%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU765^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 09:37:01 AM UTC 2026
% Result : Theorem 30.11s 5.64s
% Output : Refutation 30.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 13
% Syntax : Number of formulae : 55 ( 21 unt; 0 typ; 6 def)
% Number of atoms : 4706 (1219 equ; 0 cnn)
% Maximal formula atoms : 285 ( 85 avg)
% Number of connectives : 2865 ( 30 ~; 41 |; 864 &; 722 @)
% ( 6 <=>;1175 =>; 0 <=; 0 <~>)
% Maximal formula depth : 296 ( 40 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 447 ( 443 usr; 294 con; 0-4 aty)
% ( 27 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 104 ( 31 ^; 55 !; 18 ?; 104 :)
% 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_342,type,
sK5: $i > $i > ( $i > $o ) > $i > $i ).
thf(func_def_343,type,
sK6: $i > $i > $i > ( $i > $o ) > $i ).
thf(func_def_344,type,
sK7: $i > $i > $i ).
thf(func_def_345,type,
sK8: $i > $i > $i ).
thf(func_def_346,type,
sK9: $i > $i > $i ).
thf(func_def_347,type,
sK10: $i > $i > $i ).
thf(func_def_348,type,
sK11: $i > $i > ( $i > $o ) > $i ).
thf(func_def_349,type,
sK12: $i > $i ).
thf(func_def_350,type,
sK13: ( $i > $i > $o ) > $i > $i ).
thf(func_def_351,type,
sK14: ( $i > $i > $o ) > $i > $i ).
thf(func_def_352,type,
sK15: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_353,type,
sK16: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_354,type,
sK17: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_355,type,
sK18: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_356,type,
sK19: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_357,type,
sK20: ( $i > $i ) > $i > $i > $i ).
thf(func_def_358,type,
sK21: $i > $i > ( $i > $o ) > $i > $i ).
thf(func_def_359,type,
sK22: $i > $i > ( $i > $o ) > $i > $i ).
thf(func_def_360,type,
sK23: $i > $i > $i > $i ).
thf(func_def_361,type,
sK24: $i > $i > $i ).
thf(func_def_362,type,
sK25: $i > $i > $i > $i ).
thf(func_def_363,type,
sK26: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_364,type,
sK27: $i > ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(func_def_365,type,
sK28: ( $i > $o ) > $i ).
thf(func_def_366,type,
sK29: ( $i > $o ) > $i ).
thf(func_def_367,type,
sK30: ( $i > $o ) > $i ).
thf(func_def_368,type,
sK31: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_369,type,
sK32: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_370,type,
sK33: ( $i > $o ) > $i ).
thf(func_def_371,type,
sK34: ( $i > $o ) > $i > $i ).
thf(func_def_372,type,
sK35: ( $i > $o ) > $i > $i ).
thf(func_def_373,type,
sK36: ( $i > $o ) > $i ).
thf(func_def_374,type,
sK37: ( $i > $o ) > $i > $i ).
thf(func_def_375,type,
sK38: ( $i > $o ) > $i ).
thf(func_def_376,type,
sK39: ( $i > $o ) > $i > $i ).
thf(func_def_377,type,
sK40: ( $i > $o ) > $i > $i ).
thf(func_def_378,type,
sK41: ( $i > $o ) > $i > $i ).
thf(func_def_379,type,
sK42: ( $i > $o ) > $i > $i ).
thf(func_def_380,type,
sK43: ( $i > $o ) > $i > $i ).
thf(func_def_381,type,
sK44: ( $i > $o ) > $i > $i ).
thf(func_def_382,type,
sK45: $i > ( $i > $o ) > $i ).
thf(func_def_383,type,
sK46: ( $i > $o ) > $i > $i ).
thf(func_def_384,type,
sK47: ( $i > $o ) > $i > $i ).
thf(func_def_385,type,
sK48: $i > $i ).
thf(func_def_386,type,
sK49: $i > $i > $i > $i ).
thf(func_def_387,type,
sK50: $i > $i > $i ).
thf(func_def_388,type,
sK51: $i > $i > $i ).
thf(func_def_389,type,
sK52: $i > $i > $i ).
thf(func_def_390,type,
sK53: $i > $i ).
thf(func_def_391,type,
sK54: $i > $i ).
thf(func_def_392,type,
sK55: $i > ( $i > $i ) > $i > $i ).
thf(func_def_393,type,
sK56: $i > $i > $i > $i > $i ).
thf(func_def_394,type,
sK57: $i > $i > $i > $i > $i ).
thf(func_def_395,type,
sK58: $i > $i > $i > $i ).
thf(func_def_396,type,
sK59: $i > $i > $i > $i ).
thf(func_def_397,type,
sK60: $i > ( $i > $o ) > $i ).
thf(func_def_398,type,
sK61: $i > $i > $i > $i > $i ).
thf(func_def_399,type,
sK62: $i > $i > $i > $i > $i ).
thf(func_def_400,type,
sK63: $i > $i > $i > $i > $i ).
thf(func_def_401,type,
sK64: $i > $i > $i > $i > $i ).
thf(func_def_402,type,
sK65: $i > $i > $i > $i > $i ).
thf(func_def_403,type,
sK66: $i > $i > $i > $i > $i ).
thf(func_def_404,type,
sK67: $i > $i > $i > $i > $i ).
thf(func_def_405,type,
sK68: $i > $i ).
thf(func_def_406,type,
sK69: ( $i > $o ) > $i > $i ).
thf(func_def_407,type,
sK70: $i > $i > ( $i > $i ) > $i ).
thf(func_def_408,type,
sK71: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_409,type,
sK72: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_410,type,
sK73: ( $i > $o ) > $i > $i ).
thf(func_def_411,type,
sK74: ( $i > $o ) > $i > $i ).
thf(func_def_412,type,
sK75: ( $i > $o ) > $i > $i ).
thf(func_def_413,type,
sK76: ( $i > $o ) > $i > $i ).
thf(func_def_414,type,
sK77: ( $i > $o ) > $i > $i ).
thf(func_def_415,type,
sK78: ( $i > $o ) > $i > $i ).
thf(func_def_416,type,
sK79: ( $i > $o ) > $i > $i ).
thf(func_def_417,type,
sK80: ( $i > $o ) > $i > $i ).
thf(func_def_418,type,
sK81: $i > $i > $i ).
thf(func_def_419,type,
sK82: ( $i > $i ) > $i > $i > $i ).
thf(func_def_420,type,
sK83: ( $i > $o ) > $i ).
thf(func_def_421,type,
sK84: ( $i > $o ) > $i > $i ).
thf(func_def_422,type,
sK85: ( $i > $o ) > $i > $i ).
thf(func_def_423,type,
sK86: $i > ( $i > $o ) > $i ).
thf(func_def_424,type,
sK87: ( $i > $o ) > $i ).
thf(func_def_425,type,
sK88: ( $i > $o ) > $i > $i ).
thf(func_def_426,type,
sK89: ( $i > $o ) > $i > $i ).
thf(func_def_427,type,
sK90: ( $i > $o ) > $i ).
thf(func_def_428,type,
sK91: ( $i > $o ) > $i > $i ).
thf(func_def_429,type,
sK92: $i > $i ).
thf(func_def_430,type,
sK93: $i > ( $i > $o ) > $i ).
thf(func_def_431,type,
sK94: ( $i > $o ) > $i > $i ).
thf(func_def_432,type,
sK95: $i > $i > $i > $i ).
thf(func_def_433,type,
sK96: $i > $i > $i > $i ).
thf(func_def_434,type,
sK97: $i > $i > $i > $i > $i ).
thf(func_def_435,type,
sK98: ( $i > $i ) > $i > $i > $i ).
thf(func_def_436,type,
sK99: $i > $i > $i ).
thf(func_def_437,type,
sK100: $i > $i > $i > $i > $i ).
thf(func_def_438,type,
sK101: $i > $i > $i ).
thf(func_def_439,type,
sK102: $i > $i > $i ).
thf(func_def_440,type,
sK103: $i > $i ).
thf(func_def_441,type,
sK104: ( $i > $o ) > $i > $i ).
thf(func_def_442,type,
sK105: ( $i > $o ) > $i > $i ).
thf(func_def_443,type,
sK106: $i > $i > $i > $i > $i ).
thf(func_def_444,type,
sK107: $i > $i > $i ).
thf(func_def_445,type,
sK108: ( $i > $o ) > $i ).
thf(func_def_446,type,
sK109: ( $i > $o ) > $i > $i ).
thf(func_def_447,type,
sK110: ( $i > $o ) > $i > $i ).
thf(func_def_448,type,
sK111: $i > ( $i > $o ) > $i ).
thf(func_def_449,type,
sK112: $i > $i > $o > $i ).
thf(func_def_450,type,
sK113: ( $i > $o ) > $i ).
thf(func_def_451,type,
sK114: ( $i > $o ) > $i > $i ).
thf(func_def_452,type,
sK115: ( $i > $o ) > $i > $i ).
thf(func_def_453,type,
sK116: $i > $i > $i ).
thf(func_def_454,type,
sK117: ( $i > $o ) > $i > $i ).
thf(func_def_455,type,
sK118: ( $i > $o ) > $i > $i ).
thf(func_def_456,type,
sK119: ( $i > $o ) > $i > $i ).
thf(func_def_457,type,
ph120:
!>[X0: $tType] : X0 ).
thf(f11107,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f5065,f5071,f5094,f5099,f5116,f11102,f11106]) ).
thf(f11106,plain,
( ( $true
!= ( in @ sK3 @ ( powerset @ sK1 ) ) )
| ( $false
!= ( in @ sK3 @ ( powerset @ sK1 ) ) )
| ( $false = $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f11102,plain,
( spl4_85
| ~ spl4_14
| spl4_21
| ~ spl4_25 ),
inference(avatar_split_clause,[status(thm)],[f11101,f5113,f5096,f5062,f10743]) ).
thf(f10743,definition,
( spl4_85
<=> ( $false
= ( in @ sK3 @ ( powerset @ sK1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_85])],[avatar_definition]) ).
thf(f5062,definition,
( spl4_14
<=> ( ( in @ sK2 @ ( powerset @ sK1 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_14])],[avatar_definition]) ).
thf(f5096,definition,
( spl4_21
<=> ( ( in @ ( binintersect @ sK0 @ sK2 ) @ ( powerset @ ( binintersect @ ( binunion @ sK0 @ sK3 ) @ ( binunion @ sK2 @ sK3 ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_21])],[avatar_definition]) ).
thf(f5113,definition,
( spl4_25
<=> ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_25])],[avatar_definition]) ).
thf(f11101,plain,
( ( $false
= ( in @ sK3 @ ( powerset @ sK1 ) ) )
| ~ spl4_14
| spl4_21
| ~ spl4_25 ),
inference(trivial_inequality_removal,[status(thm)],[f11100]) ).
thf(f11100,plain,
( ( $false = $true )
| ( $false
= ( in @ sK3 @ ( powerset @ sK1 ) ) )
| ~ spl4_14
| spl4_21
| ~ spl4_25 ),
inference(forward_demodulation,[status(thm)],[f11078,f5115]) ).
thf(f5115,plain,
( ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $true )
| ~ spl4_25 ),
inference(avatar_component_clause,[status(thm)],[f5113]) ).
thf(f11078,plain,
( ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $false )
| ( $false
= ( in @ sK3 @ ( powerset @ sK1 ) ) )
| ~ spl4_14
| spl4_21 ),
inference(trivial_inequality_removal,[status(thm)],[f11069]) ).
thf(f11069,plain,
( ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $false )
| ( $false
= ( in @ sK3 @ ( powerset @ sK1 ) ) )
| ( $false = $true )
| ~ spl4_14
| spl4_21 ),
inference(superposition,[status(thm)],[f11062,f5064]) ).
thf(f5064,plain,
( ( ( in @ sK2 @ ( powerset @ sK1 ) )
= $true )
| ~ spl4_14 ),
inference(avatar_component_clause,[status(thm)],[f5062]) ).
thf(f11062,plain,
( ! [X0: $i] :
( ( $false
= ( in @ sK2 @ ( powerset @ X0 ) ) )
| ( ( in @ sK0 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ sK3 @ ( powerset @ X0 ) )
= $false ) )
| spl4_21 ),
inference(trivial_inequality_removal,[status(thm)],[f11049]) ).
thf(f11049,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $false
= ( in @ sK2 @ ( powerset @ X0 ) ) )
| ( ( in @ sK3 @ ( powerset @ X0 ) )
= $false )
| ( ( in @ sK0 @ ( powerset @ X0 ) )
= $false ) )
| spl4_21 ),
inference(superposition,[status(thm)],[f5098,f3242]) ).
thf(f3242,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( in @ ( binintersect @ X2 @ X3 ) @ ( powerset @ ( binintersect @ ( binunion @ X2 @ X4 ) @ ( binunion @ X3 @ X4 ) ) ) )
= $true )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X4 @ ( powerset @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f3241]) ).
thf(f3241,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $true
= ( ( in @ X4 @ ( powerset @ X1 ) )
=> ( in @ ( binintersect @ X2 @ X3 ) @ ( powerset @ ( binintersect @ ( binunion @ X2 @ X4 ) @ ( binunion @ X3 @ X4 ) ) ) ) ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f3240]) ).
thf(f3240,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( in @ ( binintersect @ X2 @ X3 ) @ ( powerset @ ( binintersect @ ( binunion @ X2 @ Y0 ) @ ( binunion @ X3 @ Y0 ) ) ) ) )
@ X4 ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) ) ),
inference(pi_clausification,[status(thm)],[f3239]) ).
thf(f3239,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $false
= ( in @ X3 @ ( powerset @ X1 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( in @ ( binintersect @ X2 @ X3 ) @ ( powerset @ ( binintersect @ ( binunion @ X2 @ Y0 ) @ ( binunion @ X3 @ Y0 ) ) ) ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f3238]) ).
thf(f3238,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( in @ X3 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( in @ ( binintersect @ X2 @ X3 ) @ ( powerset @ ( binintersect @ ( binunion @ X2 @ Y0 ) @ ( binunion @ X3 @ Y0 ) ) ) ) ) ) ) )
| ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f3237]) ).
thf(f3237,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ X1 ) )
=> ( in @ ( binintersect @ X2 @ Y0 ) @ ( powerset @ ( binintersect @ ( binunion @ X2 @ Y1 ) @ ( binunion @ Y0 @ Y1 ) ) ) ) ) ) )
@ X3 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f3236]) ).
thf(f3236,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ X1 ) )
=> ( in @ ( binintersect @ X2 @ Y0 ) @ ( powerset @ ( binintersect @ ( binunion @ X2 @ Y1 ) @ ( binunion @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f3235]) ).
thf(f3235,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ X1 ) )
=> ( in @ ( binintersect @ X2 @ Y0 ) @ ( powerset @ ( binintersect @ ( binunion @ X2 @ Y1 ) @ ( binunion @ Y0 @ Y1 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f3234]) ).
thf(f3234,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ X1 ) )
=> ( in @ ( binintersect @ Y0 @ Y1 ) @ ( powerset @ ( binintersect @ ( binunion @ Y0 @ Y2 ) @ ( binunion @ Y1 @ Y2 ) ) ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f3233]) ).
thf(f3233,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ X1 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ X1 ) )
=> ( in @ ( binintersect @ Y0 @ Y1 ) @ ( powerset @ ( binintersect @ ( binunion @ Y0 @ Y2 ) @ ( binunion @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f3232]) ).
thf(f3232,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( powerset @ Y0 ) )
=> ( in @ ( binintersect @ Y1 @ Y2 ) @ ( powerset @ ( binintersect @ ( binunion @ Y1 @ Y3 ) @ ( binunion @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f1552]) ).
thf(f1552,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( powerset @ Y0 ) )
=> ( in @ ( binintersect @ Y1 @ Y2 ) @ ( powerset @ ( binintersect @ ( binunion @ Y1 @ Y3 ) @ ( binunion @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f1107,f937]) ).
thf(f937,plain,
( intersectInPowersetIntersectUnions
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( powerset @ Y0 ) )
=> ( in @ ( binintersect @ Y1 @ Y2 ) @ ( powerset @ ( binintersect @ ( binunion @ Y1 @ Y3 ) @ ( binunion @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f664]) ).
thf(f664,plain,
( intersectInPowersetIntersectUnions
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( powerset @ Y0 ) )
=> ( in @ ( binintersect @ Y1 @ Y2 ) @ ( powerset @ ( binintersect @ ( binunion @ Y1 @ Y3 ) @ ( binunion @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f663]) ).
thf(f663,plain,
( intersectInPowersetIntersectUnions
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ X0 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f264]) ).
thf(f264,axiom,
( intersectInPowersetIntersectUnions
= ( ! [X11: $i,X3: $i] :
( ( in @ X11 @ ( powerset @ X3 ) )
=> ! [X16: $i] :
( ( in @ X16 @ ( powerset @ X3 ) )
=> ! [X17: $i] :
( ( in @ X17 @ ( powerset @ X3 ) )
=> ( in @ ( binintersect @ X11 @ X16 ) @ ( powerset @ ( binintersect @ ( binunion @ X11 @ X17 ) @ ( binunion @ X16 @ X17 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.50SVxc4AnF/DTF2THF_30813.p',intersectInPowersetIntersectUnions) ).
thf(f1107,plain,
intersectInPowersetIntersectUnions = $true,
inference(cnf_transformation,[status(thm)],[f860]) ).
thf(f860,plain,
( ( complementUnionInPowersetComplement = $true )
& ( complementT_lem = $true )
& ( descr__Cong = $true )
& ( binintersectER = $true )
& ( in__Cong = $true )
& ( bs114d = $true )
& ( binintersectLsub = $true )
& ( upairsetE = $true )
& ( quantDeMorgan2 = $true )
& ( contrasubsetT3 = $true )
& ( cartprodfstpairEq = $true )
& ( doubleComplementEq = $true )
& ( sepInPowerset = $true )
& ( dpsetconstrEL2 = $true )
& ( funcGraphProp1 = $true )
& ( emptyInPowerset = $true )
& ( singletonsuniq = $true )
& ( singletoninpowunion = $true )
& ( dpsetconstrI = $true )
& ( emptyE1 = $true )
& ( singletoninpowerset = $true )
& ( complementImpComplementIntersect = $true )
& ( ap2apEq2 = $true )
& ( lamp = $true )
& ( setunion__Cong = $true )
& ( cartprodmempaircEq = $true )
& ( subsetTI = $true )
& ( ap2apEq1 = $true )
& ( apProp = $true )
& ( notdexE = $true )
& ( quantDeMorgan1 = $true )
& ( cartprodpairsurjEq = $true )
& ( disjointsetsI1 = $true )
& ( upairsubunion = $true )
& ( exuE3u = $true )
& ( setukpairIR = $true )
& ( descrp = $true )
& ( setadjoinAx = $true )
& ( exuEu = $true )
& ( ubforcartprodlem3 = $true )
& ( woz13rule3 = $true )
& ( notdallE = $true )
& ( exu__Cong = $true )
& ( upairinpowunion = $true )
& ( brelnall2 = $true )
& ( ex1E1 = $true )
& ( funcext2 = $true )
& ( ap2p = $true )
& ( doubleComplementSub1 = $true )
& ( cartprodmempair = $true )
& ( setukpairIL = $true )
& ( symdiffIneg1 = $true )
& ( woz1_2 = $true )
& ( demorgan2a2 = $true )
& ( cartprodmempair1 = $true )
& ( eta1 = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( powersetE = $true )
& ( binintersectI = $true )
& ( setminusT_lem = $true )
& ( inIntersectImpInUnion2 = $true )
& ( cartprodpairmemER = $true )
& ( exuI1 = $true )
& ( complementTcontraSubset = $true )
& ( binintersectTELcontra = $true )
& ( setadjoinE = $true )
& ( demorgan1a = $true )
& ( setadjoinIR = $true )
& ( lam2p = $true )
& ( exuE3e = $true )
& ( complementSubsetComplementIntersect = $true )
& ( inPowerset = $true )
& ( setadjoinSub2 = $true )
& ( demorgan2b2 = $true )
& ( woz13rule1 = $true )
& ( symdiffIneg2 = $true )
& ( notequalI1 = $true )
& ( binunionEcases = $true )
& ( upairset2E = $true )
& ( setunionsingleton2 = $true )
& ( omega0Ax = $true )
& ( binunionTILcontra = $true )
& ( binunionRsub = $true )
& ( setOfPairsIsBReln = $true )
& ( setminusELneg = $true )
& ( woz13rule0 = $true )
& ( exuE2 = $true )
& ( sepSubset = $true )
& ( setunionI = $true )
& ( setminusILneg = $true )
& ( upairequniteq = $true )
& ( theeq = $true )
& ( eta2 = $true )
& ( cartprodsndin = $true )
& ( funcext = $true )
& ( binintersectSubset4 = $true )
& ( contrasubsetT1 = $true )
& ( setunionsingleton1 = $true )
& ( subsetemptysetimpeq = $true )
& ( replAx = $true )
& ( nonemptyI1 = $true )
& ( iffalseProp1 = $true )
& ( binintersectTERcontra = $true )
& ( notsubsetI = $true )
& ( ubforcartprodlem2 = $true )
& ( setminusSubset1 = $true )
& ( nonemptyImpWitness = $true )
& ( funcextLem = $true )
& ( lamProp = $true )
& ( lam2lamEq = $true )
& ( ex1I2 = $true )
& ( setextsub = $true )
& ( powersetAx = $true )
& ( ex1I = $true )
& ( binunionT_lem = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( setadjoinIL = $true )
& ( dpsetconstrERa = $true )
& ( setminusERneg = $true )
& ( ksndsingleton = $true )
& ( contrasubsetT = $true )
& ( powersetTI1 = $true )
& ( binunionE = $true )
& ( omegaIndAx = $true )
& ( binintersectT_lem = $true )
& ( prop2setE = $true )
& ( iffalseProp2 = $true )
& ( contrasubsetT2 = $true )
& ( symdiffE = $true )
& ( setukpairinjR1 = $true )
& ( infuncsetfunc = $true )
& ( inIntersectImpInUnion = $true )
& ( quantDeMorgan3 = $true )
& ( dpsetconstrER = $true )
& ( doubleComplementE1 = $true )
& ( binunionTEcontra = $true )
& ( nonemptyI = $true )
& ( funcImageSingleton = $true )
& ( emptyinPowerset = $true )
& ( dsetconstrEL = $true )
& ( funcinfuncset = $true )
& ( emptysetimpfalse = $true )
& ( setminusSubset2 = $true )
& ( subsetI2 = $true )
& ( upairsetIR = $true )
& ( inCongP = $true )
& ( setukpairinjL1 = $true )
& ( subsetE2 = $true )
& ( setoftrueEq = $true )
& ( binintersectSubset5 = $true )
& ( singletonsswitch = $true )
& ( binintersectSubset2 = $true )
& ( powersetsubset = $true )
& ( setadjoinSub = $true )
& ( uniqinunit = $true )
& ( symdiffI1 = $true )
& ( doubleComplementI1 = $true )
& ( brelnall1 = $true )
& ( ( in @ ( binintersect @ sK0 @ sK2 ) @ ( powerset @ ( binintersect @ ( binunion @ sK0 @ sK3 ) @ ( binunion @ sK2 @ sK3 ) ) ) )
!= $true )
& ( $true
= ( in @ sK3 @ ( powerset @ sK1 ) ) )
& ( ( in @ sK2 @ ( powerset @ sK1 ) )
= $true )
& ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $true )
& ( setextAx = $true )
& ( setukpairinjR12 = $true )
& ( setunionAx = $true )
& ( setadjoin__Cong = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( omegaSAx = $true )
& ( dpsetconstrEL1 = $true )
& ( kfstpairEq = $true )
& ( eqbreln = $true )
& ( ifp = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( dsetconstrI = $true )
& ( setminusIRneg = $true )
& ( binunionLsub = $true )
& ( woz13rule2 = $true )
& ( demorgan2b = $true )
& ( binintersectSubset1 = $true )
& ( powersetE1 = $true )
& ( prop2set2propI = $true )
& ( setukpairinjR = $true )
& ( funcGraphProp4 = $true )
& ( theprop = $true )
& ( ex1E2 = $true )
& ( demorgan1 = $true )
& ( exuE1 = $true )
& ( subsetTrans = $true )
& ( kpairiskpair = $true )
& ( exuI3 = $true )
& ( dpsetconstrSub = $true )
& ( dsetconstr__Cong = $true )
& ( setukpairinjL2 = $true )
& ( subbreln = $true )
& ( vacuousDall = $true )
& ( subPowSU = $true )
& ( wellorderingAx = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( iffalse = $true )
& ( setextT = $true )
& ( eqimpsubset1 = $true )
& ( exuI2 = $true )
& ( singletonsubset = $true )
& ( complementTE1 = $true )
& ( secondinupair = $true )
& ( notinemptyset = $true )
& ( emptysetE = $true )
& ( iftrueProp2 = $true )
& ( emptyI = $true )
& ( prop2setI = $true )
& ( beta2 = $true )
& ( demorgan1b = $true )
& ( setukpairinjR2 = $true )
& ( upairsetIL = $true )
& ( emptysetAx = $true )
& ( cartprodsndpairEq = $true )
& ( setext = $true )
& ( demorgan2 = $true )
& ( emptysetsubset = $true )
& ( powersetI1 = $true )
& ( emptyset__Cong = $true )
& ( complementTI1 = $true )
& ( setunionsingleton = $true )
& ( binintersectEL = $true )
& ( omega__Cong = $true )
& ( kfstsingleton = $true )
& ( funcGraphProp3 = $true )
& ( demorgan2a1 = $true )
& ( singletonprop = $true )
& ( binunionIR = $true )
& ( ksndpairEq = $true )
& ( binintersectRsub = $true )
& ( powersetTE1 = $true )
& ( kpairsurjEq = $true )
& ( doubleComplementSub2 = $true )
& ( woz1_1 = $true )
& ( quantDeMorgan4 = $true )
& ( ubforcartprodlem1 = $true )
& ( setminusER = $true )
& ( iftrueProp1 = $true )
& ( emptyinunitempty = $true )
& ( powersetT_lem = $true )
& ( binunionIL = $true )
& ( kpairp = $true )
& ( funcGraphProp2 = $true )
& ( setunionE = $true )
& ( notinsingleton = $true )
& ( beta1 = $true )
& ( subsetE = $true )
& ( foundationAx = $true )
& ( subset2powerset = $true )
& ( setminusLsub = $true )
& ( upairset2IR = $true )
& ( contraSubsetComplement = $true )
& ( setadjoinOr = $true )
& ( subsetRefl = $true )
& ( noeltsimpempty = $true )
& ( powerset__Cong = $true )
& ( cartprodpairin = $true )
& ( cartprodfstin = $true )
& ( setunionE2 = $true )
& ( cartprodpairmemEL = $true )
& ( eqimpsubset2 = $true )
& ( iftrue = $true )
& ( dsetconstrER = $true )
& ( setukpairinjL = $true )
& ( binunionTE = $true )
& ( app = $true )
& ( notequalI2 = $true )
& ( woz13rule4 = $true )
& ( setminusI = $true )
& ( symdiffI2 = $true )
& ( setukpairinjR11 = $true )
& ( binunionTIRcontra = $true )
& ( binintersectSubset3 = $true )
& ( setminusEL = $true )
& ( complementTnotintersectT = $true )
& ( powersetI = $true )
& ( iftrueorfalse = $true )
& ( ifSingleton = $true )
& ( demorgan2a = $true )
& ( subsetI1 = $true )
& ( setbeta = $true )
& ( nonemptyE1 = $true )
& ( eqinunit = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f856,f859,f858,f857]) ).
thf(f857,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ X0 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) )
!= $true )
& ( ( in @ X3 @ ( powerset @ X1 ) )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
=> ( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( in @ ( binintersect @ sK0 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ sK0 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) )
& ( ( in @ X3 @ ( powerset @ sK1 ) )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ sK1 ) ) ) )
& ( ( in @ sK0 @ ( powerset @ sK1 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f858,plain,
( ? [X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( in @ ( binintersect @ sK0 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ sK0 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) )
& ( ( in @ X3 @ ( powerset @ sK1 ) )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ sK1 ) ) ) )
=> ( ? [X3: $i] :
( ( $true
!= ( in @ ( binintersect @ sK0 @ sK2 ) @ ( powerset @ ( binintersect @ ( binunion @ sK0 @ X3 ) @ ( binunion @ sK2 @ X3 ) ) ) ) )
& ( ( in @ X3 @ ( powerset @ sK1 ) )
= $true ) )
& ( ( in @ sK2 @ ( powerset @ sK1 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f859,plain,
( ? [X3: $i] :
( ( $true
!= ( in @ ( binintersect @ sK0 @ sK2 ) @ ( powerset @ ( binintersect @ ( binunion @ sK0 @ X3 ) @ ( binunion @ sK2 @ X3 ) ) ) ) )
& ( ( in @ X3 @ ( powerset @ sK1 ) )
= $true ) )
=> ( ( ( in @ ( binintersect @ sK0 @ sK2 ) @ ( powerset @ ( binintersect @ ( binunion @ sK0 @ sK3 ) @ ( binunion @ sK2 @ sK3 ) ) ) )
!= $true )
& ( $true
= ( in @ sK3 @ ( powerset @ sK1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f856,plain,
( ( complementUnionInPowersetComplement = $true )
& ( complementT_lem = $true )
& ( descr__Cong = $true )
& ( binintersectER = $true )
& ( in__Cong = $true )
& ( bs114d = $true )
& ( binintersectLsub = $true )
& ( upairsetE = $true )
& ( quantDeMorgan2 = $true )
& ( contrasubsetT3 = $true )
& ( cartprodfstpairEq = $true )
& ( doubleComplementEq = $true )
& ( sepInPowerset = $true )
& ( dpsetconstrEL2 = $true )
& ( funcGraphProp1 = $true )
& ( emptyInPowerset = $true )
& ( singletonsuniq = $true )
& ( singletoninpowunion = $true )
& ( dpsetconstrI = $true )
& ( emptyE1 = $true )
& ( singletoninpowerset = $true )
& ( complementImpComplementIntersect = $true )
& ( ap2apEq2 = $true )
& ( lamp = $true )
& ( setunion__Cong = $true )
& ( cartprodmempaircEq = $true )
& ( subsetTI = $true )
& ( ap2apEq1 = $true )
& ( apProp = $true )
& ( notdexE = $true )
& ( quantDeMorgan1 = $true )
& ( cartprodpairsurjEq = $true )
& ( disjointsetsI1 = $true )
& ( upairsubunion = $true )
& ( exuE3u = $true )
& ( setukpairIR = $true )
& ( descrp = $true )
& ( setadjoinAx = $true )
& ( exuEu = $true )
& ( ubforcartprodlem3 = $true )
& ( woz13rule3 = $true )
& ( notdallE = $true )
& ( exu__Cong = $true )
& ( upairinpowunion = $true )
& ( brelnall2 = $true )
& ( ex1E1 = $true )
& ( funcext2 = $true )
& ( ap2p = $true )
& ( doubleComplementSub1 = $true )
& ( cartprodmempair = $true )
& ( setukpairIL = $true )
& ( symdiffIneg1 = $true )
& ( woz1_2 = $true )
& ( demorgan2a2 = $true )
& ( cartprodmempair1 = $true )
& ( eta1 = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( powersetE = $true )
& ( binintersectI = $true )
& ( setminusT_lem = $true )
& ( inIntersectImpInUnion2 = $true )
& ( cartprodpairmemER = $true )
& ( exuI1 = $true )
& ( complementTcontraSubset = $true )
& ( binintersectTELcontra = $true )
& ( setadjoinE = $true )
& ( demorgan1a = $true )
& ( setadjoinIR = $true )
& ( lam2p = $true )
& ( exuE3e = $true )
& ( complementSubsetComplementIntersect = $true )
& ( inPowerset = $true )
& ( setadjoinSub2 = $true )
& ( demorgan2b2 = $true )
& ( woz13rule1 = $true )
& ( symdiffIneg2 = $true )
& ( notequalI1 = $true )
& ( binunionEcases = $true )
& ( upairset2E = $true )
& ( setunionsingleton2 = $true )
& ( omega0Ax = $true )
& ( binunionTILcontra = $true )
& ( binunionRsub = $true )
& ( setOfPairsIsBReln = $true )
& ( setminusELneg = $true )
& ( woz13rule0 = $true )
& ( exuE2 = $true )
& ( sepSubset = $true )
& ( setunionI = $true )
& ( setminusILneg = $true )
& ( upairequniteq = $true )
& ( theeq = $true )
& ( eta2 = $true )
& ( cartprodsndin = $true )
& ( funcext = $true )
& ( binintersectSubset4 = $true )
& ( contrasubsetT1 = $true )
& ( setunionsingleton1 = $true )
& ( subsetemptysetimpeq = $true )
& ( replAx = $true )
& ( nonemptyI1 = $true )
& ( iffalseProp1 = $true )
& ( binintersectTERcontra = $true )
& ( notsubsetI = $true )
& ( ubforcartprodlem2 = $true )
& ( setminusSubset1 = $true )
& ( nonemptyImpWitness = $true )
& ( funcextLem = $true )
& ( lamProp = $true )
& ( lam2lamEq = $true )
& ( ex1I2 = $true )
& ( setextsub = $true )
& ( powersetAx = $true )
& ( ex1I = $true )
& ( binunionT_lem = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( setadjoinIL = $true )
& ( dpsetconstrERa = $true )
& ( setminusERneg = $true )
& ( ksndsingleton = $true )
& ( contrasubsetT = $true )
& ( powersetTI1 = $true )
& ( binunionE = $true )
& ( omegaIndAx = $true )
& ( binintersectT_lem = $true )
& ( prop2setE = $true )
& ( iffalseProp2 = $true )
& ( contrasubsetT2 = $true )
& ( symdiffE = $true )
& ( setukpairinjR1 = $true )
& ( infuncsetfunc = $true )
& ( inIntersectImpInUnion = $true )
& ( quantDeMorgan3 = $true )
& ( dpsetconstrER = $true )
& ( doubleComplementE1 = $true )
& ( binunionTEcontra = $true )
& ( nonemptyI = $true )
& ( funcImageSingleton = $true )
& ( emptyinPowerset = $true )
& ( dsetconstrEL = $true )
& ( funcinfuncset = $true )
& ( emptysetimpfalse = $true )
& ( setminusSubset2 = $true )
& ( subsetI2 = $true )
& ( upairsetIR = $true )
& ( inCongP = $true )
& ( setukpairinjL1 = $true )
& ( subsetE2 = $true )
& ( setoftrueEq = $true )
& ( binintersectSubset5 = $true )
& ( singletonsswitch = $true )
& ( binintersectSubset2 = $true )
& ( powersetsubset = $true )
& ( setadjoinSub = $true )
& ( uniqinunit = $true )
& ( symdiffI1 = $true )
& ( doubleComplementI1 = $true )
& ( brelnall1 = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ X0 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) )
!= $true )
& ( ( in @ X3 @ ( powerset @ X1 ) )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( setextAx = $true )
& ( setukpairinjR12 = $true )
& ( setunionAx = $true )
& ( setadjoin__Cong = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( omegaSAx = $true )
& ( dpsetconstrEL1 = $true )
& ( kfstpairEq = $true )
& ( eqbreln = $true )
& ( ifp = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( dsetconstrI = $true )
& ( setminusIRneg = $true )
& ( binunionLsub = $true )
& ( woz13rule2 = $true )
& ( demorgan2b = $true )
& ( binintersectSubset1 = $true )
& ( powersetE1 = $true )
& ( prop2set2propI = $true )
& ( setukpairinjR = $true )
& ( funcGraphProp4 = $true )
& ( theprop = $true )
& ( ex1E2 = $true )
& ( demorgan1 = $true )
& ( exuE1 = $true )
& ( subsetTrans = $true )
& ( kpairiskpair = $true )
& ( exuI3 = $true )
& ( dpsetconstrSub = $true )
& ( dsetconstr__Cong = $true )
& ( setukpairinjL2 = $true )
& ( subbreln = $true )
& ( vacuousDall = $true )
& ( subPowSU = $true )
& ( wellorderingAx = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( iffalse = $true )
& ( setextT = $true )
& ( eqimpsubset1 = $true )
& ( exuI2 = $true )
& ( singletonsubset = $true )
& ( complementTE1 = $true )
& ( secondinupair = $true )
& ( notinemptyset = $true )
& ( emptysetE = $true )
& ( iftrueProp2 = $true )
& ( emptyI = $true )
& ( prop2setI = $true )
& ( beta2 = $true )
& ( demorgan1b = $true )
& ( setukpairinjR2 = $true )
& ( upairsetIL = $true )
& ( emptysetAx = $true )
& ( cartprodsndpairEq = $true )
& ( setext = $true )
& ( demorgan2 = $true )
& ( emptysetsubset = $true )
& ( powersetI1 = $true )
& ( emptyset__Cong = $true )
& ( complementTI1 = $true )
& ( setunionsingleton = $true )
& ( binintersectEL = $true )
& ( omega__Cong = $true )
& ( kfstsingleton = $true )
& ( funcGraphProp3 = $true )
& ( demorgan2a1 = $true )
& ( singletonprop = $true )
& ( binunionIR = $true )
& ( ksndpairEq = $true )
& ( binintersectRsub = $true )
& ( powersetTE1 = $true )
& ( kpairsurjEq = $true )
& ( doubleComplementSub2 = $true )
& ( woz1_1 = $true )
& ( quantDeMorgan4 = $true )
& ( ubforcartprodlem1 = $true )
& ( setminusER = $true )
& ( iftrueProp1 = $true )
& ( emptyinunitempty = $true )
& ( powersetT_lem = $true )
& ( binunionIL = $true )
& ( kpairp = $true )
& ( funcGraphProp2 = $true )
& ( setunionE = $true )
& ( notinsingleton = $true )
& ( beta1 = $true )
& ( subsetE = $true )
& ( foundationAx = $true )
& ( subset2powerset = $true )
& ( setminusLsub = $true )
& ( upairset2IR = $true )
& ( contraSubsetComplement = $true )
& ( setadjoinOr = $true )
& ( subsetRefl = $true )
& ( noeltsimpempty = $true )
& ( powerset__Cong = $true )
& ( cartprodpairin = $true )
& ( cartprodfstin = $true )
& ( setunionE2 = $true )
& ( cartprodpairmemEL = $true )
& ( eqimpsubset2 = $true )
& ( iftrue = $true )
& ( dsetconstrER = $true )
& ( setukpairinjL = $true )
& ( binunionTE = $true )
& ( app = $true )
& ( notequalI2 = $true )
& ( woz13rule4 = $true )
& ( setminusI = $true )
& ( symdiffI2 = $true )
& ( setukpairinjR11 = $true )
& ( binunionTIRcontra = $true )
& ( binintersectSubset3 = $true )
& ( setminusEL = $true )
& ( complementTnotintersectT = $true )
& ( powersetI = $true )
& ( iftrueorfalse = $true )
& ( ifSingleton = $true )
& ( demorgan2a = $true )
& ( subsetI1 = $true )
& ( setbeta = $true )
& ( nonemptyE1 = $true )
& ( eqinunit = $true ) ),
inference(flattening,[status(thm)],[f855]) ).
thf(f855,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ X0 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) )
!= $true )
& ( ( in @ X3 @ ( powerset @ X1 ) )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $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)],[f682]) ).
thf(f682,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 )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ ( powerset @ X1 ) )
= $true )
=> ( ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ X0 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f681]) ).
thf(f681,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
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ( in @ ( binintersect @ X0 @ X2 ) @ ( powerset @ ( binintersect @ ( binunion @ X0 @ X3 ) @ ( binunion @ X2 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f287]) ).
thf(f287,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
=> ! [X11: $i,X3: $i] :
( ( in @ X11 @ ( powerset @ X3 ) )
=> ! [X16: $i] :
( ( in @ X16 @ ( powerset @ X3 ) )
=> ! [X17: $i] :
( ( in @ X17 @ ( powerset @ X3 ) )
=> ( in @ ( binintersect @ X11 @ X16 ) @ ( powerset @ ( binintersect @ ( binunion @ X11 @ X17 ) @ ( binunion @ X16 @ X17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f286]) ).
thf(f286,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
=> ! [X11: $i,X3: $i] :
( ( in @ X11 @ ( powerset @ X3 ) )
=> ! [X16: $i] :
( ( in @ X16 @ ( powerset @ X3 ) )
=> ! [X17: $i] :
( ( in @ X17 @ ( powerset @ X3 ) )
=> ( in @ ( binintersect @ X11 @ X16 ) @ ( powerset @ ( binintersect @ ( binunion @ X11 @ X17 ) @ ( binunion @ X16 @ X17 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.50SVxc4AnF/DTF2THF_30813.p',woz1_3) ).
thf(f5098,plain,
( ( ( in @ ( binintersect @ sK0 @ sK2 ) @ ( powerset @ ( binintersect @ ( binunion @ sK0 @ sK3 ) @ ( binunion @ sK2 @ sK3 ) ) ) )
!= $true )
| spl4_21 ),
inference(avatar_component_clause,[status(thm)],[f5096]) ).
thf(f5116,plain,
spl4_25,
inference(avatar_split_clause,[status(thm)],[f1143,f5113]) ).
thf(f1143,plain,
( ( in @ sK0 @ ( powerset @ sK1 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f860]) ).
thf(f5099,plain,
~ spl4_21,
inference(avatar_split_clause,[status(thm)],[f1146,f5096]) ).
thf(f1146,plain,
( ( in @ ( binintersect @ sK0 @ sK2 ) @ ( powerset @ ( binintersect @ ( binunion @ sK0 @ sK3 ) @ ( binunion @ sK2 @ sK3 ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f860]) ).
thf(f5094,plain,
~ spl4_20,
inference(avatar_split_clause,[status(thm)],[f288,f5091]) ).
thf(f5091,definition,
( spl4_20
<=> ( $false = $true ) ),
introduced(definition,[new_symbols(naming,[spl4_20])],[avatar_definition]) ).
thf(f288,plain,
$false != $true,
introduced(definition,[],[fool_axiom]) ).
thf(f5071,plain,
spl4_15,
inference(avatar_split_clause,[status(thm)],[f1145,f5068]) ).
thf(f5068,definition,
( spl4_15
<=> ( $true
= ( in @ sK3 @ ( powerset @ sK1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_15])],[avatar_definition]) ).
thf(f1145,plain,
( $true
= ( in @ sK3 @ ( powerset @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f860]) ).
thf(f5065,plain,
spl4_14,
inference(avatar_split_clause,[status(thm)],[f1144,f5062]) ).
thf(f1144,plain,
( ( in @ sK2 @ ( powerset @ sK1 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f860]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU765^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n011.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 12:33:02 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SEU765^1 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.46 % Domain : Set Theory
% 0.29/0.46 % Problem : Typed Set Theory - First Wizard of Oz Examples - WoZ1 Problems
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.29/0.46 % (! Z:i.in Z (powerset A) -> in (binintersect X Y)
% 0.29/0.46 % (powerset (binintersect (binunion X Z) (binunion Y Z))))))
% 0.29/0.46
% 0.29/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.29/0.46 % Source : [Bro08]
% 0.29/0.46 % Names : ZFC267g [Bro08]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.22 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.23 v8.1.0, 0.09 v7.5.0, 0.29 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v6.1.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v5.2.0, 0.80 v4.1.0, 1.00 v3.7.0
% 0.29/0.46 % Syntax : Number of formulae : 605 ( 285 unt; 319 typ; 285 def)
% 0.29/0.46 % Number of atoms : 1705 ( 414 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 285 ( 5 avg)
% 0.29/0.46 % Number of connectives : 3639 ( 73 ~; 12 |; 44 &;2634 @)
% 0.29/0.46 % ( 14 <=>; 862 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 295 ( 2 avg)
% 0.29/0.46 % Number of types : 2 ( 0 usr)
% 0.29/0.46 % Number of type conns : 132 ( 132 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 322 ( 319 usr; 285 con; 0-4 aty)
% 0.29/0.46 % Number of variables : 977 ( 74 ^; 868 !; 35 ?; 977 :)
% 0.29/0.46 % SPC : TH0_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : http://mathgate.info/detsetitem.php?id=326
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(in_type,type,
% 0.29/0.46 in: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(exu_type,type,
% 0.29/0.46 exu: ( $i > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(exu,definition,
% 0.29/0.46 ( exu
% 0.29/0.46 = ( ^ [Xphi: $i > $o] :
% 0.29/0.46 ? [Xx: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 & ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setextAx_type,type,
% 0.29/0.46 setextAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setextAx,definition,
% 0.29/0.46 ( setextAx
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 <=> ( in @ Xx @ B ) )
% 0.29/0.46 => ( A = B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyset_type,type,
% 0.29/0.46 emptyset: $i ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetAx_type,type,
% 0.29/0.46 emptysetAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetAx,definition,
% 0.29/0.46 ( emptysetAx
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoin_type,type,
% 0.29/0.46 setadjoin: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinAx_type,type,
% 0.29/0.46 setadjoinAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinAx,definition,
% 0.29/0.46 ( setadjoinAx
% 0.29/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.46 <=> ( ( Xy = Xx )
% 0.29/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powerset_type,type,
% 0.29/0.46 powerset: $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(powersetAx_type,type,
% 0.29/0.46 powersetAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetAx,definition,
% 0.29/0.46 ( powersetAx
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.46 <=> ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunion_type,type,
% 0.29/0.46 setunion: $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(setunionAx_type,type,
% 0.29/0.46 setunionAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionAx,definition,
% 0.29/0.46 ( setunionAx
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.46 <=> ? [B: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 & ( in @ B @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(omega_type,type,
% 0.29/0.46 omega: $i ).
% 0.29/0.46
% 0.29/0.46 thf(omega0Ax_type,type,
% 0.29/0.46 omega0Ax: $o ).
% 0.29/0.46
% 0.29/0.46 thf(omega0Ax,definition,
% 0.29/0.46 ( omega0Ax
% 0.29/0.46 = ( in @ emptyset @ omega ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(omegaSAx_type,type,
% 0.29/0.46 omegaSAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(omegaSAx,definition,
% 0.29/0.46 ( omegaSAx
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ omega )
% 0.29/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(omegaIndAx_type,type,
% 0.29/0.46 omegaIndAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(omegaIndAx,definition,
% 0.29/0.46 ( omegaIndAx
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( ( in @ emptyset @ A )
% 0.29/0.46 & ! [Xx: $i] :
% 0.29/0.46 ( ( ( in @ Xx @ omega )
% 0.29/0.46 & ( in @ Xx @ A ) )
% 0.29/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ omega )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(replAx_type,type,
% 0.29/0.46 replAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(replAx,definition,
% 0.29/0.46 ( replAx
% 0.29/0.46 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( exu
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.29/0.46 => ? [B: $i] :
% 0.29/0.46 ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 <=> ? [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(foundationAx_type,type,
% 0.29/0.46 foundationAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(foundationAx,definition,
% 0.29/0.46 ( foundationAx
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.29/0.46 => ? [B: $i] :
% 0.29/0.46 ( ( in @ B @ A )
% 0.29/0.46 & ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(wellorderingAx_type,type,
% 0.29/0.46 wellorderingAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(wellorderingAx,definition,
% 0.29/0.46 ( wellorderingAx
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ? [B: $i] :
% 0.29/0.46 ( ! [C: $i] :
% 0.29/0.46 ( ( in @ C @ B )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ C )
% 0.29/0.46 => ( in @ Xx @ A ) ) )
% 0.29/0.46 & ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( ( in @ Xx @ A )
% 0.29/0.46 & ( in @ Xy @ A ) )
% 0.29/0.46 => ( ! [C: $i] :
% 0.29/0.46 ( ( in @ C @ B )
% 0.29/0.46 => ( ( in @ Xx @ C )
% 0.29/0.46 <=> ( in @ Xy @ C ) ) )
% 0.29/0.46 => ( Xx = Xy ) ) )
% 0.29/0.46 & ! [C: $i,D: $i] :
% 0.29/0.46 ( ( ( in @ C @ B )
% 0.29/0.46 & ( in @ D @ B ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ C )
% 0.29/0.46 => ( in @ Xx @ D ) )
% 0.29/0.46 | ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ D )
% 0.29/0.46 => ( in @ Xx @ C ) ) ) )
% 0.29/0.46 & ! [C: $i] :
% 0.29/0.46 ( ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ C )
% 0.29/0.46 => ( in @ Xx @ A ) )
% 0.29/0.46 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.29/0.46 => ? [D: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ D @ B )
% 0.29/0.46 & ( in @ Xx @ C )
% 0.29/0.46 & ~ ? [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ D )
% 0.29/0.46 & ( in @ Xy @ C ) )
% 0.29/0.46 & ! [E: $i] :
% 0.29/0.46 ( ( in @ E @ B )
% 0.29/0.46 => ( ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ E )
% 0.29/0.46 => ( in @ Xy @ D ) )
% 0.29/0.46 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(descr_type,type,
% 0.29/0.46 descr: ( $i > $o ) > $i ).
% 0.29/0.46
% 0.29/0.46 thf(descrp_type,type,
% 0.29/0.46 descrp: $o ).
% 0.29/0.46
% 0.29/0.46 thf(descrp,definition,
% 0.29/0.46 ( descrp
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ( Xphi
% 0.29/0.46 @ ( descr
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstr_type,type,
% 0.29/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrI_type,type,
% 0.29/0.46 dsetconstrI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrI,definition,
% 0.29/0.46 ( dsetconstrI
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrEL_type,type,
% 0.29/0.46 dsetconstrEL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrEL,definition,
% 0.29/0.46 ( dsetconstrEL
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrER_type,type,
% 0.29/0.46 dsetconstrER: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrER,definition,
% 0.29/0.46 ( dsetconstrER
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuE1_type,type,
% 0.29/0.46 exuE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuE1,definition,
% 0.29/0.46 ( exuE1
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 & ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(prop2set_type,type,
% 0.29/0.46 prop2set: $o > $i ).
% 0.29/0.46
% 0.29/0.46 thf(prop2setE_type,type,
% 0.29/0.46 prop2setE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(prop2setE,definition,
% 0.29/0.46 ( prop2setE
% 0.29/0.46 = ( ! [Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.29/0.46 => Xphi ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetE_type,type,
% 0.29/0.46 emptysetE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetE,definition,
% 0.29/0.46 ( emptysetE
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ emptyset )
% 0.29/0.46 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetimpfalse_type,type,
% 0.29/0.46 emptysetimpfalse: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetimpfalse,definition,
% 0.29/0.46 ( emptysetimpfalse
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ emptyset )
% 0.29/0.46 => $false ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notinemptyset_type,type,
% 0.29/0.46 notinemptyset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notinemptyset,definition,
% 0.29/0.46 ( notinemptyset
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuE3e_type,type,
% 0.29/0.46 exuE3e: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuE3e,definition,
% 0.29/0.46 ( exuE3e
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setext_type,type,
% 0.29/0.46 setext: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setext,definition,
% 0.29/0.46 ( setext
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ A ) )
% 0.29/0.46 => ( A = B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyI_type,type,
% 0.29/0.46 emptyI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyI,definition,
% 0.29/0.46 ( emptyI
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ~ ( in @ Xx @ A )
% 0.29/0.46 => ( A = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(noeltsimpempty_type,type,
% 0.29/0.46 noeltsimpempty: $o ).
