%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU779^1 : 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 : n005.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 09:37:07 AM UTC 2026
% Result : Theorem 27.61s 5.13s
% Output : Refutation 27.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 18
% Syntax : Number of formulae : 83 ( 36 unt; 0 typ; 8 def)
% Number of atoms : 5498 (1378 equ; 0 cnn)
% Maximal formula atoms : 303 ( 66 avg)
% Number of connectives : 3540 ( 54 ~; 89 |; 983 &;1094 @)
% ( 8 <=>;1262 =>; 0 <=; 0 <~>)
% Maximal formula depth : 314 ( 29 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 48 ( 48 >; 0 *; 0 +; 0 <<)
% Number of symbols : 481 ( 476 usr; 313 con; 0-4 aty)
% ( 41 !!; 9 ??; 0 @@+; 0 @@-)
% Number of variables : 227 ( 101 ^; 86 !; 40 ?; 227 :)
% 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_369,type,
sK7: ( $i > $o ) > $i > $i ).
thf(func_def_370,type,
sK8: ( $i > $o ) > $i ).
thf(func_def_371,type,
sK9: ( $i > $i > $o ) > $i > $i ).
thf(func_def_372,type,
sK10: ( $i > $i > $o ) > $i > $i ).
thf(func_def_373,type,
sK11: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_374,type,
sK12: ( $i > $i > $o ) > $i > $i ).
thf(func_def_375,type,
sK13: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_376,type,
sK14: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_377,type,
sK15: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_378,type,
sK16: ( $i > $o ) > $i > $i > $i ).
thf(func_def_379,type,
sK17: ( $i > $o ) > $i > $i > $i ).
thf(func_def_380,type,
sK18: $i > $i > $i ).
thf(func_def_381,type,
sK19: $i > $i > $i > $i > $i ).
thf(func_def_382,type,
sK20: $i > $i > $i ).
thf(func_def_383,type,
sK21: $i > $i > $i ).
thf(func_def_384,type,
sK22: $i > $i > $i ).
thf(func_def_385,type,
sK23: $i > $i > $i ).
thf(func_def_386,type,
sK24: $i > $i > $i > $i ).
thf(func_def_387,type,
sK25: $i > $i > $i > $i ).
thf(func_def_388,type,
sK26: $i > $i ).
thf(func_def_389,type,
sK27: ( $i > $o ) > $i > $i ).
thf(func_def_390,type,
sK28: ( $i > $o ) > $i > $i ).
thf(func_def_391,type,
sK29: $i > $i > ( $i > $i ) > $i ).
thf(func_def_392,type,
sK30: $i > $i > $i > $i ).
thf(func_def_393,type,
sK31: $i > $i > $i > $i ).
thf(func_def_394,type,
sK32: $i > $i > $i > $i ).
thf(func_def_395,type,
sK33: $i > $i > $i ).
thf(func_def_396,type,
sK34: ( $i > $o ) > $i > $i > $i ).
thf(func_def_397,type,
sK35: ( $i > $o ) > $i > $i > $i ).
thf(func_def_398,type,
sK36: $i > $i > $i ).
thf(func_def_399,type,
sK37: ( $i > $o ) > $i > $i ).
thf(func_def_400,type,
sK38: ( $i > $o ) > $i ).
thf(func_def_401,type,
sK39: ( $i > $o ) > $i ).
thf(func_def_402,type,
sK40: $i > $i ).
thf(func_def_403,type,
sK41: ( $i > $i ) > $i > $i > $i ).
thf(func_def_404,type,
sK42: ( $i > $o ) > $i > $i ).
thf(func_def_405,type,
sK43: $i > $i > $i ).
thf(func_def_406,type,
sK44: $i > ( $i > $o ) > $i ).
thf(func_def_407,type,
sK45: ( $i > $o ) > $i ).
thf(func_def_408,type,
sK46: ( $i > $o ) > $i ).
thf(func_def_409,type,
sK47: ( $i > $o ) > $i ).
thf(func_def_410,type,
sK48: $i > $i > $i > $i > $i ).
thf(func_def_411,type,
sK49: $i > $i > $i > $i > $i ).
thf(func_def_412,type,
sK50: $i > $i > $i > $i > $i ).
thf(func_def_413,type,
sK51: $i > $i > $i > $i > $i ).
thf(func_def_414,type,
sK52: $i > $i > $i > $i > $i ).
thf(func_def_415,type,
sK53: $i > $i > $i > $i > $i ).
thf(func_def_416,type,
sK54: $i > $i > ( $i > $i ) > $i ).
thf(func_def_417,type,
sK55: $i > $o > $i > $i ).
thf(func_def_418,type,
sK56: ( $i > $o ) > $i > $i ).
thf(func_def_419,type,
sK57: $i > $i ).
thf(func_def_420,type,
sK58: $i > $i > $i > $i > $i ).
thf(func_def_421,type,
sK59: $i > $i > $i ).
thf(func_def_422,type,
sK60: $i > $i > $i > $i ).
thf(func_def_423,type,
sK61: ( $i > $o ) > $i ).
thf(func_def_424,type,
sK62: ( $i > $o ) > $i > $i ).
thf(func_def_425,type,
sK63: ( $i > $o ) > $i > $i ).
thf(func_def_426,type,
sK64: ( $i > $o ) > $i > $i ).
thf(func_def_427,type,
sK65: ( $i > $o ) > $i > $i ).
thf(func_def_428,type,
sK66: $i > $i ).
thf(func_def_429,type,
sK67: $i > $i > $i > $i ).
thf(func_def_430,type,
sK68: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_431,type,
sK69: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_432,type,
sK70: ( $i > $o ) > $i > $i ).
thf(func_def_433,type,
sK71: ( $i > $o ) > $i > $i ).
thf(func_def_434,type,
sK72: ( $i > $o ) > $i > $i ).
thf(func_def_435,type,
sK73: ( $i > $o ) > $i > $i ).
thf(func_def_436,type,
sK74: ( $i > $o ) > $i > $i ).
thf(func_def_437,type,
sK75: $i > $i ).
thf(func_def_438,type,
sK76: $i > $i > $i > $i > $i ).
thf(func_def_439,type,
sK77: $i > $i > $i > $i > $i ).
thf(func_def_440,type,
sK78: ( $i > $o ) > $i > $i ).
thf(func_def_441,type,
sK79: $i > ( $i > $o ) > $i ).
thf(func_def_442,type,
sK80: ( $i > $o ) > $i > $i ).
thf(func_def_443,type,
sK81: ( $i > $o ) > $i > $i ).
thf(func_def_444,type,
sK82: $i > $i ).
thf(func_def_445,type,
sK83: $i > ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(func_def_446,type,
sK84: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_447,type,
sK85: ( $i > $o ) > $i > $i ).
thf(func_def_448,type,
sK86: ( $i > $o ) > $i ).
thf(func_def_449,type,
sK87: ( $i > $i ) > $i > $i > $i ).
thf(func_def_450,type,
sK88: $i > $i > ( $i > $i ) > $i ).
thf(func_def_451,type,
sK89: ( $i > $o ) > $i > $i ).
thf(func_def_452,type,
sK90: ( $i > $o ) > $i > $i ).
thf(func_def_453,type,
sK91: $i > $i > $i > $i > $i ).
thf(func_def_454,type,
sK92: ( $i > $o ) > $i > $i ).
thf(func_def_455,type,
sK93: $i > $i > ( $i > $o ) > $i > $i ).
thf(func_def_456,type,
sK94: $i > $i > ( $i > $o ) > $i > $i ).
thf(func_def_457,type,
sK95: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_458,type,
sK96: $i > $i > ( $i > $o ) > $i ).
thf(func_def_459,type,
sK97: $i > $i > $i > $i ).
thf(func_def_460,type,
sK98: $i > $i > $i > $i ).
thf(func_def_461,type,
sK99: $i > $i ).
thf(func_def_462,type,
sK100: $i > $i > $i > $i ).
thf(func_def_463,type,
sK101: $i > $i > $i ).
thf(func_def_464,type,
sK102: $i > $i > $i ).
thf(func_def_465,type,
sK103: $i > $i > $i ).
thf(func_def_466,type,
sK104: $i > $i > $i ).
thf(func_def_467,type,
sK105: $i > $i > $i ).
thf(func_def_468,type,
sK106: $i > $i > $i ).
thf(func_def_469,type,
sK107: $i > $i > ( $i > $o ) > $i > $i ).
thf(func_def_470,type,
sK108: $i > $i > ( $i > $o ) > $i > $i ).
thf(func_def_471,type,
sK109: ( $i > $o ) > $i ).
thf(func_def_472,type,
sK110: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_473,type,
sK111: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_474,type,
sK112: ( $i > $o ) > $i > $i ).
thf(func_def_475,type,
sK113: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_476,type,
sK114: ( $i > $o ) > $i > $i ).
thf(func_def_477,type,
sK115: ( $i > $o ) > $i > $i ).
thf(func_def_478,type,
sK116: ( $i > $o ) > $i > $i ).
thf(func_def_479,type,
sK117: ( $i > $o ) > $i ).
thf(func_def_480,type,
sK118: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_481,type,
sK119: ( $i > $o ) > $i > $i ).
thf(func_def_482,type,
sK120: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_483,type,
sK121: $i > $i > $i > $i ).
thf(func_def_484,type,
sK122: $i > $i > $i > $i ).
thf(func_def_485,type,
sK123: $i > $i > $i > $i ).
thf(func_def_486,type,
sK124: $i > $i > $i > $i ).
thf(func_def_487,type,
sK125: $i > $i > $i > $i ).
thf(func_def_488,type,
sK126: $i > $i > $i > $i ).
thf(func_def_489,type,
ph127:
!>[X0: $tType] : X0 ).
thf(f7028,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f5285,f5313,f5318,f5323,f5328,f5357,f5401,f7025,f7027]) ).
thf(f7027,plain,
( ( $false
!= ( in @ ( kpair @ sK5 @ sK4 ) @ sK2 ) )
| ( $true
!= ( in @ ( kpair @ sK5 @ sK4 ) @ sK2 ) )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f7025,plain,
( spl6_66
| ~ spl6_2
| ~ spl6_10
| ~ spl6_12
| ~ spl6_19
| spl6_29 ),
inference(avatar_split_clause,[status(thm)],[f7024,f5398,f5354,f5325,f5315,f5282,f7019]) ).
thf(f7019,definition,
( spl6_66
<=> ( $false
= ( in @ ( kpair @ sK5 @ sK4 ) @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl6_66])],[avatar_definition]) ).
thf(f5282,definition,
( spl6_2
<=> ( $true
= ( in @ sK4 @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition]) ).
thf(f5315,definition,
( spl6_10
<=> ( $true
= ( in @ ( kpair @ sK3 @ sK5 ) @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl6_10])],[avatar_definition]) ).
thf(f5325,definition,
( spl6_12
<=> ( $true
= ( in @ sK5 @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl6_12])],[avatar_definition]) ).
thf(f5354,definition,
( spl6_19
<=> ( $true
= ( in @ sK3 @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl6_19])],[avatar_definition]) ).
thf(f5398,definition,
( spl6_29
<=> ( ( in @ ( kpair @ sK3 @ sK4 )
@ ( dpsetconstr @ sK1 @ sK1
@ ^ [Y0: $i,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK1 )
& ( in @ ( kpair @ Y0 @ Y2 ) @ sK0 )
& ( in @ ( kpair @ Y2 @ Y1 ) @ sK2 ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl6_29])],[avatar_definition]) ).
thf(f7024,plain,
( ( $false
= ( in @ ( kpair @ sK5 @ sK4 ) @ sK2 ) )
| ~ spl6_2
| ~ spl6_10
| ~ spl6_12
| ~ spl6_19
| spl6_29 ),
inference(trivial_inequality_removal,[status(thm)],[f7023]) ).
thf(f7023,plain,
( ( $false = $true )
| ( $false
= ( in @ ( kpair @ sK5 @ sK4 ) @ sK2 ) )
| ~ spl6_2
| ~ spl6_10
| ~ spl6_12
| ~ spl6_19
| spl6_29 ),
inference(forward_demodulation,[status(thm)],[f7010,f5327]) ).
thf(f5327,plain,
( ( $true
= ( in @ sK5 @ sK1 ) )
| ~ spl6_12 ),
inference(avatar_component_clause,[status(thm)],[f5325]) ).
thf(f7010,plain,
( ( $false
= ( in @ ( kpair @ sK5 @ sK4 ) @ sK2 ) )
| ( $false
= ( in @ sK5 @ sK1 ) )
| ~ spl6_2
| ~ spl6_10
| ~ spl6_19
| spl6_29 ),
inference(trivial_inequality_removal,[status(thm)],[f7006]) ).
thf(f7006,plain,
( ( $false
= ( in @ sK5 @ sK1 ) )
| ( $false
= ( in @ ( kpair @ sK5 @ sK4 ) @ sK2 ) )
| ( $false = $true )
| ~ spl6_2
| ~ spl6_10
| ~ spl6_19
| spl6_29 ),
inference(superposition,[status(thm)],[f5317,f6999]) ).
thf(f6999,plain,
( ! [X1: $i] :
( ( $false
= ( in @ ( kpair @ sK3 @ X1 ) @ sK0 ) )
| ( $false
= ( in @ ( kpair @ X1 @ sK4 ) @ sK2 ) )
| ( $false
= ( in @ X1 @ sK1 ) ) )
| ~ spl6_2
| ~ spl6_19
| spl6_29 ),
inference(trivial_inequality_removal,[status(thm)],[f6998]) ).
thf(f6998,plain,
( ! [X1: $i] :
( ( $false
= ( in @ ( kpair @ X1 @ sK4 ) @ sK2 ) )
| ( $false = $true )
| ( $false
= ( in @ ( kpair @ sK3 @ X1 ) @ sK0 ) )
| ( $false
= ( in @ X1 @ sK1 ) ) )
| ~ spl6_2
| ~ spl6_19
| spl6_29 ),
inference(forward_demodulation,[status(thm)],[f6997,f5284]) ).
thf(f5284,plain,
( ( $true
= ( in @ sK4 @ sK1 ) )
| ~ spl6_2 ),
inference(avatar_component_clause,[status(thm)],[f5282]) ).
thf(f6997,plain,
( ! [X1: $i] :
( ( $false
= ( in @ ( kpair @ X1 @ sK4 ) @ sK2 ) )
| ( $false
= ( in @ sK4 @ sK1 ) )
| ( $false
= ( in @ ( kpair @ sK3 @ X1 ) @ sK0 ) )
| ( $false
= ( in @ X1 @ sK1 ) ) )
| ~ spl6_19
| spl6_29 ),
inference(trivial_inequality_removal,[status(thm)],[f6996]) ).
thf(f6996,plain,
( ! [X1: $i] :
( ( $false
= ( in @ sK4 @ sK1 ) )
| ( $false
= ( in @ X1 @ sK1 ) )
| ( $false
= ( in @ ( kpair @ X1 @ sK4 ) @ sK2 ) )
| ( $false
= ( in @ ( kpair @ sK3 @ X1 ) @ sK0 ) )
| ( $false = $true ) )
| ~ spl6_19
| spl6_29 ),
inference(forward_demodulation,[status(thm)],[f6992,f5356]) ).
thf(f5356,plain,
( ( $true
= ( in @ sK3 @ sK1 ) )
| ~ spl6_19 ),
inference(avatar_component_clause,[status(thm)],[f5354]) ).
thf(f6992,plain,
( ! [X1: $i] :
( ( $false
= ( in @ sK3 @ sK1 ) )
| ( $false
= ( in @ ( kpair @ X1 @ sK4 ) @ sK2 ) )
| ( $false
= ( in @ ( kpair @ sK3 @ X1 ) @ sK0 ) )
| ( $false
= ( in @ sK4 @ sK1 ) )
| ( $false
= ( in @ X1 @ sK1 ) ) )
| spl6_29 ),
inference(binary_proxy_clausification,[status(thm)],[f6991]) ).
thf(f6991,plain,
( ! [X1: $i] :
( ( $false
= ( in @ sK3 @ sK1 ) )
| ( $false
= ( in @ sK4 @ sK1 ) )
| ( $false
= ( in @ ( kpair @ X1 @ sK4 ) @ sK2 ) )
| ( $false
= ( ( in @ X1 @ sK1 )
& ( in @ ( kpair @ sK3 @ X1 ) @ sK0 ) ) ) )
| spl6_29 ),
inference(binary_proxy_clausification,[status(thm)],[f6990]) ).
thf(f6990,plain,
( ! [X1: $i] :
( ( $false
= ( ( in @ X1 @ sK1 )
& ( in @ ( kpair @ sK3 @ X1 ) @ sK0 )
& ( in @ ( kpair @ X1 @ sK4 ) @ sK2 ) ) )
| ( $false
= ( in @ sK3 @ sK1 ) )
| ( $false
= ( in @ sK4 @ sK1 ) ) )
| spl6_29 ),
inference(beta_eta_normalization,[status(thm)],[f6989]) ).
thf(f6989,plain,
( ! [X1: $i] :
( ( $false
= ( in @ sK3 @ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
& ( in @ ( kpair @ sK3 @ Y0 ) @ sK0 )
& ( in @ ( kpair @ Y0 @ sK4 ) @ sK2 ) )
@ X1 ) )
| ( $false
= ( in @ sK4 @ sK1 ) ) )
| spl6_29 ),
inference(pi_clausification,[status(thm)],[f6988]) ).
thf(f6988,plain,
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK1 )
& ( in @ ( kpair @ sK3 @ Y0 ) @ sK0 )
& ( in @ ( kpair @ Y0 @ sK4 ) @ sK2 ) ) ) )
| ( $false
= ( in @ sK4 @ sK1 ) )
| ( $false
= ( in @ sK3 @ sK1 ) )
| spl6_29 ),
inference(beta_eta_normalization,[status(thm)],[f6987]) ).
thf(f6987,plain,
( ( $false
= ( ^ [Y0: $i,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK1 )
& ( in @ ( kpair @ Y0 @ Y2 ) @ sK0 )
& ( in @ ( kpair @ Y2 @ Y1 ) @ sK2 ) ) )
@ sK3
@ sK4 ) )
| ( $false
= ( in @ sK3 @ sK1 ) )
| ( $false
= ( in @ sK4 @ sK1 ) )
| spl6_29 ),
inference(trivial_inequality_removal,[status(thm)],[f6981]) ).
thf(f6981,plain,
( ( $false
= ( in @ sK3 @ sK1 ) )
| ( $false
= ( in @ sK4 @ sK1 ) )
| ( $true != $true )
| ( $false
= ( ^ [Y0: $i,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK1 )
& ( in @ ( kpair @ Y0 @ Y2 ) @ sK0 )
& ( in @ ( kpair @ Y2 @ Y1 ) @ sK2 ) ) )
@ sK3
@ sK4 ) )
| spl6_29 ),
inference(superposition,[status(thm)],[f5400,f2262]) ).
thf(f2262,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o,X4: $i,X5: $i] :
( ( ( in @ ( kpair @ X2 @ X5 ) @ ( dpsetconstr @ X4 @ X3 @ X1 ) )
= $true )
| ( ( X1 @ X2 @ X5 )
= $false )
| ( $false
= ( in @ X5 @ X3 ) )
| ( ( in @ X2 @ X4 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f2261]) ).
thf(f2261,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o,X4: $i,X5: $i] :
( ( $true
= ( ( X1 @ X2 @ X5 )
=> ( in @ ( kpair @ X2 @ X5 ) @ ( dpsetconstr @ X4 @ X3 @ X1 ) ) ) )
| ( ( in @ X2 @ X4 )
= $false )
| ( $false
= ( in @ X5 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f2260]) ).
thf(f2260,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o,X4: $i,X5: $i] :
( ( ( ( in @ X5 @ X3 )
=> ( ( X1 @ X2 @ X5 )
=> ( in @ ( kpair @ X2 @ X5 ) @ ( dpsetconstr @ X4 @ X3 @ X1 ) ) ) )
= $true )
| ( ( in @ X2 @ X4 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f2259]) ).
thf(f2259,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o,X4: $i,X5: $i] :
( ( ( in @ X2 @ X4 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ( X1 @ X2 @ Y0 )
=> ( in @ ( kpair @ X2 @ Y0 ) @ ( dpsetconstr @ X4 @ X3 @ X1 ) ) ) )
@ X5 ) ) ),
inference(pi_clausification,[status(thm)],[f2258]) ).
thf(f2258,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ( X1 @ X2 @ Y0 )
=> ( in @ ( kpair @ X2 @ Y0 ) @ ( dpsetconstr @ X4 @ X3 @ X1 ) ) ) ) )
= $true )
| ( ( in @ X2 @ X4 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f2257]) ).
thf(f2257,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o,X4: $i] :
( $true
= ( ( in @ X2 @ X4 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ( X1 @ X2 @ Y0 )
=> ( in @ ( kpair @ X2 @ Y0 ) @ ( dpsetconstr @ X4 @ X3 @ X1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2256]) ).
thf(f2256,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o,X4: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X3 )
=> ( ( X1 @ X2 @ Y1 )
=> ( in @ ( kpair @ X2 @ Y1 ) @ ( dpsetconstr @ Y0 @ X3 @ X1 ) ) ) ) ) )
@ X4 ) ),
inference(pi_clausification,[status(thm)],[f2255]) ).
thf(f2255,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X3 )
=> ( ( X1 @ X2 @ Y1 )
=> ( in @ ( kpair @ X2 @ Y1 ) @ ( dpsetconstr @ Y0 @ X3 @ X1 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2254]) ).
thf(f2254,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X2 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( X1 @ X2 @ Y2 )
=> ( in @ ( kpair @ X2 @ Y2 ) @ ( dpsetconstr @ Y1 @ Y0 @ X1 ) ) ) ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f2253]) ).
thf(f2253,plain,
! [X2: $i,X1: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X2 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( X1 @ X2 @ Y2 )
=> ( in @ ( kpair @ X2 @ Y2 ) @ ( dpsetconstr @ Y1 @ Y0 @ X1 ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2252]) ).
thf(f2252,plain,
! [X2: $i,X1: $i > $i > $o] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( X1 @ Y0 @ Y3 )
=> ( in @ ( kpair @ Y0 @ Y3 ) @ ( dpsetconstr @ Y2 @ Y1 @ X1 ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f2251]) ).
thf(f2251,plain,
! [X1: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( X1 @ Y0 @ Y3 )
=> ( in @ ( kpair @ Y0 @ Y3 ) @ ( dpsetconstr @ Y2 @ Y1 @ X1 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2250]) ).
thf(f2250,plain,
! [X1: $i > $i > $o] :
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y1 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( Y0 @ Y1 @ Y4 )
=> ( in @ ( kpair @ Y1 @ Y4 ) @ ( dpsetconstr @ Y3 @ Y2 @ Y0 ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f2249]) ).
thf(f2249,plain,
( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y1 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( Y0 @ Y1 @ Y4 )
=> ( in @ ( kpair @ Y1 @ Y4 ) @ ( dpsetconstr @ Y3 @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1638]) ).
thf(f1638,plain,
( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y1 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( Y0 @ Y1 @ Y4 )
=> ( in @ ( kpair @ Y1 @ Y4 )
@ ( dpsetconstr @ Y3 @ Y2
@ ^ [Y5: $i,Y6: $i] : ( Y0 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f1221,f1019]) ).
thf(f1019,plain,
( dpsetconstrI
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y1 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( Y0 @ Y1 @ Y4 )
=> ( in @ ( kpair @ Y1 @ Y4 )
@ ( dpsetconstr @ Y3 @ Y2
@ ^ [Y5: $i,Y6: $i] : ( Y0 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f562]) ).
thf(f562,plain,
( dpsetconstrI
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y1 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y2 )
=> ( ( Y0 @ Y1 @ Y4 )
=> ( in @ ( kpair @ Y1 @ Y4 )
@ ( dpsetconstr @ Y3 @ Y2
@ ^ [Y5: $i,Y6: $i] : ( Y0 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f561]) ).
thf(f561,plain,
( dpsetconstrI
= ( ! [X0: $i,X1: $i,X2: $i,X3: $i > $i > $o] :
( ( in @ X2 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( X3 @ X2 @ X4 )
=> ( in @ ( kpair @ X2 @ X4 )
@ ( dpsetconstr @ X0 @ X1
@ ^ [X5: $i,X6: $i] : ( X3 @ X5 @ X6 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f185]) ).
thf(f185,axiom,
( dpsetconstrI
= ( ! [X3: $i,X4: $i,X1: $i,X0: $i > $i > $o] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( X0 @ X1 @ X2 )
=> ( in @ ( kpair @ X1 @ X2 )
@ ( dpsetconstr @ X3 @ X4
@ ^ [X8: $i,X10: $i] : ( X0 @ X8 @ X10 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.V1n9lFWd3k/DTF2THF_22754.p',dpsetconstrI) ).
thf(f1221,plain,
dpsetconstrI = $true,
inference(cnf_transformation,[status(thm)],[f907]) ).
thf(f907,plain,
( ( binunionTE = $true )
& ( binintersectLsub = $true )
& ( setunionsingleton2 = $true )
& ( lamProp = $true )
& ( iffalseProp2 = $true )
& ( doubleComplementSub2 = $true )
& ( binunionT_lem = $true )
& ( setminusLsub = $true )
& ( theprop = $true )
& ( complementImpComplementIntersect = $true )
& ( emptyset__Cong = $true )
& ( iftrueProp2 = $true )
& ( binintersectI = $true )
& ( setukpairinjL2 = $true )
& ( notequalI2 = $true )
& ( binintersectSubset5 = $true )
& ( brelnall1 = $true )
& ( breln1invprop = $true )
& ( notinemptyset = $true )
& ( breln1all2 = $true )
& ( notdallE = $true )
& ( cartprodpairmemER = $true )
& ( cartprodpairmemEL = $true )
& ( exuE3u = $true )
& ( binintersectTERcontra = $true )
& ( theeq = $true )
& ( binunionE = $true )
& ( funcextLem = $true )
& ( funcGraphProp1 = $true )
& ( upairsetIR = $true )
& ( powersetE = $true )
& ( ubforcartprodlem2 = $true )
& ( setminusELneg = $true )
& ( omegaIndAx = $true )
& ( prop2setI = $true )
& ( dpsetconstrERa = $true )
& ( doubleComplementSub1 = $true )
& ( setminusILneg = $true )
& ( eqimpsubset1 = $true )
& ( ap2apEq1 = $true )
& ( inPowerset = $true )
& ( funcinfuncset = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( setoftrueEq = $true )
& ( quantDeMorgan4 = $true )
& ( setadjoinE = $true )
& ( exuE1 = $true )
& ( notsubsetI = $true )
& ( dpsetconstrER = $true )
& ( descrp = $true )
& ( emptysetE = $true )
& ( dsetconstrER = $true )
& ( powersetI1 = $true )
& ( powersetE1 = $true )
& ( contrasubsetT1 = $true )
& ( setadjoin__Cong = $true )
& ( setunion__Cong = $true )
& ( subbreln1 = $true )
& ( eqbreln1 = $true )
& ( disjointsetsI1 = $true )
& ( brelnall2 = $true )
& ( contrasubsetT = $true )
& ( funcext = $true )
& ( uniqinunit = $true )
& ( quantDeMorgan1 = $true )
& ( doubleComplementE1 = $true )
& ( breln1invE = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( cartprodmempair = $true )
& ( wellorderingAx = $true )
& ( lam2p = $true )
& ( setukpairinjR2 = $true )
& ( singletonsubset = $true )
& ( vacuousDall = $true )
& ( emptysetsubset = $true )
& ( ubforcartprodlem3 = $true )
& ( powersetAx = $true )
& ( inIntersectImpInUnion = $true )
& ( demorgan2a = $true )
& ( dpsetconstrSub = $true )
& ( powersetT_lem = $true )
& ( upairequniteq = $true )
& ( emptyInPowerset = $true )
& ( upairsetE = $true )
& ( setadjoinSub = $true )
& ( dsetconstrEL = $true )
& ( app = $true )
& ( demorgan2 = $true )
& ( binintersectSubset4 = $true )
& ( funcImageSingleton = $true )
& ( exuE3e = $true )
& ( nonemptyI = $true )
& ( binintersectTELcontra = $true )
& ( setextT = $true )
& ( ex1E1 = $true )
& ( complementTcontraSubset = $true )
& ( singletonsswitch = $true )
& ( setukpairinjL = $true )
& ( symdiffIneg1 = $true )
& ( subsetTI = $true )
& ( woz13rule1 = $true )
& ( foundationAx = $true )
& ( cartprodmempair1 = $true )
& ( doubleComplementEq = $true )
& ( powersetI = $true )
& ( binintersectEL = $true )
& ( funcGraphProp3 = $true )
& ( setukpairinjL1 = $true )
& ( subsetemptysetimpeq = $true )
& ( ex1E2 = $true )
& ( setunionE = $true )
& ( beta2 = $true )
& ( binunionTIRcontra = $true )
& ( singletonsuniq = $true )
& ( breln1invI = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( exuI3 = $true )
& ( in__Cong = $true )
& ( setukpairinjR1 = $true )
& ( demorgan1a = $true )
& ( bs114d = $true )
& ( powersetsubset = $true )
& ( setminusSubset1 = $true )
& ( ex1I2 = $true )
& ( binintersectSubset1 = $true )
& ( subset2powerset = $true )
& ( contrasubsetT3 = $true )
& ( doubleComplementI1 = $true )
& ( ex1I = $true )
& ( dsetconstr__Cong = $true )
& ( notequalI1 = $true )
& ( complementSubsetComplementIntersect = $true )
& ( ifSingleton = $true )
& ( exu__Cong = $true )
& ( symdiffI2 = $true )
& ( kpairsurjEq = $true )
& ( complementTnotintersectT = $true )
& ( symdiffI1 = $true )
& ( omega__Cong = $true )
& ( ap2p = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( sepInPowerset = $true )
& ( subPowSU = $true )
& ( emptyinPowerset = $true )
& ( sepSubset = $true )
& ( upairsetIL = $true )
& ( breln1all1 = $true )
& ( dsetconstrI = $true )
& ( secondinupair = $true )
& ( setextAx = $true )
& ( cartprodmempaircEq = $true )
& ( setminusERneg = $true )
& ( binunionIL = $true )
& ( exuI2 = $true )
& ( replAx = $true )
& ( contraSubsetComplement = $true )
& ( setbeta = $true )
& ( notinsingleton = $true )
& ( subsetE = $true )
& ( binunionEcases = $true )
& ( woz13rule3 = $true )
& ( woz1_5 = $true )
& ( quantDeMorgan3 = $true )
& ( contrasubsetT2 = $true )
& ( emptyI = $true )
& ( woz1_2 = $true )
& ( nonemptyE1 = $true )
& ( setminusT_lem = $true )
& ( woz1_4 = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( setminusI = $true )
& ( prop2setE = $true )
& ( dpsetconstrI = $true )
& ( setOfPairsIsBReln = $true )
& ( exuI1 = $true )
& ( choice2fnsingleton = $true )
& ( exuE2 = $true )
& ( cartprodfstin = $true )
& ( subsetRefl = $true )
& ( prop2set2propI = $true )
& ( noeltsimpempty = $true )
& ( emptysetAx = $true )
& ( subsetE2 = $true )
& ( subbreln = $true )
& ( dpsetconstrEL2 = $true )
& ( setadjoinIR = $true )
& ( setunionsingleton = $true )
& ( setadjoinIL = $true )
& ( powersetTI1 = $true )
& ( cartprodfstpairEq = $true )
& ( nonemptyI1 = $true )
& ( setunionsingleton1 = $true )
& ( binunionTILcontra = $true )
& ( kfstsingleton = $true )
& ( setukpairinjR11 = $true )
& ( emptyE1 = $true )
& ( singletoninpowerset = $true )
& ( emptysetimpfalse = $true )
& ( kpairiskpair = $true )
& ( setadjoinAx = $true )
& ( lamp = $true )
& ( binintersectER = $true )
& ( lam2lamEq = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( woz13rule4 = $true )
& ( upairset2E = $true )
& ( setOfPairsIsBReln1 = $true )
& ( beta1 = $true )
& ( kfstpairEq = $true )
& ( inCongP = $true )
& ( setext = $true )
& ( setukpairIL = $true )
& ( woz13rule0 = $true )
& ( symdiffE = $true )
& ( upairsubunion = $true )
& ( cartprodsndin = $true )
& ( iffalseProp1 = $true )
& ( complementT_lem = $true )
& ( setminusER = $true )
& ( setunionE2 = $true )
& ( funcGraphProp2 = $true )
& ( ubforcartprodlem1 = $true )
& ( setminusIRneg = $true )
& ( demorgan1b = $true )
& ( binintersectSubset3 = $true )
& ( cartprodsndpairEq = $true )
& ( binintersectRsub = $true )
& ( eqimpsubset2 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( breln1compprop = $true )
& ( powerset__Cong = $true )
& ( dpsetconstrEL1 = $true )
& ( inIntersectImpInUnion2 = $true )
& ( funcGraphProp4 = $true )
& ( notdexE = $true )
& ( demorgan2b2 = $true )
& ( binintersectSubset2 = $true )
& ( subsetTrans = $true )
& ( eqbreln = $true )
& ( setadjoinOr = $true )
& ( setunionAx = $true )
& ( binunionIR = $true )
& ( subsetI2 = $true )
& ( iftrueProp1 = $true )
& ( breln1SetBreln1 = $true )
& ( funcext2 = $true )
& ( woz1_1 = $true )
& ( eta2 = $true )
& ( upairinpowunion = $true )
& ( demorgan2b = $true )
& ( woz13rule2 = $true )
& ( powersetTE1 = $true )
& ( exuEu = $true )
& ( setukpairinjR = $true )
& ( complementTI1 = $true )
& ( ifp = $true )
& ( iffalse = $true )
& ( kpairp = $true )
& ( setminusSubset2 = $true )
& ( quantDeMorgan2 = $true )
& ( infuncsetfunc = $true )
& ( demorgan2a1 = $true )
& ( nonemptyImpWitness = $true )
& ( $true
= ( in @ sK3 @ sK1 ) )
& ( $true
= ( in @ sK4 @ sK1 ) )
& ( $true
= ( in @ ( kpair @ sK5 @ sK4 ) @ sK2 ) )
& ( $true
= ( in @ ( kpair @ sK3 @ sK5 ) @ sK0 ) )
& ( $true
= ( in @ sK5 @ sK1 ) )
& ( $true
!= ( in @ ( kpair @ sK3 @ sK4 ) @ ( breln1compset @ sK1 @ sK0 @ sK2 ) ) )
& ( $true
= ( breln1 @ sK1 @ sK2 ) )
& ( $true
= ( breln1 @ sK1 @ sK0 ) )
& ( apProp = $true )
& ( setukpairinjR12 = $true )
& ( setukpairIR = $true )
& ( omega0Ax = $true )
& ( setminusEL = $true )
& ( ksndpairEq = $true )
& ( setextsub = $true )
& ( descr__Cong = $true )
& ( ap2apEq2 = $true )
& ( binunionTEcontra = $true )
& ( iftrue = $true )
& ( setadjoinSub2 = $true )
& ( cartprodpairin = $true )
& ( demorgan2a2 = $true )
& ( woz1_3 = $true )
& ( demorgan1 = $true )
& ( singletonprop = $true )
& ( iftrueorfalse = $true )
& ( omegaSAx = $true )
& ( emptyinunitempty = $true )
& ( subsetI1 = $true )
& ( ksndsingleton = $true )
& ( upairset2IR = $true )
& ( eqinunit = $true )
& ( binintersectT_lem = $true )
& ( complementTE1 = $true )
& ( cartprodpairsurjEq = $true )
& ( symdiffIneg2 = $true )
& ( setunionI = $true )
& ( eta1 = $true )
& ( singletoninpowunion = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f901,f906,f905,f904,f903,f902]) ).
thf(f902,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ? [X4: $i] :
( ( $true
= ( in @ X4 @ X1 ) )
& ? [X5: $i] :
( ( ( in @ ( kpair @ X5 @ X4 ) @ X2 )
= $true )
& ( ( in @ ( kpair @ X3 @ X5 ) @ X0 )
= $true )
& ( $true
= ( in @ X5 @ X1 ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X1 @ X0 @ X2 ) )
!= $true ) ) ) )
& ( ( breln1 @ X1 @ X2 )
= $true ) )
& ( $true
= ( breln1 @ X1 @ X0 ) ) )
=> ( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK1 ) )
& ? [X4: $i] :
( ( ( in @ X4 @ sK1 )
= $true )
& ? [X5: $i] :
( ( ( in @ ( kpair @ X5 @ X4 ) @ X2 )
= $true )
& ( ( in @ ( kpair @ X3 @ X5 ) @ sK0 )
= $true )
& ( $true
= ( in @ X5 @ sK1 ) )
& ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ sK1 @ sK0 @ X2 ) ) ) ) ) )
& ( $true
= ( breln1 @ sK1 @ X2 ) ) )
& ( $true
= ( breln1 @ sK1 @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f903,plain,
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK1 ) )
& ? [X4: $i] :
( ( ( in @ X4 @ sK1 )
= $true )
& ? [X5: $i] :
( ( ( in @ ( kpair @ X5 @ X4 ) @ X2 )
= $true )
& ( ( in @ ( kpair @ X3 @ X5 ) @ sK0 )
= $true )
& ( $true
= ( in @ X5 @ sK1 ) )
& ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ sK1 @ sK0 @ X2 ) ) ) ) ) )
& ( $true
= ( breln1 @ sK1 @ X2 ) ) )
=> ( ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK1 ) )
& ? [X4: $i] :
( ( ( in @ X4 @ sK1 )
= $true )
& ? [X5: $i] :
( ( $true
= ( in @ ( kpair @ X5 @ X4 ) @ sK2 ) )
& ( ( in @ ( kpair @ X3 @ X5 ) @ sK0 )
= $true )
& ( $true
= ( in @ X5 @ sK1 ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ sK1 @ sK0 @ sK2 ) )
!= $true ) ) ) )
& ( $true
= ( breln1 @ sK1 @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f904,plain,
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ sK1 ) )
& ? [X4: $i] :
( ( ( in @ X4 @ sK1 )
= $true )
& ? [X5: $i] :
( ( $true
= ( in @ ( kpair @ X5 @ X4 ) @ sK2 ) )
& ( ( in @ ( kpair @ X3 @ X5 ) @ sK0 )
= $true )
& ( $true
= ( in @ X5 @ sK1 ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ sK1 @ sK0 @ sK2 ) )
!= $true ) ) ) )
=> ( ( $true
= ( in @ sK3 @ sK1 ) )
& ? [X4: $i] :
( ( ( in @ X4 @ sK1 )
= $true )
& ? [X5: $i] :
( ( $true
= ( in @ ( kpair @ X5 @ X4 ) @ sK2 ) )
& ( $true
= ( in @ ( kpair @ sK3 @ X5 ) @ sK0 ) )
& ( $true
= ( in @ X5 @ sK1 ) )
& ( ( in @ ( kpair @ sK3 @ X4 ) @ ( breln1compset @ sK1 @ sK0 @ sK2 ) )
!= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f905,plain,
( ? [X4: $i] :
( ( ( in @ X4 @ sK1 )
= $true )
& ? [X5: $i] :
( ( $true
= ( in @ ( kpair @ X5 @ X4 ) @ sK2 ) )
& ( $true
= ( in @ ( kpair @ sK3 @ X5 ) @ sK0 ) )
& ( $true
= ( in @ X5 @ sK1 ) )
& ( ( in @ ( kpair @ sK3 @ X4 ) @ ( breln1compset @ sK1 @ sK0 @ sK2 ) )
!= $true ) ) )
=> ( ( $true
= ( in @ sK4 @ sK1 ) )
& ? [X5: $i] :
( ( $true
= ( in @ ( kpair @ X5 @ sK4 ) @ sK2 ) )
& ( $true
= ( in @ ( kpair @ sK3 @ X5 ) @ sK0 ) )
& ( $true
= ( in @ X5 @ sK1 ) )
& ( $true
!= ( in @ ( kpair @ sK3 @ sK4 ) @ ( breln1compset @ sK1 @ sK0 @ sK2 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f906,plain,
( ? [X5: $i] :
( ( $true
= ( in @ ( kpair @ X5 @ sK4 ) @ sK2 ) )
& ( $true
= ( in @ ( kpair @ sK3 @ X5 ) @ sK0 ) )
& ( $true
= ( in @ X5 @ sK1 ) )
& ( $true
!= ( in @ ( kpair @ sK3 @ sK4 ) @ ( breln1compset @ sK1 @ sK0 @ sK2 ) ) ) )
=> ( ( $true
= ( in @ ( kpair @ sK5 @ sK4 ) @ sK2 ) )
& ( $true
= ( in @ ( kpair @ sK3 @ sK5 ) @ sK0 ) )
& ( $true
= ( in @ sK5 @ sK1 ) )
& ( $true
!= ( in @ ( kpair @ sK3 @ sK4 ) @ ( breln1compset @ sK1 @ sK0 @ sK2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f901,plain,
( ( binunionTE = $true )
& ( binintersectLsub = $true )
& ( setunionsingleton2 = $true )
& ( lamProp = $true )
& ( iffalseProp2 = $true )
& ( doubleComplementSub2 = $true )
& ( binunionT_lem = $true )
& ( setminusLsub = $true )
& ( theprop = $true )
& ( complementImpComplementIntersect = $true )
& ( emptyset__Cong = $true )
& ( iftrueProp2 = $true )
& ( binintersectI = $true )
& ( setukpairinjL2 = $true )
& ( notequalI2 = $true )
& ( binintersectSubset5 = $true )
& ( brelnall1 = $true )
& ( breln1invprop = $true )
& ( notinemptyset = $true )
& ( breln1all2 = $true )
& ( notdallE = $true )
& ( cartprodpairmemER = $true )
& ( cartprodpairmemEL = $true )
& ( exuE3u = $true )
& ( binintersectTERcontra = $true )
& ( theeq = $true )
& ( binunionE = $true )
& ( funcextLem = $true )
& ( funcGraphProp1 = $true )
& ( upairsetIR = $true )
& ( powersetE = $true )
& ( ubforcartprodlem2 = $true )
& ( setminusELneg = $true )
& ( omegaIndAx = $true )
& ( prop2setI = $true )
& ( dpsetconstrERa = $true )
& ( doubleComplementSub1 = $true )
& ( setminusILneg = $true )
& ( eqimpsubset1 = $true )
& ( ap2apEq1 = $true )
& ( inPowerset = $true )
& ( funcinfuncset = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( setoftrueEq = $true )
& ( quantDeMorgan4 = $true )
& ( setadjoinE = $true )
& ( exuE1 = $true )
& ( notsubsetI = $true )
& ( dpsetconstrER = $true )
& ( descrp = $true )
& ( emptysetE = $true )
& ( dsetconstrER = $true )
& ( powersetI1 = $true )
& ( powersetE1 = $true )
& ( contrasubsetT1 = $true )
& ( setadjoin__Cong = $true )
& ( setunion__Cong = $true )
& ( subbreln1 = $true )
& ( eqbreln1 = $true )
& ( disjointsetsI1 = $true )
& ( brelnall2 = $true )
& ( contrasubsetT = $true )
& ( funcext = $true )
& ( uniqinunit = $true )
& ( quantDeMorgan1 = $true )
& ( doubleComplementE1 = $true )
& ( breln1invE = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( cartprodmempair = $true )
& ( wellorderingAx = $true )
& ( lam2p = $true )
& ( setukpairinjR2 = $true )
& ( singletonsubset = $true )
& ( vacuousDall = $true )
& ( emptysetsubset = $true )
& ( ubforcartprodlem3 = $true )
& ( powersetAx = $true )
& ( inIntersectImpInUnion = $true )
& ( demorgan2a = $true )
& ( dpsetconstrSub = $true )
& ( powersetT_lem = $true )
& ( upairequniteq = $true )
& ( emptyInPowerset = $true )
& ( upairsetE = $true )
& ( setadjoinSub = $true )
& ( dsetconstrEL = $true )
& ( app = $true )
& ( demorgan2 = $true )
& ( binintersectSubset4 = $true )
& ( funcImageSingleton = $true )
& ( exuE3e = $true )
& ( nonemptyI = $true )
& ( binintersectTELcontra = $true )
& ( setextT = $true )
& ( ex1E1 = $true )
& ( complementTcontraSubset = $true )
& ( singletonsswitch = $true )
& ( setukpairinjL = $true )
& ( symdiffIneg1 = $true )
& ( subsetTI = $true )
& ( woz13rule1 = $true )
& ( foundationAx = $true )
& ( cartprodmempair1 = $true )
& ( doubleComplementEq = $true )
& ( powersetI = $true )
& ( binintersectEL = $true )
& ( funcGraphProp3 = $true )
& ( setukpairinjL1 = $true )
& ( subsetemptysetimpeq = $true )
& ( ex1E2 = $true )
& ( setunionE = $true )
& ( beta2 = $true )
& ( binunionTIRcontra = $true )
& ( singletonsuniq = $true )
& ( breln1invI = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( exuI3 = $true )
& ( in__Cong = $true )
& ( setukpairinjR1 = $true )
& ( demorgan1a = $true )
& ( bs114d = $true )
& ( powersetsubset = $true )
& ( setminusSubset1 = $true )
& ( ex1I2 = $true )
& ( binintersectSubset1 = $true )
& ( subset2powerset = $true )
& ( contrasubsetT3 = $true )
& ( doubleComplementI1 = $true )
& ( ex1I = $true )
& ( dsetconstr__Cong = $true )
& ( notequalI1 = $true )
& ( complementSubsetComplementIntersect = $true )
& ( ifSingleton = $true )
& ( exu__Cong = $true )
& ( symdiffI2 = $true )
& ( kpairsurjEq = $true )
& ( complementTnotintersectT = $true )
& ( symdiffI1 = $true )
& ( omega__Cong = $true )
& ( ap2p = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( sepInPowerset = $true )
& ( subPowSU = $true )
& ( emptyinPowerset = $true )
& ( sepSubset = $true )
& ( upairsetIL = $true )
& ( breln1all1 = $true )
& ( dsetconstrI = $true )
& ( secondinupair = $true )
& ( setextAx = $true )
& ( cartprodmempaircEq = $true )
& ( setminusERneg = $true )
& ( binunionIL = $true )
& ( exuI2 = $true )
& ( replAx = $true )
& ( contraSubsetComplement = $true )
& ( setbeta = $true )
& ( notinsingleton = $true )
& ( subsetE = $true )
& ( binunionEcases = $true )
& ( woz13rule3 = $true )
& ( woz1_5 = $true )
& ( quantDeMorgan3 = $true )
& ( contrasubsetT2 = $true )
& ( emptyI = $true )
& ( woz1_2 = $true )
& ( nonemptyE1 = $true )
& ( setminusT_lem = $true )
& ( woz1_4 = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( setminusI = $true )
& ( prop2setE = $true )
& ( dpsetconstrI = $true )
& ( setOfPairsIsBReln = $true )
& ( exuI1 = $true )
& ( choice2fnsingleton = $true )
& ( exuE2 = $true )
& ( cartprodfstin = $true )
& ( subsetRefl = $true )
& ( prop2set2propI = $true )
& ( noeltsimpempty = $true )
& ( emptysetAx = $true )
& ( subsetE2 = $true )
& ( subbreln = $true )
& ( dpsetconstrEL2 = $true )
& ( setadjoinIR = $true )
& ( setunionsingleton = $true )
& ( setadjoinIL = $true )
& ( powersetTI1 = $true )
& ( cartprodfstpairEq = $true )
& ( nonemptyI1 = $true )
& ( setunionsingleton1 = $true )
& ( binunionTILcontra = $true )
& ( kfstsingleton = $true )
& ( setukpairinjR11 = $true )
& ( emptyE1 = $true )
& ( singletoninpowerset = $true )
& ( emptysetimpfalse = $true )
& ( kpairiskpair = $true )
& ( setadjoinAx = $true )
& ( lamp = $true )
& ( binintersectER = $true )
& ( lam2lamEq = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( woz13rule4 = $true )
& ( upairset2E = $true )
& ( setOfPairsIsBReln1 = $true )
& ( beta1 = $true )
& ( kfstpairEq = $true )
& ( inCongP = $true )
& ( setext = $true )
& ( setukpairIL = $true )
& ( woz13rule0 = $true )
& ( symdiffE = $true )
& ( upairsubunion = $true )
& ( cartprodsndin = $true )
& ( iffalseProp1 = $true )
& ( complementT_lem = $true )
& ( setminusER = $true )
& ( setunionE2 = $true )
& ( funcGraphProp2 = $true )
& ( ubforcartprodlem1 = $true )
& ( setminusIRneg = $true )
& ( demorgan1b = $true )
& ( binintersectSubset3 = $true )
& ( cartprodsndpairEq = $true )
& ( binintersectRsub = $true )
& ( eqimpsubset2 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( breln1compprop = $true )
& ( powerset__Cong = $true )
& ( dpsetconstrEL1 = $true )
& ( inIntersectImpInUnion2 = $true )
& ( funcGraphProp4 = $true )
& ( notdexE = $true )
& ( demorgan2b2 = $true )
& ( binintersectSubset2 = $true )
& ( subsetTrans = $true )
& ( eqbreln = $true )
& ( setadjoinOr = $true )
& ( setunionAx = $true )
& ( binunionIR = $true )
& ( subsetI2 = $true )
& ( iftrueProp1 = $true )
& ( breln1SetBreln1 = $true )
& ( funcext2 = $true )
& ( woz1_1 = $true )
& ( eta2 = $true )
& ( upairinpowunion = $true )
& ( demorgan2b = $true )
& ( woz13rule2 = $true )
& ( powersetTE1 = $true )
& ( exuEu = $true )
& ( setukpairinjR = $true )
& ( complementTI1 = $true )
& ( ifp = $true )
& ( iffalse = $true )
& ( kpairp = $true )
& ( setminusSubset2 = $true )
& ( quantDeMorgan2 = $true )
& ( infuncsetfunc = $true )
& ( demorgan2a1 = $true )
& ( nonemptyImpWitness = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ? [X4: $i] :
( ( $true
= ( in @ X4 @ X1 ) )
& ? [X5: $i] :
( ( ( in @ ( kpair @ X5 @ X4 ) @ X2 )
= $true )
& ( ( in @ ( kpair @ X3 @ X5 ) @ X0 )
= $true )
& ( $true
= ( in @ X5 @ X1 ) )
& ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X1 @ X0 @ X2 ) )
!= $true ) ) ) )
& ( ( breln1 @ X1 @ X2 )
= $true ) )
& ( $true
= ( breln1 @ X1 @ X0 ) ) )
& ( apProp = $true )
& ( setukpairinjR12 = $true )
& ( setukpairIR = $true )
& ( omega0Ax = $true )
& ( setminusEL = $true )
& ( ksndpairEq = $true )
& ( setextsub = $true )
& ( descr__Cong = $true )
& ( ap2apEq2 = $true )
& ( binunionTEcontra = $true )
& ( iftrue = $true )
& ( setadjoinSub2 = $true )
& ( cartprodpairin = $true )
& ( demorgan2a2 = $true )
& ( woz1_3 = $true )
& ( demorgan1 = $true )
& ( singletonprop = $true )
& ( iftrueorfalse = $true )
& ( omegaSAx = $true )
& ( emptyinunitempty = $true )
& ( subsetI1 = $true )
& ( ksndsingleton = $true )
& ( upairset2IR = $true )
& ( eqinunit = $true )
& ( binintersectT_lem = $true )
& ( complementTE1 = $true )
& ( cartprodpairsurjEq = $true )
& ( symdiffIneg2 = $true )
& ( setunionI = $true )
& ( eta1 = $true )
& ( singletoninpowunion = $true ) ),
inference(flattening,[status(thm)],[f900]) ).
thf(f900,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ? [X5: $i] :
( ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X1 @ X0 @ X2 ) )
!= $true )
& ( ( in @ ( kpair @ X5 @ X4 ) @ X2 )
= $true )
& ( ( in @ ( kpair @ X3 @ X5 ) @ X0 )
= $true )
& ( $true
= ( in @ X5 @ X1 ) ) )
& ( $true
= ( in @ X4 @ X1 ) ) )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( breln1 @ X1 @ X2 )
= $true ) )
& ( $true
= ( breln1 @ X1 @ X0 ) ) )
& ( 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)],[f666]) ).
thf(f666,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 )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( breln1 @ X1 @ X0 ) )
=> ! [X2: $i] :
( ( ( breln1 @ X1 @ X2 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ! [X4: $i] :
( ( $true
= ( in @ X4 @ X1 ) )
=> ! [X5: $i] :
( ( $true
= ( in @ X5 @ X1 ) )
=> ( ( ( in @ ( kpair @ X3 @ X5 ) @ X0 )
= $true )
=> ( ( ( in @ ( kpair @ X5 @ X4 ) @ X2 )
= $true )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X1 @ X0 @ X2 ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f665]) ).
thf(f665,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
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X1 @ X0 )
=> ! [X2: $i] :
( ( breln1 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X5 ) @ X0 )
=> ( ( in @ ( kpair @ X5 @ X4 ) @ X2 )
=> ( in @ ( kpair @ X3 @ X4 ) @ ( breln1compset @ X1 @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f302]) ).
thf(f302,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
=> ! [X13: $i,X3: $i] :
( ( breln1 @ X3 @ X13 )
=> ! [X15: $i] :
( ( breln1 @ X3 @ X15 )
=> ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X3 )
=> ! [X8: $i] :
( ( in @ X8 @ X3 )
=> ( ( in @ ( kpair @ X1 @ X8 ) @ X13 )
=> ( ( in @ ( kpair @ X8 @ X2 ) @ X15 )
=> ( in @ ( kpair @ X1 @ X2 ) @ ( breln1compset @ X3 @ X13 @ X15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f301]) ).
thf(f301,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
=> ! [X13: $i,X3: $i] :
( ( breln1 @ X3 @ X13 )
=> ! [X15: $i] :
( ( breln1 @ X3 @ X15 )
=> ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X3 )
=> ! [X8: $i] :
( ( in @ X8 @ X3 )
=> ( ( in @ ( kpair @ X1 @ X8 ) @ X13 )
=> ( ( in @ ( kpair @ X8 @ X2 ) @ X15 )
=> ( in @ ( kpair @ X1 @ X2 ) @ ( breln1compset @ X3 @ X13 @ X15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.V1n9lFWd3k/DTF2THF_22754.p',breln1compI) ).
thf(f5400,plain,
( ( ( in @ ( kpair @ sK3 @ sK4 )
@ ( dpsetconstr @ sK1 @ sK1
@ ^ [Y0: $i,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK1 )
& ( in @ ( kpair @ Y0 @ Y2 ) @ sK0 )
& ( in @ ( kpair @ Y2 @ Y1 ) @ sK2 ) ) ) ) )
!= $true )
| spl6_29 ),
inference(avatar_component_clause,[status(thm)],[f5398]) ).
thf(f5317,plain,
( ( $true
= ( in @ ( kpair @ sK3 @ sK5 ) @ sK0 ) )
| ~ spl6_10 ),
inference(avatar_component_clause,[status(thm)],[f5315]) ).
thf(f5401,plain,
~ spl6_29,
inference(avatar_split_clause,[status(thm)],[f2101,f5398]) ).
thf(f2101,plain,
( ( in @ ( kpair @ sK3 @ sK4 )
@ ( dpsetconstr @ sK1 @ sK1
@ ^ [Y0: $i,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK1 )
& ( in @ ( kpair @ Y0 @ Y2 ) @ sK0 )
& ( in @ ( kpair @ Y2 @ Y1 ) @ sK2 ) ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f1691]) ).
thf(f1691,plain,
( $true
!= ( in @ ( kpair @ sK3 @ sK4 )
@ ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y3: $i,Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y0 )
& ( in @ ( kpair @ Y3 @ Y5 ) @ Y1 )
& ( in @ ( kpair @ Y5 @ Y4 ) @ Y2 ) ) ) )
@ sK1
@ sK0
@ sK2 ) ) ),
inference(definition_unfolding,[status(thm)],[f1125,f1486]) ).
thf(f1486,plain,
( breln1compset
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y3: $i,Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y0 )
& ( in @ ( kpair @ Y3 @ Y5 ) @ Y1 )
& ( in @ ( kpair @ Y5 @ Y4 ) @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f505]) ).
thf(f505,plain,
( breln1compset
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y3: $i,Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y0 )
& ( in @ ( kpair @ Y3 @ Y5 ) @ Y1 )
& ( in @ ( kpair @ Y5 @ Y4 ) @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f504]) ).
thf(f504,plain,
( breln1compset
= ( ^ [X0: $i,X1: $i,X2: $i] :
( dpsetconstr @ X0 @ X0
@ ^ [X3: $i,X4: $i] :
? [X5: $i] :
( ( in @ ( kpair @ X5 @ X4 ) @ X2 )
& ( in @ ( kpair @ X3 @ X5 ) @ X1 )
& ( in @ X5 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f299]) ).
thf(f299,axiom,
( breln1compset
= ( ^ [X3: $i,X13: $i,X15: $i] :
( dpsetconstr @ X3 @ X3
@ ^ [X1: $i,X2: $i] :
? [X8: $i] :
( ( in @ ( kpair @ X8 @ X2 ) @ X15 )
& ( in @ ( kpair @ X1 @ X8 ) @ X13 )
& ( in @ X8 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.V1n9lFWd3k/DTF2THF_22754.p',breln1compset) ).
thf(f1125,plain,
( $true
!= ( in @ ( kpair @ sK3 @ sK4 ) @ ( breln1compset @ sK1 @ sK0 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f907]) ).
thf(f5357,plain,
spl6_19,
inference(avatar_split_clause,[status(thm)],[f1130,f5354]) ).
thf(f1130,plain,
( $true
= ( in @ sK3 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f907]) ).
thf(f5328,plain,
spl6_12,
inference(avatar_split_clause,[status(thm)],[f1126,f5325]) ).
thf(f1126,plain,
( $true
= ( in @ sK5 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f907]) ).
thf(f5323,plain,
~ spl6_11,
inference(avatar_split_clause,[status(thm)],[f303,f5320]) ).
thf(f5320,definition,
( spl6_11
<=> ( $false = $true ) ),
introduced(definition,[new_symbols(naming,[spl6_11])],[avatar_definition]) ).
thf(f303,plain,
$false != $true,
introduced(definition,[],[fool_axiom]) ).
thf(f5318,plain,
spl6_10,
inference(avatar_split_clause,[status(thm)],[f1127,f5315]) ).
thf(f1127,plain,
( $true
= ( in @ ( kpair @ sK3 @ sK5 ) @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f907]) ).
thf(f5313,plain,
spl6_9,
inference(avatar_split_clause,[status(thm)],[f1128,f5310]) ).
thf(f5310,definition,
( spl6_9
<=> ( $true
= ( in @ ( kpair @ sK5 @ sK4 ) @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl6_9])],[avatar_definition]) ).
thf(f1128,plain,
( $true
= ( in @ ( kpair @ sK5 @ sK4 ) @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f907]) ).
thf(f5285,plain,
spl6_2,
inference(avatar_split_clause,[status(thm)],[f1129,f5282]) ).
thf(f1129,plain,
( $true
= ( in @ sK4 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f907]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU779^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n005.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:33:29 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : SEU779^1 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.46 % Domain : Set Theory
% 0.20/0.46 % Problem : Binary Relations on a Set
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English : (! A:i.! R:i.breln1 A R -> (! S:i.breln1 A S -> (! x:i.in x A ->
% 0.20/0.46 % (! y:i.in y A -> (! z:i.in z A -> in (kpair x z) R ->
% 0.20/0.46 % in (kpair z y) S -> in (kpair x y) (breln1compset A R S))))))
% 0.20/0.46
% 0.20/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.20/0.46 % Source : [Bro08]
% 0.20/0.46 % Names : ZFC281g [Bro08]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.44 v9.1.0, 0.50 v9.0.0, 0.60 v8.2.0, 0.77 v8.1.0, 0.82 v7.5.0, 0.71 v7.4.0, 0.78 v7.2.0, 0.75 v7.0.0, 0.71 v6.4.0, 0.67 v6.3.0, 1.00 v6.1.0, 0.86 v5.5.0, 0.83 v5.4.0, 0.80 v5.2.0, 1.00 v3.7.0
% 0.20/0.46 % Syntax : Number of formulae : 644 ( 300 unt; 343 typ; 300 def)
% 0.20/0.46 % Number of atoms : 1820 ( 430 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 303 ( 6 avg)
% 0.20/0.46 % Number of connectives : 3945 ( 73 ~; 12 |; 48 &;2863 @)
% 0.20/0.46 % ( 14 <=>; 935 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 313 ( 2 avg)
% 0.20/0.46 % Number of types : 2 ( 0 usr)
% 0.20/0.46 % Number of type conns : 157 ( 157 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 346 ( 343 usr; 299 con; 0-4 aty)
% 0.20/0.46 % Number of variables : 1046 ( 81 ^; 928 !; 37 ?;1046 :)
% 0.20/0.46 % SPC : TH0_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : http://mathgate.info/detsetitem.php?id=345
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(in_type,type,
% 0.20/0.46 in: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(exu_type,type,
% 0.20/0.46 exu: ( $i > $o ) > $o ).
