairsubunion = $true) & (eqbreln1 = $true) & (powersetT_lem = $true) & (woz2Ex = $true) & (image1Ex = $true) & (prop2setE = $true) & (quantDeMorgan2 = $true) & (symdiffIneg2 = $true) & (iftrueProp2 = $true) & (ubforcartprodlem1 = $true) & (setadjoinSub2 = $true) & (ifSingleton = $true) & (prop2setI = $true) & (breln1unionI = $true) & (binintersectEL = $true) & (infuncsetfunc = $true) & (inPowerset = $true) & (powersetAx = $true) & (breln1unionIR = $true) & (complementTnotintersectT = $true) & (choice2fnsingleton = $true) & (setbeta = $true) & (notdallE = $true) & (binintersectTELcontra = $true) & (eta2 = $true) & (dpsetconstrEL2 = $true) & (sepInPowerset = $true) & (woz1_5 = $true) & (binintersectSubset1 = $true) & (binintersectSubset5 = $true) & (setextAx = $true) & (omegaSAx = $true) & (setextsub = $true) & (dpsetconstrER = $true) & (setminusIRneg = $true) & (setoftrueEq = $true) & (binintersectLsub = $true) & (exuE1 = $true) & (complementImpComplementIntersect = $true) & (woz2W = $true) & (woz13rule2 = $true) & (breln1unionE = $true) & (cartprodfstpairEq = $true) & (doubleComplementE1 = $true) & (setunionsingleton1 = $true) & (setukpairinjR12 = $true) & (setunionsingleton = $true) & (doubleComplementEq = $true) & (doubleComplementSub2 = $true) & (breln1unionIL = $true) & (cartprodmempair = $true) & (iffalse = $true) & (woz13rule0 = $true) & (complementTE1 = $true) & (powersetTI1 = $true) & (funcGraphProp4 = $true) & (binunionE = $true) & (subsetTrans = $true) & (injFuncInInjFuncSet = $true) & (breln1compprop = $true) & (image1Ex1 = $true) & (setminusLsub = $true) & (doubleComplementI1 = $true) & (emptyinunitempty = $true) & (funcImageSingleton = $true) & (demorgan1 = $true) & (funcextLem = $true) & (singletoninpowerset = $true) & (contrasubsetT1 = $true) & (binunionTILcontra = $true) & (eta1 = $true) & (binunionEcases = $true) & (binunionTEcontra = $true) & (demorgan2 = $true) & (emptyI = $true) & (dsetconstr__Cong = $true) & (funcext2 = $true) & (symdiffI2 = $true) & (inIntersectImpInIntersectUnions = $true) & (binunionIR = $true) & (omega0Ax = $true) & (contrasubsetT3 = $true) & (demorgan2a1 = $true) & (cartprodsndpairEq = $true) & (breln1unionCommutes = $true) & (contrasubsetT = $true) & (uniqinunit = $true) & (emptysetE = $true) & (complementT_lem = $true) & (inCongP = $true) & (theeq = $true) & (singletoninpowunion = $true) & (breln1all1 = $true) & (singletonprop = $true) & (woz13rule3 = $true) & (subbreln = $true) & (setminusSubset1 = $true) & (inIntersectImpInUnion = $true) & (singletonsuniq = $true) & (exuI2 = $true) & (setukpairinjR2 = $true) & (subsetRefl = $true) & (contraSubsetComplement = $true) & (exuEu = $true) & (bs114d = $true) & (singletonsubset = $true) & (ap2p = $true) & (setadjoinSub = $true) & (iftrue = $true) & (breln1compE = $true) & (image1I = $true) & (binintersectSubset2 = $true) & (complementSubsetComplementIntersect = $true) & (setukpairinjL = $true) & (breln1all2 = $true) & (iffalseProp1 = $true) & (exuI1 = $true) & (subsetI1 = $true) & (breln1invE = $true)),
% 19.91/4.04 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f967,f969,f968])).
% 19.91/4.04 thf(f968,plain,(
% 19.91/4.04 ? [X0 : $i,X1 : $i,X2 : $i > $i] : (! [X3 : $i] : (((in @ X3 @ X1) != $true) | ((in @ (X2 @ X3) @ X0) = $true)) & ? [X4 : $i] : (((in @ X4 @ (funcSet @ X0 @ X1)) = $true) & ($true != (surjective @ X0 @ X1 @ X4)) & ! [X5 : $i] : (((ap @ X0 @ X1 @ X4 @ (X2 @ X5)) = X5) | ($true != (in @ X5 @ X1))))) => (! [X3 : $i] : (($true != (in @ X3 @ sK1)) | ($true = (in @ (sK2 @ X3) @ sK0))) & ? [X4 : $i] : (((in @ X4 @ (funcSet @ sK0 @ sK1)) = $true) & ($true != (surjective @ sK0 @ sK1 @ X4)) & ! [X5 : $i] : (((ap @ sK0 @ sK1 @ X4 @ (sK2 @ X5)) = X5) | ($true != (in @ X5 @ sK1)))))),
% 19.91/4.04 introduced(definition,[],[choice_axiom])).