% 0.29/0.46
% 0.29/0.46 thf(noeltsimpempty,definition,
% 0.29/0.46 ( noeltsimpempty
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ~ ( in @ Xx @ A )
% 0.29/0.46 => ( A = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setbeta_type,type,
% 0.29/0.46 setbeta: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setbeta,definition,
% 0.29/0.46 ( setbeta
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.46 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonempty_type,type,
% 0.29/0.46 nonempty: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonempty,definition,
% 0.29/0.46 ( nonempty
% 0.29/0.46 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyE1_type,type,
% 0.29/0.46 nonemptyE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyE1,definition,
% 0.29/0.46 ( nonemptyE1
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( nonempty @ A )
% 0.29/0.46 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyI_type,type,
% 0.29/0.46 nonemptyI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyI,definition,
% 0.29/0.46 ( nonemptyI
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( nonempty
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyI1_type,type,
% 0.29/0.46 nonemptyI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyI1,definition,
% 0.29/0.46 ( nonemptyI1
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.29/0.46 => ( nonempty @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinIL_type,type,
% 0.29/0.46 setadjoinIL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinIL,definition,
% 0.29/0.46 ( setadjoinIL
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyinunitempty_type,type,
% 0.29/0.46 emptyinunitempty: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyinunitempty,definition,
% 0.29/0.46 ( emptyinunitempty
% 0.29/0.46 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinIR_type,type,
% 0.29/0.46 setadjoinIR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinIR,definition,
% 0.29/0.46 ( setadjoinIR
% 0.29/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinE_type,type,
% 0.29/0.46 setadjoinE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinE,definition,
% 0.29/0.46 ( setadjoinE
% 0.29/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.46 => ! [Xphi: $o] :
% 0.29/0.46 ( ( ( Xy = Xx )
% 0.29/0.46 => Xphi )
% 0.29/0.46 => ( ( ( in @ Xy @ A )
% 0.29/0.46 => Xphi )
% 0.29/0.46 => Xphi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinOr_type,type,
% 0.29/0.46 setadjoinOr: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinOr,definition,
% 0.29/0.46 ( setadjoinOr
% 0.29/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.46 => ( ( Xy = Xx )
% 0.29/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setoftrueEq_type,type,
% 0.29/0.46 setoftrueEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setoftrueEq,definition,
% 0.29/0.46 ( setoftrueEq
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : $true )
% 0.29/0.46 = A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetI_type,type,
% 0.29/0.46 powersetI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetI,definition,
% 0.29/0.46 ( powersetI
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ A ) )
% 0.29/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyinPowerset_type,type,
% 0.29/0.46 emptyinPowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyinPowerset,definition,
% 0.29/0.46 ( emptyinPowerset
% 0.29/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyInPowerset_type,type,
% 0.29/0.46 emptyInPowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyInPowerset,definition,
% 0.29/0.46 ( emptyInPowerset
% 0.29/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetE_type,type,
% 0.29/0.46 powersetE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetE,definition,
% 0.29/0.46 ( powersetE
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.46 => ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionI_type,type,
% 0.29/0.46 setunionI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionI,definition,
% 0.29/0.46 ( setunionI
% 0.29/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( ( in @ B @ A )
% 0.29/0.46 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionE_type,type,
% 0.29/0.46 setunionE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionE,definition,
% 0.29/0.46 ( setunionE
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.46 => ! [Xphi: $o] :
% 0.29/0.46 ( ! [B: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( ( in @ B @ A )
% 0.29/0.46 => Xphi ) )
% 0.29/0.46 => Xphi ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subPowSU_type,type,
% 0.29/0.46 subPowSU: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subPowSU,definition,
% 0.29/0.46 ( subPowSU
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuE2_type,type,
% 0.29/0.46 exuE2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuE2,definition,
% 0.29/0.46 ( exuE2
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyImpWitness_type,type,
% 0.29/0.46 nonemptyImpWitness: $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyImpWitness,definition,
% 0.29/0.46 ( nonemptyImpWitness
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( nonempty @ A )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & $true ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(uniqinunit_type,type,
% 0.29/0.46 uniqinunit: $o ).
% 0.29/0.46
% 0.29/0.46 thf(uniqinunit,definition,
% 0.29/0.46 ( uniqinunit
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notinsingleton_type,type,
% 0.29/0.46 notinsingleton: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notinsingleton,definition,
% 0.29/0.46 ( notinsingleton
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx != Xy )
% 0.29/0.46 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(eqinunit_type,type,
% 0.29/0.46 eqinunit: $o ).
% 0.29/0.46
% 0.29/0.46 thf(eqinunit,definition,
% 0.29/0.46 ( eqinunit
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsswitch_type,type,
% 0.29/0.46 singletonsswitch: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsswitch,definition,
% 0.29/0.46 ( singletonsswitch
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetE_type,type,
% 0.29/0.46 upairsetE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetE,definition,
% 0.29/0.46 ( upairsetE
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.29/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.29/0.46 => ( ( Xz = Xx )
% 0.29/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetIL_type,type,
% 0.29/0.46 upairsetIL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetIL,definition,
% 0.29/0.46 ( upairsetIL
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetIR_type,type,
% 0.29/0.46 upairsetIR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetIR,definition,
% 0.29/0.46 ( upairsetIR
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyE1_type,type,
% 0.29/0.46 emptyE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyE1,definition,
% 0.29/0.46 ( emptyE1
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) )
% 0.29/0.46 => ( ( ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 = emptyset )
% 0.29/0.46 => $false ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(vacuousDall_type,type,
% 0.29/0.46 vacuousDall: $o ).
% 0.29/0.46
% 0.29/0.46 thf(vacuousDall,definition,
% 0.29/0.46 ( vacuousDall
% 0.29/0.46 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ emptyset )
% 0.29/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan1_type,type,
% 0.29/0.46 quantDeMorgan1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan1,definition,
% 0.29/0.46 ( quantDeMorgan1
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ~ ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan2_type,type,
% 0.29/0.46 quantDeMorgan2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan2,definition,
% 0.29/0.46 ( quantDeMorgan2
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ~ ( Xphi @ Xx ) )
% 0.29/0.46 => ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan3_type,type,
% 0.29/0.46 quantDeMorgan3: $o ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan3,definition,
% 0.29/0.46 ( quantDeMorgan3
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan4_type,type,
% 0.29/0.46 quantDeMorgan4: $o ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan4,definition,
% 0.29/0.46 ( quantDeMorgan4
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ~ ( Xphi @ Xx ) )
% 0.29/0.46 => ~ ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(prop2setI_type,type,
% 0.29/0.46 prop2setI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(prop2setI,definition,
% 0.29/0.46 ( prop2setI
% 0.29/0.46 = ( ! [Xphi: $o] :
% 0.29/0.46 ( Xphi
% 0.29/0.46 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(set2prop_type,type,
% 0.29/0.46 set2prop: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(prop2set2propI_type,type,
% 0.29/0.46 prop2set2propI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(prop2set2propI,definition,
% 0.29/0.46 ( prop2set2propI
% 0.29/0.46 = ( ! [Xphi: $o] :
% 0.29/0.46 ( Xphi
% 0.29/0.46 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notdexE_type,type,
% 0.29/0.46 notdexE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notdexE,definition,
% 0.29/0.46 ( notdexE
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notdallE_type,type,
% 0.29/0.46 notdallE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notdallE,definition,
% 0.29/0.46 ( notdallE
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ~ ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuI1_type,type,
% 0.29/0.46 exuI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuI1,definition,
% 0.29/0.46 ( exuI1
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 & ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) )
% 0.29/0.46 => ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuI3_type,type,
% 0.29/0.46 exuI3: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuI3,definition,
% 0.29/0.46 ( exuI3
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.29/0.46 => ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) )
% 0.29/0.46 => ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuI2_type,type,
% 0.29/0.46 exuI2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuI2,definition,
% 0.29/0.46 ( exuI2
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] :
% 0.29/0.46 ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 <=> ( Xy = Xx ) )
% 0.29/0.46 => ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(inCongP_type,type,
% 0.29/0.46 inCongP: $o ).
% 0.29/0.46
% 0.29/0.46 thf(inCongP,definition,
% 0.29/0.46 ( inCongP
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(in__Cong_type,type,
% 0.29/0.46 in__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(in__Cong,definition,
% 0.29/0.46 ( in__Cong
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuE3u_type,type,
% 0.29/0.46 exuE3u: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuE3u,definition,
% 0.29/0.46 ( exuE3u
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exu__Cong_type,type,
% 0.29/0.46 exu__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exu__Cong,definition,
% 0.29/0.46 ( exu__Cong
% 0.29/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.29/0.46 => ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 <=> ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyset__Cong_type,type,
% 0.29/0.46 emptyset__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyset__Cong,definition,
% 0.29/0.46 ( emptyset__Cong
% 0.29/0.46 = ( emptyset = emptyset ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoin__Cong_type,type,
% 0.29/0.46 setadjoin__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoin__Cong,definition,
% 0.29/0.46 ( setadjoin__Cong
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ! [Xz: $i,Xu: $i] :
% 0.29/0.46 ( ( Xz = Xu )
% 0.29/0.46 => ( ( setadjoin @ Xx @ Xz )
% 0.29/0.46 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powerset__Cong_type,type,
% 0.29/0.46 powerset__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powerset__Cong,definition,
% 0.29/0.46 ( powerset__Cong
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ( ( powerset @ A )
% 0.29/0.46 = ( powerset @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunion__Cong_type,type,
% 0.29/0.46 setunion__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunion__Cong,definition,
% 0.29/0.46 ( setunion__Cong
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ( ( setunion @ A )
% 0.29/0.46 = ( setunion @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(omega__Cong_type,type,
% 0.29/0.46 omega__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(omega__Cong,definition,
% 0.29/0.46 ( omega__Cong
% 0.29/0.46 = ( omega = omega ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuEu_type,type,
% 0.29/0.46 exuEu: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuEu,definition,
% 0.29/0.46 ( exuEu
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(descr__Cong_type,type,
% 0.29/0.46 descr__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(descr__Cong,definition,
% 0.29/0.46 ( descr__Cong
% 0.29/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.29/0.46 => ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.29/0.46 => ( ( descr
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 = ( descr
% 0.29/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstr__Cong_type,type,
% 0.29/0.46 dsetconstr__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstr__Cong,definition,
% 0.29/0.46 ( dsetconstr__Cong
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( Xx = Xy )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.29/0.46 => ( ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 = ( dsetconstr @ B
% 0.29/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subset_type,type,
% 0.29/0.46 subset: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(disjoint_type,type,
% 0.29/0.46 disjoint: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(setsmeet_type,type,
% 0.29/0.46 setsmeet: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetI1_type,type,
% 0.29/0.46 subsetI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetI1,definition,
% 0.29/0.46 ( subsetI1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(eqimpsubset2_type,type,
% 0.29/0.46 eqimpsubset2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(eqimpsubset2,definition,
% 0.29/0.46 ( eqimpsubset2
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(eqimpsubset1_type,type,
% 0.29/0.46 eqimpsubset1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(eqimpsubset1,definition,
% 0.29/0.46 ( eqimpsubset1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetI2_type,type,
% 0.29/0.46 subsetI2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetI2,definition,
% 0.29/0.46 ( subsetI2
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetsubset_type,type,
% 0.29/0.46 emptysetsubset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetsubset,definition,
% 0.29/0.46 ( emptysetsubset
% 0.29/0.46 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetE_type,type,
% 0.29/0.46 subsetE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetE,definition,
% 0.29/0.46 ( subsetE
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetE2_type,type,
% 0.29/0.46 subsetE2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetE2,definition,
% 0.29/0.46 ( subsetE2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notsubsetI_type,type,
% 0.29/0.46 notsubsetI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notsubsetI,definition,
% 0.29/0.46 ( notsubsetI
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notequalI1_type,type,
% 0.29/0.46 notequalI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notequalI1,definition,
% 0.29/0.46 ( notequalI1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ~ ( subset @ A @ B )
% 0.29/0.46 => ( A != B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notequalI2_type,type,
% 0.29/0.46 notequalI2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notequalI2,definition,
% 0.29/0.46 ( notequalI2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ( A != B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetRefl_type,type,
% 0.29/0.46 subsetRefl: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetRefl,definition,
% 0.29/0.46 ( subsetRefl
% 0.29/0.46 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetTrans_type,type,
% 0.29/0.46 subsetTrans: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetTrans,definition,
% 0.29/0.46 ( subsetTrans
% 0.29/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( subset @ B @ C )
% 0.29/0.46 => ( subset @ A @ C ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinSub_type,type,
% 0.29/0.46 setadjoinSub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinSub,definition,
% 0.29/0.46 ( setadjoinSub
% 0.29/0.46 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinSub2_type,type,
% 0.29/0.46 setadjoinSub2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinSub2,definition,
% 0.29/0.46 ( setadjoinSub2
% 0.29/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subset2powerset_type,type,
% 0.29/0.46 subset2powerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subset2powerset,definition,
% 0.29/0.46 ( subset2powerset
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setextsub_type,type,
% 0.29/0.46 setextsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setextsub,definition,
% 0.29/0.46 ( setextsub
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( subset @ B @ A )
% 0.29/0.46 => ( A = B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetemptysetimpeq_type,type,
% 0.29/0.46 subsetemptysetimpeq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetemptysetimpeq,definition,
% 0.29/0.46 ( subsetemptysetimpeq
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( subset @ A @ emptyset )
% 0.29/0.46 => ( A = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetI1_type,type,
% 0.29/0.46 powersetI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetI1,definition,
% 0.29/0.46 ( powersetI1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ B @ A )
% 0.29/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetE1_type,type,
% 0.29/0.46 powersetE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetE1,definition,
% 0.29/0.46 ( powersetE1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(inPowerset_type,type,
% 0.29/0.46 inPowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(inPowerset,definition,
% 0.29/0.46 ( inPowerset
% 0.29/0.46 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetsubset_type,type,
% 0.29/0.46 powersetsubset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetsubset,definition,
% 0.29/0.46 ( powersetsubset
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sepInPowerset_type,type,
% 0.29/0.46 sepInPowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(sepInPowerset,definition,
% 0.29/0.46 ( sepInPowerset
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( in
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 @ ( powerset @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sepSubset_type,type,
% 0.29/0.46 sepSubset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(sepSubset,definition,
% 0.29/0.46 ( sepSubset
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( subset
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunion_type,type,
% 0.29/0.46 binunion: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(binunionIL_type,type,
% 0.29/0.46 binunionIL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionIL,definition,
% 0.29/0.46 ( binunionIL
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairset2IR_type,type,
% 0.29/0.46 upairset2IR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairset2IR,definition,
% 0.29/0.46 ( upairset2IR
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionIR_type,type,
% 0.29/0.46 binunionIR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionIR,definition,
% 0.29/0.46 ( binunionIR
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionEcases_type,type,
% 0.29/0.46 binunionEcases: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionEcases,definition,
% 0.29/0.46 ( binunionEcases
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.29/0.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.29/0.46 => ( ( ( in @ Xx @ A )
% 0.29/0.46 => Xphi )
% 0.29/0.46 => ( ( ( in @ Xx @ B )
% 0.29/0.46 => Xphi )
% 0.29/0.46 => Xphi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionE_type,type,
% 0.29/0.46 binunionE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionE,definition,
% 0.29/0.46 ( binunionE
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionLsub_type,type,
% 0.29/0.46 binunionLsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionLsub,definition,
% 0.29/0.46 ( binunionLsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionRsub_type,type,
% 0.29/0.46 binunionRsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionRsub,definition,
% 0.29/0.46 ( binunionRsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersect_type,type,
% 0.29/0.46 binintersect: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectI_type,type,
% 0.29/0.46 binintersectI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectI,definition,
% 0.29/0.46 ( binintersectI
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset5_type,type,
% 0.29/0.46 binintersectSubset5: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset5,definition,
% 0.29/0.46 ( binintersectSubset5
% 0.29/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.29/0.46 ( ( subset @ C @ A )
% 0.29/0.46 => ( ( subset @ C @ B )
% 0.29/0.46 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectEL_type,type,
% 0.29/0.46 binintersectEL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectEL,definition,
% 0.29/0.46 ( binintersectEL
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectLsub_type,type,
% 0.29/0.46 binintersectLsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectLsub,definition,
% 0.29/0.46 ( binintersectLsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset2_type,type,
% 0.29/0.46 binintersectSubset2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset2,definition,
% 0.29/0.46 ( binintersectSubset2
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( binintersect @ A @ B )
% 0.29/0.46 = A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset3_type,type,
% 0.29/0.46 binintersectSubset3: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset3,definition,
% 0.29/0.46 ( binintersectSubset3
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( ( binintersect @ A @ B )
% 0.29/0.46 = B )
% 0.29/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectER_type,type,
% 0.29/0.46 binintersectER: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectER,definition,
% 0.29/0.46 ( binintersectER
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.29/0.46 => ( in @ Xx @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(disjointsetsI1_type,type,
% 0.29/0.46 disjointsetsI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(disjointsetsI1,definition,
% 0.29/0.46 ( disjointsetsI1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( in @ Xx @ B ) )
% 0.29/0.46 => ( ( binintersect @ A @ B )
% 0.29/0.46 = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectRsub_type,type,
% 0.29/0.46 binintersectRsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectRsub,definition,
% 0.29/0.46 ( binintersectRsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset4_type,type,
% 0.29/0.46 binintersectSubset4: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset4,definition,
% 0.29/0.46 ( binintersectSubset4
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ B @ A )
% 0.29/0.46 => ( ( binintersect @ A @ B )
% 0.29/0.46 = B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset1_type,type,
% 0.29/0.46 binintersectSubset1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset1,definition,
% 0.29/0.46 ( binintersectSubset1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( ( binintersect @ A @ B )
% 0.29/0.46 = A )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(bs114d_type,type,
% 0.29/0.46 bs114d: $o ).
% 0.29/0.46
% 0.29/0.46 thf(bs114d,definition,
% 0.29/0.46 ( bs114d
% 0.29/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.29/0.46 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.29/0.46 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(regular_type,type,
% 0.29/0.46 regular: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminus_type,type,
% 0.29/0.46 setminus: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(setminusI_type,type,
% 0.29/0.46 setminusI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusI,definition,
% 0.29/0.46 ( setminusI
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusEL_type,type,
% 0.29/0.46 setminusEL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusEL,definition,
% 0.29/0.46 ( setminusEL
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusER_type,type,
% 0.29/0.46 setminusER: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusER,definition,
% 0.29/0.46 ( setminusER
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.46 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusSubset2_type,type,
% 0.29/0.46 setminusSubset2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusSubset2,definition,
% 0.29/0.46 ( setminusSubset2
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( setminus @ A @ B )
% 0.29/0.46 = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusERneg_type,type,
% 0.29/0.46 setminusERneg: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusERneg,definition,
% 0.29/0.46 ( setminusERneg
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusELneg_type,type,
% 0.29/0.46 setminusELneg: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusELneg,definition,
% 0.29/0.46 ( setminusELneg
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusILneg_type,type,
% 0.29/0.46 setminusILneg: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusILneg,definition,
% 0.29/0.46 ( setminusILneg
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ~ ( in @ Xx @ A )
% 0.29/0.46 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusIRneg_type,type,
% 0.29/0.46 setminusIRneg: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusIRneg,definition,
% 0.29/0.46 ( setminusIRneg
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusLsub_type,type,
% 0.29/0.46 setminusLsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusLsub,definition,
% 0.29/0.46 ( setminusLsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusSubset1_type,type,
% 0.29/0.46 setminusSubset1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusSubset1,definition,
% 0.29/0.46 ( setminusSubset1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( ( setminus @ A @ B )
% 0.29/0.46 = emptyset )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(symdiff_type,type,
% 0.29/0.46 symdiff: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffE_type,type,
% 0.29/0.46 symdiffE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffE,definition,
% 0.29/0.46 ( symdiffE
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.29/0.46 => ! [Xphi: $o] :
% 0.29/0.46 ( ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => Xphi ) )
% 0.29/0.46 => ( ( ~ ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ B )
% 0.29/0.46 => Xphi ) )
% 0.29/0.46 => Xphi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffI1_type,type,
% 0.29/0.46 symdiffI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffI1,definition,
% 0.29/0.46 ( symdiffI1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffI2_type,type,
% 0.29/0.46 symdiffI2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffI2,definition,
% 0.29/0.46 ( symdiffI2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ~ ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffIneg1_type,type,
% 0.29/0.46 symdiffIneg1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffIneg1,definition,
% 0.29/0.46 ( symdiffIneg1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ B )
% 0.29/0.46 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffIneg2_type,type,
% 0.29/0.46 symdiffIneg2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffIneg2,definition,
% 0.29/0.46 ( symdiffIneg2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ~ ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(iskpair_type,type,
% 0.29/0.46 iskpair: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(secondinupair_type,type,
% 0.29/0.46 secondinupair: $o ).
% 0.29/0.46
% 0.29/0.46 thf(secondinupair,definition,
% 0.29/0.46 ( secondinupair
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairIL_type,type,
% 0.29/0.46 setukpairIL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairIL,definition,
% 0.29/0.46 ( setukpairIL
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairIR_type,type,
% 0.29/0.46 setukpairIR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairIR,definition,
% 0.29/0.46 ( setukpairIR
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(kpairiskpair_type,type,
% 0.29/0.46 kpairiskpair: $o ).
% 0.29/0.46
% 0.29/0.46 thf(kpairiskpair,definition,
% 0.29/0.46 ( kpairiskpair
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(kpair_type,type,
% 0.29/0.46 kpair: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(kpairp_type,type,
% 0.29/0.46 kpairp: $o ).
% 0.29/0.46
% 0.29/0.46 thf(kpairp,definition,
% 0.29/0.46 ( kpairp
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprod_type,type,
% 0.29/0.46 cartprod: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsubset_type,type,
% 0.29/0.46 singletonsubset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsubset,definition,
% 0.29/0.46 ( singletonsubset
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(singletoninpowerset_type,type,
% 0.29/0.46 singletoninpowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletoninpowerset,definition,
% 0.29/0.46 ( singletoninpowerset
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(singletoninpowunion_type,type,
% 0.29/0.46 singletoninpowunion: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletoninpowunion,definition,
% 0.29/0.46 ( singletoninpowunion
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairset2E_type,type,
% 0.29/0.46 upairset2E: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairset2E,definition,
% 0.29/0.46 ( upairset2E
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.29/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.29/0.46 => ( ( Xz = Xx )
% 0.29/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairsubunion_type,type,
% 0.29/0.46 upairsubunion: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairsubunion,definition,
% 0.29/0.46 ( upairsubunion
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairinpowunion_type,type,
% 0.29/0.46 upairinpowunion: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairinpowunion,definition,
% 0.29/0.46 ( upairinpowunion
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ubforcartprodlem1_type,type,
% 0.29/0.46 ubforcartprodlem1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ubforcartprodlem1,definition,
% 0.29/0.46 ( ubforcartprodlem1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ubforcartprodlem2_type,type,
% 0.29/0.46 ubforcartprodlem2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ubforcartprodlem2,definition,
% 0.29/0.46 ( ubforcartprodlem2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ubforcartprodlem3_type,type,
% 0.29/0.46 ubforcartprodlem3: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ubforcartprodlem3,definition,
% 0.29/0.46 ( ubforcartprodlem3
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodpairin_type,type,
% 0.29/0.46 cartprodpairin: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodpairin,definition,
% 0.29/0.46 ( cartprodpairin
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodmempair1_type,type,
% 0.29/0.46 cartprodmempair1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodmempair1,definition,
% 0.29/0.46 ( cartprodmempair1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.29/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ? [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 & ( Xu
% 0.29/0.46 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodmempair_type,type,
% 0.29/0.46 cartprodmempair: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodmempair,definition,
% 0.29/0.46 ( cartprodmempair
% 0.29/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.29/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.29/0.46 => ( iskpair @ Xu ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionE2_type,type,
% 0.29/0.46 setunionE2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionE2,definition,
% 0.29/0.46 ( setunionE2
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.46 => ? [X: $i] :
% 0.29/0.46 ( ( in @ X @ A )
% 0.29/0.46 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionsingleton1_type,type,
% 0.29/0.46 setunionsingleton1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionsingleton1,definition,
% 0.29/0.46 ( setunionsingleton1
% 0.29/0.46 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionsingleton2_type,type,
% 0.29/0.46 setunionsingleton2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionsingleton2,definition,
% 0.29/0.46 ( setunionsingleton2
% 0.29/0.46 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionsingleton_type,type,
% 0.29/0.46 setunionsingleton: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionsingleton,definition,
% 0.29/0.46 ( setunionsingleton
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.29/0.46 = Xx ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(singleton_type,type,
% 0.29/0.46 singleton: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletonprop_type,type,
% 0.29/0.46 singletonprop: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletonprop,definition,
% 0.29/0.46 ( singletonprop
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) )
% 0.29/0.46 => ( ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) )
% 0.29/0.46 => ( singleton
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ex1_type,type,
% 0.29/0.46 ex1: $i > ( $i > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(ex1,definition,
% 0.29/0.46 ( ex1
% 0.29/0.46 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( singleton
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ex1E1_type,type,
% 0.29/0.46 ex1E1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ex1E1,definition,
% 0.29/0.46 ( ex1E1
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ( ex1 @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ex1I_type,type,
% 0.29/0.46 ex1I: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ex1I,definition,
% 0.29/0.46 ( ex1I
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xy = Xx ) ) )
% 0.29/0.46 => ( ex1 @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ex1I2_type,type,
% 0.29/0.46 ex1I2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ex1I2,definition,
% 0.29/0.46 ( ex1I2
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) )
% 0.29/0.46 => ( ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) )
% 0.29/0.46 => ( ex1 @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsuniq_type,type,
% 0.29/0.46 singletonsuniq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsuniq,definition,
% 0.29/0.46 ( singletonsuniq
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( ( setadjoin @ Xx @ emptyset )
% 0.29/0.46 = ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(atmost1p_type,type,
% 0.29/0.46 atmost1p: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(atleast2p_type,type,
% 0.29/0.46 atleast2p: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(atmost2p_type,type,
% 0.29/0.46 atmost2p: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetp_type,type,
% 0.29/0.46 upairsetp: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjL1_type,type,
% 0.29/0.46 setukpairinjL1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjL1,definition,
% 0.29/0.46 ( setukpairinjL1
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.29/0.46 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.29/0.46 => ( Xx = Xz ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(kfstsingleton_type,type,
% 0.29/0.46 kfstsingleton: $o ).
% 0.29/0.46
% 0.29/0.46 thf(kfstsingleton,definition,
% 0.29/0.46 ( kfstsingleton
% 0.29/0.46 = ( ! [Xu: $i] :
% 0.29/0.46 ( ( iskpair @ Xu )
% 0.29/0.46 => ( singleton
% 0.29/0.46 @ ( dsetconstr @ ( setunion @ Xu )
% 0.29/0.46 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(theprop_type,type,
% 0.29/0.46 theprop: $o ).
% 0.29/0.46
% 0.29/0.46 thf(theprop,definition,
% 0.29/0.46 ( theprop
% 0.29/0.46 = ( ! [X: $i] :
% 0.29/0.46 ( ( singleton @ X )
% 0.29/0.46 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(kfst_type,type,
% 0.29/0.46 kfst: $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(kfstpairEq_type,type,
% 0.29/0.46 kfstpairEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(kfstpairEq,definition,
% 0.29/0.46 ( kfstpairEq
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.29/0.46 = Xx ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodfstin_type,type,
% 0.29/0.46 cartprodfstin: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodfstin,definition,
% 0.29/0.46 ( cartprodfstin
% 0.29/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.29/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.29/0.46 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjL2_type,type,
% 0.29/0.46 setukpairinjL2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjL2,definition,
% 0.29/0.46 ( setukpairinjL2
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.29/0.46 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.29/0.46 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.29/0.46 => ( Xx = Xz ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjL_type,type,
% 0.29/0.46 setukpairinjL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjL,definition,
% 0.29/0.46 ( setukpairinjL
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.29/0.46 ( ( ( kpair @ Xx @ Xy )
% 0.29/0.46 = ( kpair @ Xz @ Xu ) )
% 0.29/0.46 => ( Xx = Xz ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjR11_type,type,
% 0.29/0.46 setukpairinjR11: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjR11,definition,
% 0.29/0.46 ( setukpairinjR11
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.46 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjR12_type,type,
% 0.29/0.46 setukpairinjR12: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjR12,definition,
% 0.29/0.46 ( setukpairinjR12
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.29/0.46 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjR1_type,type,
% 0.29/0.46 setukpairinjR1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjR1,definition,
% 0.29/0.46 ( setukpairinjR1
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.29/0.46 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.29/0.46 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.29/0.46 => ( ( Xz = Xu )
% 0.29/0.46 => ( Xy = Xu ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairequniteq_type,type,
% 0.29/0.46 upairequniteq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairequniteq,definition,
% 0.29/0.46 ( upairequniteq
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.29/0.46 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.46 = ( setadjoin @ Xz @ emptyset ) )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjR2_type,type,
% 0.29/0.46 setukpairinjR2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjR2,definition,
% 0.29/0.46 ( setukpairinjR2
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.29/0.46 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.29/0.46 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.29/0.46 => ( Xy = Xu ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjR_type,type,
% 0.29/0.46 setukpairinjR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjR,definition,
% 0.29/0.46 ( setukpairinjR
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.29/0.46 ( ( ( kpair @ Xx @ Xy )
% 0.29/0.46 = ( kpair @ Xz @ Xu ) )
% 0.29/0.46 => ( Xy = Xu ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ksndsingleton_type,type,
% 0.29/0.46 ksndsingleton: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ksndsingleton,definition,
% 0.29/0.46 ( ksndsingleton
% 0.29/0.46 = ( ! [Xu: $i] :
% 0.29/0.46 ( ( iskpair @ Xu )
% 0.29/0.46 => ( singleton
% 0.29/0.46 @ ( dsetconstr @ ( setunion @ Xu )
% 0.29/0.46 @ ^ [Xx: $i] :
% 0.29/0.46 ( Xu
% 0.29/0.46 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ksnd_type,type,
% 0.29/0.46 ksnd: $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(ksndpairEq_type,type,
% 0.29/0.46 ksndpairEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ksndpairEq,definition,
% 0.29/0.46 ( ksndpairEq
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.29/0.46 = Xy ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(kpairsurjEq_type,type,
% 0.29/0.46 kpairsurjEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(kpairsurjEq,definition,
% 0.29/0.46 ( kpairsurjEq
% 0.29/0.46 = ( ! [Xu: $i] :
% 0.29/0.46 ( ( iskpair @ Xu )
% 0.29/0.46 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.29/0.46 = Xu ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodsndin_type,type,
% 0.29/0.46 cartprodsndin: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodsndin,definition,
% 0.29/0.46 ( cartprodsndin
% 0.29/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.29/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.29/0.46 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodpairmemEL_type,type,
% 0.29/0.46 cartprodpairmemEL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodpairmemEL,definition,
% 0.29/0.46 ( cartprodpairmemEL
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodpairmemER_type,type,
% 0.29/0.46 cartprodpairmemER: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodpairmemER,definition,
% 0.29/0.46 ( cartprodpairmemER
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.29/0.46 => ( in @ Xy @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodmempaircEq_type,type,
% 0.29/0.46 cartprodmempaircEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodmempaircEq,definition,
% 0.29/0.46 ( cartprodmempaircEq
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( kpair @ Xx @ Xy )
% 0.29/0.46 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodfstpairEq_type,type,
% 0.29/0.46 cartprodfstpairEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodfstpairEq,definition,
% 0.29/0.46 ( cartprodfstpairEq
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.29/0.46 = Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodsndpairEq_type,type,
% 0.29/0.46 cartprodsndpairEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodsndpairEq,definition,
% 0.29/0.46 ( cartprodsndpairEq
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.29/0.46 = Xy ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodpairsurjEq_type,type,
% 0.29/0.46 cartprodpairsurjEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodpairsurjEq,definition,
% 0.29/0.46 ( cartprodpairsurjEq
% 0.29/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.29/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.29/0.46 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.29/0.46 = Xu ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(breln_type,type,
% 0.29/0.46 breln: $i > $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(breln,definition,
% 0.29/0.46 ( breln
% 0.29/0.46 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstr_type,type,
% 0.29/0.46 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrI_type,type,
% 0.29/0.46 dpsetconstrI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrI,definition,
% 0.29/0.46 ( dpsetconstrI
% 0.29/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( Xphi @ Xx @ Xy )
% 0.29/0.46 => ( in @ ( kpair @ Xx @ Xy )
% 0.29/0.46 @ ( dpsetconstr @ A @ B
% 0.29/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrSub_type,type,
% 0.29/0.46 dpsetconstrSub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrSub,definition,
% 0.29/0.46 ( dpsetconstrSub
% 0.29/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.29/0.46 ( subset
% 0.29/0.46 @ ( dpsetconstr @ A @ B
% 0.29/0.46 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.29/0.46 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setOfPairsIsBReln_type,type,
% 0.29/0.46 setOfPairsIsBReln: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setOfPairsIsBReln,definition,
% 0.29/0.46 ( setOfPairsIsBReln
% 0.29/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.29/0.46 ( breln @ A @ B
% 0.29/0.46 @ ( dpsetconstr @ A @ B
% 0.29/0.46 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrERa_type,type,
% 0.29/0.46 dpsetconstrERa: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrERa,definition,
% 0.29/0.46 ( dpsetconstrERa
% 0.29/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.29/0.46 @ ( dpsetconstr @ A @ B
% 0.29/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.29/0.46 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrEL1_type,type,
% 0.29/0.46 dpsetconstrEL1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrEL1,definition,
% 0.29/0.46 ( dpsetconstrEL1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ ( kpair @ Xx @ Xy )
% 0.29/0.46 @ ( dpsetconstr @ A @ B
% 0.29/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrEL2_type,type,
% 0.29/0.46 dpsetconstrEL2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrEL2,definition,
% 0.29/0.46 ( dpsetconstrEL2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ ( kpair @ Xx @ Xy )
% 0.29/0.46 @ ( dpsetconstr @ A @ B
% 0.29/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.29/0.46 => ( in @ Xy @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrER_type,type,
% 0.29/0.46 dpsetconstrER: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dpsetconstrER,definition,
% 0.29/0.46 ( dpsetconstrER
% 0.29/0.46 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ ( kpair @ Xx @ Xy )
% 0.29/0.46 @ ( dpsetconstr @ A @ B
% 0.29/0.46 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.29/0.46 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(func_type,type,
% 0.29/0.46 func: $i > $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(funcSet_type,type,
% 0.29/0.46 funcSet: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(funcImageSingleton_type,type,
% 0.29/0.46 funcImageSingleton: $o ).
% 0.29/0.46
% 0.29/0.46 thf(funcImageSingleton,definition,
% 0.29/0.46 ( funcImageSingleton
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xf )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( singleton
% 0.29/0.46 @ ( dsetconstr @ B
% 0.29/0.46 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(apProp_type,type,
% 0.29/0.46 apProp: $o ).
% 0.29/0.46
% 0.29/0.46 thf(apProp,definition,
% 0.29/0.46 ( apProp
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xf )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in
% 0.29/0.46 @ ( setunion
% 0.29/0.46 @ ( dsetconstr @ B
% 0.29/0.46 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.29/0.46 @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ap_type,type,
% 0.29/0.46 ap: $i > $i > $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(app_type,type,
% 0.29/0.46 app: $o ).
% 0.29/0.46
% 0.29/0.46 thf(app,definition,
% 0.29/0.46 ( app
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xf )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(infuncsetfunc_type,type,
% 0.29/0.46 infuncsetfunc: $o ).
% 0.29/0.46
% 0.29/0.46 thf(infuncsetfunc,definition,
% 0.29/0.46 ( infuncsetfunc
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.46 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ap2p_type,type,
% 0.29/0.46 ap2p: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ap2p,definition,
% 0.29/0.46 ( ap2p
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(funcinfuncset_type,type,
% 0.29/0.46 funcinfuncset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(funcinfuncset,definition,
% 0.29/0.46 ( funcinfuncset
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xf )
% 0.29/0.46 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(lamProp_type,type,
% 0.29/0.46 lamProp: $o ).
% 0.29/0.46
% 0.29/0.46 thf(lamProp,definition,
% 0.29/0.46 ( lamProp
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.29/0.46 => ( func @ A @ B
% 0.29/0.46 @ ( dpsetconstr @ A @ B
% 0.29/0.46 @ ^ [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xf @ Xx )
% 0.29/0.46 = Xy ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(lam_type,type,
% 0.29/0.46 lam: $i > $i > ( $i > $i ) > $i ).
% 0.29/0.46
% 0.29/0.46 thf(lamp_type,type,
% 0.29/0.46 lamp: $o ).
% 0.29/0.46
% 0.29/0.46 thf(lamp,definition,
% 0.29/0.46 ( lamp
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.29/0.46 => ( func @ A @ B
% 0.29/0.46 @ ( lam @ A @ B
% 0.29/0.46 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(lam2p_type,type,
% 0.29/0.46 lam2p: $o ).
% 0.29/0.46
% 0.29/0.46 thf(lam2p,definition,
% 0.29/0.46 ( lam2p
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.29/0.46 => ( in
% 0.29/0.46 @ ( lam @ A @ B
% 0.29/0.46 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.29/0.46 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(brelnall1_type,type,
% 0.29/0.46 brelnall1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(brelnall1,definition,
% 0.29/0.46 ( brelnall1
% 0.29/0.46 = ( ! [A: $i,B: $i,R: $i] :
% 0.29/0.46 ( ( breln @ A @ B @ R )
% 0.29/0.46 => ! [Xphi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.46 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ R )
% 0.29/0.46 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(brelnall2_type,type,
% 0.29/0.46 brelnall2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(brelnall2,definition,
% 0.29/0.46 ( brelnall2
% 0.29/0.46 = ( ! [A: $i,B: $i,R: $i] :
% 0.29/0.46 ( ( breln @ A @ B @ R )
% 0.29/0.46 => ! [Xphi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.46 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ R )
% 0.29/0.46 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ex1E2_type,type,
% 0.29/0.46 ex1E2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ex1E2,definition,
% 0.29/0.46 ( ex1E2
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ( ex1 @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(funcGraphProp1_type,type,
% 0.29/0.46 funcGraphProp1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(funcGraphProp1,definition,
% 0.29/0.46 ( funcGraphProp1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xf )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(funcGraphProp3_type,type,
% 0.29/0.46 funcGraphProp3: $o ).
% 0.29/0.46
% 0.29/0.46 thf(funcGraphProp3,definition,
% 0.29/0.46 ( funcGraphProp3
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(funcGraphProp2_type,type,
% 0.29/0.46 funcGraphProp2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(funcGraphProp2,definition,
% 0.29/0.46 ( funcGraphProp2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xf )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.29/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.29/0.46 = Xy ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(funcextLem_type,type,
% 0.29/0.46 funcextLem: $o ).
% 0.29/0.46
% 0.29/0.46 thf(funcextLem,definition,
% 0.29/0.46 ( funcextLem
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xf )
% 0.29/0.46 => ! [Xg: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xg )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.29/0.46 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 0.29/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(funcGraphProp4_type,type,
% 0.29/0.46 funcGraphProp4: $o ).
% 0.29/0.46
% 0.29/0.46 thf(funcGraphProp4,definition,
% 0.29/0.46 ( funcGraphProp4
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.29/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.29/0.46 = Xy ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subbreln_type,type,
% 0.29/0.46 subbreln: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subbreln,definition,
% 0.29/0.46 ( subbreln
% 0.29/0.46 = ( ! [A: $i,B: $i,R: $i] :
% 0.29/0.46 ( ( breln @ A @ B @ R )
% 0.29/0.46 => ! [S: $i] :
% 0.29/0.46 ( ( breln @ A @ B @ S )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.29/0.46 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(eqbreln_type,type,
% 0.29/0.46 eqbreln: $o ).
% 0.29/0.46
% 0.29/0.46 thf(eqbreln,definition,
% 0.29/0.46 ( eqbreln
% 0.29/0.46 = ( ! [A: $i,B: $i,R: $i] :
% 0.29/0.46 ( ( breln @ A @ B @ R )
% 0.29/0.46 => ! [S: $i] :
% 0.29/0.46 ( ( breln @ A @ B @ S )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.29/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.29/0.46 => ( R = S ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(funcext_type,type,
% 0.29/0.46 funcext: $o ).
% 0.29/0.46
% 0.29/0.46 thf(funcext,definition,
% 0.29/0.46 ( funcext
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xf )
% 0.29/0.46 => ! [Xg: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xg )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.29/0.46 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.29/0.46 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(funcext2_type,type,
% 0.29/0.46 funcext2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(funcext2,definition,
% 0.29/0.46 ( funcext2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.46 => ! [Xg: $i] :
% 0.29/0.46 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.29/0.46 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.29/0.46 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ap2apEq1_type,type,
% 0.29/0.46 ap2apEq1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ap2apEq1,definition,
% 0.29/0.46 ( ap2apEq1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.29/0.46 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ap2apEq2_type,type,
% 0.29/0.46 ap2apEq2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ap2apEq2,definition,
% 0.29/0.46 ( ap2apEq2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xf )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.29/0.46 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(beta1_type,type,
% 0.29/0.46 beta1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(beta1,definition,
% 0.29/0.46 ( beta1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( ap @ A @ B
% 0.29/0.46 @ ( lam @ A @ B
% 0.29/0.46 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.29/0.46 @ Xx )
% 0.29/0.46 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(eta1_type,type,
% 0.29/0.46 eta1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(eta1,definition,
% 0.29/0.46 ( eta1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( func @ A @ B @ Xf )
% 0.29/0.46 => ( ( lam @ A @ B
% 0.29/0.46 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.29/0.46 = Xf ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(lam2lamEq_type,type,
% 0.29/0.46 lam2lamEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(lam2lamEq,definition,
% 0.29/0.46 ( lam2lamEq
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.29/0.46 => ( ( lam @ A @ B
% 0.29/0.46 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.29/0.46 = ( lam @ A @ B
% 0.29/0.46 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(beta2_type,type,
% 0.29/0.46 beta2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(beta2,definition,
% 0.29/0.46 ( beta2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( ap @ A @ B
% 0.29/0.46 @ ( lam @ A @ B
% 0.29/0.46 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.29/0.46 @ Xx )
% 0.29/0.46 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(eta2_type,type,
% 0.29/0.46 eta2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(eta2,definition,
% 0.29/0.46 ( eta2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.46 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.46 => ( ( lam @ A @ B
% 0.29/0.46 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.29/0.46 = Xf ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(iffalseProp1_type,type,
% 0.29/0.46 iffalseProp1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(iffalseProp1,definition,
% 0.29/0.46 ( iffalseProp1
% 0.29/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( ~ Xphi
% 0.29/0.46 => ( in @ Xy
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xz: $i] :
% 0.29/0.46 ( ( Xphi
% 0.29/0.46 & ( Xz = Xx ) )
% 0.29/0.46 | ( ~ Xphi
% 0.29/0.46 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(iffalseProp2_type,type,
% 0.29/0.46 iffalseProp2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(iffalseProp2,definition,
% 0.29/0.46 ( iffalseProp2
% 0.29/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( ~ Xphi
% 0.29/0.46 => ( ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xz: $i] :
% 0.29/0.46 ( ( Xphi
% 0.29/0.46 & ( Xz = Xx ) )
% 0.29/0.46 | ( ~ Xphi
% 0.29/0.46 & ( Xz = Xy ) ) ) )
% 0.29/0.46 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(iftrueProp1_type,type,
% 0.29/0.46 iftrueProp1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(iftrueProp1,definition,
% 0.29/0.46 ( iftrueProp1
% 0.29/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( Xphi
% 0.29/0.46 => ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xz: $i] :
% 0.29/0.46 ( ( Xphi
% 0.29/0.46 & ( Xz = Xx ) )
% 0.29/0.46 | ( ~ Xphi
% 0.29/0.46 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(iftrueProp2_type,type,
% 0.29/0.46 iftrueProp2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(iftrueProp2,definition,
% 0.29/0.46 ( iftrueProp2
% 0.29/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( Xphi
% 0.29/0.46 => ( ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xz: $i] :
% 0.29/0.46 ( ( Xphi
% 0.29/0.46 & ( Xz = Xx ) )
% 0.29/0.46 | ( ~ Xphi
% 0.29/0.46 & ( Xz = Xy ) ) ) )
% 0.29/0.46 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ifSingleton_type,type,
% 0.29/0.46 ifSingleton: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ifSingleton,definition,
% 0.29/0.46 ( ifSingleton
% 0.29/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( singleton
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xz: $i] :
% 0.29/0.46 ( ( Xphi
% 0.29/0.46 & ( Xz = Xx ) )
% 0.29/0.46 | ( ~ Xphi
% 0.29/0.46 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(if_type,type,
% 0.29/0.46 if: $i > $o > $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(ifp_type,type,
% 0.29/0.46 ifp: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ifp,definition,
% 0.29/0.46 ( ifp
% 0.29/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(theeq_type,type,
% 0.29/0.46 theeq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(theeq,definition,
% 0.29/0.46 ( theeq
% 0.29/0.46 = ( ! [X: $i] :
% 0.29/0.46 ( ( singleton @ X )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ X )
% 0.29/0.46 => ( ( setunion @ X )
% 0.29/0.46 = Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(iftrue_type,type,
% 0.29/0.46 iftrue: $o ).
% 0.29/0.46
% 0.29/0.46 thf(iftrue,definition,
% 0.29/0.46 ( iftrue
% 0.29/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( Xphi
% 0.29/0.46 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.29/0.46 = Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(iffalse_type,type,
% 0.29/0.46 iffalse: $o ).
% 0.29/0.46
% 0.29/0.46 thf(iffalse,definition,
% 0.29/0.46 ( iffalse
% 0.29/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( ~ Xphi
% 0.29/0.46 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.29/0.46 = Xy ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(iftrueorfalse_type,type,
% 0.29/0.46 iftrueorfalse: $o ).
% 0.29/0.46
% 0.29/0.46 thf(iftrueorfalse,definition,
% 0.29/0.46 ( iftrueorfalse
% 0.29/0.46 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectT_lem_type,type,
% 0.29/0.46 binintersectT_lem: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectT_lem,definition,
% 0.29/0.46 ( binintersectT_lem
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionT_lem_type,type,
% 0.29/0.46 binunionT_lem: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionT_lem,definition,
% 0.29/0.46 ( binunionT_lem
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetT_lem_type,type,
% 0.29/0.46 powersetT_lem: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetT_lem,definition,
% 0.29/0.46 ( powersetT_lem
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusT_lem_type,type,
% 0.29/0.46 setminusT_lem: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusT_lem,definition,
% 0.29/0.46 ( setminusT_lem
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(complementT_lem_type,type,
% 0.29/0.46 complementT_lem: $o ).
% 0.29/0.46
% 0.29/0.46 thf(complementT_lem,definition,
% 0.29/0.46 ( complementT_lem
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setextT_type,type,
% 0.29/0.46 setextT: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setextT,definition,
% 0.29/0.46 ( setextT
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ X )
% 0.29/0.46 => ( in @ Xx @ Y ) ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ Y )
% 0.29/0.46 => ( in @ Xx @ X ) ) )
% 0.29/0.46 => ( X = Y ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetTI_type,type,
% 0.29/0.46 subsetTI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetTI,definition,
% 0.29/0.46 ( subsetTI
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ X )
% 0.29/0.46 => ( in @ Xx @ Y ) ) )
% 0.29/0.46 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetTI1_type,type,
% 0.29/0.46 powersetTI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetTI1,definition,
% 0.29/0.46 ( powersetTI1
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ X )
% 0.29/0.46 => ( in @ Xx @ Y ) ) )
% 0.29/0.46 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetTE1_type,type,
% 0.29/0.46 powersetTE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetTE1,definition,
% 0.29/0.46 ( powersetTE1
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ X @ ( powerset @ Y ) )
% 0.29/0.46 => ( ( in @ Xx @ X )
% 0.29/0.46 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(complementTI1_type,type,
% 0.29/0.46 complementTI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(complementTI1,definition,
% 0.29/0.46 ( complementTI1
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ X )
% 0.29/0.46 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(complementTE1_type,type,
% 0.29/0.46 complementTE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(complementTE1,definition,
% 0.29/0.46 ( complementTE1
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 0.29/0.46 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectTELcontra_type,type,
% 0.29/0.46 binintersectTELcontra: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectTELcontra,definition,
% 0.29/0.46 ( binintersectTELcontra
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ X )
% 0.29/0.46 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectTERcontra_type,type,
% 0.29/0.46 binintersectTERcontra: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectTERcontra,definition,
% 0.29/0.46 ( binintersectTERcontra
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ Y )
% 0.29/0.46 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(contrasubsetT_type,type,
% 0.29/0.46 contrasubsetT: $o ).
% 0.29/0.46
% 0.29/0.46 thf(contrasubsetT,definition,
% 0.29/0.46 ( contrasubsetT
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.29/0.46 => ( ( in @ Xx @ Y )
% 0.29/0.46 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(contrasubsetT1_type,type,
% 0.29/0.46 contrasubsetT1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(contrasubsetT1,definition,
% 0.29/0.46 ( contrasubsetT1
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( subset @ X @ Y )
% 0.29/0.46 => ( ~ ( in @ Xx @ Y )
% 0.29/0.46 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(contrasubsetT2_type,type,
% 0.29/0.46 contrasubsetT2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(contrasubsetT2,definition,
% 0.29/0.46 ( contrasubsetT2
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( ( subset @ X @ Y )
% 0.29/0.46 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(contrasubsetT3_type,type,
% 0.29/0.46 contrasubsetT3: $o ).
% 0.29/0.46
% 0.29/0.46 thf(contrasubsetT3,definition,
% 0.29/0.46 ( contrasubsetT3
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 0.29/0.46 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(doubleComplementI1_type,type,
% 0.29/0.46 doubleComplementI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(doubleComplementI1,definition,
% 0.29/0.46 ( doubleComplementI1
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ X )
% 0.29/0.46 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(doubleComplementE1_type,type,
% 0.29/0.46 doubleComplementE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(doubleComplementE1,definition,
% 0.29/0.46 ( doubleComplementE1
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 0.29/0.46 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(doubleComplementSub1_type,type,
% 0.29/0.46 doubleComplementSub1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(doubleComplementSub1,definition,
% 0.29/0.46 ( doubleComplementSub1
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(doubleComplementSub2_type,type,
% 0.29/0.46 doubleComplementSub2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(doubleComplementSub2,definition,
% 0.29/0.46 ( doubleComplementSub2
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(doubleComplementEq_type,type,
% 0.29/0.46 doubleComplementEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(doubleComplementEq,definition,
% 0.29/0.46 ( doubleComplementEq
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ( X
% 0.29/0.46 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(complementTnotintersectT_type,type,
% 0.29/0.46 complementTnotintersectT: $o ).
% 0.29/0.46
% 0.29/0.46 thf(complementTnotintersectT,definition,
% 0.29/0.46 ( complementTnotintersectT
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.29/0.46 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(complementImpComplementIntersect_type,type,
% 0.29/0.46 complementImpComplementIntersect: $o ).
% 0.29/0.46
% 0.29/0.46 thf(complementImpComplementIntersect,definition,
% 0.29/0.46 ( complementImpComplementIntersect
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.29/0.46 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(complementSubsetComplementIntersect_type,type,
% 0.29/0.46 complementSubsetComplementIntersect: $o ).
% 0.29/0.46
% 0.29/0.46 thf(complementSubsetComplementIntersect,definition,
% 0.29/0.46 ( complementSubsetComplementIntersect
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(complementInPowersetComplementIntersect_type,type,
% 0.29/0.46 complementInPowersetComplementIntersect: $o ).
