%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU668^1 : 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 : n001.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 09:36:04 AM UTC 2026
% Result : Theorem 42.82s 7.67s
% Output : Refutation 42.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 14
% Syntax : Number of formulae : 85 ( 46 unt; 0 typ; 6 def)
% Number of atoms : 3336 ( 875 equ; 0 cnn)
% Maximal formula atoms : 188 ( 39 avg)
% Number of connectives : 2154 ( 37 ~; 27 |; 617 &; 650 @)
% ( 6 <=>; 762 =>; 0 <=; 0 <~>)
% Maximal formula depth : 200 ( 18 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 44 ( 44 >; 0 *; 0 +; 0 <<)
% Number of symbols : 339 ( 334 usr; 200 con; 0-5 aty)
% ( 34 !!; 21 ??; 0 @@+; 0 @@-)
% Number of variables : 206 ( 120 ^; 65 !; 21 ?; 206 :)
% 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_235,type,
sK1: $i > $i > $o ).
thf(func_def_240,type,
sK6: $i > $i ).
thf(func_def_241,type,
sK7: $o > $i > $i > $i ).
thf(func_def_245,type,
sK8: $i > $i ).
thf(func_def_246,type,
sK9: $i > ( $i > $o ) > $i ).
thf(func_def_247,type,
sK10: $i > $i ).
thf(func_def_248,type,
sK11: $i > $i > $i ).
thf(func_def_249,type,
sK12: $i > $i ).
thf(func_def_250,type,
sK13: ( $i > $o ) > $i > $i ).
thf(func_def_251,type,
sK14: ( $i > $o ) > $i ).
thf(func_def_252,type,
sK15: ( $i > $o ) > $i ).
thf(func_def_253,type,
sK16: ( $i > $o ) > $i > $i ).
thf(func_def_254,type,
sK17: $i > ( $i > $o ) > $i > $i ).
thf(func_def_255,type,
sK18: $i > ( $i > $o ) > $i > $i ).
thf(func_def_256,type,
sK19: ( $i > $o ) > $i > $i ).
thf(func_def_257,type,
sK20: ( $i > $o ) > $i > $i ).
thf(func_def_258,type,
sK21: ( $i > $o ) > $i > $i ).
thf(func_def_259,type,
sK22: ( $i > $o ) > $i ).
thf(func_def_260,type,
sK23: ( $i > $o ) > $i ).
thf(func_def_261,type,
sK24: ( $i > $o ) > $i ).
thf(func_def_262,type,
sK25: ( $i > $o ) > $i ).
thf(func_def_263,type,
sK26: $i > $i > $i ).
thf(func_def_264,type,
sK27: ( $i > $o ) > $i > $i ).
thf(func_def_265,type,
sK28: ( $i > $o ) > $i ).
thf(func_def_266,type,
sK29: ( $i > $o ) > $i > $i ).
thf(func_def_267,type,
sK30: $i > $i > $i ).
thf(func_def_268,type,
sK31: $i > $i > $i ).
thf(func_def_269,type,
sK32: $i > $i > $i ).
thf(func_def_270,type,
sK33: $i > $i > $i ).
thf(func_def_271,type,
sK34: ( $i > $o ) > $i ).
thf(func_def_272,type,
sK35: ( $i > $o ) > $i > $i ).
thf(func_def_273,type,
sK36: $i > $i > $i ).
thf(func_def_274,type,
sK37: $i > $i > $i ).
thf(func_def_275,type,
sK38: $i > $i > $i ).
thf(func_def_276,type,
sK39: $i > $i > $i ).
thf(func_def_277,type,
sK40: $i > $i ).
thf(func_def_278,type,
sK41: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_279,type,
sK42: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_280,type,
sK43: $i > $i ).
thf(func_def_281,type,
sK44: $i > $i > $i ).
thf(func_def_282,type,
sK45: $i > $i > $i ).
thf(func_def_283,type,
sK46: $i > $i > $i ).
thf(func_def_284,type,
sK47: $i > $i > $i ).
thf(func_def_285,type,
sK48: $i > $i > $i ).
thf(func_def_286,type,
sK49: $i > $i > $i ).
thf(func_def_287,type,
sK50: $i > $i > $i > $i ).
thf(func_def_288,type,
sK51: $i > $i ).
thf(func_def_289,type,
sK52: $i > ( $i > $o ) > $i ).
thf(func_def_290,type,
sK53: $i > ( $i > $o ) > $i ).
thf(func_def_291,type,
sK54: $i > ( $i > $o ) > $i ).
thf(func_def_292,type,
sK55: $i > ( $i > $o ) > $i ).
thf(func_def_293,type,
sK56: ( $i > $o ) > $i > $i ).
thf(func_def_294,type,
sK57: ( $i > $o ) > $i > $i ).
thf(func_def_295,type,
sK58: ( $i > $o ) > $i > $i ).
thf(func_def_296,type,
sK59: ( $i > $o ) > $i > $i ).
thf(func_def_297,type,
sK60: ( $i > $o ) > $i > $i ).
thf(func_def_298,type,
sK61: ( $i > $o ) > $i > $i ).
thf(func_def_299,type,
sK62: ( $i > $o ) > $i > $i ).
thf(func_def_300,type,
sK63: $i > ( $i > $o ) > $i ).
thf(func_def_301,type,
sK64: ( $i > $o ) > $i > $i ).
thf(func_def_302,type,
sK65: $i > $i ).
thf(func_def_303,type,
sK66: $i > $i > $i > $i ).
thf(func_def_304,type,
sK67: $i > $i > $i > $i ).
thf(func_def_305,type,
sK68: $i > $i > $i ).
thf(func_def_306,type,
sK69: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_307,type,
sK70: ( $i > $o ) > $i > $i ).
thf(func_def_308,type,
sK71: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_309,type,
sK72: ( $i > $o ) > $i > $i ).
thf(func_def_310,type,
sK73: ( $i > $o ) > $i > $i ).
thf(func_def_311,type,
sK74: ( $i > $o ) > $i > $i ).
thf(func_def_312,type,
sK75: ( $i > $o ) > $i > $i ).
thf(func_def_313,type,
sK76: $i > $i ).
thf(func_def_315,type,
sK77: ( $i > $i > $o ) > $i > $i ).
thf(func_def_316,type,
sK78: ( $i > $i > $o ) > $i > $i ).
thf(func_def_317,type,
sK79: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_318,type,
sK80: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_319,type,
sK81: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_320,type,
sK82: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_321,type,
sK83: $i > ( $i > $o ) > $i ).
thf(func_def_322,type,
sK84: ( $i > $o ) > $i ).
thf(func_def_323,type,
sK85: ( $i > $o ) > $i > $i ).
thf(func_def_324,type,
sK86: ( $i > $o ) > $i > $i ).
thf(func_def_325,type,
sK87: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_326,type,
sK88: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_327,type,
sK89: ( $i > $o ) > $i ).
thf(func_def_328,type,
sK90: ( $i > $o ) > $i > $i ).
thf(func_def_329,type,
sK91: ( $i > $o ) > $i > $i ).
thf(func_def_330,type,
sK92: ( $i > $o ) > $i ).
thf(func_def_331,type,
sK93: ( $i > $o ) > $i > $i ).
thf(func_def_332,type,
sK94: ( $i > $o ) > $i > $i ).
thf(func_def_333,type,
sK95: ( $i > $o ) > $i ).
thf(func_def_334,type,
sK96: ( $i > $o ) > $i > $i ).
thf(func_def_335,type,
sK97: ( $i > $o ) > $i > $i ).
thf(func_def_336,type,
sK98: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_337,type,
sK99: ( $i > $o ) > $i ).
thf(func_def_338,type,
sK100: ( $i > $o ) > $i > $i ).
thf(func_def_339,type,
sK101: ( $i > $o ) > $i > $i ).
thf(func_def_340,type,
sK102: ( $i > $o ) > $i ).
thf(func_def_341,type,
sK103: ( $i > $o ) > $i > $i ).
thf(func_def_342,type,
sK104: ( $i > $o ) > $i ).
thf(func_def_343,type,
sK105: ( $i > $o ) > $i > $i ).
thf(func_def_344,type,
sK106: ( $i > $o ) > $i > $i ).
thf(func_def_345,type,
ph107:
!>[X0: $tType] : X0 ).
thf(func_def_346,type,
sK108: $i > $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_347,type,
sK109: $i > $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_352,type,
sK114: $i > $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_353,type,
sK115: $i > $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(f8370,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f3305,f3333,f7097,f7107,f8359,f8367,f8368]) ).
thf(f8368,plain,
( ( sK112 != sK0 )
| ( sK113 != sK4 )
| ( $true
!= ( sK1 @ sK112 @ sK113 ) )
| ( $true
= ( sK1 @ sK0 @ sK4 ) ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f8367,plain,
( spl5_35
| ~ spl5_25 ),
inference(avatar_split_clause,[status(thm)],[f8366,f7094,f8362]) ).
thf(f8362,definition,
( spl5_35
<=> ( sK112 = sK0 ) ),
introduced(definition,[new_symbols(naming,[spl5_35])],[avatar_definition]) ).
thf(f7094,definition,
( spl5_25
<=> ( ( kpair @ sK112 @ sK113 )
= ( kpair @ sK0 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_25])],[avatar_definition]) ).
thf(f8366,plain,
( ( sK112 = sK0 )
| ~ spl5_25 ),
inference(forward_demodulation,[status(thm)],[f8345,f3241]) ).
thf(f3241,plain,
! [X2: $i,X1: $i] :
( ( kfst @ ( kpair @ X2 @ X1 ) )
= X2 ),
inference(equality_proxy_clausification,[status(thm)],[f3240]) ).
thf(f3240,plain,
! [X2: $i,X1: $i] :
( ( ( kfst @ ( kpair @ X2 @ X1 ) )
= X2 )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f3239]) ).
thf(f3239,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( kfst @ ( kpair @ Y0 @ X1 ) )
= Y0 )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f3238]) ).
thf(f3238,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( kfst @ ( kpair @ Y0 @ X1 ) )
= Y0 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f3237]) ).
thf(f3237,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst @ ( kpair @ Y1 @ Y0 ) )
= Y1 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f1060]) ).
thf(f1060,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst @ ( kpair @ Y1 @ Y0 ) )
= Y1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f866,f620]) ).
thf(f620,plain,
kfstpairEq = $true,
inference(cnf_transformation,[status(thm)],[f574]) ).