% 19.91/4.04 thf(f969,plain,(
% 19.91/4.04 ? [X4 : $i] : (((in @ X4 @ (funcSet @ sK0 @ sK1)) = $true) & ($true != (surjective @ sK0 @ sK1 @ X4)) & ! [X5 : $i] : (((ap @ sK0 @ sK1 @ X4 @ (sK2 @ X5)) = X5) | ($true != (in @ X5 @ sK1)))) => (($true = (in @ sK3 @ (funcSet @ sK0 @ sK1))) & ($true != (surjective @ sK0 @ sK1 @ sK3)) & ! [X5 : $i] : (((ap @ sK0 @ sK1 @ sK3 @ (sK2 @ X5)) = X5) | ($true != (in @ X5 @ sK1))))),
% 19.91/4.04 introduced(definition,[],[choice_axiom])).
% 19.91/4.04 thf(f967,plain,(
% 19.91/4.04 (woz1_4 = $true) & (upairsetIL = $true) & (foundationAx = $true) & (ubforcartprodlem2 = $true) & (notsubsetI = $true) & (lam2p = $true) & (upairsetIR = $true) & (iftrueProp1 = $true) & (demorgan2b2 = $true) & (binintersectRsub = $true) & (subsetemptysetimpeq = $true) & (omegaIndAx = $true) & (app = $true) & (ex1I2 = $true) & (descr__Cong = $true) & (cartprodsndin = $true) & (dpsetconstrI = $true) & (setukpairinjR1 = $true) & ? [X0 : $i,X1 : $i,X2 : $i > $i] : (! [X3 : $i] : (((in @ X3 @ X1) != $true) | ((in @ (X2 @ X3) @ X0) = $true)) & ? [X4 : $i] : (((in @ X4 @ (funcSet @ X0 @ X1)) = $true) & ($true != (surjective @ X0 @ X1 @ X4)) & ! [X5 : $i] : (((ap @ X0 @ X1 @ X4 @ (X2 @ X5)) = X5) | ($true != (in @ X5 @ X1))))) & (binunionTE = $true) & (exuI3 = $true) & (upairequniteq = $true) & (woz13rule4 = $true) & (cartprodfstin = $true) & (setadjoinOr = $true) & (image1Equiv = $true) & (breln1unionprop = $true) & (doubleComplementSub1 = $true) & (funcext = $true) & (woz13rule1 = $true) & (dpsetconstrSub = $true) & (exuE3u = $true) & (upairset2E = $true) & (setadjoinIL = $true) & (dsetconstrEL = $true) & (emptyset__Cong = $true) & (ap2apEq1 = $true) & (injFuncSetFuncInj = $true) & (contrasubsetT2 = $true) & (surjFuncSetFuncSurj = $true) & (emptyInPowerset = $true) & (binintersectTERcontra = $true) & (binunionT_lem = $true) & (setadjoin__Cong = $true) & (setunionI = $true) & (binunionTIRcontra = $true) & (binunionIL = $true) & (notdexE = $true) & (lam2lamEq = $true) & (lamProp = $true) & (binintersectSubset3 = $true) & (subbreln1 = $true) & (setminusI = $true) & (breln1unionEcases = $true) & (powersetI1 = $true) & (ubforcartprodlem3 = $true) & (setunionsingleton2 = $true) & (cartprodpairsurjEq = $true) & (lamp = $true) & (woz1_3 = $true) & (in__Cong = $true) & (powersetE = $true) & (setext = $true) & (inIntersectImpInUnion2 = $true) & (eqbreln = $true) & (beta2 = $true) & (setminusT_lem = $true) & (setukpairIR = $true) & (eqinunit = $true) & (setminusER = $true) & (demorgan2a2 = $true) & (ex1I = $true) & (setunionE = $true) & (binintersectER = $true) & (complementTcontraSubset = $true) & (vacuousDall = $true) & (ifp = $true) & (emptyE1 = $true) & (surjFuncSetFuncIn = $true) & (binintersectSubset4 = $true) & (quantDeMorgan4 = $true) & (powersetTE1 = $true) & (cartprodpairmemER = $true) & (complementTI1 = $true) & (exuE2 = $true) & (setadjoinAx = $true) & (setukpairinjL1 = $true) & (dsetconstrER = $true) & (subsetE = $true) & (cartprodpairin = $true) & (dsetconstrI = $true) & (setadjoinE = $true) & (ex1E2 = $true) & (quantDeMorgan1 = $true) & (eqimpsubset2 = $true) & (kfstpairEq = $true) & (brelnall1 = $true) & (kpairsurjEq = $true) & (subsetTI = $true) & (nonemptyI1 = $true) & (inComplementUnionImpInComplement1 = $true) & (ap2apEq2 = $true) & (funcGraphProp3 = $true) & (setminusELneg = $true) & (setunionAx = $true) & (breln1invI = $true) & (powerset__Cong = $true) & (setukpairIL = $true) & (ksndpairEq = $true) & (wellorderingAx = $true) & (symdiffIneg1 = $true) & (upairinpowunion = $true) & (singletonsswitch = $true) & (quantDeMorgan3 = $true) & (iffalseProp2 = $true) & (woz1_1 = $true) & (notequalI1 = $true) & (woz2B = $true) & (binintersectT_lem = $true) & (woz1_2 = $true) & (emptysetsubset = $true) & (injFuncSetFuncIn = $true) & (breln1SetBreln1 = $true) & (symdiffE = $true) & (binintersectI = $true) & (emptysetimpfalse = $true) & (setminusEL = $true) & (kfstsingleton = $true) & (demorgan1a = $true) & (powersetI = $true) & (omega__Cong = $true) & (setextT = $true) & (nonemptyImpWitness = $true) & (complementUnionInPowersetComplement = $true) & (intersectInPowersetIntersectUnions = $true) & (setminusILneg = $true) & (dpsetconstrERa = $true) & (sepSubset = $true) & (setminusSubset2 = $true) & (demorgan2b = $true) & (eqimpsubset1 = $true) & (prop2set2propI = $true) & (breln1compI = $true) & (subsetI2 = $true) & (disjointsetsI1 = $true) & (cartprodmempair1 = $true) & (powersetE1 = $true) & (subsetE2 = $true) & (upairsetE = $true) & (breln1invprop = $true) & (setukpairinjL2 = $true) & (exuE3e = $true) & (binunionLsub = $true) & (cartprodpairmemEL = $true) & (setOfPairsIsBReln = $true) & (secondinupair = $true) & (subset2powerset = $true) & (setunion__Cong = $true) & (image1E = $true) & (ex1E1 = $true) & (replAx = $true) & (emptysetAx = $true) & (cartprodmempaircEq = $true) & (dpsetconstrEL1 = $true) & (nonemptyI = $true) & (iftrueorfalse = $true) & (funcGraphProp2 = $true) & (demorgan1b = $true) & (nonemptyE1 = $true) & (setadjoinIR = $true) & (setukpairinjR11 = $true) & (inComplementUnionImpNotIn1 = $true) & (brelnall2 = $true) & (noeltsimpempty = $true) & (breln1compEex = $true) & (theprop = $true) & (setminusERneg = $true) & (apProp = $true) & (notinemptyset = $true) & (complementInPowersetComplementIntersect = $true) & (kpairp = $true) & (emptyinPowerset = $true) & (demorgan2a = $true) & (descrp = $true) & (symdiffI1 = $true) & (notequalI2 = $true) & (notinsingleton = $true) & (setunionE2 = $true) & (funcGraphProp1 = $true) & (ksndsingleton = $true) & (powersetsubset = $true) & (upairset2IR = $true) & (binunionRsub = $true) & (setOfPairsIsBReln1 = $true) & (funcinfuncset = $true) & (setukpairinjR = $true) & (woz2A = $true) & (kpairiskpair = $true) & (exu__Cong = $true) & (subPowSU = $true) & (beta1 = $true) & (upairsubunion = $true) & (eqbreln1 = $true) & (powersetT_lem = $true) & (woz2Ex = $true) & (image1Ex = $true) & (prop2setE = $true) & (quantDeMorgan2 = $true) & (symdiffIneg2 = $true) & (iftrueProp2 = $true) & (ubforcartprodlem1 = $true) & (setadjoinSub2 = $true) & (ifSingleton = $true) & (prop2setI = $true) & (breln1unionI = $true) & (binintersectEL = $true) & (infuncsetfunc = $true) & (inPowerset = $true) & (powersetAx = $true) & (breln1unionIR = $true) & (complementTnotintersectT = $true) & (choice2fnsingleton = $true) & (setbeta = $true) & (notdallE = $true) & (binintersectTELcontra = $true) & (eta2 = $true) & (dpsetconstrEL2 = $true) & (sepInPowerset = $true) & (woz1_5 = $true) & (binintersectSubset1 = $true) & (binintersectSubset5 = $true) & (setextAx = $true) & (omegaSAx = $true) & (setextsub = $true) & (dpsetconstrER = $true) & (setminusIRneg = $true) & (setoftrueEq = $true) & (binintersectLsub = $true) & (exuE1 = $true) & (complementImpComplementIntersect = $true) & (woz2W = $true) & (woz13rule2 = $true) & (breln1unionE = $true) & (cartprodfstpairEq = $true) & (doubleComplementE1 = $true) & (setunionsingleton1 = $true) & (setukpairinjR12 = $true) & (setunionsingleton = $true) & (doubleComplementEq = $true) & (doubleComplementSub2 = $true) & (breln1unionIL = $true) & (cartprodmempair = $true) & (iffalse = $true) & (woz13rule0 = $true) & (complementTE1 = $true) & (powersetTI1 = $true) & (funcGraphProp4 = $true) & (binunionE = $true) & (subsetTrans = $true) & (injFuncInInjFuncSet = $true) & (breln1compprop = $true) & (image1Ex1 = $true) & (setminusLsub = $true) & (doubleComplementI1 = $true) & (emptyinunitempty = $true) & (funcImageSingleton = $true) & (demorgan1 = $true) & (funcextLem = $true) & (singletoninpowerset = $true) & (contrasubsetT1 = $true) & (binunionTILcontra = $true) & (eta1 = $true) & (binunionEcases = $true) & (binunionTEcontra = $true) & (demorgan2 = $true) & (emptyI = $true) & (dsetconstr__Cong = $true) & (funcext2 = $true) & (symdiffI2 = $true) & (inIntersectImpInIntersectUnions = $true) & (binunionIR = $true) & (omega0Ax = $true) & (contrasubsetT3 = $true) & (demorgan2a1 = $true) & (cartprodsndpairEq = $true) & (breln1unionCommutes = $true) & (contrasubsetT = $true) & (uniqinunit = $true) & (emptysetE = $true) & (complementT_lem = $true) & (inCongP = $true) & (theeq = $true) & (singletoninpowunion = $true) & (breln1all1 = $true) & (singletonprop = $true) & (woz13rule3 = $true) & (subbreln = $true) & (setminusSubset1 = $true) & (inIntersectImpInUnion = $true) & (singletonsuniq = $true) & (exuI2 = $true) & (setukpairinjR2 = $true) & (subsetRefl = $true) & (contraSubsetComplement = $true) & (exuEu = $true) & (bs114d = $true) & (singletonsubset = $true) & (ap2p = $true) & (setadjoinSub = $true) & (iftrue = $true) & (breln1compE = $true) & (image1I = $true) & (binintersectSubset2 = $true) & (complementSubsetComplementIntersect = $true) & (setukpairinjL = $true) & (breln1all2 = $true) & (iffalseProp1 = $true) & (exuI1 = $true) & (subsetI1 = $true) & (breln1invE = $true)),
% 19.91/4.04 inference(flattening,[status(thm)],[f966])).
% 19.91/4.04 thf(f966,plain,(
% 19.91/4.04 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i > $i] : (? [X4 : $i] : ((($true != (surjective @ X0 @ X1 @ X4)) & ! [X5 : $i] : (((ap @ X0 @ X1 @ X4 @ (X2 @ X5)) = X5) | ($true != (in @ X5 @ X1)))) & ((in @ X4 @ (funcSet @ X0 @ X1)) = $true)) & ! [X3 : $i] : (((in @ X3 @ X1) != $true) | ((in @ (X2 @ X3) @ X0) = $true))) & (surjFuncSetFuncSurj = $true)) & (surjFuncSetFuncIn = $true)) & (injFuncSetFuncInj = $true)) & (injFuncSetFuncIn = $true)) & (injFuncInInjFuncSet = $true)) & (image1I = $true)) & (image1E = $true)) & (image1Equiv = $true)) & (image1Ex1 = $true)) & (image1Ex = $true)) & (woz2B = $true)) & (woz2A = $true)) & (woz2W = $true)) & (woz2Ex = $true)) & (breln1unionCommutes = $true)) & (breln1unionEcases = $true)) & (breln1unionE = $true)) & (breln1unionI = $true)) & (breln1unionIR = $true)) & (breln1unionIL = $true)) & (breln1unionprop = $true)) & (breln1compEex = $true)) & (breln1compE = $true)) & (breln1compI = $true)) & (breln1compprop = $true)) & (breln1invE = $true)) & (breln1invI = $true)) & (breln1invprop = $true)) & (eqbreln1 = $true)) & (subbreln1 = $true)) & (breln1all1 = $true)) & (setOfPairsIsBReln1 = $true)) & (choice2fnsingleton = $true)) & (breln1SetBreln1 = $true)) & (breln1all2 = $true)) & (woz1_5 = $true)) & (woz1_4 = $true)) & (woz1_3 = $true)) & (woz1_2 = $true)) & (woz1_1 = $true)) & (woz13rule4 = $true)) & (woz13rule3 = $true)) & (woz13rule2 = $true)) & (woz13rule1 = $true)) & (woz13rule0 = $true)) & (demorgan2 = $true)) & (demorgan2b = $true)) & (demorgan2b2 = $true)) & (demorgan2a = $true)) & (demorgan1 = $true)) & (demorgan1b = $true)) & (demorgan1a = $true)) & (demorgan2a2 = $true)) & (complementUnionInPowersetComplement = $true)) & (demorgan2a1 = $true)) & (binunionTEcontra = $true)) & (binunionTE = $true)) & (inComplementUnionImpInComplement1 = $true)) & (inComplementUnionImpNotIn1 = $true)) & (intersectInPowersetIntersectUnions = $true)) & (inIntersectImpInIntersectUnions = $true)) & (inIntersectImpInUnion2 = $true)) & (inIntersectImpInUnion = $true)) & (binunionTIRcontra = $true)) & (binunionTILcontra = $true)) & (complementTcontraSubset = $true)) & (contraSubsetComplement = $true)) & (complementInPowersetComplementIntersect = $true)) & (complementSubsetComplementIntersect = $true)) & (complementImpComplementIntersect = $true)) & (complementTnotintersectT = $true)) & (doubleComplementEq = $true)) & (doubleComplementSub2 = $true)) & (doubleComplementSub1 = $true)) & (doubleComplementE1 = $true)) & (doubleComplementI1 = $true)) & (contrasubsetT3 = $true)) & (contrasubsetT2 = $true)) & (contrasubsetT1 = $true)) & (contrasubsetT = $true)) & (binintersectTERcontra = $true)) & (binintersectTELcontra = $true)) & (complementTE1 = $true)) & (complementTI1 = $true)) & (powersetTE1 = $true)) & (powersetTI1 = $true)) & (subsetTI = $true)) & (setextT = $true)) & (complementT_lem = $true)) & (setminusT_lem = $true)) & (powersetT_lem = $true)) & (binunionT_lem = $true)) & (binintersectT_lem = $true)) & (iftrueorfalse = $true)) & (iffalse = $true)) & (iftrue = $true)) & (theeq = $true)) & (ifp = $true)) & (ifSingleton = $true)) & (iftrueProp2 = $true)) & (iftrueProp1 = $true)) & (iffalseProp2 = $true)) & (iffalseProp1 = $true)) & (eta2 = $true)) & (beta2 = $true)) & (lam2lamEq = $true)) & (eta1 = $true)) & (beta1 = $true)) & (ap2apEq2 = $true)) & (ap2apEq1 = $true)) & (funcext2 = $true)) & (funcext = $true)) & (eqbreln = $true)) & (subbreln = $true)) & (funcGraphProp4 = $true)) & (funcextLem = $true)) & (funcGraphProp2 = $true)) & (funcGraphProp3 = $true)) & (funcGraphProp1 = $true)) & (ex1E2 = $true)) & (brelnall2 = $true)) & (brelnall1 = $true)) & (lam2p = $true)) & (lamp = $true)) & (lamProp = $true)) & (funcinfuncset = $true)) & (ap2p = $true)) & (infuncsetfunc = $true)) & (app = $true)) & (apProp = $true)) & (funcImageSingleton = $true)) & (dpsetconstrER = $true)) & (dpsetconstrEL2 = $true)) & (dpsetconstrEL1 = $true)) & (dpsetconstrERa = $true)) & (setOfPairsIsBReln = $true)) & (dpsetconstrSub = $true)) & (dpsetconstrI = $true)) & (cartprodpairsurjEq = $true)) & (cartprodsndpairEq = $true)) & (cartprodfstpairEq = $true)) & (cartprodmempaircEq = $true)) & (cartprodpairmemER = $true)) & (cartprodpairmemEL = $true)) & (cartprodsndin = $true)) & (kpairsurjEq = $true)) & (ksndpairEq = $true)) & (ksndsingleton = $true)) & (setukpairinjR = $true)) & (setukpairinjR2 = $true)) & (upairequniteq = $true)) & (setukpairinjR1 = $true)) & (setukpairinjR12 = $true)) & (setukpairinjR11 = $true)) & (setukpairinjL = $true)) & (setukpairinjL2 = $true)) & (cartprodfstin = $true)) & (kfstpairEq = $true)) & (theprop = $true)) & (kfstsingleton = $true)) & (setukpairinjL1 = $true)) & (singletonsuniq = $true)) & (ex1I2 = $true)) & (ex1I = $true)) & (ex1E1 = $true)) & (singletonprop = $true)) & (setunionsingleton = $true)) & (setunionsingleton2 = $true)) & (setunionsingleton1 = $true)) & (setunionE2 = $true)) & (cartprodmempair = $true)) & (cartprodmempair1 = $true)) & (cartprodpairin = $true)) & (ubforcartprodlem3 = $true)) & (ubforcartprodlem2 = $true)) & (ubforcartprodlem1 = $true)) & (upairinpowunion = $true)) & (upairsubunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (singletoninpowerset = $true)) & (singletonsubset = $true)) & (kpairp = $true)) & (kpairiskpair = $true)) & (setukpairIR = $true)) & (setukpairIL = $true)) & (secondinupair = $true)) & (symdiffIneg2 = $true)) & (symdiffIneg1 = $true)) & (symdiffI2 = $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 19.91/4.04 inference(ennf_transformation,[status(thm)],[f463])).