% 0.20/0.46
% 0.20/0.46 thf(exu,definition,
% 0.20/0.46 ( exu
% 0.20/0.46 = ( ^ [Xphi: $i > $o] :
% 0.20/0.46 ? [Xx: $i] :
% 0.20/0.46 ( ( Xphi @ Xx )
% 0.20/0.46 & ! [Xy: $i] :
% 0.20/0.46 ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setextAx_type,type,
% 0.20/0.46 setextAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setextAx,definition,
% 0.20/0.46 ( setextAx
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 <=> ( in @ Xx @ B ) )
% 0.20/0.46 => ( A = B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptyset_type,type,
% 0.20/0.46 emptyset: $i ).
% 0.20/0.46
% 0.20/0.46 thf(emptysetAx_type,type,
% 0.20/0.46 emptysetAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptysetAx,definition,
% 0.20/0.46 ( emptysetAx
% 0.20/0.46 = ( ! [Xx: $i] :
% 0.20/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoin_type,type,
% 0.20/0.46 setadjoin: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinAx_type,type,
% 0.20/0.46 setadjoinAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinAx,definition,
% 0.20/0.46 ( setadjoinAx
% 0.20/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.20/0.46 <=> ( ( Xy = Xx )
% 0.20/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powerset_type,type,
% 0.20/0.46 powerset: $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(powersetAx_type,type,
% 0.20/0.46 powersetAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powersetAx,definition,
% 0.20/0.46 ( powersetAx
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.20/0.46 <=> ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setunion_type,type,
% 0.20/0.46 setunion: $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(setunionAx_type,type,
% 0.20/0.46 setunionAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setunionAx,definition,
% 0.20/0.46 ( setunionAx
% 0.20/0.46 = ( ! [A: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.20/0.46 <=> ? [B: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 & ( in @ B @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(omega_type,type,
% 0.20/0.46 omega: $i ).
% 0.20/0.46
% 0.20/0.46 thf(omega0Ax_type,type,
% 0.20/0.46 omega0Ax: $o ).
% 0.20/0.46
% 0.20/0.46 thf(omega0Ax,definition,
% 0.20/0.46 ( omega0Ax
% 0.20/0.46 = ( in @ emptyset @ omega ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(omegaSAx_type,type,
% 0.20/0.46 omegaSAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(omegaSAx,definition,
% 0.20/0.46 ( omegaSAx
% 0.20/0.46 = ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ omega )
% 0.20/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(omegaIndAx_type,type,
% 0.20/0.46 omegaIndAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(omegaIndAx,definition,
% 0.20/0.46 ( omegaIndAx
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ( ( in @ emptyset @ A )
% 0.20/0.46 & ! [Xx: $i] :
% 0.20/0.46 ( ( ( in @ Xx @ omega )
% 0.20/0.46 & ( in @ Xx @ A ) )
% 0.20/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ omega )
% 0.20/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(replAx_type,type,
% 0.20/0.46 replAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(replAx,definition,
% 0.20/0.46 ( replAx
% 0.20/0.46 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( exu
% 0.20/0.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.20/0.46 => ? [B: $i] :
% 0.20/0.46 ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 <=> ? [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(foundationAx_type,type,
% 0.20/0.46 foundationAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(foundationAx,definition,
% 0.20/0.46 ( foundationAx
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.20/0.46 => ? [B: $i] :
% 0.20/0.46 ( ( in @ B @ A )
% 0.20/0.46 & ~ ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(wellorderingAx_type,type,
% 0.20/0.46 wellorderingAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(wellorderingAx,definition,
% 0.20/0.46 ( wellorderingAx
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ? [B: $i] :
% 0.20/0.46 ( ! [C: $i] :
% 0.20/0.46 ( ( in @ C @ B )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ C )
% 0.20/0.46 => ( in @ Xx @ A ) ) )
% 0.20/0.46 & ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( ( in @ Xx @ A )
% 0.20/0.46 & ( in @ Xy @ A ) )
% 0.20/0.46 => ( ! [C: $i] :
% 0.20/0.46 ( ( in @ C @ B )
% 0.20/0.46 => ( ( in @ Xx @ C )
% 0.20/0.46 <=> ( in @ Xy @ C ) ) )
% 0.20/0.46 => ( Xx = Xy ) ) )
% 0.20/0.46 & ! [C: $i,D: $i] :
% 0.20/0.46 ( ( ( in @ C @ B )
% 0.20/0.46 & ( in @ D @ B ) )
% 0.20/0.46 => ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ C )
% 0.20/0.46 => ( in @ Xx @ D ) )
% 0.20/0.46 | ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ D )
% 0.20/0.46 => ( in @ Xx @ C ) ) ) )
% 0.20/0.46 & ! [C: $i] :
% 0.20/0.46 ( ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ C )
% 0.20/0.46 => ( in @ Xx @ A ) )
% 0.20/0.46 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.20/0.46 => ? [D: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ D @ B )
% 0.20/0.46 & ( in @ Xx @ C )
% 0.20/0.46 & ~ ? [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ D )
% 0.20/0.46 & ( in @ Xy @ C ) )
% 0.20/0.46 & ! [E: $i] :
% 0.20/0.46 ( ( in @ E @ B )
% 0.20/0.46 => ( ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ E )
% 0.20/0.46 => ( in @ Xy @ D ) )
% 0.20/0.46 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(descr_type,type,
% 0.20/0.46 descr: ( $i > $o ) > $i ).
% 0.20/0.46
% 0.20/0.46 thf(descrp_type,type,
% 0.20/0.46 descrp: $o ).
% 0.20/0.46
% 0.20/0.46 thf(descrp,definition,
% 0.20/0.46 ( descrp
% 0.20/0.46 = ( ! [Xphi: $i > $o] :
% 0.20/0.46 ( ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 => ( Xphi
% 0.20/0.46 @ ( descr
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstr_type,type,
% 0.20/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstrI_type,type,
% 0.20/0.46 dsetconstrI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstrI,definition,
% 0.20/0.46 ( dsetconstrI
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( Xphi @ Xx )
% 0.20/0.46 => ( in @ Xx
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstrEL_type,type,
% 0.20/0.46 dsetconstrEL: $o ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstrEL,definition,
% 0.20/0.46 ( dsetconstrEL
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.20/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstrER_type,type,
% 0.20/0.46 dsetconstrER: $o ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstrER,definition,
% 0.20/0.46 ( dsetconstrER
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.20/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(exuE1_type,type,
% 0.20/0.46 exuE1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(exuE1,definition,
% 0.20/0.46 ( exuE1
% 0.20/0.46 = ( ! [Xphi: $i > $o] :
% 0.20/0.46 ( ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 => ? [Xx: $i] :
% 0.20/0.46 ( ( Xphi @ Xx )
% 0.20/0.46 & ! [Xy: $i] :
% 0.20/0.46 ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(prop2set_type,type,
% 0.20/0.46 prop2set: $o > $i ).
% 0.20/0.46
% 0.20/0.46 thf(prop2setE_type,type,
% 0.20/0.46 prop2setE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(prop2setE,definition,
% 0.20/0.46 ( prop2setE
% 0.20/0.46 = ( ! [Xphi: $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.20/0.46 => Xphi ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptysetE_type,type,
% 0.20/0.46 emptysetE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptysetE,definition,
% 0.20/0.46 ( emptysetE
% 0.20/0.46 = ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ emptyset )
% 0.20/0.46 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptysetimpfalse_type,type,
% 0.20/0.46 emptysetimpfalse: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptysetimpfalse,definition,
% 0.20/0.46 ( emptysetimpfalse
% 0.20/0.46 = ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ emptyset )
% 0.20/0.46 => $false ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(notinemptyset_type,type,
% 0.20/0.46 notinemptyset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(notinemptyset,definition,
% 0.20/0.46 ( notinemptyset
% 0.20/0.46 = ( ! [Xx: $i] :
% 0.20/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(exuE3e_type,type,
% 0.20/0.46 exuE3e: $o ).
% 0.20/0.46
% 0.20/0.46 thf(exuE3e,definition,
% 0.20/0.46 ( exuE3e
% 0.20/0.46 = ( ! [Xphi: $i > $o] :
% 0.20/0.46 ( ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setext_type,type,
% 0.20/0.46 setext: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setext,definition,
% 0.20/0.46 ( setext
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xx @ B ) )
% 0.20/0.46 => ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 => ( in @ Xx @ A ) )
% 0.20/0.46 => ( A = B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptyI_type,type,
% 0.20/0.46 emptyI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptyI,definition,
% 0.20/0.46 ( emptyI
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ~ ( in @ Xx @ A )
% 0.20/0.46 => ( A = emptyset ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(noeltsimpempty_type,type,
% 0.20/0.46 noeltsimpempty: $o ).
% 0.20/0.46
% 0.20/0.46 thf(noeltsimpempty,definition,
% 0.20/0.46 ( noeltsimpempty
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ~ ( in @ Xx @ A )
% 0.20/0.46 => ( A = emptyset ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setbeta_type,type,
% 0.20/0.46 setbeta: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setbeta,definition,
% 0.20/0.46 ( setbeta
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.20/0.46 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(nonempty_type,type,
% 0.20/0.46 nonempty: $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(nonempty,definition,
% 0.20/0.46 ( nonempty
% 0.20/0.46 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(nonemptyE1_type,type,
% 0.20/0.46 nonemptyE1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(nonemptyE1,definition,
% 0.20/0.46 ( nonemptyE1
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ( nonempty @ A )
% 0.20/0.46 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(nonemptyI_type,type,
% 0.20/0.46 nonemptyI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(nonemptyI,definition,
% 0.20/0.46 ( nonemptyI
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( Xphi @ Xx )
% 0.20/0.46 => ( nonempty
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(nonemptyI1_type,type,
% 0.20/0.46 nonemptyI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(nonemptyI1,definition,
% 0.20/0.46 ( nonemptyI1
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.20/0.46 => ( nonempty @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinIL_type,type,
% 0.20/0.46 setadjoinIL: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinIL,definition,
% 0.20/0.46 ( setadjoinIL
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptyinunitempty_type,type,
% 0.20/0.46 emptyinunitempty: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptyinunitempty,definition,
% 0.20/0.46 ( emptyinunitempty
% 0.20/0.46 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinIR_type,type,
% 0.20/0.46 setadjoinIR: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinIR,definition,
% 0.20/0.46 ( setadjoinIR
% 0.20/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinE_type,type,
% 0.20/0.46 setadjoinE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinE,definition,
% 0.20/0.46 ( setadjoinE
% 0.20/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.20/0.46 => ! [Xphi: $o] :
% 0.20/0.46 ( ( ( Xy = Xx )
% 0.20/0.46 => Xphi )
% 0.20/0.46 => ( ( ( in @ Xy @ A )
% 0.20/0.46 => Xphi )
% 0.20/0.46 => Xphi ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinOr_type,type,
% 0.20/0.46 setadjoinOr: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinOr,definition,
% 0.20/0.46 ( setadjoinOr
% 0.20/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.20/0.46 => ( ( Xy = Xx )
% 0.20/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setoftrueEq_type,type,
% 0.20/0.46 setoftrueEq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setoftrueEq,definition,
% 0.20/0.46 ( setoftrueEq
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xx: $i] : $true )
% 0.20/0.46 = A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powersetI_type,type,
% 0.20/0.46 powersetI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powersetI,definition,
% 0.20/0.46 ( powersetI
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 => ( in @ Xx @ A ) )
% 0.20/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptyinPowerset_type,type,
% 0.20/0.46 emptyinPowerset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptyinPowerset,definition,
% 0.20/0.46 ( emptyinPowerset
% 0.20/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptyInPowerset_type,type,
% 0.20/0.46 emptyInPowerset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptyInPowerset,definition,
% 0.20/0.46 ( emptyInPowerset
% 0.20/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powersetE_type,type,
% 0.20/0.46 powersetE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powersetE,definition,
% 0.20/0.46 ( powersetE
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.20/0.46 => ( ( in @ Xx @ B )
% 0.20/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setunionI_type,type,
% 0.20/0.46 setunionI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setunionI,definition,
% 0.20/0.46 ( setunionI
% 0.20/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 => ( ( in @ B @ A )
% 0.20/0.46 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setunionE_type,type,
% 0.20/0.46 setunionE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setunionE,definition,
% 0.20/0.46 ( setunionE
% 0.20/0.46 = ( ! [A: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.20/0.46 => ! [Xphi: $o] :
% 0.20/0.46 ( ! [B: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 => ( ( in @ B @ A )
% 0.20/0.46 => Xphi ) )
% 0.20/0.46 => Xphi ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subPowSU_type,type,
% 0.20/0.46 subPowSU: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subPowSU,definition,
% 0.20/0.46 ( subPowSU
% 0.20/0.46 = ( ! [A: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(exuE2_type,type,
% 0.20/0.46 exuE2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(exuE2,definition,
% 0.20/0.46 ( exuE2
% 0.20/0.46 = ( ! [Xphi: $i > $o] :
% 0.20/0.46 ( ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 => ? [Xx: $i] :
% 0.20/0.46 ! [Xy: $i] :
% 0.20/0.46 ( ( Xphi @ Xy )
% 0.20/0.46 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(nonemptyImpWitness_type,type,
% 0.20/0.46 nonemptyImpWitness: $o ).
% 0.20/0.46
% 0.20/0.46 thf(nonemptyImpWitness,definition,
% 0.20/0.46 ( nonemptyImpWitness
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ( nonempty @ A )
% 0.20/0.46 => ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & $true ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(uniqinunit_type,type,
% 0.20/0.46 uniqinunit: $o ).
% 0.20/0.46
% 0.20/0.46 thf(uniqinunit,definition,
% 0.20/0.46 ( uniqinunit
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(notinsingleton_type,type,
% 0.20/0.46 notinsingleton: $o ).
% 0.20/0.46
% 0.20/0.46 thf(notinsingleton,definition,
% 0.20/0.46 ( notinsingleton
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx != Xy )
% 0.20/0.46 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(eqinunit_type,type,
% 0.20/0.46 eqinunit: $o ).
% 0.20/0.46
% 0.20/0.46 thf(eqinunit,definition,
% 0.20/0.46 ( eqinunit
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx = Xy )
% 0.20/0.46 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(singletonsswitch_type,type,
% 0.20/0.46 singletonsswitch: $o ).
% 0.20/0.46
% 0.20/0.46 thf(singletonsswitch,definition,
% 0.20/0.46 ( singletonsswitch
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.20/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(upairsetE_type,type,
% 0.20/0.46 upairsetE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(upairsetE,definition,
% 0.20/0.46 ( upairsetE
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.20/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.20/0.46 => ( ( Xz = Xx )
% 0.20/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(upairsetIL_type,type,
% 0.20/0.46 upairsetIL: $o ).
% 0.20/0.46
% 0.20/0.46 thf(upairsetIL,definition,
% 0.20/0.46 ( upairsetIL
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(upairsetIR_type,type,
% 0.20/0.46 upairsetIR: $o ).
% 0.20/0.46
% 0.20/0.46 thf(upairsetIR,definition,
% 0.20/0.46 ( upairsetIR
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptyE1_type,type,
% 0.20/0.46 emptyE1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptyE1,definition,
% 0.20/0.46 ( emptyE1
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ( Xphi @ Xx ) )
% 0.20/0.46 => ( ( ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 = emptyset )
% 0.20/0.46 => $false ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(vacuousDall_type,type,
% 0.20/0.46 vacuousDall: $o ).
% 0.20/0.46
% 0.20/0.46 thf(vacuousDall,definition,
% 0.20/0.46 ( vacuousDall
% 0.20/0.46 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ emptyset )
% 0.20/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(quantDeMorgan1_type,type,
% 0.20/0.46 quantDeMorgan1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(quantDeMorgan1,definition,
% 0.20/0.46 ( quantDeMorgan1
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ~ ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( Xphi @ Xx ) )
% 0.20/0.46 => ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(quantDeMorgan2_type,type,
% 0.20/0.46 quantDeMorgan2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(quantDeMorgan2,definition,
% 0.20/0.46 ( quantDeMorgan2
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ~ ( Xphi @ Xx ) )
% 0.20/0.46 => ~ ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(quantDeMorgan3_type,type,
% 0.20/0.46 quantDeMorgan3: $o ).
% 0.20/0.46
% 0.20/0.46 thf(quantDeMorgan3,definition,
% 0.20/0.46 ( quantDeMorgan3
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ~ ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ( Xphi @ Xx ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(quantDeMorgan4_type,type,
% 0.20/0.46 quantDeMorgan4: $o ).
% 0.20/0.46
% 0.20/0.46 thf(quantDeMorgan4,definition,
% 0.20/0.46 ( quantDeMorgan4
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ~ ( Xphi @ Xx ) )
% 0.20/0.46 => ~ ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(prop2setI_type,type,
% 0.20/0.46 prop2setI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(prop2setI,definition,
% 0.20/0.46 ( prop2setI
% 0.20/0.46 = ( ! [Xphi: $o] :
% 0.20/0.46 ( Xphi
% 0.20/0.46 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(set2prop_type,type,
% 0.20/0.46 set2prop: $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(prop2set2propI_type,type,
% 0.20/0.46 prop2set2propI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(prop2set2propI,definition,
% 0.20/0.46 ( prop2set2propI
% 0.20/0.46 = ( ! [Xphi: $o] :
% 0.20/0.46 ( Xphi
% 0.20/0.46 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(notdexE_type,type,
% 0.20/0.46 notdexE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(notdexE,definition,
% 0.20/0.46 ( notdexE
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ~ ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ( Xphi @ Xx ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(notdallE_type,type,
% 0.20/0.46 notdallE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(notdallE,definition,
% 0.20/0.46 ( notdallE
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ~ ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( Xphi @ Xx ) )
% 0.20/0.46 => ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(exuI1_type,type,
% 0.20/0.46 exuI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(exuI1,definition,
% 0.20/0.46 ( exuI1
% 0.20/0.46 = ( ! [Xphi: $i > $o] :
% 0.20/0.46 ( ? [Xx: $i] :
% 0.20/0.46 ( ( Xphi @ Xx )
% 0.20/0.46 & ! [Xy: $i] :
% 0.20/0.46 ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xx = Xy ) ) )
% 0.20/0.46 => ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(exuI3_type,type,
% 0.20/0.46 exuI3: $o ).
% 0.20/0.46
% 0.20/0.46 thf(exuI3,definition,
% 0.20/0.46 ( exuI3
% 0.20/0.46 = ( ! [Xphi: $i > $o] :
% 0.20/0.46 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.20/0.46 => ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xphi @ Xx )
% 0.20/0.46 => ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xx = Xy ) ) )
% 0.20/0.46 => ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(exuI2_type,type,
% 0.20/0.46 exuI2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(exuI2,definition,
% 0.20/0.46 ( exuI2
% 0.20/0.46 = ( ! [Xphi: $i > $o] :
% 0.20/0.46 ( ? [Xx: $i] :
% 0.20/0.46 ! [Xy: $i] :
% 0.20/0.46 ( ( Xphi @ Xy )
% 0.20/0.46 <=> ( Xy = Xx ) )
% 0.20/0.46 => ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(inCongP_type,type,
% 0.20/0.46 inCongP: $o ).
% 0.20/0.46
% 0.20/0.46 thf(inCongP,definition,
% 0.20/0.46 ( inCongP
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( A = B )
% 0.20/0.46 => ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx = Xy )
% 0.20/0.46 => ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(in__Cong_type,type,
% 0.20/0.46 in__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(in__Cong,definition,
% 0.20/0.46 ( in__Cong
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( A = B )
% 0.20/0.46 => ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx = Xy )
% 0.20/0.46 => ( ( in @ Xx @ A )
% 0.20/0.46 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(exuE3u_type,type,
% 0.20/0.46 exuE3u: $o ).
% 0.20/0.46
% 0.20/0.46 thf(exuE3u,definition,
% 0.20/0.46 ( exuE3u
% 0.20/0.46 = ( ! [Xphi: $i > $o] :
% 0.20/0.46 ( ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 => ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xphi @ Xx )
% 0.20/0.46 => ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(exu__Cong_type,type,
% 0.20/0.46 exu__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(exu__Cong,definition,
% 0.20/0.46 ( exu__Cong
% 0.20/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.20/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx = Xy )
% 0.20/0.46 => ( ( Xphi @ Xx )
% 0.20/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.20/0.46 => ( ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 <=> ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptyset__Cong_type,type,
% 0.20/0.46 emptyset__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptyset__Cong,definition,
% 0.20/0.46 ( emptyset__Cong
% 0.20/0.46 = ( emptyset = emptyset ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoin__Cong_type,type,
% 0.20/0.46 setadjoin__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoin__Cong,definition,
% 0.20/0.46 ( setadjoin__Cong
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx = Xy )
% 0.20/0.46 => ! [Xz: $i,Xu: $i] :
% 0.20/0.46 ( ( Xz = Xu )
% 0.20/0.46 => ( ( setadjoin @ Xx @ Xz )
% 0.20/0.46 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powerset__Cong_type,type,
% 0.20/0.46 powerset__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powerset__Cong,definition,
% 0.20/0.46 ( powerset__Cong
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( A = B )
% 0.20/0.46 => ( ( powerset @ A )
% 0.20/0.46 = ( powerset @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setunion__Cong_type,type,
% 0.20/0.46 setunion__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setunion__Cong,definition,
% 0.20/0.46 ( setunion__Cong
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( A = B )
% 0.20/0.46 => ( ( setunion @ A )
% 0.20/0.46 = ( setunion @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(omega__Cong_type,type,
% 0.20/0.46 omega__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(omega__Cong,definition,
% 0.20/0.46 ( omega__Cong
% 0.20/0.46 = ( omega = omega ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(exuEu_type,type,
% 0.20/0.46 exuEu: $o ).
% 0.20/0.46
% 0.20/0.46 thf(exuEu,definition,
% 0.20/0.46 ( exuEu
% 0.20/0.46 = ( ! [Xphi: $i > $o] :
% 0.20/0.46 ( ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 => ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xphi @ Xx )
% 0.20/0.46 => ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(descr__Cong_type,type,
% 0.20/0.46 descr__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(descr__Cong,definition,
% 0.20/0.46 ( descr__Cong
% 0.20/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.20/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx = Xy )
% 0.20/0.46 => ( ( Xphi @ Xx )
% 0.20/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.20/0.46 => ( ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 => ( ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.20/0.46 => ( ( descr
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 = ( descr
% 0.20/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstr__Cong_type,type,
% 0.20/0.46 dsetconstr__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstr__Cong,definition,
% 0.20/0.46 ( dsetconstr__Cong
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( A = B )
% 0.20/0.46 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( ( Xx = Xy )
% 0.20/0.46 => ( ( Xphi @ Xx )
% 0.20/0.46 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.20/0.46 => ( ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 = ( dsetconstr @ B
% 0.20/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subset_type,type,
% 0.20/0.46 subset: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(disjoint_type,type,
% 0.20/0.46 disjoint: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(setsmeet_type,type,
% 0.20/0.46 setsmeet: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetI1_type,type,
% 0.20/0.46 subsetI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetI1,definition,
% 0.20/0.46 ( subsetI1
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xx @ B ) )
% 0.20/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(eqimpsubset2_type,type,
% 0.20/0.46 eqimpsubset2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(eqimpsubset2,definition,
% 0.20/0.46 ( eqimpsubset2
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( A = B )
% 0.20/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(eqimpsubset1_type,type,
% 0.20/0.46 eqimpsubset1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(eqimpsubset1,definition,
% 0.20/0.46 ( eqimpsubset1
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( A = B )
% 0.20/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subsetI2_type,type,
% 0.20/0.46 subsetI2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetI2,definition,
% 0.20/0.46 ( subsetI2
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xx @ B ) )
% 0.20/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptysetsubset_type,type,
% 0.20/0.46 emptysetsubset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptysetsubset,definition,
% 0.20/0.46 ( emptysetsubset
% 0.20/0.46 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subsetE_type,type,
% 0.20/0.46 subsetE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetE,definition,
% 0.20/0.46 ( subsetE
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subsetE2_type,type,
% 0.20/0.46 subsetE2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetE2,definition,
% 0.20/0.46 ( subsetE2
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( ~ ( in @ Xx @ B )
% 0.20/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(notsubsetI_type,type,
% 0.20/0.46 notsubsetI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(notsubsetI,definition,
% 0.20/0.46 ( notsubsetI
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ~ ( in @ Xx @ B )
% 0.20/0.46 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(notequalI1_type,type,
% 0.20/0.46 notequalI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(notequalI1,definition,
% 0.20/0.46 ( notequalI1
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ~ ( subset @ A @ B )
% 0.20/0.46 => ( A != B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(notequalI2_type,type,
% 0.20/0.46 notequalI2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(notequalI2,definition,
% 0.20/0.46 ( notequalI2
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ~ ( in @ Xx @ B )
% 0.20/0.46 => ( A != B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subsetRefl_type,type,
% 0.20/0.46 subsetRefl: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetRefl,definition,
% 0.20/0.46 ( subsetRefl
% 0.20/0.46 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subsetTrans_type,type,
% 0.20/0.46 subsetTrans: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetTrans,definition,
% 0.20/0.46 ( subsetTrans
% 0.20/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( ( subset @ B @ C )
% 0.20/0.46 => ( subset @ A @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinSub_type,type,
% 0.20/0.46 setadjoinSub: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinSub,definition,
% 0.20/0.46 ( setadjoinSub
% 0.20/0.46 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinSub2_type,type,
% 0.20/0.46 setadjoinSub2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinSub2,definition,
% 0.20/0.46 ( setadjoinSub2
% 0.20/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subset2powerset_type,type,
% 0.20/0.46 subset2powerset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subset2powerset,definition,
% 0.20/0.46 ( subset2powerset
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setextsub_type,type,
% 0.20/0.46 setextsub: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setextsub,definition,
% 0.20/0.46 ( setextsub
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( ( subset @ B @ A )
% 0.20/0.46 => ( A = B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subsetemptysetimpeq_type,type,
% 0.20/0.46 subsetemptysetimpeq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetemptysetimpeq,definition,
% 0.20/0.46 ( subsetemptysetimpeq
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ( subset @ A @ emptyset )
% 0.20/0.46 => ( A = emptyset ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powersetI1_type,type,
% 0.20/0.46 powersetI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powersetI1,definition,
% 0.20/0.46 ( powersetI1
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( subset @ B @ A )
% 0.20/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powersetE1_type,type,
% 0.20/0.46 powersetE1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powersetE1,definition,
% 0.20/0.46 ( powersetE1
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.20/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(inPowerset_type,type,
% 0.20/0.46 inPowerset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(inPowerset,definition,
% 0.20/0.46 ( inPowerset
% 0.20/0.46 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powersetsubset_type,type,
% 0.20/0.46 powersetsubset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powersetsubset,definition,
% 0.20/0.46 ( powersetsubset
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sepInPowerset_type,type,
% 0.20/0.46 sepInPowerset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(sepInPowerset,definition,
% 0.20/0.46 ( sepInPowerset
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( in
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 @ ( powerset @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sepSubset_type,type,
% 0.20/0.46 sepSubset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(sepSubset,definition,
% 0.20/0.46 ( sepSubset
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( subset
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binunion_type,type,
% 0.20/0.46 binunion: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(binunionIL_type,type,
% 0.20/0.46 binunionIL: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binunionIL,definition,
% 0.20/0.46 ( binunionIL
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(upairset2IR_type,type,
% 0.20/0.46 upairset2IR: $o ).
% 0.20/0.46
% 0.20/0.46 thf(upairset2IR,definition,
% 0.20/0.46 ( upairset2IR
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binunionIR_type,type,
% 0.20/0.46 binunionIR: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binunionIR,definition,
% 0.20/0.46 ( binunionIR
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binunionEcases_type,type,
% 0.20/0.46 binunionEcases: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binunionEcases,definition,
% 0.20/0.46 ( binunionEcases
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.20/0.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.20/0.46 => ( ( ( in @ Xx @ A )
% 0.20/0.46 => Xphi )
% 0.20/0.46 => ( ( ( in @ Xx @ B )
% 0.20/0.46 => Xphi )
% 0.20/0.46 => Xphi ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binunionE_type,type,
% 0.20/0.46 binunionE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binunionE,definition,
% 0.20/0.46 ( binunionE
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.20/0.46 => ( ( in @ Xx @ A )
% 0.20/0.46 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binunionLsub_type,type,
% 0.20/0.46 binunionLsub: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binunionLsub,definition,
% 0.20/0.46 ( binunionLsub
% 0.20/0.46 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binunionRsub_type,type,
% 0.20/0.46 binunionRsub: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binunionRsub,definition,
% 0.20/0.46 ( binunionRsub
% 0.20/0.46 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersect_type,type,
% 0.20/0.46 binintersect: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectI_type,type,
% 0.20/0.46 binintersectI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectI,definition,
% 0.20/0.46 ( binintersectI
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ B )
% 0.20/0.46 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset5_type,type,
% 0.20/0.46 binintersectSubset5: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset5,definition,
% 0.20/0.46 ( binintersectSubset5
% 0.20/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.20/0.46 ( ( subset @ C @ A )
% 0.20/0.46 => ( ( subset @ C @ B )
% 0.20/0.46 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectEL_type,type,
% 0.20/0.46 binintersectEL: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectEL,definition,
% 0.20/0.46 ( binintersectEL
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.20/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectLsub_type,type,
% 0.20/0.46 binintersectLsub: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectLsub,definition,
% 0.20/0.46 ( binintersectLsub
% 0.20/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset2_type,type,
% 0.20/0.46 binintersectSubset2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset2,definition,
% 0.20/0.46 ( binintersectSubset2
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( ( binintersect @ A @ B )
% 0.20/0.46 = A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset3_type,type,
% 0.20/0.46 binintersectSubset3: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset3,definition,
% 0.20/0.46 ( binintersectSubset3
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( ( binintersect @ A @ B )
% 0.20/0.46 = B )
% 0.20/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectER_type,type,
% 0.20/0.46 binintersectER: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectER,definition,
% 0.20/0.46 ( binintersectER
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.20/0.46 => ( in @ Xx @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(disjointsetsI1_type,type,
% 0.20/0.46 disjointsetsI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(disjointsetsI1,definition,
% 0.20/0.46 ( disjointsetsI1
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ~ ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ( in @ Xx @ B ) )
% 0.20/0.46 => ( ( binintersect @ A @ B )
% 0.20/0.46 = emptyset ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectRsub_type,type,
% 0.20/0.46 binintersectRsub: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectRsub,definition,
% 0.20/0.46 ( binintersectRsub
% 0.20/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset4_type,type,
% 0.20/0.46 binintersectSubset4: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset4,definition,
% 0.20/0.46 ( binintersectSubset4
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( subset @ B @ A )
% 0.20/0.46 => ( ( binintersect @ A @ B )
% 0.20/0.46 = B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset1_type,type,
% 0.20/0.46 binintersectSubset1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset1,definition,
% 0.20/0.46 ( binintersectSubset1
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( ( binintersect @ A @ B )
% 0.20/0.46 = A )
% 0.20/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(bs114d_type,type,
% 0.20/0.46 bs114d: $o ).
% 0.20/0.46
% 0.20/0.46 thf(bs114d,definition,
% 0.20/0.46 ( bs114d
% 0.20/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.20/0.46 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.20/0.46 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(regular_type,type,
% 0.20/0.46 regular: $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminus_type,type,
% 0.20/0.46 setminus: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(setminusI_type,type,
% 0.20/0.46 setminusI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusI,definition,
% 0.20/0.46 ( setminusI
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ~ ( in @ Xx @ B )
% 0.20/0.46 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusEL_type,type,
% 0.20/0.46 setminusEL: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusEL,definition,
% 0.20/0.46 ( setminusEL
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.20/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusER_type,type,
% 0.20/0.46 setminusER: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusER,definition,
% 0.20/0.46 ( setminusER
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.20/0.46 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusSubset2_type,type,
% 0.20/0.46 setminusSubset2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusSubset2,definition,
% 0.20/0.46 ( setminusSubset2
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( ( setminus @ A @ B )
% 0.20/0.46 = emptyset ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusERneg_type,type,
% 0.20/0.46 setminusERneg: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusERneg,definition,
% 0.20/0.46 ( setminusERneg
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.20/0.46 => ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusELneg_type,type,
% 0.20/0.46 setminusELneg: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusELneg,definition,
% 0.20/0.46 ( setminusELneg
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.20/0.46 => ( ~ ( in @ Xx @ B )
% 0.20/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusILneg_type,type,
% 0.20/0.46 setminusILneg: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusILneg,definition,
% 0.20/0.46 ( setminusILneg
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ~ ( in @ Xx @ A )
% 0.20/0.46 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusIRneg_type,type,
% 0.20/0.46 setminusIRneg: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusIRneg,definition,
% 0.20/0.46 ( setminusIRneg
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusLsub_type,type,
% 0.20/0.46 setminusLsub: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusLsub,definition,
% 0.20/0.46 ( setminusLsub
% 0.20/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusSubset1_type,type,
% 0.20/0.46 setminusSubset1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusSubset1,definition,
% 0.20/0.46 ( setminusSubset1
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( ( setminus @ A @ B )
% 0.20/0.46 = emptyset )
% 0.20/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(symdiff_type,type,
% 0.20/0.47 symdiff: $i > $i > $i ).
% 0.20/0.47
% 0.20/0.47 thf(symdiffE_type,type,
% 0.20/0.47 symdiffE: $o ).
% 0.20/0.47
% 0.20/0.47 thf(symdiffE,definition,
% 0.20/0.47 ( symdiffE
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.20/0.47 => ! [Xphi: $o] :
% 0.20/0.47 ( ( ( in @ Xx @ A )
% 0.20/0.47 => ( ~ ( in @ Xx @ B )
% 0.20/0.47 => Xphi ) )
% 0.20/0.47 => ( ( ~ ( in @ Xx @ A )
% 0.20/0.47 => ( ( in @ Xx @ B )
% 0.20/0.47 => Xphi ) )
% 0.20/0.47 => Xphi ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(symdiffI1_type,type,
% 0.20/0.47 symdiffI1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(symdiffI1,definition,
% 0.20/0.47 ( symdiffI1
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( ~ ( in @ Xx @ B )
% 0.20/0.47 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(symdiffI2_type,type,
% 0.20/0.47 symdiffI2: $o ).
% 0.20/0.47
% 0.20/0.47 thf(symdiffI2,definition,
% 0.20/0.47 ( symdiffI2
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ~ ( in @ Xx @ A )
% 0.20/0.47 => ( ( in @ Xx @ B )
% 0.20/0.47 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(symdiffIneg1_type,type,
% 0.20/0.47 symdiffIneg1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(symdiffIneg1,definition,
% 0.20/0.47 ( symdiffIneg1
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( ( in @ Xx @ B )
% 0.20/0.47 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(symdiffIneg2_type,type,
% 0.20/0.47 symdiffIneg2: $o ).
% 0.20/0.47
% 0.20/0.47 thf(symdiffIneg2,definition,
% 0.20/0.47 ( symdiffIneg2
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ~ ( in @ Xx @ A )
% 0.20/0.47 => ( ~ ( in @ Xx @ B )
% 0.20/0.47 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(iskpair_type,type,
% 0.20/0.47 iskpair: $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(secondinupair_type,type,
% 0.20/0.47 secondinupair: $o ).
% 0.20/0.47
% 0.20/0.47 thf(secondinupair,definition,
% 0.20/0.47 ( secondinupair
% 0.20/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setukpairIL_type,type,
% 0.20/0.47 setukpairIL: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setukpairIL,definition,
% 0.20/0.47 ( setukpairIL
% 0.20/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setukpairIR_type,type,
% 0.20/0.47 setukpairIR: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setukpairIR,definition,
% 0.20/0.47 ( setukpairIR
% 0.20/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(kpairiskpair_type,type,
% 0.20/0.47 kpairiskpair: $o ).
% 0.20/0.47
% 0.20/0.47 thf(kpairiskpair,definition,
% 0.20/0.47 ( kpairiskpair
% 0.20/0.47 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(kpair_type,type,
% 0.20/0.47 kpair: $i > $i > $i ).
% 0.20/0.47
% 0.20/0.47 thf(kpairp_type,type,
% 0.20/0.47 kpairp: $o ).
% 0.20/0.47
% 0.20/0.47 thf(kpairp,definition,
% 0.20/0.47 ( kpairp
% 0.20/0.47 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(cartprod_type,type,
% 0.20/0.47 cartprod: $i > $i > $i ).
% 0.20/0.47
% 0.20/0.47 thf(singletonsubset_type,type,
% 0.20/0.47 singletonsubset: $o ).
% 0.20/0.47
% 0.20/0.47 thf(singletonsubset,definition,
% 0.20/0.47 ( singletonsubset
% 0.20/0.47 = ( ! [A: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(singletoninpowerset_type,type,
% 0.20/0.47 singletoninpowerset: $o ).
% 0.20/0.47
% 0.20/0.47 thf(singletoninpowerset,definition,
% 0.20/0.47 ( singletoninpowerset
% 0.20/0.47 = ( ! [A: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(singletoninpowunion_type,type,
% 0.20/0.47 singletoninpowunion: $o ).
% 0.20/0.47
% 0.20/0.47 thf(singletoninpowunion,definition,
% 0.20/0.47 ( singletoninpowunion
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(upairset2E_type,type,
% 0.20/0.47 upairset2E: $o ).
% 0.20/0.47
% 0.20/0.47 thf(upairset2E,definition,
% 0.20/0.47 ( upairset2E
% 0.20/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.20/0.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.20/0.47 => ( ( Xz = Xx )
% 0.20/0.47 | ( Xz = Xy ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(upairsubunion_type,type,
% 0.20/0.47 upairsubunion: $o ).
% 0.20/0.47
% 0.20/0.47 thf(upairsubunion,definition,
% 0.20/0.47 ( upairsubunion
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ! [Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ B )
% 0.20/0.47 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(upairinpowunion_type,type,
% 0.20/0.47 upairinpowunion: $o ).
% 0.20/0.47
% 0.20/0.47 thf(upairinpowunion,definition,
% 0.20/0.47 ( upairinpowunion
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ! [Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ B )
% 0.20/0.47 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(ubforcartprodlem1_type,type,
% 0.20/0.47 ubforcartprodlem1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(ubforcartprodlem1,definition,
% 0.20/0.47 ( ubforcartprodlem1
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ! [Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ B )
% 0.20/0.47 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(ubforcartprodlem2_type,type,
% 0.20/0.47 ubforcartprodlem2: $o ).
% 0.20/0.47
% 0.20/0.47 thf(ubforcartprodlem2,definition,
% 0.20/0.47 ( ubforcartprodlem2
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ! [Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ B )
% 0.20/0.47 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(ubforcartprodlem3_type,type,
% 0.20/0.47 ubforcartprodlem3: $o ).
% 0.20/0.47
% 0.20/0.47 thf(ubforcartprodlem3,definition,
% 0.20/0.47 ( ubforcartprodlem3
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ! [Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ B )
% 0.20/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(cartprodpairin_type,type,
% 0.20/0.47 cartprodpairin: $o ).
% 0.20/0.47
% 0.20/0.47 thf(cartprodpairin,definition,
% 0.20/0.47 ( cartprodpairin
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ! [Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ B )
% 0.20/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(cartprodmempair1_type,type,
% 0.20/0.47 cartprodmempair1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(cartprodmempair1,definition,
% 0.20/0.47 ( cartprodmempair1
% 0.20/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.20/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.20/0.47 => ? [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 & ? [Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ B )
% 0.20/0.47 & ( Xu
% 0.20/0.47 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(cartprodmempair_type,type,
% 0.20/0.47 cartprodmempair: $o ).
% 0.20/0.47
% 0.20/0.47 thf(cartprodmempair,definition,
% 0.20/0.47 ( cartprodmempair
% 0.20/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.20/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.20/0.47 => ( iskpair @ Xu ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setunionE2_type,type,
% 0.20/0.47 setunionE2: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setunionE2,definition,
% 0.20/0.47 ( setunionE2
% 0.20/0.47 = ( ! [A: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.20/0.47 => ? [X: $i] :
% 0.20/0.47 ( ( in @ X @ A )
% 0.20/0.47 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setunionsingleton1_type,type,
% 0.20/0.47 setunionsingleton1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setunionsingleton1,definition,
% 0.20/0.47 ( setunionsingleton1
% 0.20/0.47 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setunionsingleton2_type,type,
% 0.20/0.47 setunionsingleton2: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setunionsingleton2,definition,
% 0.20/0.47 ( setunionsingleton2
% 0.20/0.47 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setunionsingleton_type,type,
% 0.20/0.47 setunionsingleton: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setunionsingleton,definition,
% 0.20/0.47 ( setunionsingleton
% 0.20/0.47 = ( ! [Xx: $i] :
% 0.20/0.47 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.20/0.47 = Xx ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(singleton_type,type,
% 0.20/0.47 singleton: $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(singletonprop_type,type,
% 0.20/0.47 singletonprop: $o ).
% 0.20/0.47
% 0.20/0.47 thf(singletonprop,definition,
% 0.20/0.47 ( singletonprop
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.47 ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ! [Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ A )
% 0.20/0.47 => ( ( Xphi @ Xx )
% 0.20/0.47 => ( ( Xphi @ Xy )
% 0.20/0.47 => ( Xx = Xy ) ) ) ) )
% 0.20/0.47 => ( ? [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 & ( Xphi @ Xx ) )
% 0.20/0.47 => ( singleton
% 0.20/0.47 @ ( dsetconstr @ A
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(ex1_type,type,
% 0.20/0.47 ex1: $i > ( $i > $o ) > $o ).
% 0.20/0.47
% 0.20/0.47 thf(ex1E1_type,type,
% 0.20/0.47 ex1E1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(ex1E1,definition,
% 0.20/0.47 ( ex1E1
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.47 ( ( ex1 @ A
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.47 => ? [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(ex1I_type,type,
% 0.20/0.47 ex1I: $o ).
% 0.20/0.47
% 0.20/0.47 thf(ex1I,definition,
% 0.20/0.47 ( ex1I
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( ( Xphi @ Xx )
% 0.20/0.47 => ( ! [Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ A )
% 0.20/0.47 => ( ( Xphi @ Xy )
% 0.20/0.47 => ( Xy = Xx ) ) )
% 0.20/0.47 => ( ex1 @ A
% 0.20/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(ex1I2_type,type,
% 0.20/0.47 ex1I2: $o ).
% 0.20/0.47
% 0.20/0.47 thf(ex1I2,definition,
% 0.20/0.47 ( ex1I2
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.47 ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ! [Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ A )
% 0.20/0.47 => ( ( Xphi @ Xx )
% 0.20/0.47 => ( ( Xphi @ Xy )
% 0.20/0.47 => ( Xx = Xy ) ) ) ) )
% 0.20/0.47 => ( ? [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 & ( Xphi @ Xx ) )
% 0.20/0.47 => ( ex1 @ A
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(singletonsuniq_type,type,
% 0.20/0.47 singletonsuniq: $o ).
% 0.20/0.47
% 0.20/0.47 thf(singletonsuniq,definition,
% 0.20/0.47 ( singletonsuniq
% 0.20/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.47 ( ( ( setadjoin @ Xx @ emptyset )
% 0.20/0.47 = ( setadjoin @ Xy @ emptyset ) )
% 0.20/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(atmost1p_type,type,
% 0.20/0.47 atmost1p: $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(atleast2p_type,type,
% 0.20/0.47 atleast2p: $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(atmost2p_type,type,
% 0.20/0.47 atmost2p: $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(upairsetp_type,type,
% 0.20/0.47 upairsetp: $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(setukpairinjL1_type,type,
% 0.20/0.47 setukpairinjL1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setukpairinjL1,definition,
% 0.20/0.47 ( setukpairinjL1
% 0.20/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.31/0.47 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.31/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(kfstsingleton_type,type,
% 0.31/0.47 kfstsingleton: $o ).
% 0.31/0.47
% 0.31/0.47 thf(kfstsingleton,definition,
% 0.31/0.47 ( kfstsingleton
% 0.31/0.47 = ( ! [Xu: $i] :
% 0.31/0.47 ( ( iskpair @ Xu )
% 0.31/0.47 => ( singleton
% 0.31/0.47 @ ( dsetconstr @ ( setunion @ Xu )
% 0.31/0.47 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(theprop_type,type,
% 0.31/0.47 theprop: $o ).
% 0.31/0.47
% 0.31/0.47 thf(theprop,definition,
% 0.31/0.47 ( theprop
% 0.31/0.47 = ( ! [X: $i] :
% 0.31/0.47 ( ( singleton @ X )
% 0.31/0.47 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(kfst_type,type,
% 0.31/0.47 kfst: $i > $i ).
% 0.31/0.47
% 0.31/0.47 thf(kfstpairEq_type,type,
% 0.31/0.47 kfstpairEq: $o ).
% 0.31/0.47
% 0.31/0.47 thf(kfstpairEq,definition,
% 0.31/0.47 ( kfstpairEq
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.31/0.47 = Xx ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(cartprodfstin_type,type,
% 0.31/0.47 cartprodfstin: $o ).
% 0.31/0.47
% 0.31/0.47 thf(cartprodfstin,definition,
% 0.31/0.47 ( cartprodfstin
% 0.31/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.31/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.31/0.47 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setukpairinjL2_type,type,
% 0.31/0.47 setukpairinjL2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setukpairinjL2,definition,
% 0.31/0.47 ( setukpairinjL2
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.31/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.31/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.31/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setukpairinjL_type,type,
% 0.31/0.47 setukpairinjL: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setukpairinjL,definition,
% 0.31/0.47 ( setukpairinjL
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.31/0.47 ( ( ( kpair @ Xx @ Xy )
% 0.31/0.47 = ( kpair @ Xz @ Xu ) )
% 0.31/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setukpairinjR11_type,type,
% 0.31/0.47 setukpairinjR11: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setukpairinjR11,definition,
% 0.31/0.47 ( setukpairinjR11
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xx = Xy )
% 0.31/0.47 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.31/0.47 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setukpairinjR12_type,type,
% 0.31/0.47 setukpairinjR12: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setukpairinjR12,definition,
% 0.31/0.47 ( setukpairinjR12
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xx = Xy )
% 0.31/0.47 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.31/0.47 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setukpairinjR1_type,type,
% 0.31/0.47 setukpairinjR1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setukpairinjR1,definition,
% 0.31/0.47 ( setukpairinjR1
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.31/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.31/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.31/0.47 => ( ( Xz = Xu )
% 0.31/0.47 => ( Xy = Xu ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(upairequniteq_type,type,
% 0.31/0.47 upairequniteq: $o ).
% 0.31/0.47
% 0.31/0.47 thf(upairequniteq,definition,
% 0.31/0.47 ( upairequniteq
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.31/0.47 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.31/0.47 = ( setadjoin @ Xz @ emptyset ) )
% 0.31/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setukpairinjR2_type,type,
% 0.31/0.47 setukpairinjR2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setukpairinjR2,definition,
% 0.31/0.47 ( setukpairinjR2
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.31/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.31/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.31/0.47 => ( Xy = Xu ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setukpairinjR_type,type,
% 0.31/0.47 setukpairinjR: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setukpairinjR,definition,
% 0.31/0.47 ( setukpairinjR
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.31/0.47 ( ( ( kpair @ Xx @ Xy )
% 0.31/0.47 = ( kpair @ Xz @ Xu ) )
% 0.31/0.47 => ( Xy = Xu ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(ksndsingleton_type,type,
% 0.31/0.47 ksndsingleton: $o ).
% 0.31/0.47
% 0.31/0.47 thf(ksndsingleton,definition,
% 0.31/0.47 ( ksndsingleton
% 0.31/0.47 = ( ! [Xu: $i] :
% 0.31/0.47 ( ( iskpair @ Xu )
% 0.31/0.47 => ( singleton
% 0.31/0.47 @ ( dsetconstr @ ( setunion @ Xu )
% 0.31/0.47 @ ^ [Xx: $i] :
% 0.31/0.47 ( Xu
% 0.31/0.47 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(ksnd_type,type,
% 0.31/0.47 ksnd: $i > $i ).
% 0.31/0.47
% 0.31/0.47 thf(ksndpairEq_type,type,
% 0.31/0.47 ksndpairEq: $o ).
% 0.31/0.47
% 0.31/0.47 thf(ksndpairEq,definition,
% 0.31/0.47 ( ksndpairEq
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.31/0.47 = Xy ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(kpairsurjEq_type,type,
% 0.31/0.47 kpairsurjEq: $o ).
% 0.31/0.47
% 0.31/0.47 thf(kpairsurjEq,definition,
% 0.31/0.47 ( kpairsurjEq
% 0.31/0.47 = ( ! [Xu: $i] :
% 0.31/0.47 ( ( iskpair @ Xu )
% 0.31/0.47 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.31/0.47 = Xu ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(cartprodsndin_type,type,
% 0.31/0.47 cartprodsndin: $o ).
% 0.31/0.47
% 0.31/0.47 thf(cartprodsndin,definition,
% 0.31/0.47 ( cartprodsndin
% 0.31/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.31/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.31/0.47 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(cartprodpairmemEL_type,type,
% 0.31/0.47 cartprodpairmemEL: $o ).
% 0.31/0.47
% 0.31/0.47 thf(cartprodpairmemEL,definition,
% 0.31/0.47 ( cartprodpairmemEL
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.31/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(cartprodpairmemER_type,type,
% 0.31/0.47 cartprodpairmemER: $o ).
% 0.31/0.47
% 0.31/0.47 thf(cartprodpairmemER,definition,
% 0.31/0.47 ( cartprodpairmemER
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.31/0.47 => ( in @ Xy @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(cartprodmempaircEq_type,type,
% 0.31/0.47 cartprodmempaircEq: $o ).
% 0.31/0.47
% 0.31/0.47 thf(cartprodmempaircEq,definition,
% 0.31/0.47 ( cartprodmempaircEq
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ B )
% 0.31/0.47 => ( ( kpair @ Xx @ Xy )
% 0.31/0.47 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(cartprodfstpairEq_type,type,
% 0.31/0.47 cartprodfstpairEq: $o ).
% 0.31/0.47
% 0.31/0.47 thf(cartprodfstpairEq,definition,
% 0.31/0.47 ( cartprodfstpairEq
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ B )
% 0.31/0.47 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.31/0.47 = Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(cartprodsndpairEq_type,type,
% 0.31/0.47 cartprodsndpairEq: $o ).
% 0.31/0.47
% 0.31/0.47 thf(cartprodsndpairEq,definition,
% 0.31/0.47 ( cartprodsndpairEq
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ B )
% 0.31/0.47 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.31/0.47 = Xy ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(cartprodpairsurjEq_type,type,
% 0.31/0.47 cartprodpairsurjEq: $o ).
% 0.31/0.47
% 0.31/0.47 thf(cartprodpairsurjEq,definition,
% 0.31/0.47 ( cartprodpairsurjEq
% 0.31/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.31/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.31/0.47 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.31/0.47 = Xu ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(breln_type,type,
% 0.31/0.47 breln: $i > $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(breln,definition,
% 0.31/0.47 ( breln
% 0.31/0.47 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(dpsetconstr_type,type,
% 0.31/0.47 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.31/0.47
% 0.31/0.47 thf(dpsetconstrI_type,type,
% 0.31/0.47 dpsetconstrI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(dpsetconstrI,definition,
% 0.31/0.47 ( dpsetconstrI
% 0.31/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ B )
% 0.31/0.47 => ( ( Xphi @ Xx @ Xy )
% 0.31/0.47 => ( in @ ( kpair @ Xx @ Xy )
% 0.31/0.47 @ ( dpsetconstr @ A @ B
% 0.31/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(dpsetconstrSub_type,type,
% 0.31/0.47 dpsetconstrSub: $o ).
% 0.31/0.47
% 0.31/0.47 thf(dpsetconstrSub,definition,
% 0.31/0.47 ( dpsetconstrSub
% 0.31/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.31/0.47 ( subset
% 0.31/0.47 @ ( dpsetconstr @ A @ B
% 0.31/0.47 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.31/0.47 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setOfPairsIsBReln_type,type,
% 0.31/0.47 setOfPairsIsBReln: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setOfPairsIsBReln,definition,
% 0.31/0.47 ( setOfPairsIsBReln
% 0.31/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.31/0.47 ( breln @ A @ B
% 0.31/0.47 @ ( dpsetconstr @ A @ B
% 0.31/0.47 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(dpsetconstrERa_type,type,
% 0.31/0.47 dpsetconstrERa: $o ).
% 0.31/0.47
% 0.31/0.47 thf(dpsetconstrERa,definition,
% 0.31/0.47 ( dpsetconstrERa
% 0.31/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ B )
% 0.31/0.47 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.31/0.47 @ ( dpsetconstr @ A @ B
% 0.31/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.31/0.47 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(dpsetconstrEL1_type,type,
% 0.31/0.47 dpsetconstrEL1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(dpsetconstrEL1,definition,
% 0.31/0.47 ( dpsetconstrEL1
% 0.31/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ ( kpair @ Xx @ Xy )
% 0.31/0.47 @ ( dpsetconstr @ A @ B
% 0.31/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.31/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(dpsetconstrEL2_type,type,
% 0.31/0.47 dpsetconstrEL2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(dpsetconstrEL2,definition,
% 0.31/0.47 ( dpsetconstrEL2
% 0.31/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ ( kpair @ Xx @ Xy )
% 0.31/0.47 @ ( dpsetconstr @ A @ B
% 0.31/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.31/0.47 => ( in @ Xy @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(dpsetconstrER_type,type,
% 0.31/0.47 dpsetconstrER: $o ).
% 0.31/0.47
% 0.31/0.47 thf(dpsetconstrER,definition,
% 0.31/0.47 ( dpsetconstrER
% 0.31/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ ( kpair @ Xx @ Xy )
% 0.31/0.47 @ ( dpsetconstr @ A @ B
% 0.31/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.31/0.47 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(func_type,type,
% 0.31/0.47 func: $i > $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(funcSet_type,type,
% 0.31/0.47 funcSet: $i > $i > $i ).
% 0.31/0.47
% 0.31/0.47 thf(funcImageSingleton_type,type,
% 0.31/0.47 funcImageSingleton: $o ).
% 0.31/0.47
% 0.31/0.47 thf(funcImageSingleton,definition,
% 0.31/0.47 ( funcImageSingleton
% 0.31/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.47 ( ( func @ A @ B @ Xf )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( singleton
% 0.31/0.47 @ ( dsetconstr @ B
% 0.31/0.47 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(apProp_type,type,
% 0.31/0.47 apProp: $o ).
% 0.31/0.47
% 0.31/0.47 thf(apProp,definition,
% 0.31/0.47 ( apProp
% 0.31/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.47 ( ( func @ A @ B @ Xf )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( in
% 0.31/0.47 @ ( setunion
% 0.31/0.47 @ ( dsetconstr @ B
% 0.31/0.47 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.31/0.47 @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(ap_type,type,
% 0.31/0.47 ap: $i > $i > $i > $i > $i ).
% 0.31/0.47
% 0.31/0.47 thf(app_type,type,
% 0.31/0.47 app: $o ).
% 0.31/0.47
% 0.31/0.47 thf(app,definition,
% 0.31/0.47 ( app
% 0.31/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.47 ( ( func @ A @ B @ Xf )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(infuncsetfunc_type,type,
% 0.31/0.47 infuncsetfunc: $o ).
% 0.31/0.47
% 0.31/0.47 thf(infuncsetfunc,definition,
% 0.31/0.47 ( infuncsetfunc
% 0.31/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.31/0.47 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(ap2p_type,type,
% 0.31/0.47 ap2p: $o ).
% 0.31/0.47
% 0.31/0.47 thf(ap2p,definition,
% 0.31/0.47 ( ap2p
% 0.31/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(funcinfuncset_type,type,
% 0.31/0.47 funcinfuncset: $o ).
% 0.31/0.47
% 0.31/0.47 thf(funcinfuncset,definition,
% 0.31/0.47 ( funcinfuncset
% 0.31/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.47 ( ( func @ A @ B @ Xf )
% 0.31/0.47 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(lamProp_type,type,
% 0.31/0.47 lamProp: $o ).
% 0.31/0.47
% 0.31/0.47 thf(lamProp,definition,
% 0.31/0.47 ( lamProp
% 0.31/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.31/0.47 => ( func @ A @ B
% 0.31/0.47 @ ( dpsetconstr @ A @ B
% 0.31/0.47 @ ^ [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xf @ Xx )
% 0.31/0.47 = Xy ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(lam_type,type,
% 0.31/0.47 lam: $i > $i > ( $i > $i ) > $i ).
% 0.31/0.47
% 0.31/0.47 thf(lamp_type,type,
% 0.31/0.47 lamp: $o ).
% 0.31/0.47
% 0.31/0.47 thf(lamp,definition,
% 0.31/0.47 ( lamp
% 0.31/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.31/0.47 => ( func @ A @ B
% 0.31/0.47 @ ( lam @ A @ B
% 0.31/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(lam2p_type,type,
% 0.31/0.47 lam2p: $o ).