thf(f574,plain,
( ( setextsub = $true )
& ( subsetemptysetimpeq = $true )
& ( binintersectSubset4 = $true )
& ( singletoninpowunion = $true )
& ( setadjoin__Cong = $true )
& ( upairset2IR = $true )
& ( setadjoinOr = $true )
& ( dsetconstr__Cong = $true )
& ( omegaSAx = $true )
& ( setminusEL = $true )
& ( ex1I2 = $true )
& ( binintersectSubset1 = $true )
& ( exuE1 = $true )
& ( symdiffI1 = $true )
& ( binintersectI = $true )
& ( exuE3e = $true )
& ( prop2setI = $true )
& ( descrp = $true )
& ( setunionAx = $true )
& ( subset2powerset = $true )
& ( subPowSU = $true )
& ( notequalI2 = $true )
& ( subsetE = $true )
& ( inPowerset = $true )
& ( cartprodfstpairEq = $true )
& ( binunionE = $true )
& ( upairequniteq = $true )
& ( exu__Cong = $true )
& ( setminusELneg = $true )
& ( cartprodmempair = $true )
& ( setminusI = $true )
& ( binunionLsub = $true )
& ( setunionI = $true )
& ( binintersectLsub = $true )
& ( foundationAx = $true )
& ( setminusSubset1 = $true )
& ( theprop = $true )
& ( bs114d = $true )
& ( exuEu = $true )
& ( subsetRefl = $true )
& ( subsetI2 = $true )
& ( singletoninpowerset = $true )
& ( setukpairinjL = $true )
& ( ( in @ sK4 @ sK2 )
= $true )
& ( $true
!= ( sK1 @ sK0 @ sK4 ) )
& ( ( in @ ( kpair @ sK0 @ sK4 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y0: $i,Y1: $i] : ( sK1 @ Y0 @ Y1 ) ) )
= $true )
& ( $true
= ( in @ sK0 @ sK3 ) )
& ( subsetTrans = $true )
& ( upairinpowunion = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodpairsurjEq = $true )
& ( singletonsuniq = $true )
& ( dpsetconstrSub = $true )
& ( binintersectEL = $true )
& ( emptysetAx = $true )
& ( omegaIndAx = $true )
& ( symdiffIneg2 = $true )
& ( kpairsurjEq = $true )
& ( setunionsingleton2 = $true )
& ( ubforcartprodlem3 = $true )
& ( dsetconstrI = $true )
& ( binintersectRsub = $true )
& ( uniqinunit = $true )
& ( nonemptyI1 = $true )
& ( quantDeMorgan1 = $true )
& ( setminusLsub = $true )
& ( setunionsingleton1 = $true )
& ( setextAx = $true )
& ( notsubsetI = $true )
& ( powersetE = $true )
& ( exuI1 = $true )
& ( upairset2E = $true )
& ( secondinupair = $true )
& ( singletonprop = $true )
& ( notequalI1 = $true )
& ( cartprodsndin = $true )
& ( in__Cong = $true )
& ( descr__Cong = $true )
& ( powersetI = $true )
& ( subsetE2 = $true )
& ( setukpairinjR1 = $true )
& ( eqimpsubset1 = $true )
& ( sepSubset = $true )
& ( setminusILneg = $true )
& ( eqimpsubset2 = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrER = $true )
& ( sepInPowerset = $true )
& ( ex1I = $true )
& ( binunionEcases = $true )
& ( exuE2 = $true )
& ( binintersectSubset3 = $true )
& ( prop2setE = $true )
& ( upairsetE = $true )
& ( setukpairinjR = $true )
& ( setadjoinIL = $true )
& ( binunionIR = $true )
& ( quantDeMorgan3 = $true )
& ( disjointsetsI1 = $true )
& ( cartprodsndpairEq = $true )
& ( emptyset__Cong = $true )
& ( setoftrueEq = $true )
& ( notinemptyset = $true )
& ( setunionsingleton = $true )
& ( symdiffI2 = $true )
& ( cartprodpairmemEL = $true )
& ( setminusIRneg = $true )
& ( setunion__Cong = $true )
& ( wellorderingAx = $true )
& ( singletonsswitch = $true )
& ( ksndpairEq = $true )
& ( upairsetIR = $true )
& ( replAx = $true )
& ( powersetAx = $true )
& ( singletonsubset = $true )
& ( inCongP = $true )
& ( cartprodmempair1 = $true )
& ( binunionRsub = $true )
& ( setukpairinjR2 = $true )
& ( emptyE1 = $true )
& ( quantDeMorgan2 = $true )
& ( notinsingleton = $true )
& ( setunionE2 = $true )
& ( powersetE1 = $true )
& ( setukpairinjL1 = $true )
& ( binintersectER = $true )
& ( setadjoinE = $true )
& ( binunionIL = $true )
& ( exuI3 = $true )
& ( setext = $true )
& ( powersetsubset = $true )
& ( omega0Ax = $true )
& ( kfstsingleton = $true )
& ( eqinunit = $true )
& ( ubforcartprodlem2 = $true )
& ( setadjoinSub = $true )
& ( ex1E1 = $true )
& ( setukpairIL = $true )
& ( emptysetE = $true )
& ( subsetI1 = $true )
& ( binintersectSubset2 = $true )
& ( kpairp = $true )
& ( emptyI = $true )
& ( setukpairinjL2 = $true )
& ( setminusERneg = $true )
& ( cartprodpairmemER = $true )
& ( ksndsingleton = $true )
& ( nonemptyI = $true )
& ( omega__Cong = $true )
& ( powersetI1 = $true )
& ( exuI2 = $true )
& ( prop2set2propI = $true )
& ( setukpairinjR11 = $true )
& ( powerset__Cong = $true )
& ( ubforcartprodlem1 = $true )
& ( binintersectSubset5 = $true )
& ( nonemptyE1 = $true )
& ( symdiffE = $true )
& ( notdallE = $true )
& ( setadjoinAx = $true )
& ( exuE3u = $true )
& ( emptysetimpfalse = $true )
& ( cartprodpairin = $true )
& ( emptyinunitempty = $true )
& ( setminusSubset2 = $true )
& ( symdiffIneg1 = $true )
& ( quantDeMorgan4 = $true )
& ( setukpairIR = $true )
& ( setunionE = $true )
& ( setadjoinSub2 = $true )
& ( kpairiskpair = $true )
& ( dpsetconstrI = $true )
& ( emptyInPowerset = $true )
& ( emptysetsubset = $true )
& ( setadjoinIR = $true )
& ( vacuousDall = $true )
& ( setminusER = $true )
& ( kfstpairEq = $true )
& ( upairsetIL = $true )
& ( setbeta = $true )
& ( notdexE = $true )
& ( setukpairinjR12 = $true )
& ( setOfPairsIsBReln = $true )
& ( emptyinPowerset = $true )
& ( nonemptyImpWitness = $true )
& ( cartprodfstin = $true )
& ( noeltsimpempty = $true )
& ( upairsubunion = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f571,f573,f572]) ).
thf(f572,plain,
( ? [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ X2 ) )
& ( $true
!= ( X1 @ X0 @ X4 ) )
& ( $true
= ( in @ ( kpair @ X0 @ X4 )
@ ( dpsetconstr @ X3 @ X2
@ ^ [Y0: $i,Y1: $i] : ( X1 @ Y0 @ Y1 ) ) ) ) )
& ( ( in @ X0 @ X3 )
= $true ) )
=> ( ? [X4: $i] :
( ( $true
= ( in @ X4 @ sK2 ) )
& ( $true
!= ( sK1 @ sK0 @ X4 ) )
& ( ( in @ ( kpair @ sK0 @ X4 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y0: $i,Y1: $i] : ( sK1 @ Y0 @ Y1 ) ) )
= $true ) )
& ( $true
= ( in @ sK0 @ sK3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f573,plain,
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ sK2 ) )
& ( $true
!= ( sK1 @ sK0 @ X4 ) )
& ( ( in @ ( kpair @ sK0 @ X4 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y0: $i,Y1: $i] : ( sK1 @ Y0 @ Y1 ) ) )
= $true ) )
=> ( ( ( in @ sK4 @ sK2 )
= $true )
& ( $true
!= ( sK1 @ sK0 @ sK4 ) )
& ( ( in @ ( kpair @ sK0 @ sK4 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y0: $i,Y1: $i] : ( sK1 @ Y0 @ Y1 ) ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f571,plain,
( ( setextsub = $true )
& ( subsetemptysetimpeq = $true )
& ( binintersectSubset4 = $true )
& ( singletoninpowunion = $true )
& ( setadjoin__Cong = $true )
& ( upairset2IR = $true )
& ( setadjoinOr = $true )
& ( dsetconstr__Cong = $true )
& ( omegaSAx = $true )
& ( setminusEL = $true )
& ( ex1I2 = $true )
& ( binintersectSubset1 = $true )
& ( exuE1 = $true )
& ( symdiffI1 = $true )
& ( binintersectI = $true )
& ( exuE3e = $true )
& ( prop2setI = $true )
& ( descrp = $true )
& ( setunionAx = $true )
& ( subset2powerset = $true )
& ( subPowSU = $true )
& ( notequalI2 = $true )
& ( subsetE = $true )
& ( inPowerset = $true )
& ( cartprodfstpairEq = $true )
& ( binunionE = $true )
& ( upairequniteq = $true )
& ( exu__Cong = $true )
& ( setminusELneg = $true )
& ( cartprodmempair = $true )
& ( setminusI = $true )
& ( binunionLsub = $true )
& ( setunionI = $true )
& ( binintersectLsub = $true )
& ( foundationAx = $true )
& ( setminusSubset1 = $true )
& ( theprop = $true )
& ( bs114d = $true )
& ( exuEu = $true )
& ( subsetRefl = $true )
& ( subsetI2 = $true )
& ( singletoninpowerset = $true )
& ( setukpairinjL = $true )
& ? [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ X2 ) )
& ( $true
!= ( X1 @ X0 @ X4 ) )
& ( $true
= ( in @ ( kpair @ X0 @ X4 )
@ ( dpsetconstr @ X3 @ X2
@ ^ [Y0: $i,Y1: $i] : ( X1 @ Y0 @ Y1 ) ) ) ) )
& ( ( in @ X0 @ X3 )
= $true ) )
& ( subsetTrans = $true )
& ( upairinpowunion = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodpairsurjEq = $true )
& ( singletonsuniq = $true )
& ( dpsetconstrSub = $true )
& ( binintersectEL = $true )
& ( emptysetAx = $true )
& ( omegaIndAx = $true )
& ( symdiffIneg2 = $true )
& ( kpairsurjEq = $true )
& ( setunionsingleton2 = $true )
& ( ubforcartprodlem3 = $true )
& ( dsetconstrI = $true )
& ( binintersectRsub = $true )
& ( uniqinunit = $true )
& ( nonemptyI1 = $true )
& ( quantDeMorgan1 = $true )
& ( setminusLsub = $true )
& ( setunionsingleton1 = $true )
& ( setextAx = $true )
& ( notsubsetI = $true )
& ( powersetE = $true )
& ( exuI1 = $true )
& ( upairset2E = $true )
& ( secondinupair = $true )
& ( singletonprop = $true )
& ( notequalI1 = $true )
& ( cartprodsndin = $true )
& ( in__Cong = $true )
& ( descr__Cong = $true )
& ( powersetI = $true )
& ( subsetE2 = $true )
& ( setukpairinjR1 = $true )
& ( eqimpsubset1 = $true )
& ( sepSubset = $true )
& ( setminusILneg = $true )
& ( eqimpsubset2 = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrER = $true )
& ( sepInPowerset = $true )
& ( ex1I = $true )
& ( binunionEcases = $true )
& ( exuE2 = $true )
& ( binintersectSubset3 = $true )
& ( prop2setE = $true )
& ( upairsetE = $true )
& ( setukpairinjR = $true )
& ( setadjoinIL = $true )
& ( binunionIR = $true )
& ( quantDeMorgan3 = $true )
& ( disjointsetsI1 = $true )
& ( cartprodsndpairEq = $true )
& ( emptyset__Cong = $true )
& ( setoftrueEq = $true )
& ( notinemptyset = $true )
& ( setunionsingleton = $true )
& ( symdiffI2 = $true )
& ( cartprodpairmemEL = $true )
& ( setminusIRneg = $true )
& ( setunion__Cong = $true )
& ( wellorderingAx = $true )
& ( singletonsswitch = $true )
& ( ksndpairEq = $true )
& ( upairsetIR = $true )
& ( replAx = $true )
& ( powersetAx = $true )
& ( singletonsubset = $true )
& ( inCongP = $true )
& ( cartprodmempair1 = $true )
& ( binunionRsub = $true )
& ( setukpairinjR2 = $true )
& ( emptyE1 = $true )
& ( quantDeMorgan2 = $true )
& ( notinsingleton = $true )
& ( setunionE2 = $true )
& ( powersetE1 = $true )
& ( setukpairinjL1 = $true )
& ( binintersectER = $true )
& ( setadjoinE = $true )
& ( binunionIL = $true )
& ( exuI3 = $true )
& ( setext = $true )
& ( powersetsubset = $true )
& ( omega0Ax = $true )
& ( kfstsingleton = $true )
& ( eqinunit = $true )
& ( ubforcartprodlem2 = $true )
& ( setadjoinSub = $true )
& ( ex1E1 = $true )
& ( setukpairIL = $true )
& ( emptysetE = $true )
& ( subsetI1 = $true )
& ( binintersectSubset2 = $true )
& ( kpairp = $true )
& ( emptyI = $true )
& ( setukpairinjL2 = $true )
& ( setminusERneg = $true )
& ( cartprodpairmemER = $true )
& ( ksndsingleton = $true )
& ( nonemptyI = $true )
& ( omega__Cong = $true )
& ( powersetI1 = $true )
& ( exuI2 = $true )
& ( prop2set2propI = $true )
& ( setukpairinjR11 = $true )
& ( powerset__Cong = $true )
& ( ubforcartprodlem1 = $true )
& ( binintersectSubset5 = $true )
& ( nonemptyE1 = $true )
& ( symdiffE = $true )
& ( notdallE = $true )
& ( setadjoinAx = $true )
& ( exuE3u = $true )
& ( emptysetimpfalse = $true )
& ( cartprodpairin = $true )
& ( emptyinunitempty = $true )
& ( setminusSubset2 = $true )
& ( symdiffIneg1 = $true )
& ( quantDeMorgan4 = $true )
& ( setukpairIR = $true )
& ( setunionE = $true )
& ( setadjoinSub2 = $true )
& ( kpairiskpair = $true )
& ( dpsetconstrI = $true )
& ( emptyInPowerset = $true )
& ( emptysetsubset = $true )
& ( setadjoinIR = $true )
& ( vacuousDall = $true )
& ( setminusER = $true )
& ( kfstpairEq = $true )
& ( upairsetIL = $true )
& ( setbeta = $true )
& ( notdexE = $true )
& ( setukpairinjR12 = $true )
& ( setOfPairsIsBReln = $true )
& ( emptyinPowerset = $true )
& ( nonemptyImpWitness = $true )
& ( cartprodfstin = $true )
& ( noeltsimpempty = $true )
& ( upairsubunion = $true ) ),
inference(flattening,[status(thm)],[f570]) ).