% 0.29/0.46
% 0.29/0.46 thf(complementInPowersetComplementIntersect,definition,
% 0.29/0.46 ( complementInPowersetComplementIntersect
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(contraSubsetComplement_type,type,
% 0.29/0.46 contraSubsetComplement: $o ).
% 0.29/0.46
% 0.29/0.46 thf(contraSubsetComplement,definition,
% 0.29/0.46 ( contraSubsetComplement
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ Y )
% 0.29/0.46 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(complementTcontraSubset_type,type,
% 0.29/0.46 complementTcontraSubset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(complementTcontraSubset,definition,
% 0.29/0.46 ( complementTcontraSubset
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.29/0.46 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionTILcontra_type,type,
% 0.29/0.46 binunionTILcontra: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionTILcontra,definition,
% 0.29/0.46 ( binunionTILcontra
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.29/0.46 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionTIRcontra_type,type,
% 0.29/0.46 binunionTIRcontra: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionTIRcontra,definition,
% 0.29/0.46 ( binunionTIRcontra
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.29/0.46 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(inIntersectImpInUnion_type,type,
% 0.29/0.46 inIntersectImpInUnion: $o ).
% 0.29/0.46
% 0.29/0.46 thf(inIntersectImpInUnion,definition,
% 0.29/0.46 ( inIntersectImpInUnion
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Z: $i] :
% 0.29/0.46 ( ( in @ Z @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.29/0.46 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(inIntersectImpInUnion2_type,type,
% 0.29/0.46 inIntersectImpInUnion2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(inIntersectImpInUnion2,definition,
% 0.29/0.46 ( inIntersectImpInUnion2
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Z: $i] :
% 0.29/0.46 ( ( in @ Z @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.29/0.46 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(inIntersectImpInIntersectUnions_type,type,
% 0.29/0.46 inIntersectImpInIntersectUnions: $o ).
% 0.29/0.46
% 0.29/0.46 thf(inIntersectImpInIntersectUnions,definition,
% 0.29/0.46 ( inIntersectImpInIntersectUnions
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Z: $i] :
% 0.29/0.46 ( ( in @ Z @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.29/0.46 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(intersectInPowersetIntersectUnions_type,type,
% 0.29/0.46 intersectInPowersetIntersectUnions: $o ).
% 0.29/0.46
% 0.29/0.46 thf(intersectInPowersetIntersectUnions,definition,
% 0.29/0.46 ( intersectInPowersetIntersectUnions
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Z: $i] :
% 0.29/0.46 ( ( in @ Z @ ( powerset @ A ) )
% 0.29/0.46 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(inComplementUnionImpNotIn1_type,type,
% 0.29/0.46 inComplementUnionImpNotIn1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(inComplementUnionImpNotIn1,definition,
% 0.29/0.46 ( inComplementUnionImpNotIn1
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.29/0.46 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(inComplementUnionImpInComplement1_type,type,
% 0.29/0.46 inComplementUnionImpInComplement1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(inComplementUnionImpInComplement1,definition,
% 0.29/0.46 ( inComplementUnionImpInComplement1
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.29/0.46 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionTE_type,type,
% 0.29/0.46 binunionTE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionTE,definition,
% 0.29/0.46 ( binunionTE
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.29/0.46 => ( ( ( in @ Xx @ X )
% 0.29/0.46 => Xphi )
% 0.29/0.46 => ( ( ( in @ Xx @ Y )
% 0.29/0.46 => Xphi )
% 0.29/0.46 => Xphi ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionTEcontra_type,type,
% 0.29/0.46 binunionTEcontra: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionTEcontra,definition,
% 0.29/0.46 ( binunionTEcontra
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ X )
% 0.29/0.46 => ( ~ ( in @ Xx @ Y )
% 0.29/0.46 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(demorgan2a1_type,type,
% 0.29/0.46 demorgan2a1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(demorgan2a1,definition,
% 0.29/0.46 ( demorgan2a1
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.29/0.46 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(complementUnionInPowersetComplement_type,type,
% 0.29/0.46 complementUnionInPowersetComplement: $o ).
% 0.29/0.46
% 0.29/0.46 thf(complementUnionInPowersetComplement,definition,
% 0.29/0.46 ( complementUnionInPowersetComplement
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(demorgan2a2_type,type,
% 0.29/0.46 demorgan2a2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(demorgan2a2,definition,
% 0.29/0.46 ( demorgan2a2
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.29/0.46 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(demorgan1a_type,type,
% 0.29/0.46 demorgan1a: $o ).
% 0.29/0.46
% 0.29/0.46 thf(demorgan1a,definition,
% 0.29/0.46 ( demorgan1a
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 0.29/0.46 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(demorgan1b_type,type,
% 0.29/0.46 demorgan1b: $o ).
% 0.29/0.46
% 0.29/0.46 thf(demorgan1b,definition,
% 0.29/0.46 ( demorgan1b
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.29/0.46 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(demorgan1_type,type,
% 0.29/0.46 demorgan1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(demorgan1,definition,
% 0.29/0.46 ( demorgan1
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 0.29/0.46 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(demorgan2a_type,type,
% 0.29/0.46 demorgan2a: $o ).
% 0.29/0.46
% 0.29/0.46 thf(demorgan2a,definition,
% 0.29/0.46 ( demorgan2a
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.29/0.46 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(demorgan2b2_type,type,
% 0.29/0.46 demorgan2b2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(demorgan2b2,definition,
% 0.29/0.46 ( demorgan2b2
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.29/0.46 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 0.29/0.46 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(demorgan2b_type,type,
% 0.29/0.46 demorgan2b: $o ).
% 0.29/0.46
% 0.29/0.46 thf(demorgan2b,definition,
% 0.29/0.46 ( demorgan2b
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.29/0.46 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(demorgan2_type,type,
% 0.29/0.46 demorgan2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(demorgan2,definition,
% 0.29/0.46 ( demorgan2
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 0.29/0.46 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(woz13rule0_type,type,
% 0.29/0.46 woz13rule0: $o ).
% 0.29/0.46
% 0.29/0.46 thf(woz13rule0,definition,
% 0.29/0.46 ( woz13rule0
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(woz13rule1_type,type,
% 0.29/0.46 woz13rule1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(woz13rule1,definition,
% 0.29/0.46 ( woz13rule1
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Z: $i] :
% 0.29/0.46 ( ( in @ Z @ ( powerset @ A ) )
% 0.29/0.46 => ( ( subset @ X @ Z )
% 0.29/0.46 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(woz13rule2_type,type,
% 0.29/0.46 woz13rule2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(woz13rule2,definition,
% 0.29/0.46 ( woz13rule2
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Z: $i] :
% 0.29/0.46 ( ( in @ Z @ ( powerset @ A ) )
% 0.29/0.46 => ( ( subset @ Y @ Z )
% 0.29/0.46 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(woz13rule3_type,type,
% 0.29/0.46 woz13rule3: $o ).
% 0.29/0.46
% 0.29/0.46 thf(woz13rule3,definition,
% 0.29/0.46 ( woz13rule3
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Z: $i] :
% 0.29/0.46 ( ( in @ Z @ ( powerset @ A ) )
% 0.29/0.46 => ( ( subset @ X @ Y )
% 0.29/0.46 => ( ( subset @ X @ Z )
% 0.29/0.46 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(woz13rule4_type,type,
% 0.29/0.46 woz13rule4: $o ).
% 0.29/0.46
% 0.29/0.46 thf(woz13rule4,definition,
% 0.29/0.46 ( woz13rule4
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Z: $i] :
% 0.29/0.46 ( ( in @ Z @ ( powerset @ A ) )
% 0.29/0.46 => ! [W: $i] :
% 0.29/0.46 ( ( in @ W @ ( powerset @ A ) )
% 0.29/0.46 => ( ( subset @ X @ Z )
% 0.29/0.46 => ( ( subset @ Y @ W )
% 0.29/0.46 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(woz1_1_type,type,
% 0.29/0.46 woz1_1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(woz1_1,definition,
% 0.29/0.46 ( woz1_1
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(woz1_2_type,type,
% 0.29/0.46 woz1_2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(woz1_2,definition,
% 0.29/0.46 ( woz1_2
% 0.29/0.46 = ( ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Z: $i] :
% 0.29/0.46 ( ( in @ Z @ ( powerset @ A ) )
% 0.29/0.46 => ! [W: $i] :
% 0.29/0.46 ( ( in @ W @ ( powerset @ A ) )
% 0.29/0.46 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 0.29/0.46 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(woz1_3,conjecture,
% 0.29/0.46 ( setextAx
% 0.29/0.46 => ( emptysetAx
% 0.29/0.46 => ( setadjoinAx
% 0.29/0.46 => ( powersetAx
% 0.29/0.46 => ( setunionAx
% 0.29/0.46 => ( omega0Ax
% 0.29/0.46 => ( omegaSAx
% 0.29/0.46 => ( omegaIndAx
% 0.29/0.46 => ( replAx
% 0.29/0.46 => ( foundationAx
% 0.29/0.46 => ( wellorderingAx
% 0.29/0.46 => ( descrp
% 0.29/0.46 => ( dsetconstrI
% 0.29/0.46 => ( dsetconstrEL
% 0.29/0.46 => ( dsetconstrER
% 0.29/0.46 => ( exuE1
% 0.29/0.46 => ( prop2setE
% 0.29/0.46 => ( emptysetE
% 0.29/0.46 => ( emptysetimpfalse
% 0.29/0.46 => ( notinemptyset
% 0.29/0.46 => ( exuE3e
% 0.29/0.46 => ( setext
% 0.29/0.46 => ( emptyI
% 0.29/0.46 => ( noeltsimpempty
% 0.29/0.46 => ( setbeta
% 0.29/0.46 => ( nonemptyE1
% 0.29/0.46 => ( nonemptyI
% 0.29/0.46 => ( nonemptyI1
% 0.29/0.46 => ( setadjoinIL
% 0.29/0.46 => ( emptyinunitempty
% 0.29/0.46 => ( setadjoinIR
% 0.29/0.46 => ( setadjoinE
% 0.29/0.46 => ( setadjoinOr
% 0.29/0.46 => ( setoftrueEq
% 0.29/0.46 => ( powersetI
% 0.29/0.46 => ( emptyinPowerset
% 0.29/0.46 => ( emptyInPowerset
% 0.29/0.46 => ( powersetE
% 0.29/0.46 => ( setunionI
% 0.29/0.46 => ( setunionE
% 0.29/0.46 => ( subPowSU
% 0.29/0.46 => ( exuE2
% 0.29/0.46 => ( nonemptyImpWitness
% 0.29/0.46 => ( uniqinunit
% 0.29/0.46 => ( notinsingleton
% 0.29/0.46 => ( eqinunit
% 0.29/0.46 => ( singletonsswitch
% 0.29/0.46 => ( upairsetE
% 0.29/0.46 => ( upairsetIL
% 0.29/0.46 => ( upairsetIR
% 0.29/0.46 => ( emptyE1
% 0.29/0.46 => ( vacuousDall
% 0.29/0.46 => ( quantDeMorgan1
% 0.29/0.46 => ( quantDeMorgan2
% 0.29/0.46 => ( quantDeMorgan3
% 0.29/0.46 => ( quantDeMorgan4
% 0.29/0.46 => ( prop2setI
% 0.29/0.46 => ( prop2set2propI
% 0.29/0.46 => ( notdexE
% 0.29/0.46 => ( notdallE
% 0.29/0.46 => ( exuI1
% 0.29/0.46 => ( exuI3
% 0.29/0.46 => ( exuI2
% 0.29/0.46 => ( inCongP
% 0.29/0.46 => ( in__Cong
% 0.29/0.46 => ( exuE3u
% 0.29/0.46 => ( exu__Cong
% 0.29/0.46 => ( emptyset__Cong
% 0.29/0.46 => ( setadjoin__Cong
% 0.29/0.46 => ( powerset__Cong
% 0.29/0.46 => ( setunion__Cong
% 0.29/0.46 => ( omega__Cong
% 0.29/0.46 => ( exuEu
% 0.29/0.46 => ( descr__Cong
% 0.29/0.46 => ( dsetconstr__Cong
% 0.29/0.46 => ( subsetI1
% 0.29/0.46 => ( eqimpsubset2
% 0.29/0.46 => ( eqimpsubset1
% 0.29/0.46 => ( subsetI2
% 0.29/0.46 => ( emptysetsubset
% 0.29/0.46 => ( subsetE
% 0.29/0.46 => ( subsetE2
% 0.29/0.46 => ( notsubsetI
% 0.29/0.46 => ( notequalI1
% 0.29/0.46 => ( notequalI2
% 0.29/0.46 => ( subsetRefl
% 0.29/0.46 => ( subsetTrans
% 0.29/0.46 => ( setadjoinSub
% 0.29/0.46 => ( setadjoinSub2
% 0.29/0.46 => ( subset2powerset
% 0.29/0.46 => ( setextsub
% 0.29/0.46 => ( subsetemptysetimpeq
% 0.29/0.46 => ( powersetI1
% 0.29/0.46 => ( powersetE1
% 0.29/0.46 => ( inPowerset
% 0.29/0.46 => ( powersetsubset
% 0.29/0.46 => ( sepInPowerset
% 0.29/0.46 => ( sepSubset
% 0.29/0.46 => ( binunionIL
% 0.29/0.46 => ( upairset2IR
% 0.29/0.46 => ( binunionIR
% 0.29/0.46 => ( binunionEcases
% 0.29/0.46 => ( binunionE
% 0.29/0.46 => ( binunionLsub
% 0.29/0.46 => ( binunionRsub
% 0.29/0.46 => ( binintersectI
% 0.29/0.46 => ( binintersectSubset5
% 0.29/0.46 => ( binintersectEL
% 0.29/0.46 => ( binintersectLsub
% 0.29/0.46 => ( binintersectSubset2
% 0.29/0.46 => ( binintersectSubset3
% 0.29/0.46 => ( binintersectER
% 0.29/0.46 => ( disjointsetsI1
% 0.29/0.46 => ( binintersectRsub
% 0.29/0.46 => ( binintersectSubset4
% 0.29/0.46 => ( binintersectSubset1
% 0.29/0.46 => ( bs114d
% 0.29/0.46 => ( setminusI
% 0.29/0.46 => ( setminusEL
% 0.29/0.46 => ( setminusER
% 0.29/0.46 => ( setminusSubset2
% 0.29/0.46 => ( setminusERneg
% 0.29/0.46 => ( setminusELneg
% 0.29/0.46 => ( setminusILneg
% 0.29/0.46 => ( setminusIRneg
% 0.29/0.46 => ( setminusLsub
% 0.29/0.46 => ( setminusSubset1
% 0.29/0.46 => ( symdiffE
% 0.29/0.46 => ( symdiffI1
% 0.29/0.46 => ( symdiffI2
% 0.29/0.46 => ( symdiffIneg1
% 0.29/0.46 => ( symdiffIneg2
% 0.29/0.46 => ( secondinupair
% 0.29/0.46 => ( setukpairIL
% 0.29/0.46 => ( setukpairIR
% 0.29/0.46 => ( kpairiskpair
% 0.29/0.46 => ( kpairp
% 0.29/0.46 => ( singletonsubset
% 0.29/0.46 => ( singletoninpowerset
% 0.29/0.46 => ( singletoninpowunion
% 0.29/0.46 => ( upairset2E
% 0.29/0.46 => ( upairsubunion
% 0.29/0.46 => ( upairinpowunion
% 0.29/0.46 => ( ubforcartprodlem1
% 0.29/0.46 => ( ubforcartprodlem2
% 0.29/0.46 => ( ubforcartprodlem3
% 0.29/0.46 => ( cartprodpairin
% 0.29/0.46 => ( cartprodmempair1
% 0.29/0.46 => ( cartprodmempair
% 0.29/0.46 => ( setunionE2
% 0.29/0.46 => ( setunionsingleton1
% 0.29/0.46 => ( setunionsingleton2
% 0.29/0.46 => ( setunionsingleton
% 0.29/0.46 => ( singletonprop
% 0.29/0.46 => ( ex1E1
% 0.29/0.46 => ( ex1I
% 0.29/0.46 => ( ex1I2
% 0.29/0.46 => ( singletonsuniq
% 0.29/0.46 => ( setukpairinjL1
% 0.29/0.46 => ( kfstsingleton
% 0.29/0.46 => ( theprop
% 0.29/0.46 => ( kfstpairEq
% 0.29/0.46 => ( cartprodfstin
% 0.29/0.46 => ( setukpairinjL2
% 0.29/0.46 => ( setukpairinjL
% 0.29/0.46 => ( setukpairinjR11
% 0.29/0.46 => ( setukpairinjR12
% 0.29/0.46 => ( setukpairinjR1
% 0.29/0.46 => ( upairequniteq
% 0.29/0.46 => ( setukpairinjR2
% 0.29/0.46 => ( setukpairinjR
% 0.29/0.46 => ( ksndsingleton
% 0.29/0.46 => ( ksndpairEq
% 0.29/0.46 => ( kpairsurjEq
% 0.29/0.46 => ( cartprodsndin
% 0.29/0.46 => ( cartprodpairmemEL
% 0.29/0.46 => ( cartprodpairmemER
% 0.29/0.46 => ( cartprodmempaircEq
% 0.29/0.46 => ( cartprodfstpairEq
% 0.29/0.46 => ( cartprodsndpairEq
% 0.29/0.46 => ( cartprodpairsurjEq
% 0.29/0.46 => ( dpsetconstrI
% 0.29/0.46 => ( dpsetconstrSub
% 0.29/0.46 => ( setOfPairsIsBReln
% 0.29/0.46 => ( dpsetconstrERa
% 0.29/0.46 => ( dpsetconstrEL1
% 0.29/0.46 => ( dpsetconstrEL2
% 0.29/0.46 => ( dpsetconstrER
% 0.29/0.46 => ( funcImageSingleton
% 0.29/0.46 => ( apProp
% 0.29/0.46 => ( app
% 0.29/0.46 => ( infuncsetfunc
% 0.29/0.46 => ( ap2p
% 0.29/0.46 => ( funcinfuncset
% 0.29/0.46 => ( lamProp
% 0.29/0.46 => ( lamp
% 0.29/0.46 => ( lam2p
% 0.29/0.46 => ( brelnall1
% 0.29/0.46 => ( brelnall2
% 0.29/0.46 => ( ex1E2
% 0.29/0.46 => ( funcGraphProp1
% 0.29/0.46 => ( funcGraphProp3
% 0.29/0.46 => ( funcGraphProp2
% 0.29/0.46 => ( funcextLem
% 0.29/0.46 => ( funcGraphProp4
% 0.29/0.46 => ( subbreln
% 0.29/0.46 => ( eqbreln
% 0.29/0.46 => ( funcext
% 0.29/0.46 => ( funcext2
% 0.29/0.46 => ( ap2apEq1
% 0.29/0.46 => ( ap2apEq2
% 0.29/0.46 => ( beta1
% 0.29/0.46 => ( eta1
% 0.29/0.46 => ( lam2lamEq
% 0.29/0.46 => ( beta2
% 0.29/0.46 => ( eta2
% 0.29/0.46 => ( iffalseProp1
% 0.29/0.46 => ( iffalseProp2
% 0.29/0.46 => ( iftrueProp1
% 0.29/0.46 => ( iftrueProp2
% 0.29/0.46 => ( ifSingleton
% 0.29/0.46 => ( ifp
% 0.29/0.46 => ( theeq
% 0.29/0.46 => ( iftrue
% 0.29/0.46 => ( iffalse
% 0.29/0.46 => ( iftrueorfalse
% 0.29/0.46 => ( binintersectT_lem
% 0.29/0.46 => ( binunionT_lem
% 0.29/0.46 => ( powersetT_lem
% 0.29/0.46 => ( setminusT_lem
% 0.29/0.46 => ( complementT_lem
% 0.29/0.46 => ( setextT
% 0.29/0.46 => ( subsetTI
% 0.29/0.46 => ( powersetTI1
% 0.29/0.46 => ( powersetTE1
% 0.29/0.46 => ( complementTI1
% 0.29/0.46 => ( complementTE1
% 0.29/0.46 => ( binintersectTELcontra
% 0.29/0.46 => ( binintersectTERcontra
% 0.29/0.46 => ( contrasubsetT
% 0.29/0.46 => ( contrasubsetT1
% 0.29/0.46 => ( contrasubsetT2
% 0.29/0.46 => ( contrasubsetT3
% 0.29/0.46 => ( doubleComplementI1
% 0.29/0.46 => ( doubleComplementE1
% 0.29/0.46 => ( doubleComplementSub1
% 0.29/0.46 => ( doubleComplementSub2
% 0.29/0.46 => ( doubleComplementEq
% 0.29/0.46 => ( complementTnotintersectT
% 0.29/0.46 => ( complementImpComplementIntersect
% 0.29/0.46 => ( complementSubsetComplementIntersect
% 0.29/0.46 => ( complementInPowersetComplementIntersect
% 0.29/0.46 => ( contraSubsetComplement
% 0.29/0.46 => ( complementTcontraSubset
% 0.29/0.46 => ( binunionTILcontra
% 0.29/0.46 => ( binunionTIRcontra
% 0.29/0.46 => ( inIntersectImpInUnion
% 0.29/0.46 => ( inIntersectImpInUnion2
% 0.29/0.46 => ( inIntersectImpInIntersectUnions
% 0.29/0.46 => ( intersectInPowersetIntersectUnions
% 0.29/0.46 => ( inComplementUnionImpNotIn1
% 0.29/0.46 => ( inComplementUnionImpInComplement1
% 0.29/0.46 => ( binunionTE
% 0.29/0.46 => ( binunionTEcontra
% 0.29/0.46 => ( demorgan2a1
% 0.29/0.46 => ( complementUnionInPowersetComplement
% 0.29/0.46 => ( demorgan2a2
% 0.29/0.46 => ( demorgan1a
% 0.29/0.46 => ( demorgan1b
% 0.29/0.46 => ( demorgan1
% 0.29/0.46 => ( demorgan2a
% 0.29/0.46 => ( demorgan2b2
% 0.29/0.46 => ( demorgan2b
% 0.29/0.46 => ( demorgan2
% 0.29/0.46 => ( woz13rule0
% 0.29/0.46 => ( woz13rule1
% 0.29/0.46 => ( woz13rule2
% 0.29/0.46 => ( woz13rule3
% 0.29/0.46 => ( woz13rule4
% 0.29/0.46 => ( woz1_1
% 0.29/0.46 => ( woz1_2
% 0.29/0.46 => ! [A: $i,X: $i] :
% 0.29/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.29/0.46 => ! [Y: $i] :
% 0.29/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.29/0.46 => ! [Z: $i] :
% 0.29/0.46 ( ( in @ Z @ ( powerset @ A ) )
% 0.29/0.46 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 2.89/1.55 ---- Embedded in THF ---
% 2.89/1.55 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.89/1.55 %%% Generated on Tue Feb 24 12:33:03 EST 2026
% 2.89/1.55 %%% using '$$dhol' embedding, version 1.3.0.
% 2.89/1.55 %%% Logic specification used:
% 2.89/1.55 %%% thf(spec, logic, $$dhol).
% 2.89/1.55
% 2.89/1.55 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.50SVxc4AnF/DTF2DTF30813.p
% See solution above
% 2.89/1.55 ------------------------
% 2.98/1.61 ---- Cleaned THF ---
% 2.98/1.61 thf(in_type,type,
% 2.98/1.61 in: $i > $i > $o ).
% 2.98/1.61
% 2.98/1.61 thf(exu_type,type,
% 2.98/1.61 exu: ( $i > $o ) > $o ).
% 2.98/1.61
% 2.98/1.61 thf(exu,definition,
% 2.98/1.61 ( exu
% 2.98/1.61 = ( ^ [Xphi: $i > $o] :
% 2.98/1.61 ? [Xx: $i] :
% 2.98/1.61 ( ( Xphi @ Xx )
% 2.98/1.61 & ! [Xy: $i] :
% 2.98/1.61 ( ( Xphi @ Xy )
% 2.98/1.61 => ( Xx = Xy ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setextAx_type,type,
% 2.98/1.61 setextAx: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setextAx,definition,
% 2.98/1.61 ( setextAx
% 2.98/1.61 = ( ! [A: $i,B: $i] :
% 2.98/1.61 ( ! [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 <=> ( in @ Xx @ B ) )
% 2.98/1.61 => ( A = B ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(emptyset_type,type,
% 2.98/1.61 emptyset: $i ).
% 2.98/1.61
% 2.98/1.61 thf(emptysetAx_type,type,
% 2.98/1.61 emptysetAx: $o ).
% 2.98/1.61
% 2.98/1.61 thf(emptysetAx,definition,
% 2.98/1.61 ( emptysetAx
% 2.98/1.61 = ( ! [Xx: $i] :
% 2.98/1.61 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setadjoin_type,type,
% 2.98/1.61 setadjoin: $i > $i > $i ).
% 2.98/1.61
% 2.98/1.61 thf(setadjoinAx_type,type,
% 2.98/1.61 setadjoinAx: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setadjoinAx,definition,
% 2.98/1.61 ( setadjoinAx
% 2.98/1.61 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.98/1.61 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.98/1.61 <=> ( ( Xy = Xx )
% 2.98/1.61 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(powerset_type,type,
% 2.98/1.61 powerset: $i > $i ).
% 2.98/1.61
% 2.98/1.61 thf(powersetAx_type,type,
% 2.98/1.61 powersetAx: $o ).
% 2.98/1.61
% 2.98/1.61 thf(powersetAx,definition,
% 2.98/1.61 ( powersetAx
% 2.98/1.61 = ( ! [A: $i,B: $i] :
% 2.98/1.61 ( ( in @ B @ ( powerset @ A ) )
% 2.98/1.61 <=> ! [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ B )
% 2.98/1.61 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setunion_type,type,
% 2.98/1.61 setunion: $i > $i ).
% 2.98/1.61
% 2.98/1.61 thf(setunionAx_type,type,
% 2.98/1.61 setunionAx: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setunionAx,definition,
% 2.98/1.61 ( setunionAx
% 2.98/1.61 = ( ! [A: $i,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ ( setunion @ A ) )
% 2.98/1.61 <=> ? [B: $i] :
% 2.98/1.61 ( ( in @ Xx @ B )
% 2.98/1.61 & ( in @ B @ A ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(omega_type,type,
% 2.98/1.61 omega: $i ).
% 2.98/1.61
% 2.98/1.61 thf(omega0Ax_type,type,
% 2.98/1.61 omega0Ax: $o ).
% 2.98/1.61
% 2.98/1.61 thf(omega0Ax,definition,
% 2.98/1.61 ( omega0Ax
% 2.98/1.61 = ( in @ emptyset @ omega ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(omegaSAx_type,type,
% 2.98/1.61 omegaSAx: $o ).
% 2.98/1.61
% 2.98/1.61 thf(omegaSAx,definition,
% 2.98/1.61 ( omegaSAx
% 2.98/1.61 = ( ! [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ omega )
% 2.98/1.61 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(omegaIndAx_type,type,
% 2.98/1.61 omegaIndAx: $o ).
% 2.98/1.61
% 2.98/1.61 thf(omegaIndAx,definition,
% 2.98/1.61 ( omegaIndAx
% 2.98/1.61 = ( ! [A: $i] :
% 2.98/1.61 ( ( ( in @ emptyset @ A )
% 2.98/1.61 & ! [Xx: $i] :
% 2.98/1.61 ( ( ( in @ Xx @ omega )
% 2.98/1.61 & ( in @ Xx @ A ) )
% 2.98/1.61 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.98/1.61 => ! [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ omega )
% 2.98/1.61 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(replAx_type,type,
% 2.98/1.61 replAx: $o ).
% 2.98/1.61
% 2.98/1.61 thf(replAx,definition,
% 2.98/1.61 ( replAx
% 2.98/1.61 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.98/1.61 ( ! [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ( exu
% 2.98/1.61 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.98/1.61 => ? [B: $i] :
% 2.98/1.61 ! [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ B )
% 2.98/1.61 <=> ? [Xy: $i] :
% 2.98/1.61 ( ( in @ Xy @ A )
% 2.98/1.61 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(foundationAx_type,type,
% 2.98/1.61 foundationAx: $o ).
% 2.98/1.61
% 2.98/1.61 thf(foundationAx,definition,
% 2.98/1.61 ( foundationAx
% 2.98/1.61 = ( ! [A: $i] :
% 2.98/1.61 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.98/1.61 => ? [B: $i] :
% 2.98/1.61 ( ( in @ B @ A )
% 2.98/1.61 & ~ ? [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ B )
% 2.98/1.61 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(wellorderingAx_type,type,
% 2.98/1.61 wellorderingAx: $o ).
% 2.98/1.61
% 2.98/1.61 thf(wellorderingAx,definition,
% 2.98/1.61 ( wellorderingAx
% 2.98/1.61 = ( ! [A: $i] :
% 2.98/1.61 ? [B: $i] :
% 2.98/1.61 ( ! [C: $i] :
% 2.98/1.61 ( ( in @ C @ B )
% 2.98/1.61 => ! [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ C )
% 2.98/1.61 => ( in @ Xx @ A ) ) )
% 2.98/1.61 & ! [Xx: $i,Xy: $i] :
% 2.98/1.61 ( ( ( in @ Xx @ A )
% 2.98/1.61 & ( in @ Xy @ A ) )
% 2.98/1.61 => ( ! [C: $i] :
% 2.98/1.61 ( ( in @ C @ B )
% 2.98/1.61 => ( ( in @ Xx @ C )
% 2.98/1.61 <=> ( in @ Xy @ C ) ) )
% 2.98/1.61 => ( Xx = Xy ) ) )
% 2.98/1.61 & ! [C: $i,D: $i] :
% 2.98/1.61 ( ( ( in @ C @ B )
% 2.98/1.61 & ( in @ D @ B ) )
% 2.98/1.61 => ( ! [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ C )
% 2.98/1.61 => ( in @ Xx @ D ) )
% 2.98/1.61 | ! [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ D )
% 2.98/1.61 => ( in @ Xx @ C ) ) ) )
% 2.98/1.61 & ! [C: $i] :
% 2.98/1.61 ( ( ! [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ C )
% 2.98/1.61 => ( in @ Xx @ A ) )
% 2.98/1.61 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.98/1.61 => ? [D: $i,Xx: $i] :
% 2.98/1.61 ( ( in @ D @ B )
% 2.98/1.61 & ( in @ Xx @ C )
% 2.98/1.61 & ~ ? [Xy: $i] :
% 2.98/1.61 ( ( in @ Xy @ D )
% 2.98/1.61 & ( in @ Xy @ C ) )
% 2.98/1.61 & ! [E: $i] :
% 2.98/1.61 ( ( in @ E @ B )
% 2.98/1.61 => ( ! [Xy: $i] :
% 2.98/1.61 ( ( in @ Xy @ E )
% 2.98/1.61 => ( in @ Xy @ D ) )
% 2.98/1.61 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(descr_type,type,
% 2.98/1.61 descr: ( $i > $o ) > $i ).
% 2.98/1.61
% 2.98/1.61 thf(descrp_type,type,
% 2.98/1.61 descrp: $o ).
% 2.98/1.61
% 2.98/1.61 thf(descrp,definition,
% 2.98/1.61 ( descrp
% 2.98/1.61 = ( ! [Xphi: $i > $o] :
% 2.98/1.61 ( ( exu
% 2.98/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.98/1.61 => ( Xphi
% 2.98/1.61 @ ( descr
% 2.98/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(dsetconstr_type,type,
% 2.98/1.61 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.98/1.61
% 2.98/1.61 thf(dsetconstrI_type,type,
% 2.98/1.61 dsetconstrI: $o ).
% 2.98/1.61
% 2.98/1.61 thf(dsetconstrI,definition,
% 2.98/1.61 ( dsetconstrI
% 2.98/1.61 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ( ( Xphi @ Xx )
% 2.98/1.61 => ( in @ Xx
% 2.98/1.61 @ ( dsetconstr @ A
% 2.98/1.61 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(dsetconstrEL_type,type,
% 2.98/1.61 dsetconstrEL: $o ).
% 2.98/1.61
% 2.98/1.61 thf(dsetconstrEL,definition,
% 2.98/1.61 ( dsetconstrEL
% 2.98/1.61 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx
% 2.98/1.61 @ ( dsetconstr @ A
% 2.98/1.61 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.98/1.61 => ( in @ Xx @ A ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(dsetconstrER_type,type,
% 2.98/1.61 dsetconstrER: $o ).
% 2.98/1.61
% 2.98/1.61 thf(dsetconstrER,definition,
% 2.98/1.61 ( dsetconstrER
% 2.98/1.61 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx
% 2.98/1.61 @ ( dsetconstr @ A
% 2.98/1.61 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.98/1.61 => ( Xphi @ Xx ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(exuE1_type,type,
% 2.98/1.61 exuE1: $o ).
% 2.98/1.61
% 2.98/1.61 thf(exuE1,definition,
% 2.98/1.61 ( exuE1
% 2.98/1.61 = ( ! [Xphi: $i > $o] :
% 2.98/1.61 ( ( exu
% 2.98/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.98/1.61 => ? [Xx: $i] :
% 2.98/1.61 ( ( Xphi @ Xx )
% 2.98/1.61 & ! [Xy: $i] :
% 2.98/1.61 ( ( Xphi @ Xy )
% 2.98/1.61 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(prop2set_type,type,
% 2.98/1.61 prop2set: $o > $i ).
% 2.98/1.61
% 2.98/1.61 thf(prop2setE_type,type,
% 2.98/1.61 prop2setE: $o ).
% 2.98/1.61
% 2.98/1.61 thf(prop2setE,definition,
% 2.98/1.61 ( prop2setE
% 2.98/1.61 = ( ! [Xphi: $o,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.98/1.61 => Xphi ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(emptysetE_type,type,
% 2.98/1.61 emptysetE: $o ).
% 2.98/1.61
% 2.98/1.61 thf(emptysetE,definition,
% 2.98/1.61 ( emptysetE
% 2.98/1.61 = ( ! [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ emptyset )
% 2.98/1.61 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(emptysetimpfalse_type,type,
% 2.98/1.61 emptysetimpfalse: $o ).
% 2.98/1.61
% 2.98/1.61 thf(emptysetimpfalse,definition,
% 2.98/1.61 ( emptysetimpfalse
% 2.98/1.61 = ( ! [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ emptyset )
% 2.98/1.61 => $false ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(notinemptyset_type,type,
% 2.98/1.61 notinemptyset: $o ).
% 2.98/1.61
% 2.98/1.61 thf(notinemptyset,definition,
% 2.98/1.61 ( notinemptyset
% 2.98/1.61 = ( ! [Xx: $i] :
% 2.98/1.61 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(exuE3e_type,type,
% 2.98/1.61 exuE3e: $o ).
% 2.98/1.61
% 2.98/1.61 thf(exuE3e,definition,
% 2.98/1.61 ( exuE3e
% 2.98/1.61 = ( ! [Xphi: $i > $o] :
% 2.98/1.61 ( ( exu
% 2.98/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.98/1.61 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setext_type,type,
% 2.98/1.61 setext: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setext,definition,
% 2.98/1.61 ( setext
% 2.98/1.61 = ( ! [A: $i,B: $i] :
% 2.98/1.61 ( ! [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ( in @ Xx @ B ) )
% 2.98/1.61 => ( ! [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ B )
% 2.98/1.61 => ( in @ Xx @ A ) )
% 2.98/1.61 => ( A = B ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(emptyI_type,type,
% 2.98/1.61 emptyI: $o ).
% 2.98/1.61
% 2.98/1.61 thf(emptyI,definition,
% 2.98/1.61 ( emptyI
% 2.98/1.61 = ( ! [A: $i] :
% 2.98/1.61 ( ! [Xx: $i] :
% 2.98/1.61 ~ ( in @ Xx @ A )
% 2.98/1.61 => ( A = emptyset ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(noeltsimpempty_type,type,
% 2.98/1.61 noeltsimpempty: $o ).
% 2.98/1.61
% 2.98/1.61 thf(noeltsimpempty,definition,
% 2.98/1.61 ( noeltsimpempty
% 2.98/1.61 = ( ! [A: $i] :
% 2.98/1.61 ( ! [Xx: $i] :
% 2.98/1.61 ~ ( in @ Xx @ A )
% 2.98/1.61 => ( A = emptyset ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setbeta_type,type,
% 2.98/1.61 setbeta: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setbeta,definition,
% 2.98/1.61 ( setbeta
% 2.98/1.61 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ( ( in @ Xx
% 2.98/1.61 @ ( dsetconstr @ A
% 2.98/1.61 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.98/1.61 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(nonempty_type,type,
% 2.98/1.61 nonempty: $i > $o ).
% 2.98/1.61
% 2.98/1.61 thf(nonempty,definition,
% 2.98/1.61 ( nonempty
% 2.98/1.61 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(nonemptyE1_type,type,
% 2.98/1.61 nonemptyE1: $o ).
% 2.98/1.61
% 2.98/1.61 thf(nonemptyE1,definition,
% 2.98/1.61 ( nonemptyE1
% 2.98/1.61 = ( ! [A: $i] :
% 2.98/1.61 ( ( nonempty @ A )
% 2.98/1.61 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(nonemptyI_type,type,
% 2.98/1.61 nonemptyI: $o ).
% 2.98/1.61
% 2.98/1.61 thf(nonemptyI,definition,
% 2.98/1.61 ( nonemptyI
% 2.98/1.61 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ( ( Xphi @ Xx )
% 2.98/1.61 => ( nonempty
% 2.98/1.61 @ ( dsetconstr @ A
% 2.98/1.61 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(nonemptyI1_type,type,
% 2.98/1.61 nonemptyI1: $o ).
% 2.98/1.61
% 2.98/1.61 thf(nonemptyI1,definition,
% 2.98/1.61 ( nonemptyI1
% 2.98/1.61 = ( ! [A: $i] :
% 2.98/1.61 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.98/1.61 => ( nonempty @ A ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setadjoinIL_type,type,
% 2.98/1.61 setadjoinIL: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setadjoinIL,definition,
% 2.98/1.61 ( setadjoinIL
% 2.98/1.61 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(emptyinunitempty_type,type,
% 2.98/1.61 emptyinunitempty: $o ).
% 2.98/1.61
% 2.98/1.61 thf(emptyinunitempty,definition,
% 2.98/1.61 ( emptyinunitempty
% 2.98/1.61 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setadjoinIR_type,type,
% 2.98/1.61 setadjoinIR: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setadjoinIR,definition,
% 2.98/1.61 ( setadjoinIR
% 2.98/1.61 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.98/1.61 ( ( in @ Xy @ A )
% 2.98/1.61 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setadjoinE_type,type,
% 2.98/1.61 setadjoinE: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setadjoinE,definition,
% 2.98/1.61 ( setadjoinE
% 2.98/1.61 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.98/1.61 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.98/1.61 => ! [Xphi: $o] :
% 2.98/1.61 ( ( ( Xy = Xx )
% 2.98/1.61 => Xphi )
% 2.98/1.61 => ( ( ( in @ Xy @ A )
% 2.98/1.61 => Xphi )
% 2.98/1.61 => Xphi ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setadjoinOr_type,type,
% 2.98/1.61 setadjoinOr: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setadjoinOr,definition,
% 2.98/1.61 ( setadjoinOr
% 2.98/1.61 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.98/1.61 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.98/1.61 => ( ( Xy = Xx )
% 2.98/1.61 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setoftrueEq_type,type,
% 2.98/1.61 setoftrueEq: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setoftrueEq,definition,
% 2.98/1.61 ( setoftrueEq
% 2.98/1.61 = ( ! [A: $i] :
% 2.98/1.61 ( ( dsetconstr @ A
% 2.98/1.61 @ ^ [Xx: $i] : $true )
% 2.98/1.61 = A ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(powersetI_type,type,
% 2.98/1.61 powersetI: $o ).
% 2.98/1.61
% 2.98/1.61 thf(powersetI,definition,
% 2.98/1.61 ( powersetI
% 2.98/1.61 = ( ! [A: $i,B: $i] :
% 2.98/1.61 ( ! [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ B )
% 2.98/1.61 => ( in @ Xx @ A ) )
% 2.98/1.61 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(emptyinPowerset_type,type,
% 2.98/1.61 emptyinPowerset: $o ).
% 2.98/1.61
% 2.98/1.61 thf(emptyinPowerset,definition,
% 2.98/1.61 ( emptyinPowerset
% 2.98/1.61 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(emptyInPowerset_type,type,
% 2.98/1.61 emptyInPowerset: $o ).
% 2.98/1.61
% 2.98/1.61 thf(emptyInPowerset,definition,
% 2.98/1.61 ( emptyInPowerset
% 2.98/1.61 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(powersetE_type,type,
% 2.98/1.61 powersetE: $o ).
% 2.98/1.61
% 2.98/1.61 thf(powersetE,definition,
% 2.98/1.61 ( powersetE
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.61 ( ( in @ B @ ( powerset @ A ) )
% 2.98/1.61 => ( ( in @ Xx @ B )
% 2.98/1.61 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setunionI_type,type,
% 2.98/1.61 setunionI: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setunionI,definition,
% 2.98/1.61 ( setunionI
% 2.98/1.61 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.98/1.61 ( ( in @ Xx @ B )
% 2.98/1.61 => ( ( in @ B @ A )
% 2.98/1.61 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setunionE_type,type,
% 2.98/1.61 setunionE: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setunionE,definition,
% 2.98/1.61 ( setunionE
% 2.98/1.61 = ( ! [A: $i,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ ( setunion @ A ) )
% 2.98/1.61 => ! [Xphi: $o] :
% 2.98/1.61 ( ! [B: $i] :
% 2.98/1.61 ( ( in @ Xx @ B )
% 2.98/1.61 => ( ( in @ B @ A )
% 2.98/1.61 => Xphi ) )
% 2.98/1.61 => Xphi ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(subPowSU_type,type,
% 2.98/1.61 subPowSU: $o ).
% 2.98/1.61
% 2.98/1.61 thf(subPowSU,definition,
% 2.98/1.61 ( subPowSU
% 2.98/1.61 = ( ! [A: $i,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(exuE2_type,type,
% 2.98/1.61 exuE2: $o ).
% 2.98/1.61
% 2.98/1.61 thf(exuE2,definition,
% 2.98/1.61 ( exuE2
% 2.98/1.61 = ( ! [Xphi: $i > $o] :
% 2.98/1.61 ( ( exu
% 2.98/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.98/1.61 => ? [Xx: $i] :
% 2.98/1.61 ! [Xy: $i] :
% 2.98/1.61 ( ( Xphi @ Xy )
% 2.98/1.61 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(nonemptyImpWitness_type,type,
% 2.98/1.61 nonemptyImpWitness: $o ).
% 2.98/1.61
% 2.98/1.61 thf(nonemptyImpWitness,definition,
% 2.98/1.61 ( nonemptyImpWitness
% 2.98/1.61 = ( ! [A: $i] :
% 2.98/1.61 ( ( nonempty @ A )
% 2.98/1.61 => ? [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 & $true ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(uniqinunit_type,type,
% 2.98/1.61 uniqinunit: $o ).
% 2.98/1.61
% 2.98/1.61 thf(uniqinunit,definition,
% 2.98/1.61 ( uniqinunit
% 2.98/1.61 = ( ! [Xx: $i,Xy: $i] :
% 2.98/1.61 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.98/1.61 => ( Xx = Xy ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(notinsingleton_type,type,
% 2.98/1.61 notinsingleton: $o ).
% 2.98/1.61
% 2.98/1.61 thf(notinsingleton,definition,
% 2.98/1.61 ( notinsingleton
% 2.98/1.61 = ( ! [Xx: $i,Xy: $i] :
% 2.98/1.61 ( ( Xx != Xy )
% 2.98/1.61 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(eqinunit_type,type,
% 2.98/1.61 eqinunit: $o ).
% 2.98/1.61
% 2.98/1.61 thf(eqinunit,definition,
% 2.98/1.61 ( eqinunit
% 2.98/1.61 = ( ! [Xx: $i,Xy: $i] :
% 2.98/1.61 ( ( Xx = Xy )
% 2.98/1.61 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(singletonsswitch_type,type,
% 2.98/1.61 singletonsswitch: $o ).
% 2.98/1.61
% 2.98/1.61 thf(singletonsswitch,definition,
% 2.98/1.61 ( singletonsswitch
% 2.98/1.61 = ( ! [Xx: $i,Xy: $i] :
% 2.98/1.61 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.98/1.61 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(upairsetE_type,type,
% 2.98/1.61 upairsetE: $o ).
% 2.98/1.61
% 2.98/1.61 thf(upairsetE,definition,
% 2.98/1.61 ( upairsetE
% 2.98/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.98/1.61 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.98/1.61 => ( ( Xz = Xx )
% 2.98/1.61 | ( Xz = Xy ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(upairsetIL_type,type,
% 2.98/1.61 upairsetIL: $o ).
% 2.98/1.61
% 2.98/1.61 thf(upairsetIL,definition,
% 2.98/1.61 ( upairsetIL
% 2.98/1.61 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(upairsetIR_type,type,
% 2.98/1.61 upairsetIR: $o ).
% 2.98/1.61
% 2.98/1.61 thf(upairsetIR,definition,
% 2.98/1.61 ( upairsetIR
% 2.98/1.61 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(emptyE1_type,type,
% 2.98/1.61 emptyE1: $o ).
% 2.98/1.61
% 2.98/1.61 thf(emptyE1,definition,
% 2.98/1.61 ( emptyE1
% 2.98/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 2.98/1.61 ( ? [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 & ( Xphi @ Xx ) )
% 2.98/1.61 => ( ( ( dsetconstr @ A
% 2.98/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.98/1.61 = emptyset )
% 2.98/1.61 => $false ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(vacuousDall_type,type,
% 2.98/1.61 vacuousDall: $o ).
% 2.98/1.61
% 2.98/1.61 thf(vacuousDall,definition,
% 2.98/1.61 ( vacuousDall
% 2.98/1.61 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ emptyset )
% 2.98/1.61 => ( Xphi @ Xx ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(quantDeMorgan1_type,type,
% 2.98/1.61 quantDeMorgan1: $o ).
% 2.98/1.61
% 2.98/1.61 thf(quantDeMorgan1,definition,
% 2.98/1.61 ( quantDeMorgan1
% 2.98/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 2.98/1.61 ( ~ ! [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ( Xphi @ Xx ) )
% 2.98/1.61 => ? [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(quantDeMorgan2_type,type,
% 2.98/1.61 quantDeMorgan2: $o ).
% 2.98/1.61
% 2.98/1.61 thf(quantDeMorgan2,definition,
% 2.98/1.61 ( quantDeMorgan2
% 2.98/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 2.98/1.61 ( ! [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ~ ( Xphi @ Xx ) )
% 2.98/1.61 => ~ ? [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(quantDeMorgan3_type,type,
% 2.98/1.61 quantDeMorgan3: $o ).
% 2.98/1.61
% 2.98/1.61 thf(quantDeMorgan3,definition,
% 2.98/1.61 ( quantDeMorgan3
% 2.98/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 2.98/1.61 ( ~ ? [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 & ( Xphi @ Xx ) )
% 2.98/1.61 => ! [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(quantDeMorgan4_type,type,
% 2.98/1.61 quantDeMorgan4: $o ).
% 2.98/1.61
% 2.98/1.61 thf(quantDeMorgan4,definition,
% 2.98/1.61 ( quantDeMorgan4
% 2.98/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 2.98/1.61 ( ? [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 & ~ ( Xphi @ Xx ) )
% 2.98/1.61 => ~ ! [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(prop2setI_type,type,
% 2.98/1.61 prop2setI: $o ).
% 2.98/1.61
% 2.98/1.61 thf(prop2setI,definition,
% 2.98/1.61 ( prop2setI
% 2.98/1.61 = ( ! [Xphi: $o] :
% 2.98/1.61 ( Xphi
% 2.98/1.61 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(set2prop_type,type,
% 2.98/1.61 set2prop: $i > $o ).
% 2.98/1.61
% 2.98/1.61 thf(prop2set2propI_type,type,
% 2.98/1.61 prop2set2propI: $o ).
% 2.98/1.61
% 2.98/1.61 thf(prop2set2propI,definition,
% 2.98/1.61 ( prop2set2propI
% 2.98/1.61 = ( ! [Xphi: $o] :
% 2.98/1.61 ( Xphi
% 2.98/1.61 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(notdexE_type,type,
% 2.98/1.61 notdexE: $o ).
% 2.98/1.61
% 2.98/1.61 thf(notdexE,definition,
% 2.98/1.61 ( notdexE
% 2.98/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 2.98/1.61 ( ~ ? [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 & ( Xphi @ Xx ) )
% 2.98/1.61 => ! [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(notdallE_type,type,
% 2.98/1.61 notdallE: $o ).
% 2.98/1.61
% 2.98/1.61 thf(notdallE,definition,
% 2.98/1.61 ( notdallE
% 2.98/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 2.98/1.61 ( ~ ! [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ( Xphi @ Xx ) )
% 2.98/1.61 => ? [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(exuI1_type,type,
% 2.98/1.61 exuI1: $o ).
% 2.98/1.61
% 2.98/1.61 thf(exuI1,definition,
% 2.98/1.61 ( exuI1
% 2.98/1.61 = ( ! [Xphi: $i > $o] :
% 2.98/1.61 ( ? [Xx: $i] :
% 2.98/1.61 ( ( Xphi @ Xx )
% 2.98/1.61 & ! [Xy: $i] :
% 2.98/1.61 ( ( Xphi @ Xy )
% 2.98/1.61 => ( Xx = Xy ) ) )
% 2.98/1.61 => ( exu
% 2.98/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(exuI3_type,type,
% 2.98/1.61 exuI3: $o ).
% 2.98/1.61
% 2.98/1.61 thf(exuI3,definition,
% 2.98/1.61 ( exuI3
% 2.98/1.61 = ( ! [Xphi: $i > $o] :
% 2.98/1.61 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.98/1.61 => ( ! [Xx: $i,Xy: $i] :
% 2.98/1.61 ( ( Xphi @ Xx )
% 2.98/1.61 => ( ( Xphi @ Xy )
% 2.98/1.61 => ( Xx = Xy ) ) )
% 2.98/1.61 => ( exu
% 2.98/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(exuI2_type,type,
% 2.98/1.61 exuI2: $o ).
% 2.98/1.61
% 2.98/1.61 thf(exuI2,definition,
% 2.98/1.61 ( exuI2
% 2.98/1.61 = ( ! [Xphi: $i > $o] :
% 2.98/1.61 ( ? [Xx: $i] :
% 2.98/1.61 ! [Xy: $i] :
% 2.98/1.61 ( ( Xphi @ Xy )
% 2.98/1.61 <=> ( Xy = Xx ) )
% 2.98/1.61 => ( exu
% 2.98/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(inCongP_type,type,
% 2.98/1.61 inCongP: $o ).
% 2.98/1.61
% 2.98/1.61 thf(inCongP,definition,
% 2.98/1.61 ( inCongP
% 2.98/1.61 = ( ! [A: $i,B: $i] :
% 2.98/1.61 ( ( A = B )
% 2.98/1.61 => ! [Xx: $i,Xy: $i] :
% 2.98/1.61 ( ( Xx = Xy )
% 2.98/1.61 => ( ( in @ Xx @ A )
% 2.98/1.61 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(in__Cong_type,type,
% 2.98/1.61 in__Cong: $o ).