% 0.31/0.47
% 0.31/0.47 thf(lam2p,definition,
% 0.31/0.47 ( lam2p
% 0.31/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.31/0.47 => ( in
% 0.31/0.47 @ ( lam @ A @ B
% 0.31/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.31/0.47 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(brelnall1_type,type,
% 0.31/0.47 brelnall1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(brelnall1,definition,
% 0.31/0.47 ( brelnall1
% 0.31/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.31/0.47 ( ( breln @ A @ B @ R )
% 0.31/0.47 => ! [Xphi: $i > $o] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ B )
% 0.31/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.31/0.47 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ R )
% 0.31/0.47 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(brelnall2_type,type,
% 0.31/0.47 brelnall2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(brelnall2,definition,
% 0.31/0.47 ( brelnall2
% 0.31/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.31/0.47 ( ( breln @ A @ B @ R )
% 0.31/0.47 => ! [Xphi: $i > $o] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ B )
% 0.31/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.31/0.47 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ R )
% 0.31/0.47 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(ex1E2_type,type,
% 0.31/0.47 ex1E2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(ex1E2,definition,
% 0.31/0.47 ( ex1E2
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.47 ( ( ex1 @ A
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ A )
% 0.31/0.47 => ( ( Xphi @ Xx )
% 0.31/0.47 => ( ( Xphi @ Xy )
% 0.31/0.47 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(funcGraphProp1_type,type,
% 0.31/0.47 funcGraphProp1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(funcGraphProp1,definition,
% 0.31/0.47 ( funcGraphProp1
% 0.31/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.47 ( ( func @ A @ B @ Xf )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(funcGraphProp3_type,type,
% 0.31/0.47 funcGraphProp3: $o ).
% 0.31/0.47
% 0.31/0.47 thf(funcGraphProp3,definition,
% 0.31/0.47 ( funcGraphProp3
% 0.31/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(funcGraphProp2_type,type,
% 0.31/0.47 funcGraphProp2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(funcGraphProp2,definition,
% 0.31/0.47 ( funcGraphProp2
% 0.31/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.47 ( ( func @ A @ B @ Xf )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ B )
% 0.31/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.31/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.31/0.47 = Xy ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(funcextLem_type,type,
% 0.31/0.47 funcextLem: $o ).
% 0.31/0.47
% 0.31/0.47 thf(funcextLem,definition,
% 0.31/0.47 ( funcextLem
% 0.31/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.47 ( ( func @ A @ B @ Xf )
% 0.31/0.47 => ! [Xg: $i] :
% 0.31/0.47 ( ( func @ A @ B @ Xg )
% 0.31/0.47 => ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.31/0.47 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ B )
% 0.31/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 0.31/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(funcGraphProp4_type,type,
% 0.31/0.47 funcGraphProp4: $o ).
% 0.31/0.47
% 0.31/0.47 thf(funcGraphProp4,definition,
% 0.31/0.47 ( funcGraphProp4
% 0.31/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ B )
% 0.31/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.31/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.31/0.47 = Xy ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subbreln_type,type,
% 0.31/0.47 subbreln: $o ).
% 0.31/0.47
% 0.31/0.47 thf(subbreln,definition,
% 0.31/0.47 ( subbreln
% 0.31/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.31/0.47 ( ( breln @ A @ B @ R )
% 0.31/0.47 => ! [S: $i] :
% 0.31/0.47 ( ( breln @ A @ B @ S )
% 0.31/0.47 => ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ B )
% 0.31/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.31/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.31/0.47 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(eqbreln_type,type,
% 0.31/0.47 eqbreln: $o ).
% 0.31/0.47
% 0.31/0.47 thf(eqbreln,definition,
% 0.31/0.47 ( eqbreln
% 0.31/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.31/0.47 ( ( breln @ A @ B @ R )
% 0.31/0.47 => ! [S: $i] :
% 0.31/0.47 ( ( breln @ A @ B @ S )
% 0.31/0.47 => ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ B )
% 0.31/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.31/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.31/0.47 => ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ B )
% 0.31/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.31/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.31/0.47 => ( R = S ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(funcext_type,type,
% 0.31/0.47 funcext: $o ).
% 0.31/0.47
% 0.31/0.47 thf(funcext,definition,
% 0.31/0.47 ( funcext
% 0.31/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.47 ( ( func @ A @ B @ Xf )
% 0.31/0.47 => ! [Xg: $i] :
% 0.31/0.47 ( ( func @ A @ B @ Xg )
% 0.31/0.47 => ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.31/0.47 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.31/0.47 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(funcext2_type,type,
% 0.31/0.47 funcext2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(funcext2,definition,
% 0.31/0.47 ( funcext2
% 0.31/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.31/0.47 => ! [Xg: $i] :
% 0.31/0.47 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 0.31/0.47 => ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.31/0.47 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.31/0.47 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(ap2apEq1_type,type,
% 0.31/0.47 ap2apEq1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(ap2apEq1,definition,
% 0.31/0.47 ( ap2apEq1
% 0.31/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.31/0.47 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(ap2apEq2_type,type,
% 0.31/0.47 ap2apEq2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(ap2apEq2,definition,
% 0.31/0.47 ( ap2apEq2
% 0.31/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.47 ( ( func @ A @ B @ Xf )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.31/0.47 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(beta1_type,type,
% 0.31/0.47 beta1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(beta1,definition,
% 0.31/0.47 ( beta1
% 0.31/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( ap @ A @ B
% 0.31/0.47 @ ( lam @ A @ B
% 0.31/0.47 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.31/0.47 @ Xx )
% 0.31/0.47 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(eta1_type,type,
% 0.31/0.47 eta1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(eta1,definition,
% 0.31/0.47 ( eta1
% 0.31/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.47 ( ( func @ A @ B @ Xf )
% 0.31/0.47 => ( ( lam @ A @ B
% 0.31/0.47 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.31/0.47 = Xf ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(lam2lamEq_type,type,
% 0.31/0.47 lam2lamEq: $o ).
% 0.31/0.47
% 0.31/0.47 thf(lam2lamEq,definition,
% 0.31/0.47 ( lam2lamEq
% 0.31/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.31/0.47 => ( ( lam @ A @ B
% 0.31/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.31/0.47 = ( lam @ A @ B
% 0.31/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(beta2_type,type,
% 0.31/0.47 beta2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(beta2,definition,
% 0.31/0.47 ( beta2
% 0.31/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( ap @ A @ B
% 0.31/0.47 @ ( lam @ A @ B
% 0.31/0.47 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.31/0.47 @ Xx )
% 0.31/0.47 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(eta2_type,type,
% 0.31/0.47 eta2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(eta2,definition,
% 0.31/0.47 ( eta2
% 0.31/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.31/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.31/0.47 => ( ( lam @ A @ B
% 0.31/0.47 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.31/0.47 = Xf ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(iffalseProp1_type,type,
% 0.31/0.47 iffalseProp1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(iffalseProp1,definition,
% 0.31/0.47 ( iffalseProp1
% 0.31/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ A )
% 0.31/0.47 => ( ~ Xphi
% 0.31/0.47 => ( in @ Xy
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xz: $i] :
% 0.31/0.47 ( ( Xphi
% 0.31/0.47 & ( Xz = Xx ) )
% 0.31/0.47 | ( ~ Xphi
% 0.31/0.47 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(iffalseProp2_type,type,
% 0.31/0.47 iffalseProp2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(iffalseProp2,definition,
% 0.31/0.47 ( iffalseProp2
% 0.31/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ A )
% 0.31/0.47 => ( ~ Xphi
% 0.31/0.47 => ( ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xz: $i] :
% 0.31/0.47 ( ( Xphi
% 0.31/0.47 & ( Xz = Xx ) )
% 0.31/0.47 | ( ~ Xphi
% 0.31/0.47 & ( Xz = Xy ) ) ) )
% 0.31/0.47 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(iftrueProp1_type,type,
% 0.31/0.47 iftrueProp1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(iftrueProp1,definition,
% 0.31/0.47 ( iftrueProp1
% 0.31/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ A )
% 0.31/0.47 => ( Xphi
% 0.31/0.47 => ( in @ Xx
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xz: $i] :
% 0.31/0.47 ( ( Xphi
% 0.31/0.47 & ( Xz = Xx ) )
% 0.31/0.47 | ( ~ Xphi
% 0.31/0.47 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(iftrueProp2_type,type,
% 0.31/0.47 iftrueProp2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(iftrueProp2,definition,
% 0.31/0.47 ( iftrueProp2
% 0.31/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ A )
% 0.31/0.47 => ( Xphi
% 0.31/0.47 => ( ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xz: $i] :
% 0.31/0.47 ( ( Xphi
% 0.31/0.47 & ( Xz = Xx ) )
% 0.31/0.47 | ( ~ Xphi
% 0.31/0.47 & ( Xz = Xy ) ) ) )
% 0.31/0.47 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(ifSingleton_type,type,
% 0.31/0.47 ifSingleton: $o ).
% 0.31/0.47
% 0.31/0.47 thf(ifSingleton,definition,
% 0.31/0.47 ( ifSingleton
% 0.31/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ A )
% 0.31/0.47 => ( singleton
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xz: $i] :
% 0.31/0.47 ( ( Xphi
% 0.31/0.47 & ( Xz = Xx ) )
% 0.31/0.47 | ( ~ Xphi
% 0.31/0.47 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(if_type,type,
% 0.31/0.47 if: $i > $o > $i > $i > $i ).
% 0.31/0.47
% 0.31/0.47 thf(ifp_type,type,
% 0.31/0.47 ifp: $o ).
% 0.31/0.47
% 0.31/0.47 thf(ifp,definition,
% 0.31/0.47 ( ifp
% 0.31/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ A )
% 0.31/0.47 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(theeq_type,type,
% 0.31/0.47 theeq: $o ).
% 0.31/0.47
% 0.31/0.47 thf(theeq,definition,
% 0.31/0.47 ( theeq
% 0.31/0.47 = ( ! [X: $i] :
% 0.31/0.47 ( ( singleton @ X )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ X )
% 0.31/0.47 => ( ( setunion @ X )
% 0.31/0.47 = Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(iftrue_type,type,
% 0.31/0.47 iftrue: $o ).
% 0.31/0.47
% 0.31/0.47 thf(iftrue,definition,
% 0.31/0.47 ( iftrue
% 0.31/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ A )
% 0.31/0.47 => ( Xphi
% 0.31/0.47 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.31/0.47 = Xx ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(iffalse_type,type,
% 0.31/0.47 iffalse: $o ).
% 0.31/0.47
% 0.31/0.47 thf(iffalse,definition,
% 0.31/0.47 ( iffalse
% 0.31/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ A )
% 0.31/0.47 => ( ~ Xphi
% 0.31/0.47 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.31/0.47 = Xy ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(iftrueorfalse_type,type,
% 0.31/0.47 iftrueorfalse: $o ).
% 0.31/0.47
% 0.31/0.47 thf(iftrueorfalse,definition,
% 0.31/0.47 ( iftrueorfalse
% 0.31/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ A )
% 0.31/0.47 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(binintersectT_lem_type,type,
% 0.31/0.47 binintersectT_lem: $o ).
% 0.31/0.47
% 0.31/0.47 thf(binintersectT_lem,definition,
% 0.31/0.47 ( binintersectT_lem
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(binunionT_lem_type,type,
% 0.31/0.47 binunionT_lem: $o ).
% 0.31/0.47
% 0.31/0.47 thf(binunionT_lem,definition,
% 0.31/0.47 ( binunionT_lem
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(powersetT_lem_type,type,
% 0.31/0.47 powersetT_lem: $o ).
% 0.31/0.47
% 0.31/0.47 thf(powersetT_lem,definition,
% 0.31/0.47 ( powersetT_lem
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setminusT_lem_type,type,
% 0.31/0.47 setminusT_lem: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setminusT_lem,definition,
% 0.31/0.47 ( setminusT_lem
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(complementT_lem_type,type,
% 0.31/0.47 complementT_lem: $o ).
% 0.31/0.47
% 0.31/0.47 thf(complementT_lem,definition,
% 0.31/0.47 ( complementT_lem
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setextT_type,type,
% 0.31/0.47 setextT: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setextT,definition,
% 0.31/0.47 ( setextT
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( in @ Xx @ X )
% 0.31/0.47 => ( in @ Xx @ Y ) ) )
% 0.31/0.47 => ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( in @ Xx @ Y )
% 0.31/0.47 => ( in @ Xx @ X ) ) )
% 0.31/0.47 => ( X = Y ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subsetTI_type,type,
% 0.31/0.47 subsetTI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(subsetTI,definition,
% 0.31/0.47 ( subsetTI
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( in @ Xx @ X )
% 0.31/0.47 => ( in @ Xx @ Y ) ) )
% 0.31/0.47 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(powersetTI1_type,type,
% 0.31/0.47 powersetTI1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(powersetTI1,definition,
% 0.31/0.47 ( powersetTI1
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( in @ Xx @ X )
% 0.31/0.47 => ( in @ Xx @ Y ) ) )
% 0.31/0.47 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(powersetTE1_type,type,
% 0.31/0.47 powersetTE1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(powersetTE1,definition,
% 0.31/0.47 ( powersetTE1
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( in @ X @ ( powerset @ Y ) )
% 0.31/0.47 => ( ( in @ Xx @ X )
% 0.31/0.47 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(complementTI1_type,type,
% 0.31/0.47 complementTI1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(complementTI1,definition,
% 0.31/0.47 ( complementTI1
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( in @ Xx @ X )
% 0.31/0.47 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(complementTE1_type,type,
% 0.31/0.47 complementTE1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(complementTE1,definition,
% 0.31/0.47 ( complementTE1
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 0.31/0.47 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(binintersectTELcontra_type,type,
% 0.31/0.47 binintersectTELcontra: $o ).
% 0.31/0.47
% 0.31/0.47 thf(binintersectTELcontra,definition,
% 0.31/0.47 ( binintersectTELcontra
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ~ ( in @ Xx @ X )
% 0.31/0.47 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(binintersectTERcontra_type,type,
% 0.31/0.47 binintersectTERcontra: $o ).
% 0.31/0.47
% 0.31/0.47 thf(binintersectTERcontra,definition,
% 0.31/0.47 ( binintersectTERcontra
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ~ ( in @ Xx @ Y )
% 0.31/0.47 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(contrasubsetT_type,type,
% 0.31/0.47 contrasubsetT: $o ).
% 0.31/0.47
% 0.31/0.47 thf(contrasubsetT,definition,
% 0.31/0.47 ( contrasubsetT
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.31/0.47 => ( ( in @ Xx @ Y )
% 0.31/0.47 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(contrasubsetT1_type,type,
% 0.31/0.47 contrasubsetT1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(contrasubsetT1,definition,
% 0.31/0.47 ( contrasubsetT1
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( subset @ X @ Y )
% 0.31/0.47 => ( ~ ( in @ Xx @ Y )
% 0.31/0.47 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(contrasubsetT2_type,type,
% 0.31/0.47 contrasubsetT2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(contrasubsetT2,definition,
% 0.31/0.47 ( contrasubsetT2
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ( ( subset @ X @ Y )
% 0.31/0.47 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(contrasubsetT3_type,type,
% 0.31/0.47 contrasubsetT3: $o ).
% 0.31/0.47
% 0.31/0.47 thf(contrasubsetT3,definition,
% 0.31/0.47 ( contrasubsetT3
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 0.31/0.47 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(doubleComplementI1_type,type,
% 0.31/0.47 doubleComplementI1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(doubleComplementI1,definition,
% 0.31/0.47 ( doubleComplementI1
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( in @ Xx @ X )
% 0.31/0.47 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(doubleComplementE1_type,type,
% 0.31/0.47 doubleComplementE1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(doubleComplementE1,definition,
% 0.31/0.47 ( doubleComplementE1
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 0.31/0.47 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(doubleComplementSub1_type,type,
% 0.31/0.47 doubleComplementSub1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(doubleComplementSub1,definition,
% 0.31/0.47 ( doubleComplementSub1
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(doubleComplementSub2_type,type,
% 0.31/0.47 doubleComplementSub2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(doubleComplementSub2,definition,
% 0.31/0.47 ( doubleComplementSub2
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(doubleComplementEq_type,type,
% 0.31/0.47 doubleComplementEq: $o ).
% 0.31/0.47
% 0.31/0.47 thf(doubleComplementEq,definition,
% 0.31/0.47 ( doubleComplementEq
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ( X
% 0.31/0.47 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(complementTnotintersectT_type,type,
% 0.31/0.47 complementTnotintersectT: $o ).
% 0.31/0.47
% 0.31/0.47 thf(complementTnotintersectT,definition,
% 0.31/0.47 ( complementTnotintersectT
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.31/0.47 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(complementImpComplementIntersect_type,type,
% 0.31/0.47 complementImpComplementIntersect: $o ).
% 0.31/0.47
% 0.31/0.47 thf(complementImpComplementIntersect,definition,
% 0.31/0.47 ( complementImpComplementIntersect
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.31/0.47 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(complementSubsetComplementIntersect_type,type,
% 0.31/0.47 complementSubsetComplementIntersect: $o ).
% 0.31/0.47
% 0.31/0.47 thf(complementSubsetComplementIntersect,definition,
% 0.31/0.47 ( complementSubsetComplementIntersect
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(complementInPowersetComplementIntersect_type,type,
% 0.31/0.47 complementInPowersetComplementIntersect: $o ).
% 0.31/0.47
% 0.31/0.47 thf(complementInPowersetComplementIntersect,definition,
% 0.31/0.47 ( complementInPowersetComplementIntersect
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(contraSubsetComplement_type,type,
% 0.31/0.47 contraSubsetComplement: $o ).
% 0.31/0.47
% 0.31/0.47 thf(contraSubsetComplement,definition,
% 0.31/0.47 ( contraSubsetComplement
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( in @ Xx @ Y )
% 0.31/0.47 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(complementTcontraSubset_type,type,
% 0.31/0.47 complementTcontraSubset: $o ).
% 0.31/0.47
% 0.31/0.47 thf(complementTcontraSubset,definition,
% 0.31/0.47 ( complementTcontraSubset
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.31/0.47 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(binunionTILcontra_type,type,
% 0.31/0.47 binunionTILcontra: $o ).
% 0.31/0.47
% 0.31/0.47 thf(binunionTILcontra,definition,
% 0.31/0.47 ( binunionTILcontra
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.31/0.47 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(binunionTIRcontra_type,type,
% 0.31/0.47 binunionTIRcontra: $o ).
% 0.31/0.47
% 0.31/0.47 thf(binunionTIRcontra,definition,
% 0.31/0.47 ( binunionTIRcontra
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.31/0.47 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(inIntersectImpInUnion_type,type,
% 0.31/0.47 inIntersectImpInUnion: $o ).
% 0.31/0.47
% 0.31/0.47 thf(inIntersectImpInUnion,definition,
% 0.31/0.47 ( inIntersectImpInUnion
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ! [Z: $i] :
% 0.31/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.31/0.47 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(inIntersectImpInUnion2_type,type,
% 0.31/0.47 inIntersectImpInUnion2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(inIntersectImpInUnion2,definition,
% 0.31/0.47 ( inIntersectImpInUnion2
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ! [Z: $i] :
% 0.31/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.31/0.47 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(inIntersectImpInIntersectUnions_type,type,
% 0.31/0.47 inIntersectImpInIntersectUnions: $o ).
% 0.31/0.47
% 0.31/0.47 thf(inIntersectImpInIntersectUnions,definition,
% 0.31/0.47 ( inIntersectImpInIntersectUnions
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ! [Z: $i] :
% 0.31/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.31/0.47 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(intersectInPowersetIntersectUnions_type,type,
% 0.31/0.47 intersectInPowersetIntersectUnions: $o ).
% 0.31/0.47
% 0.31/0.47 thf(intersectInPowersetIntersectUnions,definition,
% 0.31/0.47 ( intersectInPowersetIntersectUnions
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ! [Z: $i] :
% 0.31/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.31/0.47 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(inComplementUnionImpNotIn1_type,type,
% 0.31/0.47 inComplementUnionImpNotIn1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(inComplementUnionImpNotIn1,definition,
% 0.31/0.47 ( inComplementUnionImpNotIn1
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.31/0.47 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(inComplementUnionImpInComplement1_type,type,
% 0.31/0.47 inComplementUnionImpInComplement1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(inComplementUnionImpInComplement1,definition,
% 0.31/0.47 ( inComplementUnionImpInComplement1
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.31/0.47 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(binunionTE_type,type,
% 0.31/0.47 binunionTE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(binunionTE,definition,
% 0.31/0.47 ( binunionTE
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ! [Xphi: $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.31/0.47 => ( ( ( in @ Xx @ X )
% 0.31/0.47 => Xphi )
% 0.31/0.47 => ( ( ( in @ Xx @ Y )
% 0.31/0.47 => Xphi )
% 0.31/0.47 => Xphi ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(binunionTEcontra_type,type,
% 0.31/0.47 binunionTEcontra: $o ).
% 0.31/0.47
% 0.31/0.47 thf(binunionTEcontra,definition,
% 0.31/0.47 ( binunionTEcontra
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ~ ( in @ Xx @ X )
% 0.31/0.47 => ( ~ ( in @ Xx @ Y )
% 0.31/0.47 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(demorgan2a1_type,type,
% 0.31/0.47 demorgan2a1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(demorgan2a1,definition,
% 0.31/0.47 ( demorgan2a1
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.31/0.47 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(complementUnionInPowersetComplement_type,type,
% 0.31/0.47 complementUnionInPowersetComplement: $o ).
% 0.31/0.47
% 0.31/0.47 thf(complementUnionInPowersetComplement,definition,
% 0.31/0.47 ( complementUnionInPowersetComplement
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(demorgan2a2_type,type,
% 0.31/0.47 demorgan2a2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(demorgan2a2,definition,
% 0.31/0.47 ( demorgan2a2
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.31/0.47 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(demorgan1a_type,type,
% 0.31/0.47 demorgan1a: $o ).
% 0.31/0.47
% 0.31/0.47 thf(demorgan1a,definition,
% 0.31/0.47 ( demorgan1a
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 0.31/0.47 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(demorgan1b_type,type,
% 0.31/0.47 demorgan1b: $o ).
% 0.31/0.47
% 0.31/0.47 thf(demorgan1b,definition,
% 0.31/0.47 ( demorgan1b
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.31/0.47 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(demorgan1_type,type,
% 0.31/0.47 demorgan1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(demorgan1,definition,
% 0.31/0.47 ( demorgan1
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 0.31/0.47 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(demorgan2a_type,type,
% 0.31/0.47 demorgan2a: $o ).
% 0.31/0.47
% 0.31/0.47 thf(demorgan2a,definition,
% 0.31/0.47 ( demorgan2a
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.31/0.47 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(demorgan2b2_type,type,
% 0.31/0.47 demorgan2b2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(demorgan2b2,definition,
% 0.31/0.47 ( demorgan2b2
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.31/0.47 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 0.31/0.47 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(demorgan2b_type,type,
% 0.31/0.47 demorgan2b: $o ).
% 0.31/0.47
% 0.31/0.47 thf(demorgan2b,definition,
% 0.31/0.47 ( demorgan2b
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.31/0.47 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(demorgan2_type,type,
% 0.31/0.47 demorgan2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(demorgan2,definition,
% 0.31/0.47 ( demorgan2
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 0.31/0.47 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(woz13rule0_type,type,
% 0.31/0.47 woz13rule0: $o ).
% 0.31/0.47
% 0.31/0.47 thf(woz13rule0,definition,
% 0.31/0.47 ( woz13rule0
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.31/0.47 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(woz13rule1_type,type,
% 0.31/0.47 woz13rule1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(woz13rule1,definition,
% 0.31/0.47 ( woz13rule1
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ! [Z: $i] :
% 0.31/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.31/0.47 => ( ( subset @ X @ Z )
% 0.31/0.47 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(woz13rule2_type,type,
% 0.31/0.47 woz13rule2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(woz13rule2,definition,
% 0.31/0.47 ( woz13rule2
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ! [Z: $i] :
% 0.31/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.31/0.47 => ( ( subset @ Y @ Z )
% 0.31/0.47 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(woz13rule3_type,type,
% 0.31/0.47 woz13rule3: $o ).
% 0.31/0.47
% 0.31/0.47 thf(woz13rule3,definition,
% 0.31/0.47 ( woz13rule3
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ! [Z: $i] :
% 0.31/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.31/0.47 => ( ( subset @ X @ Y )
% 0.31/0.47 => ( ( subset @ X @ Z )
% 0.31/0.47 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(woz13rule4_type,type,
% 0.31/0.47 woz13rule4: $o ).
% 0.31/0.47
% 0.31/0.47 thf(woz13rule4,definition,
% 0.31/0.47 ( woz13rule4
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ! [Z: $i] :
% 0.31/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.31/0.47 => ! [W: $i] :
% 0.31/0.47 ( ( in @ W @ ( powerset @ A ) )
% 0.31/0.47 => ( ( subset @ X @ Z )
% 0.31/0.47 => ( ( subset @ Y @ W )
% 0.31/0.47 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(woz1_1_type,type,
% 0.31/0.47 woz1_1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(woz1_1,definition,
% 0.31/0.47 ( woz1_1
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(woz1_2_type,type,
% 0.31/0.47 woz1_2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(woz1_2,definition,
% 0.31/0.47 ( woz1_2
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ! [Z: $i] :
% 0.31/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.31/0.47 => ! [W: $i] :
% 0.31/0.47 ( ( in @ W @ ( powerset @ A ) )
% 0.31/0.47 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 0.31/0.47 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(woz1_3_type,type,
% 0.31/0.47 woz1_3: $o ).
% 0.31/0.47
% 0.31/0.47 thf(woz1_3,definition,
% 0.31/0.47 ( woz1_3
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ! [Z: $i] :
% 0.31/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.31/0.47 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(woz1_4_type,type,
% 0.31/0.47 woz1_4: $o ).
% 0.31/0.47
% 0.31/0.47 thf(woz1_4,definition,
% 0.31/0.47 ( woz1_4
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.31/0.47 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(woz1_5_type,type,
% 0.31/0.47 woz1_5: $o ).
% 0.31/0.47
% 0.31/0.47 thf(woz1_5,definition,
% 0.31/0.47 ( woz1_5
% 0.31/0.47 = ( ! [A: $i,X: $i] :
% 0.31/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.31/0.47 => ! [Y: $i] :
% 0.31/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.31/0.47 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(breln1_type,type,
% 0.31/0.47 breln1: $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(breln1,definition,
% 0.31/0.47 ( breln1
% 0.31/0.47 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(breln1all2_type,type,
% 0.31/0.47 breln1all2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(breln1all2,definition,
% 0.31/0.47 ( breln1all2
% 0.31/0.47 = ( ! [A: $i,R: $i] :
% 0.31/0.47 ( ( breln1 @ A @ R )
% 0.31/0.47 => ! [Xphi: $i > $o] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ A )
% 0.31/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.31/0.47 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ R )
% 0.31/0.47 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(breln1Set_type,type,
% 0.31/0.47 breln1Set: $i > $i ).
% 0.31/0.47
% 0.31/0.47 thf(breln1SetBreln1_type,type,
% 0.31/0.47 breln1SetBreln1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(breln1SetBreln1,definition,
% 0.31/0.47 ( breln1SetBreln1
% 0.31/0.47 = ( ! [A: $i,R: $i] :
% 0.31/0.47 ( ( in @ R @ ( breln1Set @ A ) )
% 0.31/0.47 => ( breln1 @ A @ R ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(transitive_type,type,
% 0.31/0.47 transitive: $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(antisymmetric_type,type,
% 0.31/0.47 antisymmetric: $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(reflexive_type,type,
% 0.31/0.47 reflexive: $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(refltransitive_type,type,
% 0.31/0.47 refltransitive: $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(refllinearorder_type,type,
% 0.31/0.47 refllinearorder: $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(reflwellordering_type,type,
% 0.31/0.47 reflwellordering: $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(choice2fnsingleton_type,type,
% 0.31/0.47 choice2fnsingleton: $o ).
% 0.31/0.47
% 0.31/0.47 thf(choice2fnsingleton,definition,
% 0.31/0.47 ( choice2fnsingleton
% 0.31/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ? [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ B )
% 0.31/0.48 & ( Xphi @ Xx @ Xy ) ) )
% 0.31/0.48 => ! [R: $i] :
% 0.31/0.48 ( ( in @ R @ ( breln1Set @ B ) )
% 0.31/0.48 => ( ( reflwellordering @ B @ R )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ( singleton
% 0.31/0.48 @ ( dsetconstr @ B
% 0.31/0.48 @ ^ [Xy: $i] :
% 0.31/0.48 ( ( Xphi @ Xx @ Xy )
% 0.31/0.48 & ! [Xz: $i] :
% 0.31/0.48 ( ( in @ Xz @ B )
% 0.31/0.48 => ( ( Xphi @ Xx @ Xz )
% 0.31/0.48 => ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(setOfPairsIsBReln1_type,type,
% 0.31/0.48 setOfPairsIsBReln1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(setOfPairsIsBReln1,definition,
% 0.31/0.48 ( setOfPairsIsBReln1
% 0.31/0.48 = ( ! [A: $i,Xphi: $i > $i > $o] :
% 0.31/0.48 ( breln1 @ A
% 0.31/0.48 @ ( dpsetconstr @ A @ A
% 0.31/0.48 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(breln1all1_type,type,
% 0.31/0.48 breln1all1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(breln1all1,definition,
% 0.31/0.48 ( breln1all1
% 0.31/0.48 = ( ! [A: $i,R: $i] :
% 0.31/0.48 ( ( breln1 @ A @ R )
% 0.31/0.48 => ! [Xphi: $i > $o] :
% 0.31/0.48 ( ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.31/0.48 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ R )
% 0.31/0.48 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(subbreln1_type,type,
% 0.31/0.48 subbreln1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(subbreln1,definition,
% 0.31/0.48 ( subbreln1
% 0.31/0.48 = ( ! [A: $i,R: $i] :
% 0.31/0.48 ( ( breln1 @ A @ R )
% 0.31/0.48 => ! [S: $i] :
% 0.31/0.48 ( ( breln1 @ A @ S )
% 0.31/0.48 => ( ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.31/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.31/0.48 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(eqbreln1_type,type,
% 0.31/0.48 eqbreln1: $o ).
% 0.31/0.48
% 0.31/0.48 thf(eqbreln1,definition,
% 0.31/0.48 ( eqbreln1
% 0.31/0.48 = ( ! [A: $i,R: $i] :
% 0.31/0.48 ( ( breln1 @ A @ R )
% 0.31/0.48 => ! [S: $i] :
% 0.31/0.48 ( ( breln1 @ A @ S )
% 0.31/0.48 => ( ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.31/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.31/0.48 => ( ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.31/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.31/0.48 => ( R = S ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(breln1invset_type,type,
% 0.31/0.48 breln1invset: $i > $i > $i ).
% 0.31/0.48
% 0.31/0.48 thf(breln1invprop_type,type,
% 0.31/0.48 breln1invprop: $o ).
% 0.31/0.48
% 0.31/0.48 thf(breln1invprop,definition,
% 0.31/0.48 ( breln1invprop
% 0.31/0.48 = ( ! [A: $i,R: $i] :
% 0.31/0.48 ( ( breln1 @ A @ R )
% 0.31/0.48 => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(breln1invI_type,type,
% 0.31/0.48 breln1invI: $o ).
% 0.31/0.48
% 0.31/0.48 thf(breln1invI,definition,
% 0.31/0.48 ( breln1invI
% 0.31/0.48 = ( ! [A: $i,R: $i] :
% 0.31/0.48 ( ( breln1 @ A @ R )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.31/0.48 => ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(breln1invE_type,type,
% 0.31/0.48 breln1invE: $o ).
% 0.31/0.48
% 0.31/0.48 thf(breln1invE,definition,
% 0.31/0.48 ( breln1invE
% 0.31/0.48 = ( ! [A: $i,R: $i] :
% 0.31/0.48 ( ( breln1 @ A @ R )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
% 0.31/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(breln1compset_type,type,
% 0.31/0.48 breln1compset: $i > $i > $i > $i ).
% 0.31/0.48
% 0.31/0.48 thf(breln1compset,definition,
% 0.31/0.48 ( breln1compset
% 0.31/0.48 = ( ^ [A: $i,R: $i,S: $i] :
% 0.31/0.48 ( dpsetconstr @ A @ A
% 0.31/0.48 @ ^ [Xx: $i,Xy: $i] :
% 0.31/0.48 ? [Xz: $i] :
% 0.31/0.48 ( ( in @ Xz @ A )
% 0.31/0.48 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.31/0.48 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(breln1compprop_type,type,
% 0.31/0.48 breln1compprop: $o ).
% 0.31/0.48
% 0.31/0.48 thf(breln1compprop,definition,
% 0.31/0.48 ( breln1compprop
% 0.31/0.48 = ( ! [A: $i,R: $i] :
% 0.31/0.48 ( ( breln1 @ A @ R )
% 0.31/0.48 => ! [S: $i] :
% 0.31/0.48 ( ( breln1 @ A @ S )
% 0.31/0.48 => ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(breln1compI,conjecture,
% 0.31/0.48 ( setextAx
% 0.31/0.48 => ( emptysetAx
% 0.31/0.48 => ( setadjoinAx
% 0.31/0.48 => ( powersetAx
% 0.31/0.48 => ( setunionAx
% 0.31/0.48 => ( omega0Ax
% 0.31/0.48 => ( omegaSAx
% 0.31/0.48 => ( omegaIndAx
% 0.31/0.48 => ( replAx
% 0.31/0.48 => ( foundationAx
% 0.31/0.48 => ( wellorderingAx
% 0.31/0.48 => ( descrp
% 0.31/0.48 => ( dsetconstrI
% 0.31/0.48 => ( dsetconstrEL
% 0.31/0.48 => ( dsetconstrER
% 0.31/0.48 => ( exuE1
% 0.31/0.48 => ( prop2setE
% 0.31/0.48 => ( emptysetE
% 0.31/0.48 => ( emptysetimpfalse
% 0.31/0.48 => ( notinemptyset
% 0.31/0.48 => ( exuE3e
% 0.31/0.48 => ( setext
% 0.31/0.48 => ( emptyI
% 0.31/0.48 => ( noeltsimpempty
% 0.31/0.48 => ( setbeta
% 0.31/0.48 => ( nonemptyE1
% 0.31/0.48 => ( nonemptyI
% 0.31/0.48 => ( nonemptyI1
% 0.31/0.48 => ( setadjoinIL
% 0.31/0.48 => ( emptyinunitempty
% 0.31/0.48 => ( setadjoinIR
% 0.31/0.48 => ( setadjoinE
% 0.31/0.48 => ( setadjoinOr
% 0.31/0.48 => ( setoftrueEq
% 0.31/0.48 => ( powersetI
% 0.31/0.48 => ( emptyinPowerset
% 0.31/0.48 => ( emptyInPowerset
% 0.31/0.48 => ( powersetE
% 0.31/0.48 => ( setunionI
% 0.31/0.48 => ( setunionE
% 0.31/0.48 => ( subPowSU
% 0.31/0.48 => ( exuE2
% 0.31/0.48 => ( nonemptyImpWitness
% 0.31/0.48 => ( uniqinunit
% 0.31/0.48 => ( notinsingleton
% 0.31/0.48 => ( eqinunit
% 0.31/0.48 => ( singletonsswitch
% 0.31/0.48 => ( upairsetE
% 0.31/0.48 => ( upairsetIL
% 0.31/0.48 => ( upairsetIR
% 0.31/0.48 => ( emptyE1
% 0.31/0.48 => ( vacuousDall
% 0.31/0.48 => ( quantDeMorgan1
% 0.31/0.48 => ( quantDeMorgan2
% 0.31/0.48 => ( quantDeMorgan3
% 0.31/0.48 => ( quantDeMorgan4
% 0.31/0.48 => ( prop2setI
% 0.31/0.48 => ( prop2set2propI
% 0.31/0.48 => ( notdexE
% 0.31/0.48 => ( notdallE
% 0.31/0.48 => ( exuI1
% 0.31/0.48 => ( exuI3
% 0.31/0.48 => ( exuI2
% 0.31/0.48 => ( inCongP
% 0.31/0.48 => ( in__Cong
% 0.31/0.48 => ( exuE3u
% 0.31/0.48 => ( exu__Cong
% 0.31/0.48 => ( emptyset__Cong
% 0.31/0.48 => ( setadjoin__Cong
% 0.31/0.48 => ( powerset__Cong
% 0.31/0.48 => ( setunion__Cong
% 0.31/0.48 => ( omega__Cong
% 0.31/0.48 => ( exuEu
% 0.31/0.48 => ( descr__Cong
% 0.31/0.48 => ( dsetconstr__Cong
% 0.31/0.48 => ( subsetI1
% 0.31/0.48 => ( eqimpsubset2
% 0.31/0.48 => ( eqimpsubset1
% 0.31/0.48 => ( subsetI2
% 0.31/0.48 => ( emptysetsubset
% 0.31/0.48 => ( subsetE
% 0.31/0.48 => ( subsetE2
% 0.31/0.48 => ( notsubsetI
% 0.31/0.48 => ( notequalI1
% 0.31/0.48 => ( notequalI2
% 0.31/0.48 => ( subsetRefl
% 0.31/0.48 => ( subsetTrans
% 0.31/0.48 => ( setadjoinSub
% 0.31/0.48 => ( setadjoinSub2
% 0.31/0.48 => ( subset2powerset
% 0.31/0.48 => ( setextsub
% 0.31/0.48 => ( subsetemptysetimpeq
% 0.31/0.48 => ( powersetI1
% 0.31/0.48 => ( powersetE1
% 0.31/0.48 => ( inPowerset
% 0.31/0.48 => ( powersetsubset
% 0.31/0.48 => ( sepInPowerset
% 0.31/0.48 => ( sepSubset
% 0.31/0.48 => ( binunionIL
% 0.31/0.48 => ( upairset2IR
% 0.31/0.48 => ( binunionIR
% 0.31/0.48 => ( binunionEcases
% 0.31/0.48 => ( binunionE
% 0.31/0.48 => ( binunionLsub
% 0.31/0.48 => ( binunionRsub
% 0.31/0.48 => ( binintersectI
% 0.31/0.48 => ( binintersectSubset5
% 0.31/0.48 => ( binintersectEL
% 0.31/0.48 => ( binintersectLsub
% 0.31/0.48 => ( binintersectSubset2
% 0.31/0.48 => ( binintersectSubset3
% 0.31/0.48 => ( binintersectER
% 0.31/0.48 => ( disjointsetsI1
% 0.31/0.48 => ( binintersectRsub
% 0.31/0.48 => ( binintersectSubset4
% 0.31/0.48 => ( binintersectSubset1
% 0.31/0.48 => ( bs114d
% 0.31/0.48 => ( setminusI
% 0.31/0.48 => ( setminusEL
% 0.31/0.48 => ( setminusER
% 0.31/0.48 => ( setminusSubset2
% 0.31/0.48 => ( setminusERneg
% 0.31/0.48 => ( setminusELneg
% 0.31/0.48 => ( setminusILneg
% 0.31/0.48 => ( setminusIRneg
% 0.31/0.48 => ( setminusLsub
% 0.31/0.48 => ( setminusSubset1
% 0.31/0.48 => ( symdiffE
% 0.31/0.48 => ( symdiffI1
% 0.31/0.48 => ( symdiffI2
% 0.31/0.48 => ( symdiffIneg1
% 0.31/0.48 => ( symdiffIneg2
% 0.31/0.48 => ( secondinupair
% 0.31/0.48 => ( setukpairIL
% 0.31/0.48 => ( setukpairIR
% 0.31/0.48 => ( kpairiskpair
% 0.31/0.48 => ( kpairp
% 0.31/0.48 => ( singletonsubset
% 0.31/0.48 => ( singletoninpowerset
% 0.31/0.48 => ( singletoninpowunion
% 0.31/0.48 => ( upairset2E
% 0.31/0.48 => ( upairsubunion
% 0.31/0.48 => ( upairinpowunion
% 0.31/0.48 => ( ubforcartprodlem1
% 0.31/0.48 => ( ubforcartprodlem2
% 0.31/0.48 => ( ubforcartprodlem3
% 0.31/0.48 => ( cartprodpairin
% 0.31/0.48 => ( cartprodmempair1
% 0.31/0.48 => ( cartprodmempair
% 0.31/0.48 => ( setunionE2
% 0.31/0.48 => ( setunionsingleton1
% 0.31/0.48 => ( setunionsingleton2
% 0.31/0.48 => ( setunionsingleton
% 0.31/0.48 => ( singletonprop
% 0.31/0.48 => ( ex1E1
% 0.31/0.48 => ( ex1I
% 0.31/0.48 => ( ex1I2
% 0.31/0.48 => ( singletonsuniq
% 0.31/0.48 => ( setukpairinjL1
% 0.31/0.48 => ( kfstsingleton
% 0.31/0.48 => ( theprop
% 0.31/0.48 => ( kfstpairEq
% 0.31/0.48 => ( cartprodfstin
% 0.31/0.48 => ( setukpairinjL2
% 0.31/0.48 => ( setukpairinjL
% 0.31/0.48 => ( setukpairinjR11
% 0.31/0.48 => ( setukpairinjR12
% 0.31/0.48 => ( setukpairinjR1
% 0.31/0.48 => ( upairequniteq
% 0.31/0.48 => ( setukpairinjR2
% 0.31/0.48 => ( setukpairinjR
% 0.31/0.48 => ( ksndsingleton
% 0.31/0.48 => ( ksndpairEq
% 0.31/0.48 => ( kpairsurjEq
% 0.31/0.48 => ( cartprodsndin
% 0.31/0.48 => ( cartprodpairmemEL
% 0.31/0.48 => ( cartprodpairmemER
% 0.31/0.48 => ( cartprodmempaircEq
% 0.31/0.48 => ( cartprodfstpairEq
% 0.31/0.48 => ( cartprodsndpairEq
% 0.31/0.48 => ( cartprodpairsurjEq
% 0.31/0.48 => ( dpsetconstrI
% 0.31/0.48 => ( dpsetconstrSub
% 0.31/0.48 => ( setOfPairsIsBReln
% 0.31/0.48 => ( dpsetconstrERa
% 0.31/0.48 => ( dpsetconstrEL1
% 0.31/0.48 => ( dpsetconstrEL2
% 0.31/0.48 => ( dpsetconstrER
% 0.31/0.48 => ( funcImageSingleton
% 0.31/0.48 => ( apProp
% 0.31/0.48 => ( app
% 0.31/0.48 => ( infuncsetfunc
% 0.31/0.48 => ( ap2p
% 0.31/0.48 => ( funcinfuncset
% 0.31/0.48 => ( lamProp
% 0.31/0.48 => ( lamp
% 0.31/0.48 => ( lam2p
% 0.31/0.48 => ( brelnall1
% 0.31/0.48 => ( brelnall2
% 0.31/0.48 => ( ex1E2
% 0.31/0.48 => ( funcGraphProp1
% 0.31/0.48 => ( funcGraphProp3
% 0.31/0.48 => ( funcGraphProp2
% 0.31/0.48 => ( funcextLem
% 0.31/0.48 => ( funcGraphProp4
% 0.31/0.48 => ( subbreln
% 0.31/0.48 => ( eqbreln
% 0.31/0.48 => ( funcext
% 0.31/0.48 => ( funcext2
% 0.31/0.48 => ( ap2apEq1
% 0.31/0.48 => ( ap2apEq2
% 0.31/0.48 => ( beta1
% 0.31/0.48 => ( eta1
% 0.31/0.48 => ( lam2lamEq
% 0.31/0.48 => ( beta2
% 0.31/0.48 => ( eta2
% 0.31/0.48 => ( iffalseProp1
% 0.31/0.48 => ( iffalseProp2
% 0.31/0.48 => ( iftrueProp1
% 0.31/0.48 => ( iftrueProp2
% 0.31/0.48 => ( ifSingleton
% 0.31/0.48 => ( ifp
% 0.31/0.48 => ( theeq
% 0.31/0.48 => ( iftrue
% 0.31/0.48 => ( iffalse
% 0.31/0.48 => ( iftrueorfalse
% 0.31/0.48 => ( binintersectT_lem
% 0.31/0.48 => ( binunionT_lem
% 0.31/0.48 => ( powersetT_lem
% 0.31/0.48 => ( setminusT_lem
% 0.31/0.48 => ( complementT_lem
% 0.31/0.48 => ( setextT
% 0.31/0.48 => ( subsetTI
% 0.31/0.48 => ( powersetTI1
% 0.31/0.48 => ( powersetTE1
% 0.31/0.48 => ( complementTI1
% 0.31/0.48 => ( complementTE1
% 0.31/0.48 => ( binintersectTELcontra
% 0.31/0.48 => ( binintersectTERcontra
% 0.31/0.48 => ( contrasubsetT
% 0.31/0.48 => ( contrasubsetT1
% 0.31/0.48 => ( contrasubsetT2
% 0.31/0.48 => ( contrasubsetT3
% 0.31/0.48 => ( doubleComplementI1
% 0.31/0.48 => ( doubleComplementE1
% 0.31/0.48 => ( doubleComplementSub1
% 0.31/0.48 => ( doubleComplementSub2
% 0.31/0.48 => ( doubleComplementEq
% 0.31/0.48 => ( complementTnotintersectT
% 0.31/0.48 => ( complementImpComplementIntersect
% 0.31/0.48 => ( complementSubsetComplementIntersect
% 0.31/0.48 => ( complementInPowersetComplementIntersect
% 0.31/0.48 => ( contraSubsetComplement
% 0.31/0.48 => ( complementTcontraSubset
% 0.31/0.48 => ( binunionTILcontra
% 0.31/0.48 => ( binunionTIRcontra
% 0.31/0.48 => ( inIntersectImpInUnion
% 0.31/0.48 => ( inIntersectImpInUnion2
% 0.31/0.48 => ( inIntersectImpInIntersectUnions
% 0.31/0.48 => ( intersectInPowersetIntersectUnions
% 0.31/0.48 => ( inComplementUnionImpNotIn1
% 0.31/0.48 => ( inComplementUnionImpInComplement1
% 0.31/0.48 => ( binunionTE
% 0.31/0.48 => ( binunionTEcontra
% 0.31/0.48 => ( demorgan2a1
% 0.31/0.48 => ( complementUnionInPowersetComplement
% 0.31/0.48 => ( demorgan2a2
% 0.31/0.48 => ( demorgan1a
% 0.31/0.48 => ( demorgan1b
% 0.31/0.48 => ( demorgan1
% 0.31/0.48 => ( demorgan2a
% 0.31/0.48 => ( demorgan2b2
% 0.31/0.48 => ( demorgan2b
% 0.31/0.48 => ( demorgan2
% 0.31/0.48 => ( woz13rule0
% 0.31/0.48 => ( woz13rule1
% 0.31/0.48 => ( woz13rule2
% 0.31/0.48 => ( woz13rule3
% 0.31/0.48 => ( woz13rule4
% 0.31/0.48 => ( woz1_1
% 0.31/0.48 => ( woz1_2
% 0.31/0.48 => ( woz1_3
% 0.31/0.48 => ( woz1_4
% 0.31/0.48 => ( woz1_5
% 0.31/0.48 => ( breln1all2
% 0.31/0.48 => ( breln1SetBreln1
% 0.31/0.48 => ( choice2fnsingleton
% 0.31/0.48 => ( setOfPairsIsBReln1
% 0.31/0.48 => ( breln1all1
% 0.31/0.48 => ( subbreln1
% 0.31/0.48 => ( eqbreln1
% 0.31/0.48 => ( breln1invprop
% 0.31/0.48 => ( breln1invI
% 0.31/0.48 => ( breln1invE
% 0.31/0.48 => ( breln1compprop
% 0.31/0.48 => ! [A: $i,R: $i] :
% 0.31/0.48 ( ( breln1 @ A @ R )
% 0.31/0.48 => ! [S: $i] :
% 0.31/0.48 ( ( breln1 @ A @ S )
% 0.31/0.48 => ! [Xx: $i] :
% 0.31/0.48 ( ( in @ Xx @ A )
% 0.31/0.48 => ! [Xy: $i] :
% 0.31/0.48 ( ( in @ Xy @ A )
% 0.31/0.48 => ! [Xz: $i] :
% 0.31/0.48 ( ( in @ Xz @ A )
% 0.31/0.48 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 0.31/0.48 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 0.31/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 %------------------------------------------------------------------------------
% 0.31/0.48 ------------------------
% 2.99/1.53 ---- Embedded in THF ---
% 2.99/1.53 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.99/1.53 %%% Generated on Tue Feb 24 12:33:30 EST 2026
% 2.99/1.53 %%% using '$$dhol' embedding, version 1.3.0.
% 2.99/1.53 %%% Logic specification used:
% 2.99/1.53 %%% thf(spec, logic, $$dhol).
% 2.99/1.53
% 2.99/1.53 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.V1n9lFWd3k/DTF2DTF22754.p
% See solution above
% 2.99/1.54 ------------------------
% 2.99/1.57 ---- Cleaned THF ---
% 2.99/1.57 thf(in_type,type,
% 2.99/1.57 in: $i > $i > $o ).
% 2.99/1.57
% 2.99/1.57 thf(exu_type,type,
% 2.99/1.57 exu: ( $i > $o ) > $o ).
% 2.99/1.57
% 2.99/1.57 thf(exu,definition,
% 2.99/1.57 ( exu
% 2.99/1.57 = ( ^ [Xphi: $i > $o] :
% 2.99/1.57 ? [Xx: $i] :
% 2.99/1.57 ( ( Xphi @ Xx )
% 2.99/1.57 & ! [Xy: $i] :
% 2.99/1.57 ( ( Xphi @ Xy )
% 2.99/1.57 => ( Xx = Xy ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(setextAx_type,type,
% 2.99/1.57 setextAx: $o ).
% 2.99/1.57
% 2.99/1.57 thf(setextAx,definition,
% 2.99/1.57 ( setextAx
% 2.99/1.57 = ( ! [A: $i,B: $i] :
% 2.99/1.57 ( ! [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 <=> ( in @ Xx @ B ) )
% 2.99/1.57 => ( A = B ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(emptyset_type,type,
% 2.99/1.57 emptyset: $i ).
% 2.99/1.57
% 2.99/1.57 thf(emptysetAx_type,type,
% 2.99/1.57 emptysetAx: $o ).
% 2.99/1.57
% 2.99/1.57 thf(emptysetAx,definition,
% 2.99/1.57 ( emptysetAx
% 2.99/1.57 = ( ! [Xx: $i] :
% 2.99/1.57 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(setadjoin_type,type,
% 2.99/1.57 setadjoin: $i > $i > $i ).
% 2.99/1.57
% 2.99/1.57 thf(setadjoinAx_type,type,
% 2.99/1.57 setadjoinAx: $o ).
% 2.99/1.57
% 2.99/1.57 thf(setadjoinAx,definition,
% 2.99/1.57 ( setadjoinAx
% 2.99/1.57 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.99/1.57 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.99/1.57 <=> ( ( Xy = Xx )
% 2.99/1.57 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(powerset_type,type,
% 2.99/1.57 powerset: $i > $i ).
% 2.99/1.57
% 2.99/1.57 thf(powersetAx_type,type,
% 2.99/1.57 powersetAx: $o ).
% 2.99/1.57
% 2.99/1.57 thf(powersetAx,definition,
% 2.99/1.57 ( powersetAx
% 2.99/1.57 = ( ! [A: $i,B: $i] :
% 2.99/1.57 ( ( in @ B @ ( powerset @ A ) )
% 2.99/1.57 <=> ! [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ B )
% 2.99/1.57 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(setunion_type,type,
% 2.99/1.57 setunion: $i > $i ).
% 2.99/1.57
% 2.99/1.57 thf(setunionAx_type,type,
% 2.99/1.57 setunionAx: $o ).
% 2.99/1.57
% 2.99/1.57 thf(setunionAx,definition,
% 2.99/1.57 ( setunionAx
% 2.99/1.57 = ( ! [A: $i,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ ( setunion @ A ) )
% 2.99/1.57 <=> ? [B: $i] :
% 2.99/1.57 ( ( in @ Xx @ B )
% 2.99/1.57 & ( in @ B @ A ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(omega_type,type,
% 2.99/1.57 omega: $i ).
% 2.99/1.57
% 2.99/1.57 thf(omega0Ax_type,type,
% 2.99/1.57 omega0Ax: $o ).
% 2.99/1.57
% 2.99/1.57 thf(omega0Ax,definition,
% 2.99/1.57 ( omega0Ax
% 2.99/1.57 = ( in @ emptyset @ omega ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(omegaSAx_type,type,
% 2.99/1.57 omegaSAx: $o ).
% 2.99/1.57
% 2.99/1.57 thf(omegaSAx,definition,
% 2.99/1.57 ( omegaSAx
% 2.99/1.57 = ( ! [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ omega )
% 2.99/1.57 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(omegaIndAx_type,type,
% 2.99/1.57 omegaIndAx: $o ).
% 2.99/1.57
% 2.99/1.57 thf(omegaIndAx,definition,
% 2.99/1.57 ( omegaIndAx
% 2.99/1.57 = ( ! [A: $i] :
% 2.99/1.57 ( ( ( in @ emptyset @ A )
% 2.99/1.57 & ! [Xx: $i] :
% 2.99/1.57 ( ( ( in @ Xx @ omega )
% 2.99/1.57 & ( in @ Xx @ A ) )
% 2.99/1.57 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.99/1.57 => ! [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ omega )
% 2.99/1.57 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(replAx_type,type,
% 2.99/1.57 replAx: $o ).
% 2.99/1.57
% 2.99/1.57 thf(replAx,definition,
% 2.99/1.57 ( replAx
% 2.99/1.57 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.99/1.57 ( ! [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 => ( exu
% 2.99/1.57 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.99/1.57 => ? [B: $i] :
% 2.99/1.57 ! [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ B )
% 2.99/1.57 <=> ? [Xy: $i] :
% 2.99/1.57 ( ( in @ Xy @ A )
% 2.99/1.57 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(foundationAx_type,type,
% 2.99/1.57 foundationAx: $o ).
% 2.99/1.57
% 2.99/1.57 thf(foundationAx,definition,
% 2.99/1.57 ( foundationAx
% 2.99/1.57 = ( ! [A: $i] :
% 2.99/1.57 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.99/1.57 => ? [B: $i] :
% 2.99/1.57 ( ( in @ B @ A )
% 2.99/1.57 & ~ ? [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ B )
% 2.99/1.57 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(wellorderingAx_type,type,
% 2.99/1.57 wellorderingAx: $o ).
% 2.99/1.57
% 2.99/1.57 thf(wellorderingAx,definition,
% 2.99/1.57 ( wellorderingAx
% 2.99/1.57 = ( ! [A: $i] :
% 2.99/1.57 ? [B: $i] :
% 2.99/1.57 ( ! [C: $i] :
% 2.99/1.57 ( ( in @ C @ B )
% 2.99/1.57 => ! [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ C )
% 2.99/1.57 => ( in @ Xx @ A ) ) )
% 2.99/1.57 & ! [Xx: $i,Xy: $i] :
% 2.99/1.57 ( ( ( in @ Xx @ A )
% 2.99/1.57 & ( in @ Xy @ A ) )
% 2.99/1.57 => ( ! [C: $i] :
% 2.99/1.57 ( ( in @ C @ B )
% 2.99/1.57 => ( ( in @ Xx @ C )
% 2.99/1.57 <=> ( in @ Xy @ C ) ) )
% 2.99/1.57 => ( Xx = Xy ) ) )
% 2.99/1.57 & ! [C: $i,D: $i] :
% 2.99/1.57 ( ( ( in @ C @ B )
% 2.99/1.57 & ( in @ D @ B ) )
% 2.99/1.57 => ( ! [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ C )
% 2.99/1.57 => ( in @ Xx @ D ) )
% 2.99/1.57 | ! [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ D )
% 2.99/1.57 => ( in @ Xx @ C ) ) ) )
% 2.99/1.57 & ! [C: $i] :
% 2.99/1.57 ( ( ! [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ C )
% 2.99/1.57 => ( in @ Xx @ A ) )
% 2.99/1.57 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.99/1.57 => ? [D: $i,Xx: $i] :
% 2.99/1.57 ( ( in @ D @ B )
% 2.99/1.57 & ( in @ Xx @ C )
% 2.99/1.57 & ~ ? [Xy: $i] :
% 2.99/1.57 ( ( in @ Xy @ D )
% 2.99/1.57 & ( in @ Xy @ C ) )
% 2.99/1.57 & ! [E: $i] :
% 2.99/1.57 ( ( in @ E @ B )
% 2.99/1.57 => ( ! [Xy: $i] :
% 2.99/1.57 ( ( in @ Xy @ E )
% 2.99/1.57 => ( in @ Xy @ D ) )
% 2.99/1.57 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(descr_type,type,
% 2.99/1.57 descr: ( $i > $o ) > $i ).
% 2.99/1.57
% 2.99/1.57 thf(descrp_type,type,
% 2.99/1.57 descrp: $o ).
% 2.99/1.57
% 2.99/1.57 thf(descrp,definition,
% 2.99/1.57 ( descrp
% 2.99/1.57 = ( ! [Xphi: $i > $o] :
% 2.99/1.57 ( ( exu
% 2.99/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.57 => ( Xphi
% 2.99/1.57 @ ( descr
% 2.99/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(dsetconstr_type,type,
% 2.99/1.57 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.99/1.57
% 2.99/1.57 thf(dsetconstrI_type,type,
% 2.99/1.57 dsetconstrI: $o ).
% 2.99/1.57
% 2.99/1.57 thf(dsetconstrI,definition,
% 2.99/1.57 ( dsetconstrI
% 2.99/1.57 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 => ( ( Xphi @ Xx )
% 2.99/1.57 => ( in @ Xx
% 2.99/1.57 @ ( dsetconstr @ A
% 2.99/1.57 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(dsetconstrEL_type,type,
% 2.99/1.57 dsetconstrEL: $o ).
% 2.99/1.57
% 2.99/1.57 thf(dsetconstrEL,definition,
% 2.99/1.57 ( dsetconstrEL
% 2.99/1.57 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx
% 2.99/1.57 @ ( dsetconstr @ A
% 2.99/1.57 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.99/1.57 => ( in @ Xx @ A ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(dsetconstrER_type,type,
% 2.99/1.57 dsetconstrER: $o ).
% 2.99/1.57
% 2.99/1.57 thf(dsetconstrER,definition,
% 2.99/1.57 ( dsetconstrER
% 2.99/1.57 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx
% 2.99/1.57 @ ( dsetconstr @ A
% 2.99/1.57 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.99/1.57 => ( Xphi @ Xx ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(exuE1_type,type,
% 2.99/1.57 exuE1: $o ).
% 2.99/1.57
% 2.99/1.57 thf(exuE1,definition,
% 2.99/1.57 ( exuE1
% 2.99/1.57 = ( ! [Xphi: $i > $o] :
% 2.99/1.57 ( ( exu
% 2.99/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.57 => ? [Xx: $i] :
% 2.99/1.57 ( ( Xphi @ Xx )
% 2.99/1.57 & ! [Xy: $i] :
% 2.99/1.57 ( ( Xphi @ Xy )
% 2.99/1.57 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(prop2set_type,type,
% 2.99/1.57 prop2set: $o > $i ).
% 2.99/1.57
% 2.99/1.57 thf(prop2setE_type,type,
% 2.99/1.57 prop2setE: $o ).