thf(f570,plain,
( ? [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i] :
( ? [X4: $i] :
( ( $true
!= ( X1 @ X0 @ X4 ) )
& ( $true
= ( in @ ( kpair @ X0 @ X4 )
@ ( dpsetconstr @ X3 @ X2
@ ^ [Y0: $i,Y1: $i] : ( X1 @ Y0 @ Y1 ) ) ) )
& ( $true
= ( in @ X4 @ X2 ) ) )
& ( ( in @ X0 @ X3 )
= $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)],[f555]) ).
thf(f555,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 )
=> ! [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i] :
( ( ( in @ X0 @ X3 )
= $true )
=> ! [X4: $i] :
( ( $true
= ( in @ X4 @ X2 ) )
=> ( ( $true
= ( in @ ( kpair @ X0 @ X4 )
@ ( dpsetconstr @ X3 @ X2
@ ^ [Y0: $i,Y1: $i] : ( X1 @ Y0 @ Y1 ) ) ) )
=> ( $true
= ( X1 @ X0 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f554]) ).
thf(f554,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
=> ! [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i] :
( ( in @ X0 @ X3 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( in @ ( kpair @ X0 @ X4 )
@ ( dpsetconstr @ X3 @ X2
@ ^ [X5: $i,X6: $i] : ( X1 @ X5 @ X6 ) ) )
=> ( X1 @ X0 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f192]) ).
thf(f192,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
=> ! [X1: $i,X0: $i > $i > $o,X4: $i,X3: $i] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ ( kpair @ X1 @ X2 )
@ ( dpsetconstr @ X3 @ X4
@ ^ [X8: $i,X10: $i] : ( X0 @ X8 @ X10 ) ) )
=> ( X0 @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f191]) ).
thf(f191,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
=> ! [X1: $i,X0: $i > $i > $o,X4: $i,X3: $i] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ ( kpair @ X1 @ X2 )
@ ( dpsetconstr @ X3 @ X4
@ ^ [X8: $i,X10: $i] : ( X0 @ X8 @ X10 ) ) )
=> ( X0 @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.pZ9OXiV362/DTF2THF_30834.p',dpsetconstrERa) ).
thf(f866,plain,
( kfstpairEq
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst @ ( kpair @ Y1 @ Y0 ) )
= Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f215]) ).
thf(f215,plain,
( kfstpairEq
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst @ ( kpair @ Y1 @ Y0 ) )
= Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f214]) ).
thf(f214,plain,
! [X0: $i,X1: $i] :
( ( ( kfst @ ( kpair @ X0 @ X1 ) )
= X0 )
= kfstpairEq ),
inference(rectify,[status(thm)],[f166]) ).
thf(f166,axiom,
! [X1: $i,X2: $i] :
( ( ( kfst @ ( kpair @ X1 @ X2 ) )
= X1 )
= kfstpairEq ),
file('/export/starexec/sandbox/tmp/tmp.pZ9OXiV362/DTF2THF_30834.p',kfstpairEq) ).
thf(f8345,plain,
( ( ( kfst @ ( kpair @ sK0 @ sK4 ) )
= sK112 )
| ~ spl5_25 ),
inference(superposition,[status(thm)],[f3241,f7096]) ).
thf(f7096,plain,
( ( ( kpair @ sK112 @ sK113 )
= ( kpair @ sK0 @ sK4 ) )
| ~ spl5_25 ),
inference(avatar_component_clause,[status(thm)],[f7094]) ).
thf(f8359,plain,
( spl5_34
| ~ spl5_25 ),
inference(avatar_split_clause,[status(thm)],[f8358,f7094,f8354]) ).
thf(f8354,definition,
( spl5_34
<=> ( sK113 = sK4 ) ),
introduced(definition,[new_symbols(naming,[spl5_34])],[avatar_definition]) ).
thf(f8358,plain,
( ( sK113 = sK4 )
| ~ spl5_25 ),
inference(forward_demodulation,[status(thm)],[f8338,f1805]) ).
thf(f1805,plain,
! [X2: $i,X1: $i] :
( ( ksnd @ ( kpair @ X2 @ X1 ) )
= X1 ),
inference(equality_proxy_clausification,[status(thm)],[f1804]) ).
thf(f1804,plain,
! [X2: $i,X1: $i] :
( ( ( ksnd @ ( kpair @ X2 @ X1 ) )
= X1 )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1803]) ).
thf(f1803,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ksnd @ ( kpair @ Y0 @ X1 ) )
= X1 )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f1802]) ).
thf(f1802,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ksnd @ ( kpair @ Y0 @ X1 ) )
= X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1801]) ).
thf(f1801,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ksnd @ ( kpair @ Y1 @ Y0 ) )
= Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f1139]) ).
thf(f1139,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ksnd @ ( kpair @ Y1 @ Y0 ) )
= Y0 ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f947,f687]) ).
thf(f687,plain,
ksndpairEq = $true,
inference(cnf_transformation,[status(thm)],[f574]) ).
thf(f947,plain,
( ksndpairEq
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ksnd @ ( kpair @ Y1 @ Y0 ) )
= Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f415]) ).
thf(f415,plain,
( ksndpairEq
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ksnd @ ( kpair @ Y1 @ Y0 ) )
= Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f414]) ).
thf(f414,plain,
( ksndpairEq
= ( ! [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X0 @ X1 ) )
= X1 ) ) ),
inference(rectify,[status(thm)],[f177]) ).
thf(f177,axiom,
( ksndpairEq
= ( ! [X1: $i,X2: $i] :
( ( ksnd @ ( kpair @ X1 @ X2 ) )
= X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.pZ9OXiV362/DTF2THF_30834.p',ksndpairEq) ).
thf(f8338,plain,
( ( sK113
= ( ksnd @ ( kpair @ sK0 @ sK4 ) ) )
| ~ spl5_25 ),
inference(superposition,[status(thm)],[f1805,f7096]) ).
thf(f7107,plain,
( spl5_27
| ~ spl5_21 ),
inference(avatar_split_clause,[status(thm)],[f7068,f3330,f7104]) ).
thf(f7104,definition,
( spl5_27
<=> ( $true
= ( sK1 @ sK112 @ sK113 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_27])],[avatar_definition]) ).
thf(f3330,definition,
( spl5_21
<=> ( $true
= ( in @ ( kpair @ sK0 @ sK4 )
@ ( dsetconstr @ ( cartprod @ sK3 @ sK2 )
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y1 @ Y2 )
& ( in @ Y2 @ sK2 )
& ( ( kpair @ Y1 @ Y2 )
= Y0 ) ) )
& ( in @ Y1 @ sK3 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl5_21])],[avatar_definition]) ).
thf(f7068,plain,
( ( $true
= ( sK1 @ sK112 @ sK113 ) )
| ~ spl5_21 ),
inference(binary_proxy_clausification,[status(thm)],[f7066]) ).
thf(f7066,plain,
( ( $true
= ( ( sK1 @ sK112 @ sK113 )
& ( in @ sK113 @ sK2 ) ) )
| ~ spl5_21 ),
inference(binary_proxy_clausification,[status(thm)],[f7064]) ).
thf(f7064,plain,
( ( $true
= ( ( sK1 @ sK112 @ sK113 )
& ( in @ sK113 @ sK2 )
& ( ( kpair @ sK112 @ sK113 )
= ( kpair @ sK0 @ sK4 ) ) ) )
| ~ spl5_21 ),
inference(beta_eta_normalization,[status(thm)],[f7063]) ).
thf(f7063,plain,
( ( ( ^ [Y0: $i] :
( ( sK1 @ sK112 @ Y0 )
& ( in @ Y0 @ sK2 )
& ( ( kpair @ sK112 @ Y0 )
= ( kpair @ sK0 @ sK4 ) ) )
@ sK113 )
= $true )
| ~ spl5_21 ),
inference(sigma_clausification,[status(thm)],[f7062]) ).
thf(f7062,plain,
( ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ sK112 @ Y0 )
& ( in @ Y0 @ sK2 )
& ( ( kpair @ sK112 @ Y0 )
= ( kpair @ sK0 @ sK4 ) ) ) ) )
| ~ spl5_21 ),
inference(binary_proxy_clausification,[status(thm)],[f7060]) ).
thf(f7060,plain,
( ( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ sK112 @ Y0 )
& ( in @ Y0 @ sK2 )
& ( ( kpair @ sK112 @ Y0 )
= ( kpair @ sK0 @ sK4 ) ) ) )
& ( in @ sK112 @ sK3 ) )
= $true )
| ~ spl5_21 ),
inference(beta_eta_normalization,[status(thm)],[f7059]) ).
thf(f7059,plain,
( ( ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y0 @ Y1 )
& ( in @ Y1 @ sK2 )
& ( ( kpair @ Y0 @ Y1 )
= ( kpair @ sK0 @ sK4 ) ) ) )
& ( in @ Y0 @ sK3 ) )
@ sK112 )
= $true )
| ~ spl5_21 ),
inference(sigma_clausification,[status(thm)],[f7058]) ).
thf(f7058,plain,
( ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y0 @ Y1 )
& ( in @ Y1 @ sK2 )
& ( ( kpair @ Y0 @ Y1 )
= ( kpair @ sK0 @ sK4 ) ) ) )
& ( in @ Y0 @ sK3 ) ) ) )
| ~ spl5_21 ),
inference(beta_eta_normalization,[status(thm)],[f7057]) ).
thf(f7057,plain,
( ( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y1 @ Y2 )
& ( in @ Y2 @ sK2 )
& ( ( kpair @ Y1 @ Y2 )
= Y0 ) ) )
& ( in @ Y1 @ sK3 ) ) )
@ ( kpair @ sK0 @ sK4 ) )
= $true )
| ~ spl5_21 ),
inference(trivial_inequality_removal,[status(thm)],[f7012]) ).
thf(f7012,plain,
( ( $true = $false )
| ( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y1 @ Y2 )
& ( in @ Y2 @ sK2 )
& ( ( kpair @ Y1 @ Y2 )
= Y0 ) ) )
& ( in @ Y1 @ sK3 ) ) )
@ ( kpair @ sK0 @ sK4 ) )
= $true )
| ~ spl5_21 ),
inference(superposition,[status(thm)],[f3332,f2569]) ).
thf(f2569,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
= $false )
| ( $true
= ( X2 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f2568]) ).
thf(f2568,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
=> ( X2 @ X3 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2567]) ).
thf(f2567,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X1 @ X2 ) )
=> ( X2 @ Y0 ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f2566]) ).
thf(f2566,plain,
! [X2: $i > $o,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X1 @ X2 ) )
=> ( X2 @ Y0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2565]) ).
thf(f2565,plain,
! [X2: $i > $o,X1: $i] :
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ X1 @ Y0 ) )
=> ( Y0 @ Y1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f2564]) ).
thf(f2564,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ X1 @ Y0 ) )
=> ( Y0 @ Y1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2563]) ).
thf(f2563,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ Y2 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f2562]) ).
thf(f2562,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ Y2 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f971]) ).
thf(f971,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y2 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f711,f581]) ).
thf(f581,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f350]) ).
thf(f350,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f349]) ).
thf(f349,plain,
( dsetconstrER
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X0
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,axiom,
( dsetconstrER
= ( ! [X1: $i,X0: $i > $o,X3: $i] :
( ( in @ X1
@ ( dsetconstr @ X3
@ ^ [X2: $i] : ( X0 @ X2 ) ) )
=> ( X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.pZ9OXiV362/DTF2THF_30834.p',dsetconstrER) ).
thf(f711,plain,
dsetconstrER = $true,
inference(cnf_transformation,[status(thm)],[f574]) ).