% 2.98/1.61
% 2.98/1.61 thf(in__Cong,definition,
% 2.98/1.61 ( in__Cong
% 2.98/1.61 = ( ! [A: $i,B: $i] :
% 2.98/1.61 ( ( A = B )
% 2.98/1.61 => ! [Xx: $i,Xy: $i] :
% 2.98/1.61 ( ( Xx = Xy )
% 2.98/1.61 => ( ( in @ Xx @ A )
% 2.98/1.61 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(exuE3u_type,type,
% 2.98/1.61 exuE3u: $o ).
% 2.98/1.61
% 2.98/1.61 thf(exuE3u,definition,
% 2.98/1.61 ( exuE3u
% 2.98/1.61 = ( ! [Xphi: $i > $o] :
% 2.98/1.61 ( ( exu
% 2.98/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.98/1.61 => ! [Xx: $i,Xy: $i] :
% 2.98/1.61 ( ( Xphi @ Xx )
% 2.98/1.61 => ( ( Xphi @ Xy )
% 2.98/1.61 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(exu__Cong_type,type,
% 2.98/1.61 exu__Cong: $o ).
% 2.98/1.61
% 2.98/1.61 thf(exu__Cong,definition,
% 2.98/1.61 ( exu__Cong
% 2.98/1.61 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.98/1.61 ( ! [Xx: $i,Xy: $i] :
% 2.98/1.61 ( ( Xx = Xy )
% 2.98/1.61 => ( ( Xphi @ Xx )
% 2.98/1.61 <=> ( Xpsi @ Xy ) ) )
% 2.98/1.61 => ( ( exu
% 2.98/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.98/1.61 <=> ( exu
% 2.98/1.61 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(emptyset__Cong_type,type,
% 2.98/1.61 emptyset__Cong: $o ).
% 2.98/1.61
% 2.98/1.61 thf(emptyset__Cong,definition,
% 2.98/1.61 ( emptyset__Cong
% 2.98/1.61 = ( emptyset = emptyset ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setadjoin__Cong_type,type,
% 2.98/1.61 setadjoin__Cong: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setadjoin__Cong,definition,
% 2.98/1.61 ( setadjoin__Cong
% 2.98/1.61 = ( ! [Xx: $i,Xy: $i] :
% 2.98/1.61 ( ( Xx = Xy )
% 2.98/1.61 => ! [Xz: $i,Xu: $i] :
% 2.98/1.61 ( ( Xz = Xu )
% 2.98/1.61 => ( ( setadjoin @ Xx @ Xz )
% 2.98/1.61 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(powerset__Cong_type,type,
% 2.98/1.61 powerset__Cong: $o ).
% 2.98/1.61
% 2.98/1.61 thf(powerset__Cong,definition,
% 2.98/1.61 ( powerset__Cong
% 2.98/1.61 = ( ! [A: $i,B: $i] :
% 2.98/1.61 ( ( A = B )
% 2.98/1.61 => ( ( powerset @ A )
% 2.98/1.61 = ( powerset @ B ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setunion__Cong_type,type,
% 2.98/1.61 setunion__Cong: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setunion__Cong,definition,
% 2.98/1.61 ( setunion__Cong
% 2.98/1.61 = ( ! [A: $i,B: $i] :
% 2.98/1.61 ( ( A = B )
% 2.98/1.61 => ( ( setunion @ A )
% 2.98/1.61 = ( setunion @ B ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(omega__Cong_type,type,
% 2.98/1.61 omega__Cong: $o ).
% 2.98/1.61
% 2.98/1.61 thf(omega__Cong,definition,
% 2.98/1.61 ( omega__Cong
% 2.98/1.61 = ( omega = omega ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(exuEu_type,type,
% 2.98/1.61 exuEu: $o ).
% 2.98/1.61
% 2.98/1.61 thf(exuEu,definition,
% 2.98/1.61 ( exuEu
% 2.98/1.61 = ( ! [Xphi: $i > $o] :
% 2.98/1.61 ( ( exu
% 2.98/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.98/1.61 => ! [Xx: $i,Xy: $i] :
% 2.98/1.61 ( ( Xphi @ Xx )
% 2.98/1.61 => ( ( Xphi @ Xy )
% 2.98/1.61 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(descr__Cong_type,type,
% 2.98/1.61 descr__Cong: $o ).
% 2.98/1.61
% 2.98/1.61 thf(descr__Cong,definition,
% 2.98/1.61 ( descr__Cong
% 2.98/1.61 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.98/1.61 ( ! [Xx: $i,Xy: $i] :
% 2.98/1.61 ( ( Xx = Xy )
% 2.98/1.61 => ( ( Xphi @ Xx )
% 2.98/1.61 <=> ( Xpsi @ Xy ) ) )
% 2.98/1.61 => ( ( exu
% 2.98/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.98/1.61 => ( ( exu
% 2.98/1.61 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.98/1.61 => ( ( descr
% 2.98/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.98/1.61 = ( descr
% 2.98/1.61 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(dsetconstr__Cong_type,type,
% 2.98/1.61 dsetconstr__Cong: $o ).
% 2.98/1.61
% 2.98/1.61 thf(dsetconstr__Cong,definition,
% 2.98/1.61 ( dsetconstr__Cong
% 2.98/1.61 = ( ! [A: $i,B: $i] :
% 2.98/1.61 ( ( A = B )
% 2.98/1.61 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.98/1.61 ( ! [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ! [Xy: $i] :
% 2.98/1.61 ( ( in @ Xy @ B )
% 2.98/1.61 => ( ( Xx = Xy )
% 2.98/1.61 => ( ( Xphi @ Xx )
% 2.98/1.61 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.98/1.61 => ( ( dsetconstr @ A
% 2.98/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.98/1.61 = ( dsetconstr @ B
% 2.98/1.61 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(subset_type,type,
% 2.98/1.61 subset: $i > $i > $o ).
% 2.98/1.61
% 2.98/1.61 thf(disjoint_type,type,
% 2.98/1.61 disjoint: $i > $i > $o ).
% 2.98/1.61
% 2.98/1.61 thf(setsmeet_type,type,
% 2.98/1.61 setsmeet: $i > $i > $o ).
% 2.98/1.61
% 2.98/1.61 thf(subsetI1_type,type,
% 2.98/1.61 subsetI1: $o ).
% 2.98/1.61
% 2.98/1.61 thf(subsetI1,definition,
% 2.98/1.61 ( subsetI1
% 2.98/1.61 = ( ! [A: $i,B: $i] :
% 2.98/1.61 ( ! [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ( in @ Xx @ B ) )
% 2.98/1.61 => ( subset @ A @ B ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(eqimpsubset2_type,type,
% 2.98/1.61 eqimpsubset2: $o ).
% 2.98/1.61
% 2.98/1.61 thf(eqimpsubset2,definition,
% 2.98/1.61 ( eqimpsubset2
% 2.98/1.61 = ( ! [A: $i,B: $i] :
% 2.98/1.61 ( ( A = B )
% 2.98/1.61 => ( subset @ B @ A ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(eqimpsubset1_type,type,
% 2.98/1.61 eqimpsubset1: $o ).
% 2.98/1.61
% 2.98/1.61 thf(eqimpsubset1,definition,
% 2.98/1.61 ( eqimpsubset1
% 2.98/1.61 = ( ! [A: $i,B: $i] :
% 2.98/1.61 ( ( A = B )
% 2.98/1.61 => ( subset @ A @ B ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(subsetI2_type,type,
% 2.98/1.61 subsetI2: $o ).
% 2.98/1.61
% 2.98/1.61 thf(subsetI2,definition,
% 2.98/1.61 ( subsetI2
% 2.98/1.61 = ( ! [A: $i,B: $i] :
% 2.98/1.61 ( ! [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ( in @ Xx @ B ) )
% 2.98/1.61 => ( subset @ A @ B ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(emptysetsubset_type,type,
% 2.98/1.61 emptysetsubset: $o ).
% 2.98/1.61
% 2.98/1.61 thf(emptysetsubset,definition,
% 2.98/1.61 ( emptysetsubset
% 2.98/1.61 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(subsetE_type,type,
% 2.98/1.61 subsetE: $o ).
% 2.98/1.61
% 2.98/1.61 thf(subsetE,definition,
% 2.98/1.61 ( subsetE
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.61 ( ( subset @ A @ B )
% 2.98/1.61 => ( ( in @ Xx @ A )
% 2.98/1.61 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(subsetE2_type,type,
% 2.98/1.61 subsetE2: $o ).
% 2.98/1.61
% 2.98/1.61 thf(subsetE2,definition,
% 2.98/1.61 ( subsetE2
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.61 ( ( subset @ A @ B )
% 2.98/1.61 => ( ~ ( in @ Xx @ B )
% 2.98/1.61 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(notsubsetI_type,type,
% 2.98/1.61 notsubsetI: $o ).
% 2.98/1.61
% 2.98/1.61 thf(notsubsetI,definition,
% 2.98/1.61 ( notsubsetI
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ( ~ ( in @ Xx @ B )
% 2.98/1.61 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(notequalI1_type,type,
% 2.98/1.61 notequalI1: $o ).
% 2.98/1.61
% 2.98/1.61 thf(notequalI1,definition,
% 2.98/1.61 ( notequalI1
% 2.98/1.61 = ( ! [A: $i,B: $i] :
% 2.98/1.61 ( ~ ( subset @ A @ B )
% 2.98/1.61 => ( A != B ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(notequalI2_type,type,
% 2.98/1.61 notequalI2: $o ).
% 2.98/1.61
% 2.98/1.61 thf(notequalI2,definition,
% 2.98/1.61 ( notequalI2
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ( ~ ( in @ Xx @ B )
% 2.98/1.61 => ( A != B ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(subsetRefl_type,type,
% 2.98/1.61 subsetRefl: $o ).
% 2.98/1.61
% 2.98/1.61 thf(subsetRefl,definition,
% 2.98/1.61 ( subsetRefl
% 2.98/1.61 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(subsetTrans_type,type,
% 2.98/1.61 subsetTrans: $o ).
% 2.98/1.61
% 2.98/1.61 thf(subsetTrans,definition,
% 2.98/1.61 ( subsetTrans
% 2.98/1.61 = ( ! [A: $i,B: $i,C: $i] :
% 2.98/1.61 ( ( subset @ A @ B )
% 2.98/1.61 => ( ( subset @ B @ C )
% 2.98/1.61 => ( subset @ A @ C ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setadjoinSub_type,type,
% 2.98/1.61 setadjoinSub: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setadjoinSub,definition,
% 2.98/1.61 ( setadjoinSub
% 2.98/1.61 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setadjoinSub2_type,type,
% 2.98/1.61 setadjoinSub2: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setadjoinSub2,definition,
% 2.98/1.61 ( setadjoinSub2
% 2.98/1.61 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.98/1.61 ( ( subset @ A @ B )
% 2.98/1.61 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(subset2powerset_type,type,
% 2.98/1.61 subset2powerset: $o ).
% 2.98/1.61
% 2.98/1.61 thf(subset2powerset,definition,
% 2.98/1.61 ( subset2powerset
% 2.98/1.61 = ( ! [A: $i,B: $i] :
% 2.98/1.61 ( ( subset @ A @ B )
% 2.98/1.61 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setextsub_type,type,
% 2.98/1.61 setextsub: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setextsub,definition,
% 2.98/1.61 ( setextsub
% 2.98/1.61 = ( ! [A: $i,B: $i] :
% 2.98/1.61 ( ( subset @ A @ B )
% 2.98/1.61 => ( ( subset @ B @ A )
% 2.98/1.61 => ( A = B ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(subsetemptysetimpeq_type,type,
% 2.98/1.61 subsetemptysetimpeq: $o ).
% 2.98/1.61
% 2.98/1.61 thf(subsetemptysetimpeq,definition,
% 2.98/1.61 ( subsetemptysetimpeq
% 2.98/1.61 = ( ! [A: $i] :
% 2.98/1.61 ( ( subset @ A @ emptyset )
% 2.98/1.61 => ( A = emptyset ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(powersetI1_type,type,
% 2.98/1.61 powersetI1: $o ).
% 2.98/1.61
% 2.98/1.61 thf(powersetI1,definition,
% 2.98/1.61 ( powersetI1
% 2.98/1.61 = ( ! [A: $i,B: $i] :
% 2.98/1.61 ( ( subset @ B @ A )
% 2.98/1.61 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(powersetE1_type,type,
% 2.98/1.61 powersetE1: $o ).
% 2.98/1.61
% 2.98/1.61 thf(powersetE1,definition,
% 2.98/1.61 ( powersetE1
% 2.98/1.61 = ( ! [A: $i,B: $i] :
% 2.98/1.61 ( ( in @ B @ ( powerset @ A ) )
% 2.98/1.61 => ( subset @ B @ A ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(inPowerset_type,type,
% 2.98/1.61 inPowerset: $o ).
% 2.98/1.61
% 2.98/1.61 thf(inPowerset,definition,
% 2.98/1.61 ( inPowerset
% 2.98/1.61 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(powersetsubset_type,type,
% 2.98/1.61 powersetsubset: $o ).
% 2.98/1.61
% 2.98/1.61 thf(powersetsubset,definition,
% 2.98/1.61 ( powersetsubset
% 2.98/1.61 = ( ! [A: $i,B: $i] :
% 2.98/1.61 ( ( subset @ A @ B )
% 2.98/1.61 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(sepInPowerset_type,type,
% 2.98/1.61 sepInPowerset: $o ).
% 2.98/1.61
% 2.98/1.61 thf(sepInPowerset,definition,
% 2.98/1.61 ( sepInPowerset
% 2.98/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 2.98/1.61 ( in
% 2.98/1.61 @ ( dsetconstr @ A
% 2.98/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.98/1.61 @ ( powerset @ A ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(sepSubset_type,type,
% 2.98/1.61 sepSubset: $o ).
% 2.98/1.61
% 2.98/1.61 thf(sepSubset,definition,
% 2.98/1.61 ( sepSubset
% 2.98/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 2.98/1.61 ( subset
% 2.98/1.61 @ ( dsetconstr @ A
% 2.98/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.98/1.61 @ A ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(binunion_type,type,
% 2.98/1.61 binunion: $i > $i > $i ).
% 2.98/1.61
% 2.98/1.61 thf(binunionIL_type,type,
% 2.98/1.61 binunionIL: $o ).
% 2.98/1.61
% 2.98/1.61 thf(binunionIL,definition,
% 2.98/1.61 ( binunionIL
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(upairset2IR_type,type,
% 2.98/1.61 upairset2IR: $o ).
% 2.98/1.61
% 2.98/1.61 thf(upairset2IR,definition,
% 2.98/1.61 ( upairset2IR
% 2.98/1.61 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(binunionIR_type,type,
% 2.98/1.61 binunionIR: $o ).
% 2.98/1.61
% 2.98/1.61 thf(binunionIR,definition,
% 2.98/1.61 ( binunionIR
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ B )
% 2.98/1.61 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(binunionEcases_type,type,
% 2.98/1.61 binunionEcases: $o ).
% 2.98/1.61
% 2.98/1.61 thf(binunionEcases,definition,
% 2.98/1.61 ( binunionEcases
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.98/1.61 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.98/1.61 => ( ( ( in @ Xx @ A )
% 2.98/1.61 => Xphi )
% 2.98/1.61 => ( ( ( in @ Xx @ B )
% 2.98/1.61 => Xphi )
% 2.98/1.61 => Xphi ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(binunionE_type,type,
% 2.98/1.61 binunionE: $o ).
% 2.98/1.61
% 2.98/1.61 thf(binunionE,definition,
% 2.98/1.61 ( binunionE
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.98/1.61 => ( ( in @ Xx @ A )
% 2.98/1.61 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(binunionLsub_type,type,
% 2.98/1.61 binunionLsub: $o ).
% 2.98/1.61
% 2.98/1.61 thf(binunionLsub,definition,
% 2.98/1.61 ( binunionLsub
% 2.98/1.61 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(binunionRsub_type,type,
% 2.98/1.61 binunionRsub: $o ).
% 2.98/1.61
% 2.98/1.61 thf(binunionRsub,definition,
% 2.98/1.61 ( binunionRsub
% 2.98/1.61 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(binintersect_type,type,
% 2.98/1.61 binintersect: $i > $i > $i ).
% 2.98/1.61
% 2.98/1.61 thf(binintersectI_type,type,
% 2.98/1.61 binintersectI: $o ).
% 2.98/1.61
% 2.98/1.61 thf(binintersectI,definition,
% 2.98/1.61 ( binintersectI
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ( ( in @ Xx @ B )
% 2.98/1.61 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(binintersectSubset5_type,type,
% 2.98/1.61 binintersectSubset5: $o ).
% 2.98/1.61
% 2.98/1.61 thf(binintersectSubset5,definition,
% 2.98/1.61 ( binintersectSubset5
% 2.98/1.61 = ( ! [A: $i,B: $i,C: $i] :
% 2.98/1.61 ( ( subset @ C @ A )
% 2.98/1.61 => ( ( subset @ C @ B )
% 2.98/1.61 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(binintersectEL_type,type,
% 2.98/1.61 binintersectEL: $o ).
% 2.98/1.61
% 2.98/1.61 thf(binintersectEL,definition,
% 2.98/1.61 ( binintersectEL
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.98/1.61 => ( in @ Xx @ A ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(binintersectLsub_type,type,
% 2.98/1.61 binintersectLsub: $o ).
% 2.98/1.61
% 2.98/1.61 thf(binintersectLsub,definition,
% 2.98/1.61 ( binintersectLsub
% 2.98/1.61 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(binintersectSubset2_type,type,
% 2.98/1.61 binintersectSubset2: $o ).
% 2.98/1.61
% 2.98/1.61 thf(binintersectSubset2,definition,
% 2.98/1.61 ( binintersectSubset2
% 2.98/1.61 = ( ! [A: $i,B: $i] :
% 2.98/1.61 ( ( subset @ A @ B )
% 2.98/1.61 => ( ( binintersect @ A @ B )
% 2.98/1.61 = A ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(binintersectSubset3_type,type,
% 2.98/1.61 binintersectSubset3: $o ).
% 2.98/1.61
% 2.98/1.61 thf(binintersectSubset3,definition,
% 2.98/1.61 ( binintersectSubset3
% 2.98/1.61 = ( ! [A: $i,B: $i] :
% 2.98/1.61 ( ( ( binintersect @ A @ B )
% 2.98/1.61 = B )
% 2.98/1.61 => ( subset @ B @ A ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(binintersectER_type,type,
% 2.98/1.61 binintersectER: $o ).
% 2.98/1.61
% 2.98/1.61 thf(binintersectER,definition,
% 2.98/1.61 ( binintersectER
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.98/1.61 => ( in @ Xx @ B ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(disjointsetsI1_type,type,
% 2.98/1.61 disjointsetsI1: $o ).
% 2.98/1.61
% 2.98/1.61 thf(disjointsetsI1,definition,
% 2.98/1.61 ( disjointsetsI1
% 2.98/1.61 = ( ! [A: $i,B: $i] :
% 2.98/1.61 ( ~ ? [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 & ( in @ Xx @ B ) )
% 2.98/1.61 => ( ( binintersect @ A @ B )
% 2.98/1.61 = emptyset ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(binintersectRsub_type,type,
% 2.98/1.61 binintersectRsub: $o ).
% 2.98/1.61
% 2.98/1.61 thf(binintersectRsub,definition,
% 2.98/1.61 ( binintersectRsub
% 2.98/1.61 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(binintersectSubset4_type,type,
% 2.98/1.61 binintersectSubset4: $o ).
% 2.98/1.61
% 2.98/1.61 thf(binintersectSubset4,definition,
% 2.98/1.61 ( binintersectSubset4
% 2.98/1.61 = ( ! [A: $i,B: $i] :
% 2.98/1.61 ( ( subset @ B @ A )
% 2.98/1.61 => ( ( binintersect @ A @ B )
% 2.98/1.61 = B ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(binintersectSubset1_type,type,
% 2.98/1.61 binintersectSubset1: $o ).
% 2.98/1.61
% 2.98/1.61 thf(binintersectSubset1,definition,
% 2.98/1.61 ( binintersectSubset1
% 2.98/1.61 = ( ! [A: $i,B: $i] :
% 2.98/1.61 ( ( ( binintersect @ A @ B )
% 2.98/1.61 = A )
% 2.98/1.61 => ( subset @ A @ B ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(bs114d_type,type,
% 2.98/1.61 bs114d: $o ).
% 2.98/1.61
% 2.98/1.61 thf(bs114d,definition,
% 2.98/1.61 ( bs114d
% 2.98/1.61 = ( ! [A: $i,B: $i,C: $i] :
% 2.98/1.61 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.98/1.61 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(regular_type,type,
% 2.98/1.61 regular: $i > $o ).
% 2.98/1.61
% 2.98/1.61 thf(setminus_type,type,
% 2.98/1.61 setminus: $i > $i > $i ).
% 2.98/1.61
% 2.98/1.61 thf(setminusI_type,type,
% 2.98/1.61 setminusI: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setminusI,definition,
% 2.98/1.61 ( setminusI
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ( ~ ( in @ Xx @ B )
% 2.98/1.61 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setminusEL_type,type,
% 2.98/1.61 setminusEL: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setminusEL,definition,
% 2.98/1.61 ( setminusEL
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.98/1.61 => ( in @ Xx @ A ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setminusER_type,type,
% 2.98/1.61 setminusER: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setminusER,definition,
% 2.98/1.61 ( setminusER
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.98/1.61 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setminusSubset2_type,type,
% 2.98/1.61 setminusSubset2: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setminusSubset2,definition,
% 2.98/1.61 ( setminusSubset2
% 2.98/1.61 = ( ! [A: $i,B: $i] :
% 2.98/1.61 ( ( subset @ A @ B )
% 2.98/1.61 => ( ( setminus @ A @ B )
% 2.98/1.61 = emptyset ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setminusERneg_type,type,
% 2.98/1.61 setminusERneg: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setminusERneg,definition,
% 2.98/1.61 ( setminusERneg
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.61 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.98/1.61 => ( ( in @ Xx @ A )
% 2.98/1.61 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setminusELneg_type,type,
% 2.98/1.61 setminusELneg: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setminusELneg,definition,
% 2.98/1.61 ( setminusELneg
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.61 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.98/1.61 => ( ~ ( in @ Xx @ B )
% 2.98/1.61 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setminusILneg_type,type,
% 2.98/1.61 setminusILneg: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setminusILneg,definition,
% 2.98/1.61 ( setminusILneg
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.61 ( ~ ( in @ Xx @ A )
% 2.98/1.61 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setminusIRneg_type,type,
% 2.98/1.61 setminusIRneg: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setminusIRneg,definition,
% 2.98/1.61 ( setminusIRneg
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ B )
% 2.98/1.61 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setminusLsub_type,type,
% 2.98/1.61 setminusLsub: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setminusLsub,definition,
% 2.98/1.61 ( setminusLsub
% 2.98/1.61 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setminusSubset1_type,type,
% 2.98/1.61 setminusSubset1: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setminusSubset1,definition,
% 2.98/1.61 ( setminusSubset1
% 2.98/1.61 = ( ! [A: $i,B: $i] :
% 2.98/1.61 ( ( ( setminus @ A @ B )
% 2.98/1.61 = emptyset )
% 2.98/1.61 => ( subset @ A @ B ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(symdiff_type,type,
% 2.98/1.61 symdiff: $i > $i > $i ).
% 2.98/1.61
% 2.98/1.61 thf(symdiffE_type,type,
% 2.98/1.61 symdiffE: $o ).
% 2.98/1.61
% 2.98/1.61 thf(symdiffE,definition,
% 2.98/1.61 ( symdiffE
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.98/1.61 => ! [Xphi: $o] :
% 2.98/1.61 ( ( ( in @ Xx @ A )
% 2.98/1.61 => ( ~ ( in @ Xx @ B )
% 2.98/1.61 => Xphi ) )
% 2.98/1.61 => ( ( ~ ( in @ Xx @ A )
% 2.98/1.61 => ( ( in @ Xx @ B )
% 2.98/1.61 => Xphi ) )
% 2.98/1.61 => Xphi ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(symdiffI1_type,type,
% 2.98/1.61 symdiffI1: $o ).
% 2.98/1.61
% 2.98/1.61 thf(symdiffI1,definition,
% 2.98/1.61 ( symdiffI1
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ( ~ ( in @ Xx @ B )
% 2.98/1.61 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(symdiffI2_type,type,
% 2.98/1.61 symdiffI2: $o ).
% 2.98/1.61
% 2.98/1.61 thf(symdiffI2,definition,
% 2.98/1.61 ( symdiffI2
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.61 ( ~ ( in @ Xx @ A )
% 2.98/1.61 => ( ( in @ Xx @ B )
% 2.98/1.61 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(symdiffIneg1_type,type,
% 2.98/1.61 symdiffIneg1: $o ).
% 2.98/1.61
% 2.98/1.61 thf(symdiffIneg1,definition,
% 2.98/1.61 ( symdiffIneg1
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ( ( in @ Xx @ B )
% 2.98/1.61 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(symdiffIneg2_type,type,
% 2.98/1.61 symdiffIneg2: $o ).
% 2.98/1.61
% 2.98/1.61 thf(symdiffIneg2,definition,
% 2.98/1.61 ( symdiffIneg2
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.61 ( ~ ( in @ Xx @ A )
% 2.98/1.61 => ( ~ ( in @ Xx @ B )
% 2.98/1.61 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(iskpair_type,type,
% 2.98/1.61 iskpair: $i > $o ).
% 2.98/1.61
% 2.98/1.61 thf(secondinupair_type,type,
% 2.98/1.61 secondinupair: $o ).
% 2.98/1.61
% 2.98/1.61 thf(secondinupair,definition,
% 2.98/1.61 ( secondinupair
% 2.98/1.61 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setukpairIL_type,type,
% 2.98/1.61 setukpairIL: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setukpairIL,definition,
% 2.98/1.61 ( setukpairIL
% 2.98/1.61 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setukpairIR_type,type,
% 2.98/1.61 setukpairIR: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setukpairIR,definition,
% 2.98/1.61 ( setukpairIR
% 2.98/1.61 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(kpairiskpair_type,type,
% 2.98/1.61 kpairiskpair: $o ).
% 2.98/1.61
% 2.98/1.61 thf(kpairiskpair,definition,
% 2.98/1.61 ( kpairiskpair
% 2.98/1.61 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(kpair_type,type,
% 2.98/1.61 kpair: $i > $i > $i ).
% 2.98/1.61
% 2.98/1.61 thf(kpairp_type,type,
% 2.98/1.61 kpairp: $o ).
% 2.98/1.61
% 2.98/1.61 thf(kpairp,definition,
% 2.98/1.61 ( kpairp
% 2.98/1.61 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(cartprod_type,type,
% 2.98/1.61 cartprod: $i > $i > $i ).
% 2.98/1.61
% 2.98/1.61 thf(singletonsubset_type,type,
% 2.98/1.61 singletonsubset: $o ).
% 2.98/1.61
% 2.98/1.61 thf(singletonsubset,definition,
% 2.98/1.61 ( singletonsubset
% 2.98/1.61 = ( ! [A: $i,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(singletoninpowerset_type,type,
% 2.98/1.61 singletoninpowerset: $o ).
% 2.98/1.61
% 2.98/1.61 thf(singletoninpowerset,definition,
% 2.98/1.61 ( singletoninpowerset
% 2.98/1.61 = ( ! [A: $i,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(singletoninpowunion_type,type,
% 2.98/1.61 singletoninpowunion: $o ).
% 2.98/1.61
% 2.98/1.61 thf(singletoninpowunion,definition,
% 2.98/1.61 ( singletoninpowunion
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(upairset2E_type,type,
% 2.98/1.61 upairset2E: $o ).
% 2.98/1.61
% 2.98/1.61 thf(upairset2E,definition,
% 2.98/1.61 ( upairset2E
% 2.98/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.98/1.61 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.98/1.61 => ( ( Xz = Xx )
% 2.98/1.61 | ( Xz = Xy ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(upairsubunion_type,type,
% 2.98/1.61 upairsubunion: $o ).
% 2.98/1.61
% 2.98/1.61 thf(upairsubunion,definition,
% 2.98/1.61 ( upairsubunion
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ! [Xy: $i] :
% 2.98/1.61 ( ( in @ Xy @ B )
% 2.98/1.61 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(upairinpowunion_type,type,
% 2.98/1.61 upairinpowunion: $o ).
% 2.98/1.61
% 2.98/1.61 thf(upairinpowunion,definition,
% 2.98/1.61 ( upairinpowunion
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ! [Xy: $i] :
% 2.98/1.61 ( ( in @ Xy @ B )
% 2.98/1.61 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(ubforcartprodlem1_type,type,
% 2.98/1.61 ubforcartprodlem1: $o ).
% 2.98/1.61
% 2.98/1.61 thf(ubforcartprodlem1,definition,
% 2.98/1.61 ( ubforcartprodlem1
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ! [Xy: $i] :
% 2.98/1.61 ( ( in @ Xy @ B )
% 2.98/1.61 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(ubforcartprodlem2_type,type,
% 2.98/1.61 ubforcartprodlem2: $o ).
% 2.98/1.61
% 2.98/1.61 thf(ubforcartprodlem2,definition,
% 2.98/1.61 ( ubforcartprodlem2
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ! [Xy: $i] :
% 2.98/1.61 ( ( in @ Xy @ B )
% 2.98/1.61 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(ubforcartprodlem3_type,type,
% 2.98/1.61 ubforcartprodlem3: $o ).
% 2.98/1.61
% 2.98/1.61 thf(ubforcartprodlem3,definition,
% 2.98/1.61 ( ubforcartprodlem3
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ! [Xy: $i] :
% 2.98/1.61 ( ( in @ Xy @ B )
% 2.98/1.61 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(cartprodpairin_type,type,
% 2.98/1.61 cartprodpairin: $o ).
% 2.98/1.61
% 2.98/1.61 thf(cartprodpairin,definition,
% 2.98/1.61 ( cartprodpairin
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ! [Xy: $i] :
% 2.98/1.61 ( ( in @ Xy @ B )
% 2.98/1.61 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(cartprodmempair1_type,type,
% 2.98/1.61 cartprodmempair1: $o ).
% 2.98/1.61
% 2.98/1.61 thf(cartprodmempair1,definition,
% 2.98/1.61 ( cartprodmempair1
% 2.98/1.61 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.98/1.61 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.98/1.61 => ? [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 & ? [Xy: $i] :
% 2.98/1.61 ( ( in @ Xy @ B )
% 2.98/1.61 & ( Xu
% 2.98/1.61 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(cartprodmempair_type,type,
% 2.98/1.61 cartprodmempair: $o ).
% 2.98/1.61
% 2.98/1.61 thf(cartprodmempair,definition,
% 2.98/1.61 ( cartprodmempair
% 2.98/1.61 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.98/1.61 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.98/1.61 => ( iskpair @ Xu ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setunionE2_type,type,
% 2.98/1.61 setunionE2: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setunionE2,definition,
% 2.98/1.61 ( setunionE2
% 2.98/1.61 = ( ! [A: $i,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ ( setunion @ A ) )
% 2.98/1.61 => ? [X: $i] :
% 2.98/1.61 ( ( in @ X @ A )
% 2.98/1.61 & ( in @ Xx @ X ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setunionsingleton1_type,type,
% 2.98/1.61 setunionsingleton1: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setunionsingleton1,definition,
% 2.98/1.61 ( setunionsingleton1
% 2.98/1.61 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setunionsingleton2_type,type,
% 2.98/1.61 setunionsingleton2: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setunionsingleton2,definition,
% 2.98/1.61 ( setunionsingleton2
% 2.98/1.61 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setunionsingleton_type,type,
% 2.98/1.61 setunionsingleton: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setunionsingleton,definition,
% 2.98/1.61 ( setunionsingleton
% 2.98/1.61 = ( ! [Xx: $i] :
% 2.98/1.61 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 2.98/1.61 = Xx ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(singleton_type,type,
% 2.98/1.61 singleton: $i > $o ).
% 2.98/1.61
% 2.98/1.61 thf(singletonprop_type,type,
% 2.98/1.61 singletonprop: $o ).
% 2.98/1.61
% 2.98/1.61 thf(singletonprop,definition,
% 2.98/1.61 ( singletonprop
% 2.98/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 2.98/1.61 ( ! [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ! [Xy: $i] :
% 2.98/1.61 ( ( in @ Xy @ A )
% 2.98/1.61 => ( ( Xphi @ Xx )
% 2.98/1.61 => ( ( Xphi @ Xy )
% 2.98/1.61 => ( Xx = Xy ) ) ) ) )
% 2.98/1.61 => ( ? [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 & ( Xphi @ Xx ) )
% 2.98/1.61 => ( singleton
% 2.98/1.61 @ ( dsetconstr @ A
% 2.98/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(ex1_type,type,
% 2.98/1.61 ex1: $i > ( $i > $o ) > $o ).
% 2.98/1.61
% 2.98/1.61 thf(ex1,definition,
% 2.98/1.61 ( ex1
% 2.98/1.61 = ( ^ [A: $i,Xphi: $i > $o] :
% 2.98/1.61 ( singleton
% 2.98/1.61 @ ( dsetconstr @ A
% 2.98/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(ex1E1_type,type,
% 2.98/1.61 ex1E1: $o ).
% 2.98/1.61
% 2.98/1.61 thf(ex1E1,definition,
% 2.98/1.61 ( ex1E1
% 2.98/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 2.98/1.61 ( ( ex1 @ A
% 2.98/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.98/1.61 => ? [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(ex1I_type,type,
% 2.98/1.61 ex1I: $o ).
% 2.98/1.61
% 2.98/1.61 thf(ex1I,definition,
% 2.98/1.61 ( ex1I
% 2.98/1.61 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ( ( Xphi @ Xx )
% 2.98/1.61 => ( ! [Xy: $i] :
% 2.98/1.61 ( ( in @ Xy @ A )
% 2.98/1.61 => ( ( Xphi @ Xy )
% 2.98/1.61 => ( Xy = Xx ) ) )
% 2.98/1.61 => ( ex1 @ A
% 2.98/1.61 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(ex1I2_type,type,
% 2.98/1.61 ex1I2: $o ).
% 2.98/1.61
% 2.98/1.61 thf(ex1I2,definition,
% 2.98/1.61 ( ex1I2
% 2.98/1.61 = ( ! [A: $i,Xphi: $i > $o] :
% 2.98/1.61 ( ! [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ! [Xy: $i] :
% 2.98/1.61 ( ( in @ Xy @ A )
% 2.98/1.61 => ( ( Xphi @ Xx )
% 2.98/1.61 => ( ( Xphi @ Xy )
% 2.98/1.61 => ( Xx = Xy ) ) ) ) )
% 2.98/1.61 => ( ? [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 & ( Xphi @ Xx ) )
% 2.98/1.61 => ( ex1 @ A
% 2.98/1.61 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(singletonsuniq_type,type,
% 2.98/1.61 singletonsuniq: $o ).
% 2.98/1.61
% 2.98/1.61 thf(singletonsuniq,definition,
% 2.98/1.61 ( singletonsuniq
% 2.98/1.61 = ( ! [Xx: $i,Xy: $i] :
% 2.98/1.61 ( ( ( setadjoin @ Xx @ emptyset )
% 2.98/1.61 = ( setadjoin @ Xy @ emptyset ) )
% 2.98/1.61 => ( Xx = Xy ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(atmost1p_type,type,
% 2.98/1.61 atmost1p: $i > $o ).
% 2.98/1.61
% 2.98/1.61 thf(atleast2p_type,type,
% 2.98/1.61 atleast2p: $i > $o ).
% 2.98/1.61
% 2.98/1.61 thf(atmost2p_type,type,
% 2.98/1.61 atmost2p: $i > $o ).
% 2.98/1.61
% 2.98/1.61 thf(upairsetp_type,type,
% 2.98/1.61 upairsetp: $i > $o ).
% 2.98/1.61
% 2.98/1.61 thf(setukpairinjL1_type,type,
% 2.98/1.61 setukpairinjL1: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setukpairinjL1,definition,
% 2.98/1.61 ( setukpairinjL1
% 2.98/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.98/1.61 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 2.98/1.61 => ( Xx = Xz ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(kfstsingleton_type,type,
% 2.98/1.61 kfstsingleton: $o ).
% 2.98/1.61
% 2.98/1.61 thf(kfstsingleton,definition,
% 2.98/1.61 ( kfstsingleton
% 2.98/1.61 = ( ! [Xu: $i] :
% 2.98/1.61 ( ( iskpair @ Xu )
% 2.98/1.61 => ( singleton
% 2.98/1.61 @ ( dsetconstr @ ( setunion @ Xu )
% 2.98/1.61 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(theprop_type,type,
% 2.98/1.61 theprop: $o ).
% 2.98/1.61
% 2.98/1.61 thf(theprop,definition,
% 2.98/1.61 ( theprop
% 2.98/1.61 = ( ! [X: $i] :
% 2.98/1.61 ( ( singleton @ X )
% 2.98/1.61 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(kfst_type,type,
% 2.98/1.61 kfst: $i > $i ).
% 2.98/1.61
% 2.98/1.61 thf(kfstpairEq_type,type,
% 2.98/1.61 kfstpairEq: $o ).
% 2.98/1.61
% 2.98/1.61 thf(kfstpairEq,definition,
% 2.98/1.61 ( kfstpairEq
% 2.98/1.61 = ( ! [Xx: $i,Xy: $i] :
% 2.98/1.61 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.98/1.61 = Xx ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(cartprodfstin_type,type,
% 2.98/1.61 cartprodfstin: $o ).
% 2.98/1.61
% 2.98/1.61 thf(cartprodfstin,definition,
% 2.98/1.61 ( cartprodfstin
% 2.98/1.61 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.98/1.61 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.98/1.61 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setukpairinjL2_type,type,
% 2.98/1.61 setukpairinjL2: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setukpairinjL2,definition,
% 2.98/1.61 ( setukpairinjL2
% 2.98/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.98/1.61 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.98/1.61 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.98/1.61 => ( Xx = Xz ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setukpairinjL_type,type,
% 2.98/1.61 setukpairinjL: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setukpairinjL,definition,
% 2.98/1.61 ( setukpairinjL
% 2.98/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.98/1.61 ( ( ( kpair @ Xx @ Xy )
% 2.98/1.61 = ( kpair @ Xz @ Xu ) )
% 2.98/1.61 => ( Xx = Xz ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setukpairinjR11_type,type,
% 2.98/1.61 setukpairinjR11: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setukpairinjR11,definition,
% 2.98/1.61 ( setukpairinjR11
% 2.98/1.61 = ( ! [Xx: $i,Xy: $i] :
% 2.98/1.61 ( ( Xx = Xy )
% 2.98/1.61 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.98/1.61 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setukpairinjR12_type,type,
% 2.98/1.61 setukpairinjR12: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setukpairinjR12,definition,
% 2.98/1.61 ( setukpairinjR12
% 2.98/1.61 = ( ! [Xx: $i,Xy: $i] :
% 2.98/1.61 ( ( Xx = Xy )
% 2.98/1.61 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.98/1.61 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setukpairinjR1_type,type,
% 2.98/1.61 setukpairinjR1: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setukpairinjR1,definition,
% 2.98/1.61 ( setukpairinjR1
% 2.98/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.98/1.61 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.98/1.61 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.98/1.61 => ( ( Xz = Xu )
% 2.98/1.61 => ( Xy = Xu ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(upairequniteq_type,type,
% 2.98/1.61 upairequniteq: $o ).
% 2.98/1.61
% 2.98/1.61 thf(upairequniteq,definition,
% 2.98/1.61 ( upairequniteq
% 2.98/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.98/1.61 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.98/1.61 = ( setadjoin @ Xz @ emptyset ) )
% 2.98/1.61 => ( Xx = Xy ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setukpairinjR2_type,type,
% 2.98/1.61 setukpairinjR2: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setukpairinjR2,definition,
% 2.98/1.61 ( setukpairinjR2
% 2.98/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.98/1.61 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.98/1.61 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.98/1.61 => ( Xy = Xu ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setukpairinjR_type,type,
% 2.98/1.61 setukpairinjR: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setukpairinjR,definition,
% 2.98/1.61 ( setukpairinjR
% 2.98/1.61 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.98/1.61 ( ( ( kpair @ Xx @ Xy )
% 2.98/1.61 = ( kpair @ Xz @ Xu ) )
% 2.98/1.61 => ( Xy = Xu ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(ksndsingleton_type,type,
% 2.98/1.61 ksndsingleton: $o ).
% 2.98/1.61
% 2.98/1.61 thf(ksndsingleton,definition,
% 2.98/1.61 ( ksndsingleton
% 2.98/1.61 = ( ! [Xu: $i] :
% 2.98/1.61 ( ( iskpair @ Xu )
% 2.98/1.61 => ( singleton
% 2.98/1.61 @ ( dsetconstr @ ( setunion @ Xu )
% 2.98/1.61 @ ^ [Xx: $i] :
% 2.98/1.61 ( Xu
% 2.98/1.61 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(ksnd_type,type,
% 2.98/1.61 ksnd: $i > $i ).
% 2.98/1.61
% 2.98/1.61 thf(ksndpairEq_type,type,
% 2.98/1.61 ksndpairEq: $o ).
% 2.98/1.61
% 2.98/1.61 thf(ksndpairEq,definition,
% 2.98/1.61 ( ksndpairEq
% 2.98/1.61 = ( ! [Xx: $i,Xy: $i] :
% 2.98/1.61 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.98/1.61 = Xy ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(kpairsurjEq_type,type,
% 2.98/1.61 kpairsurjEq: $o ).
% 2.98/1.61
% 2.98/1.61 thf(kpairsurjEq,definition,
% 2.98/1.61 ( kpairsurjEq
% 2.98/1.61 = ( ! [Xu: $i] :
% 2.98/1.61 ( ( iskpair @ Xu )
% 2.98/1.61 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.98/1.61 = Xu ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(cartprodsndin_type,type,
% 2.98/1.61 cartprodsndin: $o ).
% 2.98/1.61
% 2.98/1.61 thf(cartprodsndin,definition,
% 2.98/1.61 ( cartprodsndin
% 2.98/1.61 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.98/1.61 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.98/1.61 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(cartprodpairmemEL_type,type,
% 2.98/1.61 cartprodpairmemEL: $o ).
% 2.98/1.61
% 2.98/1.61 thf(cartprodpairmemEL,definition,
% 2.98/1.61 ( cartprodpairmemEL
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.98/1.61 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.98/1.61 => ( in @ Xx @ A ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(cartprodpairmemER_type,type,
% 2.98/1.61 cartprodpairmemER: $o ).
% 2.98/1.61
% 2.98/1.61 thf(cartprodpairmemER,definition,
% 2.98/1.61 ( cartprodpairmemER
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.98/1.61 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.98/1.61 => ( in @ Xy @ B ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(cartprodmempaircEq_type,type,
% 2.98/1.61 cartprodmempaircEq: $o ).
% 2.98/1.61
% 2.98/1.61 thf(cartprodmempaircEq,definition,
% 2.98/1.61 ( cartprodmempaircEq
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ! [Xy: $i] :
% 2.98/1.61 ( ( in @ Xy @ B )
% 2.98/1.61 => ( ( kpair @ Xx @ Xy )
% 2.98/1.61 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(cartprodfstpairEq_type,type,
% 2.98/1.61 cartprodfstpairEq: $o ).
% 2.98/1.61
% 2.98/1.61 thf(cartprodfstpairEq,definition,
% 2.98/1.61 ( cartprodfstpairEq
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ! [Xy: $i] :
% 2.98/1.61 ( ( in @ Xy @ B )
% 2.98/1.61 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.98/1.61 = Xx ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(cartprodsndpairEq_type,type,
% 2.98/1.61 cartprodsndpairEq: $o ).
% 2.98/1.61
% 2.98/1.61 thf(cartprodsndpairEq,definition,
% 2.98/1.61 ( cartprodsndpairEq
% 2.98/1.61 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ! [Xy: $i] :
% 2.98/1.61 ( ( in @ Xy @ B )
% 2.98/1.61 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.98/1.61 = Xy ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(cartprodpairsurjEq_type,type,
% 2.98/1.61 cartprodpairsurjEq: $o ).
% 2.98/1.61
% 2.98/1.61 thf(cartprodpairsurjEq,definition,
% 2.98/1.61 ( cartprodpairsurjEq
% 2.98/1.61 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.98/1.61 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.98/1.61 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.98/1.61 = Xu ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(breln_type,type,
% 2.98/1.61 breln: $i > $i > $i > $o ).
% 2.98/1.61
% 2.98/1.61 thf(breln,definition,
% 2.98/1.61 ( breln
% 2.98/1.61 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(dpsetconstr_type,type,
% 2.98/1.61 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 2.98/1.61
% 2.98/1.61 thf(dpsetconstrI_type,type,
% 2.98/1.61 dpsetconstrI: $o ).
% 2.98/1.61
% 2.98/1.61 thf(dpsetconstrI,definition,
% 2.98/1.61 ( dpsetconstrI
% 2.98/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ! [Xy: $i] :
% 2.98/1.61 ( ( in @ Xy @ B )
% 2.98/1.61 => ( ( Xphi @ Xx @ Xy )
% 2.98/1.61 => ( in @ ( kpair @ Xx @ Xy )
% 2.98/1.61 @ ( dpsetconstr @ A @ B
% 2.98/1.61 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(dpsetconstrSub_type,type,
% 2.98/1.61 dpsetconstrSub: $o ).
% 2.98/1.61
% 2.98/1.61 thf(dpsetconstrSub,definition,
% 2.98/1.61 ( dpsetconstrSub
% 2.98/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.98/1.61 ( subset
% 2.98/1.61 @ ( dpsetconstr @ A @ B
% 2.98/1.61 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 2.98/1.61 @ ( cartprod @ A @ B ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(setOfPairsIsBReln_type,type,
% 2.98/1.61 setOfPairsIsBReln: $o ).
% 2.98/1.61
% 2.98/1.61 thf(setOfPairsIsBReln,definition,
% 2.98/1.61 ( setOfPairsIsBReln
% 2.98/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.98/1.61 ( breln @ A @ B
% 2.98/1.61 @ ( dpsetconstr @ A @ B
% 2.98/1.61 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(dpsetconstrERa_type,type,
% 2.98/1.61 dpsetconstrERa: $o ).
% 2.98/1.61
% 2.98/1.61 thf(dpsetconstrERa,definition,
% 2.98/1.61 ( dpsetconstrERa
% 2.98/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ! [Xy: $i] :
% 2.98/1.61 ( ( in @ Xy @ B )
% 2.98/1.61 => ( ( in @ ( kpair @ Xx @ Xy )
% 2.98/1.61 @ ( dpsetconstr @ A @ B
% 2.98/1.61 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.98/1.61 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(dpsetconstrEL1_type,type,
% 2.98/1.61 dpsetconstrEL1: $o ).
% 2.98/1.61
% 2.98/1.61 thf(dpsetconstrEL1,definition,
% 2.98/1.61 ( dpsetconstrEL1
% 2.98/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.98/1.61 ( ( in @ ( kpair @ Xx @ Xy )
% 2.98/1.61 @ ( dpsetconstr @ A @ B
% 2.98/1.61 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.98/1.61 => ( in @ Xx @ A ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(dpsetconstrEL2_type,type,
% 2.98/1.61 dpsetconstrEL2: $o ).
% 2.98/1.61
% 2.98/1.61 thf(dpsetconstrEL2,definition,
% 2.98/1.61 ( dpsetconstrEL2
% 2.98/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.98/1.61 ( ( in @ ( kpair @ Xx @ Xy )
% 2.98/1.61 @ ( dpsetconstr @ A @ B
% 2.98/1.61 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.98/1.61 => ( in @ Xy @ B ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(dpsetconstrER_type,type,
% 2.98/1.61 dpsetconstrER: $o ).
% 2.98/1.61
% 2.98/1.61 thf(dpsetconstrER,definition,
% 2.98/1.61 ( dpsetconstrER
% 2.98/1.61 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.98/1.61 ( ( in @ ( kpair @ Xx @ Xy )
% 2.98/1.61 @ ( dpsetconstr @ A @ B
% 2.98/1.61 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.98/1.61 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(func_type,type,
% 2.98/1.61 func: $i > $i > $i > $o ).
% 2.98/1.61
% 2.98/1.61 thf(funcSet_type,type,
% 2.98/1.61 funcSet: $i > $i > $i ).
% 2.98/1.61
% 2.98/1.61 thf(funcImageSingleton_type,type,
% 2.98/1.61 funcImageSingleton: $o ).
% 2.98/1.61
% 2.98/1.61 thf(funcImageSingleton,definition,
% 2.98/1.61 ( funcImageSingleton
% 2.98/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.98/1.61 ( ( func @ A @ B @ Xf )
% 2.98/1.61 => ! [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ( singleton
% 2.98/1.61 @ ( dsetconstr @ B
% 2.98/1.61 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(apProp_type,type,
% 2.98/1.61 apProp: $o ).
% 2.98/1.61
% 2.98/1.61 thf(apProp,definition,
% 2.98/1.61 ( apProp
% 2.98/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.98/1.61 ( ( func @ A @ B @ Xf )
% 2.98/1.61 => ! [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ( in
% 2.98/1.61 @ ( setunion
% 2.98/1.61 @ ( dsetconstr @ B
% 2.98/1.61 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 2.98/1.61 @ B ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(ap_type,type,
% 2.98/1.61 ap: $i > $i > $i > $i > $i ).
% 2.98/1.61
% 2.98/1.61 thf(app_type,type,
% 2.98/1.61 app: $o ).
% 2.98/1.61
% 2.98/1.61 thf(app,definition,
% 2.98/1.61 ( app
% 2.98/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.98/1.61 ( ( func @ A @ B @ Xf )
% 2.98/1.61 => ! [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(infuncsetfunc_type,type,
% 2.98/1.61 infuncsetfunc: $o ).
% 2.98/1.61
% 2.98/1.61 thf(infuncsetfunc,definition,
% 2.98/1.61 ( infuncsetfunc
% 2.98/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.98/1.61 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.98/1.61 => ( func @ A @ B @ Xf ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(ap2p_type,type,
% 2.98/1.61 ap2p: $o ).
% 2.98/1.61
% 2.98/1.61 thf(ap2p,definition,
% 2.98/1.61 ( ap2p
% 2.98/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.98/1.61 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.98/1.61 => ! [Xx: $i] :
% 2.98/1.61 ( ( in @ Xx @ A )
% 2.98/1.61 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(funcinfuncset_type,type,
% 2.98/1.61 funcinfuncset: $o ).
% 2.98/1.61
% 2.98/1.61 thf(funcinfuncset,definition,
% 2.98/1.61 ( funcinfuncset
% 2.98/1.61 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.98/1.61 ( ( func @ A @ B @ Xf )
% 2.98/1.61 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 2.98/1.61
% 2.98/1.61 thf(lamProp_type,type,
% 2.98/1.61 lamProp: $o ).
% 2.98/1.61
% 2.98/1.61 thf(lamProp,definition,
% 2.98/1.61 ( lamProp
% 2.98/1.61 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.98/1.61 ( ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.98/1.62 => ( func @ A @ B
% 2.98/1.62 @ ( dpsetconstr @ A @ B
% 2.98/1.62 @ ^ [Xx: $i,Xy: $i] :
% 2.98/1.62 ( ( Xf @ Xx )
% 2.98/1.62 = Xy ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(lam_type,type,
% 2.98/1.62 lam: $i > $i > ( $i > $i ) > $i ).
% 2.98/1.62
% 2.98/1.62 thf(lamp_type,type,
% 2.98/1.62 lamp: $o ).