% 2.99/1.57
% 2.99/1.57 thf(prop2setE,definition,
% 2.99/1.57 ( prop2setE
% 2.99/1.57 = ( ! [Xphi: $o,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.99/1.57 => Xphi ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(emptysetE_type,type,
% 2.99/1.57 emptysetE: $o ).
% 2.99/1.57
% 2.99/1.57 thf(emptysetE,definition,
% 2.99/1.57 ( emptysetE
% 2.99/1.57 = ( ! [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ emptyset )
% 2.99/1.57 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(emptysetimpfalse_type,type,
% 2.99/1.57 emptysetimpfalse: $o ).
% 2.99/1.57
% 2.99/1.57 thf(emptysetimpfalse,definition,
% 2.99/1.57 ( emptysetimpfalse
% 2.99/1.57 = ( ! [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ emptyset )
% 2.99/1.57 => $false ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(notinemptyset_type,type,
% 2.99/1.57 notinemptyset: $o ).
% 2.99/1.57
% 2.99/1.57 thf(notinemptyset,definition,
% 2.99/1.57 ( notinemptyset
% 2.99/1.57 = ( ! [Xx: $i] :
% 2.99/1.57 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(exuE3e_type,type,
% 2.99/1.57 exuE3e: $o ).
% 2.99/1.57
% 2.99/1.57 thf(exuE3e,definition,
% 2.99/1.57 ( exuE3e
% 2.99/1.57 = ( ! [Xphi: $i > $o] :
% 2.99/1.57 ( ( exu
% 2.99/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.57 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(setext_type,type,
% 2.99/1.57 setext: $o ).
% 2.99/1.57
% 2.99/1.57 thf(setext,definition,
% 2.99/1.57 ( setext
% 2.99/1.57 = ( ! [A: $i,B: $i] :
% 2.99/1.57 ( ! [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 => ( in @ Xx @ B ) )
% 2.99/1.57 => ( ! [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ B )
% 2.99/1.57 => ( in @ Xx @ A ) )
% 2.99/1.57 => ( A = B ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(emptyI_type,type,
% 2.99/1.57 emptyI: $o ).
% 2.99/1.57
% 2.99/1.57 thf(emptyI,definition,
% 2.99/1.57 ( emptyI
% 2.99/1.57 = ( ! [A: $i] :
% 2.99/1.57 ( ! [Xx: $i] :
% 2.99/1.57 ~ ( in @ Xx @ A )
% 2.99/1.57 => ( A = emptyset ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(noeltsimpempty_type,type,
% 2.99/1.57 noeltsimpempty: $o ).
% 2.99/1.57
% 2.99/1.57 thf(noeltsimpempty,definition,
% 2.99/1.57 ( noeltsimpempty
% 2.99/1.57 = ( ! [A: $i] :
% 2.99/1.57 ( ! [Xx: $i] :
% 2.99/1.57 ~ ( in @ Xx @ A )
% 2.99/1.57 => ( A = emptyset ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(setbeta_type,type,
% 2.99/1.57 setbeta: $o ).
% 2.99/1.57
% 2.99/1.57 thf(setbeta,definition,
% 2.99/1.57 ( setbeta
% 2.99/1.57 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 => ( ( in @ Xx
% 2.99/1.57 @ ( dsetconstr @ A
% 2.99/1.57 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.99/1.57 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(nonempty_type,type,
% 2.99/1.57 nonempty: $i > $o ).
% 2.99/1.57
% 2.99/1.57 thf(nonempty,definition,
% 2.99/1.57 ( nonempty
% 2.99/1.57 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(nonemptyE1_type,type,
% 2.99/1.57 nonemptyE1: $o ).
% 2.99/1.57
% 2.99/1.57 thf(nonemptyE1,definition,
% 2.99/1.57 ( nonemptyE1
% 2.99/1.57 = ( ! [A: $i] :
% 2.99/1.57 ( ( nonempty @ A )
% 2.99/1.57 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(nonemptyI_type,type,
% 2.99/1.57 nonemptyI: $o ).
% 2.99/1.57
% 2.99/1.57 thf(nonemptyI,definition,
% 2.99/1.57 ( nonemptyI
% 2.99/1.57 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 => ( ( Xphi @ Xx )
% 2.99/1.57 => ( nonempty
% 2.99/1.57 @ ( dsetconstr @ A
% 2.99/1.57 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(nonemptyI1_type,type,
% 2.99/1.57 nonemptyI1: $o ).
% 2.99/1.57
% 2.99/1.57 thf(nonemptyI1,definition,
% 2.99/1.57 ( nonemptyI1
% 2.99/1.57 = ( ! [A: $i] :
% 2.99/1.57 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.99/1.57 => ( nonempty @ A ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(setadjoinIL_type,type,
% 2.99/1.57 setadjoinIL: $o ).
% 2.99/1.57
% 2.99/1.57 thf(setadjoinIL,definition,
% 2.99/1.57 ( setadjoinIL
% 2.99/1.57 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(emptyinunitempty_type,type,
% 2.99/1.57 emptyinunitempty: $o ).
% 2.99/1.57
% 2.99/1.57 thf(emptyinunitempty,definition,
% 2.99/1.57 ( emptyinunitempty
% 2.99/1.57 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(setadjoinIR_type,type,
% 2.99/1.57 setadjoinIR: $o ).
% 2.99/1.57
% 2.99/1.57 thf(setadjoinIR,definition,
% 2.99/1.57 ( setadjoinIR
% 2.99/1.57 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.99/1.57 ( ( in @ Xy @ A )
% 2.99/1.57 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(setadjoinE_type,type,
% 2.99/1.57 setadjoinE: $o ).
% 2.99/1.57
% 2.99/1.57 thf(setadjoinE,definition,
% 2.99/1.57 ( setadjoinE
% 2.99/1.57 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.99/1.57 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.99/1.57 => ! [Xphi: $o] :
% 2.99/1.57 ( ( ( Xy = Xx )
% 2.99/1.57 => Xphi )
% 2.99/1.57 => ( ( ( in @ Xy @ A )
% 2.99/1.57 => Xphi )
% 2.99/1.57 => Xphi ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(setadjoinOr_type,type,
% 2.99/1.57 setadjoinOr: $o ).
% 2.99/1.57
% 2.99/1.57 thf(setadjoinOr,definition,
% 2.99/1.57 ( setadjoinOr
% 2.99/1.57 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.99/1.57 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.99/1.57 => ( ( Xy = Xx )
% 2.99/1.57 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(setoftrueEq_type,type,
% 2.99/1.57 setoftrueEq: $o ).
% 2.99/1.57
% 2.99/1.57 thf(setoftrueEq,definition,
% 2.99/1.57 ( setoftrueEq
% 2.99/1.57 = ( ! [A: $i] :
% 2.99/1.57 ( ( dsetconstr @ A
% 2.99/1.57 @ ^ [Xx: $i] : $true )
% 2.99/1.57 = A ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(powersetI_type,type,
% 2.99/1.57 powersetI: $o ).
% 2.99/1.57
% 2.99/1.57 thf(powersetI,definition,
% 2.99/1.57 ( powersetI
% 2.99/1.57 = ( ! [A: $i,B: $i] :
% 2.99/1.57 ( ! [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ B )
% 2.99/1.57 => ( in @ Xx @ A ) )
% 2.99/1.57 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(emptyinPowerset_type,type,
% 2.99/1.57 emptyinPowerset: $o ).
% 2.99/1.57
% 2.99/1.57 thf(emptyinPowerset,definition,
% 2.99/1.57 ( emptyinPowerset
% 2.99/1.57 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(emptyInPowerset_type,type,
% 2.99/1.57 emptyInPowerset: $o ).
% 2.99/1.57
% 2.99/1.57 thf(emptyInPowerset,definition,
% 2.99/1.57 ( emptyInPowerset
% 2.99/1.57 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(powersetE_type,type,
% 2.99/1.57 powersetE: $o ).
% 2.99/1.57
% 2.99/1.57 thf(powersetE,definition,
% 2.99/1.57 ( powersetE
% 2.99/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.57 ( ( in @ B @ ( powerset @ A ) )
% 2.99/1.57 => ( ( in @ Xx @ B )
% 2.99/1.57 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(setunionI_type,type,
% 2.99/1.57 setunionI: $o ).
% 2.99/1.57
% 2.99/1.57 thf(setunionI,definition,
% 2.99/1.57 ( setunionI
% 2.99/1.57 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.99/1.57 ( ( in @ Xx @ B )
% 2.99/1.57 => ( ( in @ B @ A )
% 2.99/1.57 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(setunionE_type,type,
% 2.99/1.57 setunionE: $o ).
% 2.99/1.57
% 2.99/1.57 thf(setunionE,definition,
% 2.99/1.57 ( setunionE
% 2.99/1.57 = ( ! [A: $i,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ ( setunion @ A ) )
% 2.99/1.57 => ! [Xphi: $o] :
% 2.99/1.57 ( ! [B: $i] :
% 2.99/1.57 ( ( in @ Xx @ B )
% 2.99/1.57 => ( ( in @ B @ A )
% 2.99/1.57 => Xphi ) )
% 2.99/1.57 => Xphi ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(subPowSU_type,type,
% 2.99/1.57 subPowSU: $o ).
% 2.99/1.57
% 2.99/1.57 thf(subPowSU,definition,
% 2.99/1.57 ( subPowSU
% 2.99/1.57 = ( ! [A: $i,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(exuE2_type,type,
% 2.99/1.57 exuE2: $o ).
% 2.99/1.57
% 2.99/1.57 thf(exuE2,definition,
% 2.99/1.57 ( exuE2
% 2.99/1.57 = ( ! [Xphi: $i > $o] :
% 2.99/1.57 ( ( exu
% 2.99/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.57 => ? [Xx: $i] :
% 2.99/1.57 ! [Xy: $i] :
% 2.99/1.57 ( ( Xphi @ Xy )
% 2.99/1.57 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(nonemptyImpWitness_type,type,
% 2.99/1.57 nonemptyImpWitness: $o ).
% 2.99/1.57
% 2.99/1.57 thf(nonemptyImpWitness,definition,
% 2.99/1.57 ( nonemptyImpWitness
% 2.99/1.57 = ( ! [A: $i] :
% 2.99/1.57 ( ( nonempty @ A )
% 2.99/1.57 => ? [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 & $true ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(uniqinunit_type,type,
% 2.99/1.57 uniqinunit: $o ).
% 2.99/1.57
% 2.99/1.57 thf(uniqinunit,definition,
% 2.99/1.57 ( uniqinunit
% 2.99/1.57 = ( ! [Xx: $i,Xy: $i] :
% 2.99/1.57 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.99/1.57 => ( Xx = Xy ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(notinsingleton_type,type,
% 2.99/1.57 notinsingleton: $o ).
% 2.99/1.57
% 2.99/1.57 thf(notinsingleton,definition,
% 2.99/1.57 ( notinsingleton
% 2.99/1.57 = ( ! [Xx: $i,Xy: $i] :
% 2.99/1.57 ( ( Xx != Xy )
% 2.99/1.57 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(eqinunit_type,type,
% 2.99/1.57 eqinunit: $o ).
% 2.99/1.57
% 2.99/1.57 thf(eqinunit,definition,
% 2.99/1.57 ( eqinunit
% 2.99/1.57 = ( ! [Xx: $i,Xy: $i] :
% 2.99/1.57 ( ( Xx = Xy )
% 2.99/1.57 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(singletonsswitch_type,type,
% 2.99/1.57 singletonsswitch: $o ).
% 2.99/1.57
% 2.99/1.57 thf(singletonsswitch,definition,
% 2.99/1.57 ( singletonsswitch
% 2.99/1.57 = ( ! [Xx: $i,Xy: $i] :
% 2.99/1.57 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.99/1.57 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(upairsetE_type,type,
% 2.99/1.57 upairsetE: $o ).
% 2.99/1.57
% 2.99/1.57 thf(upairsetE,definition,
% 2.99/1.57 ( upairsetE
% 2.99/1.57 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.99/1.57 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.99/1.57 => ( ( Xz = Xx )
% 2.99/1.57 | ( Xz = Xy ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(upairsetIL_type,type,
% 2.99/1.57 upairsetIL: $o ).
% 2.99/1.57
% 2.99/1.57 thf(upairsetIL,definition,
% 2.99/1.57 ( upairsetIL
% 2.99/1.57 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(upairsetIR_type,type,
% 2.99/1.57 upairsetIR: $o ).
% 2.99/1.57
% 2.99/1.57 thf(upairsetIR,definition,
% 2.99/1.57 ( upairsetIR
% 2.99/1.57 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(emptyE1_type,type,
% 2.99/1.57 emptyE1: $o ).
% 2.99/1.57
% 2.99/1.57 thf(emptyE1,definition,
% 2.99/1.57 ( emptyE1
% 2.99/1.57 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.57 ( ? [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 & ( Xphi @ Xx ) )
% 2.99/1.57 => ( ( ( dsetconstr @ A
% 2.99/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.57 = emptyset )
% 2.99/1.57 => $false ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(vacuousDall_type,type,
% 2.99/1.57 vacuousDall: $o ).
% 2.99/1.57
% 2.99/1.57 thf(vacuousDall,definition,
% 2.99/1.57 ( vacuousDall
% 2.99/1.57 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ emptyset )
% 2.99/1.57 => ( Xphi @ Xx ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(quantDeMorgan1_type,type,
% 2.99/1.57 quantDeMorgan1: $o ).
% 2.99/1.57
% 2.99/1.57 thf(quantDeMorgan1,definition,
% 2.99/1.57 ( quantDeMorgan1
% 2.99/1.57 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.57 ( ~ ! [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 => ( Xphi @ Xx ) )
% 2.99/1.57 => ? [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(quantDeMorgan2_type,type,
% 2.99/1.57 quantDeMorgan2: $o ).
% 2.99/1.57
% 2.99/1.57 thf(quantDeMorgan2,definition,
% 2.99/1.57 ( quantDeMorgan2
% 2.99/1.57 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.57 ( ! [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 => ~ ( Xphi @ Xx ) )
% 2.99/1.57 => ~ ? [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(quantDeMorgan3_type,type,
% 2.99/1.57 quantDeMorgan3: $o ).
% 2.99/1.57
% 2.99/1.57 thf(quantDeMorgan3,definition,
% 2.99/1.57 ( quantDeMorgan3
% 2.99/1.57 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.57 ( ~ ? [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 & ( Xphi @ Xx ) )
% 2.99/1.57 => ! [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(quantDeMorgan4_type,type,
% 2.99/1.57 quantDeMorgan4: $o ).
% 2.99/1.57
% 2.99/1.57 thf(quantDeMorgan4,definition,
% 2.99/1.57 ( quantDeMorgan4
% 2.99/1.57 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.57 ( ? [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 & ~ ( Xphi @ Xx ) )
% 2.99/1.57 => ~ ! [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(prop2setI_type,type,
% 2.99/1.57 prop2setI: $o ).
% 2.99/1.57
% 2.99/1.57 thf(prop2setI,definition,
% 2.99/1.57 ( prop2setI
% 2.99/1.57 = ( ! [Xphi: $o] :
% 2.99/1.57 ( Xphi
% 2.99/1.57 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(set2prop_type,type,
% 2.99/1.57 set2prop: $i > $o ).
% 2.99/1.57
% 2.99/1.57 thf(prop2set2propI_type,type,
% 2.99/1.57 prop2set2propI: $o ).
% 2.99/1.57
% 2.99/1.57 thf(prop2set2propI,definition,
% 2.99/1.57 ( prop2set2propI
% 2.99/1.57 = ( ! [Xphi: $o] :
% 2.99/1.57 ( Xphi
% 2.99/1.57 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(notdexE_type,type,
% 2.99/1.57 notdexE: $o ).
% 2.99/1.57
% 2.99/1.57 thf(notdexE,definition,
% 2.99/1.57 ( notdexE
% 2.99/1.57 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.57 ( ~ ? [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 & ( Xphi @ Xx ) )
% 2.99/1.57 => ! [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(notdallE_type,type,
% 2.99/1.57 notdallE: $o ).
% 2.99/1.57
% 2.99/1.57 thf(notdallE,definition,
% 2.99/1.57 ( notdallE
% 2.99/1.57 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.57 ( ~ ! [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 => ( Xphi @ Xx ) )
% 2.99/1.57 => ? [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(exuI1_type,type,
% 2.99/1.57 exuI1: $o ).
% 2.99/1.57
% 2.99/1.57 thf(exuI1,definition,
% 2.99/1.57 ( exuI1
% 2.99/1.57 = ( ! [Xphi: $i > $o] :
% 2.99/1.57 ( ? [Xx: $i] :
% 2.99/1.57 ( ( Xphi @ Xx )
% 2.99/1.57 & ! [Xy: $i] :
% 2.99/1.57 ( ( Xphi @ Xy )
% 2.99/1.57 => ( Xx = Xy ) ) )
% 2.99/1.57 => ( exu
% 2.99/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(exuI3_type,type,
% 2.99/1.57 exuI3: $o ).
% 2.99/1.57
% 2.99/1.57 thf(exuI3,definition,
% 2.99/1.57 ( exuI3
% 2.99/1.57 = ( ! [Xphi: $i > $o] :
% 2.99/1.57 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.99/1.57 => ( ! [Xx: $i,Xy: $i] :
% 2.99/1.57 ( ( Xphi @ Xx )
% 2.99/1.57 => ( ( Xphi @ Xy )
% 2.99/1.57 => ( Xx = Xy ) ) )
% 2.99/1.57 => ( exu
% 2.99/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(exuI2_type,type,
% 2.99/1.57 exuI2: $o ).
% 2.99/1.57
% 2.99/1.57 thf(exuI2,definition,
% 2.99/1.57 ( exuI2
% 2.99/1.57 = ( ! [Xphi: $i > $o] :
% 2.99/1.57 ( ? [Xx: $i] :
% 2.99/1.57 ! [Xy: $i] :
% 2.99/1.57 ( ( Xphi @ Xy )
% 2.99/1.57 <=> ( Xy = Xx ) )
% 2.99/1.57 => ( exu
% 2.99/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(inCongP_type,type,
% 2.99/1.57 inCongP: $o ).
% 2.99/1.57
% 2.99/1.57 thf(inCongP,definition,
% 2.99/1.57 ( inCongP
% 2.99/1.57 = ( ! [A: $i,B: $i] :
% 2.99/1.57 ( ( A = B )
% 2.99/1.57 => ! [Xx: $i,Xy: $i] :
% 2.99/1.57 ( ( Xx = Xy )
% 2.99/1.57 => ( ( in @ Xx @ A )
% 2.99/1.57 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(in__Cong_type,type,
% 2.99/1.57 in__Cong: $o ).
% 2.99/1.57
% 2.99/1.57 thf(in__Cong,definition,
% 2.99/1.57 ( in__Cong
% 2.99/1.57 = ( ! [A: $i,B: $i] :
% 2.99/1.57 ( ( A = B )
% 2.99/1.57 => ! [Xx: $i,Xy: $i] :
% 2.99/1.57 ( ( Xx = Xy )
% 2.99/1.57 => ( ( in @ Xx @ A )
% 2.99/1.57 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(exuE3u_type,type,
% 2.99/1.57 exuE3u: $o ).
% 2.99/1.57
% 2.99/1.57 thf(exuE3u,definition,
% 2.99/1.57 ( exuE3u
% 2.99/1.57 = ( ! [Xphi: $i > $o] :
% 2.99/1.57 ( ( exu
% 2.99/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.57 => ! [Xx: $i,Xy: $i] :
% 2.99/1.57 ( ( Xphi @ Xx )
% 2.99/1.57 => ( ( Xphi @ Xy )
% 2.99/1.57 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(exu__Cong_type,type,
% 2.99/1.57 exu__Cong: $o ).
% 2.99/1.57
% 2.99/1.57 thf(exu__Cong,definition,
% 2.99/1.57 ( exu__Cong
% 2.99/1.57 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.99/1.57 ( ! [Xx: $i,Xy: $i] :
% 2.99/1.57 ( ( Xx = Xy )
% 2.99/1.57 => ( ( Xphi @ Xx )
% 2.99/1.57 <=> ( Xpsi @ Xy ) ) )
% 2.99/1.57 => ( ( exu
% 2.99/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.57 <=> ( exu
% 2.99/1.57 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(emptyset__Cong_type,type,
% 2.99/1.57 emptyset__Cong: $o ).
% 2.99/1.57
% 2.99/1.57 thf(emptyset__Cong,definition,
% 2.99/1.57 ( emptyset__Cong
% 2.99/1.57 = ( emptyset = emptyset ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(setadjoin__Cong_type,type,
% 2.99/1.57 setadjoin__Cong: $o ).
% 2.99/1.57
% 2.99/1.57 thf(setadjoin__Cong,definition,
% 2.99/1.57 ( setadjoin__Cong
% 2.99/1.57 = ( ! [Xx: $i,Xy: $i] :
% 2.99/1.57 ( ( Xx = Xy )
% 2.99/1.57 => ! [Xz: $i,Xu: $i] :
% 2.99/1.57 ( ( Xz = Xu )
% 2.99/1.57 => ( ( setadjoin @ Xx @ Xz )
% 2.99/1.57 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(powerset__Cong_type,type,
% 2.99/1.57 powerset__Cong: $o ).
% 2.99/1.57
% 2.99/1.57 thf(powerset__Cong,definition,
% 2.99/1.57 ( powerset__Cong
% 2.99/1.57 = ( ! [A: $i,B: $i] :
% 2.99/1.57 ( ( A = B )
% 2.99/1.57 => ( ( powerset @ A )
% 2.99/1.57 = ( powerset @ B ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(setunion__Cong_type,type,
% 2.99/1.57 setunion__Cong: $o ).
% 2.99/1.57
% 2.99/1.57 thf(setunion__Cong,definition,
% 2.99/1.57 ( setunion__Cong
% 2.99/1.57 = ( ! [A: $i,B: $i] :
% 2.99/1.57 ( ( A = B )
% 2.99/1.57 => ( ( setunion @ A )
% 2.99/1.57 = ( setunion @ B ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(omega__Cong_type,type,
% 2.99/1.57 omega__Cong: $o ).
% 2.99/1.57
% 2.99/1.57 thf(omega__Cong,definition,
% 2.99/1.57 ( omega__Cong
% 2.99/1.57 = ( omega = omega ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(exuEu_type,type,
% 2.99/1.57 exuEu: $o ).
% 2.99/1.57
% 2.99/1.57 thf(exuEu,definition,
% 2.99/1.57 ( exuEu
% 2.99/1.57 = ( ! [Xphi: $i > $o] :
% 2.99/1.57 ( ( exu
% 2.99/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.57 => ! [Xx: $i,Xy: $i] :
% 2.99/1.57 ( ( Xphi @ Xx )
% 2.99/1.57 => ( ( Xphi @ Xy )
% 2.99/1.57 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(descr__Cong_type,type,
% 2.99/1.57 descr__Cong: $o ).
% 2.99/1.57
% 2.99/1.57 thf(descr__Cong,definition,
% 2.99/1.57 ( descr__Cong
% 2.99/1.57 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.99/1.57 ( ! [Xx: $i,Xy: $i] :
% 2.99/1.57 ( ( Xx = Xy )
% 2.99/1.57 => ( ( Xphi @ Xx )
% 2.99/1.57 <=> ( Xpsi @ Xy ) ) )
% 2.99/1.57 => ( ( exu
% 2.99/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.57 => ( ( exu
% 2.99/1.57 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.99/1.57 => ( ( descr
% 2.99/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.57 = ( descr
% 2.99/1.57 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(dsetconstr__Cong_type,type,
% 2.99/1.57 dsetconstr__Cong: $o ).
% 2.99/1.57
% 2.99/1.57 thf(dsetconstr__Cong,definition,
% 2.99/1.57 ( dsetconstr__Cong
% 2.99/1.57 = ( ! [A: $i,B: $i] :
% 2.99/1.57 ( ( A = B )
% 2.99/1.57 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.99/1.57 ( ! [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 => ! [Xy: $i] :
% 2.99/1.57 ( ( in @ Xy @ B )
% 2.99/1.57 => ( ( Xx = Xy )
% 2.99/1.57 => ( ( Xphi @ Xx )
% 2.99/1.57 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.99/1.57 => ( ( dsetconstr @ A
% 2.99/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.57 = ( dsetconstr @ B
% 2.99/1.57 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(subset_type,type,
% 2.99/1.57 subset: $i > $i > $o ).
% 2.99/1.57
% 2.99/1.57 thf(disjoint_type,type,
% 2.99/1.57 disjoint: $i > $i > $o ).
% 2.99/1.57
% 2.99/1.57 thf(setsmeet_type,type,
% 2.99/1.57 setsmeet: $i > $i > $o ).
% 2.99/1.57
% 2.99/1.57 thf(subsetI1_type,type,
% 2.99/1.57 subsetI1: $o ).
% 2.99/1.57
% 2.99/1.57 thf(subsetI1,definition,
% 2.99/1.57 ( subsetI1
% 2.99/1.57 = ( ! [A: $i,B: $i] :
% 2.99/1.57 ( ! [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 => ( in @ Xx @ B ) )
% 2.99/1.57 => ( subset @ A @ B ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(eqimpsubset2_type,type,
% 2.99/1.57 eqimpsubset2: $o ).
% 2.99/1.57
% 2.99/1.57 thf(eqimpsubset2,definition,
% 2.99/1.57 ( eqimpsubset2
% 2.99/1.57 = ( ! [A: $i,B: $i] :
% 2.99/1.57 ( ( A = B )
% 2.99/1.57 => ( subset @ B @ A ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(eqimpsubset1_type,type,
% 2.99/1.57 eqimpsubset1: $o ).
% 2.99/1.57
% 2.99/1.57 thf(eqimpsubset1,definition,
% 2.99/1.57 ( eqimpsubset1
% 2.99/1.57 = ( ! [A: $i,B: $i] :
% 2.99/1.57 ( ( A = B )
% 2.99/1.57 => ( subset @ A @ B ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(subsetI2_type,type,
% 2.99/1.57 subsetI2: $o ).
% 2.99/1.57
% 2.99/1.57 thf(subsetI2,definition,
% 2.99/1.57 ( subsetI2
% 2.99/1.57 = ( ! [A: $i,B: $i] :
% 2.99/1.57 ( ! [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 => ( in @ Xx @ B ) )
% 2.99/1.57 => ( subset @ A @ B ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(emptysetsubset_type,type,
% 2.99/1.57 emptysetsubset: $o ).
% 2.99/1.57
% 2.99/1.57 thf(emptysetsubset,definition,
% 2.99/1.57 ( emptysetsubset
% 2.99/1.57 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(subsetE_type,type,
% 2.99/1.57 subsetE: $o ).
% 2.99/1.57
% 2.99/1.57 thf(subsetE,definition,
% 2.99/1.57 ( subsetE
% 2.99/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.57 ( ( subset @ A @ B )
% 2.99/1.57 => ( ( in @ Xx @ A )
% 2.99/1.57 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(subsetE2_type,type,
% 2.99/1.57 subsetE2: $o ).
% 2.99/1.57
% 2.99/1.57 thf(subsetE2,definition,
% 2.99/1.57 ( subsetE2
% 2.99/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.57 ( ( subset @ A @ B )
% 2.99/1.57 => ( ~ ( in @ Xx @ B )
% 2.99/1.57 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(notsubsetI_type,type,
% 2.99/1.57 notsubsetI: $o ).
% 2.99/1.57
% 2.99/1.57 thf(notsubsetI,definition,
% 2.99/1.57 ( notsubsetI
% 2.99/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 => ( ~ ( in @ Xx @ B )
% 2.99/1.57 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(notequalI1_type,type,
% 2.99/1.57 notequalI1: $o ).
% 2.99/1.57
% 2.99/1.57 thf(notequalI1,definition,
% 2.99/1.57 ( notequalI1
% 2.99/1.57 = ( ! [A: $i,B: $i] :
% 2.99/1.57 ( ~ ( subset @ A @ B )
% 2.99/1.57 => ( A != B ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(notequalI2_type,type,
% 2.99/1.57 notequalI2: $o ).
% 2.99/1.57
% 2.99/1.57 thf(notequalI2,definition,
% 2.99/1.57 ( notequalI2
% 2.99/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 => ( ~ ( in @ Xx @ B )
% 2.99/1.57 => ( A != B ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(subsetRefl_type,type,
% 2.99/1.57 subsetRefl: $o ).
% 2.99/1.57
% 2.99/1.57 thf(subsetRefl,definition,
% 2.99/1.57 ( subsetRefl
% 2.99/1.57 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(subsetTrans_type,type,
% 2.99/1.57 subsetTrans: $o ).
% 2.99/1.57
% 2.99/1.57 thf(subsetTrans,definition,
% 2.99/1.57 ( subsetTrans
% 2.99/1.57 = ( ! [A: $i,B: $i,C: $i] :
% 2.99/1.57 ( ( subset @ A @ B )
% 2.99/1.57 => ( ( subset @ B @ C )
% 2.99/1.57 => ( subset @ A @ C ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(setadjoinSub_type,type,
% 2.99/1.57 setadjoinSub: $o ).
% 2.99/1.57
% 2.99/1.57 thf(setadjoinSub,definition,
% 2.99/1.57 ( setadjoinSub
% 2.99/1.57 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(setadjoinSub2_type,type,
% 2.99/1.57 setadjoinSub2: $o ).
% 2.99/1.57
% 2.99/1.57 thf(setadjoinSub2,definition,
% 2.99/1.57 ( setadjoinSub2
% 2.99/1.57 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.99/1.57 ( ( subset @ A @ B )
% 2.99/1.57 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(subset2powerset_type,type,
% 2.99/1.57 subset2powerset: $o ).
% 2.99/1.57
% 2.99/1.57 thf(subset2powerset,definition,
% 2.99/1.57 ( subset2powerset
% 2.99/1.57 = ( ! [A: $i,B: $i] :
% 2.99/1.57 ( ( subset @ A @ B )
% 2.99/1.57 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(setextsub_type,type,
% 2.99/1.57 setextsub: $o ).
% 2.99/1.57
% 2.99/1.57 thf(setextsub,definition,
% 2.99/1.57 ( setextsub
% 2.99/1.57 = ( ! [A: $i,B: $i] :
% 2.99/1.57 ( ( subset @ A @ B )
% 2.99/1.57 => ( ( subset @ B @ A )
% 2.99/1.57 => ( A = B ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(subsetemptysetimpeq_type,type,
% 2.99/1.57 subsetemptysetimpeq: $o ).
% 2.99/1.57
% 2.99/1.57 thf(subsetemptysetimpeq,definition,
% 2.99/1.57 ( subsetemptysetimpeq
% 2.99/1.57 = ( ! [A: $i] :
% 2.99/1.57 ( ( subset @ A @ emptyset )
% 2.99/1.57 => ( A = emptyset ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(powersetI1_type,type,
% 2.99/1.57 powersetI1: $o ).
% 2.99/1.57
% 2.99/1.57 thf(powersetI1,definition,
% 2.99/1.57 ( powersetI1
% 2.99/1.57 = ( ! [A: $i,B: $i] :
% 2.99/1.57 ( ( subset @ B @ A )
% 2.99/1.57 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(powersetE1_type,type,
% 2.99/1.57 powersetE1: $o ).
% 2.99/1.57
% 2.99/1.57 thf(powersetE1,definition,
% 2.99/1.57 ( powersetE1
% 2.99/1.57 = ( ! [A: $i,B: $i] :
% 2.99/1.57 ( ( in @ B @ ( powerset @ A ) )
% 2.99/1.57 => ( subset @ B @ A ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(inPowerset_type,type,
% 2.99/1.57 inPowerset: $o ).
% 2.99/1.57
% 2.99/1.57 thf(inPowerset,definition,
% 2.99/1.57 ( inPowerset
% 2.99/1.57 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(powersetsubset_type,type,
% 2.99/1.57 powersetsubset: $o ).
% 2.99/1.57
% 2.99/1.57 thf(powersetsubset,definition,
% 2.99/1.57 ( powersetsubset
% 2.99/1.57 = ( ! [A: $i,B: $i] :
% 2.99/1.57 ( ( subset @ A @ B )
% 2.99/1.57 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(sepInPowerset_type,type,
% 2.99/1.57 sepInPowerset: $o ).
% 2.99/1.57
% 2.99/1.57 thf(sepInPowerset,definition,
% 2.99/1.57 ( sepInPowerset
% 2.99/1.57 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.57 ( in
% 2.99/1.57 @ ( dsetconstr @ A
% 2.99/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.57 @ ( powerset @ A ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(sepSubset_type,type,
% 2.99/1.57 sepSubset: $o ).
% 2.99/1.57
% 2.99/1.57 thf(sepSubset,definition,
% 2.99/1.57 ( sepSubset
% 2.99/1.57 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.57 ( subset
% 2.99/1.57 @ ( dsetconstr @ A
% 2.99/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.57 @ A ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(binunion_type,type,
% 2.99/1.57 binunion: $i > $i > $i ).
% 2.99/1.57
% 2.99/1.57 thf(binunionIL_type,type,
% 2.99/1.57 binunionIL: $o ).
% 2.99/1.57
% 2.99/1.57 thf(binunionIL,definition,
% 2.99/1.57 ( binunionIL
% 2.99/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(upairset2IR_type,type,
% 2.99/1.57 upairset2IR: $o ).
% 2.99/1.57
% 2.99/1.57 thf(upairset2IR,definition,
% 2.99/1.57 ( upairset2IR
% 2.99/1.57 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(binunionIR_type,type,
% 2.99/1.57 binunionIR: $o ).
% 2.99/1.57
% 2.99/1.57 thf(binunionIR,definition,
% 2.99/1.57 ( binunionIR
% 2.99/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ B )
% 2.99/1.57 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(binunionEcases_type,type,
% 2.99/1.57 binunionEcases: $o ).
% 2.99/1.57
% 2.99/1.57 thf(binunionEcases,definition,
% 2.99/1.57 ( binunionEcases
% 2.99/1.57 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.99/1.57 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.99/1.57 => ( ( ( in @ Xx @ A )
% 2.99/1.57 => Xphi )
% 2.99/1.57 => ( ( ( in @ Xx @ B )
% 2.99/1.57 => Xphi )
% 2.99/1.57 => Xphi ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(binunionE_type,type,
% 2.99/1.57 binunionE: $o ).
% 2.99/1.57
% 2.99/1.57 thf(binunionE,definition,
% 2.99/1.57 ( binunionE
% 2.99/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.99/1.57 => ( ( in @ Xx @ A )
% 2.99/1.57 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(binunionLsub_type,type,
% 2.99/1.57 binunionLsub: $o ).
% 2.99/1.57
% 2.99/1.57 thf(binunionLsub,definition,
% 2.99/1.57 ( binunionLsub
% 2.99/1.57 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(binunionRsub_type,type,
% 2.99/1.57 binunionRsub: $o ).
% 2.99/1.57
% 2.99/1.57 thf(binunionRsub,definition,
% 2.99/1.57 ( binunionRsub
% 2.99/1.57 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(binintersect_type,type,
% 2.99/1.57 binintersect: $i > $i > $i ).
% 2.99/1.57
% 2.99/1.57 thf(binintersectI_type,type,
% 2.99/1.57 binintersectI: $o ).
% 2.99/1.57
% 2.99/1.57 thf(binintersectI,definition,
% 2.99/1.57 ( binintersectI
% 2.99/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 => ( ( in @ Xx @ B )
% 2.99/1.57 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(binintersectSubset5_type,type,
% 2.99/1.57 binintersectSubset5: $o ).
% 2.99/1.57
% 2.99/1.57 thf(binintersectSubset5,definition,
% 2.99/1.57 ( binintersectSubset5
% 2.99/1.57 = ( ! [A: $i,B: $i,C: $i] :
% 2.99/1.57 ( ( subset @ C @ A )
% 2.99/1.57 => ( ( subset @ C @ B )
% 2.99/1.57 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(binintersectEL_type,type,
% 2.99/1.57 binintersectEL: $o ).
% 2.99/1.57
% 2.99/1.57 thf(binintersectEL,definition,
% 2.99/1.57 ( binintersectEL
% 2.99/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.99/1.57 => ( in @ Xx @ A ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(binintersectLsub_type,type,
% 2.99/1.57 binintersectLsub: $o ).
% 2.99/1.57
% 2.99/1.57 thf(binintersectLsub,definition,
% 2.99/1.57 ( binintersectLsub
% 2.99/1.57 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(binintersectSubset2_type,type,
% 2.99/1.57 binintersectSubset2: $o ).
% 2.99/1.57
% 2.99/1.57 thf(binintersectSubset2,definition,
% 2.99/1.57 ( binintersectSubset2
% 2.99/1.57 = ( ! [A: $i,B: $i] :
% 2.99/1.57 ( ( subset @ A @ B )
% 2.99/1.57 => ( ( binintersect @ A @ B )
% 2.99/1.57 = A ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(binintersectSubset3_type,type,
% 2.99/1.57 binintersectSubset3: $o ).
% 2.99/1.57
% 2.99/1.57 thf(binintersectSubset3,definition,
% 2.99/1.57 ( binintersectSubset3
% 2.99/1.57 = ( ! [A: $i,B: $i] :
% 2.99/1.57 ( ( ( binintersect @ A @ B )
% 2.99/1.57 = B )
% 2.99/1.57 => ( subset @ B @ A ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(binintersectER_type,type,
% 2.99/1.57 binintersectER: $o ).
% 2.99/1.57
% 2.99/1.57 thf(binintersectER,definition,
% 2.99/1.57 ( binintersectER
% 2.99/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.99/1.57 => ( in @ Xx @ B ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(disjointsetsI1_type,type,
% 2.99/1.57 disjointsetsI1: $o ).
% 2.99/1.57
% 2.99/1.57 thf(disjointsetsI1,definition,
% 2.99/1.57 ( disjointsetsI1
% 2.99/1.57 = ( ! [A: $i,B: $i] :
% 2.99/1.57 ( ~ ? [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 & ( in @ Xx @ B ) )
% 2.99/1.57 => ( ( binintersect @ A @ B )
% 2.99/1.57 = emptyset ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(binintersectRsub_type,type,
% 2.99/1.57 binintersectRsub: $o ).
% 2.99/1.57
% 2.99/1.57 thf(binintersectRsub,definition,
% 2.99/1.57 ( binintersectRsub
% 2.99/1.57 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(binintersectSubset4_type,type,
% 2.99/1.57 binintersectSubset4: $o ).
% 2.99/1.57
% 2.99/1.57 thf(binintersectSubset4,definition,
% 2.99/1.57 ( binintersectSubset4
% 2.99/1.57 = ( ! [A: $i,B: $i] :
% 2.99/1.57 ( ( subset @ B @ A )
% 2.99/1.57 => ( ( binintersect @ A @ B )
% 2.99/1.57 = B ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(binintersectSubset1_type,type,
% 2.99/1.57 binintersectSubset1: $o ).
% 2.99/1.57
% 2.99/1.57 thf(binintersectSubset1,definition,
% 2.99/1.57 ( binintersectSubset1
% 2.99/1.57 = ( ! [A: $i,B: $i] :
% 2.99/1.57 ( ( ( binintersect @ A @ B )
% 2.99/1.57 = A )
% 2.99/1.57 => ( subset @ A @ B ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(bs114d_type,type,
% 2.99/1.57 bs114d: $o ).
% 2.99/1.57
% 2.99/1.57 thf(bs114d,definition,
% 2.99/1.57 ( bs114d
% 2.99/1.57 = ( ! [A: $i,B: $i,C: $i] :
% 2.99/1.57 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.99/1.57 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(regular_type,type,
% 2.99/1.57 regular: $i > $o ).
% 2.99/1.57
% 2.99/1.57 thf(setminus_type,type,
% 2.99/1.57 setminus: $i > $i > $i ).
% 2.99/1.57
% 2.99/1.57 thf(setminusI_type,type,
% 2.99/1.57 setminusI: $o ).
% 2.99/1.57
% 2.99/1.57 thf(setminusI,definition,
% 2.99/1.57 ( setminusI
% 2.99/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 => ( ~ ( in @ Xx @ B )
% 2.99/1.57 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(setminusEL_type,type,
% 2.99/1.57 setminusEL: $o ).
% 2.99/1.57
% 2.99/1.57 thf(setminusEL,definition,
% 2.99/1.57 ( setminusEL
% 2.99/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.99/1.57 => ( in @ Xx @ A ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(setminusER_type,type,
% 2.99/1.57 setminusER: $o ).
% 2.99/1.57
% 2.99/1.57 thf(setminusER,definition,
% 2.99/1.57 ( setminusER
% 2.99/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.99/1.57 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(setminusSubset2_type,type,
% 2.99/1.57 setminusSubset2: $o ).
% 2.99/1.57
% 2.99/1.57 thf(setminusSubset2,definition,
% 2.99/1.57 ( setminusSubset2
% 2.99/1.57 = ( ! [A: $i,B: $i] :
% 2.99/1.57 ( ( subset @ A @ B )
% 2.99/1.57 => ( ( setminus @ A @ B )
% 2.99/1.57 = emptyset ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(setminusERneg_type,type,
% 2.99/1.57 setminusERneg: $o ).
% 2.99/1.57
% 2.99/1.57 thf(setminusERneg,definition,
% 2.99/1.57 ( setminusERneg
% 2.99/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.57 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.99/1.57 => ( ( in @ Xx @ A )
% 2.99/1.57 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(setminusELneg_type,type,
% 2.99/1.57 setminusELneg: $o ).
% 2.99/1.57
% 2.99/1.57 thf(setminusELneg,definition,
% 2.99/1.57 ( setminusELneg
% 2.99/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.57 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.99/1.57 => ( ~ ( in @ Xx @ B )
% 2.99/1.57 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(setminusILneg_type,type,
% 2.99/1.57 setminusILneg: $o ).
% 2.99/1.57
% 2.99/1.57 thf(setminusILneg,definition,
% 2.99/1.57 ( setminusILneg
% 2.99/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.57 ( ~ ( in @ Xx @ A )
% 2.99/1.57 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(setminusIRneg_type,type,
% 2.99/1.57 setminusIRneg: $o ).
% 2.99/1.57
% 2.99/1.57 thf(setminusIRneg,definition,
% 2.99/1.57 ( setminusIRneg
% 2.99/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ B )
% 2.99/1.57 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(setminusLsub_type,type,
% 2.99/1.57 setminusLsub: $o ).
% 2.99/1.57
% 2.99/1.57 thf(setminusLsub,definition,
% 2.99/1.57 ( setminusLsub
% 2.99/1.57 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(setminusSubset1_type,type,
% 2.99/1.57 setminusSubset1: $o ).
% 2.99/1.57
% 2.99/1.57 thf(setminusSubset1,definition,
% 2.99/1.57 ( setminusSubset1
% 2.99/1.57 = ( ! [A: $i,B: $i] :
% 2.99/1.57 ( ( ( setminus @ A @ B )
% 2.99/1.57 = emptyset )
% 2.99/1.57 => ( subset @ A @ B ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(symdiff_type,type,
% 2.99/1.57 symdiff: $i > $i > $i ).
% 2.99/1.57
% 2.99/1.57 thf(symdiffE_type,type,
% 2.99/1.57 symdiffE: $o ).
% 2.99/1.57
% 2.99/1.57 thf(symdiffE,definition,
% 2.99/1.57 ( symdiffE
% 2.99/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.99/1.57 => ! [Xphi: $o] :
% 2.99/1.57 ( ( ( in @ Xx @ A )
% 2.99/1.57 => ( ~ ( in @ Xx @ B )
% 2.99/1.57 => Xphi ) )
% 2.99/1.57 => ( ( ~ ( in @ Xx @ A )
% 2.99/1.57 => ( ( in @ Xx @ B )
% 2.99/1.57 => Xphi ) )
% 2.99/1.57 => Xphi ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(symdiffI1_type,type,
% 2.99/1.57 symdiffI1: $o ).
% 2.99/1.57
% 2.99/1.57 thf(symdiffI1,definition,
% 2.99/1.57 ( symdiffI1
% 2.99/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 => ( ~ ( in @ Xx @ B )
% 2.99/1.57 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(symdiffI2_type,type,
% 2.99/1.57 symdiffI2: $o ).
% 2.99/1.57
% 2.99/1.57 thf(symdiffI2,definition,
% 2.99/1.57 ( symdiffI2
% 2.99/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.57 ( ~ ( in @ Xx @ A )
% 2.99/1.57 => ( ( in @ Xx @ B )
% 2.99/1.57 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(symdiffIneg1_type,type,
% 2.99/1.57 symdiffIneg1: $o ).
% 2.99/1.57
% 2.99/1.57 thf(symdiffIneg1,definition,
% 2.99/1.57 ( symdiffIneg1
% 2.99/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 => ( ( in @ Xx @ B )
% 2.99/1.57 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(symdiffIneg2_type,type,
% 2.99/1.57 symdiffIneg2: $o ).
% 2.99/1.57
% 2.99/1.57 thf(symdiffIneg2,definition,
% 2.99/1.57 ( symdiffIneg2
% 2.99/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.57 ( ~ ( in @ Xx @ A )
% 2.99/1.57 => ( ~ ( in @ Xx @ B )
% 2.99/1.57 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(iskpair_type,type,
% 2.99/1.57 iskpair: $i > $o ).
% 2.99/1.57
% 2.99/1.57 thf(secondinupair_type,type,
% 2.99/1.57 secondinupair: $o ).
% 2.99/1.57
% 2.99/1.57 thf(secondinupair,definition,
% 2.99/1.57 ( secondinupair
% 2.99/1.57 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(setukpairIL_type,type,
% 2.99/1.57 setukpairIL: $o ).
% 2.99/1.57
% 2.99/1.57 thf(setukpairIL,definition,
% 2.99/1.57 ( setukpairIL
% 2.99/1.57 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(setukpairIR_type,type,
% 2.99/1.57 setukpairIR: $o ).
% 2.99/1.57
% 2.99/1.57 thf(setukpairIR,definition,
% 2.99/1.57 ( setukpairIR
% 2.99/1.57 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(kpairiskpair_type,type,
% 2.99/1.57 kpairiskpair: $o ).
% 2.99/1.57
% 2.99/1.57 thf(kpairiskpair,definition,
% 2.99/1.57 ( kpairiskpair
% 2.99/1.57 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(kpair_type,type,
% 2.99/1.57 kpair: $i > $i > $i ).
% 2.99/1.57
% 2.99/1.57 thf(kpairp_type,type,
% 2.99/1.57 kpairp: $o ).
% 2.99/1.57
% 2.99/1.57 thf(kpairp,definition,
% 2.99/1.57 ( kpairp
% 2.99/1.57 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(cartprod_type,type,
% 2.99/1.57 cartprod: $i > $i > $i ).
% 2.99/1.57
% 2.99/1.57 thf(singletonsubset_type,type,
% 2.99/1.57 singletonsubset: $o ).
% 2.99/1.57
% 2.99/1.57 thf(singletonsubset,definition,
% 2.99/1.57 ( singletonsubset
% 2.99/1.57 = ( ! [A: $i,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(singletoninpowerset_type,type,
% 2.99/1.57 singletoninpowerset: $o ).
% 2.99/1.57
% 2.99/1.57 thf(singletoninpowerset,definition,
% 2.99/1.57 ( singletoninpowerset
% 2.99/1.57 = ( ! [A: $i,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(singletoninpowunion_type,type,
% 2.99/1.57 singletoninpowunion: $o ).
% 2.99/1.57
% 2.99/1.57 thf(singletoninpowunion,definition,
% 2.99/1.57 ( singletoninpowunion
% 2.99/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(upairset2E_type,type,
% 2.99/1.57 upairset2E: $o ).
% 2.99/1.57
% 2.99/1.57 thf(upairset2E,definition,
% 2.99/1.57 ( upairset2E
% 2.99/1.57 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.99/1.57 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.99/1.57 => ( ( Xz = Xx )
% 2.99/1.57 | ( Xz = Xy ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(upairsubunion_type,type,
% 2.99/1.57 upairsubunion: $o ).
% 2.99/1.57
% 2.99/1.57 thf(upairsubunion,definition,
% 2.99/1.57 ( upairsubunion
% 2.99/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 => ! [Xy: $i] :
% 2.99/1.57 ( ( in @ Xy @ B )
% 2.99/1.57 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(upairinpowunion_type,type,
% 2.99/1.57 upairinpowunion: $o ).
% 2.99/1.57
% 2.99/1.57 thf(upairinpowunion,definition,
% 2.99/1.57 ( upairinpowunion
% 2.99/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 => ! [Xy: $i] :
% 2.99/1.57 ( ( in @ Xy @ B )
% 2.99/1.57 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(ubforcartprodlem1_type,type,
% 2.99/1.57 ubforcartprodlem1: $o ).
% 2.99/1.57
% 2.99/1.57 thf(ubforcartprodlem1,definition,
% 2.99/1.57 ( ubforcartprodlem1
% 2.99/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 => ! [Xy: $i] :
% 2.99/1.57 ( ( in @ Xy @ B )
% 2.99/1.57 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(ubforcartprodlem2_type,type,
% 2.99/1.57 ubforcartprodlem2: $o ).
% 2.99/1.57
% 2.99/1.57 thf(ubforcartprodlem2,definition,
% 2.99/1.57 ( ubforcartprodlem2
% 2.99/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 => ! [Xy: $i] :
% 2.99/1.57 ( ( in @ Xy @ B )
% 2.99/1.57 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(ubforcartprodlem3_type,type,
% 2.99/1.57 ubforcartprodlem3: $o ).
% 2.99/1.57
% 2.99/1.57 thf(ubforcartprodlem3,definition,
% 2.99/1.57 ( ubforcartprodlem3
% 2.99/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 => ! [Xy: $i] :
% 2.99/1.57 ( ( in @ Xy @ B )
% 2.99/1.57 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(cartprodpairin_type,type,
% 2.99/1.57 cartprodpairin: $o ).
% 2.99/1.57
% 2.99/1.57 thf(cartprodpairin,definition,
% 2.99/1.57 ( cartprodpairin
% 2.99/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 => ! [Xy: $i] :
% 2.99/1.57 ( ( in @ Xy @ B )
% 2.99/1.57 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(cartprodmempair1_type,type,
% 2.99/1.57 cartprodmempair1: $o ).
% 2.99/1.57
% 2.99/1.57 thf(cartprodmempair1,definition,
% 2.99/1.57 ( cartprodmempair1
% 2.99/1.57 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.99/1.57 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.99/1.57 => ? [Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ A )
% 2.99/1.57 & ? [Xy: $i] :
% 2.99/1.57 ( ( in @ Xy @ B )
% 2.99/1.57 & ( Xu
% 2.99/1.57 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(cartprodmempair_type,type,
% 2.99/1.57 cartprodmempair: $o ).
% 2.99/1.57
% 2.99/1.57 thf(cartprodmempair,definition,
% 2.99/1.57 ( cartprodmempair
% 2.99/1.57 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.99/1.57 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.99/1.57 => ( iskpair @ Xu ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(setunionE2_type,type,
% 2.99/1.57 setunionE2: $o ).
% 2.99/1.57
% 2.99/1.57 thf(setunionE2,definition,
% 2.99/1.57 ( setunionE2
% 2.99/1.57 = ( ! [A: $i,Xx: $i] :
% 2.99/1.57 ( ( in @ Xx @ ( setunion @ A ) )
% 2.99/1.57 => ? [X: $i] :
% 2.99/1.57 ( ( in @ X @ A )
% 2.99/1.57 & ( in @ Xx @ X ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(setunionsingleton1_type,type,
% 2.99/1.57 setunionsingleton1: $o ).
% 2.99/1.57
% 2.99/1.57 thf(setunionsingleton1,definition,
% 2.99/1.57 ( setunionsingleton1
% 2.99/1.57 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(setunionsingleton2_type,type,
% 2.99/1.57 setunionsingleton2: $o ).
% 2.99/1.57
% 2.99/1.57 thf(setunionsingleton2,definition,
% 2.99/1.57 ( setunionsingleton2
% 2.99/1.57 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(setunionsingleton_type,type,
% 2.99/1.57 setunionsingleton: $o ).
% 2.99/1.57
% 2.99/1.57 thf(setunionsingleton,definition,
% 2.99/1.57 ( setunionsingleton
% 2.99/1.57 = ( ! [Xx: $i] :
% 2.99/1.57 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 2.99/1.57 = Xx ) ) ) ).
% 2.99/1.57
% 2.99/1.57 thf(singleton_type,type,
% 2.99/1.57 singleton: $i > $o ).
% 2.99/1.58
% 2.99/1.58 thf(singletonprop_type,type,
% 2.99/1.58 singletonprop: $o ).
% 2.99/1.58
% 2.99/1.58 thf(singletonprop,definition,
% 2.99/1.58 ( singletonprop
% 2.99/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.58 ( ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ! [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ A )
% 2.99/1.58 => ( ( Xphi @ Xx )
% 2.99/1.58 => ( ( Xphi @ Xy )
% 2.99/1.58 => ( Xx = Xy ) ) ) ) )
% 2.99/1.58 => ( ? [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 & ( Xphi @ Xx ) )
% 2.99/1.58 => ( singleton
% 2.99/1.58 @ ( dsetconstr @ A
% 2.99/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(ex1_type,type,
% 2.99/1.58 ex1: $i > ( $i > $o ) > $o ).
% 2.99/1.58
% 2.99/1.58 thf(ex1E1_type,type,
% 2.99/1.58 ex1E1: $o ).
% 2.99/1.58
% 2.99/1.58 thf(ex1E1,definition,
% 2.99/1.58 ( ex1E1
% 2.99/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.58 ( ( ex1 @ A
% 2.99/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.58 => ? [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(ex1I_type,type,
% 2.99/1.58 ex1I: $o ).
% 2.99/1.58
% 2.99/1.58 thf(ex1I,definition,
% 2.99/1.58 ( ex1I
% 2.99/1.58 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ( Xphi @ Xx )
% 2.99/1.58 => ( ! [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ A )
% 2.99/1.58 => ( ( Xphi @ Xy )
% 2.99/1.58 => ( Xy = Xx ) ) )
% 2.99/1.58 => ( ex1 @ A
% 2.99/1.58 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(ex1I2_type,type,
% 2.99/1.58 ex1I2: $o ).
% 2.99/1.58
% 2.99/1.58 thf(ex1I2,definition,
% 2.99/1.58 ( ex1I2
% 2.99/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.58 ( ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ! [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ A )
% 2.99/1.58 => ( ( Xphi @ Xx )
% 2.99/1.58 => ( ( Xphi @ Xy )
% 2.99/1.58 => ( Xx = Xy ) ) ) ) )
% 2.99/1.58 => ( ? [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 & ( Xphi @ Xx ) )
% 2.99/1.58 => ( ex1 @ A
% 2.99/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(singletonsuniq_type,type,
% 2.99/1.58 singletonsuniq: $o ).
% 2.99/1.58
% 2.99/1.58 thf(singletonsuniq,definition,
% 2.99/1.58 ( singletonsuniq
% 2.99/1.58 = ( ! [Xx: $i,Xy: $i] :
% 2.99/1.58 ( ( ( setadjoin @ Xx @ emptyset )
% 2.99/1.58 = ( setadjoin @ Xy @ emptyset ) )
% 2.99/1.58 => ( Xx = Xy ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(atmost1p_type,type,
% 2.99/1.58 atmost1p: $i > $o ).
% 2.99/1.58
% 2.99/1.58 thf(atleast2p_type,type,
% 2.99/1.58 atleast2p: $i > $o ).
% 2.99/1.58
% 2.99/1.58 thf(atmost2p_type,type,
% 2.99/1.58 atmost2p: $i > $o ).
% 2.99/1.58
% 2.99/1.58 thf(upairsetp_type,type,
% 2.99/1.58 upairsetp: $i > $o ).
% 2.99/1.58
% 2.99/1.58 thf(setukpairinjL1_type,type,
% 2.99/1.58 setukpairinjL1: $o ).
% 2.99/1.58
% 2.99/1.58 thf(setukpairinjL1,definition,
% 2.99/1.58 ( setukpairinjL1
% 2.99/1.58 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.99/1.58 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 2.99/1.58 => ( Xx = Xz ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(kfstsingleton_type,type,
% 2.99/1.58 kfstsingleton: $o ).
% 2.99/1.58
% 2.99/1.58 thf(kfstsingleton,definition,
% 2.99/1.58 ( kfstsingleton
% 2.99/1.58 = ( ! [Xu: $i] :
% 2.99/1.58 ( ( iskpair @ Xu )
% 2.99/1.58 => ( singleton
% 2.99/1.58 @ ( dsetconstr @ ( setunion @ Xu )
% 2.99/1.58 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(theprop_type,type,
% 2.99/1.58 theprop: $o ).
% 2.99/1.58
% 2.99/1.58 thf(theprop,definition,
% 2.99/1.58 ( theprop
% 2.99/1.58 = ( ! [X: $i] :
% 2.99/1.58 ( ( singleton @ X )
% 2.99/1.58 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(kfst_type,type,
% 2.99/1.58 kfst: $i > $i ).
% 2.99/1.58
% 2.99/1.58 thf(kfstpairEq_type,type,
% 2.99/1.58 kfstpairEq: $o ).
% 2.99/1.58
% 2.99/1.58 thf(kfstpairEq,definition,
% 2.99/1.58 ( kfstpairEq
% 2.99/1.58 = ( ! [Xx: $i,Xy: $i] :
% 2.99/1.58 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.99/1.58 = Xx ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(cartprodfstin_type,type,
% 2.99/1.58 cartprodfstin: $o ).
% 2.99/1.58
% 2.99/1.58 thf(cartprodfstin,definition,
% 2.99/1.58 ( cartprodfstin
% 2.99/1.58 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.99/1.58 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.99/1.58 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(setukpairinjL2_type,type,
% 2.99/1.58 setukpairinjL2: $o ).
% 2.99/1.58
% 2.99/1.58 thf(setukpairinjL2,definition,
% 2.99/1.58 ( setukpairinjL2
% 2.99/1.58 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.99/1.58 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.99/1.58 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.99/1.58 => ( Xx = Xz ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(setukpairinjL_type,type,
% 2.99/1.58 setukpairinjL: $o ).
% 2.99/1.58
% 2.99/1.58 thf(setukpairinjL,definition,
% 2.99/1.58 ( setukpairinjL
% 2.99/1.58 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.99/1.58 ( ( ( kpair @ Xx @ Xy )
% 2.99/1.58 = ( kpair @ Xz @ Xu ) )
% 2.99/1.58 => ( Xx = Xz ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(setukpairinjR11_type,type,
% 2.99/1.58 setukpairinjR11: $o ).
% 2.99/1.58
% 2.99/1.58 thf(setukpairinjR11,definition,
% 2.99/1.58 ( setukpairinjR11
% 2.99/1.58 = ( ! [Xx: $i,Xy: $i] :
% 2.99/1.58 ( ( Xx = Xy )
% 2.99/1.58 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.99/1.58 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(setukpairinjR12_type,type,
% 2.99/1.58 setukpairinjR12: $o ).
% 2.99/1.58
% 2.99/1.58 thf(setukpairinjR12,definition,
% 2.99/1.58 ( setukpairinjR12
% 2.99/1.58 = ( ! [Xx: $i,Xy: $i] :
% 2.99/1.58 ( ( Xx = Xy )
% 2.99/1.58 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.99/1.58 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(setukpairinjR1_type,type,
% 2.99/1.58 setukpairinjR1: $o ).