% 19.91/4.04 thf(f463,plain,(
% 19.91/4.04 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ((ubforcartprodlem1 = $true) => ((ubforcartprodlem2 = $true) => ((ubforcartprodlem3 = $true) => ((cartprodpairin = $true) => ((cartprodmempair1 = $true) => ((cartprodmempair = $true) => ((setunionE2 = $true) => ((setunionsingleton1 = $true) => ((setunionsingleton2 = $true) => ((setunionsingleton = $true) => ((singletonprop = $true) => ((ex1E1 = $true) => ((ex1I = $true) => ((ex1I2 = $true) => ((singletonsuniq = $true) => ((setukpairinjL1 = $true) => ((kfstsingleton = $true) => ((theprop = $true) => ((kfstpairEq = $true) => ((cartprodfstin = $true) => ((setukpairinjL2 = $true) => ((setukpairinjL = $true) => ((setukpairinjR11 = $true) => ((setukpairinjR12 = $true) => ((setukpairinjR1 = $true) => ((upairequniteq = $true) => ((setukpairinjR2 = $true) => ((setukpairinjR = $true) => ((ksndsingleton = $true) => ((ksndpairEq = $true) => ((kpairsurjEq = $true) => ((cartprodsndin = $true) => ((cartprodpairmemEL = $true) => ((cartprodpairmemER = $true) => ((cartprodmempaircEq = $true) => ((cartprodfstpairEq = $true) => ((cartprodsndpairEq = $true) => ((cartprodpairsurjEq = $true) => ((dpsetconstrI = $true) => ((dpsetconstrSub = $true) => ((setOfPairsIsBReln = $true) => ((dpsetconstrERa = $true) => ((dpsetconstrEL1 = $true) => ((dpsetconstrEL2 = $true) => ((dpsetconstrER = $true) => ((funcImageSingleton = $true) => ((apProp = $true) => ((app = $true) => ((infuncsetfunc = $true) => ((ap2p = $true) => ((funcinfuncset = $true) => ((lamProp = $true) => ((lamp = $true) => ((lam2p = $true) => ((brelnall1 = $true) => ((brelnall2 = $true) => ((ex1E2 = $true) => ((funcGraphProp1 = $true) => ((funcGraphProp3 = $true) => ((funcGraphProp2 = $true) => ((funcextLem = $true) => ((funcGraphProp4 = $true) => ((subbreln = $true) => ((eqbreln = $true) => ((funcext = $true) => ((funcext2 = $true) => ((ap2apEq1 = $true) => ((ap2apEq2 = $true) => ((beta1 = $true) => ((eta1 = $true) => ((lam2lamEq = $true) => ((beta2 = $true) => ((eta2 = $true) => ((iffalseProp1 = $true) => ((iffalseProp2 = $true) => ((iftrueProp1 = $true) => ((iftrueProp2 = $true) => ((ifSingleton = $true) => ((ifp = $true) => ((theeq = $true) => ((iftrue = $true) => ((iffalse = $true) => ((iftrueorfalse = $true) => ((binintersectT_lem = $true) => ((binunionT_lem = $true) => ((powersetT_lem = $true) => ((setminusT_lem = $true) => ((complementT_lem = $true) => ((setextT = $true) => ((subsetTI = $true) => ((powersetTI1 = $true) => ((powersetTE1 = $true) => ((complementTI1 = $true) => ((complementTE1 = $true) => ((binintersectTELcontra = $true) => ((binintersectTERcontra = $true) => ((contrasubsetT = $true) => ((contrasubsetT1 = $true) => ((contrasubsetT2 = $true) => ((contrasubsetT3 = $true) => ((doubleComplementI1 = $true) => ((doubleComplementE1 = $true) => ((doubleComplementSub1 = $true) => ((doubleComplementSub2 = $true) => ((doubleComplementEq = $true) => ((complementTnotintersectT = $true) => ((complementImpComplementIntersect = $true) => ((complementSubsetComplementIntersect = $true) => ((complementInPowersetComplementIntersect = $true) => ((contraSubsetComplement = $true) => ((complementTcontraSubset = $true) => ((binunionTILcontra = $true) => ((binunionTIRcontra = $true) => ((inIntersectImpInUnion = $true) => ((inIntersectImpInUnion2 = $true) => ((inIntersectImpInIntersectUnions = $true) => ((intersectInPowersetIntersectUnions = $true) => ((inComplementUnionImpNotIn1 = $true) => ((inComplementUnionImpInComplement1 = $true) => ((binunionTE = $true) => ((binunionTEcontra = $true) => ((demorgan2a1 = $true) => ((complementUnionInPowersetComplement = $true) => ((demorgan2a2 = $true) => ((demorgan1a = $true) => ((demorgan1b = $true) => ((demorgan1 = $true) => ((demorgan2a = $true) => ((demorgan2b2 = $true) => ((demorgan2b = $true) => ((demorgan2 = $true) => ((woz13rule0 = $true) => ((woz13rule1 = $true) => ((woz13rule2 = $true) => ((woz13rule3 = $true) => ((woz13rule4 = $true) => ((woz1_1 = $true) => ((woz1_2 = $true) => ((woz1_3 = $true) => ((woz1_4 = $true) => ((woz1_5 = $true) => ((breln1all2 = $true) => ((breln1SetBreln1 = $true) => ((choice2fnsingleton = $true) => ((setOfPairsIsBReln1 = $true) => ((breln1all1 = $true) => ((subbreln1 = $true) => ((eqbreln1 = $true) => ((breln1invprop = $true) => ((breln1invI = $true) => ((breln1invE = $true) => ((breln1compprop = $true) => ((breln1compI = $true) => ((breln1compE = $true) => ((breln1compEex = $true) => ((breln1unionprop = $true) => ((breln1unionIL = $true) => ((breln1unionIR = $true) => ((breln1unionI = $true) => ((breln1unionE = $true) => ((breln1unionEcases = $true) => ((breln1unionCommutes = $true) => ((woz2Ex = $true) => ((woz2W = $true) => ((woz2A = $true) => ((woz2B = $true) => ((image1Ex = $true) => ((image1Ex1 = $true) => ((image1Equiv = $true) => ((image1E = $true) => ((image1I = $true) => ((injFuncInInjFuncSet = $true) => ((injFuncSetFuncIn = $true) => ((injFuncSetFuncInj = $true) => ((surjFuncSetFuncIn = $true) => ((surjFuncSetFuncSurj = $true) => ! [X0 : $i,X1 : $i,X2 : $i > $i] : (! [X3 : $i] : (((in @ X3 @ X1) = $true) => ((in @ (X2 @ X3) @ X0) = $true)) => ! [X4 : $i] : (((in @ X4 @ (funcSet @ X0 @ X1)) = $true) => (! [X5 : $i] : (($true = (in @ X5 @ X1)) => ((ap @ X0 @ X1 @ X4 @ (X2 @ X5)) = X5)) => ($true = (surjective @ X0 @ X1 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 19.91/4.04 inference(fool_elimination,[status(thm)],[f462])).
% 19.91/4.04 thf(f462,plain,(
% 19.91/4.04 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (subbreln1 => (eqbreln1 => (breln1invprop => (breln1invI => (breln1invE => (breln1compprop => (breln1compI => (breln1compE => (breln1compEex => (breln1unionprop => (breln1unionIL => (breln1unionIR => (breln1unionI => (breln1unionE => (breln1unionEcases => (breln1unionCommutes => (woz2Ex => (woz2W => (woz2A => (woz2B => (image1Ex => (image1Ex1 => (image1Equiv => (image1E => (image1I => (injFuncInInjFuncSet => (injFuncSetFuncIn => (injFuncSetFuncInj => (surjFuncSetFuncIn => (surjFuncSetFuncSurj => ! [X0 : $i,X1 : $i,X2 : $i > $i] : (! [X3 : $i] : ((in @ X3 @ X1) => (in @ (X2 @ X3) @ X0)) => ! [X4 : $i] : ((in @ X4 @ (funcSet @ X0 @ X1)) => (! [X5 : $i] : ((in @ X5 @ X1) => ((ap @ X0 @ X1 @ X4 @ (X2 @ X5)) = X5)) => (surjective @ X0 @ X1 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 19.91/4.04 inference(rectify,[status(thm)],[f324])).
% 19.91/4.04 thf(f324,negated_conjecture,(
% 19.91/4.04 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (subbreln1 => (eqbreln1 => (breln1invprop => (breln1invI => (breln1invE => (breln1compprop => (breln1compI => (breln1compE => (breln1compEex => (breln1unionprop => (breln1unionIL => (breln1unionIR => (breln1unionI => (breln1unionE => (breln1unionEcases => (breln1unionCommutes => (woz2Ex => (woz2W => (woz2A => (woz2B => (image1Ex => (image1Ex1 => (image1Equiv => (image1E => (image1I => (injFuncInInjFuncSet => (injFuncSetFuncIn => (injFuncSetFuncInj => (surjFuncSetFuncIn => (surjFuncSetFuncSurj => ! [X4 : $i,X3 : $i,X12 : $i > $i] : (! [X1 : $i] : ((in @ X1 @ X3) => (in @ (X12 @ X1) @ X4)) => ! [X14 : $i] : ((in @ X14 @ (funcSet @ X4 @ X3)) => (! [X1 : $i] : ((in @ X1 @ X3) => ((ap @ X4 @ X3 @ X14 @ (X12 @ X1)) = X1)) => (surjective @ X4 @ X3 @ X14)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 19.91/4.04 inference(negated_conjecture,[status(cth)],[f323])).