% 2.98/1.62
% 2.98/1.62 thf(lamp,definition,
% 2.98/1.62 ( lamp
% 2.98/1.62 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.98/1.62 ( ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.98/1.62 => ( func @ A @ B
% 2.98/1.62 @ ( lam @ A @ B
% 2.98/1.62 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(lam2p_type,type,
% 2.98/1.62 lam2p: $o ).
% 2.98/1.62
% 2.98/1.62 thf(lam2p,definition,
% 2.98/1.62 ( lam2p
% 2.98/1.62 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.98/1.62 ( ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.98/1.62 => ( in
% 2.98/1.62 @ ( lam @ A @ B
% 2.98/1.62 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 2.98/1.62 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(brelnall1_type,type,
% 2.98/1.62 brelnall1: $o ).
% 2.98/1.62
% 2.98/1.62 thf(brelnall1,definition,
% 2.98/1.62 ( brelnall1
% 2.98/1.62 = ( ! [A: $i,B: $i,R: $i] :
% 2.98/1.62 ( ( breln @ A @ B @ R )
% 2.98/1.62 => ! [Xphi: $i > $o] :
% 2.98/1.62 ( ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ! [Xy: $i] :
% 2.98/1.62 ( ( in @ Xy @ B )
% 2.98/1.62 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.98/1.62 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ R )
% 2.98/1.62 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(brelnall2_type,type,
% 2.98/1.62 brelnall2: $o ).
% 2.98/1.62
% 2.98/1.62 thf(brelnall2,definition,
% 2.98/1.62 ( brelnall2
% 2.98/1.62 = ( ! [A: $i,B: $i,R: $i] :
% 2.98/1.62 ( ( breln @ A @ B @ R )
% 2.98/1.62 => ! [Xphi: $i > $o] :
% 2.98/1.62 ( ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ! [Xy: $i] :
% 2.98/1.62 ( ( in @ Xy @ B )
% 2.98/1.62 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.98/1.62 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ R )
% 2.98/1.62 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(ex1E2_type,type,
% 2.98/1.62 ex1E2: $o ).
% 2.98/1.62
% 2.98/1.62 thf(ex1E2,definition,
% 2.98/1.62 ( ex1E2
% 2.98/1.62 = ( ! [A: $i,Xphi: $i > $o] :
% 2.98/1.62 ( ( ex1 @ A
% 2.98/1.62 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ! [Xy: $i] :
% 2.98/1.62 ( ( in @ Xy @ A )
% 2.98/1.62 => ( ( Xphi @ Xx )
% 2.98/1.62 => ( ( Xphi @ Xy )
% 2.98/1.62 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(funcGraphProp1_type,type,
% 2.98/1.62 funcGraphProp1: $o ).
% 2.98/1.62
% 2.98/1.62 thf(funcGraphProp1,definition,
% 2.98/1.62 ( funcGraphProp1
% 2.98/1.62 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.98/1.62 ( ( func @ A @ B @ Xf )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(funcGraphProp3_type,type,
% 2.98/1.62 funcGraphProp3: $o ).
% 2.98/1.62
% 2.98/1.62 thf(funcGraphProp3,definition,
% 2.98/1.62 ( funcGraphProp3
% 2.98/1.62 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.98/1.62 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(funcGraphProp2_type,type,
% 2.98/1.62 funcGraphProp2: $o ).
% 2.98/1.62
% 2.98/1.62 thf(funcGraphProp2,definition,
% 2.98/1.62 ( funcGraphProp2
% 2.98/1.62 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.98/1.62 ( ( func @ A @ B @ Xf )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ! [Xy: $i] :
% 2.98/1.62 ( ( in @ Xy @ B )
% 2.98/1.62 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 2.98/1.62 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.98/1.62 = Xy ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(funcextLem_type,type,
% 2.98/1.62 funcextLem: $o ).
% 2.98/1.62
% 2.98/1.62 thf(funcextLem,definition,
% 2.98/1.62 ( funcextLem
% 2.98/1.62 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.98/1.62 ( ( func @ A @ B @ Xf )
% 2.98/1.62 => ! [Xg: $i] :
% 2.98/1.62 ( ( func @ A @ B @ Xg )
% 2.98/1.62 => ( ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.98/1.62 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ! [Xy: $i] :
% 2.98/1.62 ( ( in @ Xy @ B )
% 2.98/1.62 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 2.98/1.62 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(funcGraphProp4_type,type,
% 2.98/1.62 funcGraphProp4: $o ).
% 2.98/1.62
% 2.98/1.62 thf(funcGraphProp4,definition,
% 2.98/1.62 ( funcGraphProp4
% 2.98/1.62 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.98/1.62 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ! [Xy: $i] :
% 2.98/1.62 ( ( in @ Xy @ B )
% 2.98/1.62 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 2.98/1.62 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.98/1.62 = Xy ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(subbreln_type,type,
% 2.98/1.62 subbreln: $o ).
% 2.98/1.62
% 2.98/1.62 thf(subbreln,definition,
% 2.98/1.62 ( subbreln
% 2.98/1.62 = ( ! [A: $i,B: $i,R: $i] :
% 2.98/1.62 ( ( breln @ A @ B @ R )
% 2.98/1.62 => ! [S: $i] :
% 2.98/1.62 ( ( breln @ A @ B @ S )
% 2.98/1.62 => ( ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ! [Xy: $i] :
% 2.98/1.62 ( ( in @ Xy @ B )
% 2.98/1.62 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.98/1.62 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 2.98/1.62 => ( subset @ R @ S ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(eqbreln_type,type,
% 2.98/1.62 eqbreln: $o ).
% 2.98/1.62
% 2.98/1.62 thf(eqbreln,definition,
% 2.98/1.62 ( eqbreln
% 2.98/1.62 = ( ! [A: $i,B: $i,R: $i] :
% 2.98/1.62 ( ( breln @ A @ B @ R )
% 2.98/1.62 => ! [S: $i] :
% 2.98/1.62 ( ( breln @ A @ B @ S )
% 2.98/1.62 => ( ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ! [Xy: $i] :
% 2.98/1.62 ( ( in @ Xy @ B )
% 2.98/1.62 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.98/1.62 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 2.98/1.62 => ( ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ! [Xy: $i] :
% 2.98/1.62 ( ( in @ Xy @ B )
% 2.98/1.62 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 2.98/1.62 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 2.98/1.62 => ( R = S ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(funcext_type,type,
% 2.98/1.62 funcext: $o ).
% 2.98/1.62
% 2.98/1.62 thf(funcext,definition,
% 2.98/1.62 ( funcext
% 2.98/1.62 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.98/1.62 ( ( func @ A @ B @ Xf )
% 2.98/1.62 => ! [Xg: $i] :
% 2.98/1.62 ( ( func @ A @ B @ Xg )
% 2.98/1.62 => ( ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.98/1.62 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.98/1.62 => ( Xf = Xg ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(funcext2_type,type,
% 2.98/1.62 funcext2: $o ).
% 2.98/1.62
% 2.98/1.62 thf(funcext2,definition,
% 2.98/1.62 ( funcext2
% 2.98/1.62 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.98/1.62 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.98/1.62 => ! [Xg: $i] :
% 2.98/1.62 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 2.98/1.62 => ( ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.98/1.62 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.98/1.62 => ( Xf = Xg ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(ap2apEq1_type,type,
% 2.98/1.62 ap2apEq1: $o ).
% 2.98/1.62
% 2.98/1.62 thf(ap2apEq1,definition,
% 2.98/1.62 ( ap2apEq1
% 2.98/1.62 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.98/1.62 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.98/1.62 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(ap2apEq2_type,type,
% 2.98/1.62 ap2apEq2: $o ).
% 2.98/1.62
% 2.98/1.62 thf(ap2apEq2,definition,
% 2.98/1.62 ( ap2apEq2
% 2.98/1.62 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.98/1.62 ( ( func @ A @ B @ Xf )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.98/1.62 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(beta1_type,type,
% 2.98/1.62 beta1: $o ).
% 2.98/1.62
% 2.98/1.62 thf(beta1,definition,
% 2.98/1.62 ( beta1
% 2.98/1.62 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.98/1.62 ( ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ( ap @ A @ B
% 2.98/1.62 @ ( lam @ A @ B
% 2.98/1.62 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 2.98/1.62 @ Xx )
% 2.98/1.62 = ( Xf @ Xx ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(eta1_type,type,
% 2.98/1.62 eta1: $o ).
% 2.98/1.62
% 2.98/1.62 thf(eta1,definition,
% 2.98/1.62 ( eta1
% 2.98/1.62 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.98/1.62 ( ( func @ A @ B @ Xf )
% 2.98/1.62 => ( ( lam @ A @ B
% 2.98/1.62 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 2.98/1.62 = Xf ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(lam2lamEq_type,type,
% 2.98/1.62 lam2lamEq: $o ).
% 2.98/1.62
% 2.98/1.62 thf(lam2lamEq,definition,
% 2.98/1.62 ( lam2lamEq
% 2.98/1.62 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.98/1.62 ( ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.98/1.62 => ( ( lam @ A @ B
% 2.98/1.62 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 2.98/1.62 = ( lam @ A @ B
% 2.98/1.62 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(beta2_type,type,
% 2.98/1.62 beta2: $o ).
% 2.98/1.62
% 2.98/1.62 thf(beta2,definition,
% 2.98/1.62 ( beta2
% 2.98/1.62 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.98/1.62 ( ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ( ap @ A @ B
% 2.98/1.62 @ ( lam @ A @ B
% 2.98/1.62 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 2.98/1.62 @ Xx )
% 2.98/1.62 = ( Xf @ Xx ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(eta2_type,type,
% 2.98/1.62 eta2: $o ).
% 2.98/1.62
% 2.98/1.62 thf(eta2,definition,
% 2.98/1.62 ( eta2
% 2.98/1.62 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.98/1.62 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.98/1.62 => ( ( lam @ A @ B
% 2.98/1.62 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 2.98/1.62 = Xf ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(iffalseProp1_type,type,
% 2.98/1.62 iffalseProp1: $o ).
% 2.98/1.62
% 2.98/1.62 thf(iffalseProp1,definition,
% 2.98/1.62 ( iffalseProp1
% 2.98/1.62 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ! [Xy: $i] :
% 2.98/1.62 ( ( in @ Xy @ A )
% 2.98/1.62 => ( ~ Xphi
% 2.98/1.62 => ( in @ Xy
% 2.98/1.62 @ ( dsetconstr @ A
% 2.98/1.62 @ ^ [Xz: $i] :
% 2.98/1.62 ( ( Xphi
% 2.98/1.62 & ( Xz = Xx ) )
% 2.98/1.62 | ( ~ Xphi
% 2.98/1.62 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(iffalseProp2_type,type,
% 2.98/1.62 iffalseProp2: $o ).
% 2.98/1.62
% 2.98/1.62 thf(iffalseProp2,definition,
% 2.98/1.62 ( iffalseProp2
% 2.98/1.62 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ! [Xy: $i] :
% 2.98/1.62 ( ( in @ Xy @ A )
% 2.98/1.62 => ( ~ Xphi
% 2.98/1.62 => ( ( dsetconstr @ A
% 2.98/1.62 @ ^ [Xz: $i] :
% 2.98/1.62 ( ( Xphi
% 2.98/1.62 & ( Xz = Xx ) )
% 2.98/1.62 | ( ~ Xphi
% 2.98/1.62 & ( Xz = Xy ) ) ) )
% 2.98/1.62 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(iftrueProp1_type,type,
% 2.98/1.62 iftrueProp1: $o ).
% 2.98/1.62
% 2.98/1.62 thf(iftrueProp1,definition,
% 2.98/1.62 ( iftrueProp1
% 2.98/1.62 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ! [Xy: $i] :
% 2.98/1.62 ( ( in @ Xy @ A )
% 2.98/1.62 => ( Xphi
% 2.98/1.62 => ( in @ Xx
% 2.98/1.62 @ ( dsetconstr @ A
% 2.98/1.62 @ ^ [Xz: $i] :
% 2.98/1.62 ( ( Xphi
% 2.98/1.62 & ( Xz = Xx ) )
% 2.98/1.62 | ( ~ Xphi
% 2.98/1.62 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(iftrueProp2_type,type,
% 2.98/1.62 iftrueProp2: $o ).
% 2.98/1.62
% 2.98/1.62 thf(iftrueProp2,definition,
% 2.98/1.62 ( iftrueProp2
% 2.98/1.62 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ! [Xy: $i] :
% 2.98/1.62 ( ( in @ Xy @ A )
% 2.98/1.62 => ( Xphi
% 2.98/1.62 => ( ( dsetconstr @ A
% 2.98/1.62 @ ^ [Xz: $i] :
% 2.98/1.62 ( ( Xphi
% 2.98/1.62 & ( Xz = Xx ) )
% 2.98/1.62 | ( ~ Xphi
% 2.98/1.62 & ( Xz = Xy ) ) ) )
% 2.98/1.62 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(ifSingleton_type,type,
% 2.98/1.62 ifSingleton: $o ).
% 2.98/1.62
% 2.98/1.62 thf(ifSingleton,definition,
% 2.98/1.62 ( ifSingleton
% 2.98/1.62 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ! [Xy: $i] :
% 2.98/1.62 ( ( in @ Xy @ A )
% 2.98/1.62 => ( singleton
% 2.98/1.62 @ ( dsetconstr @ A
% 2.98/1.62 @ ^ [Xz: $i] :
% 2.98/1.62 ( ( Xphi
% 2.98/1.62 & ( Xz = Xx ) )
% 2.98/1.62 | ( ~ Xphi
% 2.98/1.62 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(if_type,type,
% 2.98/1.62 if: $i > $o > $i > $i > $i ).
% 2.98/1.62
% 2.98/1.62 thf(ifp_type,type,
% 2.98/1.62 ifp: $o ).
% 2.98/1.62
% 2.98/1.62 thf(ifp,definition,
% 2.98/1.62 ( ifp
% 2.98/1.62 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ! [Xy: $i] :
% 2.98/1.62 ( ( in @ Xy @ A )
% 2.98/1.62 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(theeq_type,type,
% 2.98/1.62 theeq: $o ).
% 2.98/1.62
% 2.98/1.62 thf(theeq,definition,
% 2.98/1.62 ( theeq
% 2.98/1.62 = ( ! [X: $i] :
% 2.98/1.62 ( ( singleton @ X )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ X )
% 2.98/1.62 => ( ( setunion @ X )
% 2.98/1.62 = Xx ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(iftrue_type,type,
% 2.98/1.62 iftrue: $o ).
% 2.98/1.62
% 2.98/1.62 thf(iftrue,definition,
% 2.98/1.62 ( iftrue
% 2.98/1.62 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ! [Xy: $i] :
% 2.98/1.62 ( ( in @ Xy @ A )
% 2.98/1.62 => ( Xphi
% 2.98/1.62 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 2.98/1.62 = Xx ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(iffalse_type,type,
% 2.98/1.62 iffalse: $o ).
% 2.98/1.62
% 2.98/1.62 thf(iffalse,definition,
% 2.98/1.62 ( iffalse
% 2.98/1.62 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ! [Xy: $i] :
% 2.98/1.62 ( ( in @ Xy @ A )
% 2.98/1.62 => ( ~ Xphi
% 2.98/1.62 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 2.98/1.62 = Xy ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(iftrueorfalse_type,type,
% 2.98/1.62 iftrueorfalse: $o ).
% 2.98/1.62
% 2.98/1.62 thf(iftrueorfalse,definition,
% 2.98/1.62 ( iftrueorfalse
% 2.98/1.62 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ! [Xy: $i] :
% 2.98/1.62 ( ( in @ Xy @ A )
% 2.98/1.62 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(binintersectT_lem_type,type,
% 2.98/1.62 binintersectT_lem: $o ).
% 2.98/1.62
% 2.98/1.62 thf(binintersectT_lem,definition,
% 2.98/1.62 ( binintersectT_lem
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(binunionT_lem_type,type,
% 2.98/1.62 binunionT_lem: $o ).
% 2.98/1.62
% 2.98/1.62 thf(binunionT_lem,definition,
% 2.98/1.62 ( binunionT_lem
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(powersetT_lem_type,type,
% 2.98/1.62 powersetT_lem: $o ).
% 2.98/1.62
% 2.98/1.62 thf(powersetT_lem,definition,
% 2.98/1.62 ( powersetT_lem
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(setminusT_lem_type,type,
% 2.98/1.62 setminusT_lem: $o ).
% 2.98/1.62
% 2.98/1.62 thf(setminusT_lem,definition,
% 2.98/1.62 ( setminusT_lem
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(complementT_lem_type,type,
% 2.98/1.62 complementT_lem: $o ).
% 2.98/1.62
% 2.98/1.62 thf(complementT_lem,definition,
% 2.98/1.62 ( complementT_lem
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(setextT_type,type,
% 2.98/1.62 setextT: $o ).
% 2.98/1.62
% 2.98/1.62 thf(setextT,definition,
% 2.98/1.62 ( setextT
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ( ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ( in @ Xx @ X )
% 2.98/1.62 => ( in @ Xx @ Y ) ) )
% 2.98/1.62 => ( ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ( in @ Xx @ Y )
% 2.98/1.62 => ( in @ Xx @ X ) ) )
% 2.98/1.62 => ( X = Y ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(subsetTI_type,type,
% 2.98/1.62 subsetTI: $o ).
% 2.98/1.62
% 2.98/1.62 thf(subsetTI,definition,
% 2.98/1.62 ( subsetTI
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ( ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ( in @ Xx @ X )
% 2.98/1.62 => ( in @ Xx @ Y ) ) )
% 2.98/1.62 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(powersetTI1_type,type,
% 2.98/1.62 powersetTI1: $o ).
% 2.98/1.62
% 2.98/1.62 thf(powersetTI1,definition,
% 2.98/1.62 ( powersetTI1
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ( ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ( in @ Xx @ X )
% 2.98/1.62 => ( in @ Xx @ Y ) ) )
% 2.98/1.62 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(powersetTE1_type,type,
% 2.98/1.62 powersetTE1: $o ).
% 2.98/1.62
% 2.98/1.62 thf(powersetTE1,definition,
% 2.98/1.62 ( powersetTE1
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ( in @ X @ ( powerset @ Y ) )
% 2.98/1.62 => ( ( in @ Xx @ X )
% 2.98/1.62 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(complementTI1_type,type,
% 2.98/1.62 complementTI1: $o ).
% 2.98/1.62
% 2.98/1.62 thf(complementTI1,definition,
% 2.98/1.62 ( complementTI1
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ( in @ Xx @ X )
% 2.98/1.62 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(complementTE1_type,type,
% 2.98/1.62 complementTE1: $o ).
% 2.98/1.62
% 2.98/1.62 thf(complementTE1,definition,
% 2.98/1.62 ( complementTE1
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 2.98/1.62 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(binintersectTELcontra_type,type,
% 2.98/1.62 binintersectTELcontra: $o ).
% 2.98/1.62
% 2.98/1.62 thf(binintersectTELcontra,definition,
% 2.98/1.62 ( binintersectTELcontra
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ~ ( in @ Xx @ X )
% 2.98/1.62 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(binintersectTERcontra_type,type,
% 2.98/1.62 binintersectTERcontra: $o ).
% 2.98/1.62
% 2.98/1.62 thf(binintersectTERcontra,definition,
% 2.98/1.62 ( binintersectTERcontra
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ~ ( in @ Xx @ Y )
% 2.98/1.62 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(contrasubsetT_type,type,
% 2.98/1.62 contrasubsetT: $o ).
% 2.98/1.62
% 2.98/1.62 thf(contrasubsetT,definition,
% 2.98/1.62 ( contrasubsetT
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 2.98/1.62 => ( ( in @ Xx @ Y )
% 2.98/1.62 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(contrasubsetT1_type,type,
% 2.98/1.62 contrasubsetT1: $o ).
% 2.98/1.62
% 2.98/1.62 thf(contrasubsetT1,definition,
% 2.98/1.62 ( contrasubsetT1
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ( subset @ X @ Y )
% 2.98/1.62 => ( ~ ( in @ Xx @ Y )
% 2.98/1.62 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(contrasubsetT2_type,type,
% 2.98/1.62 contrasubsetT2: $o ).
% 2.98/1.62
% 2.98/1.62 thf(contrasubsetT2,definition,
% 2.98/1.62 ( contrasubsetT2
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ( ( subset @ X @ Y )
% 2.98/1.62 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(contrasubsetT3_type,type,
% 2.98/1.62 contrasubsetT3: $o ).
% 2.98/1.62
% 2.98/1.62 thf(contrasubsetT3,definition,
% 2.98/1.62 ( contrasubsetT3
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 2.98/1.62 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(doubleComplementI1_type,type,
% 2.98/1.62 doubleComplementI1: $o ).
% 2.98/1.62
% 2.98/1.62 thf(doubleComplementI1,definition,
% 2.98/1.62 ( doubleComplementI1
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ( in @ Xx @ X )
% 2.98/1.62 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(doubleComplementE1_type,type,
% 2.98/1.62 doubleComplementE1: $o ).
% 2.98/1.62
% 2.98/1.62 thf(doubleComplementE1,definition,
% 2.98/1.62 ( doubleComplementE1
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 2.98/1.62 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(doubleComplementSub1_type,type,
% 2.98/1.62 doubleComplementSub1: $o ).
% 2.98/1.62
% 2.98/1.62 thf(doubleComplementSub1,definition,
% 2.98/1.62 ( doubleComplementSub1
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(doubleComplementSub2_type,type,
% 2.98/1.62 doubleComplementSub2: $o ).
% 2.98/1.62
% 2.98/1.62 thf(doubleComplementSub2,definition,
% 2.98/1.62 ( doubleComplementSub2
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(doubleComplementEq_type,type,
% 2.98/1.62 doubleComplementEq: $o ).
% 2.98/1.62
% 2.98/1.62 thf(doubleComplementEq,definition,
% 2.98/1.62 ( doubleComplementEq
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ( X
% 2.98/1.62 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(complementTnotintersectT_type,type,
% 2.98/1.62 complementTnotintersectT: $o ).
% 2.98/1.62
% 2.98/1.62 thf(complementTnotintersectT,definition,
% 2.98/1.62 ( complementTnotintersectT
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 2.98/1.62 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(complementImpComplementIntersect_type,type,
% 2.98/1.62 complementImpComplementIntersect: $o ).
% 2.98/1.62
% 2.98/1.62 thf(complementImpComplementIntersect,definition,
% 2.98/1.62 ( complementImpComplementIntersect
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 2.98/1.62 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(complementSubsetComplementIntersect_type,type,
% 2.98/1.62 complementSubsetComplementIntersect: $o ).
% 2.98/1.62
% 2.98/1.62 thf(complementSubsetComplementIntersect,definition,
% 2.98/1.62 ( complementSubsetComplementIntersect
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(complementInPowersetComplementIntersect_type,type,
% 2.98/1.62 complementInPowersetComplementIntersect: $o ).
% 2.98/1.62
% 2.98/1.62 thf(complementInPowersetComplementIntersect,definition,
% 2.98/1.62 ( complementInPowersetComplementIntersect
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(contraSubsetComplement_type,type,
% 2.98/1.62 contraSubsetComplement: $o ).
% 2.98/1.62
% 2.98/1.62 thf(contraSubsetComplement,definition,
% 2.98/1.62 ( contraSubsetComplement
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ( in @ Xx @ Y )
% 2.98/1.62 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(complementTcontraSubset_type,type,
% 2.98/1.62 complementTcontraSubset: $o ).
% 2.98/1.62
% 2.98/1.62 thf(complementTcontraSubset,definition,
% 2.98/1.62 ( complementTcontraSubset
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 2.98/1.62 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(binunionTILcontra_type,type,
% 2.98/1.62 binunionTILcontra: $o ).
% 2.98/1.62
% 2.98/1.62 thf(binunionTILcontra,definition,
% 2.98/1.62 ( binunionTILcontra
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 2.98/1.62 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(binunionTIRcontra_type,type,
% 2.98/1.62 binunionTIRcontra: $o ).
% 2.98/1.62
% 2.98/1.62 thf(binunionTIRcontra,definition,
% 2.98/1.62 ( binunionTIRcontra
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 2.98/1.62 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(inIntersectImpInUnion_type,type,
% 2.98/1.62 inIntersectImpInUnion: $o ).
% 2.98/1.62
% 2.98/1.62 thf(inIntersectImpInUnion,definition,
% 2.98/1.62 ( inIntersectImpInUnion
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ! [Z: $i] :
% 2.98/1.62 ( ( in @ Z @ ( powerset @ A ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 2.98/1.62 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(inIntersectImpInUnion2_type,type,
% 2.98/1.62 inIntersectImpInUnion2: $o ).
% 2.98/1.62
% 2.98/1.62 thf(inIntersectImpInUnion2,definition,
% 2.98/1.62 ( inIntersectImpInUnion2
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ! [Z: $i] :
% 2.98/1.62 ( ( in @ Z @ ( powerset @ A ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 2.98/1.62 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(inIntersectImpInIntersectUnions_type,type,
% 2.98/1.62 inIntersectImpInIntersectUnions: $o ).
% 2.98/1.62
% 2.98/1.62 thf(inIntersectImpInIntersectUnions,definition,
% 2.98/1.62 ( inIntersectImpInIntersectUnions
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ! [Z: $i] :
% 2.98/1.62 ( ( in @ Z @ ( powerset @ A ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 2.98/1.62 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(intersectInPowersetIntersectUnions_type,type,
% 2.98/1.62 intersectInPowersetIntersectUnions: $o ).
% 2.98/1.62
% 2.98/1.62 thf(intersectInPowersetIntersectUnions,definition,
% 2.98/1.62 ( intersectInPowersetIntersectUnions
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ! [Z: $i] :
% 2.98/1.62 ( ( in @ Z @ ( powerset @ A ) )
% 2.98/1.62 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(inComplementUnionImpNotIn1_type,type,
% 2.98/1.62 inComplementUnionImpNotIn1: $o ).
% 2.98/1.62
% 2.98/1.62 thf(inComplementUnionImpNotIn1,definition,
% 2.98/1.62 ( inComplementUnionImpNotIn1
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.98/1.62 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(inComplementUnionImpInComplement1_type,type,
% 2.98/1.62 inComplementUnionImpInComplement1: $o ).
% 2.98/1.62
% 2.98/1.62 thf(inComplementUnionImpInComplement1,definition,
% 2.98/1.62 ( inComplementUnionImpInComplement1
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.98/1.62 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(binunionTE_type,type,
% 2.98/1.62 binunionTE: $o ).
% 2.98/1.62
% 2.98/1.62 thf(binunionTE,definition,
% 2.98/1.62 ( binunionTE
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ! [Xphi: $o,Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 2.98/1.62 => ( ( ( in @ Xx @ X )
% 2.98/1.62 => Xphi )
% 2.98/1.62 => ( ( ( in @ Xx @ Y )
% 2.98/1.62 => Xphi )
% 2.98/1.62 => Xphi ) ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(binunionTEcontra_type,type,
% 2.98/1.62 binunionTEcontra: $o ).
% 2.98/1.62
% 2.98/1.62 thf(binunionTEcontra,definition,
% 2.98/1.62 ( binunionTEcontra
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ~ ( in @ Xx @ X )
% 2.98/1.62 => ( ~ ( in @ Xx @ Y )
% 2.98/1.62 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(demorgan2a1_type,type,
% 2.98/1.62 demorgan2a1: $o ).
% 2.98/1.62
% 2.98/1.62 thf(demorgan2a1,definition,
% 2.98/1.62 ( demorgan2a1
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.98/1.62 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(complementUnionInPowersetComplement_type,type,
% 2.98/1.62 complementUnionInPowersetComplement: $o ).
% 2.98/1.62
% 2.98/1.62 thf(complementUnionInPowersetComplement,definition,
% 2.98/1.62 ( complementUnionInPowersetComplement
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(demorgan2a2_type,type,
% 2.98/1.62 demorgan2a2: $o ).
% 2.98/1.62
% 2.98/1.62 thf(demorgan2a2,definition,
% 2.98/1.62 ( demorgan2a2
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.98/1.62 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(demorgan1a_type,type,
% 2.98/1.62 demorgan1a: $o ).
% 2.98/1.62
% 2.98/1.62 thf(demorgan1a,definition,
% 2.98/1.62 ( demorgan1a
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 2.98/1.62 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(demorgan1b_type,type,
% 2.98/1.62 demorgan1b: $o ).
% 2.98/1.62
% 2.98/1.62 thf(demorgan1b,definition,
% 2.98/1.62 ( demorgan1b
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 2.98/1.62 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(demorgan1_type,type,
% 2.98/1.62 demorgan1: $o ).
% 2.98/1.62
% 2.98/1.62 thf(demorgan1,definition,
% 2.98/1.62 ( demorgan1
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 2.98/1.62 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(demorgan2a_type,type,
% 2.98/1.62 demorgan2a: $o ).
% 2.98/1.62
% 2.98/1.62 thf(demorgan2a,definition,
% 2.98/1.62 ( demorgan2a
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 2.98/1.62 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(demorgan2b2_type,type,
% 2.98/1.62 demorgan2b2: $o ).
% 2.98/1.62
% 2.98/1.62 thf(demorgan2b2,definition,
% 2.98/1.62 ( demorgan2b2
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 2.98/1.62 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 2.98/1.62 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(demorgan2b_type,type,
% 2.98/1.62 demorgan2b: $o ).
% 2.98/1.62
% 2.98/1.62 thf(demorgan2b,definition,
% 2.98/1.62 ( demorgan2b
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ A )
% 2.98/1.62 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 2.98/1.62 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(demorgan2_type,type,
% 2.98/1.62 demorgan2: $o ).
% 2.98/1.62
% 2.98/1.62 thf(demorgan2,definition,
% 2.98/1.62 ( demorgan2
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 2.98/1.62 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(woz13rule0_type,type,
% 2.98/1.62 woz13rule0: $o ).
% 2.98/1.62
% 2.98/1.62 thf(woz13rule0,definition,
% 2.98/1.62 ( woz13rule0
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ! [Xx: $i] :
% 2.98/1.62 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 2.98/1.62 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(woz13rule1_type,type,
% 2.98/1.62 woz13rule1: $o ).
% 2.98/1.62
% 2.98/1.62 thf(woz13rule1,definition,
% 2.98/1.62 ( woz13rule1
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ! [Z: $i] :
% 2.98/1.62 ( ( in @ Z @ ( powerset @ A ) )
% 2.98/1.62 => ( ( subset @ X @ Z )
% 2.98/1.62 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(woz13rule2_type,type,
% 2.98/1.62 woz13rule2: $o ).
% 2.98/1.62
% 2.98/1.62 thf(woz13rule2,definition,
% 2.98/1.62 ( woz13rule2
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ! [Z: $i] :
% 2.98/1.62 ( ( in @ Z @ ( powerset @ A ) )
% 2.98/1.62 => ( ( subset @ Y @ Z )
% 2.98/1.62 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(woz13rule3_type,type,
% 2.98/1.62 woz13rule3: $o ).
% 2.98/1.62
% 2.98/1.62 thf(woz13rule3,definition,
% 2.98/1.62 ( woz13rule3
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ! [Z: $i] :
% 2.98/1.62 ( ( in @ Z @ ( powerset @ A ) )
% 2.98/1.62 => ( ( subset @ X @ Y )
% 2.98/1.62 => ( ( subset @ X @ Z )
% 2.98/1.62 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(woz13rule4_type,type,
% 2.98/1.62 woz13rule4: $o ).
% 2.98/1.62
% 2.98/1.62 thf(woz13rule4,definition,
% 2.98/1.62 ( woz13rule4
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ! [Z: $i] :
% 2.98/1.62 ( ( in @ Z @ ( powerset @ A ) )
% 2.98/1.62 => ! [W: $i] :
% 2.98/1.62 ( ( in @ W @ ( powerset @ A ) )
% 2.98/1.62 => ( ( subset @ X @ Z )
% 2.98/1.62 => ( ( subset @ Y @ W )
% 2.98/1.62 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(woz1_1_type,type,
% 2.98/1.62 woz1_1: $o ).
% 2.98/1.62
% 2.98/1.62 thf(woz1_1,definition,
% 2.98/1.62 ( woz1_1
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(woz1_2_type,type,
% 2.98/1.62 woz1_2: $o ).
% 2.98/1.62
% 2.98/1.62 thf(woz1_2,definition,
% 2.98/1.62 ( woz1_2
% 2.98/1.62 = ( ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ! [Z: $i] :
% 2.98/1.62 ( ( in @ Z @ ( powerset @ A ) )
% 2.98/1.62 => ! [W: $i] :
% 2.98/1.62 ( ( in @ W @ ( powerset @ A ) )
% 2.98/1.62 => ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
% 2.98/1.62 = ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ) ).
% 2.98/1.62
% 2.98/1.62 thf(woz1_3,conjecture,
% 2.98/1.62 ( setextAx
% 2.98/1.62 => ( emptysetAx
% 2.98/1.62 => ( setadjoinAx
% 2.98/1.62 => ( powersetAx
% 2.98/1.62 => ( setunionAx
% 2.98/1.62 => ( omega0Ax
% 2.98/1.62 => ( omegaSAx
% 2.98/1.62 => ( omegaIndAx
% 2.98/1.62 => ( replAx
% 2.98/1.62 => ( foundationAx
% 2.98/1.62 => ( wellorderingAx
% 2.98/1.62 => ( descrp
% 2.98/1.62 => ( dsetconstrI
% 2.98/1.62 => ( dsetconstrEL
% 2.98/1.62 => ( dsetconstrER
% 2.98/1.62 => ( exuE1
% 2.98/1.62 => ( prop2setE
% 2.98/1.62 => ( emptysetE
% 2.98/1.62 => ( emptysetimpfalse
% 2.98/1.62 => ( notinemptyset
% 2.98/1.62 => ( exuE3e
% 2.98/1.62 => ( setext
% 2.98/1.62 => ( emptyI
% 2.98/1.62 => ( noeltsimpempty
% 2.98/1.62 => ( setbeta
% 2.98/1.62 => ( nonemptyE1
% 2.98/1.62 => ( nonemptyI
% 2.98/1.62 => ( nonemptyI1
% 2.98/1.62 => ( setadjoinIL
% 2.98/1.62 => ( emptyinunitempty
% 2.98/1.62 => ( setadjoinIR
% 2.98/1.62 => ( setadjoinE
% 2.98/1.62 => ( setadjoinOr
% 2.98/1.62 => ( setoftrueEq
% 2.98/1.62 => ( powersetI
% 2.98/1.62 => ( emptyinPowerset
% 2.98/1.62 => ( emptyInPowerset
% 2.98/1.62 => ( powersetE
% 2.98/1.62 => ( setunionI
% 2.98/1.62 => ( setunionE
% 2.98/1.62 => ( subPowSU
% 2.98/1.62 => ( exuE2
% 2.98/1.62 => ( nonemptyImpWitness
% 2.98/1.62 => ( uniqinunit
% 2.98/1.62 => ( notinsingleton
% 2.98/1.62 => ( eqinunit
% 2.98/1.62 => ( singletonsswitch
% 2.98/1.62 => ( upairsetE
% 2.98/1.62 => ( upairsetIL
% 2.98/1.62 => ( upairsetIR
% 2.98/1.62 => ( emptyE1
% 2.98/1.62 => ( vacuousDall
% 2.98/1.62 => ( quantDeMorgan1
% 2.98/1.62 => ( quantDeMorgan2
% 2.98/1.62 => ( quantDeMorgan3
% 2.98/1.62 => ( quantDeMorgan4
% 2.98/1.62 => ( prop2setI
% 2.98/1.62 => ( prop2set2propI
% 2.98/1.62 => ( notdexE
% 2.98/1.62 => ( notdallE
% 2.98/1.62 => ( exuI1
% 2.98/1.62 => ( exuI3
% 2.98/1.62 => ( exuI2
% 2.98/1.62 => ( inCongP
% 2.98/1.62 => ( in__Cong
% 2.98/1.62 => ( exuE3u
% 2.98/1.62 => ( exu__Cong
% 2.98/1.62 => ( emptyset__Cong
% 2.98/1.62 => ( setadjoin__Cong
% 2.98/1.62 => ( powerset__Cong
% 2.98/1.62 => ( setunion__Cong
% 2.98/1.62 => ( omega__Cong
% 2.98/1.62 => ( exuEu
% 2.98/1.62 => ( descr__Cong
% 2.98/1.62 => ( dsetconstr__Cong
% 2.98/1.62 => ( subsetI1
% 2.98/1.62 => ( eqimpsubset2
% 2.98/1.62 => ( eqimpsubset1
% 2.98/1.62 => ( subsetI2
% 2.98/1.62 => ( emptysetsubset
% 2.98/1.62 => ( subsetE
% 2.98/1.62 => ( subsetE2
% 2.98/1.62 => ( notsubsetI
% 2.98/1.62 => ( notequalI1
% 2.98/1.62 => ( notequalI2
% 2.98/1.62 => ( subsetRefl
% 2.98/1.62 => ( subsetTrans
% 2.98/1.62 => ( setadjoinSub
% 2.98/1.62 => ( setadjoinSub2
% 2.98/1.62 => ( subset2powerset
% 2.98/1.62 => ( setextsub
% 2.98/1.62 => ( subsetemptysetimpeq
% 2.98/1.62 => ( powersetI1
% 2.98/1.62 => ( powersetE1
% 2.98/1.62 => ( inPowerset
% 2.98/1.62 => ( powersetsubset
% 2.98/1.62 => ( sepInPowerset
% 2.98/1.62 => ( sepSubset
% 2.98/1.62 => ( binunionIL
% 2.98/1.62 => ( upairset2IR
% 2.98/1.62 => ( binunionIR
% 2.98/1.62 => ( binunionEcases
% 2.98/1.62 => ( binunionE
% 2.98/1.62 => ( binunionLsub
% 2.98/1.62 => ( binunionRsub
% 2.98/1.62 => ( binintersectI
% 2.98/1.62 => ( binintersectSubset5
% 2.98/1.62 => ( binintersectEL
% 2.98/1.62 => ( binintersectLsub
% 2.98/1.62 => ( binintersectSubset2
% 2.98/1.62 => ( binintersectSubset3
% 2.98/1.62 => ( binintersectER
% 2.98/1.62 => ( disjointsetsI1
% 2.98/1.62 => ( binintersectRsub
% 2.98/1.62 => ( binintersectSubset4
% 2.98/1.62 => ( binintersectSubset1
% 2.98/1.62 => ( bs114d
% 2.98/1.62 => ( setminusI
% 2.98/1.62 => ( setminusEL
% 2.98/1.62 => ( setminusER
% 2.98/1.62 => ( setminusSubset2
% 2.98/1.62 => ( setminusERneg
% 2.98/1.62 => ( setminusELneg
% 2.98/1.62 => ( setminusILneg
% 2.98/1.62 => ( setminusIRneg
% 2.98/1.62 => ( setminusLsub
% 2.98/1.62 => ( setminusSubset1
% 2.98/1.62 => ( symdiffE
% 2.98/1.62 => ( symdiffI1
% 2.98/1.62 => ( symdiffI2
% 2.98/1.62 => ( symdiffIneg1
% 2.98/1.62 => ( symdiffIneg2
% 2.98/1.62 => ( secondinupair
% 2.98/1.62 => ( setukpairIL
% 2.98/1.62 => ( setukpairIR
% 2.98/1.62 => ( kpairiskpair
% 2.98/1.62 => ( kpairp
% 2.98/1.62 => ( singletonsubset
% 2.98/1.62 => ( singletoninpowerset
% 2.98/1.62 => ( singletoninpowunion
% 2.98/1.62 => ( upairset2E
% 2.98/1.62 => ( upairsubunion
% 2.98/1.62 => ( upairinpowunion
% 2.98/1.62 => ( ubforcartprodlem1
% 2.98/1.62 => ( ubforcartprodlem2
% 2.98/1.62 => ( ubforcartprodlem3
% 2.98/1.62 => ( cartprodpairin
% 2.98/1.62 => ( cartprodmempair1
% 2.98/1.62 => ( cartprodmempair
% 2.98/1.62 => ( setunionE2
% 2.98/1.62 => ( setunionsingleton1
% 2.98/1.62 => ( setunionsingleton2
% 2.98/1.62 => ( setunionsingleton
% 2.98/1.62 => ( singletonprop
% 2.98/1.62 => ( ex1E1
% 2.98/1.62 => ( ex1I
% 2.98/1.62 => ( ex1I2
% 2.98/1.62 => ( singletonsuniq
% 2.98/1.62 => ( setukpairinjL1
% 2.98/1.62 => ( kfstsingleton
% 2.98/1.62 => ( theprop
% 2.98/1.62 => ( kfstpairEq
% 2.98/1.62 => ( cartprodfstin
% 2.98/1.62 => ( setukpairinjL2
% 2.98/1.62 => ( setukpairinjL
% 2.98/1.62 => ( setukpairinjR11
% 2.98/1.62 => ( setukpairinjR12
% 2.98/1.62 => ( setukpairinjR1
% 2.98/1.62 => ( upairequniteq
% 2.98/1.62 => ( setukpairinjR2
% 2.98/1.62 => ( setukpairinjR
% 2.98/1.62 => ( ksndsingleton
% 2.98/1.62 => ( ksndpairEq
% 2.98/1.62 => ( kpairsurjEq
% 2.98/1.62 => ( cartprodsndin
% 2.98/1.62 => ( cartprodpairmemEL
% 2.98/1.62 => ( cartprodpairmemER
% 2.98/1.62 => ( cartprodmempaircEq
% 2.98/1.62 => ( cartprodfstpairEq
% 2.98/1.62 => ( cartprodsndpairEq
% 2.98/1.62 => ( cartprodpairsurjEq
% 2.98/1.62 => ( dpsetconstrI
% 2.98/1.62 => ( dpsetconstrSub
% 2.98/1.62 => ( setOfPairsIsBReln
% 2.98/1.62 => ( dpsetconstrERa
% 2.98/1.62 => ( dpsetconstrEL1
% 2.98/1.62 => ( dpsetconstrEL2
% 2.98/1.62 => ( dpsetconstrER
% 2.98/1.62 => ( funcImageSingleton
% 2.98/1.62 => ( apProp
% 2.98/1.62 => ( app
% 2.98/1.62 => ( infuncsetfunc
% 2.98/1.62 => ( ap2p
% 2.98/1.62 => ( funcinfuncset
% 2.98/1.62 => ( lamProp
% 2.98/1.62 => ( lamp
% 2.98/1.62 => ( lam2p
% 2.98/1.62 => ( brelnall1
% 2.98/1.62 => ( brelnall2
% 2.98/1.62 => ( ex1E2
% 2.98/1.62 => ( funcGraphProp1
% 2.98/1.62 => ( funcGraphProp3
% 2.98/1.62 => ( funcGraphProp2
% 2.98/1.62 => ( funcextLem
% 2.98/1.62 => ( funcGraphProp4
% 2.98/1.62 => ( subbreln
% 2.98/1.62 => ( eqbreln
% 2.98/1.62 => ( funcext
% 2.98/1.62 => ( funcext2
% 2.98/1.62 => ( ap2apEq1
% 2.98/1.62 => ( ap2apEq2
% 2.98/1.62 => ( beta1
% 2.98/1.62 => ( eta1
% 2.98/1.62 => ( lam2lamEq
% 2.98/1.62 => ( beta2
% 2.98/1.62 => ( eta2
% 2.98/1.62 => ( iffalseProp1
% 2.98/1.62 => ( iffalseProp2
% 2.98/1.62 => ( iftrueProp1
% 2.98/1.62 => ( iftrueProp2
% 2.98/1.62 => ( ifSingleton
% 2.98/1.62 => ( ifp
% 2.98/1.62 => ( theeq
% 2.98/1.62 => ( iftrue
% 2.98/1.62 => ( iffalse
% 2.98/1.62 => ( iftrueorfalse
% 2.98/1.62 => ( binintersectT_lem
% 2.98/1.62 => ( binunionT_lem
% 2.98/1.62 => ( powersetT_lem
% 2.98/1.62 => ( setminusT_lem
% 2.98/1.62 => ( complementT_lem
% 2.98/1.62 => ( setextT
% 2.98/1.62 => ( subsetTI
% 2.98/1.62 => ( powersetTI1
% 2.98/1.62 => ( powersetTE1
% 2.98/1.62 => ( complementTI1
% 2.98/1.62 => ( complementTE1
% 2.98/1.62 => ( binintersectTELcontra
% 2.98/1.62 => ( binintersectTERcontra
% 2.98/1.62 => ( contrasubsetT
% 2.98/1.62 => ( contrasubsetT1
% 2.98/1.62 => ( contrasubsetT2
% 2.98/1.62 => ( contrasubsetT3
% 2.98/1.62 => ( doubleComplementI1
% 2.98/1.62 => ( doubleComplementE1
% 2.98/1.62 => ( doubleComplementSub1
% 2.98/1.62 => ( doubleComplementSub2
% 2.98/1.62 => ( doubleComplementEq
% 2.98/1.62 => ( complementTnotintersectT
% 2.98/1.62 => ( complementImpComplementIntersect
% 2.98/1.62 => ( complementSubsetComplementIntersect
% 2.98/1.62 => ( complementInPowersetComplementIntersect
% 2.98/1.62 => ( contraSubsetComplement
% 2.98/1.62 => ( complementTcontraSubset
% 2.98/1.62 => ( binunionTILcontra
% 2.98/1.62 => ( binunionTIRcontra
% 2.98/1.62 => ( inIntersectImpInUnion
% 2.98/1.62 => ( inIntersectImpInUnion2
% 2.98/1.62 => ( inIntersectImpInIntersectUnions
% 2.98/1.62 => ( intersectInPowersetIntersectUnions
% 2.98/1.62 => ( inComplementUnionImpNotIn1
% 2.98/1.62 => ( inComplementUnionImpInComplement1
% 2.98/1.62 => ( binunionTE
% 2.98/1.62 => ( binunionTEcontra
% 2.98/1.62 => ( demorgan2a1
% 2.98/1.62 => ( complementUnionInPowersetComplement
% 2.98/1.62 => ( demorgan2a2
% 2.98/1.62 => ( demorgan1a
% 2.98/1.62 => ( demorgan1b
% 2.98/1.62 => ( demorgan1
% 2.98/1.62 => ( demorgan2a
% 2.98/1.62 => ( demorgan2b2
% 2.98/1.62 => ( demorgan2b
% 2.98/1.62 => ( demorgan2
% 2.98/1.62 => ( woz13rule0
% 2.98/1.62 => ( woz13rule1
% 2.98/1.62 => ( woz13rule2
% 2.98/1.62 => ( woz13rule3
% 2.98/1.62 => ( woz13rule4
% 2.98/1.62 => ( woz1_1
% 2.98/1.62 => ( woz1_2
% 2.98/1.62 => ! [A: $i,X: $i] :
% 2.98/1.62 ( ( in @ X @ ( powerset @ A ) )
% 2.98/1.62 => ! [Y: $i] :
% 2.98/1.62 ( ( in @ Y @ ( powerset @ A ) )
% 2.98/1.62 => ! [Z: $i] :
% 2.98/1.62 ( ( in @ Z @ ( powerset @ A ) )
% 2.98/1.62 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.98/1.62 ------------------------
% 2.98/1.65 % (31092)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_30813 for (2999ds/27Mi)
% 2.98/1.65 % (31090)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30813 for (2999ds/183Mi)
% 2.98/1.65 % (31091)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_30813 for (2999ds/4Mi)
% 2.98/1.65 % (31093)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30813 for (2999ds/2Mi)
% 2.98/1.65 % (31094)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_30813 for (2999ds/2Mi)
% 2.98/1.65 % (31095)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_30813 for (2999ds/275Mi)
% 2.98/1.65 % (31096)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30813 for (2999ds/18Mi)
% 2.98/1.65 % (31092)Instruction limit reached!
% 2.98/1.65 % (31092)------------------------------
% 2.98/1.65 % (31092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.98/1.65 % (31092)Termination reason: Unknown
% 2.98/1.65 % (31092)Termination phase: shuffling
% 2.98/1.65
% 2.98/1.65 % (31092)Memory used [KB]: 2046
% 2.98/1.65 % (31092)Time elapsed: 0.010 s
% 2.98/1.65 % (31092)Instructions burned: 30 (million)
% 2.98/1.65 % (31092)------------------------------
% 2.98/1.65 % (31092)------------------------------
% 2.98/1.65 % (31093)Instruction limit reached!
% 2.98/1.65 % (31093)------------------------------
% 2.98/1.65 % (31093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.98/1.65 % (31093)Termination reason: Unknown
% 2.98/1.65 % (31093)Termination phase: shuffling
% 2.98/1.65
% 2.98/1.65 % (31093)Memory used [KB]: 1535
% 2.98/1.65 % (31093)Time elapsed: 0.003 s
% 2.98/1.65 % (31093)Instructions burned: 3 (million)
% 2.98/1.65 % (31093)------------------------------
% 2.98/1.65 % (31093)------------------------------
% 2.98/1.65 % (31094)Instruction limit reached!
% 2.98/1.65 % (31094)------------------------------
% 2.98/1.65 % (31094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.98/1.65 % (31094)Termination reason: Unknown
% 2.98/1.65 % (31094)Termination phase: shuffling
% 2.98/1.65
% 2.98/1.65 % (31094)Memory used [KB]: 1535
% 2.98/1.65 % (31094)Time elapsed: 0.003 s
% 2.98/1.65 % (31094)Instructions burned: 3 (million)
% 2.98/1.65 % (31094)------------------------------
% 2.98/1.65 % (31094)------------------------------
% 2.98/1.66 % (31091)Instruction limit reached!
% 2.98/1.66 % (31091)------------------------------
% 2.98/1.66 % (31091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.98/1.66 % (31091)Termination reason: Unknown
% 2.98/1.66 % (31091)Termination phase: shuffling
% 2.98/1.66
% 2.98/1.66 % (31091)Memory used [KB]: 1535
% 2.98/1.66 % (31091)Time elapsed: 0.004 s
% 2.98/1.66 % (31091)Instructions burned: 4 (million)
% 2.98/1.66 % (31091)------------------------------
% 2.98/1.66 % (31091)------------------------------
% 2.98/1.66 % (31097)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30813 for (2999ds/3Mi)
% 2.98/1.66 % (31096)Instruction limit reached!
% 2.98/1.66 % (31096)------------------------------
% 2.98/1.66 % (31096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.98/1.66 % (31096)Termination reason: Unknown
% 2.98/1.66 % (31096)Termination phase: shuffling
% 2.98/1.66
% 2.98/1.66 % (31096)Memory used [KB]: 1791
% 2.98/1.66 % (31096)Time elapsed: 0.013 s
% 2.98/1.66 % (31096)Instructions burned: 19 (million)
% 2.98/1.66 % (31096)------------------------------
% 2.98/1.66 % (31096)------------------------------
% 2.98/1.67 % (31097)Instruction limit reached!
% 2.98/1.67 % (31097)------------------------------
% 2.98/1.67 % (31097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.98/1.67 % (31097)Termination reason: Unknown
% 2.98/1.67 % (31097)Termination phase: shuffling
% 2.98/1.67
% 2.98/1.67 % (31097)Memory used [KB]: 1535
% 2.98/1.67 % (31097)Time elapsed: 0.003 s
% 2.98/1.67 % (31097)Instructions burned: 6 (million)
% 2.98/1.67 % (31097)------------------------------
% 2.98/1.67 % (31097)------------------------------
% 2.98/1.67 % (31098)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_30813 for (2999ds/37Mi)
% 2.98/1.67 % (31099)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_30813 for (2999ds/15Mi)
% 2.98/1.67 % (31100)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_30813 for (2999ds/3Mi)
% 2.98/1.68 % (31100)Instruction limit reached!