thf(f3332,plain,
( ( $true
= ( in @ ( kpair @ sK0 @ sK4 )
@ ( dsetconstr @ ( cartprod @ sK3 @ sK2 )
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y1 @ Y2 )
& ( in @ Y2 @ sK2 )
& ( ( kpair @ Y1 @ Y2 )
= Y0 ) ) )
& ( in @ Y1 @ sK3 ) ) ) ) ) )
| ~ spl5_21 ),
inference(avatar_component_clause,[status(thm)],[f3330]) ).
thf(f7097,plain,
( spl5_25
| ~ spl5_21 ),
inference(avatar_split_clause,[status(thm)],[f7069,f3330,f7094]) ).
thf(f7069,plain,
( ( ( kpair @ sK112 @ sK113 )
= ( kpair @ sK0 @ sK4 ) )
| ~ spl5_21 ),
inference(equality_proxy_clausification,[status(thm)],[f7065]) ).
thf(f7065,plain,
( ( $true
= ( ( kpair @ sK112 @ sK113 )
= ( kpair @ sK0 @ sK4 ) ) )
| ~ spl5_21 ),
inference(binary_proxy_clausification,[status(thm)],[f7064]) ).
thf(f3333,plain,
spl5_21,
inference(avatar_split_clause,[status(thm)],[f1340,f3330]) ).
thf(f1340,plain,
( $true
= ( in @ ( kpair @ sK0 @ sK4 )
@ ( dsetconstr @ ( cartprod @ sK3 @ sK2 )
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK1 @ Y1 @ Y2 )
& ( in @ Y2 @ sK2 )
& ( ( kpair @ Y1 @ Y2 )
= Y0 ) ) )
& ( in @ Y1 @ sK3 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f966]) ).
thf(f966,plain,
( $true
= ( in @ ( kpair @ sK0 @ sK4 )
@ ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( ?? @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
& ( in @ Y5 @ Y1 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 ) ) )
& ( in @ Y4 @ Y0 ) ) ) )
@ sK3
@ sK2
@ ^ [Y0: $i,Y1: $i] : ( sK1 @ Y0 @ Y1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f752,f843]) ).
thf(f843,plain,
( dpsetconstr
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( ?? @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
& ( in @ Y5 @ Y1 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 ) ) )
& ( in @ Y4 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f467]) ).
thf(f467,plain,
( dpsetconstr
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( ?? @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
& ( in @ Y5 @ Y1 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 ) ) )
& ( in @ Y4 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f466]) ).
thf(f466,plain,
( dpsetconstr
= ( ^ [X0: $i,X1: $i,X2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ X0 @ X1 )
@ ^ [X3: $i] :
? [X4: $i] :
( ( in @ X4 @ X0 )
& ? [X5: $i] :
( ( ( kpair @ X4 @ X5 )
= X3 )
& ( in @ X5 @ X1 )
& ( X2 @ X4 @ X5 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f187]) ).
thf(f187,axiom,
( dpsetconstr
= ( ^ [X3: $i,X4: $i,X0: $i > $i > $o] :
( dsetconstr @ ( cartprod @ X3 @ X4 )
@ ^ [X10: $i] :
? [X1: $i] :
( ( in @ X1 @ X3 )
& ? [X2: $i] :
( ( ( kpair @ X1 @ X2 )
= X10 )
& ( in @ X2 @ X4 )
& ( X0 @ X1 @ X2 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.pZ9OXiV362/DTF2THF_30834.p',dpsetconstr) ).
thf(f752,plain,
( ( in @ ( kpair @ sK0 @ sK4 )
@ ( dpsetconstr @ sK3 @ sK2
@ ^ [Y0: $i,Y1: $i] : ( sK1 @ Y0 @ Y1 ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f574]) ).
thf(f3305,plain,
~ spl5_15,
inference(avatar_split_clause,[status(thm)],[f753,f3302]) ).
thf(f3302,definition,
( spl5_15
<=> ( $true
= ( sK1 @ sK0 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl5_15])],[avatar_definition]) ).
thf(f753,plain,
( $true
!= ( sK1 @ sK0 @ sK4 ) ),
inference(cnf_transformation,[status(thm)],[f574]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU668^1 : TPTP v9.2.1. Released v3.7.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n001.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:31:05 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.21/0.48 ---- Original DTF file ---
% 0.21/0.48 thf(spec,logic,$$dhol).
% 0.21/0.48 %------------------------------------------------------------------------------
% 0.21/0.48 % File : SEU668^1 : TPTP v9.2.1. Released v3.7.0.
% 0.21/0.48 % Domain : Set Theory
% 0.21/0.48 % Problem : Ordered Pairs - Sets of Pairs
% 0.21/0.48 % Version : Especial.
% 0.21/0.48 % English : (! A:i.! B:i.! phi:i>(i>o).! x:i.in x A -> (! y:i.in y B ->
% 0.21/0.48 % in (kpair x y) (dpsetconstr A B (^ z,u:i.phi z u)) -> phi x y))
% 0.21/0.48
% 0.21/0.48 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.21/0.48 % Source : [Bro08]
% 0.21/0.48 % Names : ZFC170g [Bro08]
% 0.21/0.48
% 0.21/0.48 % Status : Theorem
% 0.21/0.48 % Rating : 0.56 v9.1.0, 0.62 v9.0.0, 0.70 v8.2.0, 0.85 v8.1.0, 0.73 v7.5.0, 0.71 v7.4.0, 0.89 v7.2.0, 0.88 v7.0.0, 1.00 v3.7.0
% 0.21/0.48 % Syntax : Number of formulae : 408 ( 190 unt; 217 typ; 190 def)
% 0.21/0.48 % Number of atoms : 1006 ( 284 equ; 0 cnn)
% 0.21/0.48 % Maximal formula atoms : 187 ( 5 avg)
% 0.21/0.48 % Number of connectives : 1794 ( 47 ~; 7 |; 38 &;1245 @)
% 0.21/0.48 % ( 14 <=>; 443 =>; 0 <=; 0 <~>)
% 0.21/0.48 % Maximal formula depth : 199 ( 2 avg)
% 0.21/0.48 % Number of types : 2 ( 0 usr)
% 0.21/0.48 % Number of type conns : 102 ( 102 >; 0 *; 0 +; 0 <<)
% 0.21/0.48 % Number of symbols : 220 ( 217 usr; 188 con; 0-3 aty)
% 0.21/0.48 % Number of variables : 574 ( 55 ^; 481 !; 38 ?; 574 :)
% 0.21/0.48 % SPC : TH0_THM_EQU_NAR
% 0.21/0.48
% 0.21/0.48 % Comments : http://mathgate.info/detsetitem.php?id=234
% 0.21/0.48 %------------------------------------------------------------------------------
% 0.21/0.48 thf(in_type,type,
% 0.21/0.48 in: $i > $i > $o ).
% 0.21/0.48
% 0.21/0.48 thf(exu_type,type,
% 0.21/0.48 exu: ( $i > $o ) > $o ).
% 0.21/0.48
% 0.21/0.48 thf(exu,definition,
% 0.21/0.48 ( exu
% 0.21/0.48 = ( ^ [Xphi: $i > $o] :
% 0.21/0.48 ? [Xx: $i] :
% 0.21/0.48 ( ( Xphi @ Xx )
% 0.21/0.48 & ! [Xy: $i] :
% 0.21/0.48 ( ( Xphi @ Xy )
% 0.21/0.48 => ( Xx = Xy ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(setextAx_type,type,
% 0.21/0.48 setextAx: $o ).
% 0.21/0.48
% 0.21/0.48 thf(setextAx,definition,
% 0.21/0.48 ( setextAx
% 0.21/0.48 = ( ! [A: $i,B: $i] :
% 0.21/0.48 ( ! [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ A )
% 0.21/0.48 <=> ( in @ Xx @ B ) )
% 0.21/0.48 => ( A = B ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(emptyset_type,type,
% 0.21/0.48 emptyset: $i ).
% 0.21/0.48
% 0.21/0.48 thf(emptysetAx_type,type,
% 0.21/0.48 emptysetAx: $o ).
% 0.21/0.48
% 0.21/0.48 thf(emptysetAx,definition,
% 0.21/0.48 ( emptysetAx
% 0.21/0.48 = ( ! [Xx: $i] :
% 0.21/0.48 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(setadjoin_type,type,
% 0.21/0.48 setadjoin: $i > $i > $i ).
% 0.21/0.48
% 0.21/0.48 thf(setadjoinAx_type,type,
% 0.21/0.48 setadjoinAx: $o ).
% 0.21/0.48
% 0.21/0.48 thf(setadjoinAx,definition,
% 0.21/0.48 ( setadjoinAx
% 0.21/0.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.21/0.48 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.21/0.48 <=> ( ( Xy = Xx )
% 0.21/0.48 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(powerset_type,type,
% 0.21/0.48 powerset: $i > $i ).
% 0.21/0.48
% 0.21/0.48 thf(powersetAx_type,type,
% 0.21/0.48 powersetAx: $o ).
% 0.21/0.48
% 0.21/0.48 thf(powersetAx,definition,
% 0.21/0.48 ( powersetAx
% 0.21/0.48 = ( ! [A: $i,B: $i] :
% 0.21/0.48 ( ( in @ B @ ( powerset @ A ) )
% 0.21/0.48 <=> ! [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ B )
% 0.21/0.48 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(setunion_type,type,
% 0.21/0.48 setunion: $i > $i ).
% 0.21/0.48
% 0.21/0.48 thf(setunionAx_type,type,
% 0.21/0.48 setunionAx: $o ).
% 0.21/0.48
% 0.21/0.48 thf(setunionAx,definition,
% 0.21/0.48 ( setunionAx
% 0.21/0.48 = ( ! [A: $i,Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ ( setunion @ A ) )
% 0.21/0.48 <=> ? [B: $i] :
% 0.21/0.48 ( ( in @ Xx @ B )
% 0.21/0.48 & ( in @ B @ A ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(omega_type,type,
% 0.21/0.48 omega: $i ).
% 0.21/0.48
% 0.21/0.48 thf(omega0Ax_type,type,
% 0.21/0.48 omega0Ax: $o ).
% 0.21/0.48
% 0.21/0.48 thf(omega0Ax,definition,
% 0.21/0.48 ( omega0Ax
% 0.21/0.48 = ( in @ emptyset @ omega ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(omegaSAx_type,type,
% 0.21/0.48 omegaSAx: $o ).
% 0.21/0.48
% 0.21/0.48 thf(omegaSAx,definition,
% 0.21/0.48 ( omegaSAx
% 0.21/0.48 = ( ! [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ omega )
% 0.21/0.48 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(omegaIndAx_type,type,
% 0.21/0.48 omegaIndAx: $o ).
% 0.21/0.48
% 0.21/0.48 thf(omegaIndAx,definition,
% 0.21/0.48 ( omegaIndAx
% 0.21/0.48 = ( ! [A: $i] :
% 0.21/0.48 ( ( ( in @ emptyset @ A )
% 0.21/0.48 & ! [Xx: $i] :
% 0.21/0.48 ( ( ( in @ Xx @ omega )
% 0.21/0.48 & ( in @ Xx @ A ) )
% 0.21/0.48 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.21/0.48 => ! [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ omega )
% 0.21/0.48 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(replAx_type,type,
% 0.21/0.48 replAx: $o ).
% 0.21/0.48
% 0.21/0.48 thf(replAx,definition,
% 0.21/0.48 ( replAx
% 0.21/0.48 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.21/0.48 ( ! [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ A )
% 0.21/0.48 => ( exu
% 0.21/0.48 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.21/0.48 => ? [B: $i] :
% 0.21/0.48 ! [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ B )
% 0.21/0.48 <=> ? [Xy: $i] :
% 0.21/0.48 ( ( in @ Xy @ A )
% 0.21/0.48 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(foundationAx_type,type,
% 0.21/0.48 foundationAx: $o ).
% 0.21/0.48
% 0.21/0.48 thf(foundationAx,definition,
% 0.21/0.48 ( foundationAx
% 0.21/0.48 = ( ! [A: $i] :
% 0.21/0.48 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.21/0.48 => ? [B: $i] :
% 0.21/0.48 ( ( in @ B @ A )
% 0.21/0.48 & ~ ? [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ B )
% 0.21/0.48 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(wellorderingAx_type,type,
% 0.21/0.48 wellorderingAx: $o ).