% 2.99/1.58
% 2.99/1.58 thf(setukpairinjR1,definition,
% 2.99/1.58 ( setukpairinjR1
% 2.99/1.58 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.99/1.58 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.99/1.58 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.99/1.58 => ( ( Xz = Xu )
% 2.99/1.58 => ( Xy = Xu ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(upairequniteq_type,type,
% 2.99/1.58 upairequniteq: $o ).
% 2.99/1.58
% 2.99/1.58 thf(upairequniteq,definition,
% 2.99/1.58 ( upairequniteq
% 2.99/1.58 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.99/1.58 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.99/1.58 = ( setadjoin @ Xz @ emptyset ) )
% 2.99/1.58 => ( Xx = Xy ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(setukpairinjR2_type,type,
% 2.99/1.58 setukpairinjR2: $o ).
% 2.99/1.58
% 2.99/1.58 thf(setukpairinjR2,definition,
% 2.99/1.58 ( setukpairinjR2
% 2.99/1.58 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.99/1.58 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.99/1.58 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.99/1.58 => ( Xy = Xu ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(setukpairinjR_type,type,
% 2.99/1.58 setukpairinjR: $o ).
% 2.99/1.58
% 2.99/1.58 thf(setukpairinjR,definition,
% 2.99/1.58 ( setukpairinjR
% 2.99/1.58 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.99/1.58 ( ( ( kpair @ Xx @ Xy )
% 2.99/1.58 = ( kpair @ Xz @ Xu ) )
% 2.99/1.58 => ( Xy = Xu ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(ksndsingleton_type,type,
% 2.99/1.58 ksndsingleton: $o ).
% 2.99/1.58
% 2.99/1.58 thf(ksndsingleton,definition,
% 2.99/1.58 ( ksndsingleton
% 2.99/1.58 = ( ! [Xu: $i] :
% 2.99/1.58 ( ( iskpair @ Xu )
% 2.99/1.58 => ( singleton
% 2.99/1.58 @ ( dsetconstr @ ( setunion @ Xu )
% 2.99/1.58 @ ^ [Xx: $i] :
% 2.99/1.58 ( Xu
% 2.99/1.58 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(ksnd_type,type,
% 2.99/1.58 ksnd: $i > $i ).
% 2.99/1.58
% 2.99/1.58 thf(ksndpairEq_type,type,
% 2.99/1.58 ksndpairEq: $o ).
% 2.99/1.58
% 2.99/1.58 thf(ksndpairEq,definition,
% 2.99/1.58 ( ksndpairEq
% 2.99/1.58 = ( ! [Xx: $i,Xy: $i] :
% 2.99/1.58 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.99/1.58 = Xy ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(kpairsurjEq_type,type,
% 2.99/1.58 kpairsurjEq: $o ).
% 2.99/1.58
% 2.99/1.58 thf(kpairsurjEq,definition,
% 2.99/1.58 ( kpairsurjEq
% 2.99/1.58 = ( ! [Xu: $i] :
% 2.99/1.58 ( ( iskpair @ Xu )
% 2.99/1.58 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.99/1.58 = Xu ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(cartprodsndin_type,type,
% 2.99/1.58 cartprodsndin: $o ).
% 2.99/1.58
% 2.99/1.58 thf(cartprodsndin,definition,
% 2.99/1.58 ( cartprodsndin
% 2.99/1.58 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.99/1.58 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.99/1.58 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(cartprodpairmemEL_type,type,
% 2.99/1.58 cartprodpairmemEL: $o ).
% 2.99/1.58
% 2.99/1.58 thf(cartprodpairmemEL,definition,
% 2.99/1.58 ( cartprodpairmemEL
% 2.99/1.58 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.99/1.58 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.99/1.58 => ( in @ Xx @ A ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(cartprodpairmemER_type,type,
% 2.99/1.58 cartprodpairmemER: $o ).
% 2.99/1.58
% 2.99/1.58 thf(cartprodpairmemER,definition,
% 2.99/1.58 ( cartprodpairmemER
% 2.99/1.58 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.99/1.58 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.99/1.58 => ( in @ Xy @ B ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(cartprodmempaircEq_type,type,
% 2.99/1.58 cartprodmempaircEq: $o ).
% 2.99/1.58
% 2.99/1.58 thf(cartprodmempaircEq,definition,
% 2.99/1.58 ( cartprodmempaircEq
% 2.99/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ! [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ B )
% 2.99/1.58 => ( ( kpair @ Xx @ Xy )
% 2.99/1.58 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(cartprodfstpairEq_type,type,
% 2.99/1.58 cartprodfstpairEq: $o ).
% 2.99/1.58
% 2.99/1.58 thf(cartprodfstpairEq,definition,
% 2.99/1.58 ( cartprodfstpairEq
% 2.99/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ! [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ B )
% 2.99/1.58 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.99/1.58 = Xx ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(cartprodsndpairEq_type,type,
% 2.99/1.58 cartprodsndpairEq: $o ).
% 2.99/1.58
% 2.99/1.58 thf(cartprodsndpairEq,definition,
% 2.99/1.58 ( cartprodsndpairEq
% 2.99/1.58 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ! [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ B )
% 2.99/1.58 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.99/1.58 = Xy ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(cartprodpairsurjEq_type,type,
% 2.99/1.58 cartprodpairsurjEq: $o ).
% 2.99/1.58
% 2.99/1.58 thf(cartprodpairsurjEq,definition,
% 2.99/1.58 ( cartprodpairsurjEq
% 2.99/1.58 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.99/1.58 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.99/1.58 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.99/1.58 = Xu ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(breln_type,type,
% 2.99/1.58 breln: $i > $i > $i > $o ).
% 2.99/1.58
% 2.99/1.58 thf(breln,definition,
% 2.99/1.58 ( breln
% 2.99/1.58 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(dpsetconstr_type,type,
% 2.99/1.58 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 2.99/1.58
% 2.99/1.58 thf(dpsetconstrI_type,type,
% 2.99/1.58 dpsetconstrI: $o ).
% 2.99/1.58
% 2.99/1.58 thf(dpsetconstrI,definition,
% 2.99/1.58 ( dpsetconstrI
% 2.99/1.58 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ! [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ B )
% 2.99/1.58 => ( ( Xphi @ Xx @ Xy )
% 2.99/1.58 => ( in @ ( kpair @ Xx @ Xy )
% 2.99/1.58 @ ( dpsetconstr @ A @ B
% 2.99/1.58 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(dpsetconstrSub_type,type,
% 2.99/1.58 dpsetconstrSub: $o ).
% 2.99/1.58
% 2.99/1.58 thf(dpsetconstrSub,definition,
% 2.99/1.58 ( dpsetconstrSub
% 2.99/1.58 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.99/1.58 ( subset
% 2.99/1.58 @ ( dpsetconstr @ A @ B
% 2.99/1.58 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 2.99/1.58 @ ( cartprod @ A @ B ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(setOfPairsIsBReln_type,type,
% 2.99/1.58 setOfPairsIsBReln: $o ).
% 2.99/1.58
% 2.99/1.58 thf(setOfPairsIsBReln,definition,
% 2.99/1.58 ( setOfPairsIsBReln
% 2.99/1.58 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.99/1.58 ( breln @ A @ B
% 2.99/1.58 @ ( dpsetconstr @ A @ B
% 2.99/1.58 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(dpsetconstrERa_type,type,
% 2.99/1.58 dpsetconstrERa: $o ).
% 2.99/1.58
% 2.99/1.58 thf(dpsetconstrERa,definition,
% 2.99/1.58 ( dpsetconstrERa
% 2.99/1.58 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ! [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ B )
% 2.99/1.58 => ( ( in @ ( kpair @ Xx @ Xy )
% 2.99/1.58 @ ( dpsetconstr @ A @ B
% 2.99/1.58 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.99/1.58 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(dpsetconstrEL1_type,type,
% 2.99/1.58 dpsetconstrEL1: $o ).
% 2.99/1.58
% 2.99/1.58 thf(dpsetconstrEL1,definition,
% 2.99/1.58 ( dpsetconstrEL1
% 2.99/1.58 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.99/1.58 ( ( in @ ( kpair @ Xx @ Xy )
% 2.99/1.58 @ ( dpsetconstr @ A @ B
% 2.99/1.58 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.99/1.58 => ( in @ Xx @ A ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(dpsetconstrEL2_type,type,
% 2.99/1.58 dpsetconstrEL2: $o ).
% 2.99/1.58
% 2.99/1.58 thf(dpsetconstrEL2,definition,
% 2.99/1.58 ( dpsetconstrEL2
% 2.99/1.58 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.99/1.58 ( ( in @ ( kpair @ Xx @ Xy )
% 2.99/1.58 @ ( dpsetconstr @ A @ B
% 2.99/1.58 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.99/1.58 => ( in @ Xy @ B ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(dpsetconstrER_type,type,
% 2.99/1.58 dpsetconstrER: $o ).
% 2.99/1.58
% 2.99/1.58 thf(dpsetconstrER,definition,
% 2.99/1.58 ( dpsetconstrER
% 2.99/1.58 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.99/1.58 ( ( in @ ( kpair @ Xx @ Xy )
% 2.99/1.58 @ ( dpsetconstr @ A @ B
% 2.99/1.58 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.99/1.58 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(func_type,type,
% 2.99/1.58 func: $i > $i > $i > $o ).
% 2.99/1.58
% 2.99/1.58 thf(funcSet_type,type,
% 2.99/1.58 funcSet: $i > $i > $i ).
% 2.99/1.58
% 2.99/1.58 thf(funcImageSingleton_type,type,
% 2.99/1.58 funcImageSingleton: $o ).
% 2.99/1.58
% 2.99/1.58 thf(funcImageSingleton,definition,
% 2.99/1.58 ( funcImageSingleton
% 2.99/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.58 ( ( func @ A @ B @ Xf )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( singleton
% 2.99/1.58 @ ( dsetconstr @ B
% 2.99/1.58 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(apProp_type,type,
% 2.99/1.58 apProp: $o ).
% 2.99/1.58
% 2.99/1.58 thf(apProp,definition,
% 2.99/1.58 ( apProp
% 2.99/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.58 ( ( func @ A @ B @ Xf )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( in
% 2.99/1.58 @ ( setunion
% 2.99/1.58 @ ( dsetconstr @ B
% 2.99/1.58 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 2.99/1.58 @ B ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(ap_type,type,
% 2.99/1.58 ap: $i > $i > $i > $i > $i ).
% 2.99/1.58
% 2.99/1.58 thf(app_type,type,
% 2.99/1.58 app: $o ).
% 2.99/1.58
% 2.99/1.58 thf(app,definition,
% 2.99/1.58 ( app
% 2.99/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.58 ( ( func @ A @ B @ Xf )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(infuncsetfunc_type,type,
% 2.99/1.58 infuncsetfunc: $o ).
% 2.99/1.58
% 2.99/1.58 thf(infuncsetfunc,definition,
% 2.99/1.58 ( infuncsetfunc
% 2.99/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.58 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.99/1.58 => ( func @ A @ B @ Xf ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(ap2p_type,type,
% 2.99/1.58 ap2p: $o ).
% 2.99/1.58
% 2.99/1.58 thf(ap2p,definition,
% 2.99/1.58 ( ap2p
% 2.99/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.58 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(funcinfuncset_type,type,
% 2.99/1.58 funcinfuncset: $o ).
% 2.99/1.58
% 2.99/1.58 thf(funcinfuncset,definition,
% 2.99/1.58 ( funcinfuncset
% 2.99/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.58 ( ( func @ A @ B @ Xf )
% 2.99/1.58 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(lamProp_type,type,
% 2.99/1.58 lamProp: $o ).
% 2.99/1.58
% 2.99/1.58 thf(lamProp,definition,
% 2.99/1.58 ( lamProp
% 2.99/1.58 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.99/1.58 ( ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.99/1.58 => ( func @ A @ B
% 2.99/1.58 @ ( dpsetconstr @ A @ B
% 2.99/1.58 @ ^ [Xx: $i,Xy: $i] :
% 2.99/1.58 ( ( Xf @ Xx )
% 2.99/1.58 = Xy ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(lam_type,type,
% 2.99/1.58 lam: $i > $i > ( $i > $i ) > $i ).
% 2.99/1.58
% 2.99/1.58 thf(lamp_type,type,
% 2.99/1.58 lamp: $o ).
% 2.99/1.58
% 2.99/1.58 thf(lamp,definition,
% 2.99/1.58 ( lamp
% 2.99/1.58 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.99/1.58 ( ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.99/1.58 => ( func @ A @ B
% 2.99/1.58 @ ( lam @ A @ B
% 2.99/1.58 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(lam2p_type,type,
% 2.99/1.58 lam2p: $o ).
% 2.99/1.58
% 2.99/1.58 thf(lam2p,definition,
% 2.99/1.58 ( lam2p
% 2.99/1.58 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.99/1.58 ( ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.99/1.58 => ( in
% 2.99/1.58 @ ( lam @ A @ B
% 2.99/1.58 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 2.99/1.58 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(brelnall1_type,type,
% 2.99/1.58 brelnall1: $o ).
% 2.99/1.58
% 2.99/1.58 thf(brelnall1,definition,
% 2.99/1.58 ( brelnall1
% 2.99/1.58 = ( ! [A: $i,B: $i,R: $i] :
% 2.99/1.58 ( ( breln @ A @ B @ R )
% 2.99/1.58 => ! [Xphi: $i > $o] :
% 2.99/1.58 ( ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ! [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ B )
% 2.99/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.99/1.58 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ R )
% 2.99/1.58 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(brelnall2_type,type,
% 2.99/1.58 brelnall2: $o ).
% 2.99/1.58
% 2.99/1.58 thf(brelnall2,definition,
% 2.99/1.58 ( brelnall2
% 2.99/1.58 = ( ! [A: $i,B: $i,R: $i] :
% 2.99/1.58 ( ( breln @ A @ B @ R )
% 2.99/1.58 => ! [Xphi: $i > $o] :
% 2.99/1.58 ( ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ! [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ B )
% 2.99/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.99/1.58 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ R )
% 2.99/1.58 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(ex1E2_type,type,
% 2.99/1.58 ex1E2: $o ).
% 2.99/1.58
% 2.99/1.58 thf(ex1E2,definition,
% 2.99/1.58 ( ex1E2
% 2.99/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 2.99/1.58 ( ( ex1 @ A
% 2.99/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ! [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ A )
% 2.99/1.58 => ( ( Xphi @ Xx )
% 2.99/1.58 => ( ( Xphi @ Xy )
% 2.99/1.58 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(funcGraphProp1_type,type,
% 2.99/1.58 funcGraphProp1: $o ).
% 2.99/1.58
% 2.99/1.58 thf(funcGraphProp1,definition,
% 2.99/1.58 ( funcGraphProp1
% 2.99/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.58 ( ( func @ A @ B @ Xf )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(funcGraphProp3_type,type,
% 2.99/1.58 funcGraphProp3: $o ).
% 2.99/1.58
% 2.99/1.58 thf(funcGraphProp3,definition,
% 2.99/1.58 ( funcGraphProp3
% 2.99/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.58 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(funcGraphProp2_type,type,
% 2.99/1.58 funcGraphProp2: $o ).
% 2.99/1.58
% 2.99/1.58 thf(funcGraphProp2,definition,
% 2.99/1.58 ( funcGraphProp2
% 2.99/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.58 ( ( func @ A @ B @ Xf )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ! [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ B )
% 2.99/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 2.99/1.58 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.99/1.58 = Xy ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(funcextLem_type,type,
% 2.99/1.58 funcextLem: $o ).
% 2.99/1.58
% 2.99/1.58 thf(funcextLem,definition,
% 2.99/1.58 ( funcextLem
% 2.99/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.58 ( ( func @ A @ B @ Xf )
% 2.99/1.58 => ! [Xg: $i] :
% 2.99/1.58 ( ( func @ A @ B @ Xg )
% 2.99/1.58 => ( ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.99/1.58 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ! [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ B )
% 2.99/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 2.99/1.58 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(funcGraphProp4_type,type,
% 2.99/1.58 funcGraphProp4: $o ).
% 2.99/1.58
% 2.99/1.58 thf(funcGraphProp4,definition,
% 2.99/1.58 ( funcGraphProp4
% 2.99/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.58 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ! [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ B )
% 2.99/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 2.99/1.58 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.99/1.58 = Xy ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(subbreln_type,type,
% 2.99/1.58 subbreln: $o ).
% 2.99/1.58
% 2.99/1.58 thf(subbreln,definition,
% 2.99/1.58 ( subbreln
% 2.99/1.58 = ( ! [A: $i,B: $i,R: $i] :
% 2.99/1.58 ( ( breln @ A @ B @ R )
% 2.99/1.58 => ! [S: $i] :
% 2.99/1.58 ( ( breln @ A @ B @ S )
% 2.99/1.58 => ( ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ! [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ B )
% 2.99/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.99/1.58 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 2.99/1.58 => ( subset @ R @ S ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(eqbreln_type,type,
% 2.99/1.58 eqbreln: $o ).
% 2.99/1.58
% 2.99/1.58 thf(eqbreln,definition,
% 2.99/1.58 ( eqbreln
% 2.99/1.58 = ( ! [A: $i,B: $i,R: $i] :
% 2.99/1.58 ( ( breln @ A @ B @ R )
% 2.99/1.58 => ! [S: $i] :
% 2.99/1.58 ( ( breln @ A @ B @ S )
% 2.99/1.58 => ( ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ! [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ B )
% 2.99/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.99/1.58 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 2.99/1.58 => ( ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ! [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ B )
% 2.99/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 2.99/1.58 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 2.99/1.58 => ( R = S ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(funcext_type,type,
% 2.99/1.58 funcext: $o ).
% 2.99/1.58
% 2.99/1.58 thf(funcext,definition,
% 2.99/1.58 ( funcext
% 2.99/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.58 ( ( func @ A @ B @ Xf )
% 2.99/1.58 => ! [Xg: $i] :
% 2.99/1.58 ( ( func @ A @ B @ Xg )
% 2.99/1.58 => ( ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.99/1.58 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.99/1.58 => ( Xf = Xg ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(funcext2_type,type,
% 2.99/1.58 funcext2: $o ).
% 2.99/1.58
% 2.99/1.58 thf(funcext2,definition,
% 2.99/1.58 ( funcext2
% 2.99/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.58 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.99/1.58 => ! [Xg: $i] :
% 2.99/1.58 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 2.99/1.58 => ( ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.99/1.58 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.99/1.58 => ( Xf = Xg ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(ap2apEq1_type,type,
% 2.99/1.58 ap2apEq1: $o ).
% 2.99/1.58
% 2.99/1.58 thf(ap2apEq1,definition,
% 2.99/1.58 ( ap2apEq1
% 2.99/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.58 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.99/1.58 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(ap2apEq2_type,type,
% 2.99/1.58 ap2apEq2: $o ).
% 2.99/1.58
% 2.99/1.58 thf(ap2apEq2,definition,
% 2.99/1.58 ( ap2apEq2
% 2.99/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.58 ( ( func @ A @ B @ Xf )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.99/1.58 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(beta1_type,type,
% 2.99/1.58 beta1: $o ).
% 2.99/1.58
% 2.99/1.58 thf(beta1,definition,
% 2.99/1.58 ( beta1
% 2.99/1.58 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.99/1.58 ( ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ( ap @ A @ B
% 2.99/1.58 @ ( lam @ A @ B
% 2.99/1.58 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 2.99/1.58 @ Xx )
% 2.99/1.58 = ( Xf @ Xx ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(eta1_type,type,
% 2.99/1.58 eta1: $o ).
% 2.99/1.58
% 2.99/1.58 thf(eta1,definition,
% 2.99/1.58 ( eta1
% 2.99/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.58 ( ( func @ A @ B @ Xf )
% 2.99/1.58 => ( ( lam @ A @ B
% 2.99/1.58 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 2.99/1.58 = Xf ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(lam2lamEq_type,type,
% 2.99/1.58 lam2lamEq: $o ).
% 2.99/1.58
% 2.99/1.58 thf(lam2lamEq,definition,
% 2.99/1.58 ( lam2lamEq
% 2.99/1.58 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.99/1.58 ( ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.99/1.58 => ( ( lam @ A @ B
% 2.99/1.58 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 2.99/1.58 = ( lam @ A @ B
% 2.99/1.58 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(beta2_type,type,
% 2.99/1.58 beta2: $o ).
% 2.99/1.58
% 2.99/1.58 thf(beta2,definition,
% 2.99/1.58 ( beta2
% 2.99/1.58 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.99/1.58 ( ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ( ap @ A @ B
% 2.99/1.58 @ ( lam @ A @ B
% 2.99/1.58 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 2.99/1.58 @ Xx )
% 2.99/1.58 = ( Xf @ Xx ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(eta2_type,type,
% 2.99/1.58 eta2: $o ).
% 2.99/1.58
% 2.99/1.58 thf(eta2,definition,
% 2.99/1.58 ( eta2
% 2.99/1.58 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.99/1.58 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.99/1.58 => ( ( lam @ A @ B
% 2.99/1.58 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 2.99/1.58 = Xf ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(iffalseProp1_type,type,
% 2.99/1.58 iffalseProp1: $o ).
% 2.99/1.58
% 2.99/1.58 thf(iffalseProp1,definition,
% 2.99/1.58 ( iffalseProp1
% 2.99/1.58 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ! [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ A )
% 2.99/1.58 => ( ~ Xphi
% 2.99/1.58 => ( in @ Xy
% 2.99/1.58 @ ( dsetconstr @ A
% 2.99/1.58 @ ^ [Xz: $i] :
% 2.99/1.58 ( ( Xphi
% 2.99/1.58 & ( Xz = Xx ) )
% 2.99/1.58 | ( ~ Xphi
% 2.99/1.58 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(iffalseProp2_type,type,
% 2.99/1.58 iffalseProp2: $o ).
% 2.99/1.58
% 2.99/1.58 thf(iffalseProp2,definition,
% 2.99/1.58 ( iffalseProp2
% 2.99/1.58 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ! [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ A )
% 2.99/1.58 => ( ~ Xphi
% 2.99/1.58 => ( ( dsetconstr @ A
% 2.99/1.58 @ ^ [Xz: $i] :
% 2.99/1.58 ( ( Xphi
% 2.99/1.58 & ( Xz = Xx ) )
% 2.99/1.58 | ( ~ Xphi
% 2.99/1.58 & ( Xz = Xy ) ) ) )
% 2.99/1.58 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(iftrueProp1_type,type,
% 2.99/1.58 iftrueProp1: $o ).
% 2.99/1.58
% 2.99/1.58 thf(iftrueProp1,definition,
% 2.99/1.58 ( iftrueProp1
% 2.99/1.58 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ! [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ A )
% 2.99/1.58 => ( Xphi
% 2.99/1.58 => ( in @ Xx
% 2.99/1.58 @ ( dsetconstr @ A
% 2.99/1.58 @ ^ [Xz: $i] :
% 2.99/1.58 ( ( Xphi
% 2.99/1.58 & ( Xz = Xx ) )
% 2.99/1.58 | ( ~ Xphi
% 2.99/1.58 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(iftrueProp2_type,type,
% 2.99/1.58 iftrueProp2: $o ).
% 2.99/1.58
% 2.99/1.58 thf(iftrueProp2,definition,
% 2.99/1.58 ( iftrueProp2
% 2.99/1.58 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ! [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ A )
% 2.99/1.58 => ( Xphi
% 2.99/1.58 => ( ( dsetconstr @ A
% 2.99/1.58 @ ^ [Xz: $i] :
% 2.99/1.58 ( ( Xphi
% 2.99/1.58 & ( Xz = Xx ) )
% 2.99/1.58 | ( ~ Xphi
% 2.99/1.58 & ( Xz = Xy ) ) ) )
% 2.99/1.58 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(ifSingleton_type,type,
% 2.99/1.58 ifSingleton: $o ).
% 2.99/1.58
% 2.99/1.58 thf(ifSingleton,definition,
% 2.99/1.58 ( ifSingleton
% 2.99/1.58 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ! [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ A )
% 2.99/1.58 => ( singleton
% 2.99/1.58 @ ( dsetconstr @ A
% 2.99/1.58 @ ^ [Xz: $i] :
% 2.99/1.58 ( ( Xphi
% 2.99/1.58 & ( Xz = Xx ) )
% 2.99/1.58 | ( ~ Xphi
% 2.99/1.58 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(if_type,type,
% 2.99/1.58 if: $i > $o > $i > $i > $i ).
% 2.99/1.58
% 2.99/1.58 thf(ifp_type,type,
% 2.99/1.58 ifp: $o ).
% 2.99/1.58
% 2.99/1.58 thf(ifp,definition,
% 2.99/1.58 ( ifp
% 2.99/1.58 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ! [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ A )
% 2.99/1.58 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(theeq_type,type,
% 2.99/1.58 theeq: $o ).
% 2.99/1.58
% 2.99/1.58 thf(theeq,definition,
% 2.99/1.58 ( theeq
% 2.99/1.58 = ( ! [X: $i] :
% 2.99/1.58 ( ( singleton @ X )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ X )
% 2.99/1.58 => ( ( setunion @ X )
% 2.99/1.58 = Xx ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(iftrue_type,type,
% 2.99/1.58 iftrue: $o ).
% 2.99/1.58
% 2.99/1.58 thf(iftrue,definition,
% 2.99/1.58 ( iftrue
% 2.99/1.58 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ! [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ A )
% 2.99/1.58 => ( Xphi
% 2.99/1.58 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 2.99/1.58 = Xx ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(iffalse_type,type,
% 2.99/1.58 iffalse: $o ).
% 2.99/1.58
% 2.99/1.58 thf(iffalse,definition,
% 2.99/1.58 ( iffalse
% 2.99/1.58 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ! [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ A )
% 2.99/1.58 => ( ~ Xphi
% 2.99/1.58 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 2.99/1.58 = Xy ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(iftrueorfalse_type,type,
% 2.99/1.58 iftrueorfalse: $o ).
% 2.99/1.58
% 2.99/1.58 thf(iftrueorfalse,definition,
% 2.99/1.58 ( iftrueorfalse
% 2.99/1.58 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ! [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ A )
% 2.99/1.58 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(binintersectT_lem_type,type,
% 2.99/1.58 binintersectT_lem: $o ).
% 2.99/1.58
% 2.99/1.58 thf(binintersectT_lem,definition,
% 2.99/1.58 ( binintersectT_lem
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(binunionT_lem_type,type,
% 2.99/1.58 binunionT_lem: $o ).
% 2.99/1.58
% 2.99/1.58 thf(binunionT_lem,definition,
% 2.99/1.58 ( binunionT_lem
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(powersetT_lem_type,type,
% 2.99/1.58 powersetT_lem: $o ).
% 2.99/1.58
% 2.99/1.58 thf(powersetT_lem,definition,
% 2.99/1.58 ( powersetT_lem
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(setminusT_lem_type,type,
% 2.99/1.58 setminusT_lem: $o ).
% 2.99/1.58
% 2.99/1.58 thf(setminusT_lem,definition,
% 2.99/1.58 ( setminusT_lem
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(complementT_lem_type,type,
% 2.99/1.58 complementT_lem: $o ).
% 2.99/1.58
% 2.99/1.58 thf(complementT_lem,definition,
% 2.99/1.58 ( complementT_lem
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(setextT_type,type,
% 2.99/1.58 setextT: $o ).
% 2.99/1.58
% 2.99/1.58 thf(setextT,definition,
% 2.99/1.58 ( setextT
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ( ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ( in @ Xx @ X )
% 2.99/1.58 => ( in @ Xx @ Y ) ) )
% 2.99/1.58 => ( ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ( in @ Xx @ Y )
% 2.99/1.58 => ( in @ Xx @ X ) ) )
% 2.99/1.58 => ( X = Y ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(subsetTI_type,type,
% 2.99/1.58 subsetTI: $o ).
% 2.99/1.58
% 2.99/1.58 thf(subsetTI,definition,
% 2.99/1.58 ( subsetTI
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ( ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ( in @ Xx @ X )
% 2.99/1.58 => ( in @ Xx @ Y ) ) )
% 2.99/1.58 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(powersetTI1_type,type,
% 2.99/1.58 powersetTI1: $o ).
% 2.99/1.58
% 2.99/1.58 thf(powersetTI1,definition,
% 2.99/1.58 ( powersetTI1
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ( ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ( in @ Xx @ X )
% 2.99/1.58 => ( in @ Xx @ Y ) ) )
% 2.99/1.58 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(powersetTE1_type,type,
% 2.99/1.58 powersetTE1: $o ).
% 2.99/1.58
% 2.99/1.58 thf(powersetTE1,definition,
% 2.99/1.58 ( powersetTE1
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ( in @ X @ ( powerset @ Y ) )
% 2.99/1.58 => ( ( in @ Xx @ X )
% 2.99/1.58 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(complementTI1_type,type,
% 2.99/1.58 complementTI1: $o ).
% 2.99/1.58
% 2.99/1.58 thf(complementTI1,definition,
% 2.99/1.58 ( complementTI1
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ( in @ Xx @ X )
% 2.99/1.58 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(complementTE1_type,type,
% 2.99/1.58 complementTE1: $o ).
% 2.99/1.58
% 2.99/1.58 thf(complementTE1,definition,
% 2.99/1.58 ( complementTE1
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 2.99/1.58 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(binintersectTELcontra_type,type,
% 2.99/1.58 binintersectTELcontra: $o ).
% 2.99/1.58
% 2.99/1.58 thf(binintersectTELcontra,definition,
% 2.99/1.58 ( binintersectTELcontra
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ~ ( in @ Xx @ X )
% 2.99/1.58 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(binintersectTERcontra_type,type,
% 2.99/1.58 binintersectTERcontra: $o ).
% 2.99/1.58
% 2.99/1.58 thf(binintersectTERcontra,definition,
% 2.99/1.58 ( binintersectTERcontra
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ~ ( in @ Xx @ Y )
% 2.99/1.58 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(contrasubsetT_type,type,
% 2.99/1.58 contrasubsetT: $o ).
% 2.99/1.58
% 2.99/1.58 thf(contrasubsetT,definition,
% 2.99/1.58 ( contrasubsetT
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 2.99/1.58 => ( ( in @ Xx @ Y )
% 2.99/1.58 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(contrasubsetT1_type,type,
% 2.99/1.58 contrasubsetT1: $o ).
% 2.99/1.58
% 2.99/1.58 thf(contrasubsetT1,definition,
% 2.99/1.58 ( contrasubsetT1
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ( subset @ X @ Y )
% 2.99/1.58 => ( ~ ( in @ Xx @ Y )
% 2.99/1.58 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(contrasubsetT2_type,type,
% 2.99/1.58 contrasubsetT2: $o ).
% 2.99/1.58
% 2.99/1.58 thf(contrasubsetT2,definition,
% 2.99/1.58 ( contrasubsetT2
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ( ( subset @ X @ Y )
% 2.99/1.58 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(contrasubsetT3_type,type,
% 2.99/1.58 contrasubsetT3: $o ).
% 2.99/1.58
% 2.99/1.58 thf(contrasubsetT3,definition,
% 2.99/1.58 ( contrasubsetT3
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 2.99/1.58 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(doubleComplementI1_type,type,
% 2.99/1.58 doubleComplementI1: $o ).
% 2.99/1.58
% 2.99/1.58 thf(doubleComplementI1,definition,
% 2.99/1.58 ( doubleComplementI1
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ( in @ Xx @ X )
% 2.99/1.58 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(doubleComplementE1_type,type,
% 2.99/1.58 doubleComplementE1: $o ).
% 2.99/1.58
% 2.99/1.58 thf(doubleComplementE1,definition,
% 2.99/1.58 ( doubleComplementE1
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 2.99/1.58 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(doubleComplementSub1_type,type,
% 2.99/1.58 doubleComplementSub1: $o ).
% 2.99/1.58
% 2.99/1.58 thf(doubleComplementSub1,definition,
% 2.99/1.58 ( doubleComplementSub1
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(doubleComplementSub2_type,type,
% 2.99/1.58 doubleComplementSub2: $o ).
% 2.99/1.58
% 2.99/1.58 thf(doubleComplementSub2,definition,
% 2.99/1.58 ( doubleComplementSub2
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(doubleComplementEq_type,type,
% 2.99/1.58 doubleComplementEq: $o ).
% 2.99/1.58
% 2.99/1.58 thf(doubleComplementEq,definition,
% 2.99/1.58 ( doubleComplementEq
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ( X
% 2.99/1.58 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(complementTnotintersectT_type,type,
% 2.99/1.58 complementTnotintersectT: $o ).
% 2.99/1.58
% 2.99/1.58 thf(complementTnotintersectT,definition,
% 2.99/1.58 ( complementTnotintersectT
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 2.99/1.58 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(complementImpComplementIntersect_type,type,
% 2.99/1.58 complementImpComplementIntersect: $o ).
% 2.99/1.58
% 2.99/1.58 thf(complementImpComplementIntersect,definition,
% 2.99/1.58 ( complementImpComplementIntersect
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 2.99/1.58 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(complementSubsetComplementIntersect_type,type,
% 2.99/1.58 complementSubsetComplementIntersect: $o ).
% 2.99/1.58
% 2.99/1.58 thf(complementSubsetComplementIntersect,definition,
% 2.99/1.58 ( complementSubsetComplementIntersect
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(complementInPowersetComplementIntersect_type,type,
% 2.99/1.58 complementInPowersetComplementIntersect: $o ).
% 2.99/1.58
% 2.99/1.58 thf(complementInPowersetComplementIntersect,definition,
% 2.99/1.58 ( complementInPowersetComplementIntersect
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(contraSubsetComplement_type,type,
% 2.99/1.58 contraSubsetComplement: $o ).
% 2.99/1.58
% 2.99/1.58 thf(contraSubsetComplement,definition,
% 2.99/1.58 ( contraSubsetComplement
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ( in @ Xx @ Y )
% 2.99/1.58 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(complementTcontraSubset_type,type,
% 2.99/1.58 complementTcontraSubset: $o ).
% 2.99/1.58
% 2.99/1.58 thf(complementTcontraSubset,definition,
% 2.99/1.58 ( complementTcontraSubset
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 2.99/1.58 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(binunionTILcontra_type,type,
% 2.99/1.58 binunionTILcontra: $o ).
% 2.99/1.58
% 2.99/1.58 thf(binunionTILcontra,definition,
% 2.99/1.58 ( binunionTILcontra
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 2.99/1.58 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(binunionTIRcontra_type,type,
% 2.99/1.58 binunionTIRcontra: $o ).
% 2.99/1.58
% 2.99/1.58 thf(binunionTIRcontra,definition,
% 2.99/1.58 ( binunionTIRcontra
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 2.99/1.58 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(inIntersectImpInUnion_type,type,
% 2.99/1.58 inIntersectImpInUnion: $o ).
% 2.99/1.58
% 2.99/1.58 thf(inIntersectImpInUnion,definition,
% 2.99/1.58 ( inIntersectImpInUnion
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ! [Z: $i] :
% 2.99/1.58 ( ( in @ Z @ ( powerset @ A ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 2.99/1.58 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(inIntersectImpInUnion2_type,type,
% 2.99/1.58 inIntersectImpInUnion2: $o ).
% 2.99/1.58
% 2.99/1.58 thf(inIntersectImpInUnion2,definition,
% 2.99/1.58 ( inIntersectImpInUnion2
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ! [Z: $i] :
% 2.99/1.58 ( ( in @ Z @ ( powerset @ A ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 2.99/1.58 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(inIntersectImpInIntersectUnions_type,type,
% 2.99/1.58 inIntersectImpInIntersectUnions: $o ).
% 2.99/1.58
% 2.99/1.58 thf(inIntersectImpInIntersectUnions,definition,
% 2.99/1.58 ( inIntersectImpInIntersectUnions
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ! [Z: $i] :
% 2.99/1.58 ( ( in @ Z @ ( powerset @ A ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 2.99/1.58 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(intersectInPowersetIntersectUnions_type,type,
% 2.99/1.58 intersectInPowersetIntersectUnions: $o ).
% 2.99/1.58
% 2.99/1.58 thf(intersectInPowersetIntersectUnions,definition,
% 2.99/1.58 ( intersectInPowersetIntersectUnions
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ! [Z: $i] :
% 2.99/1.58 ( ( in @ Z @ ( powerset @ A ) )
% 2.99/1.58 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(inComplementUnionImpNotIn1_type,type,
% 2.99/1.58 inComplementUnionImpNotIn1: $o ).
% 2.99/1.58
% 2.99/1.58 thf(inComplementUnionImpNotIn1,definition,
% 2.99/1.58 ( inComplementUnionImpNotIn1
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.99/1.58 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(inComplementUnionImpInComplement1_type,type,
% 2.99/1.58 inComplementUnionImpInComplement1: $o ).
% 2.99/1.58
% 2.99/1.58 thf(inComplementUnionImpInComplement1,definition,
% 2.99/1.58 ( inComplementUnionImpInComplement1
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.99/1.58 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(binunionTE_type,type,
% 2.99/1.58 binunionTE: $o ).
% 2.99/1.58
% 2.99/1.58 thf(binunionTE,definition,
% 2.99/1.58 ( binunionTE
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ! [Xphi: $o,Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 2.99/1.58 => ( ( ( in @ Xx @ X )
% 2.99/1.58 => Xphi )
% 2.99/1.58 => ( ( ( in @ Xx @ Y )
% 2.99/1.58 => Xphi )
% 2.99/1.58 => Xphi ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(binunionTEcontra_type,type,
% 2.99/1.58 binunionTEcontra: $o ).
% 2.99/1.58
% 2.99/1.58 thf(binunionTEcontra,definition,
% 2.99/1.58 ( binunionTEcontra
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ~ ( in @ Xx @ X )
% 2.99/1.58 => ( ~ ( in @ Xx @ Y )
% 2.99/1.58 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(demorgan2a1_type,type,
% 2.99/1.58 demorgan2a1: $o ).
% 2.99/1.58
% 2.99/1.58 thf(demorgan2a1,definition,
% 2.99/1.58 ( demorgan2a1
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.99/1.58 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(complementUnionInPowersetComplement_type,type,
% 2.99/1.58 complementUnionInPowersetComplement: $o ).
% 2.99/1.58
% 2.99/1.58 thf(complementUnionInPowersetComplement,definition,
% 2.99/1.58 ( complementUnionInPowersetComplement
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(demorgan2a2_type,type,
% 2.99/1.58 demorgan2a2: $o ).
% 2.99/1.58
% 2.99/1.58 thf(demorgan2a2,definition,
% 2.99/1.58 ( demorgan2a2
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.99/1.58 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(demorgan1a_type,type,
% 2.99/1.58 demorgan1a: $o ).
% 2.99/1.58
% 2.99/1.58 thf(demorgan1a,definition,
% 2.99/1.58 ( demorgan1a
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 2.99/1.58 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(demorgan1b_type,type,
% 2.99/1.58 demorgan1b: $o ).
% 2.99/1.58
% 2.99/1.58 thf(demorgan1b,definition,
% 2.99/1.58 ( demorgan1b
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 2.99/1.58 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(demorgan1_type,type,
% 2.99/1.58 demorgan1: $o ).
% 2.99/1.58
% 2.99/1.58 thf(demorgan1,definition,
% 2.99/1.58 ( demorgan1
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 2.99/1.58 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(demorgan2a_type,type,
% 2.99/1.58 demorgan2a: $o ).
% 2.99/1.58
% 2.99/1.58 thf(demorgan2a,definition,
% 2.99/1.58 ( demorgan2a
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.99/1.58 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(demorgan2b2_type,type,
% 2.99/1.58 demorgan2b2: $o ).
% 2.99/1.58
% 2.99/1.58 thf(demorgan2b2,definition,
% 2.99/1.58 ( demorgan2b2
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 2.99/1.58 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 2.99/1.58 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(demorgan2b_type,type,
% 2.99/1.58 demorgan2b: $o ).
% 2.99/1.58
% 2.99/1.58 thf(demorgan2b,definition,
% 2.99/1.58 ( demorgan2b
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 2.99/1.58 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(demorgan2_type,type,
% 2.99/1.58 demorgan2: $o ).
% 2.99/1.58
% 2.99/1.58 thf(demorgan2,definition,
% 2.99/1.58 ( demorgan2
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 2.99/1.58 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(woz13rule0_type,type,
% 2.99/1.58 woz13rule0: $o ).
% 2.99/1.58
% 2.99/1.58 thf(woz13rule0,definition,
% 2.99/1.58 ( woz13rule0
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 2.99/1.58 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(woz13rule1_type,type,
% 2.99/1.58 woz13rule1: $o ).
% 2.99/1.58
% 2.99/1.58 thf(woz13rule1,definition,
% 2.99/1.58 ( woz13rule1
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ! [Z: $i] :
% 2.99/1.58 ( ( in @ Z @ ( powerset @ A ) )
% 2.99/1.58 => ( ( subset @ X @ Z )
% 2.99/1.58 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(woz13rule2_type,type,
% 2.99/1.58 woz13rule2: $o ).
% 2.99/1.58
% 2.99/1.58 thf(woz13rule2,definition,
% 2.99/1.58 ( woz13rule2
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ! [Z: $i] :
% 2.99/1.58 ( ( in @ Z @ ( powerset @ A ) )
% 2.99/1.58 => ( ( subset @ Y @ Z )
% 2.99/1.58 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(woz13rule3_type,type,
% 2.99/1.58 woz13rule3: $o ).
% 2.99/1.58
% 2.99/1.58 thf(woz13rule3,definition,
% 2.99/1.58 ( woz13rule3
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ! [Z: $i] :
% 2.99/1.58 ( ( in @ Z @ ( powerset @ A ) )
% 2.99/1.58 => ( ( subset @ X @ Y )
% 2.99/1.58 => ( ( subset @ X @ Z )
% 2.99/1.58 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(woz13rule4_type,type,
% 2.99/1.58 woz13rule4: $o ).
% 2.99/1.58
% 2.99/1.58 thf(woz13rule4,definition,
% 2.99/1.58 ( woz13rule4
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ! [Z: $i] :
% 2.99/1.58 ( ( in @ Z @ ( powerset @ A ) )
% 2.99/1.58 => ! [W: $i] :
% 2.99/1.58 ( ( in @ W @ ( powerset @ A ) )
% 2.99/1.58 => ( ( subset @ X @ Z )
% 2.99/1.58 => ( ( subset @ Y @ W )
% 2.99/1.58 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(woz1_1_type,type,
% 2.99/1.58 woz1_1: $o ).
% 2.99/1.58
% 2.99/1.58 thf(woz1_1,definition,
% 2.99/1.58 ( woz1_1
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(woz1_2_type,type,
% 2.99/1.58 woz1_2: $o ).
% 2.99/1.58
% 2.99/1.58 thf(woz1_2,definition,
% 2.99/1.58 ( woz1_2
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ! [Z: $i] :
% 2.99/1.58 ( ( in @ Z @ ( powerset @ A ) )
% 2.99/1.58 => ! [W: $i] :
% 2.99/1.58 ( ( in @ W @ ( powerset @ A ) )
% 2.99/1.58 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 2.99/1.58 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(woz1_3_type,type,
% 2.99/1.58 woz1_3: $o ).
% 2.99/1.58
% 2.99/1.58 thf(woz1_3,definition,
% 2.99/1.58 ( woz1_3
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ! [Z: $i] :
% 2.99/1.58 ( ( in @ Z @ ( powerset @ A ) )
% 2.99/1.58 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(woz1_4_type,type,
% 2.99/1.58 woz1_4: $o ).
% 2.99/1.58
% 2.99/1.58 thf(woz1_4,definition,
% 2.99/1.58 ( woz1_4
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 2.99/1.58 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(woz1_5_type,type,
% 2.99/1.58 woz1_5: $o ).
% 2.99/1.58
% 2.99/1.58 thf(woz1_5,definition,
% 2.99/1.58 ( woz1_5
% 2.99/1.58 = ( ! [A: $i,X: $i] :
% 2.99/1.58 ( ( in @ X @ ( powerset @ A ) )
% 2.99/1.58 => ! [Y: $i] :
% 2.99/1.58 ( ( in @ Y @ ( powerset @ A ) )
% 2.99/1.58 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(breln1_type,type,
% 2.99/1.58 breln1: $i > $i > $o ).
% 2.99/1.58
% 2.99/1.58 thf(breln1,definition,
% 2.99/1.58 ( breln1
% 2.99/1.58 = ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(breln1all2_type,type,
% 2.99/1.58 breln1all2: $o ).
% 2.99/1.58
% 2.99/1.58 thf(breln1all2,definition,
% 2.99/1.58 ( breln1all2
% 2.99/1.58 = ( ! [A: $i,R: $i] :
% 2.99/1.58 ( ( breln1 @ A @ R )
% 2.99/1.58 => ! [Xphi: $i > $o] :
% 2.99/1.58 ( ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ! [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ A )
% 2.99/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.99/1.58 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ R )
% 2.99/1.58 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(breln1Set_type,type,
% 2.99/1.58 breln1Set: $i > $i ).
% 2.99/1.58
% 2.99/1.58 thf(breln1SetBreln1_type,type,
% 2.99/1.58 breln1SetBreln1: $o ).
% 2.99/1.58
% 2.99/1.58 thf(breln1SetBreln1,definition,
% 2.99/1.58 ( breln1SetBreln1
% 2.99/1.58 = ( ! [A: $i,R: $i] :
% 2.99/1.58 ( ( in @ R @ ( breln1Set @ A ) )
% 2.99/1.58 => ( breln1 @ A @ R ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(transitive_type,type,
% 2.99/1.58 transitive: $i > $i > $o ).
% 2.99/1.58
% 2.99/1.58 thf(antisymmetric_type,type,
% 2.99/1.58 antisymmetric: $i > $i > $o ).
% 2.99/1.58
% 2.99/1.58 thf(reflexive_type,type,
% 2.99/1.58 reflexive: $i > $i > $o ).
% 2.99/1.58
% 2.99/1.58 thf(refltransitive_type,type,
% 2.99/1.58 refltransitive: $i > $i > $o ).
% 2.99/1.58
% 2.99/1.58 thf(refllinearorder_type,type,
% 2.99/1.58 refllinearorder: $i > $i > $o ).
% 2.99/1.58
% 2.99/1.58 thf(reflwellordering_type,type,
% 2.99/1.58 reflwellordering: $i > $i > $o ).
% 2.99/1.58
% 2.99/1.58 thf(choice2fnsingleton_type,type,
% 2.99/1.58 choice2fnsingleton: $o ).
% 2.99/1.58
% 2.99/1.58 thf(choice2fnsingleton,definition,
% 2.99/1.58 ( choice2fnsingleton
% 2.99/1.58 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.99/1.58 ( ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ? [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ B )
% 2.99/1.58 & ( Xphi @ Xx @ Xy ) ) )
% 2.99/1.58 => ! [R: $i] :
% 2.99/1.58 ( ( in @ R @ ( breln1Set @ B ) )
% 2.99/1.58 => ( ( reflwellordering @ B @ R )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ( singleton
% 2.99/1.58 @ ( dsetconstr @ B
% 2.99/1.58 @ ^ [Xy: $i] :
% 2.99/1.58 ( ( Xphi @ Xx @ Xy )
% 2.99/1.58 & ! [Xz: $i] :
% 2.99/1.58 ( ( in @ Xz @ B )
% 2.99/1.58 => ( ( Xphi @ Xx @ Xz )
% 2.99/1.58 => ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(setOfPairsIsBReln1_type,type,
% 2.99/1.58 setOfPairsIsBReln1: $o ).
% 2.99/1.58
% 2.99/1.58 thf(setOfPairsIsBReln1,definition,
% 2.99/1.58 ( setOfPairsIsBReln1
% 2.99/1.58 = ( ! [A: $i,Xphi: $i > $i > $o] :
% 2.99/1.58 ( breln1 @ A
% 2.99/1.58 @ ( dpsetconstr @ A @ A
% 2.99/1.58 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(breln1all1_type,type,
% 2.99/1.58 breln1all1: $o ).
% 2.99/1.58
% 2.99/1.58 thf(breln1all1,definition,
% 2.99/1.58 ( breln1all1
% 2.99/1.58 = ( ! [A: $i,R: $i] :
% 2.99/1.58 ( ( breln1 @ A @ R )
% 2.99/1.58 => ! [Xphi: $i > $o] :
% 2.99/1.58 ( ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ! [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ A )
% 2.99/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.99/1.58 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ R )
% 2.99/1.58 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(subbreln1_type,type,
% 2.99/1.58 subbreln1: $o ).
% 2.99/1.58
% 2.99/1.58 thf(subbreln1,definition,
% 2.99/1.58 ( subbreln1
% 2.99/1.58 = ( ! [A: $i,R: $i] :
% 2.99/1.58 ( ( breln1 @ A @ R )
% 2.99/1.58 => ! [S: $i] :
% 2.99/1.58 ( ( breln1 @ A @ S )
% 2.99/1.58 => ( ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ! [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ A )
% 2.99/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.99/1.58 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 2.99/1.58 => ( subset @ R @ S ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(eqbreln1_type,type,
% 2.99/1.58 eqbreln1: $o ).
% 2.99/1.58
% 2.99/1.58 thf(eqbreln1,definition,
% 2.99/1.58 ( eqbreln1
% 2.99/1.58 = ( ! [A: $i,R: $i] :
% 2.99/1.58 ( ( breln1 @ A @ R )
% 2.99/1.58 => ! [S: $i] :
% 2.99/1.58 ( ( breln1 @ A @ S )
% 2.99/1.58 => ( ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ! [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ A )
% 2.99/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.99/1.58 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 2.99/1.58 => ( ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ! [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ A )
% 2.99/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 2.99/1.58 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 2.99/1.58 => ( R = S ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(breln1invset_type,type,
% 2.99/1.58 breln1invset: $i > $i > $i ).
% 2.99/1.58
% 2.99/1.58 thf(breln1invprop_type,type,
% 2.99/1.58 breln1invprop: $o ).
% 2.99/1.58
% 2.99/1.58 thf(breln1invprop,definition,
% 2.99/1.58 ( breln1invprop
% 2.99/1.58 = ( ! [A: $i,R: $i] :
% 2.99/1.58 ( ( breln1 @ A @ R )
% 2.99/1.58 => ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(breln1invI_type,type,
% 2.99/1.58 breln1invI: $o ).
% 2.99/1.58
% 2.99/1.58 thf(breln1invI,definition,
% 2.99/1.58 ( breln1invI
% 2.99/1.58 = ( ! [A: $i,R: $i] :
% 2.99/1.58 ( ( breln1 @ A @ R )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ! [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ A )
% 2.99/1.58 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.99/1.58 => ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(breln1invE_type,type,
% 2.99/1.58 breln1invE: $o ).
% 2.99/1.58
% 2.99/1.58 thf(breln1invE,definition,
% 2.99/1.58 ( breln1invE
% 2.99/1.58 = ( ! [A: $i,R: $i] :
% 2.99/1.58 ( ( breln1 @ A @ R )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ! [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ A )
% 2.99/1.58 => ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
% 2.99/1.58 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(breln1compset_type,type,
% 2.99/1.58 breln1compset: $i > $i > $i > $i ).
% 2.99/1.58
% 2.99/1.58 thf(breln1compset,definition,
% 2.99/1.58 ( breln1compset
% 2.99/1.58 = ( ^ [A: $i,R: $i,S: $i] :
% 2.99/1.58 ( dpsetconstr @ A @ A
% 2.99/1.58 @ ^ [Xx: $i,Xy: $i] :
% 2.99/1.58 ? [Xz: $i] :
% 2.99/1.58 ( ( in @ Xz @ A )
% 2.99/1.58 & ( in @ ( kpair @ Xx @ Xz ) @ R )
% 2.99/1.58 & ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(breln1compprop_type,type,
% 2.99/1.58 breln1compprop: $o ).
% 2.99/1.58
% 2.99/1.58 thf(breln1compprop,definition,
% 2.99/1.58 ( breln1compprop
% 2.99/1.58 = ( ! [A: $i,R: $i] :
% 2.99/1.58 ( ( breln1 @ A @ R )
% 2.99/1.58 => ! [S: $i] :
% 2.99/1.58 ( ( breln1 @ A @ S )
% 2.99/1.58 => ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ).