% 2.98/1.68 % (31100)------------------------------
% 2.98/1.68 % (31100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.98/1.68 % (31100)Termination reason: Unknown
% 2.98/1.68 % (31100)Termination phase: shuffling
% 2.98/1.68
% 2.98/1.68 % (31100)Memory used [KB]: 1535
% 2.98/1.68 % (31100)Time elapsed: 0.004 s
% 2.98/1.68 % (31100)Instructions burned: 3 (million)
% 2.98/1.68 % (31100)------------------------------
% 2.98/1.68 % (31100)------------------------------
% 2.98/1.68 % (31102)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_30813 for (2999ds/7Mi)
% 2.98/1.68 % (31102)Instruction limit reached!
% 2.98/1.68 % (31102)------------------------------
% 2.98/1.68 % (31102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.98/1.68 % (31102)Termination reason: Unknown
% 2.98/1.68 % (31102)Termination phase: shuffling
% 2.98/1.68
% 2.98/1.68 % (31102)Memory used [KB]: 1663
% 2.98/1.68 % (31102)Time elapsed: 0.004 s
% 2.98/1.68 % (31102)Instructions burned: 9 (million)
% 2.98/1.68 % (31102)------------------------------
% 2.98/1.68 % (31102)------------------------------
% 2.98/1.68 % (31099)Instruction limit reached!
% 2.98/1.68 % (31099)------------------------------
% 2.98/1.68 % (31099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.98/1.68 % (31099)Termination reason: Unknown
% 2.98/1.68 % (31099)Termination phase: shuffling
% 2.98/1.68
% 2.98/1.68 % (31099)Memory used [KB]: 1791
% 2.98/1.68 % (31099)Time elapsed: 0.011 s
% 2.98/1.68 % (31099)Instructions burned: 15 (million)
% 2.98/1.68 % (31099)------------------------------
% 2.98/1.68 % (31099)------------------------------
% 2.98/1.68 % (31101)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_30813 for (2999ds/1041Mi)
% 2.98/1.69 % (31104)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_30813 for (2999ds/3Mi)
% 2.98/1.69 % (31104)Instruction limit reached!
% 2.98/1.69 % (31104)------------------------------
% 2.98/1.69 % (31104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.98/1.69 % (31104)Termination reason: Unknown
% 2.98/1.69 % (31104)Termination phase: shuffling
% 2.98/1.69
% 2.98/1.69 % (31104)Memory used [KB]: 1535
% 2.98/1.69 % (31104)Time elapsed: 0.002 s
% 2.98/1.69 % (31104)Instructions burned: 3 (million)
% 2.98/1.69 % (31104)------------------------------
% 2.98/1.69 % (31104)------------------------------
% 2.98/1.69 % (31098)Instruction limit reached!
% 2.98/1.69 % (31098)------------------------------
% 2.98/1.69 % (31098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.98/1.69 % (31098)Termination reason: Unknown
% 2.98/1.69 % (31098)Termination phase: shuffling
% 2.98/1.69
% 2.98/1.69 % (31098)Memory used [KB]: 2302
% 2.98/1.69 % (31098)Time elapsed: 0.021 s
% 2.98/1.69 % (31098)Instructions burned: 37 (million)
% 2.98/1.69 % (31098)------------------------------
% 2.98/1.69 % (31098)------------------------------
% 2.98/1.69 % (31103)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_30813 for (2999ds/16Mi)
% 2.98/1.69 % (31105)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_30813 for (2999ds/3Mi)
% 2.98/1.70 % (31105)Instruction limit reached!
% 2.98/1.70 % (31105)------------------------------
% 2.98/1.70 % (31105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.98/1.70 % (31105)Termination reason: Unknown
% 2.98/1.70 % (31105)Termination phase: shuffling
% 2.98/1.70
% 2.98/1.70 % (31105)Memory used [KB]: 1535
% 2.98/1.70 % (31105)Time elapsed: 0.003 s
% 2.98/1.70 % (31105)Instructions burned: 3 (million)
% 2.98/1.70 % (31105)------------------------------
% 2.98/1.70 % (31105)------------------------------
% 3.05/1.70 % (31106)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_30813 for (2999ds/7Mi)
% 3.05/1.70 % (31103)Instruction limit reached!
% 3.05/1.70 % (31103)------------------------------
% 3.05/1.70 % (31103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.70 % (31103)Termination reason: Unknown
% 3.05/1.70 % (31103)Termination phase: shuffling
% 3.05/1.70
% 3.05/1.70 % (31103)Memory used [KB]: 1791
% 3.05/1.70 % (31103)Time elapsed: 0.010 s
% 3.05/1.70 % (31103)Instructions burned: 17 (million)
% 3.05/1.70 % (31103)------------------------------
% 3.05/1.70 % (31103)------------------------------
% 3.05/1.70 % (31106)Instruction limit reached!
% 3.05/1.70 % (31106)------------------------------
% 3.05/1.70 % (31106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.70 % (31106)Termination reason: Unknown
% 3.05/1.70 % (31106)Termination phase: shuffling
% 3.05/1.70
% 3.05/1.70 % (31106)Memory used [KB]: 1663
% 3.05/1.70 % (31106)Time elapsed: 0.004 s
% 3.05/1.70 % (31106)Instructions burned: 10 (million)
% 3.05/1.70 % (31106)------------------------------
% 3.05/1.70 % (31106)------------------------------
% 3.05/1.71 % (31107)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_30813 for (2999ds/3Mi)
% 3.05/1.71 % (31108)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_30813 for (2999ds/4Mi)
% 3.05/1.71 % (31107)Instruction limit reached!
% 3.05/1.71 % (31107)------------------------------
% 3.05/1.71 % (31107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.71 % (31107)Termination reason: Unknown
% 3.05/1.71 % (31107)Termination phase: shuffling
% 3.05/1.71
% 3.05/1.71 % (31107)Memory used [KB]: 1535
% 3.05/1.71 % (31107)Time elapsed: 0.003 s
% 3.05/1.71 % (31107)Instructions burned: 3 (million)
% 3.05/1.71 % (31107)------------------------------
% 3.05/1.71 % (31107)------------------------------
% 3.05/1.71 % (31108)Instruction limit reached!
% 3.05/1.71 % (31108)------------------------------
% 3.05/1.71 % (31108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.71 % (31108)Termination reason: Unknown
% 3.05/1.71 % (31108)Termination phase: shuffling
% 3.05/1.71
% 3.05/1.71 % (31108)Memory used [KB]: 1535
% 3.05/1.71 % (31108)Time elapsed: 0.003 s
% 3.05/1.71 % (31108)Instructions burned: 5 (million)
% 3.05/1.71 % (31108)------------------------------
% 3.05/1.71 % (31108)------------------------------
% 3.05/1.71 % (31110)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_30813 for (2999ds/710Mi)
% 3.05/1.71 % (31109)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_30813 for (2999ds/18Mi)
% 3.05/1.72 % (31111)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_30813 for (2999ds/6Mi)
% 3.05/1.72 % (31109)Instruction limit reached!
% 3.05/1.72 % (31109)------------------------------
% 3.05/1.72 % (31109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.72 % (31109)Termination reason: Unknown
% 3.05/1.72 % (31109)Termination phase: shuffling
% 3.05/1.72
% 3.05/1.72 % (31109)Memory used [KB]: 1791
% 3.05/1.72 % (31109)Time elapsed: 0.007 s
% 3.05/1.72 % (31109)Instructions burned: 18 (million)
% 3.05/1.72 % (31109)------------------------------
% 3.05/1.72 % (31109)------------------------------
% 3.05/1.72 % (31112)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_30813 for (2999ds/902Mi)
% 3.05/1.72 % (31111)Instruction limit reached!
% 3.05/1.72 % (31111)------------------------------
% 3.05/1.72 % (31111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.72 % (31111)Termination reason: Unknown
% 3.05/1.72 % (31111)Termination phase: shuffling
% 3.05/1.72
% 3.05/1.72 % (31111)Memory used [KB]: 1663
% 3.05/1.72 % (31111)Time elapsed: 0.004 s
% 3.05/1.72 % (31111)Instructions burned: 8 (million)
% 3.05/1.72 % (31111)------------------------------
% 3.05/1.72 % (31111)------------------------------
% 3.05/1.73 % (31090)Instruction limit reached!
% 3.05/1.73 % (31090)------------------------------
% 3.05/1.73 % (31090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.73 % (31090)Termination reason: Unknown
% 3.05/1.73 % (31090)Termination phase: Saturation
% 3.05/1.73
% 3.05/1.73 % (31090)Memory used [KB]: 7419
% 3.05/1.73 % (31090)Time elapsed: 0.075 s
% 3.05/1.73 % (31090)Instructions burned: 183 (million)
% 3.05/1.73 % (31090)------------------------------
% 3.05/1.73 % (31090)------------------------------
% 3.05/1.73 % (31113)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_30813 for (2999ds/21Mi)
% 3.05/1.73 % (31114)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_30813 for (2999ds/5Mi)
% 3.05/1.73 % (31114)Instruction limit reached!
% 3.05/1.73 % (31114)------------------------------
% 3.05/1.73 % (31114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.73 % (31114)Termination reason: Unknown
% 3.05/1.73 % (31114)Termination phase: shuffling
% 3.05/1.73
% 3.05/1.73 % (31114)Memory used [KB]: 1535
% 3.05/1.73 % (31114)Time elapsed: 0.003 s
% 3.05/1.73 % (31114)Instructions burned: 6 (million)
% 3.05/1.73 % (31114)------------------------------
% 3.05/1.73 % (31114)------------------------------
% 3.05/1.74 % (31113)Instruction limit reached!
% 3.05/1.74 % (31113)------------------------------
% 3.05/1.74 % (31113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.74 % (31113)Termination reason: Unknown
% 3.05/1.74 % (31113)Termination phase: shuffling
% 3.05/1.74
% 3.05/1.74 % (31113)Memory used [KB]: 1918
% 3.05/1.74 % (31113)Time elapsed: 0.008 s
% 3.05/1.74 % (31113)Instructions burned: 24 (million)
% 3.05/1.74 % (31113)------------------------------
% 3.05/1.74 % (31113)------------------------------
% 3.05/1.74 % (31115)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_30813 for (2999ds/6Mi)
% 3.05/1.74 % (31115)Instruction limit reached!
% 3.05/1.74 % (31115)------------------------------
% 3.05/1.74 % (31115)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.74 % (31115)Termination reason: Unknown
% 3.05/1.74 % (31115)Termination phase: shuffling
% 3.05/1.74
% 3.05/1.74 % (31115)Memory used [KB]: 1535
% 3.05/1.74 % (31115)Time elapsed: 0.003 s
% 3.05/1.74 % (31115)Instructions burned: 7 (million)
% 3.05/1.74 % (31115)------------------------------
% 3.05/1.74 % (31115)------------------------------
% 3.05/1.74 % (31116)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_30813 for (2998ds/377Mi)
% 3.05/1.75 % (31117)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_30813 for (2998ds/779Mi)
% 3.05/1.75 % (31118)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_30813 for (2998ds/19Mi)
% 3.05/1.76 % (31118)Instruction limit reached!
% 3.05/1.76 % (31118)------------------------------
% 3.05/1.76 % (31118)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.76 % (31118)Termination reason: Unknown
% 3.05/1.76 % (31118)Termination phase: shuffling
% 3.05/1.76
% 3.05/1.76 % (31118)Memory used [KB]: 1918
% 3.05/1.76 % (31118)Time elapsed: 0.007 s
% 3.05/1.76 % (31118)Instructions burned: 20 (million)
% 3.05/1.76 % (31118)------------------------------
% 3.05/1.76 % (31118)------------------------------
% 3.05/1.77 % (31119)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_30813 for (2998ds/879Mi)
% 3.05/1.78 % (31095)Instruction limit reached!
% 3.05/1.78 % (31095)------------------------------
% 3.05/1.78 % (31095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.78 % (31095)Termination reason: Unknown
% 3.05/1.78 % (31095)Termination phase: Saturation
% 3.05/1.78
% 3.05/1.78 % (31095)Memory used [KB]: 10106
% 3.05/1.78 % (31095)Time elapsed: 0.132 s
% 3.05/1.78 % (31095)Instructions burned: 275 (million)
% 3.05/1.78 % (31095)------------------------------
% 3.05/1.78 % (31095)------------------------------
% 3.05/1.79 % (31120)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_30813 for (2998ds/17Mi)
% 3.05/1.80 % (31120)Instruction limit reached!
% 3.05/1.80 % (31120)------------------------------
% 3.05/1.80 % (31120)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.80 % (31120)Termination reason: Unknown
% 3.05/1.80 % (31120)Termination phase: shuffling
% 3.05/1.80
% 3.05/1.80 % (31120)Memory used [KB]: 1791
% 3.05/1.80 % (31120)Time elapsed: 0.006 s
% 3.05/1.80 % (31120)Instructions burned: 17 (million)
% 3.05/1.80 % (31120)------------------------------
% 3.05/1.80 % (31120)------------------------------
% 3.05/1.81 % (31121)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_30813 for (2998ds/3Mi)
% 3.05/1.81 % (31121)Instruction limit reached!
% 3.05/1.81 % (31121)------------------------------
% 3.05/1.81 % (31121)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.81 % (31121)Termination reason: Unknown
% 3.05/1.81 % (31121)Termination phase: shuffling
% 3.05/1.81
% 3.05/1.81 % (31121)Memory used [KB]: 1535
% 3.05/1.81 % (31121)Time elapsed: 0.002 s
% 3.05/1.81 % (31121)Instructions burned: 3 (million)
% 3.05/1.81 % (31121)------------------------------
% 3.05/1.81 % (31121)------------------------------
% 3.05/1.82 % (31122)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_30813 for (2998ds/30Mi)
% 3.05/1.83 % (31122)Instruction limit reached!
% 3.05/1.83 % (31122)------------------------------
% 3.05/1.83 % (31122)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.83 % (31122)Termination reason: Unknown
% 3.05/1.83 % (31122)Termination phase: shuffling
% 3.05/1.83
% 3.05/1.83 % (31122)Memory used [KB]: 2046
% 3.05/1.83 % (31122)Time elapsed: 0.010 s
% 3.05/1.83 % (31122)Instructions burned: 31 (million)
% 3.05/1.83 % (31122)------------------------------
% 3.05/1.83 % (31122)------------------------------
% 3.05/1.84 % (31123)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_30813 for (2998ds/127Mi)
% 3.05/1.84 % (31116)Instruction limit reached!
% 3.05/1.84 % (31116)------------------------------
% 3.05/1.84 % (31116)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.84 % (31116)Termination reason: Unknown
% 3.05/1.84 % (31116)Termination phase: Saturation
% 3.05/1.84
% 3.05/1.84 % (31116)Memory used [KB]: 9466
% 3.05/1.84 % (31116)Time elapsed: 0.102 s
% 3.05/1.84 % (31116)Instructions burned: 377 (million)
% 3.05/1.84 % (31116)------------------------------
% 3.05/1.84 % (31116)------------------------------
% 3.05/1.85 % (31124)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_30813 for (2997ds/100Mi)
% 3.05/1.88 % (31123)Instruction limit reached!
% 3.05/1.88 % (31123)------------------------------
% 3.05/1.88 % (31123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.88 % (31123)Termination reason: Unknown
% 3.05/1.88 % (31123)Termination phase: Property scanning
% 3.05/1.88
% 3.05/1.88 % (31123)Memory used [KB]: 2686
% 3.05/1.88 % (31123)Time elapsed: 0.037 s
% 3.05/1.88 % (31123)Instructions burned: 129 (million)
% 3.05/1.88 % (31123)------------------------------
% 3.05/1.88 % (31123)------------------------------
% 3.05/1.88 % (31124)Instruction limit reached!
% 3.05/1.88 % (31124)------------------------------
% 3.05/1.88 % (31124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.88 % (31124)Termination reason: Unknown
% 3.05/1.88 % (31124)Termination phase: Property scanning
% 3.05/1.88
% 3.05/1.88 % (31124)Memory used [KB]: 2686
% 3.05/1.88 % (31124)Time elapsed: 0.027 s
% 3.05/1.88 % (31124)Instructions burned: 102 (million)
% 3.05/1.88 % (31124)------------------------------
% 3.05/1.88 % (31124)------------------------------
% 3.05/1.89 % (31126)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_30813 for (2997ds/20Mi)
% 3.05/1.89 % (31125)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_30813 for (2997ds/3Mi)
% 3.05/1.89 % (31125)Instruction limit reached!
% 3.05/1.89 % (31125)------------------------------
% 3.05/1.89 % (31125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.89 % (31125)Termination reason: Unknown
% 3.05/1.89 % (31125)Termination phase: shuffling
% 3.05/1.89
% 3.05/1.89 % (31125)Memory used [KB]: 1535
% 3.05/1.89 % (31125)Time elapsed: 0.002 s
% 3.05/1.89 % (31125)Instructions burned: 3 (million)
% 3.05/1.89 % (31125)------------------------------
% 3.05/1.89 % (31125)------------------------------
% 3.05/1.89 % (31126)Instruction limit reached!
% 3.05/1.89 % (31126)------------------------------
% 3.05/1.89 % (31126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.89 % (31126)Termination reason: Unknown
% 3.05/1.89 % (31126)Termination phase: shuffling
% 3.05/1.89
% 3.05/1.89 % (31126)Memory used [KB]: 1918
% 3.05/1.89 % (31126)Time elapsed: 0.008 s
% 3.05/1.89 % (31126)Instructions burned: 21 (million)
% 3.05/1.89 % (31126)------------------------------
% 3.05/1.89 % (31126)------------------------------
% 3.05/1.90 % (31127)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_30813 for (2997ds/86Mi)
% 3.05/1.90 % (31128)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_30813 for (2997ds/107Mi)
% 3.05/1.92 % (31110)Refutation not found, non-redundant clauses discarded% (31110)------------------------------
% 3.05/1.92 % (31110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.92 % (31110)Termination reason: Refutation not found, non-redundant clauses discarded
% 3.05/1.92
% 3.05/1.92 % (31110)Memory used [KB]: 10746
% 3.05/1.92 % (31110)Time elapsed: 0.205 s
% 3.05/1.92 % (31110)Instructions burned: 661 (million)
% 3.05/1.92 % (31110)------------------------------
% 3.05/1.92 % (31110)------------------------------
% 3.05/1.92 % (31127)Instruction limit reached!
% 3.05/1.92 % (31127)------------------------------
% 3.05/1.92 % (31127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.92 % (31127)Termination reason: Unknown
% 3.05/1.92 % (31127)Termination phase: Property scanning
% 3.05/1.92
% 3.05/1.92 % (31127)Memory used [KB]: 2558
% 3.05/1.92 % (31127)Time elapsed: 0.025 s
% 3.05/1.92 % (31127)Instructions burned: 86 (million)
% 3.05/1.92 % (31127)------------------------------
% 3.05/1.92 % (31127)------------------------------
% 3.05/1.93 % (31129)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_30813 for (2997ds/39Mi)
% 3.05/1.93 % (31128)Instruction limit reached!
% 3.05/1.93 % (31128)------------------------------
% 3.05/1.93 % (31128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.93 % (31128)Termination reason: Unknown
% 3.05/1.93 % (31128)Termination phase: shuffling
% 3.05/1.93
% 3.05/1.93 % (31128)Memory used [KB]: 2558
% 3.05/1.93 % (31128)Time elapsed: 0.029 s
% 3.05/1.93 % (31128)Instructions burned: 108 (million)
% 3.05/1.93 % (31128)------------------------------
% 3.05/1.93 % (31128)------------------------------
% 3.05/1.93 % (31130)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_30813 for (2996ds/448Mi)
% 3.05/1.94 % (31129)Instruction limit reached!
% 3.05/1.94 % (31129)------------------------------
% 3.05/1.94 % (31129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.94 % (31129)Termination reason: Unknown
% 3.05/1.94 % (31129)Termination phase: shuffling
% 3.05/1.94
% 3.05/1.94 % (31129)Memory used [KB]: 2302
% 3.05/1.94 % (31129)Time elapsed: 0.012 s
% 3.05/1.94 % (31129)Instructions burned: 40 (million)
% 3.05/1.94 % (31129)------------------------------
% 3.05/1.94 % (31129)------------------------------
% 3.05/1.94 % (31131)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_30813 for (2996ds/46Mi)
% 3.05/1.95 % (31132)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_30813 for (2996ds/98Mi)
% 3.05/1.95 % (31117)Instruction limit reached!
% 3.05/1.95 % (31117)------------------------------
% 3.05/1.95 % (31117)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.95 % (31117)Termination reason: Unknown
% 3.05/1.95 % (31117)Termination phase: Saturation
% 3.05/1.95
% 3.05/1.95 % (31117)Memory used [KB]: 7675
% 3.05/1.95 % (31117)Time elapsed: 0.205 s
% 3.05/1.95 % (31117)Instructions burned: 780 (million)
% 3.05/1.95 % (31117)------------------------------
% 3.05/1.95 % (31117)------------------------------
% 3.05/1.95 % (31131)Instruction limit reached!
% 3.05/1.95 % (31131)------------------------------
% 3.05/1.95 % (31131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.95 % (31131)Termination reason: Unknown
% 3.05/1.95 % (31131)Termination phase: shuffling
% 3.05/1.95
% 3.05/1.95 % (31131)Memory used [KB]: 2430
% 3.05/1.95 % (31131)Time elapsed: 0.014 s
% 3.05/1.95 % (31131)Instructions burned: 48 (million)
% 3.05/1.95 % (31131)------------------------------
% 3.05/1.95 % (31131)------------------------------
% 3.05/1.96 % (31133)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_30813 for (2996ds/507Mi)
% 3.05/1.96 % (31134)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_30813 for (2996ds/149Mi)
% 3.05/1.97 % (31132)Instruction limit reached!
% 3.05/1.97 % (31132)------------------------------
% 3.05/1.97 % (31132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.97 % (31132)Termination reason: Unknown
% 3.05/1.97 % (31132)Termination phase: Property scanning
% 3.05/1.97
% 3.05/1.97 % (31132)Memory used [KB]: 2558
% 3.05/1.97 % (31132)Time elapsed: 0.027 s
% 3.05/1.97 % (31132)Instructions burned: 101 (million)
% 3.05/1.97 % (31132)------------------------------
% 3.05/1.97 % (31132)------------------------------
% 3.05/1.98 % (31101)Instruction limit reached!
% 3.05/1.98 % (31101)------------------------------
% 3.05/1.98 % (31101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.98 % (31101)Termination reason: Unknown
% 3.05/1.98 % (31101)Termination phase: Saturation
% 3.05/1.98
% 3.05/1.98 % (31101)Memory used [KB]: 15991
% 3.05/1.98 % (31101)Time elapsed: 0.300 s
% 3.05/1.98 % (31101)Instructions burned: 1043 (million)
% 3.05/1.98 % (31101)------------------------------
% 3.05/1.98 % (31101)------------------------------
% 3.05/1.98 % (31135)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_30813 for (2996ds/39Mi)
% 3.05/1.99 % (31136)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_30813 for (2996ds/6Mi)
% 3.05/1.99 % (31135)Instruction limit reached!
% 3.05/1.99 % (31135)------------------------------
% 3.05/1.99 % (31135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.99 % (31135)Termination reason: Unknown
% 3.05/1.99 % (31135)Termination phase: shuffling
% 3.05/1.99
% 3.05/1.99 % (31135)Memory used [KB]: 2302
% 3.05/1.99 % (31135)Time elapsed: 0.012 s
% 3.05/1.99 % (31135)Instructions burned: 39 (million)
% 3.05/1.99 % (31135)------------------------------
% 3.05/1.99 % (31135)------------------------------
% 3.05/1.99 % (31136)Instruction limit reached!
% 3.05/1.99 % (31136)------------------------------
% 3.05/1.99 % (31136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.99 % (31136)Termination reason: Unknown
% 3.05/1.99 % (31136)Termination phase: shuffling
% 3.05/1.99
% 3.05/1.99 % (31136)Memory used [KB]: 1535
% 3.05/1.99 % (31136)Time elapsed: 0.003 s
% 3.05/1.99 % (31136)Instructions burned: 6 (million)
% 3.05/1.99 % (31136)------------------------------
% 3.05/1.99 % (31136)------------------------------
% 3.05/2.00 % (31112)Instruction limit reached!
% 3.05/2.00 % (31112)------------------------------
% 3.05/2.00 % (31112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/2.00 % (31112)Termination reason: Unknown
% 3.05/2.00 % (31112)Termination phase: Saturation
% 3.05/2.00
% 3.05/2.00 % (31112)Memory used [KB]: 12665
% 3.05/2.00 % (31112)Time elapsed: 0.282 s
% 3.05/2.00 % (31112)Instructions burned: 903 (million)
% 3.05/2.00 % (31112)------------------------------
% 3.05/2.00 % (31112)------------------------------
% 3.05/2.00 % (31137)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_30813 for (2996ds/1087Mi)
% 3.05/2.00 % (31134)Instruction limit reached!
% 3.05/2.00 % (31134)------------------------------
% 3.05/2.00 % (31134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/2.00 % (31134)Termination reason: Unknown
% 3.05/2.00 % (31134)Termination phase: Twee Goal Transformation
% 3.05/2.00
% 3.05/2.00 % (31134)Memory used [KB]: 3326
% 3.05/2.00 % (31134)Time elapsed: 0.041 s
% 3.05/2.00 % (31134)Instructions burned: 151 (million)
% 3.05/2.00 % (31134)------------------------------
% 3.05/2.00 % (31134)------------------------------
% 3.05/2.00 % (31138)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_30813 for (2996ds/47Mi)
% 3.05/2.01 % (31140)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_30813 for (2996ds/44Mi)
% 3.05/2.01 % (31141)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_30813 for (2996ds/432Mi)
% 5.63/2.02 % (31138)Instruction limit reached!
% 5.63/2.02 % (31138)------------------------------
% 5.63/2.02 % (31138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.63/2.02 % (31138)Termination reason: Unknown
% 5.63/2.02 % (31138)Termination phase: shuffling
% 5.63/2.02
% 5.63/2.02 % (31138)Memory used [KB]: 2430
% 5.63/2.02 % (31138)Time elapsed: 0.016 s
% 5.63/2.02 % (31138)Instructions burned: 48 (million)
% 5.63/2.02 % (31138)------------------------------
% 5.63/2.02 % (31138)------------------------------
% 5.63/2.02 % (31140)Instruction limit reached!
% 5.63/2.02 % (31140)------------------------------
% 5.63/2.02 % (31140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.63/2.02 % (31140)Termination reason: Unknown
% 5.63/2.02 % (31140)Termination phase: shuffling
% 5.63/2.02
% 5.63/2.02 % (31140)Memory used [KB]: 2430
% 5.63/2.02 % (31140)Time elapsed: 0.013 s
% 5.63/2.02 % (31140)Instructions burned: 45 (million)
% 5.63/2.02 % (31140)------------------------------
% 5.63/2.02 % (31140)------------------------------
% 5.63/2.03 % (31142)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_30813 for (2996ds/62Mi)
% 5.63/2.03 % (31143)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_30813 for (2996ds/31Mi)
% 5.63/2.04 % (31143)Instruction limit reached!
% 5.63/2.04 % (31143)------------------------------
% 5.63/2.04 % (31143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.63/2.04 % (31143)Termination reason: Unknown
% 5.63/2.04 % (31143)Termination phase: shuffling
% 5.63/2.04
% 5.63/2.04 % (31143)Memory used [KB]: 2174
% 5.63/2.04 % (31143)Time elapsed: 0.010 s
% 5.63/2.04 % (31143)Instructions burned: 33 (million)
% 5.63/2.04 % (31143)------------------------------
% 5.63/2.04 % (31143)------------------------------
% 5.63/2.05 % (31142)Instruction limit reached!
% 5.63/2.05 % (31142)------------------------------
% 5.63/2.05 % (31142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.63/2.05 % (31142)Termination reason: Unknown
% 5.63/2.05 % (31142)Termination phase: Property scanning
% 5.63/2.05
% 5.63/2.05 % (31142)Memory used [KB]: 2558
% 5.63/2.05 % (31142)Time elapsed: 0.019 s
% 5.63/2.05 % (31142)Instructions burned: 64 (million)
% 5.63/2.05 % (31142)------------------------------
% 5.63/2.05 % (31142)------------------------------
% 5.63/2.05 % (31144)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_30813 for (2995ds/96Mi)
% 5.63/2.05 % (31130)Instruction limit reached!
% 5.63/2.05 % (31130)------------------------------
% 5.63/2.05 % (31130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.63/2.05 % (31130)Termination reason: Unknown
% 5.63/2.05 % (31130)Termination phase: Saturation
% 5.63/2.05
% 5.63/2.05 % (31130)Memory used [KB]: 7547
% 5.63/2.05 % (31130)Time elapsed: 0.121 s
% 5.63/2.05 % (31130)Instructions burned: 450 (million)
% 5.63/2.05 % (31130)------------------------------
% 5.63/2.05 % (31130)------------------------------
% 5.63/2.06 % (31145)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_30813 for (2995ds/453Mi)
% 5.63/2.06 % (31146)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_30813 for (2995ds/71Mi)
% 5.63/2.07 % (31144)Instruction limit reached!
% 5.63/2.07 % (31144)------------------------------
% 5.63/2.07 % (31144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.63/2.07 % (31144)Termination reason: Unknown
% 5.63/2.07 % (31144)Termination phase: Property scanning
% 5.63/2.07
% 5.63/2.07 % (31144)Memory used [KB]: 2686
% 5.63/2.07 % (31144)Time elapsed: 0.026 s
% 5.63/2.07 % (31144)Instructions burned: 97 (million)
% 5.63/2.07 % (31144)------------------------------
% 5.63/2.07 % (31144)------------------------------
% 5.63/2.08 % (31146)Instruction limit reached!
% 5.63/2.08 % (31146)------------------------------
% 5.63/2.08 % (31146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.63/2.08 % (31146)Termination reason: Unknown
% 5.63/2.08 % (31146)Termination phase: Property scanning
% 5.63/2.08
% 5.63/2.08 % (31146)Memory used [KB]: 2558
% 5.63/2.08 % (31146)Time elapsed: 0.022 s
% 5.63/2.08 % (31146)Instructions burned: 74 (million)
% 5.63/2.08 % (31146)------------------------------
% 5.63/2.08 % (31146)------------------------------
% 5.63/2.08 % (31147)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_30813 for (2995ds/83Mi)
% 5.63/2.09 % (31119)Instruction limit reached!
% 5.63/2.09 % (31119)------------------------------
% 5.63/2.09 % (31119)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.63/2.09 % (31119)Termination reason: Unknown
% 5.63/2.09 % (31119)Termination phase: Saturation
% 5.63/2.09
% 5.63/2.09 % (31119)Memory used [KB]: 10106
% 5.63/2.09 % (31119)Time elapsed: 0.323 s
% 5.63/2.09 % (31119)Instructions burned: 879 (million)
% 5.63/2.09 % (31119)------------------------------
% 5.63/2.09 % (31119)------------------------------
% 5.63/2.09 % (31148)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_30813 for (2995ds/11Mi)
% 5.63/2.10 % (31148)Instruction limit reached!
% 5.63/2.10 % (31148)------------------------------
% 5.63/2.10 % (31148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.63/2.10 % (31148)Termination reason: Unknown
% 5.63/2.10 % (31148)Termination phase: shuffling
% 5.63/2.10
% 5.63/2.10 % (31148)Memory used [KB]: 1791
% 5.63/2.10 % (31148)Time elapsed: 0.005 s
% 5.63/2.10 % (31148)Instructions burned: 14 (million)
% 5.63/2.10 % (31148)------------------------------
% 5.63/2.10 % (31148)------------------------------
% 5.63/2.10 % (31149)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_30813 for (2995ds/41Mi)
% 5.63/2.11 % (31133)Instruction limit reached!
% 5.63/2.11 % (31133)------------------------------
% 5.63/2.11 % (31133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.63/2.11 % (31133)Termination reason: Unknown
% 5.63/2.11 % (31133)Termination phase: Saturation
% 5.63/2.11
% 5.63/2.11 % (31133)Memory used [KB]: 8187
% 5.63/2.11 % (31133)Time elapsed: 0.147 s
% 5.63/2.11 % (31133)Instructions burned: 510 (million)
% 5.63/2.11 % (31133)------------------------------
% 5.63/2.11 % (31133)------------------------------
% 5.63/2.11 % (31147)Instruction limit reached!
% 5.63/2.11 % (31147)------------------------------
% 5.63/2.11 % (31147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.63/2.11 % (31147)Termination reason: Unknown
% 5.63/2.11 % (31147)Termination phase: Property scanning
% 5.63/2.11
% 5.63/2.11 % (31147)Memory used [KB]: 2558
% 5.63/2.11 % (31147)Time elapsed: 0.023 s
% 5.63/2.11 % (31147)Instructions burned: 84 (million)
% 5.63/2.11 % (31147)------------------------------
% 5.63/2.11 % (31147)------------------------------
% 5.63/2.11 % (31150)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_30813 for (2995ds/6Mi)
% 5.63/2.11 % (31150)Instruction limit reached!
% 5.63/2.11 % (31150)------------------------------
% 5.63/2.11 % (31150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.63/2.11 % (31150)Termination reason: Unknown
% 5.63/2.11 % (31150)Termination phase: shuffling
% 5.63/2.11
% 5.63/2.11 % (31150)Memory used [KB]: 1663
% 5.63/2.11 % (31150)Time elapsed: 0.004 s
% 5.63/2.11 % (31150)Instructions burned: 7 (million)
% 5.63/2.11 % (31150)------------------------------
% 5.63/2.11 % (31150)------------------------------
% 6.17/2.12 % (31152)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_30813 for (2995ds/343Mi)
% 6.17/2.12 % (31151)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_30813 for (2995ds/150Mi)
% 6.17/2.12 % (31149)Instruction limit reached!
% 6.17/2.12 % (31149)------------------------------
% 6.17/2.12 % (31149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.17/2.12 % (31149)Termination reason: Unknown
% 6.17/2.12 % (31149)Termination phase: shuffling
% 6.17/2.12
% 6.17/2.12 % (31149)Memory used [KB]: 2302
% 6.17/2.12 % (31149)Time elapsed: 0.014 s
% 6.17/2.12 % (31149)Instructions burned: 43 (million)
% 6.17/2.12 % (31149)------------------------------
% 6.17/2.12 % (31149)------------------------------
% 6.17/2.12 % (31141)Instruction limit reached!
% 6.17/2.12 % (31141)------------------------------
% 6.17/2.12 % (31141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.17/2.12 % (31141)Termination reason: Unknown
% 6.17/2.12 % (31141)Termination phase: Saturation
% 6.17/2.12
% 6.17/2.12 % (31141)Memory used [KB]: 3070
% 6.17/2.12 % (31141)Time elapsed: 0.109 s
% 6.17/2.12 % (31141)Instructions burned: 434 (million)
% 6.17/2.12 % (31141)------------------------------
% 6.17/2.12 % (31141)------------------------------
% 6.17/2.12 % (31153)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_30813 for (2995ds/109Mi)
% 6.17/2.13 % (31154)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_30813 for (2995ds/253Mi)
% 6.17/2.13 % (31155)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_30813 for (2995ds/140Mi)
% 6.17/2.15 % (31153)Instruction limit reached!
% 6.17/2.15 % (31153)------------------------------
% 6.17/2.15 % (31153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.17/2.15 % (31153)Termination reason: Unknown
% 6.17/2.15 % (31153)Termination phase: Preprocessing 3
% 6.17/2.15
% 6.17/2.15 % (31153)Memory used [KB]: 2686
% 6.17/2.15 % (31153)Time elapsed: 0.031 s
% 6.17/2.15 % (31153)Instructions burned: 110 (million)
% 6.17/2.15 % (31153)------------------------------
% 6.17/2.15 % (31153)------------------------------
% 6.17/2.16 % (31156)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_30813 for (2994ds/614Mi)
% 6.17/2.16 % (31151)Instruction limit reached!
% 6.17/2.16 % (31151)------------------------------
% 6.17/2.16 % (31151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.17/2.16 % (31151)Termination reason: Unknown
% 6.17/2.16 % (31151)Termination phase: Property scanning
% 6.17/2.16
% 6.17/2.16 % (31151)Memory used [KB]: 4989
% 6.17/2.16 % (31151)Time elapsed: 0.047 s
% 6.17/2.16 % (31151)Instructions burned: 153 (million)
% 6.17/2.16 % (31151)------------------------------
% 6.17/2.16 % (31151)------------------------------
% 6.17/2.17 % (31155)Instruction limit reached!
% 6.17/2.17 % (31155)------------------------------
% 6.17/2.17 % (31155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.17/2.17 % (31155)Termination reason: Unknown
% 6.17/2.17 % (31155)Termination phase: Property scanning
% 6.17/2.17
% 6.17/2.17 % (31155)Memory used [KB]: 2814
% 6.17/2.17 % (31155)Time elapsed: 0.039 s
% 6.17/2.17 % (31155)Instructions burned: 143 (million)
% 6.17/2.17 % (31155)------------------------------
% 6.17/2.17 % (31155)------------------------------
% 6.17/2.17 % (31145)Instruction limit reached!
% 6.17/2.17 % (31145)------------------------------
% 6.17/2.17 % (31145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.17/2.17 % (31145)Termination reason: Unknown
% 6.17/2.17 % (31145)Termination phase: Saturation
% 6.17/2.17
% 6.17/2.17 % (31145)Memory used [KB]: 7547
% 6.17/2.17 % (31145)Time elapsed: 0.115 s
% 6.17/2.17 % (31145)Instructions burned: 453 (million)
% 6.17/2.17 % (31145)------------------------------
% 6.17/2.17 % (31145)------------------------------
% 6.17/2.17 % (31157)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_30813 for (2994ds/202Mi)
% 6.17/2.18 % (31158)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_30813 for (2994ds/339Mi)
% 6.17/2.18 % (31159)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_30813 for (2994ds/283Mi)
% 6.66/2.20 % (31154)Instruction limit reached!
% 6.66/2.20 % (31154)------------------------------
% 6.66/2.20 % (31154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.66/2.20 % (31154)Termination reason: Unknown
% 6.66/2.20 % (31154)Termination phase: Saturation
% 6.66/2.20
% 6.66/2.20 % (31154)Memory used [KB]: 10106
% 6.66/2.20 % (31154)Time elapsed: 0.078 s
% 6.66/2.20 % (31154)Instructions burned: 255 (million)
% 6.66/2.20 % (31154)------------------------------
% 6.66/2.20 % (31154)------------------------------
% 6.66/2.21 % (31152)Instruction limit reached!
% 6.66/2.21 % (31152)------------------------------
% 6.66/2.21 % (31152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.66/2.21 % (31152)Termination reason: Unknown
% 6.66/2.21 % (31152)Termination phase: Saturation
% 6.66/2.21
% 6.66/2.21 % (31152)Memory used [KB]: 8443
% 6.66/2.21 % (31152)Time elapsed: 0.092 s
% 6.66/2.21 % (31152)Instructions burned: 344 (million)
% 6.66/2.21 % (31152)------------------------------
% 6.66/2.21 % (31152)------------------------------
% 6.66/2.21 % (31160)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_30813 for (2994ds/134Mi)
% 6.66/2.22 % (31161)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_30813 for (2994ds/298Mi)
% 6.66/2.23 % (31157)Instruction limit reached!
% 6.66/2.23 % (31157)------------------------------
% 6.66/2.23 % (31157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.66/2.23 % (31157)Termination reason: Unknown
% 6.66/2.23 % (31157)Termination phase: Property scanning
% 6.66/2.23
% 6.66/2.23 % (31157)Memory used [KB]: 4989
% 6.66/2.23 % (31157)Time elapsed: 0.058 s
% 6.66/2.23 % (31157)Instructions burned: 202 (million)
% 6.66/2.23 % (31157)------------------------------
% 6.66/2.23 % (31157)------------------------------
% 6.66/2.24 % (31162)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_30813 for (2994ds/192Mi)
% 6.66/2.25 % (31159)Instruction limit reached!
% 6.66/2.25 % (31159)------------------------------
% 6.66/2.25 % (31159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.66/2.25 % (31159)Termination reason: Unknown
% 6.66/2.25 % (31159)Termination phase: Saturation
% 6.66/2.25
% 6.66/2.25 % (31159)Memory used [KB]: 7419
% 6.66/2.25 % (31159)Time elapsed: 0.073 s
% 6.66/2.25 % (31159)Instructions burned: 285 (million)
% 6.66/2.25 % (31159)------------------------------
% 6.66/2.25 % (31159)------------------------------
% 6.66/2.25 % (31160)Instruction limit reached!
% 6.66/2.25 % (31160)------------------------------
% 6.66/2.25 % (31160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.66/2.25 % (31160)Termination reason: Unknown
% 6.66/2.25 % (31160)Termination phase: Property scanning
% 6.66/2.25
% 6.66/2.25 % (31160)Memory used [KB]: 2814
% 6.66/2.25 % (31160)Time elapsed: 0.039 s
% 6.66/2.25 % (31160)Instructions burned: 136 (million)
% 6.66/2.25 % (31160)------------------------------
% 6.66/2.25 % (31160)------------------------------
% 6.66/2.26 % (31163)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_30813 for (2993ds/258Mi)
% 6.66/2.26 % (31164)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_30813 for (2993ds/90Mi)
% 6.66/2.27 % (31158)Instruction limit reached!
% 6.66/2.27 % (31158)------------------------------
% 6.66/2.27 % (31158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.66/2.27 % (31158)Termination reason: Unknown
% 6.66/2.27 % (31158)Termination phase: Saturation
% 6.66/2.27
% 6.66/2.27 % (31158)Memory used [KB]: 7931
% 6.66/2.27 % (31158)Time elapsed: 0.093 s
% 6.66/2.27 % (31158)Instructions burned: 340 (million)
% 6.66/2.27 % (31158)------------------------------
% 6.66/2.27 % (31158)------------------------------
% 6.66/2.28 % (31165)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_30813 for (2993ds/231Mi)
% 6.66/2.29 % (31162)Instruction limit reached!
% 6.66/2.29 % (31162)------------------------------
% 6.66/2.29 % (31162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.66/2.29 % (31162)Termination reason: Unknown
% 6.66/2.29 % (31162)Termination phase: Saturation
% 6.66/2.29
% 6.66/2.29 % (31162)Memory used [KB]: 7803
% 6.66/2.29 % (31162)Time elapsed: 0.051 s
% 6.66/2.29 % (31162)Instructions burned: 192 (million)
% 6.66/2.29 % (31162)------------------------------
% 6.66/2.29 % (31162)------------------------------
% 6.66/2.29 % (31164)Instruction limit reached!
% 6.66/2.29 % (31164)------------------------------
% 6.66/2.29 % (31164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.66/2.29 % (31164)Termination reason: Unknown
% 6.66/2.29 % (31164)Termination phase: Property scanning
% 6.66/2.29
% 6.66/2.29 % (31164)Memory used [KB]: 2686
% 6.66/2.29 % (31164)Time elapsed: 0.026 s
% 6.66/2.29 % (31164)Instructions burned: 90 (million)
% 6.66/2.29 % (31164)------------------------------
% 6.66/2.29 % (31164)------------------------------
% 6.66/2.29 % (31161)Instruction limit reached!
% 6.66/2.29 % (31161)------------------------------
% 6.66/2.29 % (31161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.66/2.29 % (31161)Termination reason: Unknown
% 6.66/2.29 % (31161)Termination phase: Saturation
% 6.66/2.29
% 6.66/2.29 % (31161)Memory used [KB]: 7419
% 6.66/2.29 % (31161)Time elapsed: 0.077 s
% 6.66/2.29 % (31161)Instructions burned: 298 (million)
% 6.66/2.29 % (31161)------------------------------
% 6.66/2.29 % (31161)------------------------------
% 7.43/2.30 % (31166)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_30813 for (2993ds/458Mi)
% 7.43/2.30 % (31167)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_30813 for (2993ds/31Mi)
% 7.43/2.30 % (31168)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_30813 for (2993ds/297Mi)
% 7.43/2.31 % (31167)Instruction limit reached!
% 7.43/2.31 % (31167)------------------------------
% 7.43/2.31 % (31167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.43/2.31 % (31167)Termination reason: Unknown
% 7.43/2.31 % (31167)Termination phase: shuffling
% 7.43/2.31
% 7.43/2.31 % (31167)Memory used [KB]: 2046
% 7.43/2.31 % (31167)Time elapsed: 0.010 s
% 7.43/2.31 % (31167)Instructions burned: 31 (million)
% 7.43/2.31 % (31167)------------------------------
% 7.43/2.31 % (31167)------------------------------
% 7.43/2.32 % (31169)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_30813 for (2993ds/987Mi)
% 7.43/2.33 % (31163)Instruction limit reached!
% 7.43/2.33 % (31163)------------------------------
% 7.43/2.33 % (31163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.43/2.33 % (31163)Termination reason: Unknown
% 7.43/2.33 % (31163)Termination phase: Saturation
% 7.43/2.33
% 7.43/2.33 % (31163)Memory used [KB]: 7931
% 7.43/2.33 % (31163)Time elapsed: 0.069 s
% 7.43/2.33 % (31163)Instructions burned: 261 (million)
% 7.43/2.33 % (31163)------------------------------
% 7.43/2.33 % (31163)------------------------------
% 7.43/2.34 % (31156)Instruction limit reached!
% 7.43/2.34 % (31156)------------------------------
% 7.43/2.34 % (31156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.43/2.34 % (31156)Termination reason: Unknown
% 7.43/2.34 % (31156)Termination phase: Saturation
% 7.43/2.34
% 7.43/2.34 % (31156)Memory used [KB]: 9978
% 7.43/2.34 % (31156)Time elapsed: 0.179 s
% 7.43/2.34 % (31156)Instructions burned: 614 (million)
% 7.43/2.34 % (31156)------------------------------
% 7.43/2.34 % (31156)------------------------------
% 7.43/2.34 % (31165)Instruction limit reached!
% 7.43/2.34 % (31165)------------------------------
% 7.43/2.34 % (31165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.43/2.34 % (31165)Termination reason: Unknown
% 7.43/2.34 % (31165)Termination phase: Saturation
% 7.43/2.34
% 7.43/2.34 % (31165)Memory used [KB]: 8443
% 7.43/2.34 % (31165)Time elapsed: 0.061 s
% 7.43/2.34 % (31165)Instructions burned: 232 (million)
% 7.43/2.34 % (31165)------------------------------
% 7.43/2.34 % (31165)------------------------------
% 7.43/2.34 % (31170)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_30813 for (2992ds/182Mi)
% 7.43/2.34 % (31137)Instruction limit reached!
% 7.43/2.34 % (31137)------------------------------
% 7.43/2.34 % (31137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.43/2.34 % (31137)Termination reason: Unknown
% 7.43/2.34 % (31137)Termination phase: Saturation
% 7.43/2.34
% 7.43/2.34 % (31137)Memory used [KB]: 12537
% 7.43/2.34 % (31137)Time elapsed: 0.343 s
% 7.43/2.34 % (31137)Instructions burned: 1087 (million)
% 7.43/2.34 % (31137)------------------------------
% 7.43/2.34 % (31137)------------------------------
% 7.43/2.35 % (31171)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_30813 for (2992ds/182Mi)
% 7.43/2.35 % (31173)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_30813 for (2992ds/79Mi)
% 7.43/2.36 % (31172)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_30813 for (2992ds/154Mi)
% 7.43/2.38 % (31173)Instruction limit reached!
% 7.43/2.38 % (31173)------------------------------
% 7.43/2.38 % (31173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.43/2.38 % (31173)Termination reason: Unknown
% 7.43/2.38 % (31173)Termination phase: Property scanning
% 7.43/2.38
% 7.43/2.38 % (31173)Memory used [KB]: 2558
% 7.43/2.38 % (31173)Time elapsed: 0.022 s
% 7.43/2.38 % (31173)Instructions burned: 81 (million)
% 7.43/2.38 % (31173)------------------------------
% 7.43/2.38 % (31173)------------------------------
% 7.43/2.38 % (31168)Instruction limit reached!
% 7.43/2.38 % (31168)------------------------------
% 7.43/2.38 % (31168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.43/2.38 % (31168)Termination reason: Unknown
% 7.43/2.38 % (31168)Termination phase: Saturation
% 7.43/2.38
% 7.43/2.38 % (31168)Memory used [KB]: 7547
% 7.43/2.38 % (31168)Time elapsed: 0.075 s
% 7.43/2.38 % (31168)Instructions burned: 300 (million)
% 7.43/2.38 % (31168)------------------------------
% 7.43/2.38 % (31168)------------------------------
% 7.43/2.38 % (31174)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_30813 for (2992ds/216Mi)
% 7.43/2.39 % (31175)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_30813 for (2992ds/114Mi)
% 7.43/2.39 % (31170)Instruction limit reached!
% 7.43/2.39 % (31170)------------------------------
% 7.43/2.39 % (31170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.43/2.39 % (31170)Termination reason: Unknown
% 7.43/2.39 % (31170)Termination phase: Saturation
% 7.43/2.39
% 7.43/2.39 % (31170)Memory used [KB]: 7419
% 7.43/2.39 % (31170)Time elapsed: 0.048 s
% 7.43/2.39 % (31170)Instructions burned: 185 (million)
% 7.43/2.39 % (31170)------------------------------
% 7.43/2.39 % (31170)------------------------------
% 7.43/2.40 % (31176)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_30813 for (2992ds/922Mi)
% 8.02/2.40 % (31171)Instruction limit reached!
% 8.02/2.40 % (31171)------------------------------
% 8.02/2.40 % (31171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.40 % (31171)Termination reason: Unknown
% 8.02/2.40 % (31171)Termination phase: Property scanning
% 8.02/2.40
% 8.02/2.40 % (31171)Memory used [KB]: 4989
% 8.02/2.40 % (31171)Time elapsed: 0.053 s
% 8.02/2.40 % (31171)Instructions burned: 185 (million)
% 8.02/2.40 % (31171)------------------------------
% 8.02/2.40 % (31171)------------------------------
% 8.02/2.41 % (31172)Instruction limit reached!
% 8.02/2.41 % (31172)------------------------------
% 8.02/2.41 % (31172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.41 % (31172)Termination reason: Unknown
% 8.02/2.41 % (31172)Termination phase: Property scanning
% 8.02/2.41
% 8.02/2.41 % (31172)Memory used [KB]: 2686
% 8.02/2.41 % (31172)Time elapsed: 0.053 s
% 8.02/2.41 % (31172)Instructions burned: 157 (million)
% 8.02/2.41 % (31172)------------------------------
% 8.02/2.41 % (31172)------------------------------
% 8.02/2.41 % (31177)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_30813 for (2992ds/182Mi)
% 8.02/2.42 % (31175)Instruction limit reached!
% 8.02/2.42 % (31175)------------------------------
% 8.02/2.42 % (31175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.42 % (31175)Termination reason: Unknown
% 8.02/2.42 % (31175)Termination phase: Property scanning
% 8.02/2.42
% 8.02/2.42 % (31175)Memory used [KB]: 2686
% 8.02/2.42 % (31175)Time elapsed: 0.031 s
% 8.02/2.42 % (31175)Instructions burned: 115 (million)
% 8.02/2.42 % (31175)------------------------------
% 8.02/2.42 % (31175)------------------------------
% 8.02/2.42 % (31178)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_30813 for (2992ds/164Mi)
% 8.02/2.42 % (31166)Instruction limit reached!