% 19.91/4.04 thf(f323,conjecture,(
% 19.91/4.04 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (subbreln1 => (eqbreln1 => (breln1invprop => (breln1invI => (breln1invE => (breln1compprop => (breln1compI => (breln1compE => (breln1compEex => (breln1unionprop => (breln1unionIL => (breln1unionIR => (breln1unionI => (breln1unionE => (breln1unionEcases => (breln1unionCommutes => (woz2Ex => (woz2W => (woz2A => (woz2B => (image1Ex => (image1Ex1 => (image1Equiv => (image1E => (image1I => (injFuncInInjFuncSet => (injFuncSetFuncIn => (injFuncSetFuncInj => (surjFuncSetFuncIn => (surjFuncSetFuncSurj => ! [X4 : $i,X3 : $i,X12 : $i > $i] : (! [X1 : $i] : ((in @ X1 @ X3) => (in @ (X12 @ X1) @ X4)) => ! [X14 : $i] : ((in @ X14 @ (funcSet @ X4 @ X3)) => (! [X1 : $i] : ((in @ X1 @ X3) => ((ap @ X4 @ X3 @ X14 @ (X12 @ X1)) = X1)) => (surjective @ X4 @ X3 @ X14))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 19.91/4.04 file('/export/starexec/sandbox2/tmp/tmp.gzAOYGIDe7/DTF2THF_7160.p',leftInvIsSurj)).
% 19.91/4.04 thf(f1356,plain,(
% 19.91/4.04 ( ! [X5 : $i] : (($true != (in @ X5 @ sK1)) | ((ap @ sK0 @ sK1 @ sK3 @ (sK2 @ X5)) = X5)) )),
% 19.91/4.04 inference(cnf_transformation,[status(thm)],[f970])).
% 19.91/4.04 thf(f3833,plain,(
% 19.91/4.04 ( ! [X1 : $i] : ((sK72 != (ap @ sK0 @ sK1 @ sK3 @ X1)) | ((in @ X1 @ sK0) = $false)) )),
% 19.91/4.04 inference(equality_proxy_clausification,[status(thm)],[f3832])).
% 19.91/4.04 thf(f3832,plain,(
% 19.91/4.04 ( ! [X1 : $i] : (((in @ X1 @ sK0) = $false) | ($false = ((ap @ sK0 @ sK1 @ sK3 @ X1) = sK72))) )),
% 19.91/4.04 inference(binary_proxy_clausification,[status(thm)],[f3831])).
% 19.91/4.04 thf(f3831,plain,(
% 19.91/4.04 ( ! [X1 : $i] : ((((in @ X1 @ sK0) & ((ap @ sK0 @ sK1 @ sK3 @ X1) = sK72)) = $false)) )),
% 19.91/4.04 inference(beta_eta_normalization,[status(thm)],[f3830])).
% 19.91/4.04 thf(f3830,plain,(
% 19.91/4.04 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ sK0) & ((ap @ sK0 @ sK1 @ sK3 @ Y0) = sK72))) @ X1) = $false)) )),
% 19.91/4.04 inference(pi_clausification,[status(thm)],[f3828])).
% 19.91/4.04 thf(f3828,plain,(
% 19.91/4.04 ($false = (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK0) & ((ap @ sK0 @ sK1 @ sK3 @ Y0) = sK72)))))),
% 19.91/4.04 inference(binary_proxy_clausification,[status(thm)],[f3827])).
% 19.91/4.04 thf(f5874,plain,(
% 19.91/4.04 ((in @ (sK2 @ sK72) @ sK0) = $true)),
% 19.91/4.04 inference(trivial_inequality_removal,[status(thm)],[f5871])).
% 19.91/4.04 thf(f5871,plain,(
% 19.91/4.04 ($true != $true) | ((in @ (sK2 @ sK72) @ sK0) = $true)),
% 19.91/4.04 inference(superposition,[status(thm)],[f1359,f3829])).
% 19.91/4.04 thf(f1359,plain,(
% 19.91/4.04 ( ! [X3 : $i] : (($true != (in @ X3 @ sK1)) | ($true = (in @ (sK2 @ X3) @ sK0))) )),
% 19.91/4.04 inference(cnf_transformation,[status(thm)],[f970])).
% 19.91/4.04 % SZS output end Proof for DTF2THF_7160
% 19.91/4.04 % (7551)------------------------------
% 19.91/4.04 % (7551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.91/4.04 % (7551)Termination reason: Refutation
% 19.91/4.04
% 19.91/4.04 % (7551)Memory used [KB]: 11001
% 19.91/4.04 % (7551)Time elapsed: 0.138 s
% 19.91/4.04 % (7551)Instructions burned: 493 (million)
% 19.91/4.04 % (7551)------------------------------
% 19.91/4.04 % (7551)------------------------------
% 19.91/4.04 % (7424)Success in time 2.447 s
%------------------------------------------------------------------------------