% 2.99/1.58
% 2.99/1.58 thf(breln1compI,conjecture,
% 2.99/1.58 ( setextAx
% 2.99/1.58 => ( emptysetAx
% 2.99/1.58 => ( setadjoinAx
% 2.99/1.58 => ( powersetAx
% 2.99/1.58 => ( setunionAx
% 2.99/1.58 => ( omega0Ax
% 2.99/1.58 => ( omegaSAx
% 2.99/1.58 => ( omegaIndAx
% 2.99/1.58 => ( replAx
% 2.99/1.58 => ( foundationAx
% 2.99/1.58 => ( wellorderingAx
% 2.99/1.58 => ( descrp
% 2.99/1.58 => ( dsetconstrI
% 2.99/1.58 => ( dsetconstrEL
% 2.99/1.58 => ( dsetconstrER
% 2.99/1.58 => ( exuE1
% 2.99/1.58 => ( prop2setE
% 2.99/1.58 => ( emptysetE
% 2.99/1.58 => ( emptysetimpfalse
% 2.99/1.58 => ( notinemptyset
% 2.99/1.58 => ( exuE3e
% 2.99/1.58 => ( setext
% 2.99/1.58 => ( emptyI
% 2.99/1.58 => ( noeltsimpempty
% 2.99/1.58 => ( setbeta
% 2.99/1.58 => ( nonemptyE1
% 2.99/1.58 => ( nonemptyI
% 2.99/1.58 => ( nonemptyI1
% 2.99/1.58 => ( setadjoinIL
% 2.99/1.58 => ( emptyinunitempty
% 2.99/1.58 => ( setadjoinIR
% 2.99/1.58 => ( setadjoinE
% 2.99/1.58 => ( setadjoinOr
% 2.99/1.58 => ( setoftrueEq
% 2.99/1.58 => ( powersetI
% 2.99/1.58 => ( emptyinPowerset
% 2.99/1.58 => ( emptyInPowerset
% 2.99/1.58 => ( powersetE
% 2.99/1.58 => ( setunionI
% 2.99/1.58 => ( setunionE
% 2.99/1.58 => ( subPowSU
% 2.99/1.58 => ( exuE2
% 2.99/1.58 => ( nonemptyImpWitness
% 2.99/1.58 => ( uniqinunit
% 2.99/1.58 => ( notinsingleton
% 2.99/1.58 => ( eqinunit
% 2.99/1.58 => ( singletonsswitch
% 2.99/1.58 => ( upairsetE
% 2.99/1.58 => ( upairsetIL
% 2.99/1.58 => ( upairsetIR
% 2.99/1.58 => ( emptyE1
% 2.99/1.58 => ( vacuousDall
% 2.99/1.58 => ( quantDeMorgan1
% 2.99/1.58 => ( quantDeMorgan2
% 2.99/1.58 => ( quantDeMorgan3
% 2.99/1.58 => ( quantDeMorgan4
% 2.99/1.58 => ( prop2setI
% 2.99/1.58 => ( prop2set2propI
% 2.99/1.58 => ( notdexE
% 2.99/1.58 => ( notdallE
% 2.99/1.58 => ( exuI1
% 2.99/1.58 => ( exuI3
% 2.99/1.58 => ( exuI2
% 2.99/1.58 => ( inCongP
% 2.99/1.58 => ( in__Cong
% 2.99/1.58 => ( exuE3u
% 2.99/1.58 => ( exu__Cong
% 2.99/1.58 => ( emptyset__Cong
% 2.99/1.58 => ( setadjoin__Cong
% 2.99/1.58 => ( powerset__Cong
% 2.99/1.58 => ( setunion__Cong
% 2.99/1.58 => ( omega__Cong
% 2.99/1.58 => ( exuEu
% 2.99/1.58 => ( descr__Cong
% 2.99/1.58 => ( dsetconstr__Cong
% 2.99/1.58 => ( subsetI1
% 2.99/1.58 => ( eqimpsubset2
% 2.99/1.58 => ( eqimpsubset1
% 2.99/1.58 => ( subsetI2
% 2.99/1.58 => ( emptysetsubset
% 2.99/1.58 => ( subsetE
% 2.99/1.58 => ( subsetE2
% 2.99/1.58 => ( notsubsetI
% 2.99/1.58 => ( notequalI1
% 2.99/1.58 => ( notequalI2
% 2.99/1.58 => ( subsetRefl
% 2.99/1.58 => ( subsetTrans
% 2.99/1.58 => ( setadjoinSub
% 2.99/1.58 => ( setadjoinSub2
% 2.99/1.58 => ( subset2powerset
% 2.99/1.58 => ( setextsub
% 2.99/1.58 => ( subsetemptysetimpeq
% 2.99/1.58 => ( powersetI1
% 2.99/1.58 => ( powersetE1
% 2.99/1.58 => ( inPowerset
% 2.99/1.58 => ( powersetsubset
% 2.99/1.58 => ( sepInPowerset
% 2.99/1.58 => ( sepSubset
% 2.99/1.58 => ( binunionIL
% 2.99/1.58 => ( upairset2IR
% 2.99/1.58 => ( binunionIR
% 2.99/1.58 => ( binunionEcases
% 2.99/1.58 => ( binunionE
% 2.99/1.58 => ( binunionLsub
% 2.99/1.58 => ( binunionRsub
% 2.99/1.58 => ( binintersectI
% 2.99/1.58 => ( binintersectSubset5
% 2.99/1.58 => ( binintersectEL
% 2.99/1.58 => ( binintersectLsub
% 2.99/1.58 => ( binintersectSubset2
% 2.99/1.58 => ( binintersectSubset3
% 2.99/1.58 => ( binintersectER
% 2.99/1.58 => ( disjointsetsI1
% 2.99/1.58 => ( binintersectRsub
% 2.99/1.58 => ( binintersectSubset4
% 2.99/1.58 => ( binintersectSubset1
% 2.99/1.58 => ( bs114d
% 2.99/1.58 => ( setminusI
% 2.99/1.58 => ( setminusEL
% 2.99/1.58 => ( setminusER
% 2.99/1.58 => ( setminusSubset2
% 2.99/1.58 => ( setminusERneg
% 2.99/1.58 => ( setminusELneg
% 2.99/1.58 => ( setminusILneg
% 2.99/1.58 => ( setminusIRneg
% 2.99/1.58 => ( setminusLsub
% 2.99/1.58 => ( setminusSubset1
% 2.99/1.58 => ( symdiffE
% 2.99/1.58 => ( symdiffI1
% 2.99/1.58 => ( symdiffI2
% 2.99/1.58 => ( symdiffIneg1
% 2.99/1.58 => ( symdiffIneg2
% 2.99/1.58 => ( secondinupair
% 2.99/1.58 => ( setukpairIL
% 2.99/1.58 => ( setukpairIR
% 2.99/1.58 => ( kpairiskpair
% 2.99/1.58 => ( kpairp
% 2.99/1.58 => ( singletonsubset
% 2.99/1.58 => ( singletoninpowerset
% 2.99/1.58 => ( singletoninpowunion
% 2.99/1.58 => ( upairset2E
% 2.99/1.58 => ( upairsubunion
% 2.99/1.58 => ( upairinpowunion
% 2.99/1.58 => ( ubforcartprodlem1
% 2.99/1.58 => ( ubforcartprodlem2
% 2.99/1.58 => ( ubforcartprodlem3
% 2.99/1.58 => ( cartprodpairin
% 2.99/1.58 => ( cartprodmempair1
% 2.99/1.58 => ( cartprodmempair
% 2.99/1.58 => ( setunionE2
% 2.99/1.58 => ( setunionsingleton1
% 2.99/1.58 => ( setunionsingleton2
% 2.99/1.58 => ( setunionsingleton
% 2.99/1.58 => ( singletonprop
% 2.99/1.58 => ( ex1E1
% 2.99/1.58 => ( ex1I
% 2.99/1.58 => ( ex1I2
% 2.99/1.58 => ( singletonsuniq
% 2.99/1.58 => ( setukpairinjL1
% 2.99/1.58 => ( kfstsingleton
% 2.99/1.58 => ( theprop
% 2.99/1.58 => ( kfstpairEq
% 2.99/1.58 => ( cartprodfstin
% 2.99/1.58 => ( setukpairinjL2
% 2.99/1.58 => ( setukpairinjL
% 2.99/1.58 => ( setukpairinjR11
% 2.99/1.58 => ( setukpairinjR12
% 2.99/1.58 => ( setukpairinjR1
% 2.99/1.58 => ( upairequniteq
% 2.99/1.58 => ( setukpairinjR2
% 2.99/1.58 => ( setukpairinjR
% 2.99/1.58 => ( ksndsingleton
% 2.99/1.58 => ( ksndpairEq
% 2.99/1.58 => ( kpairsurjEq
% 2.99/1.58 => ( cartprodsndin
% 2.99/1.58 => ( cartprodpairmemEL
% 2.99/1.58 => ( cartprodpairmemER
% 2.99/1.58 => ( cartprodmempaircEq
% 2.99/1.58 => ( cartprodfstpairEq
% 2.99/1.58 => ( cartprodsndpairEq
% 2.99/1.58 => ( cartprodpairsurjEq
% 2.99/1.58 => ( dpsetconstrI
% 2.99/1.58 => ( dpsetconstrSub
% 2.99/1.58 => ( setOfPairsIsBReln
% 2.99/1.58 => ( dpsetconstrERa
% 2.99/1.58 => ( dpsetconstrEL1
% 2.99/1.58 => ( dpsetconstrEL2
% 2.99/1.58 => ( dpsetconstrER
% 2.99/1.58 => ( funcImageSingleton
% 2.99/1.58 => ( apProp
% 2.99/1.58 => ( app
% 2.99/1.58 => ( infuncsetfunc
% 2.99/1.58 => ( ap2p
% 2.99/1.58 => ( funcinfuncset
% 2.99/1.58 => ( lamProp
% 2.99/1.58 => ( lamp
% 2.99/1.58 => ( lam2p
% 2.99/1.58 => ( brelnall1
% 2.99/1.58 => ( brelnall2
% 2.99/1.58 => ( ex1E2
% 2.99/1.58 => ( funcGraphProp1
% 2.99/1.58 => ( funcGraphProp3
% 2.99/1.58 => ( funcGraphProp2
% 2.99/1.58 => ( funcextLem
% 2.99/1.58 => ( funcGraphProp4
% 2.99/1.58 => ( subbreln
% 2.99/1.58 => ( eqbreln
% 2.99/1.58 => ( funcext
% 2.99/1.58 => ( funcext2
% 2.99/1.58 => ( ap2apEq1
% 2.99/1.58 => ( ap2apEq2
% 2.99/1.58 => ( beta1
% 2.99/1.58 => ( eta1
% 2.99/1.58 => ( lam2lamEq
% 2.99/1.58 => ( beta2
% 2.99/1.58 => ( eta2
% 2.99/1.58 => ( iffalseProp1
% 2.99/1.58 => ( iffalseProp2
% 2.99/1.58 => ( iftrueProp1
% 2.99/1.58 => ( iftrueProp2
% 2.99/1.58 => ( ifSingleton
% 2.99/1.58 => ( ifp
% 2.99/1.58 => ( theeq
% 2.99/1.58 => ( iftrue
% 2.99/1.58 => ( iffalse
% 2.99/1.58 => ( iftrueorfalse
% 2.99/1.58 => ( binintersectT_lem
% 2.99/1.58 => ( binunionT_lem
% 2.99/1.58 => ( powersetT_lem
% 2.99/1.58 => ( setminusT_lem
% 2.99/1.58 => ( complementT_lem
% 2.99/1.58 => ( setextT
% 2.99/1.58 => ( subsetTI
% 2.99/1.58 => ( powersetTI1
% 2.99/1.58 => ( powersetTE1
% 2.99/1.58 => ( complementTI1
% 2.99/1.58 => ( complementTE1
% 2.99/1.58 => ( binintersectTELcontra
% 2.99/1.58 => ( binintersectTERcontra
% 2.99/1.58 => ( contrasubsetT
% 2.99/1.58 => ( contrasubsetT1
% 2.99/1.58 => ( contrasubsetT2
% 2.99/1.58 => ( contrasubsetT3
% 2.99/1.58 => ( doubleComplementI1
% 2.99/1.58 => ( doubleComplementE1
% 2.99/1.58 => ( doubleComplementSub1
% 2.99/1.58 => ( doubleComplementSub2
% 2.99/1.58 => ( doubleComplementEq
% 2.99/1.58 => ( complementTnotintersectT
% 2.99/1.58 => ( complementImpComplementIntersect
% 2.99/1.58 => ( complementSubsetComplementIntersect
% 2.99/1.58 => ( complementInPowersetComplementIntersect
% 2.99/1.58 => ( contraSubsetComplement
% 2.99/1.58 => ( complementTcontraSubset
% 2.99/1.58 => ( binunionTILcontra
% 2.99/1.58 => ( binunionTIRcontra
% 2.99/1.58 => ( inIntersectImpInUnion
% 2.99/1.58 => ( inIntersectImpInUnion2
% 2.99/1.58 => ( inIntersectImpInIntersectUnions
% 2.99/1.58 => ( intersectInPowersetIntersectUnions
% 2.99/1.58 => ( inComplementUnionImpNotIn1
% 2.99/1.58 => ( inComplementUnionImpInComplement1
% 2.99/1.58 => ( binunionTE
% 2.99/1.58 => ( binunionTEcontra
% 2.99/1.58 => ( demorgan2a1
% 2.99/1.58 => ( complementUnionInPowersetComplement
% 2.99/1.58 => ( demorgan2a2
% 2.99/1.58 => ( demorgan1a
% 2.99/1.58 => ( demorgan1b
% 2.99/1.58 => ( demorgan1
% 2.99/1.58 => ( demorgan2a
% 2.99/1.58 => ( demorgan2b2
% 2.99/1.58 => ( demorgan2b
% 2.99/1.58 => ( demorgan2
% 2.99/1.58 => ( woz13rule0
% 2.99/1.58 => ( woz13rule1
% 2.99/1.58 => ( woz13rule2
% 2.99/1.58 => ( woz13rule3
% 2.99/1.58 => ( woz13rule4
% 2.99/1.58 => ( woz1_1
% 2.99/1.58 => ( woz1_2
% 2.99/1.58 => ( woz1_3
% 2.99/1.58 => ( woz1_4
% 2.99/1.58 => ( woz1_5
% 2.99/1.58 => ( breln1all2
% 2.99/1.58 => ( breln1SetBreln1
% 2.99/1.58 => ( choice2fnsingleton
% 2.99/1.58 => ( setOfPairsIsBReln1
% 2.99/1.58 => ( breln1all1
% 2.99/1.58 => ( subbreln1
% 2.99/1.58 => ( eqbreln1
% 2.99/1.58 => ( breln1invprop
% 2.99/1.58 => ( breln1invI
% 2.99/1.58 => ( breln1invE
% 2.99/1.58 => ( breln1compprop
% 2.99/1.58 => ! [A: $i,R: $i] :
% 2.99/1.58 ( ( breln1 @ A @ R )
% 2.99/1.58 => ! [S: $i] :
% 2.99/1.58 ( ( breln1 @ A @ S )
% 2.99/1.58 => ! [Xx: $i] :
% 2.99/1.58 ( ( in @ Xx @ A )
% 2.99/1.58 => ! [Xy: $i] :
% 2.99/1.58 ( ( in @ Xy @ A )
% 2.99/1.58 => ! [Xz: $i] :
% 2.99/1.58 ( ( in @ Xz @ A )
% 2.99/1.58 => ( ( in @ ( kpair @ Xx @ Xz ) @ R )
% 2.99/1.58 => ( ( in @ ( kpair @ Xz @ Xy ) @ S )
% 2.99/1.58 => ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.99/1.58 ------------------------
% 3.13/1.61 % (22924)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_22754 for (2999ds/275Mi)
% 3.13/1.61 % (22919)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_22754 for (2999ds/4Mi)
% 3.13/1.61 % (22922)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22754 for (2999ds/2Mi)
% 3.13/1.61 % (22923)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_22754 for (2999ds/2Mi)
% 3.13/1.61 % (22918)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22754 for (2999ds/183Mi)
% 3.13/1.61 % (22922)Instruction limit reached!
% 3.13/1.61 % (22922)------------------------------
% 3.13/1.61 % (22922)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.61 % (22922)Termination reason: Unknown
% 3.13/1.61 % (22922)Termination phase: shuffling
% 3.13/1.61 % (22923)Instruction limit reached!
% 3.13/1.61 % (22923)------------------------------
% 3.13/1.61 % (22923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.61
% 3.13/1.61 % (22922)Memory used [KB]: 1535
% 3.13/1.61 % (22922)Time elapsed: 0.003 s
% 3.13/1.61 % (22922)Instructions burned: 3 (million)
% 3.13/1.61 % (22922)------------------------------
% 3.13/1.61 % (22922)------------------------------
% 3.13/1.61 % (22923)Termination reason: Unknown
% 3.13/1.61 % (22923)Termination phase: shuffling
% 3.13/1.61
% 3.13/1.61 % (22923)Memory used [KB]: 1535
% 3.13/1.61 % (22923)Time elapsed: 0.003 s
% 3.13/1.61 % (22923)Instructions burned: 3 (million)
% 3.13/1.62 % (22923)------------------------------
% 3.13/1.62 % (22923)------------------------------
% 3.13/1.62 % (22920)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_22754 for (2999ds/27Mi)
% 3.13/1.62 % (22925)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22754 for (2999ds/18Mi)
% 3.13/1.62 % (22919)Instruction limit reached!
% 3.13/1.62 % (22919)------------------------------
% 3.13/1.62 % (22919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.62 % (22919)Termination reason: Unknown
% 3.13/1.62 % (22919)Termination phase: shuffling
% 3.13/1.62
% 3.13/1.62 % (22919)Memory used [KB]: 1535
% 3.13/1.62 % (22919)Time elapsed: 0.004 s
% 3.13/1.62 % (22919)Instructions burned: 5 (million)
% 3.13/1.62 % (22919)------------------------------
% 3.13/1.62 % (22919)------------------------------
% 3.13/1.62 % (22925)Instruction limit reached!
% 3.13/1.62 % (22925)------------------------------
% 3.13/1.62 % (22925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.62 % (22925)Termination reason: Unknown
% 3.13/1.62 % (22925)Termination phase: shuffling
% 3.13/1.63
% 3.13/1.63 % (22925)Memory used [KB]: 1791
% 3.13/1.63 % (22925)Time elapsed: 0.012 s
% 3.13/1.63 % (22925)Instructions burned: 18 (million)
% 3.13/1.63 % (22925)------------------------------
% 3.13/1.63 % (22925)------------------------------
% 3.13/1.63 % (22920)Instruction limit reached!
% 3.13/1.63 % (22920)------------------------------
% 3.13/1.63 % (22920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.63 % (22920)Termination reason: Unknown
% 3.13/1.63 % (22920)Termination phase: shuffling
% 3.13/1.63
% 3.13/1.63 % (22920)Memory used [KB]: 2046
% 3.13/1.63 % (22920)Time elapsed: 0.015 s
% 3.13/1.63 % (22920)Instructions burned: 28 (million)
% 3.13/1.63 % (22920)------------------------------
% 3.13/1.63 % (22920)------------------------------
% 3.13/1.63 % (22929)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_22754 for (2999ds/3Mi)
% 3.13/1.63 % (22930)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_22754 for (2999ds/37Mi)
% 3.13/1.63 % (22931)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_22754 for (2999ds/15Mi)
% 3.13/1.63 % (22929)Instruction limit reached!
% 3.13/1.63 % (22929)------------------------------
% 3.13/1.63 % (22929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.63 % (22929)Termination reason: Unknown
% 3.13/1.63 % (22929)Termination phase: shuffling
% 3.13/1.63
% 3.13/1.63 % (22929)Memory used [KB]: 1535
% 3.13/1.63 % (22929)Time elapsed: 0.003 s
% 3.13/1.63 % (22929)Instructions burned: 3 (million)
% 3.13/1.63 % (22929)------------------------------
% 3.13/1.63 % (22929)------------------------------
% 3.13/1.64 % (22931)Instruction limit reached!
% 3.13/1.64 % (22931)------------------------------
% 3.13/1.64 % (22931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.64 % (22931)Termination reason: Unknown
% 3.13/1.64 % (22931)Termination phase: shuffling
% 3.13/1.64
% 3.13/1.64 % (22931)Memory used [KB]: 1791
% 3.13/1.64 % (22931)Time elapsed: 0.009 s
% 3.13/1.64 % (22931)Instructions burned: 15 (million)
% 3.13/1.64 % (22931)------------------------------
% 3.13/1.64 % (22931)------------------------------
% 3.13/1.64 % (22935)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_22754 for (2999ds/3Mi)
% 3.13/1.64 % (22935)Instruction limit reached!
% 3.13/1.64 % (22935)------------------------------
% 3.13/1.64 % (22935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.64 % (22935)Termination reason: Unknown
% 3.13/1.64 % (22935)Termination phase: shuffling
% 3.13/1.64
% 3.13/1.64 % (22935)Memory used [KB]: 1535
% 3.13/1.64 % (22935)Time elapsed: 0.003 s
% 3.13/1.64 % (22935)Instructions burned: 3 (million)
% 3.13/1.64 % (22935)------------------------------
% 3.13/1.64 % (22935)------------------------------
% 3.13/1.65 % (22936)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_22754 for (2999ds/1041Mi)
% 3.13/1.65 % (22930)Instruction limit reached!
% 3.13/1.65 % (22930)------------------------------
% 3.13/1.65 % (22930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.65 % (22930)Termination reason: Unknown
% 3.13/1.65 % (22930)Termination phase: shuffling
% 3.13/1.65
% 3.13/1.65 % (22930)Memory used [KB]: 2302
% 3.13/1.65 % (22930)Time elapsed: 0.018 s
% 3.13/1.65 % (22930)Instructions burned: 37 (million)
% 3.13/1.65 % (22930)------------------------------
% 3.13/1.65 % (22930)------------------------------
% 3.13/1.65 % (22938)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_22754 for (2999ds/7Mi)
% 3.13/1.65 % (22938)Instruction limit reached!
% 3.13/1.65 % (22938)------------------------------
% 3.13/1.65 % (22938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.65 % (22938)Termination reason: Unknown
% 3.13/1.65 % (22938)Termination phase: shuffling
% 3.13/1.65
% 3.13/1.65 % (22938)Memory used [KB]: 1663
% 3.13/1.65 % (22938)Time elapsed: 0.005 s
% 3.13/1.65 % (22938)Instructions burned: 8 (million)
% 3.13/1.65 % (22938)------------------------------
% 3.13/1.65 % (22938)------------------------------
% 3.13/1.66 % (22939)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_22754 for (2999ds/16Mi)
% 3.13/1.66 % (22940)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_22754 for (2999ds/3Mi)
% 3.13/1.66 % (22939)Instruction limit reached!
% 3.13/1.66 % (22939)------------------------------
% 3.13/1.66 % (22939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.66 % (22939)Termination reason: Unknown
% 3.13/1.66 % (22939)Termination phase: shuffling
% 3.13/1.66
% 3.13/1.66 % (22939)Memory used [KB]: 1918
% 3.13/1.66 % (22939)Time elapsed: 0.009 s
% 3.13/1.66 % (22939)Instructions burned: 16 (million)
% 3.13/1.66 % (22939)------------------------------
% 3.13/1.66 % (22939)------------------------------
% 3.13/1.66 % (22940)Instruction limit reached!
% 3.13/1.66 % (22940)------------------------------
% 3.13/1.66 % (22940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.66 % (22940)Termination reason: Unknown
% 3.13/1.66 % (22940)Termination phase: shuffling
% 3.13/1.66
% 3.13/1.66 % (22940)Memory used [KB]: 1535
% 3.13/1.66 % (22940)Time elapsed: 0.004 s
% 3.13/1.66 % (22940)Instructions burned: 4 (million)
% 3.13/1.66 % (22940)------------------------------
% 3.13/1.66 % (22940)------------------------------
% 3.13/1.67 % (22943)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_22754 for (2999ds/3Mi)
% 3.13/1.67 % (22943)Instruction limit reached!
% 3.13/1.67 % (22943)------------------------------
% 3.13/1.67 % (22943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.67 % (22943)Termination reason: Unknown
% 3.13/1.67 % (22943)Termination phase: shuffling
% 3.13/1.67
% 3.13/1.67 % (22943)Memory used [KB]: 1535
% 3.13/1.67 % (22943)Time elapsed: 0.003 s
% 3.13/1.67 % (22943)Instructions burned: 3 (million)
% 3.13/1.67 % (22943)------------------------------
% 3.13/1.67 % (22943)------------------------------
% 3.13/1.67 % (22944)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_22754 for (2999ds/7Mi)
% 3.13/1.67 % (22944)Instruction limit reached!
% 3.13/1.67 % (22944)------------------------------
% 3.13/1.67 % (22944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.67 % (22944)Termination reason: Unknown
% 3.13/1.67 % (22944)Termination phase: shuffling
% 3.13/1.67
% 3.13/1.67 % (22944)Memory used [KB]: 1663
% 3.13/1.67 % (22944)Time elapsed: 0.005 s
% 3.13/1.67 % (22944)Instructions burned: 9 (million)
% 3.13/1.67 % (22944)------------------------------
% 3.13/1.67 % (22944)------------------------------
% 3.13/1.68 % (22918)Instruction limit reached!
% 3.13/1.68 % (22918)------------------------------
% 3.13/1.68 % (22918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.68 % (22918)Termination reason: Unknown
% 3.13/1.68 % (22918)Termination phase: Saturation
% 3.13/1.68
% 3.13/1.68 % (22918)Memory used [KB]: 7419
% 3.13/1.68 % (22918)Time elapsed: 0.065 s
% 3.13/1.68 % (22918)Instructions burned: 184 (million)
% 3.13/1.68 % (22918)------------------------------
% 3.13/1.68 % (22918)------------------------------
% 3.13/1.68 % (22945)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_22754 for (2999ds/3Mi)
% 3.13/1.68 % (22949)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_22754 for (2999ds/710Mi)
% 3.13/1.68 % (22945)Instruction limit reached!
% 3.13/1.68 % (22945)------------------------------
% 3.13/1.68 % (22945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.68 % (22945)Termination reason: Unknown
% 3.13/1.68 % (22945)Termination phase: shuffling
% 3.13/1.68
% 3.13/1.68 % (22945)Memory used [KB]: 1535
% 3.13/1.68 % (22945)Time elapsed: 0.003 s
% 3.13/1.68 % (22945)Instructions burned: 3 (million)
% 3.13/1.68 % (22945)------------------------------
% 3.13/1.68 % (22945)------------------------------
% 3.13/1.68 % (22946)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_22754 for (2999ds/4Mi)
% 3.13/1.68 % (22947)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_22754 for (2999ds/18Mi)
% 3.13/1.68 % (22946)Instruction limit reached!
% 3.13/1.68 % (22946)------------------------------
% 3.13/1.68 % (22946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.68 % (22946)Termination reason: Unknown
% 3.13/1.68 % (22946)Termination phase: shuffling
% 3.13/1.68
% 3.13/1.68 % (22946)Memory used [KB]: 1535
% 3.13/1.68 % (22946)Time elapsed: 0.004 s
% 3.13/1.68 % (22946)Instructions burned: 5 (million)
% 3.13/1.68 % (22946)------------------------------
% 3.13/1.68 % (22946)------------------------------
% 3.13/1.69 % (22947)Instruction limit reached!
% 3.13/1.69 % (22947)------------------------------
% 3.13/1.69 % (22947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.69 % (22947)Termination reason: Unknown
% 3.13/1.69 % (22947)Termination phase: shuffling
% 3.13/1.69
% 3.13/1.69 % (22947)Memory used [KB]: 1791
% 3.13/1.69 % (22947)Time elapsed: 0.010 s
% 3.13/1.69 % (22947)Instructions burned: 18 (million)
% 3.13/1.69 % (22947)------------------------------
% 3.13/1.69 % (22947)------------------------------
% 3.13/1.69 % (22951)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_22754 for (2999ds/6Mi)
% 3.13/1.70 % (22951)Instruction limit reached!
% 3.13/1.70 % (22951)------------------------------
% 3.13/1.70 % (22951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.70 % (22951)Termination reason: Unknown
% 3.13/1.70 % (22951)Termination phase: shuffling
% 3.13/1.70
% 3.13/1.70 % (22951)Memory used [KB]: 1535
% 3.13/1.70 % (22951)Time elapsed: 0.005 s
% 3.13/1.70 % (22951)Instructions burned: 7 (million)
% 3.13/1.70 % (22951)------------------------------
% 3.13/1.70 % (22951)------------------------------
% 3.13/1.70 % (22952)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_22754 for (2999ds/902Mi)
% 3.13/1.70 % (22953)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_22754 for (2999ds/21Mi)
% 3.13/1.70 % (22924)Instruction limit reached!
% 3.13/1.70 % (22924)------------------------------
% 3.13/1.70 % (22924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.70 % (22924)Termination reason: Unknown
% 3.13/1.70 % (22924)Termination phase: Saturation
% 3.13/1.70
% 3.13/1.70 % (22924)Memory used [KB]: 10362
% 3.13/1.70 % (22924)Time elapsed: 0.095 s
% 3.13/1.70 % (22924)Instructions burned: 276 (million)
% 3.13/1.70 % (22924)------------------------------
% 3.13/1.70 % (22924)------------------------------
% 3.13/1.71 % (22954)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_22754 for (2999ds/5Mi)
% 3.13/1.71 % (22953)Instruction limit reached!
% 3.13/1.71 % (22953)------------------------------
% 3.13/1.71 % (22953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.71 % (22953)Termination reason: Unknown
% 3.13/1.71 % (22953)Termination phase: shuffling
% 3.13/1.71
% 3.13/1.71 % (22953)Memory used [KB]: 1918
% 3.13/1.71 % (22953)Time elapsed: 0.011 s
% 3.13/1.71 % (22953)Instructions burned: 21 (million)
% 3.13/1.71 % (22953)------------------------------
% 3.13/1.71 % (22953)------------------------------
% 3.13/1.71 % (22954)Instruction limit reached!
% 3.13/1.71 % (22954)------------------------------
% 3.13/1.71 % (22954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.71 % (22954)Termination reason: Unknown
% 3.13/1.71 % (22954)Termination phase: shuffling
% 3.13/1.71
% 3.13/1.71 % (22954)Memory used [KB]: 1535
% 3.13/1.71 % (22954)Time elapsed: 0.004 s
% 3.13/1.71 % (22954)Instructions burned: 5 (million)
% 3.13/1.71 % (22954)------------------------------
% 3.13/1.71 % (22954)------------------------------
% 3.13/1.72 % (22955)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_22754 for (2998ds/6Mi)
% 3.13/1.72 % (22955)Instruction limit reached!
% 3.13/1.72 % (22955)------------------------------
% 3.13/1.72 % (22955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.72 % (22955)Termination reason: Unknown
% 3.13/1.72 % (22955)Termination phase: shuffling
% 3.13/1.72
% 3.13/1.72 % (22955)Memory used [KB]: 1663
% 3.13/1.72 % (22955)Time elapsed: 0.005 s
% 3.13/1.72 % (22955)Instructions burned: 7 (million)
% 3.13/1.72 % (22955)------------------------------
% 3.13/1.72 % (22955)------------------------------
% 3.13/1.73 % (22958)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_22754 for (2998ds/779Mi)
% 3.13/1.73 % (22959)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_22754 for (2998ds/19Mi)
% 3.13/1.73 % (22957)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_22754 for (2998ds/377Mi)
% 3.13/1.73 % (22959)Instruction limit reached!
% 3.13/1.73 % (22959)------------------------------
% 3.13/1.73 % (22959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.73 % (22959)Termination reason: Unknown
% 3.13/1.73 % (22959)Termination phase: shuffling
% 3.13/1.73
% 3.13/1.73 % (22959)Memory used [KB]: 1918
% 3.13/1.73 % (22959)Time elapsed: 0.010 s
% 3.13/1.73 % (22959)Instructions burned: 19 (million)
% 3.13/1.73 % (22959)------------------------------
% 3.13/1.73 % (22959)------------------------------
% 3.13/1.74 % (22960)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_22754 for (2998ds/879Mi)
% 3.13/1.75 % (22962)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_22754 for (2998ds/17Mi)
% 3.13/1.76 % (22962)Instruction limit reached!
% 3.13/1.76 % (22962)------------------------------
% 3.13/1.76 % (22962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.76 % (22962)Termination reason: Unknown
% 3.13/1.76 % (22962)Termination phase: shuffling
% 3.13/1.76
% 3.13/1.76 % (22962)Memory used [KB]: 1791
% 3.13/1.76 % (22962)Time elapsed: 0.010 s
% 3.13/1.76 % (22962)Instructions burned: 18 (million)
% 3.13/1.76 % (22962)------------------------------
% 3.13/1.76 % (22962)------------------------------
% 3.13/1.78 % (22964)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_22754 for (2998ds/3Mi)
% 3.13/1.78 % (22964)Instruction limit reached!
% 3.13/1.78 % (22964)------------------------------
% 3.13/1.78 % (22964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.78 % (22964)Termination reason: Unknown
% 3.13/1.78 % (22964)Termination phase: shuffling
% 3.13/1.78
% 3.13/1.78 % (22964)Memory used [KB]: 1535
% 3.13/1.78 % (22964)Time elapsed: 0.004 s
% 3.13/1.78 % (22964)Instructions burned: 4 (million)
% 3.13/1.78 % (22964)------------------------------
% 3.13/1.78 % (22964)------------------------------
% 3.13/1.80 % (22965)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_22754 for (2998ds/30Mi)
% 3.13/1.81 % (22965)Instruction limit reached!
% 3.13/1.81 % (22965)------------------------------
% 3.13/1.81 % (22965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.81 % (22965)Termination reason: Unknown
% 3.13/1.81 % (22965)Termination phase: shuffling
% 3.13/1.81
% 3.13/1.81 % (22965)Memory used [KB]: 2046
% 3.13/1.81 % (22965)Time elapsed: 0.016 s
% 3.13/1.81 % (22965)Instructions burned: 31 (million)
% 3.13/1.81 % (22965)------------------------------
% 3.13/1.81 % (22965)------------------------------
% 3.13/1.83 % (22967)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_22754 for (2997ds/127Mi)
% 3.13/1.88 % (22957)Instruction limit reached!
% 3.13/1.88 % (22957)------------------------------
% 3.13/1.88 % (22957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.88 % (22957)Termination reason: Unknown
% 3.13/1.88 % (22957)Termination phase: Saturation
% 3.13/1.88
% 3.13/1.88 % (22957)Memory used [KB]: 9466
% 3.13/1.88 % (22957)Time elapsed: 0.159 s
% 3.13/1.88 % (22957)Instructions burned: 378 (million)
% 3.13/1.88 % (22957)------------------------------
% 3.13/1.88 % (22957)------------------------------
% 3.13/1.88 % (22967)Instruction limit reached!
% 3.13/1.88 % (22967)------------------------------
% 3.13/1.88 % (22967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.88 % (22967)Termination reason: Unknown
% 3.13/1.88 % (22967)Termination phase: Property scanning
% 3.13/1.88
% 3.13/1.88 % (22967)Memory used [KB]: 2814
% 3.13/1.88 % (22967)Time elapsed: 0.057 s
% 3.13/1.88 % (22967)Instructions burned: 127 (million)
% 3.13/1.88 % (22967)------------------------------
% 3.13/1.88 % (22967)------------------------------
% 3.13/1.91 % (22974)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_22754 for (2997ds/3Mi)
% 3.13/1.91 % (22974)Instruction limit reached!
% 3.13/1.91 % (22974)------------------------------
% 3.13/1.91 % (22974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.91 % (22974)Termination reason: Unknown
% 3.13/1.91 % (22974)Termination phase: shuffling
% 3.13/1.91
% 3.13/1.91 % (22974)Memory used [KB]: 1535
% 3.13/1.91 % (22974)Time elapsed: 0.004 s
% 3.13/1.91 % (22974)Instructions burned: 4 (million)
% 3.13/1.91 % (22974)------------------------------
% 3.13/1.91 % (22974)------------------------------
% 3.13/1.91 % (22973)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_22754 for (2997ds/100Mi)
% 3.13/1.93 % (22977)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_22754 for (2996ds/20Mi)
% 3.13/1.94 % (22977)Instruction limit reached!
% 3.13/1.94 % (22977)------------------------------
% 3.13/1.94 % (22977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.94 % (22977)Termination reason: Unknown
% 3.13/1.94 % (22977)Termination phase: shuffling
% 3.13/1.94
% 3.13/1.94 % (22977)Memory used [KB]: 1918
% 3.13/1.94 % (22977)Time elapsed: 0.009 s
% 3.13/1.94 % (22977)Instructions burned: 21 (million)
% 3.13/1.94 % (22977)------------------------------
% 3.13/1.94 % (22977)------------------------------
% 3.13/1.94 % (22973)Instruction limit reached!
% 3.13/1.94 % (22973)------------------------------
% 3.13/1.94 % (22973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.94 % (22973)Termination reason: Unknown
% 3.13/1.94 % (22973)Termination phase: Property scanning
% 3.13/1.94
% 3.13/1.94 % (22973)Memory used [KB]: 2814
% 3.13/1.94 % (22973)Time elapsed: 0.032 s
% 3.13/1.94 % (22973)Instructions burned: 101 (million)
% 3.13/1.94 % (22973)------------------------------
% 3.13/1.94 % (22973)------------------------------
% 3.13/1.95 % (22982)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_22754 for (2996ds/86Mi)
% 3.13/1.95 % (22983)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_22754 for (2996ds/107Mi)
% 3.13/1.96 % (22949)Instruction limit reached!
% 3.13/1.96 % (22949)------------------------------
% 3.13/1.96 % (22949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.96 % (22949)Termination reason: Unknown
% 3.13/1.96 % (22949)Termination phase: Saturation
% 3.13/1.96
% 3.13/1.96 % (22949)Memory used [KB]: 11129
% 3.13/1.96 % (22949)Time elapsed: 0.283 s
% 3.13/1.96 % (22949)Instructions burned: 712 (million)
% 3.13/1.96 % (22949)------------------------------
% 3.13/1.96 % (22949)------------------------------
% 3.13/1.97 % (22982)Instruction limit reached!
% 3.13/1.97 % (22982)------------------------------
% 3.13/1.97 % (22982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.97 % (22982)Termination reason: Unknown
% 3.13/1.97 % (22982)Termination phase: Property scanning
% 3.13/1.97
% 3.13/1.97 % (22982)Memory used [KB]: 2558
% 3.13/1.97 % (22982)Time elapsed: 0.026 s
% 3.13/1.97 % (22982)Instructions burned: 89 (million)
% 3.13/1.97 % (22982)------------------------------
% 3.13/1.97 % (22982)------------------------------
% 3.13/1.97 % (22984)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_22754 for (2996ds/39Mi)
% 3.13/1.98 % (22936)Instruction limit reached!
% 3.13/1.98 % (22936)------------------------------
% 3.13/1.98 % (22936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.98 % (22936)Termination reason: Unknown
% 3.13/1.98 % (22936)Termination phase: Saturation
% 3.13/1.98
% 3.13/1.98 % (22936)Memory used [KB]: 16758
% 3.13/1.98 % (22936)Time elapsed: 0.318 s
% 3.13/1.98 % (22936)Instructions burned: 1042 (million)
% 3.13/1.98 % (22936)------------------------------
% 3.13/1.98 % (22936)------------------------------
% 3.13/1.98 % (22985)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_22754 for (2996ds/448Mi)
% 3.13/1.98 % (22983)Instruction limit reached!
% 3.13/1.98 % (22983)------------------------------
% 3.13/1.98 % (22983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.98 % (22983)Termination reason: Unknown
% 3.13/1.98 % (22983)Termination phase: SInE selection
% 3.13/1.98
% 3.13/1.98 % (22983)Memory used [KB]: 2558
% 3.13/1.98 % (22983)Time elapsed: 0.030 s
% 3.13/1.98 % (22983)Instructions burned: 107 (million)
% 3.13/1.98 % (22983)------------------------------
% 3.13/1.98 % (22983)------------------------------
% 3.13/1.98 % (22958)Instruction limit reached!
% 3.13/1.98 % (22958)------------------------------
% 3.13/1.98 % (22958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.98 % (22958)Termination reason: Unknown
% 3.13/1.98 % (22958)Termination phase: Saturation
% 3.13/1.98
% 3.13/1.98 % (22958)Memory used [KB]: 7803
% 3.13/1.98 % (22958)Time elapsed: 0.253 s
% 3.13/1.98 % (22958)Instructions burned: 780 (million)
% 3.13/1.98 % (22958)------------------------------
% 3.13/1.98 % (22958)------------------------------
% 3.13/1.98 % (22984)Instruction limit reached!
% 3.13/1.98 % (22984)------------------------------
% 3.13/1.98 % (22984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.98 % (22984)Termination reason: Unknown
% 3.13/1.98 % (22984)Termination phase: shuffling
% 3.13/1.98
% 3.13/1.98 % (22984)Memory used [KB]: 2302
% 3.13/1.98 % (22984)Time elapsed: 0.012 s
% 3.13/1.98 % (22984)Instructions burned: 39 (million)
% 3.13/1.98 % (22984)------------------------------
% 3.13/1.98 % (22984)------------------------------
% 3.13/1.99 % (22986)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_22754 for (2996ds/46Mi)
% 3.13/1.99 % (22987)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_22754 for (2996ds/98Mi)
% 3.13/1.99 % (22988)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_22754 for (2996ds/507Mi)
% 3.13/1.99 % (22989)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_22754 for (2996ds/149Mi)
% 3.13/2.00 % (22986)Instruction limit reached!
% 3.13/2.00 % (22986)------------------------------
% 3.13/2.00 % (22986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/2.00 % (22986)Termination reason: Unknown
% 3.13/2.00 % (22986)Termination phase: shuffling
% 3.13/2.00
% 3.13/2.00 % (22986)Memory used [KB]: 2430
% 3.13/2.00 % (22986)Time elapsed: 0.014 s
% 3.13/2.00 % (22986)Instructions burned: 47 (million)
% 3.13/2.00 % (22986)------------------------------
% 3.13/2.00 % (22986)------------------------------
% 3.13/2.01 % (22993)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_22754 for (2996ds/39Mi)
% 5.88/2.02 % (22987)Instruction limit reached!
% 5.88/2.02 % (22987)------------------------------
% 5.88/2.02 % (22987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.02 % (22987)Termination reason: Unknown
% 5.88/2.02 % (22987)Termination phase: Property scanning
% 5.88/2.02
% 5.88/2.02 % (22987)Memory used [KB]: 2686
% 5.88/2.02 % (22987)Time elapsed: 0.027 s
% 5.88/2.02 % (22987)Instructions burned: 101 (million)
% 5.88/2.02 % (22987)------------------------------
% 5.88/2.02 % (22987)------------------------------
% 5.88/2.02 % (22993)Instruction limit reached!
% 5.88/2.02 % (22993)------------------------------
% 5.88/2.02 % (22993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.02 % (22993)Termination reason: Unknown
% 5.88/2.02 % (22993)Termination phase: shuffling
% 5.88/2.02
% 5.88/2.02 % (22993)Memory used [KB]: 2302
% 5.88/2.02 % (22993)Time elapsed: 0.013 s
% 5.88/2.02 % (22993)Instructions burned: 41 (million)
% 5.88/2.02 % (22993)------------------------------
% 5.88/2.02 % (22993)------------------------------
% 5.88/2.03 % (23002)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_22754 for (2995ds/6Mi)
% 5.88/2.03 % (23002)Instruction limit reached!
% 5.88/2.03 % (23002)------------------------------
% 5.88/2.03 % (23002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.03 % (23002)Termination reason: Unknown
% 5.88/2.03 % (23002)Termination phase: shuffling
% 5.88/2.03
% 5.88/2.03 % (23002)Memory used [KB]: 1535
% 5.88/2.03 % (23002)Time elapsed: 0.003 s
% 5.88/2.03 % (23002)Instructions burned: 6 (million)
% 5.88/2.03 % (23002)------------------------------
% 5.88/2.03 % (23002)------------------------------
% 5.88/2.03 % (23005)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_22754 for (2995ds/1087Mi)
% 5.88/2.03 % (22989)Instruction limit reached!
% 5.88/2.03 % (22989)------------------------------
% 5.88/2.03 % (22989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.03 % (22989)Termination reason: Unknown
% 5.88/2.03 % (22989)Termination phase: Twee Goal Transformation
% 5.88/2.03
% 5.88/2.03 % (22989)Memory used [KB]: 3070
% 5.88/2.03 % (22989)Time elapsed: 0.041 s
% 5.88/2.03 % (22989)Instructions burned: 150 (million)
% 5.88/2.03 % (22989)------------------------------
% 5.88/2.03 % (22989)------------------------------
% 5.88/2.04 % (23010)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_22754 for (2995ds/47Mi)
% 5.88/2.04 % (23014)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_22754 for (2995ds/44Mi)
% 5.88/2.05 % (23010)Instruction limit reached!
% 5.88/2.05 % (23010)------------------------------
% 5.88/2.05 % (23010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.05 % (23010)Termination reason: Unknown
% 5.88/2.05 % (23010)Termination phase: shuffling
% 5.88/2.05
% 5.88/2.05 % (23010)Memory used [KB]: 2430
% 5.88/2.05 % (23010)Time elapsed: 0.014 s
% 5.88/2.05 % (23010)Instructions burned: 47 (million)
% 5.88/2.05 % (23010)------------------------------
% 5.88/2.05 % (23010)------------------------------
% 5.88/2.06 % (23014)Instruction limit reached!
% 5.88/2.06 % (23014)------------------------------
% 5.88/2.06 % (23014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.06 % (23014)Termination reason: Unknown
% 5.88/2.06 % (23014)Termination phase: shuffling
% 5.88/2.06
% 5.88/2.06 % (23014)Memory used [KB]: 2430
% 5.88/2.06 % (23014)Time elapsed: 0.013 s
% 5.88/2.06 % (23014)Instructions burned: 44 (million)
% 5.88/2.06 % (23014)------------------------------
% 5.88/2.06 % (23014)------------------------------
% 5.88/2.06 % (23023)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_22754 for (2995ds/432Mi)
% 5.88/2.06 % (22952)Instruction limit reached!
% 5.88/2.06 % (22952)------------------------------
% 5.88/2.06 % (22952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.06 % (22952)Termination reason: Unknown
% 5.88/2.06 % (22952)Termination phase: Saturation
% 5.88/2.06
% 5.88/2.06 % (22952)Memory used [KB]: 12920
% 5.88/2.06 % (22952)Time elapsed: 0.365 s
% 5.88/2.06 % (22952)Instructions burned: 903 (million)
% 5.88/2.06 % (22952)------------------------------
% 5.88/2.06 % (22952)------------------------------
% 5.88/2.07 % (23029)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_22754 for (2995ds/62Mi)
% 5.88/2.07 % (23033)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_22754 for (2995ds/31Mi)
% 5.88/2.08 % (23033)Instruction limit reached!
% 5.88/2.08 % (23033)------------------------------
% 5.88/2.08 % (23033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.08 % (23033)Termination reason: Unknown
% 5.88/2.08 % (23033)Termination phase: shuffling
% 5.88/2.08
% 5.88/2.08 % (23033)Memory used [KB]: 2174
% 5.88/2.08 % (23033)Time elapsed: 0.010 s
% 5.88/2.08 % (23033)Instructions burned: 31 (million)
% 5.88/2.08 % (23033)------------------------------
% 5.88/2.08 % (23033)------------------------------
% 5.88/2.08 % (23029)Instruction limit reached!
% 5.88/2.08 % (23029)------------------------------
% 5.88/2.08 % (23029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.08 % (23029)Termination reason: Unknown
% 5.88/2.08 % (23029)Termination phase: Property scanning
% 5.88/2.08
% 5.88/2.08 % (23029)Memory used [KB]: 2558
% 5.88/2.08 % (23029)Time elapsed: 0.018 s
% 5.88/2.08 % (23029)Instructions burned: 62 (million)
% 5.88/2.08 % (23029)------------------------------
% 5.88/2.08 % (23029)------------------------------
% 5.88/2.09 % (23040)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_22754 for (2995ds/96Mi)
% 5.88/2.09 % (23042)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_22754 for (2995ds/453Mi)
% 5.88/2.09 % (22985)Instruction limit reached!
% 5.88/2.09 % (22985)------------------------------
% 5.88/2.09 % (22985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.09 % (22985)Termination reason: Unknown
% 5.88/2.09 % (22985)Termination phase: Saturation
% 5.88/2.09
% 5.88/2.09 % (22985)Memory used [KB]: 7675
% 5.88/2.09 % (22985)Time elapsed: 0.113 s
% 5.88/2.09 % (22985)Instructions burned: 451 (million)
% 5.88/2.09 % (22985)------------------------------
% 5.88/2.09 % (22985)------------------------------
% 5.88/2.09 % (22960)Instruction limit reached!
% 5.88/2.09 % (22960)------------------------------
% 5.88/2.09 % (22960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.09 % (22960)Termination reason: Unknown
% 5.88/2.09 % (22960)Termination phase: Saturation
% 5.88/2.09
% 5.88/2.09 % (22960)Memory used [KB]: 10234
% 5.88/2.09 % (22960)Time elapsed: 0.360 s
% 5.88/2.09 % (22960)Instructions burned: 879 (million)
% 5.88/2.09 % (22960)------------------------------
% 5.88/2.09 % (22960)------------------------------
% 5.88/2.10 % (23048)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_22754 for (2994ds/71Mi)
% 5.88/2.10 % (23050)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_22754 for (2994ds/83Mi)
% 6.39/2.12 % (23040)Instruction limit reached!
% 6.39/2.12 % (23040)------------------------------
% 6.39/2.12 % (23040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.39/2.12 % (23040)Termination reason: Unknown
% 6.39/2.12 % (23040)Termination phase: Property scanning
% 6.39/2.12
% 6.39/2.12 % (23040)Memory used [KB]: 2814
% 6.39/2.12 % (23040)Time elapsed: 0.027 s
% 6.39/2.12 % (23040)Instructions burned: 99 (million)
% 6.39/2.12 % (23040)------------------------------
% 6.39/2.12 % (23040)------------------------------
% 6.39/2.12 % (23048)Instruction limit reached!
% 6.39/2.12 % (23048)------------------------------
% 6.39/2.12 % (23048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.39/2.12 % (23048)Termination reason: Unknown
% 6.39/2.12 % (23048)Termination phase: Property scanning
% 6.39/2.12
% 6.39/2.12 % (23048)Memory used [KB]: 2558
% 6.39/2.12 % (23048)Time elapsed: 0.021 s
% 6.39/2.12 % (23048)Instructions burned: 73 (million)
% 6.39/2.12 % (23048)------------------------------
% 6.39/2.12 % (23048)------------------------------
% 6.39/2.13 % (23059)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_22754 for (2994ds/11Mi)
% 6.39/2.13 % (23050)Instruction limit reached!
% 6.39/2.13 % (23050)------------------------------
% 6.39/2.13 % (23050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.39/2.13 % (23050)Termination reason: Unknown
% 6.39/2.13 % (23050)Termination phase: Property scanning
% 6.39/2.13
% 6.39/2.13 % (23050)Memory used [KB]: 2558
% 6.39/2.13 % (23050)Time elapsed: 0.024 s
% 6.39/2.13 % (23050)Instructions burned: 86 (million)
% 6.39/2.13 % (23050)------------------------------
% 6.39/2.13 % (23050)------------------------------
% 6.39/2.13 % (23059)Instruction limit reached!
% 6.39/2.13 % (23059)------------------------------
% 6.39/2.13 % (23059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.39/2.13 % (23059)Termination reason: Unknown
% 6.39/2.13 % (23059)Termination phase: shuffling
% 6.39/2.13
% 6.39/2.13 % (23059)Memory used [KB]: 1791
% 6.39/2.13 % (23059)Time elapsed: 0.005 s
% 6.39/2.13 % (23059)Instructions burned: 13 (million)
% 6.39/2.13 % (23059)------------------------------
% 6.39/2.13 % (23059)------------------------------
% 6.39/2.13 % (23060)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_22754 for (2994ds/41Mi)
% 6.39/2.14 % (23062)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_22754 for (2994ds/6Mi)
% 6.39/2.14 % (22988)Instruction limit reached!
% 6.39/2.14 % (22988)------------------------------
% 6.39/2.14 % (22988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.39/2.14 % (22988)Termination reason: Unknown
% 6.39/2.14 % (22988)Termination phase: Saturation
% 6.39/2.14
% 6.39/2.14 % (22988)Memory used [KB]: 8187
% 6.39/2.14 % (22988)Time elapsed: 0.169 s
% 6.39/2.14 % (22988)Instructions burned: 509 (million)
% 6.39/2.14 % (22988)------------------------------
% 6.39/2.14 % (22988)------------------------------
% 6.39/2.14 % (23062)Instruction limit reached!
% 6.39/2.14 % (23062)------------------------------
% 6.39/2.14 % (23062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.39/2.14 % (23062)Termination reason: Unknown
% 6.39/2.14 % (23062)Termination phase: shuffling
% 6.39/2.14
% 6.39/2.14 % (23062)Memory used [KB]: 1535
% 6.39/2.14 % (23062)Time elapsed: 0.003 s
% 6.39/2.14 % (23062)Instructions burned: 7 (million)
% 6.39/2.14 % (23062)------------------------------
% 6.39/2.14 % (23062)------------------------------
% 6.39/2.14 % (23065)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_22754 for (2994ds/150Mi)
% 6.39/2.14 % (23060)Instruction limit reached!
% 6.39/2.14 % (23060)------------------------------
% 6.39/2.14 % (23060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.39/2.14 % (23060)Termination reason: Unknown
% 6.39/2.14 % (23060)Termination phase: shuffling
% 6.39/2.14
% 6.39/2.14 % (23060)Memory used [KB]: 2302
% 6.39/2.14 % (23060)Time elapsed: 0.012 s
% 6.39/2.14 % (23060)Instructions burned: 41 (million)
% 6.39/2.14 % (23060)------------------------------
% 6.39/2.14 % (23060)------------------------------
% 6.39/2.15 % (23072)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_22754 for (2994ds/343Mi)
% 6.39/2.15 % (23073)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_22754 for (2994ds/109Mi)
% 6.39/2.15 % (23074)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_22754 for (2994ds/253Mi)
% 6.39/2.17 % (23023)Instruction limit reached!
% 6.39/2.17 % (23023)------------------------------
% 6.39/2.17 % (23023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.39/2.17 % (23023)Termination reason: Unknown
% 6.39/2.17 % (23023)Termination phase: Saturation
% 6.39/2.17
% 6.39/2.17 % (23023)Memory used [KB]: 3198
% 6.39/2.17 % (23023)Time elapsed: 0.110 s
% 6.39/2.17 % (23023)Instructions burned: 435 (million)
% 6.39/2.17 % (23023)------------------------------
% 6.39/2.17 % (23023)------------------------------
% 6.39/2.18 % (23073)Instruction limit reached!
% 6.39/2.18 % (23073)------------------------------
% 6.39/2.18 % (23073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.39/2.18 % (23073)Termination reason: Unknown
% 6.39/2.18 % (23073)Termination phase: SInE selection
% 6.39/2.18
% 6.39/2.18 % (23073)Memory used [KB]: 2558
% 6.39/2.18 % (23073)Time elapsed: 0.030 s
% 6.39/2.18 % (23073)Instructions burned: 109 (million)
% 6.39/2.18 % (23073)------------------------------
% 6.39/2.18 % (23073)------------------------------
% 6.39/2.18 % (23088)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_22754 for (2994ds/140Mi)
% 6.39/2.18 % (23065)Instruction limit reached!
% 6.39/2.18 % (23065)------------------------------
% 6.39/2.18 % (23065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.39/2.18 % (23065)Termination reason: Unknown
% 6.39/2.18 % (23065)Termination phase: Property scanning
% 6.39/2.18
% 6.39/2.18 % (23065)Memory used [KB]: 5117
% 6.39/2.18 % (23065)Time elapsed: 0.046 s
% 6.39/2.18 % (23065)Instructions burned: 152 (million)
% 6.39/2.18 % (23065)------------------------------
% 6.39/2.18 % (23065)------------------------------
% 6.39/2.19 % (23094)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_22754 for (2994ds/614Mi)
% 6.39/2.19 % (23097)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_22754 for (2994ds/202Mi)
% 6.78/2.21 % (23042)Instruction limit reached!
% 6.78/2.21 % (23042)------------------------------
% 6.78/2.21 % (23042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.78/2.21 % (23042)Termination reason: Unknown
% 6.78/2.21 % (23042)Termination phase: Saturation
% 6.78/2.21
% 6.78/2.21 % (23042)Memory used [KB]: 7675
% 6.78/2.21 % (23042)Time elapsed: 0.115 s
% 6.78/2.21 % (23042)Instructions burned: 454 (million)
% 6.78/2.21 % (23042)------------------------------
% 6.78/2.21 % (23042)------------------------------
% 6.78/2.22 % (23088)Instruction limit reached!
% 6.78/2.22 % (23088)------------------------------
% 6.78/2.22 % (23088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.78/2.22 % (23088)Termination reason: Unknown
% 6.78/2.22 % (23088)Termination phase: Function definition elimination
% 6.78/2.22
% 6.78/2.22 % (23088)Memory used [KB]: 2814
% 6.78/2.22 % (23088)Time elapsed: 0.038 s
% 6.78/2.22 % (23088)Instructions burned: 143 (million)
% 6.78/2.22 % (23088)------------------------------
% 6.78/2.22 % (23088)------------------------------
% 6.78/2.22 % (23110)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_22754 for (2993ds/339Mi)
% 6.78/2.22 % (23074)Instruction limit reached!
% 6.78/2.22 % (23074)------------------------------
% 6.78/2.22 % (23074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.78/2.22 % (23074)Termination reason: Unknown
% 6.78/2.22 % (23074)Termination phase: Saturation
% 6.78/2.22
% 6.78/2.22 % (23074)Memory used [KB]: 5628
% 6.78/2.22 % (23074)Time elapsed: 0.073 s
% 6.78/2.22 % (23074)Instructions burned: 253 (million)
% 6.78/2.22 % (23074)------------------------------
% 6.78/2.22 % (23074)------------------------------
% 6.78/2.23 % (23117)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_22754 for (2993ds/283Mi)
% 6.78/2.23 % (23124)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_22754 for (2993ds/134Mi)
% 6.78/2.24 % (23072)Instruction limit reached!
% 6.78/2.24 % (23072)------------------------------
% 6.78/2.24 % (23072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.78/2.24 % (23072)Termination reason: Unknown
% 6.78/2.24 % (23072)Termination phase: Saturation
% 6.78/2.24
% 6.78/2.24 % (23072)Memory used [KB]: 8315
% 6.78/2.24 % (23072)Time elapsed: 0.091 s
% 6.78/2.24 % (23072)Instructions burned: 343 (million)
% 6.78/2.24 % (23072)------------------------------
% 6.78/2.24 % (23072)------------------------------
% 6.78/2.25 % (23125)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_22754 for (2993ds/298Mi)
% 6.78/2.25 % (23097)Instruction limit reached!
% 6.78/2.25 % (23097)------------------------------
% 6.78/2.25 % (23097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.78/2.25 % (23097)Termination reason: Unknown
% 6.78/2.25 % (23097)Termination phase: Property scanning
% 6.78/2.25
% 6.78/2.25 % (23097)Memory used [KB]: 5373
% 6.78/2.25 % (23097)Time elapsed: 0.059 s
% 6.78/2.25 % (23097)Instructions burned: 204 (million)
% 6.78/2.25 % (23097)------------------------------
% 6.78/2.25 % (23097)------------------------------
% 6.78/2.26 % (23139)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_22754 for (2993ds/192Mi)
% 6.78/2.27 % (23124)Instruction limit reached!
% 6.78/2.27 % (23124)------------------------------
% 6.78/2.27 % (23124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.78/2.27 % (23124)Termination reason: Unknown
% 6.78/2.27 % (23124)Termination phase: Function definition elimination
% 6.78/2.27
% 6.78/2.27 % (23124)Memory used [KB]: 2814
% 6.78/2.27 % (23124)Time elapsed: 0.037 s
% 6.78/2.27 % (23124)Instructions burned: 135 (million)
% 6.78/2.27 % (23124)------------------------------
% 6.78/2.27 % (23124)------------------------------
% 6.78/2.28 % (23145)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_22754 for (2993ds/258Mi)
% 7.25/2.30 % (23117)Instruction limit reached!
% 7.25/2.30 % (23117)------------------------------
% 7.25/2.30 % (23117)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.25/2.30 % (23117)Termination reason: Unknown
% 7.25/2.30 % (23117)Termination phase: Saturation
% 7.25/2.30
% 7.25/2.30 % (23117)Memory used [KB]: 7547
% 7.25/2.30 % (23117)Time elapsed: 0.074 s
% 7.25/2.30 % (23117)Instructions burned: 285 (million)
% 7.25/2.30 % (23117)------------------------------
% 7.25/2.30 % (23117)------------------------------
% 7.25/2.31 % (23159)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_22754 for (2992ds/90Mi)
% 7.25/2.31 % (23110)Instruction limit reached!
% 7.25/2.31 % (23110)------------------------------
% 7.25/2.31 % (23110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.25/2.31 % (23110)Termination reason: Unknown
% 7.25/2.31 % (23110)Termination phase: Saturation
% 7.25/2.31
% 7.25/2.31 % (23110)Memory used [KB]: 7931
% 7.25/2.31 % (23110)Time elapsed: 0.095 s
% 7.25/2.31 % (23110)Instructions burned: 339 (million)
% 7.25/2.31 % (23110)------------------------------
% 7.25/2.31 % (23110)------------------------------
% 7.25/2.31 % (23139)Instruction limit reached!
% 7.25/2.31 % (23139)------------------------------
% 7.25/2.31 % (23139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.25/2.31 % (23139)Termination reason: Unknown
% 7.25/2.31 % (23139)Termination phase: Saturation
% 7.25/2.31
% 7.25/2.31 % (23139)Memory used [KB]: 7547
% 7.25/2.31 % (23139)Time elapsed: 0.051 s
% 7.25/2.31 % (23139)Instructions burned: 192 (million)
% 7.25/2.31 % (23139)------------------------------
% 7.25/2.31 % (23139)------------------------------
% 7.25/2.32 % (23165)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_22754 for (2992ds/231Mi)
% 7.25/2.32 % (23167)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_22754 for (2992ds/458Mi)
% 7.25/2.32 % (23125)Instruction limit reached!
% 7.25/2.32 % (23125)------------------------------
% 7.25/2.32 % (23125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.25/2.32 % (23125)Termination reason: Unknown
% 7.25/2.32 % (23125)Termination phase: Saturation
% 7.25/2.32
% 7.25/2.32 % (23125)Memory used [KB]: 7547
% 7.25/2.32 % (23125)Time elapsed: 0.077 s
% 7.25/2.32 % (23125)Instructions burned: 299 (million)
% 7.25/2.32 % (23125)------------------------------
% 7.25/2.32 % (23125)------------------------------
% 7.25/2.33 % (23159)Instruction limit reached!
% 7.25/2.33 % (23159)------------------------------
% 7.25/2.33 % (23159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.25/2.33 % (23159)Termination reason: Unknown
% 7.25/2.33 % (23159)Termination phase: Property scanning
% 7.25/2.33
% 7.25/2.33 % (23159)Memory used [KB]: 2558
% 7.25/2.33 % (23159)Time elapsed: 0.026 s
% 7.25/2.33 % (23159)Instructions burned: 90 (million)
% 7.25/2.33 % (23159)------------------------------
% 7.25/2.33 % (23159)------------------------------
% 7.25/2.33 % (23172)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_22754 for (2992ds/31Mi)
% 7.25/2.34 % (23172)Instruction limit reached!
% 7.25/2.34 % (23172)------------------------------
% 7.25/2.34 % (23172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.25/2.34 % (23172)Termination reason: Unknown
% 7.25/2.34 % (23172)Termination phase: shuffling
% 7.25/2.34
% 7.25/2.34 % (23172)Memory used [KB]: 2174
% 7.25/2.34 % (23172)Time elapsed: 0.010 s
% 7.25/2.34 % (23172)Instructions burned: 32 (million)
% 7.25/2.34 % (23172)------------------------------
% 7.25/2.34 % (23172)------------------------------
% 7.25/2.34 % (23176)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_22754 for (2992ds/297Mi)
% 7.25/2.35 % (23145)Instruction limit reached!
% 7.25/2.35 % (23145)------------------------------
% 7.25/2.35 % (23145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.25/2.35 % (23145)Termination reason: Unknown
% 7.25/2.35 % (23145)Termination phase: Saturation
% 7.25/2.35
% 7.25/2.35 % (23145)Memory used [KB]: 7803
% 7.25/2.35 % (23145)Time elapsed: 0.069 s
% 7.25/2.35 % (23145)Instructions burned: 259 (million)
% 7.25/2.35 % (23145)------------------------------
% 7.25/2.35 % (23145)------------------------------
% 7.25/2.35 % (23177)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_22754 for (2992ds/987Mi)
% 7.25/2.36 % (23180)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_22754 for (2992ds/182Mi)
% 7.25/2.36 % (23094)Instruction limit reached!
% 7.25/2.36 % (23094)------------------------------
% 7.25/2.36 % (23094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.25/2.36 % (23094)Termination reason: Unknown
% 7.25/2.36 % (23094)Termination phase: Saturation
% 7.25/2.36
% 7.25/2.36 % (23094)Memory used [KB]: 10362
% 7.25/2.36 % (23094)Time elapsed: 0.179 s
% 7.25/2.36 % (23094)Instructions burned: 617 (million)
% 7.25/2.36 % (23094)------------------------------
% 7.25/2.36 % (23094)------------------------------
% 7.25/2.37 % (23190)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_22754 for (2992ds/182Mi)
% 7.25/2.37 % (23005)Instruction limit reached!