% 8.02/2.42 % (31166)------------------------------
% 8.02/2.42 % (31166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.42 % (31166)Termination reason: Unknown
% 8.02/2.42 % (31166)Termination phase: Saturation
% 8.02/2.42
% 8.02/2.42 % (31166)Memory used [KB]: 9594
% 8.02/2.42 % (31166)Time elapsed: 0.127 s
% 8.02/2.42 % (31166)Instructions burned: 460 (million)
% 8.02/2.42 % (31166)------------------------------
% 8.02/2.42 % (31166)------------------------------
% 8.02/2.43 % (31179)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_30813 for (2992ds/50Mi)
% 8.02/2.43 % (31180)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_30813 for (2992ds/368Mi)
% 8.02/2.44 % (31174)Instruction limit reached!
% 8.02/2.44 % (31174)------------------------------
% 8.02/2.44 % (31174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.44 % (31174)Termination reason: Unknown
% 8.02/2.44 % (31174)Termination phase: Saturation
% 8.02/2.44
% 8.02/2.44 % (31174)Memory used [KB]: 7547
% 8.02/2.44 % (31174)Time elapsed: 0.055 s
% 8.02/2.44 % (31174)Instructions burned: 219 (million)
% 8.02/2.44 % (31174)------------------------------
% 8.02/2.44 % (31174)------------------------------
% 8.02/2.44 % (31179)Instruction limit reached!
% 8.02/2.44 % (31179)------------------------------
% 8.02/2.44 % (31179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.44 % (31179)Termination reason: Unknown
% 8.02/2.44 % (31179)Termination phase: shuffling
% 8.02/2.44
% 8.02/2.44 % (31179)Memory used [KB]: 2430
% 8.02/2.44 % (31179)Time elapsed: 0.015 s
% 8.02/2.44 % (31179)Instructions burned: 52 (million)
% 8.02/2.44 % (31179)------------------------------
% 8.02/2.44 % (31179)------------------------------
% 8.02/2.45 % (31181)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_30813 for (2991ds/1021Mi)
% 8.02/2.45 % (31182)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_30813 for (2991ds/267Mi)
% 8.02/2.46 % (31177)Instruction limit reached!
% 8.02/2.46 % (31177)------------------------------
% 8.02/2.46 % (31177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.46 % (31177)Termination reason: Unknown
% 8.02/2.46 % (31177)Termination phase: Saturation
% 8.02/2.46
% 8.02/2.46 % (31177)Memory used [KB]: 7419
% 8.02/2.46 % (31177)Time elapsed: 0.047 s
% 8.02/2.46 % (31177)Instructions burned: 184 (million)
% 8.02/2.46 % (31177)------------------------------
% 8.02/2.46 % (31177)------------------------------
% 8.02/2.46 % (31178)Instruction limit reached!
% 8.02/2.46 % (31178)------------------------------
% 8.02/2.46 % (31178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.46 % (31178)Termination reason: Unknown
% 8.02/2.46 % (31178)Termination phase: Property scanning
% 8.02/2.46
% 8.02/2.46 % (31178)Memory used [KB]: 2814
% 8.02/2.46 % (31178)Time elapsed: 0.042 s
% 8.02/2.46 % (31178)Instructions burned: 165 (million)
% 8.02/2.46 % (31178)------------------------------
% 8.02/2.46 % (31178)------------------------------
% 8.02/2.46 % (31183)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_30813 for (2991ds/204Mi)
% 8.02/2.47 % (31184)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_30813 for (2991ds/26Mi)
% 8.02/2.47 % (31184)Instruction limit reached!
% 8.02/2.47 % (31184)------------------------------
% 8.02/2.47 % (31184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.47 % (31184)Termination reason: Unknown
% 8.02/2.47 % (31184)Termination phase: shuffling
% 8.02/2.47
% 8.02/2.47 % (31184)Memory used [KB]: 1918
% 8.02/2.47 % (31184)Time elapsed: 0.008 s
% 8.02/2.47 % (31184)Instructions burned: 26 (million)
% 8.02/2.47 % (31184)------------------------------
% 8.02/2.47 % (31184)------------------------------
% 8.02/2.48 % (31185)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_30813 for (2991ds/53Mi)
% 8.53/2.50 % (31185)Instruction limit reached!
% 8.53/2.50 % (31185)------------------------------
% 8.53/2.50 % (31185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.53/2.50 % (31185)Termination reason: Unknown
% 8.53/2.50 % (31185)Termination phase: shuffling
% 8.53/2.50
% 8.53/2.50 % (31185)Memory used [KB]: 2430
% 8.53/2.50 % (31185)Time elapsed: 0.016 s
% 8.53/2.50 % (31185)Instructions burned: 53 (million)
% 8.53/2.50 % (31185)------------------------------
% 8.53/2.50 % (31185)------------------------------
% 8.53/2.51 % (31186)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_30813 for (2991ds/4436Mi)
% 8.53/2.52 % (31182)Instruction limit reached!
% 8.53/2.52 % (31182)------------------------------
% 8.53/2.52 % (31182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.53/2.52 % (31182)Termination reason: Unknown
% 8.53/2.52 % (31182)Termination phase: Saturation
% 8.53/2.52
% 8.53/2.52 % (31182)Memory used [KB]: 7419
% 8.53/2.52 % (31182)Time elapsed: 0.069 s
% 8.53/2.52 % (31182)Instructions burned: 271 (million)
% 8.53/2.52 % (31182)------------------------------
% 8.53/2.52 % (31182)------------------------------
% 8.53/2.52 % (31183)Instruction limit reached!
% 8.53/2.52 % (31183)------------------------------
% 8.53/2.52 % (31183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.53/2.52 % (31183)Termination reason: Unknown
% 8.53/2.52 % (31183)Termination phase: Saturation
% 8.53/2.52
% 8.53/2.52 % (31183)Memory used [KB]: 7291
% 8.53/2.52 % (31183)Time elapsed: 0.053 s
% 8.53/2.52 % (31183)Instructions burned: 206 (million)
% 8.53/2.52 % (31183)------------------------------
% 8.53/2.52 % (31183)------------------------------
% 8.53/2.53 % (31187)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_30813 for (2991ds/1539Mi)
% 8.53/2.53 % (31188)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_30813 for (2991ds/408Mi)
% 8.53/2.53 % (31180)Instruction limit reached!
% 8.53/2.53 % (31180)------------------------------
% 8.53/2.53 % (31180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.53/2.53 % (31180)Termination reason: Unknown
% 8.53/2.53 % (31180)Termination phase: Saturation
% 8.53/2.53
% 8.53/2.53 % (31180)Memory used [KB]: 9466
% 8.53/2.53 % (31180)Time elapsed: 0.100 s
% 8.53/2.53 % (31180)Instructions burned: 368 (million)
% 8.53/2.53 % (31180)------------------------------
% 8.53/2.53 % (31180)------------------------------
% 8.53/2.54 % (31189)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_30813 for (2990ds/5205Mi)
% 8.53/2.58 % (31169)Instruction limit reached!
% 8.53/2.58 % (31169)------------------------------
% 8.53/2.58 % (31169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.53/2.58 % (31169)Termination reason: Unknown
% 8.53/2.58 % (31169)Termination phase: Saturation
% 8.53/2.58
% 8.53/2.58 % (31169)Memory used [KB]: 16119
% 8.53/2.58 % (31169)Time elapsed: 0.261 s
% 8.53/2.58 % (31169)Instructions burned: 987 (million)
% 8.53/2.58 % (31169)------------------------------
% 8.53/2.58 % (31169)------------------------------
% 8.53/2.59 % (31190)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_30813 for (2990ds/1913Mi)
% 9.08/2.65 % (31188)Instruction limit reached!
% 9.08/2.65 % (31188)------------------------------
% 9.08/2.65 % (31188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.08/2.65 % (31188)Termination reason: Unknown
% 9.08/2.65 % (31188)Termination phase: Saturation
% 9.08/2.65
% 9.08/2.65 % (31188)Memory used [KB]: 11129
% 9.08/2.65 % (31188)Time elapsed: 0.122 s
% 9.08/2.65 % (31188)Instructions burned: 409 (million)
% 9.08/2.65 % (31188)------------------------------
% 9.08/2.65 % (31188)------------------------------
% 9.08/2.66 % (31191)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_30813 for (2989ds/4350Mi)
% 9.08/2.68 % (31176)Instruction limit reached!
% 9.08/2.68 % (31176)------------------------------
% 9.08/2.68 % (31176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.08/2.68 % (31176)Termination reason: Unknown
% 9.08/2.68 % (31176)Termination phase: Saturation
% 9.08/2.68
% 9.08/2.68 % (31176)Memory used [KB]: 12153
% 9.08/2.68 % (31176)Time elapsed: 0.288 s
% 9.08/2.68 % (31176)Instructions burned: 924 (million)
% 9.08/2.68 % (31176)------------------------------
% 9.08/2.68 % (31176)------------------------------
% 9.08/2.69 % (31192)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_30813 for (2989ds/68Mi)
% 9.51/2.71 % (31192)Instruction limit reached!
% 9.51/2.71 % (31192)------------------------------
% 9.51/2.71 % (31192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.51/2.71 % (31192)Termination reason: Unknown
% 9.51/2.71 % (31192)Termination phase: Property scanning
% 9.51/2.71
% 9.51/2.71 % (31192)Memory used [KB]: 2558
% 9.51/2.71 % (31192)Time elapsed: 0.021 s
% 9.51/2.71 % (31192)Instructions burned: 71 (million)
% 9.51/2.71 % (31192)------------------------------
% 9.51/2.71 % (31192)------------------------------
% 9.51/2.72 % (31193)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_30813 for (2989ds/358Mi)
% 9.51/2.77 % (31181)Instruction limit reached!
% 9.51/2.77 % (31181)------------------------------
% 9.51/2.77 % (31181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.51/2.77 % (31181)Termination reason: Unknown
% 9.51/2.77 % (31181)Termination phase: Saturation
% 9.51/2.77
% 9.51/2.77 % (31181)Memory used [KB]: 12665
% 9.51/2.77 % (31181)Time elapsed: 0.319 s
% 9.51/2.77 % (31181)Instructions burned: 1022 (million)
% 9.51/2.77 % (31181)------------------------------
% 9.51/2.77 % (31181)------------------------------
% 9.51/2.78 % (31194)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_30813 for (2988ds/31Mi)
% 9.51/2.79 % (31194)Instruction limit reached!
% 9.51/2.79 % (31194)------------------------------
% 9.51/2.79 % (31194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.51/2.79 % (31194)Termination reason: Unknown
% 9.51/2.79 % (31194)Termination phase: shuffling
% 9.51/2.79
% 9.51/2.79 % (31194)Memory used [KB]: 2174
% 9.51/2.79 % (31194)Time elapsed: 0.010 s
% 9.51/2.79 % (31194)Instructions burned: 32 (million)
% 9.51/2.79 % (31194)------------------------------
% 9.51/2.79 % (31194)------------------------------
% 9.51/2.80 % (31195)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_30813 for (2988ds/279Mi)
% 9.89/2.82 % (31193)Instruction limit reached!
% 9.89/2.82 % (31193)------------------------------
% 9.89/2.82 % (31193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.89/2.82 % (31193)Termination reason: Unknown
% 9.89/2.82 % (31193)Termination phase: Saturation
% 9.89/2.82
% 9.89/2.82 % (31193)Memory used [KB]: 8571
% 9.89/2.82 % (31193)Time elapsed: 0.094 s
% 9.89/2.82 % (31193)Instructions burned: 359 (million)
% 9.89/2.82 % (31193)------------------------------
% 9.89/2.82 % (31193)------------------------------
% 9.89/2.82 % (31196)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_30813 for (2988ds/258Mi)
% 9.89/2.87 % (31195)Instruction limit reached!
% 9.89/2.87 % (31195)------------------------------
% 9.89/2.87 % (31195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.89/2.87 % (31195)Termination reason: Unknown
% 9.89/2.87 % (31195)Termination phase: Saturation
% 9.89/2.87
% 9.89/2.87 % (31195)Memory used [KB]: 7547
% 9.89/2.87 % (31195)Time elapsed: 0.072 s
% 9.89/2.87 % (31195)Instructions burned: 282 (million)
% 9.89/2.87 % (31195)------------------------------
% 9.89/2.87 % (31195)------------------------------
% 9.89/2.88 % (31197)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_30813 for (2987ds/26Mi)
% 9.89/2.88 % (31197)Instruction limit reached!
% 9.89/2.88 % (31197)------------------------------
% 9.89/2.88 % (31197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.89/2.88 % (31197)Termination reason: Unknown
% 9.89/2.88 % (31197)Termination phase: shuffling
% 9.89/2.88
% 9.89/2.88 % (31197)Memory used [KB]: 1918
% 9.89/2.88 % (31197)Time elapsed: 0.008 s
% 9.89/2.88 % (31197)Instructions burned: 26 (million)
% 9.89/2.88 % (31197)------------------------------
% 9.89/2.88 % (31197)------------------------------
% 9.89/2.89 % (31198)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_30813 for (2987ds/995Mi)
% 9.89/2.89 % (31196)Instruction limit reached!
% 9.89/2.89 % (31196)------------------------------
% 9.89/2.89 % (31196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.89/2.89 % (31196)Termination reason: Unknown
% 9.89/2.89 % (31196)Termination phase: Saturation
% 9.89/2.89
% 9.89/2.89 % (31196)Memory used [KB]: 8315
% 9.89/2.89 % (31196)Time elapsed: 0.069 s
% 9.89/2.89 % (31196)Instructions burned: 258 (million)
% 9.89/2.89 % (31196)------------------------------
% 9.89/2.89 % (31196)------------------------------
% 10.17/2.90 % (31199)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_30813 for (2987ds/373Mi)
% 10.17/3.00 % (31187)Instruction limit reached!
% 10.17/3.00 % (31187)------------------------------
% 10.17/3.00 % (31187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.17/3.00 % (31187)Termination reason: Unknown
% 10.17/3.00 % (31187)Termination phase: Saturation
% 10.17/3.00
% 10.17/3.00 % (31187)Memory used [KB]: 10746
% 10.17/3.00 % (31187)Time elapsed: 0.476 s
% 10.17/3.00 % (31187)Instructions burned: 1540 (million)
% 10.17/3.00 % (31187)------------------------------
% 10.17/3.00 % (31187)------------------------------
% 10.17/3.00 % (31199)Instruction limit reached!
% 10.17/3.00 % (31199)------------------------------
% 10.17/3.00 % (31199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.17/3.00 % (31199)Termination reason: Unknown
% 10.17/3.00 % (31199)Termination phase: Saturation
% 10.17/3.00
% 10.17/3.00 % (31199)Memory used [KB]: 9466
% 10.17/3.00 % (31199)Time elapsed: 0.101 s
% 10.17/3.00 % (31199)Instructions burned: 374 (million)
% 10.17/3.00 % (31199)------------------------------
% 10.17/3.00 % (31199)------------------------------
% 10.17/3.01 % (31200)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_30813 for (2986ds/253Mi)
% 10.17/3.01 % (31201)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_30813 for (2986ds/832Mi)
% 12.64/3.07 % (31200)Instruction limit reached!
% 12.64/3.07 % (31200)------------------------------
% 12.64/3.07 % (31200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.64/3.07 % (31200)Termination reason: Unknown
% 12.64/3.07 % (31200)Termination phase: Saturation
% 12.64/3.07
% 12.64/3.07 % (31200)Memory used [KB]: 7419
% 12.64/3.07 % (31200)Time elapsed: 0.064 s
% 12.64/3.07 % (31200)Instructions burned: 253 (million)
% 12.64/3.07 % (31200)------------------------------
% 12.64/3.07 % (31200)------------------------------
% 12.64/3.08 % (31202)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_30813 for (2985ds/668Mi)
% 13.21/3.15 % (31198)Instruction limit reached!
% 13.21/3.15 % (31198)------------------------------
% 13.21/3.15 % (31198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.21/3.15 % (31198)Termination reason: Unknown
% 13.21/3.15 % (31198)Termination phase: Saturation
% 13.21/3.15
% 13.21/3.15 % (31198)Memory used [KB]: 15991
% 13.21/3.15 % (31198)Time elapsed: 0.255 s
% 13.21/3.15 % (31198)Instructions burned: 996 (million)
% 13.21/3.15 % (31198)------------------------------
% 13.21/3.15 % (31198)------------------------------
% 13.21/3.16 % (31203)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_30813 for (2984ds/40Mi)
% 13.21/3.16 % (31190)Instruction limit reached!
% 13.21/3.16 % (31190)------------------------------
% 13.21/3.16 % (31190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.21/3.16 % (31190)Termination reason: Unknown
% 13.21/3.16 % (31190)Termination phase: Saturation
% 13.21/3.16
% 13.21/3.16 % (31190)Memory used [KB]: 6140
% 13.21/3.16 % (31190)Time elapsed: 0.576 s
% 13.21/3.16 % (31190)Instructions burned: 1913 (million)
% 13.21/3.16 % (31190)------------------------------
% 13.21/3.16 % (31190)------------------------------
% 13.21/3.17 % (31203)Instruction limit reached!
% 13.21/3.17 % (31203)------------------------------
% 13.21/3.17 % (31203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.21/3.17 % (31203)Termination reason: Unknown
% 13.21/3.17 % (31203)Termination phase: shuffling
% 13.21/3.17
% 13.21/3.17 % (31203)Memory used [KB]: 2302
% 13.21/3.17 % (31203)Time elapsed: 0.012 s
% 13.21/3.17 % (31203)Instructions burned: 40 (million)
% 13.21/3.17 % (31203)------------------------------
% 13.21/3.17 % (31203)------------------------------
% 13.21/3.17 % (31204)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_30813 for (2984ds/294Mi)
% 13.21/3.18 % (31205)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_30813 for (2984ds/187Mi)
% 13.58/3.23 % (31205)Instruction limit reached!
% 13.58/3.23 % (31205)------------------------------
% 13.58/3.23 % (31205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.58/3.23 % (31205)Termination reason: Unknown
% 13.58/3.23 % (31205)Termination phase: Saturation
% 13.58/3.23
% 13.58/3.23 % (31205)Memory used [KB]: 7419
% 13.58/3.23 % (31205)Time elapsed: 0.051 s
% 13.58/3.23 % (31205)Instructions burned: 189 (million)
% 13.58/3.23 % (31205)------------------------------
% 13.58/3.23 % (31205)------------------------------
% 13.58/3.24 % (31206)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_30813 for (2983ds/371Mi)
% 13.58/3.25 % (31204)Instruction limit reached!
% 13.58/3.25 % (31204)------------------------------
% 13.58/3.25 % (31204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.58/3.25 % (31204)Termination reason: Unknown
% 13.58/3.25 % (31204)Termination phase: Saturation
% 13.58/3.25
% 13.58/3.25 % (31204)Memory used [KB]: 7547
% 13.58/3.25 % (31204)Time elapsed: 0.076 s
% 13.58/3.25 % (31204)Instructions burned: 295 (million)
% 13.58/3.25 % (31204)------------------------------
% 13.58/3.25 % (31204)------------------------------
% 13.58/3.26 % (31202)Instruction limit reached!
% 13.58/3.26 % (31202)------------------------------
% 13.58/3.26 % (31202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.58/3.26 % (31202)Termination reason: Unknown
% 13.58/3.26 % (31202)Termination phase: Saturation
% 13.58/3.26
% 13.58/3.26 % (31202)Memory used [KB]: 15607
% 13.58/3.26 % (31202)Time elapsed: 0.174 s
% 13.58/3.26 % (31202)Instructions burned: 669 (million)
% 13.58/3.26 % (31202)------------------------------
% 13.58/3.26 % (31202)------------------------------
% 13.58/3.26 % (31207)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_30813 for (2983ds/1827Mi)
% 13.58/3.27 % (31208)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_30813 for (2983ds/70Mi)
% 13.58/3.27 % (31201)Instruction limit reached!
% 13.58/3.27 % (31201)------------------------------
% 13.58/3.27 % (31201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.58/3.27 % (31201)Termination reason: Unknown
% 13.58/3.27 % (31201)Termination phase: Saturation
% 13.58/3.27
% 13.58/3.27 % (31201)Memory used [KB]: 11513
% 13.58/3.27 % (31201)Time elapsed: 0.258 s
% 13.58/3.27 % (31201)Instructions burned: 834 (million)
% 13.58/3.27 % (31201)------------------------------
% 13.58/3.27 % (31201)------------------------------
% 13.58/3.28 % (31209)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_30813 for (2983ds/316Mi)
% 13.58/3.29 % (31208)Instruction limit reached!
% 13.58/3.29 % (31208)------------------------------
% 13.58/3.29 % (31208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.58/3.29 % (31208)Termination reason: Unknown
% 13.58/3.29 % (31208)Termination phase: Property scanning
% 13.58/3.29
% 13.58/3.29 % (31208)Memory used [KB]: 2558
% 13.58/3.29 % (31208)Time elapsed: 0.020 s
% 13.58/3.29 % (31208)Instructions burned: 74 (million)
% 13.58/3.29 % (31208)------------------------------
% 13.58/3.29 % (31208)------------------------------
% 13.58/3.30 % (31210)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_30813 for (2983ds/932Mi)
% 14.50/3.34 % (31206)Instruction limit reached!
% 14.50/3.34 % (31206)------------------------------
% 14.50/3.34 % (31206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.50/3.34 % (31206)Termination reason: Unknown
% 14.50/3.34 % (31206)Termination phase: Saturation
% 14.50/3.34
% 14.50/3.34 % (31206)Memory used [KB]: 9338
% 14.50/3.34 % (31206)Time elapsed: 0.100 s
% 14.50/3.34 % (31206)Instructions burned: 372 (million)
% 14.50/3.34 % (31206)------------------------------
% 14.50/3.34 % (31206)------------------------------
% 14.50/3.35 % (31211)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_30813 for (2982ds/4714Mi)
% 14.50/3.36 % (31209)Instruction limit reached!
% 14.50/3.36 % (31209)------------------------------
% 14.50/3.36 % (31209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.50/3.36 % (31209)Termination reason: Unknown
% 14.50/3.36 % (31209)Termination phase: Saturation
% 14.50/3.36
% 14.50/3.36 % (31209)Memory used [KB]: 7547
% 14.50/3.36 % (31209)Time elapsed: 0.081 s
% 14.50/3.36 % (31209)Instructions burned: 316 (million)
% 14.50/3.36 % (31209)------------------------------
% 14.50/3.36 % (31209)------------------------------
% 14.50/3.37 % (31212)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_30813 for (2982ds/8250Mi)
% 15.30/3.54 % (31210)Instruction limit reached!
% 15.30/3.54 % (31210)------------------------------
% 15.30/3.54 % (31210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.30/3.54 % (31210)Termination reason: Unknown
% 15.30/3.54 % (31210)Termination phase: Saturation
% 15.30/3.54
% 15.30/3.54 % (31210)Memory used [KB]: 16375
% 15.30/3.54 % (31210)Time elapsed: 0.246 s
% 15.30/3.54 % (31210)Instructions burned: 933 (million)
% 15.30/3.54 % (31210)------------------------------
% 15.30/3.54 % (31210)------------------------------
% 15.30/3.55 % (31213)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_30813 for (2980ds/770Mi)
% 16.16/3.76 % (31213)Instruction limit reached!
% 16.16/3.76 % (31213)------------------------------
% 16.16/3.76 % (31213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.16/3.76 % (31213)Termination reason: Unknown
% 16.16/3.76 % (31213)Termination phase: Saturation
% 16.16/3.76
% 16.16/3.76 % (31213)Memory used [KB]: 7675
% 16.16/3.76 % (31213)Time elapsed: 0.209 s
% 16.16/3.76 % (31213)Instructions burned: 773 (million)
% 16.16/3.76 % (31213)------------------------------
% 16.16/3.76 % (31213)------------------------------
% 16.16/3.77 % (31214)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_30813 for (2978ds/794Mi)
% 16.16/3.77 % (31207)Instruction limit reached!
% 16.16/3.77 % (31207)------------------------------
% 16.16/3.77 % (31207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.16/3.77 % (31207)Termination reason: Unknown
% 16.16/3.77 % (31207)Termination phase: Saturation
% 16.16/3.77
% 16.16/3.77 % (31207)Memory used [KB]: 20980
% 16.16/3.77 % (31207)Time elapsed: 0.518 s
% 16.16/3.77 % (31207)Instructions burned: 1828 (million)
% 16.16/3.77 % (31207)------------------------------
% 16.16/3.77 % (31207)------------------------------
% 16.16/3.79 % (31215)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_30813 for (2978ds/464Mi)
% 17.52/3.91 % (31186)Instruction limit reached!
% 17.52/3.91 % (31186)------------------------------
% 17.52/3.91 % (31186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.52/3.91 % (31186)Termination reason: Unknown
% 17.52/3.91 % (31186)Termination phase: Saturation
% 17.52/3.91
% 17.52/3.91 % (31186)Memory used [KB]: 15095
% 17.52/3.91 % (31186)Time elapsed: 1.404 s
% 17.52/3.91 % (31186)Instructions burned: 4438 (million)
% 17.52/3.91 % (31186)------------------------------
% 17.52/3.91 % (31186)------------------------------
% 17.52/3.92 % (31215)Instruction limit reached!
% 17.52/3.92 % (31215)------------------------------
% 17.52/3.92 % (31215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.52/3.92 % (31215)Termination reason: Unknown
% 17.52/3.92 % (31215)Termination phase: Saturation
% 17.52/3.92
% 17.52/3.92 % (31215)Memory used [KB]: 9722
% 17.52/3.92 % (31215)Time elapsed: 0.132 s
% 17.52/3.92 % (31215)Instructions burned: 465 (million)
% 17.52/3.92 % (31215)------------------------------
% 17.52/3.92 % (31215)------------------------------
% 17.52/3.92 % (31189)Instruction limit reached!
% 17.52/3.92 % (31189)------------------------------
% 17.52/3.92 % (31189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.52/3.92 % (31189)Termination reason: Unknown
% 17.52/3.92 % (31189)Termination phase: Saturation
% 17.52/3.92
% 17.52/3.92 % (31189)Memory used [KB]: 16886
% 17.52/3.92 % (31189)Time elapsed: 1.388 s
% 17.52/3.92 % (31189)Instructions burned: 5205 (million)
% 17.52/3.92 % (31189)------------------------------
% 17.52/3.92 % (31189)------------------------------
% 17.52/3.92 % (31216)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_30813 for (2977ds/1376Mi)
% 17.52/3.93 % (31217)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_30813 for (2977ds/906Mi)
% 17.52/3.93 % (31218)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_30813 for (2977ds/434Mi)
% 17.52/4.00 % (31191)Refutation not found, non-redundant clauses discarded% (31191)------------------------------
% 17.52/4.00 % (31191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.52/4.00 % (31191)Termination reason: Refutation not found, non-redundant clauses discarded
% 17.52/4.00
% 17.52/4.00 % (31191)Memory used [KB]: 13688
% 17.52/4.00 % (31191)Time elapsed: 1.346 s
% 17.52/4.00 % (31191)Instructions burned: 4328 (million)
% 17.52/4.00 % (31191)------------------------------
% 17.52/4.00 % (31191)------------------------------
% 17.52/4.01 % (31214)Instruction limit reached!
% 17.52/4.01 % (31214)------------------------------
% 17.52/4.01 % (31214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.52/4.01 % (31214)Termination reason: Unknown
% 17.52/4.01 % (31214)Termination phase: Saturation
% 17.52/4.01
% 17.52/4.01 % (31214)Memory used [KB]: 6012
% 17.52/4.01 % (31214)Time elapsed: 0.241 s
% 17.52/4.01 % (31214)Instructions burned: 795 (million)
% 17.52/4.01 % (31214)------------------------------
% 17.52/4.01 % (31214)------------------------------
% 17.52/4.01 % (31219)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_30813 for (2976ds/865Mi)
% 17.52/4.02 % (31220)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_30813 for (2976ds/593Mi)
% 19.73/4.05 % (31218)Instruction limit reached!
% 19.73/4.05 % (31218)------------------------------
% 19.73/4.05 % (31218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.73/4.05 % (31218)Termination reason: Unknown
% 19.73/4.05 % (31218)Termination phase: Saturation
% 19.73/4.05
% 19.73/4.05 % (31218)Memory used [KB]: 11129
% 19.73/4.05 % (31218)Time elapsed: 0.127 s
% 19.73/4.05 % (31218)Instructions burned: 436 (million)
% 19.73/4.05 % (31218)------------------------------
% 19.73/4.05 % (31218)------------------------------
% 19.73/4.06 % (31221)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_30813 for (2975ds/443Mi)
% 20.17/4.16 % (31220)Instruction limit reached!
% 20.17/4.16 % (31220)------------------------------
% 20.17/4.16 % (31220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.17/4.16 % (31220)Termination reason: Unknown
% 20.17/4.16 % (31220)Termination phase: Saturation
% 20.17/4.16
% 20.17/4.16 % (31220)Memory used [KB]: 7675
% 20.17/4.16 % (31220)Time elapsed: 0.148 s
% 20.17/4.16 % (31220)Instructions burned: 596 (million)
% 20.17/4.16 % (31220)------------------------------
% 20.17/4.16 % (31220)------------------------------
% 20.17/4.18 % (31222)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_30813 for (2974ds/594Mi)
% 20.17/4.18 % (31221)Instruction limit reached!
% 20.17/4.18 % (31221)------------------------------
% 20.17/4.18 % (31221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.17/4.18 % (31221)Termination reason: Unknown
% 20.17/4.18 % (31221)Termination phase: Saturation
% 20.17/4.18
% 20.17/4.18 % (31221)Memory used [KB]: 9722
% 20.17/4.18 % (31221)Time elapsed: 0.121 s
% 20.17/4.18 % (31221)Instructions burned: 445 (million)
% 20.17/4.18 % (31221)------------------------------
% 20.17/4.18 % (31221)------------------------------
% 20.17/4.19 % (31223)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_30813 for (2974ds/327Mi)
% 20.75/4.20 % (31217)Instruction limit reached!
% 20.75/4.20 % (31217)------------------------------
% 20.75/4.20 % (31217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.75/4.20 % (31217)Termination reason: Unknown
% 20.75/4.20 % (31217)Termination phase: Saturation
% 20.75/4.20
% 20.75/4.20 % (31217)Memory used [KB]: 11257
% 20.75/4.20 % (31217)Time elapsed: 0.276 s
% 20.75/4.20 % (31217)Instructions burned: 907 (million)
% 20.75/4.20 % (31217)------------------------------
% 20.75/4.20 % (31217)------------------------------
% 20.75/4.21 % (31224)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_30813 for (2974ds/5411Mi)
% 20.75/4.27 % (31219)Instruction limit reached!
% 20.75/4.27 % (31219)------------------------------
% 20.75/4.27 % (31219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.75/4.27 % (31219)Termination reason: Unknown
% 20.75/4.27 % (31219)Termination phase: Saturation
% 20.75/4.27
% 20.75/4.27 % (31219)Memory used [KB]: 10490
% 20.75/4.27 % (31219)Time elapsed: 0.255 s
% 20.75/4.27 % (31219)Instructions burned: 865 (million)
% 20.75/4.27 % (31219)------------------------------
% 20.75/4.27 % (31219)------------------------------
% 20.75/4.27 % (31216)Instruction limit reached!
% 20.75/4.27 % (31216)------------------------------
% 20.75/4.27 % (31216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.75/4.27 % (31216)Termination reason: Unknown
% 20.75/4.27 % (31216)Termination phase: Saturation
% 20.75/4.27
% 20.75/4.27 % (31216)Memory used [KB]: 9978
% 20.75/4.27 % (31216)Time elapsed: 0.350 s
% 20.75/4.27 % (31216)Instructions burned: 1379 (million)
% 20.75/4.27 % (31216)------------------------------
% 20.75/4.27 % (31216)------------------------------
% 20.75/4.28 % (31225)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_30813 for (2973ds/1762Mi)
% 20.75/4.28 % (31226)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_30813 for (2973ds/96Mi)
% 20.75/4.29 % (31223)Instruction limit reached!
% 20.75/4.29 % (31223)------------------------------
% 20.75/4.29 % (31223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.75/4.29 % (31223)Termination reason: Unknown
% 20.75/4.29 % (31223)Termination phase: Saturation
% 20.75/4.29
% 20.75/4.29 % (31223)Memory used [KB]: 11257
% 20.75/4.29 % (31223)Time elapsed: 0.097 s
% 20.75/4.29 % (31223)Instructions burned: 327 (million)
% 20.75/4.29 % (31223)------------------------------
% 20.75/4.29 % (31223)------------------------------
% 21.40/4.30 % (31227)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_30813 for (2973ds/503Mi)
% 21.40/4.31 % (31226)Instruction limit reached!
% 21.40/4.31 % (31226)------------------------------
% 21.40/4.31 % (31226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.40/4.31 % (31226)Termination reason: Unknown
% 21.40/4.31 % (31226)Termination phase: Property scanning
% 21.40/4.31
% 21.40/4.31 % (31226)Memory used [KB]: 2558
% 21.40/4.31 % (31226)Time elapsed: 0.026 s
% 21.40/4.31 % (31226)Instructions burned: 98 (million)
% 21.40/4.31 % (31226)------------------------------
% 21.40/4.31 % (31226)------------------------------
% 21.40/4.31 % (31228)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_30813 for (2973ds/90Mi)
% 21.40/4.34 % (31228)Instruction limit reached!
% 21.40/4.34 % (31228)------------------------------
% 21.40/4.34 % (31228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.40/4.34 % (31228)Termination reason: Unknown
% 21.40/4.34 % (31228)Termination phase: Property scanning
% 21.40/4.34
% 21.40/4.34 % (31228)Memory used [KB]: 2686
% 21.40/4.34 % (31228)Time elapsed: 0.025 s
% 21.40/4.34 % (31228)Instructions burned: 92 (million)
% 21.40/4.34 % (31228)------------------------------
% 21.40/4.34 % (31228)------------------------------
% 21.40/4.34 % (31222)Instruction limit reached!
% 21.40/4.34 % (31222)------------------------------
% 21.40/4.34 % (31222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.40/4.34 % (31222)Termination reason: Unknown
% 21.40/4.34 % (31222)Termination phase: Saturation
% 21.40/4.34
% 21.40/4.34 % (31222)Memory used [KB]: 9722
% 21.40/4.34 % (31222)Time elapsed: 0.171 s
% 21.40/4.34 % (31222)Instructions burned: 596 (million)
% 21.40/4.34 % (31222)------------------------------
% 21.40/4.34 % (31222)------------------------------
% 21.40/4.35 % (31229)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_30813 for (2972ds/593Mi)
% 21.40/4.35 % (31230)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_30813 for (2972ds/1512Mi)
% 21.85/4.44 % (31227)Instruction limit reached!
% 21.85/4.44 % (31227)------------------------------
% 21.85/4.44 % (31227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.85/4.44 % (31227)Termination reason: Unknown
% 21.85/4.44 % (31227)Termination phase: Saturation
% 21.85/4.44
% 21.85/4.44 % (31227)Memory used [KB]: 9850
% 21.85/4.44 % (31227)Time elapsed: 0.139 s
% 21.85/4.44 % (31227)Instructions burned: 503 (million)
% 21.85/4.44 % (31227)------------------------------
% 21.85/4.44 % (31227)------------------------------
% 21.85/4.45 % (31231)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_30813 for (2971ds/569Mi)
% 22.20/4.52 % (31229)Instruction limit reached!
% 22.20/4.52 % (31229)------------------------------
% 22.20/4.52 % (31229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.20/4.52 % (31229)Termination reason: Unknown
% 22.20/4.52 % (31229)Termination phase: Saturation
% 22.20/4.52
% 22.20/4.52 % (31229)Memory used [KB]: 9978
% 22.20/4.52 % (31229)Time elapsed: 0.173 s
% 22.20/4.52 % (31229)Instructions burned: 593 (million)
% 22.20/4.52 % (31229)------------------------------
% 22.20/4.52 % (31229)------------------------------
% 22.20/4.52 % (31211)Instruction limit reached!
% 22.20/4.52 % (31211)------------------------------
% 22.20/4.52 % (31211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.20/4.52 % (31211)Termination reason: Unknown
% 22.20/4.52 % (31211)Termination phase: Saturation
% 22.20/4.52
% 22.20/4.52 % (31211)Memory used [KB]: 7675
% 22.20/4.52 % (31211)Time elapsed: 1.181 s
% 22.20/4.52 % (31211)Instructions burned: 4715 (million)
% 22.20/4.52 % (31211)------------------------------
% 22.20/4.52 % (31211)------------------------------
% 22.20/4.53 % (31232)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_30813 for (2970ds/501Mi)
% 22.20/4.54 % (31233)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_30813 for (2970ds/562Mi)
% 22.20/4.59 % (31231)Instruction limit reached!
% 22.20/4.59 % (31231)------------------------------
% 22.20/4.59 % (31231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.20/4.59 % (31231)Termination reason: Unknown
% 22.20/4.59 % (31231)Termination phase: Saturation
% 22.20/4.59
% 22.20/4.59 % (31231)Memory used [KB]: 7547
% 22.20/4.59 % (31231)Time elapsed: 0.148 s
% 22.20/4.59 % (31231)Instructions burned: 571 (million)
% 22.20/4.59 % (31231)------------------------------
% 22.20/4.59 % (31231)------------------------------
% 22.67/4.60 % (31234)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_30813 for (2970ds/406Mi)
% 22.67/4.68 % (31232)Instruction limit reached!
% 22.67/4.68 % (31232)------------------------------
% 22.67/4.68 % (31232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.67/4.68 % (31232)Termination reason: Unknown
% 22.67/4.68 % (31232)Termination phase: Saturation
% 22.67/4.68
% 22.67/4.68 % (31232)Memory used [KB]: 10490
% 22.67/4.68 % (31232)Time elapsed: 0.153 s
% 22.67/4.68 % (31232)Instructions burned: 501 (million)
% 22.67/4.68 % (31232)------------------------------
% 22.67/4.68 % (31232)------------------------------
% 22.67/4.69 % (31235)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_30813 for (2969ds/582Mi)
% 22.94/4.70 % (31233)Instruction limit reached!
% 22.94/4.70 % (31233)------------------------------
% 22.94/4.70 % (31233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.94/4.70 % (31233)Termination reason: Unknown
% 22.94/4.70 % (31233)Termination phase: Saturation
% 22.94/4.70
% 22.94/4.70 % (31233)Memory used [KB]: 9210
% 22.94/4.70 % (31233)Time elapsed: 0.164 s
% 22.94/4.70 % (31233)Instructions burned: 562 (million)
% 22.94/4.70 % (31233)------------------------------
% 22.94/4.70 % (31233)------------------------------
% 22.94/4.71 % (31236)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_30813 for (2969ds/456Mi)
% 22.94/4.71 % (31225)Instruction limit reached!
% 22.94/4.71 % (31225)------------------------------
% 22.94/4.71 % (31225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.94/4.71 % (31225)Termination reason: Unknown
% 22.94/4.71 % (31225)Termination phase: Saturation
% 22.94/4.71
% 22.94/4.71 % (31225)Memory used [KB]: 23027
% 22.94/4.71 % (31225)Time elapsed: 0.437 s
% 22.94/4.71 % (31225)Instructions burned: 1765 (million)
% 22.94/4.71 % (31225)------------------------------
% 22.94/4.71 % (31225)------------------------------
% 22.94/4.71 % (31234)Instruction limit reached!
% 22.94/4.71 % (31234)------------------------------
% 22.94/4.71 % (31234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.94/4.71 % (31234)Termination reason: Unknown
% 22.94/4.71 % (31234)Termination phase: Saturation
% 22.94/4.71
% 22.94/4.71 % (31234)Memory used [KB]: 7803
% 22.94/4.71 % (31234)Time elapsed: 0.110 s
% 22.94/4.71 % (31234)Instructions burned: 406 (million)
% 22.94/4.71 % (31234)------------------------------
% 22.94/4.71 % (31234)------------------------------
% 22.94/4.72 % (31237)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_30813 for (2969ds/393Mi)
% 22.94/4.72 % (31238)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_30813 for (2969ds/1335Mi)
% 23.78/4.82 % (31237)Instruction limit reached!
% 23.78/4.82 % (31237)------------------------------
% 23.78/4.82 % (31237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.78/4.82 % (31237)Termination reason: Unknown
% 23.78/4.82 % (31237)Termination phase: Saturation
% 23.78/4.82
% 23.78/4.82 % (31237)Memory used [KB]: 9722
% 23.78/4.82 % (31237)Time elapsed: 0.100 s
% 23.78/4.82 % (31237)Instructions burned: 393 (million)
% 23.78/4.82 % (31237)------------------------------
% 23.78/4.82 % (31237)------------------------------
% 23.78/4.82 % (31230)Instruction limit reached!
% 23.78/4.82 % (31230)------------------------------
% 23.78/4.82 % (31230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.78/4.82 % (31230)Termination reason: Unknown
% 23.78/4.82 % (31230)Termination phase: Saturation
% 23.78/4.82
% 23.78/4.82 % (31230)Memory used [KB]: 14456
% 23.78/4.82 % (31230)Time elapsed: 0.492 s
% 23.78/4.82 % (31230)Instructions burned: 1513 (million)
% 23.78/4.82 % (31230)------------------------------
% 23.78/4.82 % (31230)------------------------------
% 23.78/4.83 % (31236)Instruction limit reached!
% 23.78/4.83 % (31236)------------------------------
% 23.78/4.83 % (31236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.78/4.83 % (31236)Termination reason: Unknown
% 23.78/4.83 % (31236)Termination phase: Saturation
% 23.78/4.83
% 23.78/4.83 % (31236)Memory used [KB]: 9594
% 23.78/4.83 % (31236)Time elapsed: 0.125 s
% 23.78/4.83 % (31236)Instructions burned: 456 (million)
% 23.78/4.83 % (31236)------------------------------
% 23.78/4.83 % (31236)------------------------------
% 23.78/4.83 % (31239)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_30813 for (2968ds/3373Mi)
% 23.78/4.84 % (31240)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_30813 for (2967ds/474Mi)
% 23.78/4.84 % (31241)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_30813 for (2967ds/157Mi)
% 23.78/4.87 % (31235)Instruction limit reached!
% 23.78/4.87 % (31235)------------------------------
% 23.78/4.87 % (31235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.78/4.87 % (31235)Termination reason: Unknown
% 23.78/4.87 % (31235)Termination phase: Saturation
% 23.78/4.87
% 23.78/4.87 % (31235)Memory used [KB]: 10746
% 23.78/4.87 % (31235)Time elapsed: 0.177 s
% 23.78/4.87 % (31235)Instructions burned: 584 (million)
% 23.78/4.87 % (31235)------------------------------
% 23.78/4.87 % (31235)------------------------------
% 23.78/4.88 % (31242)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_30813 for (2967ds/590Mi)
% 23.78/4.88 % (31241)Instruction limit reached!
% 23.78/4.88 % (31241)------------------------------
% 23.78/4.88 % (31241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.78/4.88 % (31241)Termination reason: Unknown
% 23.78/4.88 % (31241)Termination phase: Property scanning
% 23.78/4.88
% 23.78/4.88 % (31241)Memory used [KB]: 2686
% 23.78/4.88 % (31241)Time elapsed: 0.040 s
% 23.78/4.88 % (31241)Instructions burned: 159 (million)
% 23.78/4.88 % (31241)------------------------------
% 23.78/4.88 % (31241)------------------------------
% 23.78/4.89 % (31243)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_30813 for (2967ds/104Mi)
% 24.85/4.92 % (31243)Instruction limit reached!
% 24.85/4.92 % (31243)------------------------------
% 24.85/4.92 % (31243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.85/4.92 % (31243)Termination reason: Unknown
% 24.85/4.92 % (31243)Termination phase: Property scanning
% 24.85/4.92
% 24.85/4.92 % (31243)Memory used [KB]: 2686
% 24.85/4.92 % (31243)Time elapsed: 0.030 s
% 24.85/4.92 % (31243)Instructions burned: 106 (million)
% 24.85/4.92 % (31243)------------------------------
% 24.85/4.92 % (31243)------------------------------
% 24.85/4.93 % (31244)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_30813 for (2967ds/414Mi)
% 24.85/4.95 % (31240)Instruction limit reached!
% 24.85/4.95 % (31240)------------------------------
% 24.85/4.95 % (31240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.85/4.95 % (31240)Termination reason: Unknown
% 24.85/4.95 % (31240)Termination phase: Saturation
% 24.85/4.95
% 24.85/4.95 % (31240)Memory used [KB]: 7547
% 24.85/4.95 % (31240)Time elapsed: 0.120 s
% 24.85/4.95 % (31240)Instructions burned: 475 (million)
% 24.85/4.95 % (31240)------------------------------
% 24.85/4.95 % (31240)------------------------------
% 24.85/4.96 % (31245)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_30813 for (2966ds/715Mi)
% 26.76/5.03 % (31244)Instruction limit reached!
% 26.76/5.03 % (31244)------------------------------
% 26.76/5.03 % (31244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.76/5.03 % (31244)Termination reason: Unknown
% 26.76/5.03 % (31244)Termination phase: Saturation
% 26.76/5.03
% 26.76/5.03 % (31244)Memory used [KB]: 7547
% 26.76/5.03 % (31244)Time elapsed: 0.103 s
% 26.76/5.03 % (31244)Instructions burned: 416 (million)
% 26.76/5.03 % (31244)------------------------------
% 26.76/5.03 % (31244)------------------------------
% 26.76/5.04 % (31246)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_30813 for (2966ds/961Mi)
% 26.76/5.04 % (31242)Instruction limit reached!
% 26.76/5.04 % (31242)------------------------------
% 26.76/5.04 % (31242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.76/5.04 % (31242)Termination reason: Unknown
% 26.76/5.04 % (31242)Termination phase: Saturation
% 26.76/5.04
% 26.76/5.04 % (31242)Memory used [KB]: 8827
% 26.76/5.04 % (31242)Time elapsed: 0.168 s
% 26.76/5.04 % (31242)Instructions burned: 590 (million)
% 26.76/5.04 % (31242)------------------------------
% 26.76/5.04 % (31242)------------------------------
% 26.76/5.05 % (31247)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_30813 for (2965ds/1213Mi)
% 26.76/5.11 % (31238)Instruction limit reached!
% 26.76/5.11 % (31238)------------------------------
% 26.76/5.11 % (31238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.76/5.11 % (31238)Termination reason: Unknown
% 26.76/5.11 % (31238)Termination phase: Saturation
% 26.76/5.11
% 26.76/5.11 % (31238)Memory used [KB]: 10234
% 26.76/5.11 % (31238)Time elapsed: 0.388 s
% 26.76/5.11 % (31238)Instructions burned: 1338 (million)
% 26.76/5.11 % (31238)------------------------------
% 26.76/5.11 % (31238)------------------------------
% 26.76/5.12 % (31248)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_30813 for (2965ds/1979Mi)
% 27.29/5.17 % (31245)Instruction limit reached!
% 27.29/5.17 % (31245)------------------------------
% 27.29/5.17 % (31245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.29/5.17 % (31245)Termination reason: Unknown
% 27.29/5.17 % (31245)Termination phase: Saturation
% 27.29/5.17
% 27.29/5.17 % (31245)Memory used [KB]: 5500
% 27.29/5.17 % (31245)Time elapsed: 0.210 s
% 27.29/5.17 % (31245)Instructions burned: 717 (million)
% 27.29/5.17 % (31245)------------------------------
% 27.29/5.17 % (31245)------------------------------
% 27.29/5.18 % (31249)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_30813 for (2964ds/481Mi)
% 27.86/5.30 % (31249)Instruction limit reached!
% 27.86/5.30 % (31249)------------------------------
% 27.86/5.30 % (31249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.86/5.30 % (31249)Termination reason: Unknown
% 27.86/5.30 % (31249)Termination phase: Saturation
% 27.86/5.30
% 27.86/5.30 % (31249)Memory used [KB]: 7547
% 27.86/5.30 % (31249)Time elapsed: 0.120 s
% 27.86/5.30 % (31249)Instructions burned: 482 (million)
% 27.86/5.30 % (31249)------------------------------
% 27.86/5.30 % (31249)------------------------------
% 27.86/5.31 % (31250)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_30813 for (2963ds/783Mi)
% 27.86/5.33 % (31246)Instruction limit reached!
% 27.86/5.33 % (31246)------------------------------
% 27.86/5.33 % (31246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.86/5.33 % (31246)Termination reason: Unknown
% 27.86/5.33 % (31246)Termination phase: Saturation
% 27.86/5.33
% 27.86/5.33 % (31246)Memory used [KB]: 10234
% 27.86/5.33 % (31246)Time elapsed: 0.310 s
% 27.86/5.33 % (31246)Instructions burned: 962 (million)
% 27.86/5.33 % (31246)------------------------------
% 27.86/5.33 % (31246)------------------------------
% 27.86/5.34 % (31251)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_30813 for (2962ds/432Mi)
% 28.61/5.43 % (31247)Instruction limit reached!
% 28.61/5.43 % (31247)------------------------------
% 28.61/5.43 % (31247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.61/5.43 % (31247)Termination reason: Unknown
% 28.61/5.43 % (31247)Termination phase: Saturation
% 28.61/5.43
% 28.61/5.43 % (31247)Memory used [KB]: 15095
% 28.61/5.43 % (31247)Time elapsed: 0.400 s
% 28.61/5.43 % (31247)Instructions burned: 1213 (million)
% 28.61/5.43 % (31247)------------------------------
% 28.61/5.43 % (31247)------------------------------
% 28.61/5.44 % (31252)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_30813 for (2961ds/1670Mi)
% 28.61/5.46 % (31251)Instruction limit reached!
% 28.61/5.46 % (31251)------------------------------
% 28.61/5.46 % (31251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.61/5.46 % (31251)Termination reason: Unknown
% 28.61/5.46 % (31251)Termination phase: Saturation
% 28.61/5.46
% 28.61/5.46 % (31251)Memory used [KB]: 9594
% 28.61/5.46 % (31251)Time elapsed: 0.123 s
% 28.61/5.46 % (31251)Instructions burned: 433 (million)
% 28.61/5.46 % (31251)------------------------------
% 28.61/5.46 % (31251)------------------------------
% 28.61/5.47 % (31253)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_30813 for (2961ds/90Mi)
% 28.61/5.49 % (31253)Instruction limit reached!
% 28.61/5.49 % (31253)------------------------------
% 28.61/5.49 % (31253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.61/5.49 % (31253)Termination reason: Unknown
% 28.61/5.49 % (31253)Termination phase: Property scanning
% 28.61/5.49
% 28.61/5.49 % (31253)Memory used [KB]: 2686
% 28.61/5.49 % (31253)Time elapsed: 0.025 s
% 28.61/5.49 % (31253)Instructions burned: 92 (million)
% 28.61/5.49 % (31253)------------------------------
% 28.61/5.49 % (31253)------------------------------
% 29.45/5.50 % (31254)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_30813 for (2961ds/346Mi)
% 29.45/5.56 % (31250)Instruction limit reached!
% 29.45/5.56 % (31250)------------------------------
% 29.45/5.56 % (31250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.45/5.56 % (31250)Termination reason: Unknown
% 29.45/5.56 % (31250)Termination phase: Saturation
% 29.45/5.56
% 29.45/5.56 % (31250)Memory used [KB]: 11769
% 29.45/5.56 % (31250)Time elapsed: 0.272 s
% 29.45/5.56 % (31250)Instructions burned: 784 (million)
% 29.45/5.56 % (31250)------------------------------
% 29.45/5.56 % (31250)------------------------------
% 29.45/5.57 % (31255)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_30813 for (2960ds/401Mi)
% 29.45/5.59 % (31254)Instruction limit reached!