% 0.21/0.48
% 0.21/0.48 thf(wellorderingAx,definition,
% 0.21/0.48 ( wellorderingAx
% 0.21/0.48 = ( ! [A: $i] :
% 0.21/0.48 ? [B: $i] :
% 0.21/0.48 ( ! [C: $i] :
% 0.21/0.48 ( ( in @ C @ B )
% 0.21/0.48 => ! [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ C )
% 0.21/0.48 => ( in @ Xx @ A ) ) )
% 0.21/0.48 & ! [Xx: $i,Xy: $i] :
% 0.21/0.48 ( ( ( in @ Xx @ A )
% 0.21/0.48 & ( in @ Xy @ A ) )
% 0.35/0.48 => ( ! [C: $i] :
% 0.35/0.48 ( ( in @ C @ B )
% 0.35/0.48 => ( ( in @ Xx @ C )
% 0.35/0.48 <=> ( in @ Xy @ C ) ) )
% 0.35/0.48 => ( Xx = Xy ) ) )
% 0.35/0.48 & ! [C: $i,D: $i] :
% 0.35/0.48 ( ( ( in @ C @ B )
% 0.35/0.48 & ( in @ D @ B ) )
% 0.35/0.48 => ( ! [Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ C )
% 0.35/0.48 => ( in @ Xx @ D ) )
% 0.35/0.48 | ! [Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ D )
% 0.35/0.48 => ( in @ Xx @ C ) ) ) )
% 0.35/0.48 & ! [C: $i] :
% 0.35/0.48 ( ( ! [Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ C )
% 0.35/0.48 => ( in @ Xx @ A ) )
% 0.35/0.48 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.35/0.48 => ? [D: $i,Xx: $i] :
% 0.35/0.48 ( ( in @ D @ B )
% 0.35/0.48 & ( in @ Xx @ C )
% 0.35/0.48 & ~ ? [Xy: $i] :
% 0.35/0.48 ( ( in @ Xy @ D )
% 0.35/0.48 & ( in @ Xy @ C ) )
% 0.35/0.48 & ! [E: $i] :
% 0.35/0.48 ( ( in @ E @ B )
% 0.35/0.48 => ( ! [Xy: $i] :
% 0.35/0.48 ( ( in @ Xy @ E )
% 0.35/0.48 => ( in @ Xy @ D ) )
% 0.35/0.48 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(descr_type,type,
% 0.35/0.48 descr: ( $i > $o ) > $i ).
% 0.35/0.48
% 0.35/0.48 thf(descrp_type,type,
% 0.35/0.48 descrp: $o ).
% 0.35/0.48
% 0.35/0.48 thf(descrp,definition,
% 0.35/0.48 ( descrp
% 0.35/0.48 = ( ! [Xphi: $i > $o] :
% 0.35/0.48 ( ( exu
% 0.35/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.35/0.48 => ( Xphi
% 0.35/0.48 @ ( descr
% 0.35/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(dsetconstr_type,type,
% 0.35/0.48 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.35/0.48
% 0.35/0.48 thf(dsetconstrI_type,type,
% 0.35/0.48 dsetconstrI: $o ).
% 0.35/0.48
% 0.35/0.48 thf(dsetconstrI,definition,
% 0.35/0.48 ( dsetconstrI
% 0.35/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ( ( Xphi @ Xx )
% 0.35/0.48 => ( in @ Xx
% 0.35/0.48 @ ( dsetconstr @ A
% 0.35/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(dsetconstrEL_type,type,
% 0.35/0.48 dsetconstrEL: $o ).
% 0.35/0.48
% 0.35/0.48 thf(dsetconstrEL,definition,
% 0.35/0.48 ( dsetconstrEL
% 0.35/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx
% 0.35/0.48 @ ( dsetconstr @ A
% 0.35/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.35/0.48 => ( in @ Xx @ A ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(dsetconstrER_type,type,
% 0.35/0.48 dsetconstrER: $o ).
% 0.35/0.48
% 0.35/0.48 thf(dsetconstrER,definition,
% 0.35/0.48 ( dsetconstrER
% 0.35/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx
% 0.35/0.48 @ ( dsetconstr @ A
% 0.35/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.35/0.48 => ( Xphi @ Xx ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(exuE1_type,type,
% 0.35/0.48 exuE1: $o ).
% 0.35/0.48
% 0.35/0.48 thf(exuE1,definition,
% 0.35/0.48 ( exuE1
% 0.35/0.48 = ( ! [Xphi: $i > $o] :
% 0.35/0.48 ( ( exu
% 0.35/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.35/0.48 => ? [Xx: $i] :
% 0.35/0.48 ( ( Xphi @ Xx )
% 0.35/0.48 & ! [Xy: $i] :
% 0.35/0.48 ( ( Xphi @ Xy )
% 0.35/0.48 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(prop2set_type,type,
% 0.35/0.48 prop2set: $o > $i ).
% 0.35/0.48
% 0.35/0.48 thf(prop2setE_type,type,
% 0.35/0.48 prop2setE: $o ).
% 0.35/0.48
% 0.35/0.48 thf(prop2setE,definition,
% 0.35/0.48 ( prop2setE
% 0.35/0.48 = ( ! [Xphi: $o,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.35/0.48 => Xphi ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(emptysetE_type,type,
% 0.35/0.48 emptysetE: $o ).
% 0.35/0.48
% 0.35/0.48 thf(emptysetE,definition,
% 0.35/0.48 ( emptysetE
% 0.35/0.48 = ( ! [Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ emptyset )
% 0.35/0.48 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(emptysetimpfalse_type,type,
% 0.35/0.48 emptysetimpfalse: $o ).
% 0.35/0.48
% 0.35/0.48 thf(emptysetimpfalse,definition,
% 0.35/0.48 ( emptysetimpfalse
% 0.35/0.48 = ( ! [Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ emptyset )
% 0.35/0.48 => $false ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(notinemptyset_type,type,
% 0.35/0.48 notinemptyset: $o ).
% 0.35/0.48
% 0.35/0.48 thf(notinemptyset,definition,
% 0.35/0.48 ( notinemptyset
% 0.35/0.48 = ( ! [Xx: $i] :
% 0.35/0.48 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(exuE3e_type,type,
% 0.35/0.48 exuE3e: $o ).
% 0.35/0.48
% 0.35/0.48 thf(exuE3e,definition,
% 0.35/0.48 ( exuE3e
% 0.35/0.48 = ( ! [Xphi: $i > $o] :
% 0.35/0.48 ( ( exu
% 0.35/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.35/0.48 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setext_type,type,
% 0.35/0.48 setext: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setext,definition,
% 0.35/0.48 ( setext
% 0.35/0.48 = ( ! [A: $i,B: $i] :
% 0.35/0.48 ( ! [Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ( in @ Xx @ B ) )
% 0.35/0.48 => ( ! [Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ B )
% 0.35/0.48 => ( in @ Xx @ A ) )
% 0.35/0.48 => ( A = B ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(emptyI_type,type,
% 0.35/0.48 emptyI: $o ).
% 0.35/0.48
% 0.35/0.48 thf(emptyI,definition,
% 0.35/0.48 ( emptyI
% 0.35/0.48 = ( ! [A: $i] :
% 0.35/0.48 ( ! [Xx: $i] :
% 0.35/0.48 ~ ( in @ Xx @ A )
% 0.35/0.48 => ( A = emptyset ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(noeltsimpempty_type,type,
% 0.35/0.48 noeltsimpempty: $o ).
% 0.35/0.48
% 0.35/0.48 thf(noeltsimpempty,definition,
% 0.35/0.48 ( noeltsimpempty
% 0.35/0.48 = ( ! [A: $i] :
% 0.35/0.48 ( ! [Xx: $i] :
% 0.35/0.48 ~ ( in @ Xx @ A )
% 0.35/0.48 => ( A = emptyset ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setbeta_type,type,
% 0.35/0.48 setbeta: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setbeta,definition,
% 0.35/0.48 ( setbeta
% 0.35/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ( ( in @ Xx
% 0.35/0.48 @ ( dsetconstr @ A
% 0.35/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.35/0.48 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(nonempty_type,type,
% 0.35/0.48 nonempty: $i > $o ).
% 0.35/0.48
% 0.35/0.48 thf(nonempty,definition,
% 0.35/0.48 ( nonempty
% 0.35/0.48 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(nonemptyE1_type,type,
% 0.35/0.48 nonemptyE1: $o ).
% 0.35/0.48
% 0.35/0.48 thf(nonemptyE1,definition,
% 0.35/0.48 ( nonemptyE1
% 0.35/0.48 = ( ! [A: $i] :
% 0.35/0.48 ( ( nonempty @ A )
% 0.35/0.48 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(nonemptyI_type,type,
% 0.35/0.48 nonemptyI: $o ).
% 0.35/0.48
% 0.35/0.48 thf(nonemptyI,definition,
% 0.35/0.48 ( nonemptyI
% 0.35/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ( ( Xphi @ Xx )
% 0.35/0.48 => ( nonempty
% 0.35/0.48 @ ( dsetconstr @ A
% 0.35/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(nonemptyI1_type,type,
% 0.35/0.48 nonemptyI1: $o ).
% 0.35/0.48
% 0.35/0.48 thf(nonemptyI1,definition,
% 0.35/0.48 ( nonemptyI1
% 0.35/0.48 = ( ! [A: $i] :
% 0.35/0.48 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.35/0.48 => ( nonempty @ A ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setadjoinIL_type,type,
% 0.35/0.48 setadjoinIL: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setadjoinIL,definition,
% 0.35/0.48 ( setadjoinIL
% 0.35/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(emptyinunitempty_type,type,
% 0.35/0.48 emptyinunitempty: $o ).
% 0.35/0.48
% 0.35/0.48 thf(emptyinunitempty,definition,
% 0.35/0.48 ( emptyinunitempty
% 0.35/0.48 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setadjoinIR_type,type,
% 0.35/0.48 setadjoinIR: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setadjoinIR,definition,
% 0.35/0.48 ( setadjoinIR
% 0.35/0.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.35/0.48 ( ( in @ Xy @ A )
% 0.35/0.48 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setadjoinE_type,type,
% 0.35/0.48 setadjoinE: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setadjoinE,definition,
% 0.35/0.48 ( setadjoinE
% 0.35/0.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.35/0.48 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.35/0.48 => ! [Xphi: $o] :
% 0.35/0.48 ( ( ( Xy = Xx )
% 0.35/0.48 => Xphi )
% 0.35/0.48 => ( ( ( in @ Xy @ A )
% 0.35/0.48 => Xphi )
% 0.35/0.48 => Xphi ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setadjoinOr_type,type,
% 0.35/0.48 setadjoinOr: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setadjoinOr,definition,
% 0.35/0.48 ( setadjoinOr
% 0.35/0.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.35/0.48 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.35/0.48 => ( ( Xy = Xx )
% 0.35/0.48 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setoftrueEq_type,type,
% 0.35/0.48 setoftrueEq: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setoftrueEq,definition,
% 0.35/0.48 ( setoftrueEq
% 0.35/0.48 = ( ! [A: $i] :
% 0.35/0.48 ( ( dsetconstr @ A
% 0.35/0.48 @ ^ [Xx: $i] : $true )
% 0.35/0.48 = A ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(powersetI_type,type,
% 0.35/0.48 powersetI: $o ).
% 0.35/0.48
% 0.35/0.48 thf(powersetI,definition,
% 0.35/0.48 ( powersetI
% 0.35/0.48 = ( ! [A: $i,B: $i] :
% 0.35/0.48 ( ! [Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ B )
% 0.35/0.48 => ( in @ Xx @ A ) )
% 0.35/0.48 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(emptyinPowerset_type,type,
% 0.35/0.48 emptyinPowerset: $o ).
% 0.35/0.48
% 0.35/0.48 thf(emptyinPowerset,definition,
% 0.35/0.48 ( emptyinPowerset
% 0.35/0.48 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(emptyInPowerset_type,type,
% 0.35/0.48 emptyInPowerset: $o ).
% 0.35/0.48
% 0.35/0.48 thf(emptyInPowerset,definition,
% 0.35/0.48 ( emptyInPowerset
% 0.35/0.48 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(powersetE_type,type,
% 0.35/0.48 powersetE: $o ).
% 0.35/0.48
% 0.35/0.48 thf(powersetE,definition,
% 0.35/0.48 ( powersetE
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.35/0.48 ( ( in @ B @ ( powerset @ A ) )
% 0.35/0.48 => ( ( in @ Xx @ B )
% 0.35/0.48 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setunionI_type,type,
% 0.35/0.48 setunionI: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setunionI,definition,
% 0.35/0.48 ( setunionI
% 0.35/0.48 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.35/0.48 ( ( in @ Xx @ B )
% 0.35/0.48 => ( ( in @ B @ A )
% 0.35/0.48 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setunionE_type,type,
% 0.35/0.48 setunionE: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setunionE,definition,
% 0.35/0.48 ( setunionE
% 0.35/0.48 = ( ! [A: $i,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ ( setunion @ A ) )
% 0.35/0.48 => ! [Xphi: $o] :
% 0.35/0.48 ( ! [B: $i] :
% 0.35/0.48 ( ( in @ Xx @ B )
% 0.35/0.48 => ( ( in @ B @ A )
% 0.35/0.48 => Xphi ) )
% 0.35/0.48 => Xphi ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(subPowSU_type,type,
% 0.35/0.48 subPowSU: $o ).