% 7.25/2.37 % (23005)------------------------------
% 7.25/2.37 % (23005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.25/2.37 % (23005)Termination reason: Unknown
% 7.25/2.37 % (23005)Termination phase: Saturation
% 7.25/2.37
% 7.25/2.37 % (23005)Memory used [KB]: 12025
% 7.25/2.37 % (23005)Time elapsed: 0.346 s
% 7.25/2.37 % (23005)Instructions burned: 1087 (million)
% 7.25/2.37 % (23005)------------------------------
% 7.25/2.37 % (23005)------------------------------
% 7.25/2.38 % (23165)Instruction limit reached!
% 7.25/2.38 % (23165)------------------------------
% 7.25/2.38 % (23165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.25/2.38 % (23165)Termination reason: Unknown
% 7.25/2.38 % (23165)Termination phase: Saturation
% 7.25/2.38
% 7.25/2.38 % (23165)Memory used [KB]: 8443
% 7.25/2.38 % (23165)Time elapsed: 0.061 s
% 7.25/2.38 % (23165)Instructions burned: 234 (million)
% 7.25/2.38 % (23165)------------------------------
% 7.25/2.38 % (23165)------------------------------
% 7.25/2.39 % (23194)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_22754 for (2992ds/154Mi)
% 7.25/2.39 % (23197)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_22754 for (2992ds/79Mi)
% 8.33/2.40 % (23180)Instruction limit reached!
% 8.33/2.40 % (23180)------------------------------
% 8.33/2.40 % (23180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.33/2.40 % (23180)Termination reason: Unknown
% 8.33/2.40 % (23180)Termination phase: Saturation
% 8.33/2.40
% 8.33/2.40 % (23180)Memory used [KB]: 7419
% 8.33/2.40 % (23180)Time elapsed: 0.048 s
% 8.33/2.40 % (23180)Instructions burned: 182 (million)
% 8.33/2.40 % (23180)------------------------------
% 8.33/2.40 % (23180)------------------------------
% 8.33/2.41 % (23197)Instruction limit reached!
% 8.33/2.41 % (23197)------------------------------
% 8.33/2.41 % (23197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.33/2.41 % (23197)Termination reason: Unknown
% 8.33/2.41 % (23197)Termination phase: Property scanning
% 8.33/2.41
% 8.33/2.41 % (23197)Memory used [KB]: 2558
% 8.33/2.41 % (23197)Time elapsed: 0.022 s
% 8.33/2.41 % (23197)Instructions burned: 79 (million)
% 8.33/2.41 % (23197)------------------------------
% 8.33/2.41 % (23197)------------------------------
% 8.33/2.41 % (23205)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_22754 for (2991ds/216Mi)
% 8.33/2.42 % (23176)Instruction limit reached!
% 8.33/2.42 % (23176)------------------------------
% 8.33/2.42 % (23176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.33/2.42 % (23176)Termination reason: Unknown
% 8.33/2.42 % (23176)Termination phase: Saturation
% 8.33/2.42
% 8.33/2.42 % (23176)Memory used [KB]: 7547
% 8.33/2.42 % (23176)Time elapsed: 0.075 s
% 8.33/2.42 % (23176)Instructions burned: 297 (million)
% 8.33/2.42 % (23176)------------------------------
% 8.33/2.42 % (23176)------------------------------
% 8.33/2.42 % (23210)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_22754 for (2991ds/114Mi)
% 8.33/2.42 % (23194)Instruction limit reached!
% 8.33/2.42 % (23194)------------------------------
% 8.33/2.42 % (23194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.33/2.42 % (23194)Termination reason: Unknown
% 8.33/2.42 % (23194)Termination phase: Property scanning
% 8.33/2.42
% 8.33/2.42 % (23194)Memory used [KB]: 3070
% 8.33/2.42 % (23194)Time elapsed: 0.041 s
% 8.33/2.42 % (23194)Instructions burned: 157 (million)
% 8.33/2.42 % (23194)------------------------------
% 8.33/2.42 % (23194)------------------------------
% 8.33/2.43 % (23212)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_22754 for (2991ds/922Mi)
% 8.33/2.43 % (23190)Instruction limit reached!
% 8.33/2.43 % (23190)------------------------------
% 8.33/2.43 % (23190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.33/2.43 % (23190)Termination reason: Unknown
% 8.33/2.43 % (23190)Termination phase: Property scanning
% 8.33/2.43
% 8.33/2.43 % (23190)Memory used [KB]: 5245
% 8.33/2.43 % (23190)Time elapsed: 0.054 s
% 8.33/2.43 % (23190)Instructions burned: 185 (million)
% 8.33/2.43 % (23190)------------------------------
% 8.33/2.43 % (23190)------------------------------
% 8.33/2.43 % (23218)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_22754 for (2991ds/182Mi)
% 8.33/2.44 % (23220)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_22754 for (2991ds/164Mi)
% 8.33/2.44 % (23167)Instruction limit reached!
% 8.33/2.44 % (23167)------------------------------
% 8.33/2.44 % (23167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.33/2.44 % (23167)Termination reason: Unknown
% 8.33/2.44 % (23167)Termination phase: Saturation
% 8.33/2.44
% 8.33/2.44 % (23167)Memory used [KB]: 9722
% 8.33/2.44 % (23167)Time elapsed: 0.124 s
% 8.33/2.44 % (23167)Instructions burned: 460 (million)
% 8.33/2.44 % (23167)------------------------------
% 8.33/2.44 % (23167)------------------------------
% 8.33/2.45 % (23210)Instruction limit reached!
% 8.33/2.45 % (23210)------------------------------
% 8.33/2.45 % (23210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.33/2.45 % (23210)Termination reason: Unknown
% 8.33/2.45 % (23210)Termination phase: Property scanning
% 8.33/2.45
% 8.33/2.45 % (23210)Memory used [KB]: 2814
% 8.33/2.45 % (23210)Time elapsed: 0.031 s
% 8.33/2.45 % (23210)Instructions burned: 115 (million)
% 8.33/2.45 % (23210)------------------------------
% 8.33/2.45 % (23210)------------------------------
% 8.33/2.45 % (23224)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_22754 for (2991ds/50Mi)
% 8.33/2.46 % (23228)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_22754 for (2991ds/368Mi)
% 8.33/2.47 % (23224)Instruction limit reached!
% 8.33/2.47 % (23224)------------------------------
% 8.33/2.47 % (23224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.33/2.47 % (23224)Termination reason: Unknown
% 8.33/2.47 % (23224)Termination phase: shuffling
% 8.33/2.47
% 8.33/2.47 % (23224)Memory used [KB]: 2558
% 8.33/2.47 % (23224)Time elapsed: 0.015 s
% 8.33/2.47 % (23224)Instructions burned: 52 (million)
% 8.33/2.47 % (23224)------------------------------
% 8.33/2.47 % (23224)------------------------------
% 8.33/2.47 % (23205)Instruction limit reached!
% 8.33/2.47 % (23205)------------------------------
% 8.33/2.47 % (23205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.33/2.47 % (23205)Termination reason: Unknown
% 8.33/2.47 % (23205)Termination phase: Property scanning
% 8.33/2.47
% 8.33/2.47 % (23205)Memory used [KB]: 3070
% 8.33/2.47 % (23205)Time elapsed: 0.055 s
% 8.33/2.47 % (23205)Instructions burned: 219 (million)
% 8.33/2.47 % (23205)------------------------------
% 8.33/2.47 % (23205)------------------------------
% 8.33/2.48 % (23242)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_22754 for (2991ds/1021Mi)
% 8.33/2.48 % (23243)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_22754 for (2991ds/267Mi)
% 8.33/2.48 % (23220)Instruction limit reached!
% 8.33/2.48 % (23220)------------------------------
% 8.33/2.48 % (23220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.33/2.48 % (23220)Termination reason: Unknown
% 8.33/2.48 % (23220)Termination phase: Function definition elimination
% 8.33/2.48
% 8.33/2.48 % (23220)Memory used [KB]: 2814
% 8.33/2.48 % (23220)Time elapsed: 0.043 s
% 8.33/2.48 % (23220)Instructions burned: 167 (million)
% 8.33/2.48 % (23220)------------------------------
% 8.33/2.48 % (23220)------------------------------
% 8.33/2.48 % (23218)Instruction limit reached!
% 8.33/2.48 % (23218)------------------------------
% 8.33/2.48 % (23218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.33/2.48 % (23218)Termination reason: Unknown
% 8.33/2.48 % (23218)Termination phase: Property scanning
% 8.33/2.48
% 8.33/2.48 % (23218)Memory used [KB]: 2814
% 8.33/2.48 % (23218)Time elapsed: 0.047 s
% 8.33/2.48 % (23218)Instructions burned: 183 (million)
% 8.33/2.48 % (23218)------------------------------
% 8.33/2.48 % (23218)------------------------------
% 8.33/2.49 % (23252)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_22754 for (2991ds/204Mi)
% 8.33/2.49 % (23254)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_22754 for (2991ds/26Mi)
% 8.97/2.50 % (23254)Instruction limit reached!
% 8.97/2.50 % (23254)------------------------------
% 8.97/2.50 % (23254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.97/2.50 % (23254)Termination reason: Unknown
% 8.97/2.50 % (23254)Termination phase: shuffling
% 8.97/2.50
% 8.97/2.50 % (23254)Memory used [KB]: 2174
% 8.97/2.50 % (23254)Time elapsed: 0.009 s
% 8.97/2.50 % (23254)Instructions burned: 29 (million)
% 8.97/2.50 % (23254)------------------------------
% 8.97/2.50 % (23254)------------------------------
% 8.97/2.51 % (23265)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_22754 for (2990ds/53Mi)
% 8.97/2.52 % (23265)Instruction limit reached!
% 8.97/2.52 % (23265)------------------------------
% 8.97/2.52 % (23265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.97/2.52 % (23265)Termination reason: Unknown
% 8.97/2.52 % (23265)Termination phase: shuffling
% 8.97/2.52
% 8.97/2.52 % (23265)Memory used [KB]: 2558
% 8.97/2.52 % (23265)Time elapsed: 0.016 s
% 8.97/2.52 % (23265)Instructions burned: 53 (million)
% 8.97/2.52 % (23265)------------------------------
% 8.97/2.52 % (23265)------------------------------
% 8.97/2.53 % (23271)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_22754 for (2990ds/4436Mi)
% 8.97/2.54 % (23252)Instruction limit reached!
% 8.97/2.54 % (23252)------------------------------
% 8.97/2.54 % (23252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.97/2.54 % (23252)Termination reason: Unknown
% 8.97/2.54 % (23252)Termination phase: Property scanning
% 8.97/2.54
% 8.97/2.54 % (23252)Memory used [KB]: 2942
% 8.97/2.54 % (23252)Time elapsed: 0.052 s
% 8.97/2.54 % (23252)Instructions burned: 204 (million)
% 8.97/2.54 % (23252)------------------------------
% 8.97/2.54 % (23252)------------------------------
% 8.97/2.55 % (23243)Instruction limit reached!
% 8.97/2.55 % (23243)------------------------------
% 8.97/2.55 % (23243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.97/2.55 % (23243)Termination reason: Unknown
% 8.97/2.55 % (23243)Termination phase: Saturation
% 8.97/2.55
% 8.97/2.55 % (23243)Memory used [KB]: 7547
% 8.97/2.55 % (23243)Time elapsed: 0.069 s
% 8.97/2.55 % (23243)Instructions burned: 269 (million)
% 8.97/2.55 % (23243)------------------------------
% 8.97/2.55 % (23243)------------------------------
% 8.97/2.55 % (23272)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_22754 for (2990ds/1539Mi)
% 8.97/2.56 % (23273)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_22754 for (2990ds/408Mi)
% 8.97/2.56 % (23228)Instruction limit reached!
% 8.97/2.56 % (23228)------------------------------
% 8.97/2.56 % (23228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.97/2.56 % (23228)Termination reason: Unknown
% 8.97/2.56 % (23228)Termination phase: Saturation
% 8.97/2.56
% 8.97/2.56 % (23228)Memory used [KB]: 9338
% 8.97/2.56 % (23228)Time elapsed: 0.100 s
% 8.97/2.56 % (23228)Instructions burned: 371 (million)
% 8.97/2.56 % (23228)------------------------------
% 8.97/2.56 % (23228)------------------------------
% 8.97/2.57 % (23274)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_22754 for (2990ds/5205Mi)
% 9.26/2.60 % (23177)Instruction limit reached!
% 9.26/2.60 % (23177)------------------------------
% 9.26/2.60 % (23177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/2.60 % (23177)Termination reason: Unknown
% 9.26/2.60 % (23177)Termination phase: Saturation
% 9.26/2.60
% 9.26/2.60 % (23177)Memory used [KB]: 16886
% 9.26/2.60 % (23177)Time elapsed: 0.252 s
% 9.26/2.60 % (23177)Instructions burned: 989 (million)
% 9.26/2.60 % (23177)------------------------------
% 9.26/2.60 % (23177)------------------------------
% 9.26/2.61 % (23275)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_22754 for (2989ds/1913Mi)
% 9.26/2.67 % (23273)Instruction limit reached!
% 9.26/2.67 % (23273)------------------------------
% 9.26/2.67 % (23273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/2.67 % (23273)Termination reason: Unknown
% 9.26/2.67 % (23273)Termination phase: Saturation
% 9.26/2.67
% 9.26/2.67 % (23273)Memory used [KB]: 11641
% 9.26/2.67 % (23273)Time elapsed: 0.119 s
% 9.26/2.67 % (23273)Instructions burned: 409 (million)
% 9.26/2.67 % (23273)------------------------------
% 9.26/2.67 % (23273)------------------------------
% 9.26/2.68 % (23276)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_22754 for (2989ds/4350Mi)
% 9.66/2.71 % (23212)Instruction limit reached!
% 9.66/2.71 % (23212)------------------------------
% 9.66/2.71 % (23212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.66/2.71 % (23212)Termination reason: Unknown
% 9.66/2.71 % (23212)Termination phase: Saturation
% 9.66/2.71
% 9.66/2.71 % (23212)Memory used [KB]: 12537
% 9.66/2.71 % (23212)Time elapsed: 0.284 s
% 9.66/2.71 % (23212)Instructions burned: 922 (million)
% 9.66/2.71 % (23212)------------------------------
% 9.66/2.71 % (23212)------------------------------
% 9.66/2.72 % (23277)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_22754 for (2988ds/68Mi)
% 9.66/2.74 % (23277)Instruction limit reached!
% 9.66/2.74 % (23277)------------------------------
% 9.66/2.74 % (23277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.66/2.74 % (23277)Termination reason: Unknown
% 9.66/2.74 % (23277)Termination phase: Property scanning
% 9.66/2.74
% 9.66/2.74 % (23277)Memory used [KB]: 2558
% 9.66/2.74 % (23277)Time elapsed: 0.020 s
% 9.66/2.74 % (23277)Instructions burned: 70 (million)
% 9.66/2.74 % (23277)------------------------------
% 9.66/2.74 % (23277)------------------------------
% 9.66/2.75 % (23278)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_22754 for (2988ds/358Mi)
% 9.66/2.79 % (23242)Instruction limit reached!
% 9.66/2.79 % (23242)------------------------------
% 9.66/2.79 % (23242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.66/2.79 % (23242)Termination reason: Unknown
% 9.66/2.79 % (23242)Termination phase: Saturation
% 9.66/2.79
% 9.66/2.79 % (23242)Memory used [KB]: 12665
% 9.66/2.79 % (23242)Time elapsed: 0.317 s
% 9.66/2.79 % (23242)Instructions burned: 1022 (million)
% 9.66/2.79 % (23242)------------------------------
% 9.66/2.79 % (23242)------------------------------
% 10.32/2.80 % (23279)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_22754 for (2987ds/31Mi)
% 10.32/2.81 % (23279)Instruction limit reached!
% 10.32/2.81 % (23279)------------------------------
% 10.32/2.81 % (23279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.32/2.81 % (23279)Termination reason: Unknown
% 10.32/2.81 % (23279)Termination phase: shuffling
% 10.32/2.81
% 10.32/2.81 % (23279)Memory used [KB]: 2046
% 10.32/2.81 % (23279)Time elapsed: 0.011 s
% 10.32/2.81 % (23279)Instructions burned: 33 (million)
% 10.32/2.81 % (23279)------------------------------
% 10.32/2.81 % (23279)------------------------------
% 10.32/2.82 % (23280)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_22754 for (2987ds/279Mi)
% 10.32/2.84 % (23278)Instruction limit reached!
% 10.32/2.84 % (23278)------------------------------
% 10.32/2.84 % (23278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.32/2.84 % (23278)Termination reason: Unknown
% 10.32/2.84 % (23278)Termination phase: Saturation
% 10.32/2.84
% 10.32/2.84 % (23278)Memory used [KB]: 8443
% 10.32/2.84 % (23278)Time elapsed: 0.094 s
% 10.32/2.84 % (23278)Instructions burned: 359 (million)
% 10.32/2.84 % (23278)------------------------------
% 10.32/2.84 % (23278)------------------------------
% 10.32/2.85 % (23281)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_22754 for (2987ds/258Mi)
% 10.32/2.89 % (23280)Instruction limit reached!
% 10.32/2.89 % (23280)------------------------------
% 10.32/2.89 % (23280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.32/2.89 % (23280)Termination reason: Unknown
% 10.32/2.89 % (23280)Termination phase: Saturation
% 10.32/2.89
% 10.32/2.89 % (23280)Memory used [KB]: 7547
% 10.32/2.89 % (23280)Time elapsed: 0.070 s
% 10.32/2.89 % (23280)Instructions burned: 279 (million)
% 10.32/2.89 % (23280)------------------------------
% 10.32/2.89 % (23280)------------------------------
% 10.51/2.90 % (23282)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_22754 for (2986ds/26Mi)
% 10.51/2.91 % (23282)Instruction limit reached!
% 10.51/2.91 % (23282)------------------------------
% 10.51/2.91 % (23282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.51/2.91 % (23282)Termination reason: Unknown
% 10.51/2.91 % (23282)Termination phase: shuffling
% 10.51/2.91
% 10.51/2.91 % (23282)Memory used [KB]: 2046
% 10.51/2.91 % (23282)Time elapsed: 0.009 s
% 10.51/2.91 % (23282)Instructions burned: 27 (million)
% 10.51/2.91 % (23282)------------------------------
% 10.51/2.91 % (23282)------------------------------
% 10.51/2.92 % (23283)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_22754 for (2986ds/995Mi)
% 10.51/2.92 % (23281)Instruction limit reached!
% 10.51/2.92 % (23281)------------------------------
% 10.51/2.92 % (23281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.51/2.92 % (23281)Termination reason: Unknown
% 10.51/2.92 % (23281)Termination phase: Saturation
% 10.51/2.92
% 10.51/2.92 % (23281)Memory used [KB]: 8315
% 10.51/2.92 % (23281)Time elapsed: 0.070 s
% 10.51/2.92 % (23281)Instructions burned: 260 (million)
% 10.51/2.92 % (23281)------------------------------
% 10.51/2.92 % (23281)------------------------------
% 10.51/2.93 % (23284)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_22754 for (2986ds/373Mi)
% 10.51/3.02 % (23272)Instruction limit reached!
% 10.51/3.02 % (23272)------------------------------
% 10.51/3.02 % (23272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.51/3.02 % (23272)Termination reason: Unknown
% 10.51/3.02 % (23272)Termination phase: Saturation
% 10.51/3.02
% 10.51/3.02 % (23272)Memory used [KB]: 11257
% 10.51/3.02 % (23272)Time elapsed: 0.470 s
% 10.51/3.02 % (23272)Instructions burned: 1539 (million)
% 10.51/3.02 % (23272)------------------------------
% 10.51/3.02 % (23272)------------------------------
% 13.00/3.03 % (23284)Instruction limit reached!
% 13.00/3.03 % (23284)------------------------------
% 13.00/3.03 % (23284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.00/3.03 % (23284)Termination reason: Unknown
% 13.00/3.03 % (23284)Termination phase: Saturation
% 13.00/3.03
% 13.00/3.03 % (23284)Memory used [KB]: 9338
% 13.00/3.03 % (23284)Time elapsed: 0.099 s
% 13.00/3.03 % (23284)Instructions burned: 374 (million)
% 13.00/3.03 % (23284)------------------------------
% 13.00/3.03 % (23284)------------------------------
% 13.00/3.03 % (23285)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_22754 for (2985ds/253Mi)
% 13.00/3.04 % (23286)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_22754 for (2985ds/832Mi)
% 13.00/3.09 % (23285)Instruction limit reached!
% 13.00/3.09 % (23285)------------------------------
% 13.00/3.09 % (23285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.00/3.09 % (23285)Termination reason: Unknown
% 13.00/3.09 % (23285)Termination phase: Saturation
% 13.00/3.09
% 13.00/3.09 % (23285)Memory used [KB]: 7547
% 13.00/3.09 % (23285)Time elapsed: 0.064 s
% 13.00/3.09 % (23285)Instructions burned: 253 (million)
% 13.00/3.09 % (23285)------------------------------
% 13.00/3.09 % (23285)------------------------------
% 13.00/3.10 % (23287)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_22754 for (2984ds/668Mi)
% 13.59/3.17 % (23283)Instruction limit reached!
% 13.59/3.17 % (23283)------------------------------
% 13.59/3.17 % (23283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.59/3.17 % (23283)Termination reason: Unknown
% 13.59/3.17 % (23283)Termination phase: Saturation
% 13.59/3.17
% 13.59/3.17 % (23283)Memory used [KB]: 16758
% 13.59/3.17 % (23283)Time elapsed: 0.250 s
% 13.59/3.17 % (23283)Instructions burned: 997 (million)
% 13.59/3.17 % (23283)------------------------------
% 13.59/3.17 % (23283)------------------------------
% 13.59/3.18 % (23288)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_22754 for (2984ds/40Mi)
% 13.59/3.19 % (23288)Instruction limit reached!
% 13.59/3.19 % (23288)------------------------------
% 13.59/3.19 % (23288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.59/3.19 % (23288)Termination reason: Unknown
% 13.59/3.19 % (23288)Termination phase: shuffling
% 13.59/3.19
% 13.59/3.19 % (23288)Memory used [KB]: 2302
% 13.59/3.19 % (23288)Time elapsed: 0.013 s
% 13.59/3.19 % (23288)Instructions burned: 41 (million)
% 13.59/3.19 % (23288)------------------------------
% 13.59/3.19 % (23288)------------------------------
% 13.59/3.19 % (23275)Instruction limit reached!
% 13.59/3.19 % (23275)------------------------------
% 13.59/3.19 % (23275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.59/3.19 % (23275)Termination reason: Unknown
% 13.59/3.19 % (23275)Termination phase: Saturation
% 13.59/3.19
% 13.59/3.19 % (23275)Memory used [KB]: 6268
% 13.59/3.19 % (23275)Time elapsed: 0.581 s
% 13.59/3.19 % (23275)Instructions burned: 1915 (million)
% 13.59/3.19 % (23275)------------------------------
% 13.59/3.19 % (23275)------------------------------
% 13.96/3.20 % (23289)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_22754 for (2984ds/294Mi)
% 13.96/3.20 % (23290)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_22754 for (2983ds/187Mi)
% 13.96/3.25 % (23290)Instruction limit reached!
% 13.96/3.25 % (23290)------------------------------
% 13.96/3.25 % (23290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.96/3.25 % (23290)Termination reason: Unknown
% 13.96/3.25 % (23290)Termination phase: Saturation
% 13.96/3.25
% 13.96/3.25 % (23290)Memory used [KB]: 7419
% 13.96/3.25 % (23290)Time elapsed: 0.049 s
% 13.96/3.25 % (23290)Instructions burned: 188 (million)
% 13.96/3.25 % (23290)------------------------------
% 13.96/3.25 % (23290)------------------------------
% 13.96/3.26 % (23291)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_22754 for (2983ds/371Mi)
% 13.96/3.27 % (23287)Instruction limit reached!
% 13.96/3.27 % (23287)------------------------------
% 13.96/3.27 % (23287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.96/3.27 % (23287)Termination reason: Unknown
% 13.96/3.27 % (23287)Termination phase: Saturation
% 13.96/3.27
% 13.96/3.27 % (23287)Memory used [KB]: 13432
% 13.96/3.27 % (23287)Time elapsed: 0.168 s
% 13.96/3.27 % (23287)Instructions burned: 670 (million)
% 13.96/3.27 % (23287)------------------------------
% 13.96/3.27 % (23287)------------------------------
% 13.96/3.27 % (23289)Instruction limit reached!
% 13.96/3.27 % (23289)------------------------------
% 13.96/3.27 % (23289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.96/3.27 % (23289)Termination reason: Unknown
% 13.96/3.27 % (23289)Termination phase: Saturation
% 13.96/3.27
% 13.96/3.27 % (23289)Memory used [KB]: 7547
% 13.96/3.27 % (23289)Time elapsed: 0.074 s
% 13.96/3.27 % (23289)Instructions burned: 294 (million)
% 13.96/3.27 % (23289)------------------------------
% 13.96/3.27 % (23289)------------------------------
% 13.96/3.28 % (23292)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_22754 for (2983ds/1827Mi)
% 13.96/3.28 % (23293)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_22754 for (2983ds/70Mi)
% 13.96/3.28 % (23286)Instruction limit reached!
% 13.96/3.28 % (23286)------------------------------
% 13.96/3.28 % (23286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.96/3.28 % (23286)Termination reason: Unknown
% 13.96/3.28 % (23286)Termination phase: Saturation
% 13.96/3.28
% 13.96/3.28 % (23286)Memory used [KB]: 11897
% 13.96/3.28 % (23286)Time elapsed: 0.249 s
% 13.96/3.28 % (23286)Instructions burned: 832 (million)
% 13.96/3.28 % (23286)------------------------------
% 13.96/3.28 % (23286)------------------------------
% 13.96/3.29 % (23294)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_22754 for (2983ds/316Mi)
% 14.83/3.30 % (23293)Instruction limit reached!
% 14.83/3.30 % (23293)------------------------------
% 14.83/3.30 % (23293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.83/3.30 % (23293)Termination reason: Unknown
% 14.83/3.30 % (23293)Termination phase: Property scanning
% 14.83/3.30
% 14.83/3.30 % (23293)Memory used [KB]: 2558
% 14.83/3.30 % (23293)Time elapsed: 0.020 s
% 14.83/3.30 % (23293)Instructions burned: 71 (million)
% 14.83/3.30 % (23293)------------------------------
% 14.83/3.30 % (23293)------------------------------
% 14.83/3.31 % (23295)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_22754 for (2982ds/932Mi)
% 14.83/3.36 % (23291)Instruction limit reached!
% 14.83/3.36 % (23291)------------------------------
% 14.83/3.36 % (23291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.83/3.36 % (23291)Termination reason: Unknown
% 14.83/3.36 % (23291)Termination phase: Saturation
% 14.83/3.36
% 14.83/3.36 % (23291)Memory used [KB]: 9210
% 14.83/3.36 % (23291)Time elapsed: 0.099 s
% 14.83/3.36 % (23291)Instructions burned: 372 (million)
% 14.83/3.36 % (23291)------------------------------
% 14.83/3.36 % (23291)------------------------------
% 14.83/3.37 % (23296)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_22754 for (2982ds/4714Mi)
% 14.83/3.37 % (23294)Instruction limit reached!
% 14.83/3.37 % (23294)------------------------------
% 14.83/3.37 % (23294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.83/3.37 % (23294)Termination reason: Unknown
% 14.83/3.37 % (23294)Termination phase: Saturation
% 14.83/3.37
% 14.83/3.37 % (23294)Memory used [KB]: 7547
% 14.83/3.37 % (23294)Time elapsed: 0.080 s
% 14.83/3.37 % (23294)Instructions burned: 317 (million)
% 14.83/3.37 % (23294)------------------------------
% 14.83/3.37 % (23294)------------------------------
% 14.83/3.38 % (23297)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_22754 for (2982ds/8250Mi)
% 15.67/3.55 % (23295)Instruction limit reached!
% 15.67/3.55 % (23295)------------------------------
% 15.67/3.55 % (23295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.67/3.55 % (23295)Termination reason: Unknown
% 15.67/3.55 % (23295)Termination phase: Saturation
% 15.67/3.55
% 15.67/3.55 % (23295)Memory used [KB]: 16758
% 15.67/3.55 % (23295)Time elapsed: 0.236 s
% 15.67/3.55 % (23295)Instructions burned: 933 (million)
% 15.67/3.55 % (23295)------------------------------
% 15.67/3.55 % (23295)------------------------------
% 15.67/3.56 % (23298)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_22754 for (2980ds/770Mi)
% 16.51/3.77 % (23298)Instruction limit reached!
% 16.51/3.77 % (23298)------------------------------
% 16.51/3.77 % (23298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.51/3.77 % (23298)Termination reason: Unknown
% 16.51/3.77 % (23298)Termination phase: Saturation
% 16.51/3.77
% 16.51/3.77 % (23298)Memory used [KB]: 7803
% 16.51/3.77 % (23298)Time elapsed: 0.218 s
% 16.51/3.77 % (23298)Instructions burned: 772 (million)
% 16.51/3.77 % (23298)------------------------------
% 16.51/3.77 % (23298)------------------------------
% 16.51/3.78 % (23299)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_22754 for (2978ds/794Mi)
% 17.03/3.80 % (23292)Instruction limit reached!
% 17.03/3.80 % (23292)------------------------------
% 17.03/3.80 % (23292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.03/3.80 % (23292)Termination reason: Unknown
% 17.03/3.80 % (23292)Termination phase: Saturation
% 17.03/3.80
% 17.03/3.80 % (23292)Memory used [KB]: 21364
% 17.03/3.80 % (23292)Time elapsed: 0.526 s
% 17.03/3.80 % (23292)Instructions burned: 1828 (million)
% 17.03/3.80 % (23292)------------------------------
% 17.03/3.80 % (23292)------------------------------
% 17.03/3.81 % (23300)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_22754 for (2977ds/464Mi)
% 17.03/3.85 % (23274)Instruction limit reached!
% 17.03/3.85 % (23274)------------------------------
% 17.03/3.85 % (23274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.03/3.85 % (23274)Termination reason: Unknown
% 17.03/3.85 % (23274)Termination phase: Saturation
% 17.03/3.85
% 17.03/3.85 % (23274)Memory used [KB]: 17782
% 17.03/3.85 % (23274)Time elapsed: 1.286 s
% 17.03/3.85 % (23274)Instructions burned: 5207 (million)
% 17.03/3.85 % (23274)------------------------------
% 17.03/3.85 % (23274)------------------------------
% 17.03/3.86 % (23301)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_22754 for (2977ds/1376Mi)
% 17.84/3.94 % (23300)Instruction limit reached!
% 17.84/3.94 % (23300)------------------------------
% 17.84/3.94 % (23300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.84/3.94 % (23300)Termination reason: Unknown
% 17.84/3.94 % (23300)Termination phase: Saturation
% 17.84/3.94
% 17.84/3.94 % (23300)Memory used [KB]: 9594
% 17.84/3.94 % (23300)Time elapsed: 0.129 s
% 17.84/3.94 % (23300)Instructions burned: 466 (million)
% 17.84/3.94 % (23300)------------------------------
% 17.84/3.94 % (23300)------------------------------
% 17.84/3.95 % (23302)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_22754 for (2976ds/906Mi)
% 17.84/3.95 % (23271)Instruction limit reached!
% 17.84/3.95 % (23271)------------------------------
% 17.84/3.95 % (23271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.84/3.95 % (23271)Termination reason: Unknown
% 17.84/3.95 % (23271)Termination phase: Saturation
% 17.84/3.95
% 17.84/3.95 % (23271)Memory used [KB]: 15095
% 17.84/3.95 % (23271)Time elapsed: 1.423 s
% 17.84/3.95 % (23271)Instructions burned: 4436 (million)
% 17.84/3.95 % (23271)------------------------------
% 17.84/3.95 % (23271)------------------------------
% 17.84/3.96 % (23303)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_22754 for (2976ds/434Mi)
% 17.84/4.02 % (23299)Instruction limit reached!
% 17.84/4.02 % (23299)------------------------------
% 17.84/4.02 % (23299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.84/4.02 % (23299)Termination reason: Unknown
% 17.84/4.02 % (23299)Termination phase: Saturation
% 17.84/4.02
% 17.84/4.02 % (23299)Memory used [KB]: 6140
% 17.84/4.02 % (23299)Time elapsed: 0.236 s
% 17.84/4.02 % (23299)Instructions burned: 795 (million)
% 17.84/4.02 % (23299)------------------------------
% 17.84/4.02 % (23299)------------------------------
% 20.02/4.03 % (23304)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_22754 for (2975ds/865Mi)
% 20.02/4.04 % (23276)Refutation not found, non-redundant clauses discarded% (23276)------------------------------
% 20.02/4.04 % (23276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.02/4.04 % (23276)Termination reason: Refutation not found, non-redundant clauses discarded
% 20.02/4.04
% 20.02/4.04 % (23276)Memory used [KB]: 14072
% 20.02/4.04 % (23276)Time elapsed: 1.355 s
% 20.02/4.04 % (23276)Instructions burned: 4313 (million)
% 20.02/4.04 % (23276)------------------------------
% 20.02/4.04 % (23276)------------------------------
% 20.02/4.05 % (23305)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_22754 for (2975ds/593Mi)
% 20.02/4.09 % (23303)Instruction limit reached!
% 20.02/4.09 % (23303)------------------------------
% 20.02/4.09 % (23303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.02/4.09 % (23303)Termination reason: Unknown
% 20.02/4.09 % (23303)Termination phase: Saturation
% 20.02/4.09
% 20.02/4.09 % (23303)Memory used [KB]: 11385
% 20.02/4.09 % (23303)Time elapsed: 0.148 s
% 20.02/4.09 % (23303)Instructions burned: 436 (million)
% 20.02/4.09 % (23303)------------------------------
% 20.02/4.09 % (23303)------------------------------
% 20.02/4.10 % (23306)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_22754 for (2974ds/443Mi)
% 20.54/4.19 % (23305)Instruction limit reached!
% 20.54/4.19 % (23305)------------------------------
% 20.54/4.19 % (23305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.54/4.19 % (23305)Termination reason: Unknown
% 20.54/4.19 % (23305)Termination phase: Saturation
% 20.54/4.19
% 20.54/4.19 % (23305)Memory used [KB]: 7675
% 20.54/4.19 % (23305)Time elapsed: 0.148 s
% 20.54/4.19 % (23305)Instructions burned: 594 (million)
% 20.54/4.19 % (23305)------------------------------
% 20.54/4.19 % (23305)------------------------------
% 20.97/4.20 % (23307)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_22754 for (2973ds/594Mi)
% 20.97/4.21 % (23301)Instruction limit reached!
% 20.97/4.21 % (23301)------------------------------
% 20.97/4.21 % (23301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.97/4.21 % (23301)Termination reason: Unknown
% 20.97/4.21 % (23301)Termination phase: Saturation
% 20.97/4.21
% 20.97/4.21 % (23301)Memory used [KB]: 9594
% 20.97/4.21 % (23301)Time elapsed: 0.349 s
% 20.97/4.21 % (23301)Instructions burned: 1377 (million)
% 20.97/4.21 % (23301)------------------------------
% 20.97/4.21 % (23301)------------------------------
% 20.97/4.22 % (23306)Instruction limit reached!
% 20.97/4.22 % (23306)------------------------------
% 20.97/4.22 % (23306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.97/4.22 % (23306)Termination reason: Unknown
% 20.97/4.22 % (23306)Termination phase: Saturation
% 20.97/4.22
% 20.97/4.22 % (23306)Memory used [KB]: 9594
% 20.97/4.22 % (23306)Time elapsed: 0.119 s
% 20.97/4.22 % (23306)Instructions burned: 443 (million)
% 20.97/4.22 % (23306)------------------------------
% 20.97/4.22 % (23306)------------------------------
% 20.97/4.22 % (23308)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_22754 for (2973ds/327Mi)
% 20.97/4.23 % (23302)Instruction limit reached!
% 20.97/4.23 % (23302)------------------------------
% 20.97/4.23 % (23302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.97/4.23 % (23302)Termination reason: Unknown
% 20.97/4.23 % (23302)Termination phase: Saturation
% 20.97/4.23
% 20.97/4.23 % (23302)Memory used [KB]: 11257
% 20.97/4.23 % (23302)Time elapsed: 0.276 s
% 20.97/4.23 % (23302)Instructions burned: 906 (million)
% 20.97/4.23 % (23302)------------------------------
% 20.97/4.23 % (23302)------------------------------
% 20.97/4.23 % (23309)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_22754 for (2973ds/5411Mi)
% 20.97/4.24 % (23310)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_22754 for (2973ds/1762Mi)
% 20.97/4.28 % (23304)Instruction limit reached!
% 20.97/4.28 % (23304)------------------------------
% 20.97/4.28 % (23304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.97/4.28 % (23304)Termination reason: Unknown
% 20.97/4.28 % (23304)Termination phase: Saturation
% 20.97/4.28
% 20.97/4.28 % (23304)Memory used [KB]: 10618
% 20.97/4.28 % (23304)Time elapsed: 0.255 s
% 20.97/4.28 % (23304)Instructions burned: 866 (million)
% 20.97/4.28 % (23304)------------------------------
% 20.97/4.28 % (23304)------------------------------
% 20.97/4.29 % (23311)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_22754 for (2973ds/96Mi)
% 21.63/4.31 % (23308)Instruction limit reached!
% 21.63/4.31 % (23308)------------------------------
% 21.63/4.31 % (23308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.63/4.31 % (23308)Termination reason: Unknown
% 21.63/4.31 % (23308)Termination phase: Saturation
% 21.63/4.31
% 21.63/4.31 % (23308)Memory used [KB]: 11257
% 21.63/4.32 % (23308)Time elapsed: 0.095 s
% 21.63/4.32 % (23308)Instructions burned: 327 (million)
% 21.63/4.32 % (23308)------------------------------
% 21.63/4.32 % (23308)------------------------------
% 21.63/4.32 % (23311)Instruction limit reached!
% 21.63/4.32 % (23311)------------------------------
% 21.63/4.32 % (23311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.63/4.32 % (23311)Termination reason: Unknown
% 21.63/4.32 % (23311)Termination phase: Property scanning
% 21.63/4.32
% 21.63/4.32 % (23311)Memory used [KB]: 2686
% 21.63/4.32 % (23311)Time elapsed: 0.026 s
% 21.63/4.32 % (23311)Instructions burned: 97 (million)
% 21.63/4.32 % (23311)------------------------------
% 21.63/4.32 % (23311)------------------------------
% 21.63/4.33 % (23312)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_22754 for (2972ds/503Mi)
% 21.63/4.33 % (23313)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_22754 for (2972ds/90Mi)
% 21.63/4.35 % (23313)Instruction limit reached!
% 21.63/4.35 % (23313)------------------------------
% 21.63/4.35 % (23313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.63/4.35 % (23313)Termination reason: Unknown
% 21.63/4.35 % (23313)Termination phase: Property scanning
% 21.63/4.35
% 21.63/4.35 % (23313)Memory used [KB]: 2558
% 21.63/4.35 % (23313)Time elapsed: 0.026 s
% 21.63/4.35 % (23313)Instructions burned: 92 (million)
% 21.63/4.35 % (23313)------------------------------
% 21.63/4.35 % (23313)------------------------------
% 21.63/4.36 % (23314)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_22754 for (2972ds/593Mi)
% 21.63/4.37 % (23307)Instruction limit reached!
% 21.63/4.37 % (23307)------------------------------
% 21.63/4.37 % (23307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.63/4.37 % (23307)Termination reason: Unknown
% 21.63/4.37 % (23307)Termination phase: Saturation
% 21.63/4.37
% 21.63/4.37 % (23307)Memory used [KB]: 9850
% 21.63/4.37 % (23307)Time elapsed: 0.170 s
% 21.63/4.37 % (23307)Instructions burned: 596 (million)
% 21.63/4.37 % (23307)------------------------------
% 21.63/4.37 % (23307)------------------------------
% 21.63/4.38 % (23315)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_22754 for (2972ds/1512Mi)
% 22.19/4.47 % (23312)Instruction limit reached!
% 22.19/4.47 % (23312)------------------------------
% 22.19/4.47 % (23312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.19/4.47 % (23312)Termination reason: Unknown
% 22.19/4.47 % (23312)Termination phase: Saturation
% 22.19/4.47
% 22.19/4.47 % (23312)Memory used [KB]: 9978
% 22.19/4.47 % (23312)Time elapsed: 0.143 s
% 22.19/4.47 % (23312)Instructions burned: 503 (million)
% 22.19/4.47 % (23312)------------------------------
% 22.19/4.47 % (23312)------------------------------
% 22.19/4.48 % (23316)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_22754 for (2971ds/569Mi)
% 22.54/4.53 % (23314)Instruction limit reached!
% 22.54/4.53 % (23314)------------------------------
% 22.54/4.53 % (23314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.54/4.53 % (23314)Termination reason: Unknown
% 22.54/4.53 % (23314)Termination phase: Saturation
% 22.54/4.53
% 22.54/4.53 % (23314)Memory used [KB]: 10234
% 22.54/4.53 % (23314)Time elapsed: 0.172 s
% 22.54/4.53 % (23314)Instructions burned: 595 (million)
% 22.54/4.53 % (23314)------------------------------
% 22.54/4.53 % (23314)------------------------------
% 22.54/4.54 % (23317)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_22754 for (2970ds/501Mi)
% 22.54/4.56 % (23296)Instruction limit reached!
% 22.54/4.56 % (23296)------------------------------
% 22.54/4.56 % (23296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.54/4.56 % (23296)Termination reason: Unknown
% 22.54/4.56 % (23296)Termination phase: Saturation
% 22.54/4.56
% 22.54/4.56 % (23296)Memory used [KB]: 7803
% 22.54/4.56 % (23296)Time elapsed: 1.194 s
% 22.54/4.56 % (23296)Instructions burned: 4714 (million)
% 22.54/4.56 % (23296)------------------------------
% 22.54/4.56 % (23296)------------------------------
% 22.54/4.57 % (23318)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_22754 for (2970ds/562Mi)
% 22.89/4.62 % (23316)Instruction limit reached!
% 22.89/4.62 % (23316)------------------------------
% 22.89/4.62 % (23316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.89/4.62 % (23316)Termination reason: Unknown
% 22.89/4.62 % (23316)Termination phase: Saturation
% 22.89/4.62
% 22.89/4.62 % (23316)Memory used [KB]: 7675
% 22.89/4.62 % (23316)Time elapsed: 0.143 s
% 22.89/4.62 % (23316)Instructions burned: 570 (million)
% 22.89/4.62 % (23316)------------------------------
% 22.89/4.62 % (23316)------------------------------
% 22.89/4.63 % (23319)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_22754 for (2969ds/406Mi)
% 22.89/4.67 % (23310)Instruction limit reached!
% 22.89/4.67 % (23310)------------------------------
% 22.89/4.67 % (23310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.89/4.67 % (23310)Termination reason: Unknown
% 22.89/4.67 % (23310)Termination phase: Saturation
% 22.89/4.67
% 22.89/4.67 % (23310)Memory used [KB]: 21236
% 22.89/4.67 % (23310)Time elapsed: 0.433 s
% 22.89/4.67 % (23310)Instructions burned: 1763 (million)
% 22.89/4.67 % (23310)------------------------------
% 22.89/4.67 % (23310)------------------------------
% 22.89/4.68 % (23320)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_22754 for (2969ds/582Mi)
% 22.89/4.69 % (23317)Instruction limit reached!
% 22.89/4.69 % (23317)------------------------------
% 22.89/4.69 % (23317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.89/4.69 % (23317)Termination reason: Unknown
% 22.89/4.69 % (23317)Termination phase: Saturation
% 22.89/4.69
% 22.89/4.69 % (23317)Memory used [KB]: 10746
% 22.89/4.69 % (23317)Time elapsed: 0.147 s
% 22.89/4.69 % (23317)Instructions burned: 502 (million)
% 22.89/4.69 % (23317)------------------------------
% 22.89/4.69 % (23317)------------------------------
% 23.75/4.70 % (23321)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_22754 for (2969ds/456Mi)
% 23.75/4.72 % (23318)Instruction limit reached!
% 23.75/4.72 % (23318)------------------------------
% 23.75/4.72 % (23318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.75/4.72 % (23318)Termination reason: Unknown
% 23.75/4.72 % (23318)Termination phase: Saturation
% 23.75/4.72
% 23.75/4.72 % (23318)Memory used [KB]: 8187
% 23.75/4.72 % (23318)Time elapsed: 0.151 s
% 23.75/4.72 % (23318)Instructions burned: 562 (million)
% 23.75/4.72 % (23318)------------------------------
% 23.75/4.72 % (23318)------------------------------
% 23.75/4.73 % (23322)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_22754 for (2968ds/393Mi)
% 23.75/4.74 % (23319)Instruction limit reached!
% 23.75/4.74 % (23319)------------------------------
% 23.75/4.74 % (23319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.75/4.74 % (23319)Termination reason: Unknown
% 23.75/4.74 % (23319)Termination phase: Saturation
% 23.75/4.74
% 23.75/4.74 % (23319)Memory used [KB]: 7803
% 23.75/4.74 % (23319)Time elapsed: 0.108 s
% 23.75/4.74 % (23319)Instructions burned: 409 (million)
% 23.75/4.74 % (23319)------------------------------
% 23.75/4.74 % (23319)------------------------------
% 23.75/4.75 % (23323)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_22754 for (2968ds/1335Mi)
% 24.13/4.82 % (23321)Instruction limit reached!
% 24.13/4.82 % (23321)------------------------------
% 24.13/4.82 % (23321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.13/4.82 % (23321)Termination reason: Unknown
% 24.13/4.82 % (23321)Termination phase: Saturation
% 24.13/4.82
% 24.13/4.82 % (23321)Memory used [KB]: 9722
% 24.13/4.82 % (23321)Time elapsed: 0.127 s
% 24.13/4.82 % (23321)Instructions burned: 456 (million)
% 24.13/4.82 % (23321)------------------------------
% 24.13/4.82 % (23321)------------------------------
% 24.13/4.84 % (23324)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_22754 for (2967ds/3373Mi)
% 24.13/4.84 % (23322)Instruction limit reached!
% 24.13/4.84 % (23322)------------------------------
% 24.13/4.84 % (23322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.13/4.84 % (23322)Termination reason: Unknown
% 24.13/4.84 % (23322)Termination phase: Saturation
% 24.13/4.84
% 24.13/4.84 % (23322)Memory used [KB]: 10106
% 24.13/4.84 % (23322)Time elapsed: 0.111 s
% 24.13/4.84 % (23322)Instructions burned: 393 (million)
% 24.13/4.84 % (23322)------------------------------
% 24.13/4.84 % (23322)------------------------------
% 24.13/4.85 % (23325)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_22754 for (2967ds/474Mi)
% 24.13/4.85 % (23315)Instruction limit reached!
% 24.13/4.85 % (23315)------------------------------
% 24.13/4.85 % (23315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.13/4.85 % (23315)Termination reason: Unknown
% 24.13/4.85 % (23315)Termination phase: Saturation
% 24.13/4.85
% 24.13/4.85 % (23315)Memory used [KB]: 14328
% 24.13/4.85 % (23315)Time elapsed: 0.471 s
% 24.13/4.85 % (23315)Instructions burned: 1512 (million)
% 24.13/4.85 % (23315)------------------------------
% 24.13/4.85 % (23315)------------------------------
% 24.13/4.86 % (23320)Instruction limit reached!
% 24.13/4.86 % (23320)------------------------------
% 24.13/4.86 % (23320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.13/4.86 % (23320)Termination reason: Unknown
% 24.13/4.86 % (23320)Termination phase: Saturation
% 24.13/4.86
% 24.13/4.86 % (23320)Memory used [KB]: 11001
% 24.13/4.86 % (23320)Time elapsed: 0.180 s
% 24.13/4.86 % (23320)Instructions burned: 584 (million)
% 24.13/4.86 % (23320)------------------------------
% 24.13/4.86 % (23320)------------------------------
% 24.13/4.86 % (23326)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_22754 for (2967ds/157Mi)
% 24.13/4.87 % (23327)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_22754 for (2967ds/590Mi)
% 25.15/4.90 % (23326)Instruction limit reached!
% 25.15/4.90 % (23326)------------------------------
% 25.15/4.90 % (23326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.15/4.90 % (23326)Termination reason: Unknown
% 25.15/4.90 % (23326)Termination phase: Function definition elimination
% 25.15/4.90
% 25.15/4.90 % (23326)Memory used [KB]: 2814
% 25.15/4.90 % (23326)Time elapsed: 0.040 s
% 25.15/4.90 % (23326)Instructions burned: 157 (million)
% 25.15/4.90 % (23326)------------------------------
% 25.15/4.90 % (23326)------------------------------
% 25.15/4.91 % (23328)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_22754 for (2966ds/104Mi)
% 25.15/4.94 % (23328)Instruction limit reached!
% 25.15/4.94 % (23328)------------------------------
% 25.15/4.94 % (23328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.15/4.94 % (23328)Termination reason: Unknown
% 25.15/4.94 % (23328)Termination phase: Property scanning
% 25.15/4.94
% 25.15/4.94 % (23328)Memory used [KB]: 2814
% 25.15/4.94 % (23328)Time elapsed: 0.029 s
% 25.15/4.94 % (23328)Instructions burned: 106 (million)
% 25.15/4.94 % (23328)------------------------------
% 25.15/4.94 % (23328)------------------------------
% 25.15/4.95 % (23329)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_22754 for (2966ds/414Mi)
% 25.15/4.97 % (23325)Instruction limit reached!
% 25.15/4.97 % (23325)------------------------------
% 25.15/4.97 % (23325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.15/4.97 % (23325)Termination reason: Unknown
% 25.15/4.97 % (23325)Termination phase: Saturation
% 25.15/4.97
% 25.15/4.97 % (23325)Memory used [KB]: 7675
% 25.15/4.97 % (23325)Time elapsed: 0.119 s
% 25.15/4.97 % (23325)Instructions burned: 476 (million)
% 25.15/4.97 % (23325)------------------------------
% 25.15/4.97 % (23325)------------------------------
% 25.15/4.98 % (23330)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_22754 for (2966ds/715Mi)
% 27.05/5.03 % (23327)Instruction limit reached!
% 27.05/5.03 % (23327)------------------------------
% 27.05/5.03 % (23327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.05/5.03 % (23327)Termination reason: Unknown
% 27.05/5.03 % (23327)Termination phase: Saturation
% 27.05/5.03
% 27.05/5.03 % (23327)Memory used [KB]: 9338
% 27.05/5.03 % (23327)Time elapsed: 0.168 s
% 27.05/5.03 % (23327)Instructions burned: 592 (million)
% 27.05/5.03 % (23327)------------------------------
% 27.05/5.03 % (23327)------------------------------
% 27.05/5.05 % (23331)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_22754 for (2965ds/961Mi)
% 27.05/5.05 % (23329)Instruction limit reached!
% 27.05/5.05 % (23329)------------------------------
% 27.05/5.05 % (23329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.05/5.05 % (23329)Termination reason: Unknown
% 27.05/5.05 % (23329)Termination phase: Saturation
% 27.05/5.05
% 27.05/5.05 % (23329)Memory used [KB]: 7675
% 27.05/5.05 % (23329)Time elapsed: 0.104 s
% 27.05/5.05 % (23329)Instructions burned: 417 (million)
% 27.05/5.05 % (23329)------------------------------
% 27.05/5.05 % (23329)------------------------------
% 27.05/5.06 % (23332)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_22754 for (2965ds/1213Mi)
% 27.61/5.13 % (23324)First to succeed.
% 27.61/5.13 % (23324)Refutation found. Thanks to Tanya!
% 27.61/5.13 % SZS status Theorem for DTF2THF_22754
% 27.61/5.13 % SZS output start Proof for DTF2THF_22754
% 27.61/5.13 thf(func_def_0, type, in: $i > $i > $o).
% 27.61/5.13 thf(func_def_1, type, exu: ($i > $o) > $o).
% 27.61/5.13 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 27.61/5.13 thf(func_def_8, type, powerset: $i > $i).
% 27.61/5.13 thf(func_def_10, type, setunion: $i > $i).
% 27.61/5.13 thf(func_def_19, type, descr: ($i > $o) > $i).
% 27.61/5.13 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 27.61/5.13 thf(func_def_26, type, prop2set: $o > $i).
% 27.61/5.13 thf(func_def_36, type, nonempty: $i > $o).
% 27.61/5.13 thf(func_def_69, type, set2prop: $i > $o).
% 27.61/5.13 thf(func_def_88, type, subset: $i > $i > $o).
% 27.61/5.13 thf(func_def_89, type, disjoint: $i > $i > $o).
% 27.61/5.13 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 27.61/5.13 thf(func_def_114, type, binunion: $i > $i > $i).
% 27.61/5.13 thf(func_def_122, type, binintersect: $i > $i > $i).
% 27.61/5.13 thf(func_def_135, type, regular: $i > $o).
% 27.61/5.13 thf(func_def_136, type, setminus: $i > $i > $i).
% 27.61/5.13 thf(func_def_147, type, symdiff: $i > $i > $i).
% 27.61/5.13 thf(func_def_153, type, iskpair: $i > $o).
% 27.61/5.13 thf(func_def_158, type, kpair: $i > $i > $i).
% 27.61/5.13 thf(func_def_160, type, cartprod: $i > $i > $i).
% 27.61/5.13 thf(func_def_177, type, singleton: $i > $o).
% 27.61/5.13 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 27.61/5.13 thf(func_def_184, type, atmost1p: $i > $o).
% 27.61/5.13 thf(func_def_185, type, atleast2p: $i > $o).
% 27.61/5.13 thf(func_def_186, type, atmost2p: $i > $o).
% 27.61/5.13 thf(func_def_187, type, upairsetp: $i > $o).
% 27.61/5.13 thf(func_def_191, type, kfst: $i > $i).
% 27.61/5.13 thf(func_def_203, type, ksnd: $i > $i).
% 27.61/5.13 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 27.61/5.13 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 27.61/5.13 thf(func_def_222, type, func: $i > $i > $i > $o).
% 27.61/5.13 thf(func_def_223, type, funcSet: $i > $i > $i).
% 27.61/5.13 thf(func_def_226, type, ap: $i > $i > $i > $i > $i).
% 27.61/5.13 thf(func_def_232, type, lam: $i > $i > ($i > $i) > $i).
% 27.61/5.13 thf(func_def_259, type, if: $i > $o > $i > $i > $i).
% 27.61/5.13 thf(func_def_323, type, breln1: $i > $i > $o).
% 27.61/5.13 thf(func_def_325, type, breln1Set: $i > $i).
% 27.61/5.13 thf(func_def_327, type, transitive: $i > $i > $o).
% 27.61/5.13 thf(func_def_328, type, antisymmetric: $i > $i > $o).
% 27.61/5.13 thf(func_def_329, type, reflexive: $i > $i > $o).
% 27.61/5.13 thf(func_def_330, type, refltransitive: $i > $i > $o).
% 27.61/5.13 thf(func_def_331, type, refllinearorder: $i > $i > $o).
% 27.61/5.13 thf(func_def_332, type, reflwellordering: $i > $i > $o).
% 27.61/5.13 thf(func_def_338, type, breln1invset: $i > $i > $i).
% 27.61/5.13 thf(func_def_342, type, breln1compset: $i > $i > $i > $i).
% 27.61/5.13 thf(func_def_369, type, sK7: ($i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_370, type, sK8: ($i > $o) > $i).
% 27.61/5.13 thf(func_def_371, type, sK9: ($i > $i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_372, type, sK10: ($i > $i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_373, type, sK11: $i > ($i > $i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_374, type, sK12: ($i > $i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_375, type, sK13: $i > ($i > $i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_376, type, sK14: $i > ($i > $i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_377, type, sK15: $i > ($i > $i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_378, type, sK16: ($i > $o) > $i > $i > $i).
% 27.61/5.13 thf(func_def_379, type, sK17: ($i > $o) > $i > $i > $i).
% 27.61/5.13 thf(func_def_380, type, sK18: $i > $i > $i).
% 27.61/5.13 thf(func_def_381, type, sK19: $i > $i > $i > $i > $i).
% 27.61/5.13 thf(func_def_382, type, sK20: $i > $i > $i).
% 27.61/5.13 thf(func_def_383, type, sK21: $i > $i > $i).
% 27.61/5.13 thf(func_def_384, type, sK22: $i > $i > $i).
% 27.61/5.13 thf(func_def_385, type, sK23: $i > $i > $i).
% 27.61/5.13 thf(func_def_386, type, sK24: $i > $i > $i > $i).
% 27.61/5.13 thf(func_def_387, type, sK25: $i > $i > $i > $i).
% 27.61/5.13 thf(func_def_388, type, sK26: $i > $i).
% 27.61/5.13 thf(func_def_389, type, sK27: ($i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_390, type, sK28: ($i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_391, type, sK29: $i > $i > ($i > $i) > $i).
% 27.61/5.13 thf(func_def_392, type, sK30: $i > $i > $i > $i).
% 27.61/5.13 thf(func_def_393, type, sK31: $i > $i > $i > $i).
% 27.61/5.13 thf(func_def_394, type, sK32: $i > $i > $i > $i).
% 27.61/5.13 thf(func_def_395, type, sK33: $i > $i > $i).
% 27.61/5.13 thf(func_def_396, type, sK34: ($i > $o) > $i > $i > $i).
% 27.61/5.13 thf(func_def_397, type, sK35: ($i > $o) > $i > $i > $i).
% 27.61/5.13 thf(func_def_398, type, sK36: $i > $i > $i).
% 27.61/5.13 thf(func_def_399, type, sK37: ($i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_400, type, sK38: ($i > $o) > $i).
% 27.61/5.13 thf(func_def_401, type, sK39: ($i > $o) > $i).
% 27.61/5.13 thf(func_def_402, type, sK40: $i > $i).
% 27.61/5.13 thf(func_def_403, type, sK41: ($i > $i) > $i > $i > $i).
% 27.61/5.13 thf(func_def_404, type, sK42: ($i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_405, type, sK43: $i > $i > $i).
% 27.61/5.13 thf(func_def_406, type, sK44: $i > ($i > $o) > $i).
% 27.61/5.13 thf(func_def_407, type, sK45: ($i > $o) > $i).
% 27.61/5.13 thf(func_def_408, type, sK46: ($i > $o) > $i).
% 27.61/5.13 thf(func_def_409, type, sK47: ($i > $o) > $i).
% 27.61/5.13 thf(func_def_410, type, sK48: $i > $i > $i > $i > $i).
% 27.61/5.13 thf(func_def_411, type, sK49: $i > $i > $i > $i > $i).
% 27.61/5.13 thf(func_def_412, type, sK50: $i > $i > $i > $i > $i).
% 27.61/5.13 thf(func_def_413, type, sK51: $i > $i > $i > $i > $i).
% 27.61/5.13 thf(func_def_414, type, sK52: $i > $i > $i > $i > $i).
% 27.61/5.13 thf(func_def_415, type, sK53: $i > $i > $i > $i > $i).
% 27.61/5.13 thf(func_def_416, type, sK54: $i > $i > ($i > $i) > $i).