% 29.45/5.59 % (31254)------------------------------
% 29.45/5.59 % (31254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.45/5.59 % (31254)Termination reason: Unknown
% 29.45/5.59 % (31254)Termination phase: Saturation
% 29.45/5.59
% 29.45/5.59 % (31254)Memory used [KB]: 7547
% 29.45/5.59 % (31254)Time elapsed: 0.087 s
% 29.45/5.59 % (31254)Instructions burned: 346 (million)
% 29.45/5.59 % (31254)------------------------------
% 29.45/5.59 % (31254)------------------------------
% 30.11/5.60 % (31256)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_30813 for (2960ds/6454Mi)
% 30.11/5.64 % (31239)First to succeed.
% 30.11/5.64 % (31239)Refutation found. Thanks to Tanya!
% 30.11/5.64 % SZS status Theorem for DTF2THF_30813
% 30.11/5.64 % SZS output start Proof for DTF2THF_30813
% 30.11/5.64 thf(func_def_0, type, in: $i > $i > $o).
% 30.11/5.64 thf(func_def_1, type, exu: ($i > $o) > $o).
% 30.11/5.64 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 30.11/5.64 thf(func_def_8, type, powerset: $i > $i).
% 30.11/5.64 thf(func_def_10, type, setunion: $i > $i).
% 30.11/5.64 thf(func_def_19, type, descr: ($i > $o) > $i).
% 30.11/5.64 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 30.11/5.64 thf(func_def_26, type, prop2set: $o > $i).
% 30.11/5.64 thf(func_def_36, type, nonempty: $i > $o).
% 30.11/5.64 thf(func_def_69, type, set2prop: $i > $o).
% 30.11/5.64 thf(func_def_88, type, subset: $i > $i > $o).
% 30.11/5.64 thf(func_def_89, type, disjoint: $i > $i > $o).
% 30.11/5.64 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 30.11/5.64 thf(func_def_114, type, binunion: $i > $i > $i).
% 30.11/5.64 thf(func_def_122, type, binintersect: $i > $i > $i).
% 30.11/5.64 thf(func_def_135, type, regular: $i > $o).
% 30.11/5.64 thf(func_def_136, type, setminus: $i > $i > $i).
% 30.11/5.64 thf(func_def_147, type, symdiff: $i > $i > $i).
% 30.11/5.64 thf(func_def_153, type, iskpair: $i > $o).
% 30.11/5.64 thf(func_def_158, type, kpair: $i > $i > $i).
% 30.11/5.64 thf(func_def_160, type, cartprod: $i > $i > $i).
% 30.11/5.64 thf(func_def_177, type, singleton: $i > $o).
% 30.11/5.64 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 30.11/5.64 thf(func_def_184, type, atmost1p: $i > $o).
% 30.11/5.64 thf(func_def_185, type, atleast2p: $i > $o).
% 30.11/5.64 thf(func_def_186, type, atmost2p: $i > $o).
% 30.11/5.64 thf(func_def_187, type, upairsetp: $i > $o).
% 30.11/5.64 thf(func_def_191, type, kfst: $i > $i).
% 30.11/5.64 thf(func_def_203, type, ksnd: $i > $i).
% 30.11/5.64 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 30.11/5.64 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 30.11/5.64 thf(func_def_222, type, func: $i > $i > $i > $o).
% 30.11/5.64 thf(func_def_223, type, funcSet: $i > $i > $i).
% 30.11/5.64 thf(func_def_226, type, ap: $i > $i > $i > $i > $i).
% 30.11/5.64 thf(func_def_232, type, lam: $i > $i > ($i > $i) > $i).
% 30.11/5.64 thf(func_def_259, type, if: $i > $o > $i > $i > $i).
% 30.11/5.64 thf(func_def_342, type, sK5: $i > $i > ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_343, type, sK6: $i > $i > $i > ($i > $o) > $i).
% 30.11/5.64 thf(func_def_344, type, sK7: $i > $i > $i).
% 30.11/5.64 thf(func_def_345, type, sK8: $i > $i > $i).
% 30.11/5.64 thf(func_def_346, type, sK9: $i > $i > $i).
% 30.11/5.64 thf(func_def_347, type, sK10: $i > $i > $i).
% 30.11/5.64 thf(func_def_348, type, sK11: $i > $i > ($i > $o) > $i).
% 30.11/5.64 thf(func_def_349, type, sK12: $i > $i).
% 30.11/5.64 thf(func_def_350, type, sK13: ($i > $i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_351, type, sK14: ($i > $i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_352, type, sK15: ($i > $i > $o) > $i > $i > $i).
% 30.11/5.64 thf(func_def_353, type, sK16: ($i > $i > $o) > $i > $i > $i).
% 30.11/5.64 thf(func_def_354, type, sK17: ($i > $i > $o) > $i > $i > $i).
% 30.11/5.64 thf(func_def_355, type, sK18: ($i > $i > $o) > $i > $i > $i).
% 30.11/5.64 thf(func_def_356, type, sK19: ($i > $i > $o) > $i > $i > $i).
% 30.11/5.64 thf(func_def_357, type, sK20: ($i > $i) > $i > $i > $i).
% 30.11/5.64 thf(func_def_358, type, sK21: $i > $i > ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_359, type, sK22: $i > $i > ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_360, type, sK23: $i > $i > $i > $i).
% 30.11/5.64 thf(func_def_361, type, sK24: $i > $i > $i).
% 30.11/5.64 thf(func_def_362, type, sK25: $i > $i > $i > $i).
% 30.11/5.64 thf(func_def_363, type, sK26: $i > $i > ($i > $o) > ($i > $o) > $i).
% 30.11/5.64 thf(func_def_364, type, sK27: $i > ($i > $o) > ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_365, type, sK28: ($i > $o) > $i).
% 30.11/5.64 thf(func_def_366, type, sK29: ($i > $o) > $i).
% 30.11/5.64 thf(func_def_367, type, sK30: ($i > $o) > $i).
% 30.11/5.64 thf(func_def_368, type, sK31: ($i > $o) > ($i > $o) > $i).
% 30.11/5.64 thf(func_def_369, type, sK32: ($i > $o) > ($i > $o) > $i).
% 30.11/5.64 thf(func_def_370, type, sK33: ($i > $o) > $i).
% 30.11/5.64 thf(func_def_371, type, sK34: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_372, type, sK35: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_373, type, sK36: ($i > $o) > $i).
% 30.11/5.64 thf(func_def_374, type, sK37: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_375, type, sK38: ($i > $o) > $i).
% 30.11/5.64 thf(func_def_376, type, sK39: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_377, type, sK40: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_378, type, sK41: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_379, type, sK42: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_380, type, sK43: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_381, type, sK44: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_382, type, sK45: $i > ($i > $o) > $i).
% 30.11/5.64 thf(func_def_383, type, sK46: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_384, type, sK47: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_385, type, sK48: $i > $i).
% 30.11/5.64 thf(func_def_386, type, sK49: $i > $i > $i > $i).
% 30.11/5.64 thf(func_def_387, type, sK50: $i > $i > $i).
% 30.11/5.64 thf(func_def_388, type, sK51: $i > $i > $i).
% 30.11/5.64 thf(func_def_389, type, sK52: $i > $i > $i).
% 30.11/5.64 thf(func_def_390, type, sK53: $i > $i).
% 30.11/5.64 thf(func_def_391, type, sK54: $i > $i).
% 30.11/5.64 thf(func_def_392, type, sK55: $i > ($i > $i) > $i > $i).
% 30.11/5.64 thf(func_def_393, type, sK56: $i > $i > $i > $i > $i).
% 30.11/5.64 thf(func_def_394, type, sK57: $i > $i > $i > $i > $i).
% 30.11/5.64 thf(func_def_395, type, sK58: $i > $i > $i > $i).
% 30.11/5.64 thf(func_def_396, type, sK59: $i > $i > $i > $i).
% 30.11/5.64 thf(func_def_397, type, sK60: $i > ($i > $o) > $i).
% 30.11/5.64 thf(func_def_398, type, sK61: $i > $i > $i > $i > $i).
% 30.11/5.64 thf(func_def_399, type, sK62: $i > $i > $i > $i > $i).
% 30.11/5.64 thf(func_def_400, type, sK63: $i > $i > $i > $i > $i).
% 30.11/5.64 thf(func_def_401, type, sK64: $i > $i > $i > $i > $i).
% 30.11/5.64 thf(func_def_402, type, sK65: $i > $i > $i > $i > $i).
% 30.11/5.64 thf(func_def_403, type, sK66: $i > $i > $i > $i > $i).
% 30.11/5.64 thf(func_def_404, type, sK67: $i > $i > $i > $i > $i).
% 30.11/5.64 thf(func_def_405, type, sK68: $i > $i).
% 30.11/5.64 thf(func_def_406, type, sK69: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_407, type, sK70: $i > $i > ($i > $i) > $i).
% 30.11/5.64 thf(func_def_408, type, sK71: ($i > $o) > ($i > $o) > $i).
% 30.11/5.64 thf(func_def_409, type, sK72: ($i > $o) > ($i > $o) > $i).
% 30.11/5.64 thf(func_def_410, type, sK73: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_411, type, sK74: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_412, type, sK75: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_413, type, sK76: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_414, type, sK77: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_415, type, sK78: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_416, type, sK79: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_417, type, sK80: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_418, type, sK81: $i > $i > $i).
% 30.11/5.64 thf(func_def_419, type, sK82: ($i > $i) > $i > $i > $i).
% 30.11/5.64 thf(func_def_420, type, sK83: ($i > $o) > $i).
% 30.11/5.64 thf(func_def_421, type, sK84: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_422, type, sK85: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_423, type, sK86: $i > ($i > $o) > $i).
% 30.11/5.64 thf(func_def_424, type, sK87: ($i > $o) > $i).
% 30.11/5.64 thf(func_def_425, type, sK88: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_426, type, sK89: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_427, type, sK90: ($i > $o) > $i).
% 30.11/5.64 thf(func_def_428, type, sK91: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_429, type, sK92: $i > $i).
% 30.11/5.64 thf(func_def_430, type, sK93: $i > ($i > $o) > $i).
% 30.11/5.64 thf(func_def_431, type, sK94: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_432, type, sK95: $i > $i > $i > $i).
% 30.11/5.64 thf(func_def_433, type, sK96: $i > $i > $i > $i).
% 30.11/5.64 thf(func_def_434, type, sK97: $i > $i > $i > $i > $i).
% 30.11/5.64 thf(func_def_435, type, sK98: ($i > $i) > $i > $i > $i).
% 30.11/5.64 thf(func_def_436, type, sK99: $i > $i > $i).
% 30.11/5.64 thf(func_def_437, type, sK100: $i > $i > $i > $i > $i).
% 30.11/5.64 thf(func_def_438, type, sK101: $i > $i > $i).
% 30.11/5.64 thf(func_def_439, type, sK102: $i > $i > $i).
% 30.11/5.64 thf(func_def_440, type, sK103: $i > $i).
% 30.11/5.64 thf(func_def_441, type, sK104: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_442, type, sK105: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_443, type, sK106: $i > $i > $i > $i > $i).
% 30.11/5.64 thf(func_def_444, type, sK107: $i > $i > $i).
% 30.11/5.64 thf(func_def_445, type, sK108: ($i > $o) > $i).
% 30.11/5.64 thf(func_def_446, type, sK109: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_447, type, sK110: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_448, type, sK111: $i > ($i > $o) > $i).
% 30.11/5.64 thf(func_def_449, type, sK112: $i > $i > $o > $i).
% 30.11/5.64 thf(func_def_450, type, sK113: ($i > $o) > $i).
% 30.11/5.64 thf(func_def_451, type, sK114: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_452, type, sK115: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_453, type, sK116: $i > $i > $i).
% 30.11/5.64 thf(func_def_454, type, sK117: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_455, type, sK118: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_456, type, sK119: ($i > $o) > $i > $i).
% 30.11/5.64 thf(func_def_457, type, ph120: !>[X0: $tType]:(X0)).
% 30.11/5.64 thf(f11107,plain,(
% 30.11/5.64 $false),
% 30.11/5.64 inference(avatar_sat_refutation,[status(thm)],[f5065,f5071,f5094,f5099,f5116,f11102,f11106])).
% 30.11/5.64 thf(f11106,plain,(
% 30.11/5.64 ($true != (in @ sK3 @ (powerset @ sK1))) | ($false != (in @ sK3 @ (powerset @ sK1))) | ($false = $true)),
% 30.11/5.64 introduced(definition,[],[theory_tautology_sat_conflict])).
% 30.11/5.64 thf(f11102,plain,(
% 30.11/5.64 spl4_85 | ~spl4_14 | spl4_21 | ~spl4_25),
% 30.11/5.64 inference(avatar_split_clause,[status(thm)],[f11101,f5113,f5096,f5062,f10743])).
% 30.11/5.64 thf(f10743,definition,(
% 30.11/5.64 spl4_85 <=> ($false = (in @ sK3 @ (powerset @ sK1)))),
% 30.11/5.64 introduced(definition,[new_symbols(naming,[spl4_85])],[avatar_definition])).
% 30.11/5.64 thf(f5062,definition,(
% 30.11/5.64 spl4_14 <=> ((in @ sK2 @ (powerset @ sK1)) = $true)),
% 30.11/5.64 introduced(definition,[new_symbols(naming,[spl4_14])],[avatar_definition])).
% 30.11/5.64 thf(f5096,definition,(
% 30.11/5.64 spl4_21 <=> ((in @ (binintersect @ sK0 @ sK2) @ (powerset @ (binintersect @ (binunion @ sK0 @ sK3) @ (binunion @ sK2 @ sK3)))) = $true)),
% 30.11/5.64 introduced(definition,[new_symbols(naming,[spl4_21])],[avatar_definition])).
% 30.11/5.64 thf(f5113,definition,(
% 30.11/5.64 spl4_25 <=> ((in @ sK0 @ (powerset @ sK1)) = $true)),
% 30.11/5.64 introduced(definition,[new_symbols(naming,[spl4_25])],[avatar_definition])).
% 30.11/5.64 thf(f11101,plain,(
% 30.11/5.64 ($false = (in @ sK3 @ (powerset @ sK1))) | (~spl4_14 | spl4_21 | ~spl4_25)),
% 30.11/5.64 inference(trivial_inequality_removal,[status(thm)],[f11100])).
% 30.11/5.64 thf(f11100,plain,(
% 30.11/5.64 ($false = $true) | ($false = (in @ sK3 @ (powerset @ sK1))) | (~spl4_14 | spl4_21 | ~spl4_25)),
% 30.11/5.64 inference(forward_demodulation,[status(thm)],[f11078,f5115])).
% 30.11/5.64 thf(f5115,plain,(
% 30.11/5.64 ((in @ sK0 @ (powerset @ sK1)) = $true) | ~spl4_25),
% 30.11/5.64 inference(avatar_component_clause,[status(thm)],[f5113])).
% 30.11/5.64 thf(f11078,plain,(
% 30.11/5.64 ((in @ sK0 @ (powerset @ sK1)) = $false) | ($false = (in @ sK3 @ (powerset @ sK1))) | (~spl4_14 | spl4_21)),
% 30.11/5.64 inference(trivial_inequality_removal,[status(thm)],[f11069])).
% 30.11/5.64 thf(f11069,plain,(
% 30.11/5.64 ((in @ sK0 @ (powerset @ sK1)) = $false) | ($false = (in @ sK3 @ (powerset @ sK1))) | ($false = $true) | (~spl4_14 | spl4_21)),
% 30.11/5.64 inference(superposition,[status(thm)],[f11062,f5064])).
% 30.11/5.64 thf(f5064,plain,(
% 30.11/5.64 ((in @ sK2 @ (powerset @ sK1)) = $true) | ~spl4_14),
% 30.11/5.64 inference(avatar_component_clause,[status(thm)],[f5062])).
% 30.11/5.64 thf(f11062,plain,(
% 30.11/5.64 ( ! [X0 : $i] : (($false = (in @ sK2 @ (powerset @ X0))) | ((in @ sK0 @ (powerset @ X0)) = $false) | ((in @ sK3 @ (powerset @ X0)) = $false)) ) | spl4_21),
% 30.11/5.64 inference(trivial_inequality_removal,[status(thm)],[f11049])).
% 30.11/5.64 thf(f11049,plain,(
% 30.11/5.64 ( ! [X0 : $i] : (($true != $true) | ($false = (in @ sK2 @ (powerset @ X0))) | ((in @ sK3 @ (powerset @ X0)) = $false) | ((in @ sK0 @ (powerset @ X0)) = $false)) ) | spl4_21),
% 30.11/5.64 inference(superposition,[status(thm)],[f5098,f3242])).
% 30.11/5.64 thf(f3242,plain,(
% 30.11/5.64 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((in @ (binintersect @ X2 @ X3) @ (powerset @ (binintersect @ (binunion @ X2 @ X4) @ (binunion @ X3 @ X4)))) = $true) | ($false = (in @ X2 @ (powerset @ X1))) | ($false = (in @ X3 @ (powerset @ X1))) | ($false = (in @ X4 @ (powerset @ X1)))) )),
% 30.11/5.64 inference(binary_proxy_clausification,[status(thm)],[f3241])).
% 30.11/5.64 thf(f3241,plain,(
% 30.11/5.64 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (in @ X3 @ (powerset @ X1))) | ($true = ((in @ X4 @ (powerset @ X1)) => (in @ (binintersect @ X2 @ X3) @ (powerset @ (binintersect @ (binunion @ X2 @ X4) @ (binunion @ X3 @ X4)))))) | ($false = (in @ X2 @ (powerset @ X1)))) )),
% 30.11/5.64 inference(beta_eta_normalization,[status(thm)],[f3240])).
% 30.11/5.64 thf(f3240,plain,(
% 30.11/5.64 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (in @ X3 @ (powerset @ X1))) | ($true = ((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => (in @ (binintersect @ X2 @ X3) @ (powerset @ (binintersect @ (binunion @ X2 @ Y0) @ (binunion @ X3 @ Y0)))))) @ X4)) | ($false = (in @ X2 @ (powerset @ X1)))) )),
% 30.11/5.64 inference(pi_clausification,[status(thm)],[f3239])).
% 30.11/5.64 thf(f3239,plain,(
% 30.11/5.64 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X2 @ (powerset @ X1))) | ($false = (in @ X3 @ (powerset @ X1))) | ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => (in @ (binintersect @ X2 @ X3) @ (powerset @ (binintersect @ (binunion @ X2 @ Y0) @ (binunion @ X3 @ Y0))))))) = $true)) )),
% 30.11/5.64 inference(binary_proxy_clausification,[status(thm)],[f3238])).
% 30.11/5.64 thf(f3238,plain,(
% 30.11/5.64 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X3 @ (powerset @ X1)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => (in @ (binintersect @ X2 @ X3) @ (powerset @ (binintersect @ (binunion @ X2 @ Y0) @ (binunion @ X3 @ Y0))))))))) | ($false = (in @ X2 @ (powerset @ X1)))) )),
% 30.11/5.64 inference(beta_eta_normalization,[status(thm)],[f3237])).
% 30.11/5.64 thf(f3237,plain,(
% 30.11/5.64 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X2 @ (powerset @ X1))) | (((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ X1)) => (in @ (binintersect @ X2 @ Y0) @ (powerset @ (binintersect @ (binunion @ X2 @ Y1) @ (binunion @ Y0 @ Y1))))))))) @ X3) = $true)) )),
% 30.11/5.64 inference(pi_clausification,[status(thm)],[f3236])).
% 30.11/5.64 thf(f3236,plain,(
% 30.11/5.64 ( ! [X2 : $i,X1 : $i] : (($false = (in @ X2 @ (powerset @ X1))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ X1)) => (in @ (binintersect @ X2 @ Y0) @ (powerset @ (binintersect @ (binunion @ X2 @ Y1) @ (binunion @ Y0 @ Y1)))))))))))) )),
% 30.11/5.64 inference(binary_proxy_clausification,[status(thm)],[f3235])).
% 30.11/5.64 thf(f3235,plain,(
% 30.11/5.64 ( ! [X2 : $i,X1 : $i] : ((((in @ X2 @ (powerset @ X1)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ X1)) => (in @ (binintersect @ X2 @ Y0) @ (powerset @ (binintersect @ (binunion @ X2 @ Y1) @ (binunion @ Y0 @ Y1))))))))))) = $true)) )),
% 30.11/5.64 inference(beta_eta_normalization,[status(thm)],[f3234])).
% 30.11/5.64 thf(f3234,plain,(
% 30.11/5.64 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ X1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ X1)) => (in @ (binintersect @ Y0 @ Y1) @ (powerset @ (binintersect @ (binunion @ Y0 @ Y2) @ (binunion @ Y1 @ Y2)))))))))))) @ X2) = $true)) )),
% 30.11/5.64 inference(pi_clausification,[status(thm)],[f3233])).
% 30.11/5.64 thf(f3233,plain,(
% 30.11/5.64 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X1)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ X1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ X1)) => (in @ (binintersect @ Y0 @ Y1) @ (powerset @ (binintersect @ (binunion @ Y0 @ Y2) @ (binunion @ Y1 @ Y2))))))))))))))) )),
% 30.11/5.64 inference(beta_eta_normalization,[status(thm)],[f3232])).
% 30.11/5.64 thf(f3232,plain,(
% 30.11/5.64 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y0)) => (in @ (binintersect @ Y1 @ Y2) @ (powerset @ (binintersect @ (binunion @ Y1 @ Y3) @ (binunion @ Y2 @ Y3)))))))))))))) @ X1))) )),
% 30.11/5.64 inference(pi_clausification,[status(thm)],[f1552])).
% 30.11/5.64 thf(f1552,plain,(
% 30.11/5.64 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y0)) => (in @ (binintersect @ Y1 @ Y2) @ (powerset @ (binintersect @ (binunion @ Y1 @ Y3) @ (binunion @ Y2 @ Y3))))))))))))))) = $true)),
% 30.11/5.64 inference(definition_unfolding,[status(thm)],[f1107,f937])).
% 30.11/5.64 thf(f937,plain,(
% 30.11/5.64 (intersectInPowersetIntersectUnions = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y0)) => (in @ (binintersect @ Y1 @ Y2) @ (powerset @ (binintersect @ (binunion @ Y1 @ Y3) @ (binunion @ Y2 @ Y3))))))))))))))))),
% 30.11/5.64 inference(cnf_transformation,[status(thm)],[f664])).
% 30.11/5.64 thf(f664,plain,(
% 30.11/5.64 (intersectInPowersetIntersectUnions = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y0)) => (in @ (binintersect @ Y1 @ Y2) @ (powerset @ (binintersect @ (binunion @ Y1 @ Y3) @ (binunion @ Y2 @ Y3))))))))))))))))),
% 30.11/5.64 inference(fool_elimination,[status(thm)],[f663])).
% 30.11/5.64 thf(f663,plain,(
% 30.11/5.64 (intersectInPowersetIntersectUnions = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X1)) => (in @ (binintersect @ X0 @ X2) @ (powerset @ (binintersect @ (binunion @ X0 @ X3) @ (binunion @ X2 @ X3))))))))),
% 30.11/5.64 inference(rectify,[status(thm)],[f264])).
% 30.11/5.64 thf(f264,axiom,(
% 30.11/5.64 (intersectInPowersetIntersectUnions = ! [X11 : $i,X3 : $i] : ((in @ X11 @ (powerset @ X3)) => ! [X16 : $i] : ((in @ X16 @ (powerset @ X3)) => ! [X17 : $i] : ((in @ X17 @ (powerset @ X3)) => (in @ (binintersect @ X11 @ X16) @ (powerset @ (binintersect @ (binunion @ X11 @ X17) @ (binunion @ X16 @ X17))))))))),
% 30.11/5.64 file('/export/starexec/sandbox/tmp/tmp.50SVxc4AnF/DTF2THF_30813.p',intersectInPowersetIntersectUnions)).
% 30.11/5.64 thf(f1107,plain,(
% 30.11/5.64 (intersectInPowersetIntersectUnions = $true)),
% 30.11/5.64 inference(cnf_transformation,[status(thm)],[f860])).
% 30.11/5.64 thf(f860,plain,(
% 30.11/5.64 (complementUnionInPowersetComplement = $true) & (complementT_lem = $true) & (descr__Cong = $true) & (binintersectER = $true) & (in__Cong = $true) & (bs114d = $true) & (binintersectLsub = $true) & (upairsetE = $true) & (quantDeMorgan2 = $true) & (contrasubsetT3 = $true) & (cartprodfstpairEq = $true) & (doubleComplementEq = $true) & (sepInPowerset = $true) & (dpsetconstrEL2 = $true) & (funcGraphProp1 = $true) & (emptyInPowerset = $true) & (singletonsuniq = $true) & (singletoninpowunion = $true) & (dpsetconstrI = $true) & (emptyE1 = $true) & (singletoninpowerset = $true) & (complementImpComplementIntersect = $true) & (ap2apEq2 = $true) & (lamp = $true) & (setunion__Cong = $true) & (cartprodmempaircEq = $true) & (subsetTI = $true) & (ap2apEq1 = $true) & (apProp = $true) & (notdexE = $true) & (quantDeMorgan1 = $true) & (cartprodpairsurjEq = $true) & (disjointsetsI1 = $true) & (upairsubunion = $true) & (exuE3u = $true) & (setukpairIR = $true) & (descrp = $true) & (setadjoinAx = $true) & (exuEu = $true) & (ubforcartprodlem3 = $true) & (woz13rule3 = $true) & (notdallE = $true) & (exu__Cong = $true) & (upairinpowunion = $true) & (brelnall2 = $true) & (ex1E1 = $true) & (funcext2 = $true) & (ap2p = $true) & (doubleComplementSub1 = $true) & (cartprodmempair = $true) & (setukpairIL = $true) & (symdiffIneg1 = $true) & (woz1_2 = $true) & (demorgan2a2 = $true) & (cartprodmempair1 = $true) & (eta1 = $true) & (inIntersectImpInIntersectUnions = $true) & (powersetE = $true) & (binintersectI = $true) & (setminusT_lem = $true) & (inIntersectImpInUnion2 = $true) & (cartprodpairmemER = $true) & (exuI1 = $true) & (complementTcontraSubset = $true) & (binintersectTELcontra = $true) & (setadjoinE = $true) & (demorgan1a = $true) & (setadjoinIR = $true) & (lam2p = $true) & (exuE3e = $true) & (complementSubsetComplementIntersect = $true) & (inPowerset = $true) & (setadjoinSub2 = $true) & (demorgan2b2 = $true) & (woz13rule1 = $true) & (symdiffIneg2 = $true) & (notequalI1 = $true) & (binunionEcases = $true) & (upairset2E = $true) & (setunionsingleton2 = $true) & (omega0Ax = $true) & (binunionTILcontra = $true) & (binunionRsub = $true) & (setOfPairsIsBReln = $true) & (setminusELneg = $true) & (woz13rule0 = $true) & (exuE2 = $true) & (sepSubset = $true) & (setunionI = $true) & (setminusILneg = $true) & (upairequniteq = $true) & (theeq = $true) & (eta2 = $true) & (cartprodsndin = $true) & (funcext = $true) & (binintersectSubset4 = $true) & (contrasubsetT1 = $true) & (setunionsingleton1 = $true) & (subsetemptysetimpeq = $true) & (replAx = $true) & (nonemptyI1 = $true) & (iffalseProp1 = $true) & (binintersectTERcontra = $true) & (notsubsetI = $true) & (ubforcartprodlem2 = $true) & (setminusSubset1 = $true) & (nonemptyImpWitness = $true) & (funcextLem = $true) & (lamProp = $true) & (lam2lamEq = $true) & (ex1I2 = $true) & (setextsub = $true) & (powersetAx = $true) & (ex1I = $true) & (binunionT_lem = $true) & (inComplementUnionImpNotIn1 = $true) & (setadjoinIL = $true) & (dpsetconstrERa = $true) & (setminusERneg = $true) & (ksndsingleton = $true) & (contrasubsetT = $true) & (powersetTI1 = $true) & (binunionE = $true) & (omegaIndAx = $true) & (binintersectT_lem = $true) & (prop2setE = $true) & (iffalseProp2 = $true) & (contrasubsetT2 = $true) & (symdiffE = $true) & (setukpairinjR1 = $true) & (infuncsetfunc = $true) & (inIntersectImpInUnion = $true) & (quantDeMorgan3 = $true) & (dpsetconstrER = $true) & (doubleComplementE1 = $true) & (binunionTEcontra = $true) & (nonemptyI = $true) & (funcImageSingleton = $true) & (emptyinPowerset = $true) & (dsetconstrEL = $true) & (funcinfuncset = $true) & (emptysetimpfalse = $true) & (setminusSubset2 = $true) & (subsetI2 = $true) & (upairsetIR = $true) & (inCongP = $true) & (setukpairinjL1 = $true) & (subsetE2 = $true) & (setoftrueEq = $true) & (binintersectSubset5 = $true) & (singletonsswitch = $true) & (binintersectSubset2 = $true) & (powersetsubset = $true) & (setadjoinSub = $true) & (uniqinunit = $true) & (symdiffI1 = $true) & (doubleComplementI1 = $true) & (brelnall1 = $true) & (((((in @ (binintersect @ sK0 @ sK2) @ (powerset @ (binintersect @ (binunion @ sK0 @ sK3) @ (binunion @ sK2 @ sK3)))) != $true) & ($true = (in @ sK3 @ (powerset @ sK1)))) & ((in @ sK2 @ (powerset @ sK1)) = $true)) & ((in @ sK0 @ (powerset @ sK1)) = $true)) & (setextAx = $true) & (setukpairinjR12 = $true) & (setunionAx = $true) & (setadjoin__Cong = $true) & (complementInPowersetComplementIntersect = $true) & (omegaSAx = $true) & (dpsetconstrEL1 = $true) & (kfstpairEq = $true) & (eqbreln = $true) & (ifp = $true) & (inComplementUnionImpInComplement1 = $true) & (dsetconstrI = $true) & (setminusIRneg = $true) & (binunionLsub = $true) & (woz13rule2 = $true) & (demorgan2b = $true) & (binintersectSubset1 = $true) & (powersetE1 = $true) & (prop2set2propI = $true) & (setukpairinjR = $true) & (funcGraphProp4 = $true) & (theprop = $true) & (ex1E2 = $true) & (demorgan1 = $true) & (exuE1 = $true) & (subsetTrans = $true) & (kpairiskpair = $true) & (exuI3 = $true) & (dpsetconstrSub = $true) & (dsetconstr__Cong = $true) & (setukpairinjL2 = $true) & (subbreln = $true) & (vacuousDall = $true) & (subPowSU = $true) & (wellorderingAx = $true) & (intersectInPowersetIntersectUnions = $true) & (iffalse = $true) & (setextT = $true) & (eqimpsubset1 = $true) & (exuI2 = $true) & (singletonsubset = $true) & (complementTE1 = $true) & (secondinupair = $true) & (notinemptyset = $true) & (emptysetE = $true) & (iftrueProp2 = $true) & (emptyI = $true) & (prop2setI = $true) & (beta2 = $true) & (demorgan1b = $true) & (setukpairinjR2 = $true) & (upairsetIL = $true) & (emptysetAx = $true) & (cartprodsndpairEq = $true) & (setext = $true) & (demorgan2 = $true) & (emptysetsubset = $true) & (powersetI1 = $true) & (emptyset__Cong = $true) & (complementTI1 = $true) & (setunionsingleton = $true) & (binintersectEL = $true) & (omega__Cong = $true) & (kfstsingleton = $true) & (funcGraphProp3 = $true) & (demorgan2a1 = $true) & (singletonprop = $true) & (binunionIR = $true) & (ksndpairEq = $true) & (binintersectRsub = $true) & (powersetTE1 = $true) & (kpairsurjEq = $true) & (doubleComplementSub2 = $true) & (woz1_1 = $true) & (quantDeMorgan4 = $true) & (ubforcartprodlem1 = $true) & (setminusER = $true) & (iftrueProp1 = $true) & (emptyinunitempty = $true) & (powersetT_lem = $true) & (binunionIL = $true) & (kpairp = $true) & (funcGraphProp2 = $true) & (setunionE = $true) & (notinsingleton = $true) & (beta1 = $true) & (subsetE = $true) & (foundationAx = $true) & (subset2powerset = $true) & (setminusLsub = $true) & (upairset2IR = $true) & (contraSubsetComplement = $true) & (setadjoinOr = $true) & (subsetRefl = $true) & (noeltsimpempty = $true) & (powerset__Cong = $true) & (cartprodpairin = $true) & (cartprodfstin = $true) & (setunionE2 = $true) & (cartprodpairmemEL = $true) & (eqimpsubset2 = $true) & (iftrue = $true) & (dsetconstrER = $true) & (setukpairinjL = $true) & (binunionTE = $true) & (app = $true) & (notequalI2 = $true) & (woz13rule4 = $true) & (setminusI = $true) & (symdiffI2 = $true) & (setukpairinjR11 = $true) & (binunionTIRcontra = $true) & (binintersectSubset3 = $true) & (setminusEL = $true) & (complementTnotintersectT = $true) & (powersetI = $true) & (iftrueorfalse = $true) & (ifSingleton = $true) & (demorgan2a = $true) & (subsetI1 = $true) & (setbeta = $true) & (nonemptyE1 = $true) & (eqinunit = $true)),
% 30.11/5.64 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f856,f859,f858,f857])).
% 30.11/5.64 thf(f857,plain,(
% 30.11/5.64 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((in @ (binintersect @ X0 @ X2) @ (powerset @ (binintersect @ (binunion @ X0 @ X3) @ (binunion @ X2 @ X3)))) != $true) & ((in @ X3 @ (powerset @ X1)) = $true)) & ($true = (in @ X2 @ (powerset @ X1)))) & ((in @ X0 @ (powerset @ X1)) = $true)) => (? [X2 : $i] : (? [X3 : $i] : (($true != (in @ (binintersect @ sK0 @ X2) @ (powerset @ (binintersect @ (binunion @ sK0 @ X3) @ (binunion @ X2 @ X3))))) & ((in @ X3 @ (powerset @ sK1)) = $true)) & ($true = (in @ X2 @ (powerset @ sK1)))) & ((in @ sK0 @ (powerset @ sK1)) = $true))),
% 30.11/5.64 introduced(definition,[],[choice_axiom])).
% 30.11/5.64 thf(f858,plain,(
% 30.11/5.64 ? [X2 : $i] : (? [X3 : $i] : (($true != (in @ (binintersect @ sK0 @ X2) @ (powerset @ (binintersect @ (binunion @ sK0 @ X3) @ (binunion @ X2 @ X3))))) & ((in @ X3 @ (powerset @ sK1)) = $true)) & ($true = (in @ X2 @ (powerset @ sK1)))) => (? [X3 : $i] : (($true != (in @ (binintersect @ sK0 @ sK2) @ (powerset @ (binintersect @ (binunion @ sK0 @ X3) @ (binunion @ sK2 @ X3))))) & ((in @ X3 @ (powerset @ sK1)) = $true)) & ((in @ sK2 @ (powerset @ sK1)) = $true))),
% 30.11/5.64 introduced(definition,[],[choice_axiom])).
% 30.11/5.64 thf(f859,plain,(
% 30.11/5.64 ? [X3 : $i] : (($true != (in @ (binintersect @ sK0 @ sK2) @ (powerset @ (binintersect @ (binunion @ sK0 @ X3) @ (binunion @ sK2 @ X3))))) & ((in @ X3 @ (powerset @ sK1)) = $true)) => (((in @ (binintersect @ sK0 @ sK2) @ (powerset @ (binintersect @ (binunion @ sK0 @ sK3) @ (binunion @ sK2 @ sK3)))) != $true) & ($true = (in @ sK3 @ (powerset @ sK1))))),
% 30.11/5.64 introduced(definition,[],[choice_axiom])).
% 30.11/5.64 thf(f856,plain,(
% 30.11/5.64 (complementUnionInPowersetComplement = $true) & (complementT_lem = $true) & (descr__Cong = $true) & (binintersectER = $true) & (in__Cong = $true) & (bs114d = $true) & (binintersectLsub = $true) & (upairsetE = $true) & (quantDeMorgan2 = $true) & (contrasubsetT3 = $true) & (cartprodfstpairEq = $true) & (doubleComplementEq = $true) & (sepInPowerset = $true) & (dpsetconstrEL2 = $true) & (funcGraphProp1 = $true) & (emptyInPowerset = $true) & (singletonsuniq = $true) & (singletoninpowunion = $true) & (dpsetconstrI = $true) & (emptyE1 = $true) & (singletoninpowerset = $true) & (complementImpComplementIntersect = $true) & (ap2apEq2 = $true) & (lamp = $true) & (setunion__Cong = $true) & (cartprodmempaircEq = $true) & (subsetTI = $true) & (ap2apEq1 = $true) & (apProp = $true) & (notdexE = $true) & (quantDeMorgan1 = $true) & (cartprodpairsurjEq = $true) & (disjointsetsI1 = $true) & (upairsubunion = $true) & (exuE3u = $true) & (setukpairIR = $true) & (descrp = $true) & (setadjoinAx = $true) & (exuEu = $true) & (ubforcartprodlem3 = $true) & (woz13rule3 = $true) & (notdallE = $true) & (exu__Cong = $true) & (upairinpowunion = $true) & (brelnall2 = $true) & (ex1E1 = $true) & (funcext2 = $true) & (ap2p = $true) & (doubleComplementSub1 = $true) & (cartprodmempair = $true) & (setukpairIL = $true) & (symdiffIneg1 = $true) & (woz1_2 = $true) & (demorgan2a2 = $true) & (cartprodmempair1 = $true) & (eta1 = $true) & (inIntersectImpInIntersectUnions = $true) & (powersetE = $true) & (binintersectI = $true) & (setminusT_lem = $true) & (inIntersectImpInUnion2 = $true) & (cartprodpairmemER = $true) & (exuI1 = $true) & (complementTcontraSubset = $true) & (binintersectTELcontra = $true) & (setadjoinE = $true) & (demorgan1a = $true) & (setadjoinIR = $true) & (lam2p = $true) & (exuE3e = $true) & (complementSubsetComplementIntersect = $true) & (inPowerset = $true) & (setadjoinSub2 = $true) & (demorgan2b2 = $true) & (woz13rule1 = $true) & (symdiffIneg2 = $true) & (notequalI1 = $true) & (binunionEcases = $true) & (upairset2E = $true) & (setunionsingleton2 = $true) & (omega0Ax = $true) & (binunionTILcontra = $true) & (binunionRsub = $true) & (setOfPairsIsBReln = $true) & (setminusELneg = $true) & (woz13rule0 = $true) & (exuE2 = $true) & (sepSubset = $true) & (setunionI = $true) & (setminusILneg = $true) & (upairequniteq = $true) & (theeq = $true) & (eta2 = $true) & (cartprodsndin = $true) & (funcext = $true) & (binintersectSubset4 = $true) & (contrasubsetT1 = $true) & (setunionsingleton1 = $true) & (subsetemptysetimpeq = $true) & (replAx = $true) & (nonemptyI1 = $true) & (iffalseProp1 = $true) & (binintersectTERcontra = $true) & (notsubsetI = $true) & (ubforcartprodlem2 = $true) & (setminusSubset1 = $true) & (nonemptyImpWitness = $true) & (funcextLem = $true) & (lamProp = $true) & (lam2lamEq = $true) & (ex1I2 = $true) & (setextsub = $true) & (powersetAx = $true) & (ex1I = $true) & (binunionT_lem = $true) & (inComplementUnionImpNotIn1 = $true) & (setadjoinIL = $true) & (dpsetconstrERa = $true) & (setminusERneg = $true) & (ksndsingleton = $true) & (contrasubsetT = $true) & (powersetTI1 = $true) & (binunionE = $true) & (omegaIndAx = $true) & (binintersectT_lem = $true) & (prop2setE = $true) & (iffalseProp2 = $true) & (contrasubsetT2 = $true) & (symdiffE = $true) & (setukpairinjR1 = $true) & (infuncsetfunc = $true) & (inIntersectImpInUnion = $true) & (quantDeMorgan3 = $true) & (dpsetconstrER = $true) & (doubleComplementE1 = $true) & (binunionTEcontra = $true) & (nonemptyI = $true) & (funcImageSingleton = $true) & (emptyinPowerset = $true) & (dsetconstrEL = $true) & (funcinfuncset = $true) & (emptysetimpfalse = $true) & (setminusSubset2 = $true) & (subsetI2 = $true) & (upairsetIR = $true) & (inCongP = $true) & (setukpairinjL1 = $true) & (subsetE2 = $true) & (setoftrueEq = $true) & (binintersectSubset5 = $true) & (singletonsswitch = $true) & (binintersectSubset2 = $true) & (powersetsubset = $true) & (setadjoinSub = $true) & (uniqinunit = $true) & (symdiffI1 = $true) & (doubleComplementI1 = $true) & (brelnall1 = $true) & ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((in @ (binintersect @ X0 @ X2) @ (powerset @ (binintersect @ (binunion @ X0 @ X3) @ (binunion @ X2 @ X3)))) != $true) & ((in @ X3 @ (powerset @ X1)) = $true)) & ($true = (in @ X2 @ (powerset @ X1)))) & ((in @ X0 @ (powerset @ X1)) = $true)) & (setextAx = $true) & (setukpairinjR12 = $true) & (setunionAx = $true) & (setadjoin__Cong = $true) & (complementInPowersetComplementIntersect = $true) & (omegaSAx = $true) & (dpsetconstrEL1 = $true) & (kfstpairEq = $true) & (eqbreln = $true) & (ifp = $true) & (inComplementUnionImpInComplement1 = $true) & (dsetconstrI = $true) & (setminusIRneg = $true) & (binunionLsub = $true) & (woz13rule2 = $true) & (demorgan2b = $true) & (binintersectSubset1 = $true) & (powersetE1 = $true) & (prop2set2propI = $true) & (setukpairinjR = $true) & (funcGraphProp4 = $true) & (theprop = $true) & (ex1E2 = $true) & (demorgan1 = $true) & (exuE1 = $true) & (subsetTrans = $true) & (kpairiskpair = $true) & (exuI3 = $true) & (dpsetconstrSub = $true) & (dsetconstr__Cong = $true) & (setukpairinjL2 = $true) & (subbreln = $true) & (vacuousDall = $true) & (subPowSU = $true) & (wellorderingAx = $true) & (intersectInPowersetIntersectUnions = $true) & (iffalse = $true) & (setextT = $true) & (eqimpsubset1 = $true) & (exuI2 = $true) & (singletonsubset = $true) & (complementTE1 = $true) & (secondinupair = $true) & (notinemptyset = $true) & (emptysetE = $true) & (iftrueProp2 = $true) & (emptyI = $true) & (prop2setI = $true) & (beta2 = $true) & (demorgan1b = $true) & (setukpairinjR2 = $true) & (upairsetIL = $true) & (emptysetAx = $true) & (cartprodsndpairEq = $true) & (setext = $true) & (demorgan2 = $true) & (emptysetsubset = $true) & (powersetI1 = $true) & (emptyset__Cong = $true) & (complementTI1 = $true) & (setunionsingleton = $true) & (binintersectEL = $true) & (omega__Cong = $true) & (kfstsingleton = $true) & (funcGraphProp3 = $true) & (demorgan2a1 = $true) & (singletonprop = $true) & (binunionIR = $true) & (ksndpairEq = $true) & (binintersectRsub = $true) & (powersetTE1 = $true) & (kpairsurjEq = $true) & (doubleComplementSub2 = $true) & (woz1_1 = $true) & (quantDeMorgan4 = $true) & (ubforcartprodlem1 = $true) & (setminusER = $true) & (iftrueProp1 = $true) & (emptyinunitempty = $true) & (powersetT_lem = $true) & (binunionIL = $true) & (kpairp = $true) & (funcGraphProp2 = $true) & (setunionE = $true) & (notinsingleton = $true) & (beta1 = $true) & (subsetE = $true) & (foundationAx = $true) & (subset2powerset = $true) & (setminusLsub = $true) & (upairset2IR = $true) & (contraSubsetComplement = $true) & (setadjoinOr = $true) & (subsetRefl = $true) & (noeltsimpempty = $true) & (powerset__Cong = $true) & (cartprodpairin = $true) & (cartprodfstin = $true) & (setunionE2 = $true) & (cartprodpairmemEL = $true) & (eqimpsubset2 = $true) & (iftrue = $true) & (dsetconstrER = $true) & (setukpairinjL = $true) & (binunionTE = $true) & (app = $true) & (notequalI2 = $true) & (woz13rule4 = $true) & (setminusI = $true) & (symdiffI2 = $true) & (setukpairinjR11 = $true) & (binunionTIRcontra = $true) & (binintersectSubset3 = $true) & (setminusEL = $true) & (complementTnotintersectT = $true) & (powersetI = $true) & (iftrueorfalse = $true) & (ifSingleton = $true) & (demorgan2a = $true) & (subsetI1 = $true) & (setbeta = $true) & (nonemptyE1 = $true) & (eqinunit = $true)),
% 30.11/5.64 inference(flattening,[status(thm)],[f855])).
% 30.11/5.64 thf(f855,plain,(
% 30.11/5.64 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((in @ (binintersect @ X0 @ X2) @ (powerset @ (binintersect @ (binunion @ X0 @ X3) @ (binunion @ X2 @ X3)))) != $true) & ((in @ X3 @ (powerset @ X1)) = $true)) & ($true = (in @ X2 @ (powerset @ X1)))) & ((in @ X0 @ (powerset @ X1)) = $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)),
% 30.11/5.64 inference(ennf_transformation,[status(thm)],[f682])).
% 30.11/5.64 thf(f682,plain,(
% 30.11/5.64 ~((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) => ! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) => ! [X3 : $i] : (((in @ X3 @ (powerset @ X1)) = $true) => ((in @ (binintersect @ X0 @ X2) @ (powerset @ (binintersect @ (binunion @ X0 @ X3) @ (binunion @ X2 @ X3)))) = $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 30.11/5.64 inference(fool_elimination,[status(thm)],[f681])).
% 30.11/5.64 thf(f681,plain,(
% 30.11/5.64 ~(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 => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X1)) => (in @ (binintersect @ X0 @ X2) @ (powerset @ (binintersect @ (binunion @ X0 @ X3) @ (binunion @ X2 @ X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 30.11/5.64 inference(rectify,[status(thm)],[f287])).
% 30.11/5.64 thf(f287,negated_conjecture,(
% 30.11/5.64 ~(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 => ! [X11 : $i,X3 : $i] : ((in @ X11 @ (powerset @ X3)) => ! [X16 : $i] : ((in @ X16 @ (powerset @ X3)) => ! [X17 : $i] : ((in @ X17 @ (powerset @ X3)) => (in @ (binintersect @ X11 @ X16) @ (powerset @ (binintersect @ (binunion @ X11 @ X17) @ (binunion @ X16 @ X17))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 30.11/5.64 inference(negated_conjecture,[status(cth)],[f286])).
% 30.11/5.64 thf(f286,conjecture,(
% 30.11/5.64 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 => ! [X11 : $i,X3 : $i] : ((in @ X11 @ (powerset @ X3)) => ! [X16 : $i] : ((in @ X16 @ (powerset @ X3)) => ! [X17 : $i] : ((in @ X17 @ (powerset @ X3)) => (in @ (binintersect @ X11 @ X16) @ (powerset @ (binintersect @ (binunion @ X11 @ X17) @ (binunion @ X16 @ X17)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 30.11/5.64 file('/export/starexec/sandbox/tmp/tmp.50SVxc4AnF/DTF2THF_30813.p',woz1_3)).
% 30.11/5.64 thf(f5098,plain,(
% 30.11/5.64 ((in @ (binintersect @ sK0 @ sK2) @ (powerset @ (binintersect @ (binunion @ sK0 @ sK3) @ (binunion @ sK2 @ sK3)))) != $true) | spl4_21),
% 30.11/5.64 inference(avatar_component_clause,[status(thm)],[f5096])).
% 30.11/5.64 thf(f5116,plain,(
% 30.11/5.64 spl4_25),
% 30.11/5.64 inference(avatar_split_clause,[status(thm)],[f1143,f5113])).
% 30.11/5.64 thf(f1143,plain,(
% 30.11/5.64 ((in @ sK0 @ (powerset @ sK1)) = $true)),
% 30.11/5.64 inference(cnf_transformation,[status(thm)],[f860])).
% 30.11/5.64 thf(f5099,plain,(
% 30.11/5.64 ~spl4_21),
% 30.11/5.64 inference(avatar_split_clause,[status(thm)],[f1146,f5096])).
% 30.11/5.64 thf(f1146,plain,(
% 30.11/5.64 ((in @ (binintersect @ sK0 @ sK2) @ (powerset @ (binintersect @ (binunion @ sK0 @ sK3) @ (binunion @ sK2 @ sK3)))) != $true)),
% 30.11/5.64 inference(cnf_transformation,[status(thm)],[f860])).
% 30.11/5.64 thf(f5094,plain,(
% 30.11/5.64 ~spl4_20),
% 30.11/5.64 inference(avatar_split_clause,[status(thm)],[f288,f5091])).
% 30.11/5.64 thf(f5091,definition,(
% 30.11/5.64 spl4_20 <=> ($false = $true)),
% 30.11/5.64 introduced(definition,[new_symbols(naming,[spl4_20])],[avatar_definition])).
% 30.11/5.64 thf(f288,plain,(
% 30.11/5.64 ($false != $true)),
% 30.11/5.64 introduced(definition,[],[fool_axiom])).
% 30.11/5.64 thf(f5071,plain,(
% 30.11/5.64 spl4_15),
% 30.11/5.64 inference(avatar_split_clause,[status(thm)],[f1145,f5068])).
% 30.11/5.64 thf(f5068,definition,(
% 30.11/5.64 spl4_15 <=> ($true = (in @ sK3 @ (powerset @ sK1)))),
% 30.11/5.64 introduced(definition,[new_symbols(naming,[spl4_15])],[avatar_definition])).
% 30.11/5.64 thf(f1145,plain,(
% 30.11/5.64 ($true = (in @ sK3 @ (powerset @ sK1)))),
% 30.11/5.64 inference(cnf_transformation,[status(thm)],[f860])).
% 30.11/5.64 thf(f5065,plain,(
% 30.11/5.64 spl4_14),
% 30.11/5.64 inference(avatar_split_clause,[status(thm)],[f1144,f5062])).
% 30.11/5.64 thf(f1144,plain,(
% 30.11/5.64 ((in @ sK2 @ (powerset @ sK1)) = $true)),
% 30.11/5.64 inference(cnf_transformation,[status(thm)],[f860])).
% 30.11/5.64 % SZS output end Proof for DTF2THF_30813
% 30.11/5.64 % (31239)------------------------------
% 30.11/5.64 % (31239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.11/5.64 % (31239)Termination reason: Refutation
% 30.11/5.64
% 30.11/5.64 % (31239)Memory used [KB]: 12281
% 30.11/5.64 % (31239)Time elapsed: 0.810 s
% 30.11/5.64 % (31239)Instructions burned: 2653 (million)
% 30.11/5.64 % (31239)------------------------------
% 30.11/5.64 % (31239)------------------------------
% 30.11/5.64 % (31089)Success in time 4.022 s
%------------------------------------------------------------------------------