% 0.35/0.48
% 0.35/0.48 thf(subPowSU,definition,
% 0.35/0.48 ( subPowSU
% 0.35/0.48 = ( ! [A: $i,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(exuE2_type,type,
% 0.35/0.48 exuE2: $o ).
% 0.35/0.48
% 0.35/0.48 thf(exuE2,definition,
% 0.35/0.48 ( exuE2
% 0.35/0.48 = ( ! [Xphi: $i > $o] :
% 0.35/0.48 ( ( exu
% 0.35/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.35/0.48 => ? [Xx: $i] :
% 0.35/0.48 ! [Xy: $i] :
% 0.35/0.48 ( ( Xphi @ Xy )
% 0.35/0.48 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(nonemptyImpWitness_type,type,
% 0.35/0.48 nonemptyImpWitness: $o ).
% 0.35/0.48
% 0.35/0.48 thf(nonemptyImpWitness,definition,
% 0.35/0.48 ( nonemptyImpWitness
% 0.35/0.48 = ( ! [A: $i] :
% 0.35/0.48 ( ( nonempty @ A )
% 0.35/0.48 => ? [Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 & $true ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(uniqinunit_type,type,
% 0.35/0.48 uniqinunit: $o ).
% 0.35/0.48
% 0.35/0.48 thf(uniqinunit,definition,
% 0.35/0.48 ( uniqinunit
% 0.35/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.35/0.48 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.35/0.48 => ( Xx = Xy ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(notinsingleton_type,type,
% 0.35/0.48 notinsingleton: $o ).
% 0.35/0.48
% 0.35/0.48 thf(notinsingleton,definition,
% 0.35/0.48 ( notinsingleton
% 0.35/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.35/0.48 ( ( Xx != Xy )
% 0.35/0.48 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(eqinunit_type,type,
% 0.35/0.48 eqinunit: $o ).
% 0.35/0.48
% 0.35/0.48 thf(eqinunit,definition,
% 0.35/0.48 ( eqinunit
% 0.35/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.35/0.48 ( ( Xx = Xy )
% 0.35/0.48 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(singletonsswitch_type,type,
% 0.35/0.48 singletonsswitch: $o ).
% 0.35/0.48
% 0.35/0.48 thf(singletonsswitch,definition,
% 0.35/0.48 ( singletonsswitch
% 0.35/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.35/0.48 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.35/0.48 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(upairsetE_type,type,
% 0.35/0.48 upairsetE: $o ).
% 0.35/0.48
% 0.35/0.48 thf(upairsetE,definition,
% 0.35/0.48 ( upairsetE
% 0.35/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.35/0.48 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.35/0.48 => ( ( Xz = Xx )
% 0.35/0.48 | ( Xz = Xy ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(upairsetIL_type,type,
% 0.35/0.48 upairsetIL: $o ).
% 0.35/0.48
% 0.35/0.48 thf(upairsetIL,definition,
% 0.35/0.48 ( upairsetIL
% 0.35/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(upairsetIR_type,type,
% 0.35/0.48 upairsetIR: $o ).
% 0.35/0.48
% 0.35/0.48 thf(upairsetIR,definition,
% 0.35/0.48 ( upairsetIR
% 0.35/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(emptyE1_type,type,
% 0.35/0.48 emptyE1: $o ).
% 0.35/0.48
% 0.35/0.48 thf(emptyE1,definition,
% 0.35/0.48 ( emptyE1
% 0.35/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.35/0.48 ( ? [Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 & ( Xphi @ Xx ) )
% 0.35/0.48 => ( ( ( dsetconstr @ A
% 0.35/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.35/0.48 = emptyset )
% 0.35/0.48 => $false ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(vacuousDall_type,type,
% 0.35/0.48 vacuousDall: $o ).
% 0.35/0.48
% 0.35/0.48 thf(vacuousDall,definition,
% 0.35/0.48 ( vacuousDall
% 0.35/0.48 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ emptyset )
% 0.35/0.48 => ( Xphi @ Xx ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(quantDeMorgan1_type,type,
% 0.35/0.48 quantDeMorgan1: $o ).
% 0.35/0.48
% 0.35/0.48 thf(quantDeMorgan1,definition,
% 0.35/0.48 ( quantDeMorgan1
% 0.35/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.35/0.48 ( ~ ! [Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ( Xphi @ Xx ) )
% 0.35/0.48 => ? [Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(quantDeMorgan2_type,type,
% 0.35/0.48 quantDeMorgan2: $o ).
% 0.35/0.48
% 0.35/0.48 thf(quantDeMorgan2,definition,
% 0.35/0.48 ( quantDeMorgan2
% 0.35/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.35/0.48 ( ! [Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ~ ( Xphi @ Xx ) )
% 0.35/0.48 => ~ ? [Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(quantDeMorgan3_type,type,
% 0.35/0.48 quantDeMorgan3: $o ).
% 0.35/0.48
% 0.35/0.48 thf(quantDeMorgan3,definition,
% 0.35/0.48 ( quantDeMorgan3
% 0.35/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.35/0.48 ( ~ ? [Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 & ( Xphi @ Xx ) )
% 0.35/0.48 => ! [Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(quantDeMorgan4_type,type,
% 0.35/0.48 quantDeMorgan4: $o ).
% 0.35/0.48
% 0.35/0.48 thf(quantDeMorgan4,definition,
% 0.35/0.48 ( quantDeMorgan4
% 0.35/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.35/0.48 ( ? [Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 & ~ ( Xphi @ Xx ) )
% 0.35/0.48 => ~ ! [Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(prop2setI_type,type,
% 0.35/0.48 prop2setI: $o ).
% 0.35/0.48
% 0.35/0.48 thf(prop2setI,definition,
% 0.35/0.48 ( prop2setI
% 0.35/0.48 = ( ! [Xphi: $o] :
% 0.35/0.48 ( Xphi
% 0.35/0.48 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(set2prop_type,type,
% 0.35/0.48 set2prop: $i > $o ).
% 0.35/0.48
% 0.35/0.48 thf(prop2set2propI_type,type,
% 0.35/0.48 prop2set2propI: $o ).
% 0.35/0.48
% 0.35/0.48 thf(prop2set2propI,definition,
% 0.35/0.48 ( prop2set2propI
% 0.35/0.48 = ( ! [Xphi: $o] :
% 0.35/0.48 ( Xphi
% 0.35/0.48 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(notdexE_type,type,
% 0.35/0.48 notdexE: $o ).
% 0.35/0.48
% 0.35/0.48 thf(notdexE,definition,
% 0.35/0.48 ( notdexE
% 0.35/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.35/0.48 ( ~ ? [Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 & ( Xphi @ Xx ) )
% 0.35/0.48 => ! [Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(notdallE_type,type,
% 0.35/0.48 notdallE: $o ).
% 0.35/0.48
% 0.35/0.48 thf(notdallE,definition,
% 0.35/0.48 ( notdallE
% 0.35/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.35/0.48 ( ~ ! [Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ( Xphi @ Xx ) )
% 0.35/0.48 => ? [Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(exuI1_type,type,
% 0.35/0.48 exuI1: $o ).
% 0.35/0.48
% 0.35/0.48 thf(exuI1,definition,
% 0.35/0.48 ( exuI1
% 0.35/0.48 = ( ! [Xphi: $i > $o] :
% 0.35/0.48 ( ? [Xx: $i] :
% 0.35/0.48 ( ( Xphi @ Xx )
% 0.35/0.48 & ! [Xy: $i] :
% 0.35/0.48 ( ( Xphi @ Xy )
% 0.35/0.48 => ( Xx = Xy ) ) )
% 0.35/0.48 => ( exu
% 0.35/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(exuI3_type,type,
% 0.35/0.48 exuI3: $o ).
% 0.35/0.48
% 0.35/0.48 thf(exuI3,definition,
% 0.35/0.48 ( exuI3
% 0.35/0.48 = ( ! [Xphi: $i > $o] :
% 0.35/0.48 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.35/0.48 => ( ! [Xx: $i,Xy: $i] :
% 0.35/0.48 ( ( Xphi @ Xx )
% 0.35/0.48 => ( ( Xphi @ Xy )
% 0.35/0.48 => ( Xx = Xy ) ) )
% 0.35/0.48 => ( exu
% 0.35/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(exuI2_type,type,
% 0.35/0.48 exuI2: $o ).
% 0.35/0.48
% 0.35/0.48 thf(exuI2,definition,
% 0.35/0.48 ( exuI2
% 0.35/0.48 = ( ! [Xphi: $i > $o] :
% 0.35/0.48 ( ? [Xx: $i] :
% 0.35/0.48 ! [Xy: $i] :
% 0.35/0.48 ( ( Xphi @ Xy )
% 0.35/0.48 <=> ( Xy = Xx ) )
% 0.35/0.48 => ( exu
% 0.35/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(inCongP_type,type,
% 0.35/0.48 inCongP: $o ).
% 0.35/0.48
% 0.35/0.48 thf(inCongP,definition,
% 0.35/0.48 ( inCongP
% 0.35/0.48 = ( ! [A: $i,B: $i] :
% 0.35/0.48 ( ( A = B )
% 0.35/0.48 => ! [Xx: $i,Xy: $i] :
% 0.35/0.48 ( ( Xx = Xy )
% 0.35/0.48 => ( ( in @ Xx @ A )
% 0.35/0.48 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(in__Cong_type,type,
% 0.35/0.48 in__Cong: $o ).
% 0.35/0.48
% 0.35/0.48 thf(in__Cong,definition,
% 0.35/0.48 ( in__Cong
% 0.35/0.48 = ( ! [A: $i,B: $i] :
% 0.35/0.48 ( ( A = B )
% 0.35/0.48 => ! [Xx: $i,Xy: $i] :
% 0.35/0.48 ( ( Xx = Xy )
% 0.35/0.48 => ( ( in @ Xx @ A )
% 0.35/0.48 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(exuE3u_type,type,
% 0.35/0.48 exuE3u: $o ).
% 0.35/0.48
% 0.35/0.48 thf(exuE3u,definition,
% 0.35/0.48 ( exuE3u
% 0.35/0.48 = ( ! [Xphi: $i > $o] :
% 0.35/0.48 ( ( exu
% 0.35/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.35/0.48 => ! [Xx: $i,Xy: $i] :
% 0.35/0.48 ( ( Xphi @ Xx )
% 0.35/0.48 => ( ( Xphi @ Xy )
% 0.35/0.48 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(exu__Cong_type,type,
% 0.35/0.48 exu__Cong: $o ).
% 0.35/0.48
% 0.35/0.48 thf(exu__Cong,definition,
% 0.35/0.48 ( exu__Cong
% 0.35/0.48 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.35/0.48 ( ! [Xx: $i,Xy: $i] :
% 0.35/0.48 ( ( Xx = Xy )
% 0.35/0.48 => ( ( Xphi @ Xx )
% 0.35/0.48 <=> ( Xpsi @ Xy ) ) )
% 0.35/0.48 => ( ( exu
% 0.35/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.35/0.48 <=> ( exu
% 0.35/0.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(emptyset__Cong_type,type,
% 0.35/0.48 emptyset__Cong: $o ).
% 0.35/0.48
% 0.35/0.48 thf(emptyset__Cong,definition,
% 0.35/0.48 ( emptyset__Cong
% 0.35/0.48 = ( emptyset = emptyset ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setadjoin__Cong_type,type,
% 0.35/0.48 setadjoin__Cong: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setadjoin__Cong,definition,
% 0.35/0.48 ( setadjoin__Cong
% 0.35/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.35/0.48 ( ( Xx = Xy )
% 0.35/0.48 => ! [Xz: $i,Xu: $i] :
% 0.35/0.48 ( ( Xz = Xu )
% 0.35/0.48 => ( ( setadjoin @ Xx @ Xz )
% 0.35/0.48 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(powerset__Cong_type,type,
% 0.35/0.48 powerset__Cong: $o ).