% 27.61/5.13 thf(func_def_417, type, sK55: $i > $o > $i > $i).
% 27.61/5.13 thf(func_def_418, type, sK56: ($i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_419, type, sK57: $i > $i).
% 27.61/5.13 thf(func_def_420, type, sK58: $i > $i > $i > $i > $i).
% 27.61/5.13 thf(func_def_421, type, sK59: $i > $i > $i).
% 27.61/5.13 thf(func_def_422, type, sK60: $i > $i > $i > $i).
% 27.61/5.13 thf(func_def_423, type, sK61: ($i > $o) > $i).
% 27.61/5.13 thf(func_def_424, type, sK62: ($i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_425, type, sK63: ($i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_426, type, sK64: ($i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_427, type, sK65: ($i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_428, type, sK66: $i > $i).
% 27.61/5.13 thf(func_def_429, type, sK67: $i > $i > $i > $i).
% 27.61/5.13 thf(func_def_430, type, sK68: ($i > $o) > ($i > $o) > $i).
% 27.61/5.13 thf(func_def_431, type, sK69: ($i > $o) > ($i > $o) > $i).
% 27.61/5.13 thf(func_def_432, type, sK70: ($i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_433, type, sK71: ($i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_434, type, sK72: ($i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_435, type, sK73: ($i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_436, type, sK74: ($i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_437, type, sK75: $i > $i).
% 27.61/5.13 thf(func_def_438, type, sK76: $i > $i > $i > $i > $i).
% 27.61/5.13 thf(func_def_439, type, sK77: $i > $i > $i > $i > $i).
% 27.61/5.13 thf(func_def_440, type, sK78: ($i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_441, type, sK79: $i > ($i > $o) > $i).
% 27.61/5.13 thf(func_def_442, type, sK80: ($i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_443, type, sK81: ($i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_444, type, sK82: $i > $i).
% 27.61/5.13 thf(func_def_445, type, sK83: $i > ($i > $o) > ($i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_446, type, sK84: $i > $i > ($i > $o) > ($i > $o) > $i).
% 27.61/5.13 thf(func_def_447, type, sK85: ($i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_448, type, sK86: ($i > $o) > $i).
% 27.61/5.13 thf(func_def_449, type, sK87: ($i > $i) > $i > $i > $i).
% 27.61/5.13 thf(func_def_450, type, sK88: $i > $i > ($i > $i) > $i).
% 27.61/5.13 thf(func_def_451, type, sK89: ($i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_452, type, sK90: ($i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_453, type, sK91: $i > $i > $i > $i > $i).
% 27.61/5.13 thf(func_def_454, type, sK92: ($i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_455, type, sK93: $i > $i > ($i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_456, type, sK94: $i > $i > ($i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_457, type, sK95: $i > ($i > $i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_458, type, sK96: $i > $i > ($i > $o) > $i).
% 27.61/5.13 thf(func_def_459, type, sK97: $i > $i > $i > $i).
% 27.61/5.13 thf(func_def_460, type, sK98: $i > $i > $i > $i).
% 27.61/5.13 thf(func_def_461, type, sK99: $i > $i).
% 27.61/5.13 thf(func_def_462, type, sK100: $i > $i > $i > $i).
% 27.61/5.13 thf(func_def_463, type, sK101: $i > $i > $i).
% 27.61/5.13 thf(func_def_464, type, sK102: $i > $i > $i).
% 27.61/5.13 thf(func_def_465, type, sK103: $i > $i > $i).
% 27.61/5.13 thf(func_def_466, type, sK104: $i > $i > $i).
% 27.61/5.13 thf(func_def_467, type, sK105: $i > $i > $i).
% 27.61/5.13 thf(func_def_468, type, sK106: $i > $i > $i).
% 27.61/5.13 thf(func_def_469, type, sK107: $i > $i > ($i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_470, type, sK108: $i > $i > ($i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_471, type, sK109: ($i > $o) > $i).
% 27.61/5.13 thf(func_def_472, type, sK110: ($i > $o) > ($i > $o) > $i).
% 27.61/5.13 thf(func_def_473, type, sK111: ($i > $o) > ($i > $o) > $i).
% 27.61/5.13 thf(func_def_474, type, sK112: ($i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_475, type, sK113: ($i > $o) > ($i > $o) > $i).
% 27.61/5.13 thf(func_def_476, type, sK114: ($i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_477, type, sK115: ($i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_478, type, sK116: ($i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_479, type, sK117: ($i > $o) > $i).
% 27.61/5.13 thf(func_def_480, type, sK118: ($i > $o) > ($i > $o) > $i).
% 27.61/5.13 thf(func_def_481, type, sK119: ($i > $o) > $i > $i).
% 27.61/5.13 thf(func_def_482, type, sK120: ($i > $o) > ($i > $o) > $i).
% 27.61/5.13 thf(func_def_483, type, sK121: $i > $i > $i > $i).
% 27.61/5.13 thf(func_def_484, type, sK122: $i > $i > $i > $i).
% 27.61/5.13 thf(func_def_485, type, sK123: $i > $i > $i > $i).
% 27.61/5.13 thf(func_def_486, type, sK124: $i > $i > $i > $i).
% 27.61/5.13 thf(func_def_487, type, sK125: $i > $i > $i > $i).
% 27.61/5.13 thf(func_def_488, type, sK126: $i > $i > $i > $i).
% 27.61/5.13 thf(func_def_489, type, ph127: !>[X0: $tType]:(X0)).
% 27.61/5.13 thf(f7028,plain,(
% 27.61/5.13 $false),
% 27.61/5.13 inference(avatar_sat_refutation,[status(thm)],[f5285,f5313,f5318,f5323,f5328,f5357,f5401,f7025,f7027])).
% 27.61/5.13 thf(f7027,plain,(
% 27.61/5.13 ($false != (in @ (kpair @ sK5 @ sK4) @ sK2)) | ($true != (in @ (kpair @ sK5 @ sK4) @ sK2)) | ($false = $true)),
% 27.61/5.13 introduced(definition,[],[theory_tautology_sat_conflict])).
% 27.61/5.13 thf(f7025,plain,(
% 27.61/5.13 spl6_66 | ~spl6_2 | ~spl6_10 | ~spl6_12 | ~spl6_19 | spl6_29),
% 27.61/5.13 inference(avatar_split_clause,[status(thm)],[f7024,f5398,f5354,f5325,f5315,f5282,f7019])).
% 27.61/5.13 thf(f7019,definition,(
% 27.61/5.13 spl6_66 <=> ($false = (in @ (kpair @ sK5 @ sK4) @ sK2))),
% 27.61/5.13 introduced(definition,[new_symbols(naming,[spl6_66])],[avatar_definition])).
% 27.61/5.13 thf(f5282,definition,(
% 27.61/5.13 spl6_2 <=> ($true = (in @ sK4 @ sK1))),
% 27.61/5.13 introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition])).
% 27.61/5.13 thf(f5315,definition,(
% 27.61/5.13 spl6_10 <=> ($true = (in @ (kpair @ sK3 @ sK5) @ sK0))),
% 27.61/5.13 introduced(definition,[new_symbols(naming,[spl6_10])],[avatar_definition])).
% 27.61/5.13 thf(f5325,definition,(
% 27.61/5.13 spl6_12 <=> ($true = (in @ sK5 @ sK1))),
% 27.61/5.13 introduced(definition,[new_symbols(naming,[spl6_12])],[avatar_definition])).
% 27.61/5.13 thf(f5354,definition,(
% 27.61/5.13 spl6_19 <=> ($true = (in @ sK3 @ sK1))),
% 27.61/5.13 introduced(definition,[new_symbols(naming,[spl6_19])],[avatar_definition])).
% 27.61/5.13 thf(f5398,definition,(
% 27.61/5.13 spl6_29 <=> ((in @ (kpair @ sK3 @ sK4) @ (dpsetconstr @ sK1 @ sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ sK1) & (in @ (kpair @ Y0 @ Y2) @ sK0)) & (in @ (kpair @ Y2 @ Y1) @ sK2))))))))) = $true)),
% 27.61/5.13 introduced(definition,[new_symbols(naming,[spl6_29])],[avatar_definition])).
% 27.61/5.13 thf(f7024,plain,(
% 27.61/5.13 ($false = (in @ (kpair @ sK5 @ sK4) @ sK2)) | (~spl6_2 | ~spl6_10 | ~spl6_12 | ~spl6_19 | spl6_29)),
% 27.61/5.13 inference(trivial_inequality_removal,[status(thm)],[f7023])).
% 27.61/5.13 thf(f7023,plain,(
% 27.61/5.13 ($false = $true) | ($false = (in @ (kpair @ sK5 @ sK4) @ sK2)) | (~spl6_2 | ~spl6_10 | ~spl6_12 | ~spl6_19 | spl6_29)),
% 27.61/5.13 inference(forward_demodulation,[status(thm)],[f7010,f5327])).
% 27.61/5.13 thf(f5327,plain,(
% 27.61/5.13 ($true = (in @ sK5 @ sK1)) | ~spl6_12),
% 27.61/5.13 inference(avatar_component_clause,[status(thm)],[f5325])).
% 27.61/5.13 thf(f7010,plain,(
% 27.61/5.13 ($false = (in @ (kpair @ sK5 @ sK4) @ sK2)) | ($false = (in @ sK5 @ sK1)) | (~spl6_2 | ~spl6_10 | ~spl6_19 | spl6_29)),
% 27.61/5.13 inference(trivial_inequality_removal,[status(thm)],[f7006])).
% 27.61/5.13 thf(f7006,plain,(
% 27.61/5.13 ($false = (in @ sK5 @ sK1)) | ($false = (in @ (kpair @ sK5 @ sK4) @ sK2)) | ($false = $true) | (~spl6_2 | ~spl6_10 | ~spl6_19 | spl6_29)),
% 27.61/5.13 inference(superposition,[status(thm)],[f5317,f6999])).
% 27.61/5.13 thf(f6999,plain,(
% 27.61/5.13 ( ! [X1 : $i] : (($false = (in @ (kpair @ sK3 @ X1) @ sK0)) | ($false = (in @ (kpair @ X1 @ sK4) @ sK2)) | ($false = (in @ X1 @ sK1))) ) | (~spl6_2 | ~spl6_19 | spl6_29)),
% 27.61/5.13 inference(trivial_inequality_removal,[status(thm)],[f6998])).
% 27.61/5.13 thf(f6998,plain,(
% 27.61/5.13 ( ! [X1 : $i] : (($false = (in @ (kpair @ X1 @ sK4) @ sK2)) | ($false = $true) | ($false = (in @ (kpair @ sK3 @ X1) @ sK0)) | ($false = (in @ X1 @ sK1))) ) | (~spl6_2 | ~spl6_19 | spl6_29)),
% 27.61/5.13 inference(forward_demodulation,[status(thm)],[f6997,f5284])).
% 27.61/5.13 thf(f5284,plain,(
% 27.61/5.13 ($true = (in @ sK4 @ sK1)) | ~spl6_2),
% 27.61/5.13 inference(avatar_component_clause,[status(thm)],[f5282])).
% 27.61/5.13 thf(f6997,plain,(
% 27.61/5.13 ( ! [X1 : $i] : (($false = (in @ (kpair @ X1 @ sK4) @ sK2)) | ($false = (in @ sK4 @ sK1)) | ($false = (in @ (kpair @ sK3 @ X1) @ sK0)) | ($false = (in @ X1 @ sK1))) ) | (~spl6_19 | spl6_29)),
% 27.61/5.13 inference(trivial_inequality_removal,[status(thm)],[f6996])).
% 27.61/5.13 thf(f6996,plain,(
% 27.61/5.13 ( ! [X1 : $i] : (($false = (in @ sK4 @ sK1)) | ($false = (in @ X1 @ sK1)) | ($false = (in @ (kpair @ X1 @ sK4) @ sK2)) | ($false = (in @ (kpair @ sK3 @ X1) @ sK0)) | ($false = $true)) ) | (~spl6_19 | spl6_29)),
% 27.61/5.13 inference(forward_demodulation,[status(thm)],[f6992,f5356])).
% 27.61/5.13 thf(f5356,plain,(
% 27.61/5.13 ($true = (in @ sK3 @ sK1)) | ~spl6_19),
% 27.61/5.13 inference(avatar_component_clause,[status(thm)],[f5354])).
% 27.61/5.13 thf(f6992,plain,(
% 27.61/5.13 ( ! [X1 : $i] : (($false = (in @ sK3 @ sK1)) | ($false = (in @ (kpair @ X1 @ sK4) @ sK2)) | ($false = (in @ (kpair @ sK3 @ X1) @ sK0)) | ($false = (in @ sK4 @ sK1)) | ($false = (in @ X1 @ sK1))) ) | spl6_29),
% 27.61/5.13 inference(binary_proxy_clausification,[status(thm)],[f6991])).
% 27.61/5.13 thf(f6991,plain,(
% 27.61/5.13 ( ! [X1 : $i] : (($false = (in @ sK3 @ sK1)) | ($false = (in @ sK4 @ sK1)) | ($false = (in @ (kpair @ X1 @ sK4) @ sK2)) | ($false = ((in @ X1 @ sK1) & (in @ (kpair @ sK3 @ X1) @ sK0)))) ) | spl6_29),
% 27.61/5.13 inference(binary_proxy_clausification,[status(thm)],[f6990])).
% 27.61/5.13 thf(f6990,plain,(
% 27.61/5.13 ( ! [X1 : $i] : (($false = (((in @ X1 @ sK1) & (in @ (kpair @ sK3 @ X1) @ sK0)) & (in @ (kpair @ X1 @ sK4) @ sK2))) | ($false = (in @ sK3 @ sK1)) | ($false = (in @ sK4 @ sK1))) ) | spl6_29),
% 27.61/5.13 inference(beta_eta_normalization,[status(thm)],[f6989])).
% 27.61/5.13 thf(f6989,plain,(
% 27.61/5.13 ( ! [X1 : $i] : (($false = (in @ sK3 @ sK1)) | ($false = ((^[Y0 : $i]: (((in @ Y0 @ sK1) & (in @ (kpair @ sK3 @ Y0) @ sK0)) & (in @ (kpair @ Y0 @ sK4) @ sK2))) @ X1)) | ($false = (in @ sK4 @ sK1))) ) | spl6_29),
% 27.61/5.13 inference(pi_clausification,[status(thm)],[f6988])).
% 27.61/5.13 thf(f6988,plain,(
% 27.61/5.13 ($false = (?? @ $i @ (^[Y0 : $i]: (((in @ Y0 @ sK1) & (in @ (kpair @ sK3 @ Y0) @ sK0)) & (in @ (kpair @ Y0 @ sK4) @ sK2))))) | ($false = (in @ sK4 @ sK1)) | ($false = (in @ sK3 @ sK1)) | spl6_29),
% 27.61/5.13 inference(beta_eta_normalization,[status(thm)],[f6987])).
% 27.61/5.13 thf(f6987,plain,(
% 27.61/5.13 ($false = ((^[Y0 : $i]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ sK1) & (in @ (kpair @ Y0 @ Y2) @ sK0)) & (in @ (kpair @ Y2 @ Y1) @ sK2))))))) @ sK3 @ sK4)) | ($false = (in @ sK3 @ sK1)) | ($false = (in @ sK4 @ sK1)) | spl6_29),
% 27.61/5.13 inference(trivial_inequality_removal,[status(thm)],[f6981])).
% 27.61/5.13 thf(f6981,plain,(
% 27.61/5.13 ($false = (in @ sK3 @ sK1)) | ($false = (in @ sK4 @ sK1)) | ($true != $true) | ($false = ((^[Y0 : $i]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ sK1) & (in @ (kpair @ Y0 @ Y2) @ sK0)) & (in @ (kpair @ Y2 @ Y1) @ sK2))))))) @ sK3 @ sK4)) | spl6_29),
% 27.61/5.13 inference(superposition,[status(thm)],[f5400,f2262])).
% 27.61/5.13 thf(f2262,plain,(
% 27.61/5.13 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o,X4 : $i,X5 : $i] : (((in @ (kpair @ X2 @ X5) @ (dpsetconstr @ X4 @ X3 @ X1)) = $true) | ((X1 @ X2 @ X5) = $false) | ($false = (in @ X5 @ X3)) | ((in @ X2 @ X4) = $false)) )),
% 27.61/5.13 inference(binary_proxy_clausification,[status(thm)],[f2261])).
% 27.61/5.13 thf(f2261,plain,(
% 27.61/5.13 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o,X4 : $i,X5 : $i] : (($true = ((X1 @ X2 @ X5) => (in @ (kpair @ X2 @ X5) @ (dpsetconstr @ X4 @ X3 @ X1)))) | ((in @ X2 @ X4) = $false) | ($false = (in @ X5 @ X3))) )),
% 27.61/5.13 inference(binary_proxy_clausification,[status(thm)],[f2260])).
% 27.61/5.13 thf(f2260,plain,(
% 27.61/5.13 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o,X4 : $i,X5 : $i] : ((((in @ X5 @ X3) => ((X1 @ X2 @ X5) => (in @ (kpair @ X2 @ X5) @ (dpsetconstr @ X4 @ X3 @ X1)))) = $true) | ((in @ X2 @ X4) = $false)) )),
% 27.61/5.13 inference(beta_eta_normalization,[status(thm)],[f2259])).
% 27.61/5.13 thf(f2259,plain,(
% 27.61/5.13 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o,X4 : $i,X5 : $i] : (((in @ X2 @ X4) = $false) | ($true = ((^[Y0 : $i]: ((in @ Y0 @ X3) => ((X1 @ X2 @ Y0) => (in @ (kpair @ X2 @ Y0) @ (dpsetconstr @ X4 @ X3 @ X1))))) @ X5))) )),
% 27.61/5.13 inference(pi_clausification,[status(thm)],[f2258])).
% 27.61/5.13 thf(f2258,plain,(
% 27.61/5.13 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o,X4 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => ((X1 @ X2 @ Y0) => (in @ (kpair @ X2 @ Y0) @ (dpsetconstr @ X4 @ X3 @ X1)))))) = $true) | ((in @ X2 @ X4) = $false)) )),
% 27.61/5.13 inference(binary_proxy_clausification,[status(thm)],[f2257])).
% 27.61/5.13 thf(f2257,plain,(
% 27.61/5.13 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o,X4 : $i] : (($true = ((in @ X2 @ X4) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => ((X1 @ X2 @ Y0) => (in @ (kpair @ X2 @ Y0) @ (dpsetconstr @ X4 @ X3 @ X1))))))))) )),
% 27.61/5.13 inference(beta_eta_normalization,[status(thm)],[f2256])).
% 27.61/5.13 thf(f2256,plain,(
% 27.61/5.13 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o,X4 : $i] : (($true = ((^[Y0 : $i]: ((in @ X2 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X3) => ((X1 @ X2 @ Y1) => (in @ (kpair @ X2 @ Y1) @ (dpsetconstr @ Y0 @ X3 @ X1)))))))) @ X4))) )),
% 27.61/5.13 inference(pi_clausification,[status(thm)],[f2255])).
% 27.61/5.13 thf(f2255,plain,(
% 27.61/5.13 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o] : (((!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X3) => ((X1 @ X2 @ Y1) => (in @ (kpair @ X2 @ Y1) @ (dpsetconstr @ Y0 @ X3 @ X1))))))))) = $true)) )),
% 27.61/5.13 inference(beta_eta_normalization,[status(thm)],[f2254])).
% 27.61/5.13 thf(f2254,plain,(
% 27.61/5.13 ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X2 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((X1 @ X2 @ Y2) => (in @ (kpair @ X2 @ Y2) @ (dpsetconstr @ Y1 @ Y0 @ X1)))))))))) @ X3))) )),
% 27.61/5.13 inference(pi_clausification,[status(thm)],[f2253])).
% 27.61/5.13 thf(f2253,plain,(
% 27.61/5.13 ( ! [X2 : $i,X1 : $i > $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X2 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((X1 @ X2 @ Y2) => (in @ (kpair @ X2 @ Y2) @ (dpsetconstr @ Y1 @ Y0 @ X1))))))))))) = $true)) )),
% 27.61/5.13 inference(beta_eta_normalization,[status(thm)],[f2252])).
% 27.61/5.13 thf(f2252,plain,(
% 27.61/5.13 ( ! [X2 : $i,X1 : $i > $i > $o] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((X1 @ Y0 @ Y3) => (in @ (kpair @ Y0 @ Y3) @ (dpsetconstr @ Y2 @ Y1 @ X1)))))))))))) @ X2))) )),
% 27.61/5.13 inference(pi_clausification,[status(thm)],[f2251])).
% 27.61/5.13 thf(f2251,plain,(
% 27.61/5.13 ( ! [X1 : $i > $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((X1 @ Y0 @ Y3) => (in @ (kpair @ Y0 @ Y3) @ (dpsetconstr @ Y2 @ Y1 @ X1))))))))))))) = $true)) )),
% 27.61/5.13 inference(beta_eta_normalization,[status(thm)],[f2250])).
% 27.61/5.13 thf(f2250,plain,(
% 27.61/5.13 ( ! [X1 : $i > $i > $o] : (($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y0 @ Y1 @ Y4) => (in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y3 @ Y2 @ Y0)))))))))))))) @ X1))) )),
% 27.61/5.13 inference(pi_clausification,[status(thm)],[f2249])).
% 27.61/5.13 thf(f2249,plain,(
% 27.61/5.13 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y0 @ Y1 @ Y4) => (in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y3 @ Y2 @ Y0))))))))))))))) = $true)),
% 27.61/5.13 inference(beta_eta_normalization,[status(thm)],[f1638])).
% 27.61/5.13 thf(f1638,plain,(
% 27.61/5.13 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y0 @ Y1 @ Y4) => (in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y3 @ Y2 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y0 @ Y5 @ Y6))))))))))))))))))) = $true)),
% 27.61/5.13 inference(definition_unfolding,[status(thm)],[f1221,f1019])).
% 27.61/5.13 thf(f1019,plain,(
% 27.61/5.13 (dpsetconstrI = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y0 @ Y1 @ Y4) => (in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y3 @ Y2 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y0 @ Y5 @ Y6))))))))))))))))))))),
% 27.61/5.13 inference(cnf_transformation,[status(thm)],[f562])).
% 27.61/5.13 thf(f562,plain,(
% 27.61/5.13 (dpsetconstrI = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y0 @ Y1 @ Y4) => (in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y3 @ Y2 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y0 @ Y5 @ Y6))))))))))))))))))))),
% 27.61/5.13 inference(fool_elimination,[status(thm)],[f561])).
% 27.61/5.13 thf(f561,plain,(
% 27.61/5.13 (dpsetconstrI = ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i > $i > $o] : ((in @ X2 @ X0) => ! [X4 : $i] : ((in @ X4 @ X1) => ((X3 @ X2 @ X4) => (in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X0 @ X1 @ (^[X5 : $i, X6 : $i] : (X3 @ X5 @ X6))))))))),
% 27.61/5.13 inference(rectify,[status(thm)],[f185])).
% 27.61/5.13 thf(f185,axiom,(
% 27.61/5.13 (dpsetconstrI = ! [X3 : $i,X4 : $i,X1 : $i,X0 : $i > $i > $o] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X4) => ((X0 @ X1 @ X2) => (in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X3 @ X4 @ (^[X8 : $i, X10 : $i] : (X0 @ X8 @ X10))))))))),
% 27.61/5.13 file('/export/starexec/sandbox2/tmp/tmp.V1n9lFWd3k/DTF2THF_22754.p',dpsetconstrI)).
% 27.61/5.13 thf(f1221,plain,(
% 27.61/5.13 (dpsetconstrI = $true)),
% 27.61/5.13 inference(cnf_transformation,[status(thm)],[f907])).
% 27.61/5.13 thf(f907,plain,(
% 27.61/5.13 (binunionTE = $true) & (binintersectLsub = $true) & (setunionsingleton2 = $true) & (lamProp = $true) & (iffalseProp2 = $true) & (doubleComplementSub2 = $true) & (binunionT_lem = $true) & (setminusLsub = $true) & (theprop = $true) & (complementImpComplementIntersect = $true) & (emptyset__Cong = $true) & (iftrueProp2 = $true) & (binintersectI = $true) & (setukpairinjL2 = $true) & (notequalI2 = $true) & (binintersectSubset5 = $true) & (brelnall1 = $true) & (breln1invprop = $true) & (notinemptyset = $true) & (breln1all2 = $true) & (notdallE = $true) & (cartprodpairmemER = $true) & (cartprodpairmemEL = $true) & (exuE3u = $true) & (binintersectTERcontra = $true) & (theeq = $true) & (binunionE = $true) & (funcextLem = $true) & (funcGraphProp1 = $true) & (upairsetIR = $true) & (powersetE = $true) & (ubforcartprodlem2 = $true) & (setminusELneg = $true) & (omegaIndAx = $true) & (prop2setI = $true) & (dpsetconstrERa = $true) & (doubleComplementSub1 = $true) & (setminusILneg = $true) & (eqimpsubset1 = $true) & (ap2apEq1 = $true) & (inPowerset = $true) & (funcinfuncset = $true) & (inComplementUnionImpNotIn1 = $true) & (setoftrueEq = $true) & (quantDeMorgan4 = $true) & (setadjoinE = $true) & (exuE1 = $true) & (notsubsetI = $true) & (dpsetconstrER = $true) & (descrp = $true) & (emptysetE = $true) & (dsetconstrER = $true) & (powersetI1 = $true) & (powersetE1 = $true) & (contrasubsetT1 = $true) & (setadjoin__Cong = $true) & (setunion__Cong = $true) & (subbreln1 = $true) & (eqbreln1 = $true) & (disjointsetsI1 = $true) & (brelnall2 = $true) & (contrasubsetT = $true) & (funcext = $true) & (uniqinunit = $true) & (quantDeMorgan1 = $true) & (doubleComplementE1 = $true) & (breln1invE = $true) & (complementInPowersetComplementIntersect = $true) & (cartprodmempair = $true) & (wellorderingAx = $true) & (lam2p = $true) & (setukpairinjR2 = $true) & (singletonsubset = $true) & (vacuousDall = $true) & (emptysetsubset = $true) & (ubforcartprodlem3 = $true) & (powersetAx = $true) & (inIntersectImpInUnion = $true) & (demorgan2a = $true) & (dpsetconstrSub = $true) & (powersetT_lem = $true) & (upairequniteq = $true) & (emptyInPowerset = $true) & (upairsetE = $true) & (setadjoinSub = $true) & (dsetconstrEL = $true) & (app = $true) & (demorgan2 = $true) & (binintersectSubset4 = $true) & (funcImageSingleton = $true) & (exuE3e = $true) & (nonemptyI = $true) & (binintersectTELcontra = $true) & (setextT = $true) & (ex1E1 = $true) & (complementTcontraSubset = $true) & (singletonsswitch = $true) & (setukpairinjL = $true) & (symdiffIneg1 = $true) & (subsetTI = $true) & (woz13rule1 = $true) & (foundationAx = $true) & (cartprodmempair1 = $true) & (doubleComplementEq = $true) & (powersetI = $true) & (binintersectEL = $true) & (funcGraphProp3 = $true) & (setukpairinjL1 = $true) & (subsetemptysetimpeq = $true) & (ex1E2 = $true) & (setunionE = $true) & (beta2 = $true) & (binunionTIRcontra = $true) & (singletonsuniq = $true) & (breln1invI = $true) & (intersectInPowersetIntersectUnions = $true) & (exuI3 = $true) & (in__Cong = $true) & (setukpairinjR1 = $true) & (demorgan1a = $true) & (bs114d = $true) & (powersetsubset = $true) & (setminusSubset1 = $true) & (ex1I2 = $true) & (binintersectSubset1 = $true) & (subset2powerset = $true) & (contrasubsetT3 = $true) & (doubleComplementI1 = $true) & (ex1I = $true) & (dsetconstr__Cong = $true) & (notequalI1 = $true) & (complementSubsetComplementIntersect = $true) & (ifSingleton = $true) & (exu__Cong = $true) & (symdiffI2 = $true) & (kpairsurjEq = $true) & (complementTnotintersectT = $true) & (symdiffI1 = $true) & (omega__Cong = $true) & (ap2p = $true) & (binunionRsub = $true) & (binunionLsub = $true) & (sepInPowerset = $true) & (subPowSU = $true) & (emptyinPowerset = $true) & (sepSubset = $true) & (upairsetIL = $true) & (breln1all1 = $true) & (dsetconstrI = $true) & (secondinupair = $true) & (setextAx = $true) & (cartprodmempaircEq = $true) & (setminusERneg = $true) & (binunionIL = $true) & (exuI2 = $true) & (replAx = $true) & (contraSubsetComplement = $true) & (setbeta = $true) & (notinsingleton = $true) & (subsetE = $true) & (binunionEcases = $true) & (woz13rule3 = $true) & (woz1_5 = $true) & (quantDeMorgan3 = $true) & (contrasubsetT2 = $true) & (emptyI = $true) & (woz1_2 = $true) & (nonemptyE1 = $true) & (setminusT_lem = $true) & (woz1_4 = $true) & (inComplementUnionImpInComplement1 = $true) & (setminusI = $true) & (prop2setE = $true) & (dpsetconstrI = $true) & (setOfPairsIsBReln = $true) & (exuI1 = $true) & (choice2fnsingleton = $true) & (exuE2 = $true) & (cartprodfstin = $true) & (subsetRefl = $true) & (prop2set2propI = $true) & (noeltsimpempty = $true) & (emptysetAx = $true) & (subsetE2 = $true) & (subbreln = $true) & (dpsetconstrEL2 = $true) & (setadjoinIR = $true) & (setunionsingleton = $true) & (setadjoinIL = $true) & (powersetTI1 = $true) & (cartprodfstpairEq = $true) & (nonemptyI1 = $true) & (setunionsingleton1 = $true) & (binunionTILcontra = $true) & (kfstsingleton = $true) & (setukpairinjR11 = $true) & (emptyE1 = $true) & (singletoninpowerset = $true) & (emptysetimpfalse = $true) & (kpairiskpair = $true) & (setadjoinAx = $true) & (lamp = $true) & (binintersectER = $true) & (lam2lamEq = $true) & (inIntersectImpInIntersectUnions = $true) & (woz13rule4 = $true) & (upairset2E = $true) & (setOfPairsIsBReln1 = $true) & (beta1 = $true) & (kfstpairEq = $true) & (inCongP = $true) & (setext = $true) & (setukpairIL = $true) & (woz13rule0 = $true) & (symdiffE = $true) & (upairsubunion = $true) & (cartprodsndin = $true) & (iffalseProp1 = $true) & (complementT_lem = $true) & (setminusER = $true) & (setunionE2 = $true) & (funcGraphProp2 = $true) & (ubforcartprodlem1 = $true) & (setminusIRneg = $true) & (demorgan1b = $true) & (binintersectSubset3 = $true) & (cartprodsndpairEq = $true) & (binintersectRsub = $true) & (eqimpsubset2 = $true) & (complementUnionInPowersetComplement = $true) & (breln1compprop = $true) & (powerset__Cong = $true) & (dpsetconstrEL1 = $true) & (inIntersectImpInUnion2 = $true) & (funcGraphProp4 = $true) & (notdexE = $true) & (demorgan2b2 = $true) & (binintersectSubset2 = $true) & (subsetTrans = $true) & (eqbreln = $true) & (setadjoinOr = $true) & (setunionAx = $true) & (binunionIR = $true) & (subsetI2 = $true) & (iftrueProp1 = $true) & (breln1SetBreln1 = $true) & (funcext2 = $true) & (woz1_1 = $true) & (eta2 = $true) & (upairinpowunion = $true) & (demorgan2b = $true) & (woz13rule2 = $true) & (powersetTE1 = $true) & (exuEu = $true) & (setukpairinjR = $true) & (complementTI1 = $true) & (ifp = $true) & (iffalse = $true) & (kpairp = $true) & (setminusSubset2 = $true) & (quantDeMorgan2 = $true) & (infuncsetfunc = $true) & (demorgan2a1 = $true) & (nonemptyImpWitness = $true) & (((($true = (in @ sK3 @ sK1)) & (($true = (in @ sK4 @ sK1)) & (($true = (in @ (kpair @ sK5 @ sK4) @ sK2)) & ($true = (in @ (kpair @ sK3 @ sK5) @ sK0)) & ($true = (in @ sK5 @ sK1)) & ($true != (in @ (kpair @ sK3 @ sK4) @ (breln1compset @ sK1 @ sK0 @ sK2)))))) & ($true = (breln1 @ sK1 @ sK2))) & ($true = (breln1 @ sK1 @ sK0))) & (apProp = $true) & (setukpairinjR12 = $true) & (setukpairIR = $true) & (omega0Ax = $true) & (setminusEL = $true) & (ksndpairEq = $true) & (setextsub = $true) & (descr__Cong = $true) & (ap2apEq2 = $true) & (binunionTEcontra = $true) & (iftrue = $true) & (setadjoinSub2 = $true) & (cartprodpairin = $true) & (demorgan2a2 = $true) & (woz1_3 = $true) & (demorgan1 = $true) & (singletonprop = $true) & (iftrueorfalse = $true) & (omegaSAx = $true) & (emptyinunitempty = $true) & (subsetI1 = $true) & (ksndsingleton = $true) & (upairset2IR = $true) & (eqinunit = $true) & (binintersectT_lem = $true) & (complementTE1 = $true) & (cartprodpairsurjEq = $true) & (symdiffIneg2 = $true) & (setunionI = $true) & (eta1 = $true) & (singletoninpowunion = $true)),
% 27.61/5.13 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f901,f906,f905,f904,f903,f902])).
% 27.61/5.13 thf(f902,plain,(
% 27.61/5.13 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X1) = $true) & ? [X4 : $i] : (($true = (in @ X4 @ X1)) & ? [X5 : $i] : (((in @ (kpair @ X5 @ X4) @ X2) = $true) & ((in @ (kpair @ X3 @ X5) @ X0) = $true) & ($true = (in @ X5 @ X1)) & ((in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)) != $true)))) & ((breln1 @ X1 @ X2) = $true)) & ($true = (breln1 @ X1 @ X0))) => (? [X2 : $i] : (? [X3 : $i] : (($true = (in @ X3 @ sK1)) & ? [X4 : $i] : (((in @ X4 @ sK1) = $true) & ? [X5 : $i] : (((in @ (kpair @ X5 @ X4) @ X2) = $true) & ((in @ (kpair @ X3 @ X5) @ sK0) = $true) & ($true = (in @ X5 @ sK1)) & ($true != (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK1 @ sK0 @ X2)))))) & ($true = (breln1 @ sK1 @ X2))) & ($true = (breln1 @ sK1 @ sK0)))),
% 27.61/5.13 introduced(definition,[],[choice_axiom])).
% 27.61/5.13 thf(f903,plain,(
% 27.61/5.13 ? [X2 : $i] : (? [X3 : $i] : (($true = (in @ X3 @ sK1)) & ? [X4 : $i] : (((in @ X4 @ sK1) = $true) & ? [X5 : $i] : (((in @ (kpair @ X5 @ X4) @ X2) = $true) & ((in @ (kpair @ X3 @ X5) @ sK0) = $true) & ($true = (in @ X5 @ sK1)) & ($true != (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK1 @ sK0 @ X2)))))) & ($true = (breln1 @ sK1 @ X2))) => (? [X3 : $i] : (($true = (in @ X3 @ sK1)) & ? [X4 : $i] : (((in @ X4 @ sK1) = $true) & ? [X5 : $i] : (($true = (in @ (kpair @ X5 @ X4) @ sK2)) & ((in @ (kpair @ X3 @ X5) @ sK0) = $true) & ($true = (in @ X5 @ sK1)) & ((in @ (kpair @ X3 @ X4) @ (breln1compset @ sK1 @ sK0 @ sK2)) != $true)))) & ($true = (breln1 @ sK1 @ sK2)))),
% 27.61/5.13 introduced(definition,[],[choice_axiom])).
% 27.61/5.13 thf(f904,plain,(
% 27.61/5.13 ? [X3 : $i] : (($true = (in @ X3 @ sK1)) & ? [X4 : $i] : (((in @ X4 @ sK1) = $true) & ? [X5 : $i] : (($true = (in @ (kpair @ X5 @ X4) @ sK2)) & ((in @ (kpair @ X3 @ X5) @ sK0) = $true) & ($true = (in @ X5 @ sK1)) & ((in @ (kpair @ X3 @ X4) @ (breln1compset @ sK1 @ sK0 @ sK2)) != $true)))) => (($true = (in @ sK3 @ sK1)) & ? [X4 : $i] : (((in @ X4 @ sK1) = $true) & ? [X5 : $i] : (($true = (in @ (kpair @ X5 @ X4) @ sK2)) & ($true = (in @ (kpair @ sK3 @ X5) @ sK0)) & ($true = (in @ X5 @ sK1)) & ((in @ (kpair @ sK3 @ X4) @ (breln1compset @ sK1 @ sK0 @ sK2)) != $true))))),
% 27.61/5.13 introduced(definition,[],[choice_axiom])).
% 27.61/5.13 thf(f905,plain,(
% 27.61/5.13 ? [X4 : $i] : (((in @ X4 @ sK1) = $true) & ? [X5 : $i] : (($true = (in @ (kpair @ X5 @ X4) @ sK2)) & ($true = (in @ (kpair @ sK3 @ X5) @ sK0)) & ($true = (in @ X5 @ sK1)) & ((in @ (kpair @ sK3 @ X4) @ (breln1compset @ sK1 @ sK0 @ sK2)) != $true))) => (($true = (in @ sK4 @ sK1)) & ? [X5 : $i] : (($true = (in @ (kpair @ X5 @ sK4) @ sK2)) & ($true = (in @ (kpair @ sK3 @ X5) @ sK0)) & ($true = (in @ X5 @ sK1)) & ($true != (in @ (kpair @ sK3 @ sK4) @ (breln1compset @ sK1 @ sK0 @ sK2)))))),
% 27.61/5.13 introduced(definition,[],[choice_axiom])).
% 27.61/5.13 thf(f906,plain,(
% 27.61/5.13 ? [X5 : $i] : (($true = (in @ (kpair @ X5 @ sK4) @ sK2)) & ($true = (in @ (kpair @ sK3 @ X5) @ sK0)) & ($true = (in @ X5 @ sK1)) & ($true != (in @ (kpair @ sK3 @ sK4) @ (breln1compset @ sK1 @ sK0 @ sK2)))) => (($true = (in @ (kpair @ sK5 @ sK4) @ sK2)) & ($true = (in @ (kpair @ sK3 @ sK5) @ sK0)) & ($true = (in @ sK5 @ sK1)) & ($true != (in @ (kpair @ sK3 @ sK4) @ (breln1compset @ sK1 @ sK0 @ sK2))))),
% 27.61/5.13 introduced(definition,[],[choice_axiom])).
% 27.61/5.13 thf(f901,plain,(
% 27.61/5.13 (binunionTE = $true) & (binintersectLsub = $true) & (setunionsingleton2 = $true) & (lamProp = $true) & (iffalseProp2 = $true) & (doubleComplementSub2 = $true) & (binunionT_lem = $true) & (setminusLsub = $true) & (theprop = $true) & (complementImpComplementIntersect = $true) & (emptyset__Cong = $true) & (iftrueProp2 = $true) & (binintersectI = $true) & (setukpairinjL2 = $true) & (notequalI2 = $true) & (binintersectSubset5 = $true) & (brelnall1 = $true) & (breln1invprop = $true) & (notinemptyset = $true) & (breln1all2 = $true) & (notdallE = $true) & (cartprodpairmemER = $true) & (cartprodpairmemEL = $true) & (exuE3u = $true) & (binintersectTERcontra = $true) & (theeq = $true) & (binunionE = $true) & (funcextLem = $true) & (funcGraphProp1 = $true) & (upairsetIR = $true) & (powersetE = $true) & (ubforcartprodlem2 = $true) & (setminusELneg = $true) & (omegaIndAx = $true) & (prop2setI = $true) & (dpsetconstrERa = $true) & (doubleComplementSub1 = $true) & (setminusILneg = $true) & (eqimpsubset1 = $true) & (ap2apEq1 = $true) & (inPowerset = $true) & (funcinfuncset = $true) & (inComplementUnionImpNotIn1 = $true) & (setoftrueEq = $true) & (quantDeMorgan4 = $true) & (setadjoinE = $true) & (exuE1 = $true) & (notsubsetI = $true) & (dpsetconstrER = $true) & (descrp = $true) & (emptysetE = $true) & (dsetconstrER = $true) & (powersetI1 = $true) & (powersetE1 = $true) & (contrasubsetT1 = $true) & (setadjoin__Cong = $true) & (setunion__Cong = $true) & (subbreln1 = $true) & (eqbreln1 = $true) & (disjointsetsI1 = $true) & (brelnall2 = $true) & (contrasubsetT = $true) & (funcext = $true) & (uniqinunit = $true) & (quantDeMorgan1 = $true) & (doubleComplementE1 = $true) & (breln1invE = $true) & (complementInPowersetComplementIntersect = $true) & (cartprodmempair = $true) & (wellorderingAx = $true) & (lam2p = $true) & (setukpairinjR2 = $true) & (singletonsubset = $true) & (vacuousDall = $true) & (emptysetsubset = $true) & (ubforcartprodlem3 = $true) & (powersetAx = $true) & (inIntersectImpInUnion = $true) & (demorgan2a = $true) & (dpsetconstrSub = $true) & (powersetT_lem = $true) & (upairequniteq = $true) & (emptyInPowerset = $true) & (upairsetE = $true) & (setadjoinSub = $true) & (dsetconstrEL = $true) & (app = $true) & (demorgan2 = $true) & (binintersectSubset4 = $true) & (funcImageSingleton = $true) & (exuE3e = $true) & (nonemptyI = $true) & (binintersectTELcontra = $true) & (setextT = $true) & (ex1E1 = $true) & (complementTcontraSubset = $true) & (singletonsswitch = $true) & (setukpairinjL = $true) & (symdiffIneg1 = $true) & (subsetTI = $true) & (woz13rule1 = $true) & (foundationAx = $true) & (cartprodmempair1 = $true) & (doubleComplementEq = $true) & (powersetI = $true) & (binintersectEL = $true) & (funcGraphProp3 = $true) & (setukpairinjL1 = $true) & (subsetemptysetimpeq = $true) & (ex1E2 = $true) & (setunionE = $true) & (beta2 = $true) & (binunionTIRcontra = $true) & (singletonsuniq = $true) & (breln1invI = $true) & (intersectInPowersetIntersectUnions = $true) & (exuI3 = $true) & (in__Cong = $true) & (setukpairinjR1 = $true) & (demorgan1a = $true) & (bs114d = $true) & (powersetsubset = $true) & (setminusSubset1 = $true) & (ex1I2 = $true) & (binintersectSubset1 = $true) & (subset2powerset = $true) & (contrasubsetT3 = $true) & (doubleComplementI1 = $true) & (ex1I = $true) & (dsetconstr__Cong = $true) & (notequalI1 = $true) & (complementSubsetComplementIntersect = $true) & (ifSingleton = $true) & (exu__Cong = $true) & (symdiffI2 = $true) & (kpairsurjEq = $true) & (complementTnotintersectT = $true) & (symdiffI1 = $true) & (omega__Cong = $true) & (ap2p = $true) & (binunionRsub = $true) & (binunionLsub = $true) & (sepInPowerset = $true) & (subPowSU = $true) & (emptyinPowerset = $true) & (sepSubset = $true) & (upairsetIL = $true) & (breln1all1 = $true) & (dsetconstrI = $true) & (secondinupair = $true) & (setextAx = $true) & (cartprodmempaircEq = $true) & (setminusERneg = $true) & (binunionIL = $true) & (exuI2 = $true) & (replAx = $true) & (contraSubsetComplement = $true) & (setbeta = $true) & (notinsingleton = $true) & (subsetE = $true) & (binunionEcases = $true) & (woz13rule3 = $true) & (woz1_5 = $true) & (quantDeMorgan3 = $true) & (contrasubsetT2 = $true) & (emptyI = $true) & (woz1_2 = $true) & (nonemptyE1 = $true) & (setminusT_lem = $true) & (woz1_4 = $true) & (inComplementUnionImpInComplement1 = $true) & (setminusI = $true) & (prop2setE = $true) & (dpsetconstrI = $true) & (setOfPairsIsBReln = $true) & (exuI1 = $true) & (choice2fnsingleton = $true) & (exuE2 = $true) & (cartprodfstin = $true) & (subsetRefl = $true) & (prop2set2propI = $true) & (noeltsimpempty = $true) & (emptysetAx = $true) & (subsetE2 = $true) & (subbreln = $true) & (dpsetconstrEL2 = $true) & (setadjoinIR = $true) & (setunionsingleton = $true) & (setadjoinIL = $true) & (powersetTI1 = $true) & (cartprodfstpairEq = $true) & (nonemptyI1 = $true) & (setunionsingleton1 = $true) & (binunionTILcontra = $true) & (kfstsingleton = $true) & (setukpairinjR11 = $true) & (emptyE1 = $true) & (singletoninpowerset = $true) & (emptysetimpfalse = $true) & (kpairiskpair = $true) & (setadjoinAx = $true) & (lamp = $true) & (binintersectER = $true) & (lam2lamEq = $true) & (inIntersectImpInIntersectUnions = $true) & (woz13rule4 = $true) & (upairset2E = $true) & (setOfPairsIsBReln1 = $true) & (beta1 = $true) & (kfstpairEq = $true) & (inCongP = $true) & (setext = $true) & (setukpairIL = $true) & (woz13rule0 = $true) & (symdiffE = $true) & (upairsubunion = $true) & (cartprodsndin = $true) & (iffalseProp1 = $true) & (complementT_lem = $true) & (setminusER = $true) & (setunionE2 = $true) & (funcGraphProp2 = $true) & (ubforcartprodlem1 = $true) & (setminusIRneg = $true) & (demorgan1b = $true) & (binintersectSubset3 = $true) & (cartprodsndpairEq = $true) & (binintersectRsub = $true) & (eqimpsubset2 = $true) & (complementUnionInPowersetComplement = $true) & (breln1compprop = $true) & (powerset__Cong = $true) & (dpsetconstrEL1 = $true) & (inIntersectImpInUnion2 = $true) & (funcGraphProp4 = $true) & (notdexE = $true) & (demorgan2b2 = $true) & (binintersectSubset2 = $true) & (subsetTrans = $true) & (eqbreln = $true) & (setadjoinOr = $true) & (setunionAx = $true) & (binunionIR = $true) & (subsetI2 = $true) & (iftrueProp1 = $true) & (breln1SetBreln1 = $true) & (funcext2 = $true) & (woz1_1 = $true) & (eta2 = $true) & (upairinpowunion = $true) & (demorgan2b = $true) & (woz13rule2 = $true) & (powersetTE1 = $true) & (exuEu = $true) & (setukpairinjR = $true) & (complementTI1 = $true) & (ifp = $true) & (iffalse = $true) & (kpairp = $true) & (setminusSubset2 = $true) & (quantDeMorgan2 = $true) & (infuncsetfunc = $true) & (demorgan2a1 = $true) & (nonemptyImpWitness = $true) & ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X1) = $true) & ? [X4 : $i] : (($true = (in @ X4 @ X1)) & ? [X5 : $i] : (((in @ (kpair @ X5 @ X4) @ X2) = $true) & ((in @ (kpair @ X3 @ X5) @ X0) = $true) & ($true = (in @ X5 @ X1)) & ((in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)) != $true)))) & ((breln1 @ X1 @ X2) = $true)) & ($true = (breln1 @ X1 @ X0))) & (apProp = $true) & (setukpairinjR12 = $true) & (setukpairIR = $true) & (omega0Ax = $true) & (setminusEL = $true) & (ksndpairEq = $true) & (setextsub = $true) & (descr__Cong = $true) & (ap2apEq2 = $true) & (binunionTEcontra = $true) & (iftrue = $true) & (setadjoinSub2 = $true) & (cartprodpairin = $true) & (demorgan2a2 = $true) & (woz1_3 = $true) & (demorgan1 = $true) & (singletonprop = $true) & (iftrueorfalse = $true) & (omegaSAx = $true) & (emptyinunitempty = $true) & (subsetI1 = $true) & (ksndsingleton = $true) & (upairset2IR = $true) & (eqinunit = $true) & (binintersectT_lem = $true) & (complementTE1 = $true) & (cartprodpairsurjEq = $true) & (symdiffIneg2 = $true) & (setunionI = $true) & (eta1 = $true) & (singletoninpowunion = $true)),
% 27.61/5.13 inference(flattening,[status(thm)],[f900])).
% 27.61/5.13 thf(f900,plain,(
% 27.61/5.13 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (? [X5 : $i] : (((((in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)) != $true) & ((in @ (kpair @ X5 @ X4) @ X2) = $true)) & ((in @ (kpair @ X3 @ X5) @ X0) = $true)) & ($true = (in @ X5 @ X1))) & ($true = (in @ X4 @ X1))) & ((in @ X3 @ X1) = $true)) & ((breln1 @ X1 @ X2) = $true)) & ($true = (breln1 @ X1 @ X0))) & (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)),
% 27.61/5.13 inference(ennf_transformation,[status(thm)],[f666])).
% 27.61/5.13 thf(f666,plain,(
% 27.61/5.13 ~((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) => ! [X0 : $i,X1 : $i] : (($true = (breln1 @ X1 @ X0)) => ! [X2 : $i] : (((breln1 @ X1 @ X2) = $true) => ! [X3 : $i] : (((in @ X3 @ X1) = $true) => ! [X4 : $i] : (($true = (in @ X4 @ X1)) => ! [X5 : $i] : (($true = (in @ X5 @ X1)) => (((in @ (kpair @ X3 @ X5) @ X0) = $true) => (((in @ (kpair @ X5 @ X4) @ X2) = $true) => ((in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)) = $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 27.61/5.13 inference(fool_elimination,[status(thm)],[f665])).
% 27.61/5.13 thf(f665,plain,(
% 27.61/5.13 ~(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 => ! [X0 : $i,X1 : $i] : ((breln1 @ X1 @ X0) => ! [X2 : $i] : ((breln1 @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X1) => ! [X4 : $i] : ((in @ X4 @ X1) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X3 @ X5) @ X0) => ((in @ (kpair @ X5 @ X4) @ X2) => (in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 27.61/5.13 inference(rectify,[status(thm)],[f302])).
% 27.61/5.13 thf(f302,negated_conjecture,(
% 27.61/5.13 ~(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 => ! [X13 : $i,X3 : $i] : ((breln1 @ X3 @ X13) => ! [X15 : $i] : ((breln1 @ X3 @ X15) => ! [X1 : $i] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X3) => ! [X8 : $i] : ((in @ X8 @ X3) => ((in @ (kpair @ X1 @ X8) @ X13) => ((in @ (kpair @ X8 @ X2) @ X15) => (in @ (kpair @ X1 @ X2) @ (breln1compset @ X3 @ X13 @ X15))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 27.61/5.13 inference(negated_conjecture,[status(cth)],[f301])).
% 27.61/5.13 thf(f301,conjecture,(
% 27.61/5.13 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 => ! [X13 : $i,X3 : $i] : ((breln1 @ X3 @ X13) => ! [X15 : $i] : ((breln1 @ X3 @ X15) => ! [X1 : $i] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X3) => ! [X8 : $i] : ((in @ X8 @ X3) => ((in @ (kpair @ X1 @ X8) @ X13) => ((in @ (kpair @ X8 @ X2) @ X15) => (in @ (kpair @ X1 @ X2) @ (breln1compset @ X3 @ X13 @ X15)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 27.61/5.13 file('/export/starexec/sandbox2/tmp/tmp.V1n9lFWd3k/DTF2THF_22754.p',breln1compI)).
% 27.61/5.13 thf(f5400,plain,(
% 27.61/5.13 ((in @ (kpair @ sK3 @ sK4) @ (dpsetconstr @ sK1 @ sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ sK1) & (in @ (kpair @ Y0 @ Y2) @ sK0)) & (in @ (kpair @ Y2 @ Y1) @ sK2))))))))) != $true) | spl6_29),
% 27.61/5.13 inference(avatar_component_clause,[status(thm)],[f5398])).
% 27.61/5.13 thf(f5317,plain,(
% 27.61/5.13 ($true = (in @ (kpair @ sK3 @ sK5) @ sK0)) | ~spl6_10),
% 27.61/5.13 inference(avatar_component_clause,[status(thm)],[f5315])).
% 27.61/5.13 thf(f5401,plain,(
% 27.61/5.13 ~spl6_29),
% 27.61/5.13 inference(avatar_split_clause,[status(thm)],[f2101,f5398])).
% 27.61/5.13 thf(f2101,plain,(
% 27.61/5.13 ((in @ (kpair @ sK3 @ sK4) @ (dpsetconstr @ sK1 @ sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((in @ Y2 @ sK1) & (in @ (kpair @ Y0 @ Y2) @ sK0)) & (in @ (kpair @ Y2 @ Y1) @ sK2))))))))) != $true)),
% 27.61/5.13 inference(beta_eta_normalization,[status(thm)],[f1691])).
% 27.61/5.13 thf(f1691,plain,(
% 27.61/5.13 ($true != (in @ (kpair @ sK3 @ sK4) @ ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y0) & (in @ (kpair @ Y3 @ Y5) @ Y1)) & (in @ (kpair @ Y5 @ Y4) @ Y2))))))))))))) @ sK1 @ sK0 @ sK2)))),
% 27.61/5.13 inference(definition_unfolding,[status(thm)],[f1125,f1486])).
% 27.61/5.13 thf(f1486,plain,(
% 27.61/5.13 (breln1compset = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y0) & (in @ (kpair @ Y3 @ Y5) @ Y1)) & (in @ (kpair @ Y5 @ Y4) @ Y2))))))))))))))),
% 27.61/5.13 inference(cnf_transformation,[status(thm)],[f505])).
% 27.61/5.13 thf(f505,plain,(
% 27.61/5.13 (breln1compset = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (((in @ Y5 @ Y0) & (in @ (kpair @ Y3 @ Y5) @ Y1)) & (in @ (kpair @ Y5 @ Y4) @ Y2))))))))))))))),
% 27.61/5.13 inference(fool_elimination,[status(thm)],[f504])).
% 27.61/5.13 thf(f504,plain,(
% 27.61/5.13 (breln1compset = (^[X0 : $i, X1 : $i, X2 : $i] : (dpsetconstr @ X0 @ X0 @ (^[X3 : $i, X4 : $i] : (? [X5 : $i] : ((in @ (kpair @ X5 @ X4) @ X2) & (in @ (kpair @ X3 @ X5) @ X1) & (in @ X5 @ X0)))))))),
% 27.61/5.13 inference(rectify,[status(thm)],[f299])).
% 27.61/5.13 thf(f299,axiom,(
% 27.61/5.13 (breln1compset = (^[X3 : $i, X13 : $i, X15 : $i] : (dpsetconstr @ X3 @ X3 @ (^[X1 : $i, X2 : $i] : (? [X8 : $i] : ((in @ (kpair @ X8 @ X2) @ X15) & (in @ (kpair @ X1 @ X8) @ X13) & (in @ X8 @ X3)))))))),
% 27.61/5.13 file('/export/starexec/sandbox2/tmp/tmp.V1n9lFWd3k/DTF2THF_22754.p',breln1compset)).
% 27.61/5.13 thf(f1125,plain,(
% 27.61/5.13 ($true != (in @ (kpair @ sK3 @ sK4) @ (breln1compset @ sK1 @ sK0 @ sK2)))),
% 27.61/5.13 inference(cnf_transformation,[status(thm)],[f907])).
% 27.61/5.13 thf(f5357,plain,(
% 27.61/5.13 spl6_19),
% 27.61/5.13 inference(avatar_split_clause,[status(thm)],[f1130,f5354])).
% 27.61/5.13 thf(f1130,plain,(
% 27.61/5.13 ($true = (in @ sK3 @ sK1))),
% 27.61/5.13 inference(cnf_transformation,[status(thm)],[f907])).
% 27.61/5.13 thf(f5328,plain,(
% 27.61/5.13 spl6_12),
% 27.61/5.13 inference(avatar_split_clause,[status(thm)],[f1126,f5325])).
% 27.61/5.13 thf(f1126,plain,(
% 27.61/5.13 ($true = (in @ sK5 @ sK1))),
% 27.61/5.13 inference(cnf_transformation,[status(thm)],[f907])).
% 27.61/5.13 thf(f5323,plain,(
% 27.61/5.13 ~spl6_11),
% 27.61/5.13 inference(avatar_split_clause,[status(thm)],[f303,f5320])).
% 27.61/5.13 thf(f5320,definition,(
% 27.61/5.13 spl6_11 <=> ($false = $true)),
% 27.61/5.13 introduced(definition,[new_symbols(naming,[spl6_11])],[avatar_definition])).
% 27.61/5.13 thf(f303,plain,(
% 27.61/5.13 ($false != $true)),
% 27.61/5.13 introduced(definition,[],[fool_axiom])).
% 27.61/5.13 thf(f5318,plain,(
% 27.61/5.13 spl6_10),
% 27.61/5.13 inference(avatar_split_clause,[status(thm)],[f1127,f5315])).
% 27.61/5.13 thf(f1127,plain,(
% 27.61/5.13 ($true = (in @ (kpair @ sK3 @ sK5) @ sK0))),
% 27.61/5.13 inference(cnf_transformation,[status(thm)],[f907])).
% 27.61/5.13 thf(f5313,plain,(
% 27.61/5.13 spl6_9),
% 27.61/5.13 inference(avatar_split_clause,[status(thm)],[f1128,f5310])).
% 27.61/5.13 thf(f5310,definition,(
% 27.61/5.13 spl6_9 <=> ($true = (in @ (kpair @ sK5 @ sK4) @ sK2))),
% 27.61/5.13 introduced(definition,[new_symbols(naming,[spl6_9])],[avatar_definition])).
% 27.61/5.13 thf(f1128,plain,(
% 27.61/5.13 ($true = (in @ (kpair @ sK5 @ sK4) @ sK2))),
% 27.61/5.13 inference(cnf_transformation,[status(thm)],[f907])).
% 27.61/5.13 thf(f5285,plain,(
% 27.61/5.13 spl6_2),
% 27.61/5.13 inference(avatar_split_clause,[status(thm)],[f1129,f5282])).
% 27.61/5.13 thf(f1129,plain,(
% 27.61/5.13 ($true = (in @ sK4 @ sK1))),
% 27.61/5.13 inference(cnf_transformation,[status(thm)],[f907])).
% 27.61/5.13 % SZS output end Proof for DTF2THF_22754
% 27.61/5.13 % (23324)------------------------------
% 27.61/5.13 % (23324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.61/5.13 % (23324)Termination reason: Refutation
% 27.61/5.13
% 27.61/5.13 % (23324)Memory used [KB]: 11129
% 27.61/5.13 % (23324)Time elapsed: 0.297 s
% 27.61/5.13 % (23324)Instructions burned: 983 (million)
% 27.61/5.13 % (23324)------------------------------
% 27.61/5.13 % (23324)------------------------------
% 27.61/5.13 % (22912)Success in time 3.547 s
%------------------------------------------------------------------------------