% 0.35/0.48
% 0.35/0.48 thf(powerset__Cong,definition,
% 0.35/0.48 ( powerset__Cong
% 0.35/0.48 = ( ! [A: $i,B: $i] :
% 0.35/0.48 ( ( A = B )
% 0.35/0.48 => ( ( powerset @ A )
% 0.35/0.48 = ( powerset @ B ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setunion__Cong_type,type,
% 0.35/0.48 setunion__Cong: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setunion__Cong,definition,
% 0.35/0.48 ( setunion__Cong
% 0.35/0.48 = ( ! [A: $i,B: $i] :
% 0.35/0.48 ( ( A = B )
% 0.35/0.48 => ( ( setunion @ A )
% 0.35/0.48 = ( setunion @ B ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(omega__Cong_type,type,
% 0.35/0.48 omega__Cong: $o ).
% 0.35/0.48
% 0.35/0.48 thf(omega__Cong,definition,
% 0.35/0.48 ( omega__Cong
% 0.35/0.48 = ( omega = omega ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(exuEu_type,type,
% 0.35/0.48 exuEu: $o ).
% 0.35/0.48
% 0.35/0.48 thf(exuEu,definition,
% 0.35/0.48 ( exuEu
% 0.35/0.48 = ( ! [Xphi: $i > $o] :
% 0.35/0.48 ( ( exu
% 0.35/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.35/0.48 => ! [Xx: $i,Xy: $i] :
% 0.35/0.48 ( ( Xphi @ Xx )
% 0.35/0.48 => ( ( Xphi @ Xy )
% 0.35/0.48 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(descr__Cong_type,type,
% 0.35/0.48 descr__Cong: $o ).
% 0.35/0.48
% 0.35/0.48 thf(descr__Cong,definition,
% 0.35/0.48 ( descr__Cong
% 0.35/0.48 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.35/0.48 ( ! [Xx: $i,Xy: $i] :
% 0.35/0.48 ( ( Xx = Xy )
% 0.35/0.48 => ( ( Xphi @ Xx )
% 0.35/0.48 <=> ( Xpsi @ Xy ) ) )
% 0.35/0.48 => ( ( exu
% 0.35/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.35/0.48 => ( ( exu
% 0.35/0.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.35/0.48 => ( ( descr
% 0.35/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.35/0.48 = ( descr
% 0.35/0.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(dsetconstr__Cong_type,type,
% 0.35/0.48 dsetconstr__Cong: $o ).
% 0.35/0.48
% 0.35/0.48 thf(dsetconstr__Cong,definition,
% 0.35/0.48 ( dsetconstr__Cong
% 0.35/0.48 = ( ! [A: $i,B: $i] :
% 0.35/0.48 ( ( A = B )
% 0.35/0.48 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.35/0.48 ( ! [Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ! [Xy: $i] :
% 0.35/0.48 ( ( in @ Xy @ B )
% 0.35/0.48 => ( ( Xx = Xy )
% 0.35/0.48 => ( ( Xphi @ Xx )
% 0.35/0.48 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.35/0.48 => ( ( dsetconstr @ A
% 0.35/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.35/0.48 = ( dsetconstr @ B
% 0.35/0.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(subset_type,type,
% 0.35/0.48 subset: $i > $i > $o ).
% 0.35/0.48
% 0.35/0.48 thf(disjoint_type,type,
% 0.35/0.48 disjoint: $i > $i > $o ).
% 0.35/0.48
% 0.35/0.48 thf(setsmeet_type,type,
% 0.35/0.48 setsmeet: $i > $i > $o ).
% 0.35/0.48
% 0.35/0.48 thf(subsetI1_type,type,
% 0.35/0.48 subsetI1: $o ).
% 0.35/0.48
% 0.35/0.48 thf(subsetI1,definition,
% 0.35/0.48 ( subsetI1
% 0.35/0.48 = ( ! [A: $i,B: $i] :
% 0.35/0.48 ( ! [Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ( in @ Xx @ B ) )
% 0.35/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(eqimpsubset2_type,type,
% 0.35/0.48 eqimpsubset2: $o ).
% 0.35/0.48
% 0.35/0.48 thf(eqimpsubset2,definition,
% 0.35/0.48 ( eqimpsubset2
% 0.35/0.48 = ( ! [A: $i,B: $i] :
% 0.35/0.48 ( ( A = B )
% 0.35/0.48 => ( subset @ B @ A ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(eqimpsubset1_type,type,
% 0.35/0.48 eqimpsubset1: $o ).
% 0.35/0.48
% 0.35/0.48 thf(eqimpsubset1,definition,
% 0.35/0.48 ( eqimpsubset1
% 0.35/0.48 = ( ! [A: $i,B: $i] :
% 0.35/0.48 ( ( A = B )
% 0.35/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(subsetI2_type,type,
% 0.35/0.48 subsetI2: $o ).
% 0.35/0.48
% 0.35/0.48 thf(subsetI2,definition,
% 0.35/0.48 ( subsetI2
% 0.35/0.48 = ( ! [A: $i,B: $i] :
% 0.35/0.48 ( ! [Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ( in @ Xx @ B ) )
% 0.35/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(emptysetsubset_type,type,
% 0.35/0.48 emptysetsubset: $o ).
% 0.35/0.48
% 0.35/0.48 thf(emptysetsubset,definition,
% 0.35/0.48 ( emptysetsubset
% 0.35/0.48 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(subsetE_type,type,
% 0.35/0.48 subsetE: $o ).
% 0.35/0.48
% 0.35/0.48 thf(subsetE,definition,
% 0.35/0.48 ( subsetE
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.35/0.48 ( ( subset @ A @ B )
% 0.35/0.48 => ( ( in @ Xx @ A )
% 0.35/0.48 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(subsetE2_type,type,
% 0.35/0.48 subsetE2: $o ).
% 0.35/0.48
% 0.35/0.48 thf(subsetE2,definition,
% 0.35/0.48 ( subsetE2
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.35/0.48 ( ( subset @ A @ B )
% 0.35/0.48 => ( ~ ( in @ Xx @ B )
% 0.35/0.48 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(notsubsetI_type,type,
% 0.35/0.48 notsubsetI: $o ).
% 0.35/0.48
% 0.35/0.48 thf(notsubsetI,definition,
% 0.35/0.48 ( notsubsetI
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ( ~ ( in @ Xx @ B )
% 0.35/0.48 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(notequalI1_type,type,
% 0.35/0.48 notequalI1: $o ).
% 0.35/0.48
% 0.35/0.48 thf(notequalI1,definition,
% 0.35/0.48 ( notequalI1
% 0.35/0.48 = ( ! [A: $i,B: $i] :
% 0.35/0.48 ( ~ ( subset @ A @ B )
% 0.35/0.48 => ( A != B ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(notequalI2_type,type,
% 0.35/0.48 notequalI2: $o ).
% 0.35/0.48
% 0.35/0.48 thf(notequalI2,definition,
% 0.35/0.48 ( notequalI2
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ( ~ ( in @ Xx @ B )
% 0.35/0.48 => ( A != B ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(subsetRefl_type,type,
% 0.35/0.48 subsetRefl: $o ).
% 0.35/0.48
% 0.35/0.48 thf(subsetRefl,definition,
% 0.35/0.48 ( subsetRefl
% 0.35/0.48 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(subsetTrans_type,type,
% 0.35/0.48 subsetTrans: $o ).
% 0.35/0.48
% 0.35/0.48 thf(subsetTrans,definition,
% 0.35/0.48 ( subsetTrans
% 0.35/0.48 = ( ! [A: $i,B: $i,C: $i] :
% 0.35/0.48 ( ( subset @ A @ B )
% 0.35/0.48 => ( ( subset @ B @ C )
% 0.35/0.48 => ( subset @ A @ C ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setadjoinSub_type,type,
% 0.35/0.48 setadjoinSub: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setadjoinSub,definition,
% 0.35/0.48 ( setadjoinSub
% 0.35/0.48 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setadjoinSub2_type,type,
% 0.35/0.48 setadjoinSub2: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setadjoinSub2,definition,
% 0.35/0.48 ( setadjoinSub2
% 0.35/0.48 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.35/0.48 ( ( subset @ A @ B )
% 0.35/0.48 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(subset2powerset_type,type,
% 0.35/0.48 subset2powerset: $o ).
% 0.35/0.48
% 0.35/0.48 thf(subset2powerset,definition,
% 0.35/0.48 ( subset2powerset
% 0.35/0.48 = ( ! [A: $i,B: $i] :
% 0.35/0.48 ( ( subset @ A @ B )
% 0.35/0.48 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setextsub_type,type,
% 0.35/0.48 setextsub: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setextsub,definition,
% 0.35/0.48 ( setextsub
% 0.35/0.48 = ( ! [A: $i,B: $i] :
% 0.35/0.48 ( ( subset @ A @ B )
% 0.35/0.48 => ( ( subset @ B @ A )
% 0.35/0.48 => ( A = B ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(subsetemptysetimpeq_type,type,
% 0.35/0.48 subsetemptysetimpeq: $o ).
% 0.35/0.48
% 0.35/0.48 thf(subsetemptysetimpeq,definition,
% 0.35/0.48 ( subsetemptysetimpeq
% 0.35/0.48 = ( ! [A: $i] :
% 0.35/0.48 ( ( subset @ A @ emptyset )
% 0.35/0.48 => ( A = emptyset ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(powersetI1_type,type,
% 0.35/0.48 powersetI1: $o ).
% 0.35/0.48
% 0.35/0.48 thf(powersetI1,definition,
% 0.35/0.48 ( powersetI1
% 0.35/0.48 = ( ! [A: $i,B: $i] :
% 0.35/0.48 ( ( subset @ B @ A )
% 0.35/0.48 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(powersetE1_type,type,
% 0.35/0.48 powersetE1: $o ).
% 0.35/0.48
% 0.35/0.48 thf(powersetE1,definition,
% 0.35/0.48 ( powersetE1
% 0.35/0.48 = ( ! [A: $i,B: $i] :
% 0.35/0.48 ( ( in @ B @ ( powerset @ A ) )
% 0.35/0.48 => ( subset @ B @ A ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(inPowerset_type,type,
% 0.35/0.48 inPowerset: $o ).
% 0.35/0.48
% 0.35/0.48 thf(inPowerset,definition,
% 0.35/0.48 ( inPowerset
% 0.35/0.48 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(powersetsubset_type,type,
% 0.35/0.48 powersetsubset: $o ).
% 0.35/0.48
% 0.35/0.48 thf(powersetsubset,definition,
% 0.35/0.48 ( powersetsubset
% 0.35/0.48 = ( ! [A: $i,B: $i] :
% 0.35/0.48 ( ( subset @ A @ B )
% 0.35/0.48 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(sepInPowerset_type,type,
% 0.35/0.48 sepInPowerset: $o ).
% 0.35/0.48
% 0.35/0.48 thf(sepInPowerset,definition,
% 0.35/0.48 ( sepInPowerset
% 0.35/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.35/0.48 ( in
% 0.35/0.48 @ ( dsetconstr @ A
% 0.35/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.35/0.48 @ ( powerset @ A ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(sepSubset_type,type,
% 0.35/0.48 sepSubset: $o ).
% 0.35/0.48
% 0.35/0.48 thf(sepSubset,definition,
% 0.35/0.48 ( sepSubset
% 0.35/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.35/0.48 ( subset
% 0.35/0.48 @ ( dsetconstr @ A
% 0.35/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.35/0.48 @ A ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(binunion_type,type,
% 0.35/0.48 binunion: $i > $i > $i ).
% 0.35/0.48
% 0.35/0.48 thf(binunionIL_type,type,
% 0.35/0.48 binunionIL: $o ).
% 0.35/0.48
% 0.35/0.48 thf(binunionIL,definition,
% 0.35/0.48 ( binunionIL
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(upairset2IR_type,type,
% 0.35/0.48 upairset2IR: $o ).
% 0.35/0.48
% 0.35/0.48 thf(upairset2IR,definition,
% 0.35/0.48 ( upairset2IR
% 0.35/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(binunionIR_type,type,
% 0.35/0.48 binunionIR: $o ).
% 0.35/0.48
% 0.35/0.48 thf(binunionIR,definition,
% 0.35/0.48 ( binunionIR
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ B )
% 0.35/0.48 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(binunionEcases_type,type,
% 0.35/0.48 binunionEcases: $o ).
% 0.35/0.48
% 0.35/0.48 thf(binunionEcases,definition,
% 0.35/0.48 ( binunionEcases
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.35/0.48 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.35/0.48 => ( ( ( in @ Xx @ A )
% 0.35/0.48 => Xphi )
% 0.35/0.48 => ( ( ( in @ Xx @ B )
% 0.35/0.48 => Xphi )
% 0.35/0.48 => Xphi ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(binunionE_type,type,
% 0.35/0.48 binunionE: $o ).
% 0.35/0.48
% 0.35/0.48 thf(binunionE,definition,
% 0.35/0.48 ( binunionE
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.35/0.48 => ( ( in @ Xx @ A )
% 0.35/0.48 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(binunionLsub_type,type,
% 0.35/0.48 binunionLsub: $o ).
% 0.35/0.48
% 0.35/0.48 thf(binunionLsub,definition,
% 0.35/0.48 ( binunionLsub
% 0.35/0.48 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(binunionRsub_type,type,
% 0.35/0.48 binunionRsub: $o ).
% 0.35/0.48
% 0.35/0.48 thf(binunionRsub,definition,
% 0.35/0.48 ( binunionRsub
% 0.35/0.48 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(binintersect_type,type,
% 0.35/0.48 binintersect: $i > $i > $i ).
% 0.35/0.48
% 0.35/0.48 thf(binintersectI_type,type,
% 0.35/0.48 binintersectI: $o ).
% 0.35/0.48
% 0.35/0.48 thf(binintersectI,definition,
% 0.35/0.48 ( binintersectI
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ( ( in @ Xx @ B )
% 0.35/0.48 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(binintersectSubset5_type,type,
% 0.35/0.48 binintersectSubset5: $o ).
% 0.35/0.48
% 0.35/0.48 thf(binintersectSubset5,definition,
% 0.35/0.48 ( binintersectSubset5
% 0.35/0.48 = ( ! [A: $i,B: $i,C: $i] :
% 0.35/0.48 ( ( subset @ C @ A )
% 0.35/0.48 => ( ( subset @ C @ B )
% 0.35/0.48 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(binintersectEL_type,type,
% 0.35/0.48 binintersectEL: $o ).
% 0.35/0.48
% 0.35/0.48 thf(binintersectEL,definition,
% 0.35/0.48 ( binintersectEL
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.35/0.48 => ( in @ Xx @ A ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(binintersectLsub_type,type,
% 0.35/0.48 binintersectLsub: $o ).
% 0.35/0.48
% 0.35/0.48 thf(binintersectLsub,definition,
% 0.35/0.48 ( binintersectLsub
% 0.35/0.48 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(binintersectSubset2_type,type,
% 0.35/0.48 binintersectSubset2: $o ).
% 0.35/0.48
% 0.35/0.48 thf(binintersectSubset2,definition,
% 0.35/0.48 ( binintersectSubset2
% 0.35/0.48 = ( ! [A: $i,B: $i] :
% 0.35/0.48 ( ( subset @ A @ B )
% 0.35/0.48 => ( ( binintersect @ A @ B )
% 0.35/0.48 = A ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(binintersectSubset3_type,type,
% 0.35/0.48 binintersectSubset3: $o ).
% 0.35/0.48
% 0.35/0.48 thf(binintersectSubset3,definition,
% 0.35/0.48 ( binintersectSubset3
% 0.35/0.48 = ( ! [A: $i,B: $i] :
% 0.35/0.48 ( ( ( binintersect @ A @ B )
% 0.35/0.48 = B )
% 0.35/0.48 => ( subset @ B @ A ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(binintersectER_type,type,
% 0.35/0.48 binintersectER: $o ).
% 0.35/0.48
% 0.35/0.48 thf(binintersectER,definition,
% 0.35/0.48 ( binintersectER
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.35/0.48 => ( in @ Xx @ B ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(disjointsetsI1_type,type,
% 0.35/0.48 disjointsetsI1: $o ).
% 0.35/0.48
% 0.35/0.48 thf(disjointsetsI1,definition,
% 0.35/0.48 ( disjointsetsI1
% 0.35/0.48 = ( ! [A: $i,B: $i] :
% 0.35/0.48 ( ~ ? [Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 & ( in @ Xx @ B ) )
% 0.35/0.48 => ( ( binintersect @ A @ B )
% 0.35/0.48 = emptyset ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(binintersectRsub_type,type,
% 0.35/0.48 binintersectRsub: $o ).
% 0.35/0.48
% 0.35/0.48 thf(binintersectRsub,definition,
% 0.35/0.48 ( binintersectRsub
% 0.35/0.48 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(binintersectSubset4_type,type,
% 0.35/0.48 binintersectSubset4: $o ).
% 0.35/0.48
% 0.35/0.48 thf(binintersectSubset4,definition,
% 0.35/0.48 ( binintersectSubset4
% 0.35/0.48 = ( ! [A: $i,B: $i] :
% 0.35/0.48 ( ( subset @ B @ A )
% 0.35/0.48 => ( ( binintersect @ A @ B )
% 0.35/0.48 = B ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(binintersectSubset1_type,type,
% 0.35/0.48 binintersectSubset1: $o ).
% 0.35/0.48
% 0.35/0.48 thf(binintersectSubset1,definition,
% 0.35/0.48 ( binintersectSubset1
% 0.35/0.48 = ( ! [A: $i,B: $i] :
% 0.35/0.48 ( ( ( binintersect @ A @ B )
% 0.35/0.48 = A )
% 0.35/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(bs114d_type,type,
% 0.35/0.48 bs114d: $o ).
% 0.35/0.48
% 0.35/0.48 thf(bs114d,definition,
% 0.35/0.48 ( bs114d
% 0.35/0.48 = ( ! [A: $i,B: $i,C: $i] :
% 0.35/0.48 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.35/0.48 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(regular_type,type,
% 0.35/0.48 regular: $i > $o ).
% 0.35/0.48
% 0.35/0.48 thf(setminus_type,type,
% 0.35/0.48 setminus: $i > $i > $i ).
% 0.35/0.48
% 0.35/0.48 thf(setminusI_type,type,
% 0.35/0.48 setminusI: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setminusI,definition,
% 0.35/0.48 ( setminusI
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ( ~ ( in @ Xx @ B )
% 0.35/0.48 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setminusEL_type,type,
% 0.35/0.48 setminusEL: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setminusEL,definition,
% 0.35/0.48 ( setminusEL
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.35/0.48 => ( in @ Xx @ A ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setminusER_type,type,
% 0.35/0.48 setminusER: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setminusER,definition,
% 0.35/0.48 ( setminusER
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.35/0.48 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setminusSubset2_type,type,
% 0.35/0.48 setminusSubset2: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setminusSubset2,definition,
% 0.35/0.48 ( setminusSubset2
% 0.35/0.48 = ( ! [A: $i,B: $i] :
% 0.35/0.48 ( ( subset @ A @ B )
% 0.35/0.48 => ( ( setminus @ A @ B )
% 0.35/0.48 = emptyset ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setminusERneg_type,type,
% 0.35/0.48 setminusERneg: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setminusERneg,definition,
% 0.35/0.48 ( setminusERneg
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.35/0.48 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.35/0.48 => ( ( in @ Xx @ A )
% 0.35/0.48 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setminusELneg_type,type,
% 0.35/0.48 setminusELneg: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setminusELneg,definition,
% 0.35/0.48 ( setminusELneg
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.35/0.48 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.35/0.48 => ( ~ ( in @ Xx @ B )
% 0.35/0.48 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setminusILneg_type,type,
% 0.35/0.48 setminusILneg: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setminusILneg,definition,
% 0.35/0.48 ( setminusILneg
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.35/0.48 ( ~ ( in @ Xx @ A )
% 0.35/0.48 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setminusIRneg_type,type,
% 0.35/0.48 setminusIRneg: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setminusIRneg,definition,
% 0.35/0.48 ( setminusIRneg
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ B )
% 0.35/0.48 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setminusLsub_type,type,
% 0.35/0.48 setminusLsub: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setminusLsub,definition,
% 0.35/0.48 ( setminusLsub
% 0.35/0.48 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setminusSubset1_type,type,
% 0.35/0.48 setminusSubset1: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setminusSubset1,definition,
% 0.35/0.48 ( setminusSubset1
% 0.35/0.48 = ( ! [A: $i,B: $i] :
% 0.35/0.48 ( ( ( setminus @ A @ B )
% 0.35/0.48 = emptyset )
% 0.35/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(symdiff_type,type,
% 0.35/0.48 symdiff: $i > $i > $i ).
% 0.35/0.48
% 0.35/0.48 thf(symdiffE_type,type,
% 0.35/0.48 symdiffE: $o ).
% 0.35/0.48
% 0.35/0.48 thf(symdiffE,definition,
% 0.35/0.48 ( symdiffE
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.35/0.48 => ! [Xphi: $o] :
% 0.35/0.48 ( ( ( in @ Xx @ A )
% 0.35/0.48 => ( ~ ( in @ Xx @ B )
% 0.35/0.48 => Xphi ) )
% 0.35/0.48 => ( ( ~ ( in @ Xx @ A )
% 0.35/0.48 => ( ( in @ Xx @ B )
% 0.35/0.48 => Xphi ) )
% 0.35/0.48 => Xphi ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(symdiffI1_type,type,
% 0.35/0.48 symdiffI1: $o ).
% 0.35/0.48
% 0.35/0.48 thf(symdiffI1,definition,
% 0.35/0.48 ( symdiffI1
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ( ~ ( in @ Xx @ B )
% 0.35/0.48 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(symdiffI2_type,type,
% 0.35/0.48 symdiffI2: $o ).
% 0.35/0.48
% 0.35/0.48 thf(symdiffI2,definition,
% 0.35/0.48 ( symdiffI2
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.35/0.48 ( ~ ( in @ Xx @ A )
% 0.35/0.48 => ( ( in @ Xx @ B )
% 0.35/0.48 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(symdiffIneg1_type,type,
% 0.35/0.48 symdiffIneg1: $o ).
% 0.35/0.48
% 0.35/0.48 thf(symdiffIneg1,definition,
% 0.35/0.48 ( symdiffIneg1
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ( ( in @ Xx @ B )
% 0.35/0.48 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(symdiffIneg2_type,type,
% 0.35/0.48 symdiffIneg2: $o ).
% 0.35/0.48
% 0.35/0.48 thf(symdiffIneg2,definition,
% 0.35/0.48 ( symdiffIneg2
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.35/0.48 ( ~ ( in @ Xx @ A )
% 0.35/0.48 => ( ~ ( in @ Xx @ B )
% 0.35/0.48 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(iskpair_type,type,
% 0.35/0.48 iskpair: $i > $o ).
% 0.35/0.48
% 0.35/0.48 thf(secondinupair_type,type,
% 0.35/0.48 secondinupair: $o ).
% 0.35/0.48
% 0.35/0.48 thf(secondinupair,definition,
% 0.35/0.48 ( secondinupair
% 0.35/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setukpairIL_type,type,
% 0.35/0.48 setukpairIL: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setukpairIL,definition,
% 0.35/0.48 ( setukpairIL
% 0.35/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setukpairIR_type,type,
% 0.35/0.48 setukpairIR: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setukpairIR,definition,
% 0.35/0.48 ( setukpairIR
% 0.35/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(kpairiskpair_type,type,
% 0.35/0.48 kpairiskpair: $o ).
% 0.35/0.48
% 0.35/0.48 thf(kpairiskpair,definition,
% 0.35/0.48 ( kpairiskpair
% 0.35/0.48 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(kpair_type,type,
% 0.35/0.48 kpair: $i > $i > $i ).
% 0.35/0.48
% 0.35/0.48 thf(kpairp_type,type,
% 0.35/0.48 kpairp: $o ).
% 0.35/0.48
% 0.35/0.48 thf(kpairp,definition,
% 0.35/0.48 ( kpairp
% 0.35/0.48 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(cartprod_type,type,
% 0.35/0.48 cartprod: $i > $i > $i ).
% 0.35/0.48
% 0.35/0.48 thf(singletonsubset_type,type,
% 0.35/0.48 singletonsubset: $o ).
% 0.35/0.48
% 0.35/0.48 thf(singletonsubset,definition,
% 0.35/0.48 ( singletonsubset
% 0.35/0.48 = ( ! [A: $i,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(singletoninpowerset_type,type,
% 0.35/0.48 singletoninpowerset: $o ).
% 0.35/0.48
% 0.35/0.48 thf(singletoninpowerset,definition,
% 0.35/0.48 ( singletoninpowerset
% 0.35/0.48 = ( ! [A: $i,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(singletoninpowunion_type,type,
% 0.35/0.48 singletoninpowunion: $o ).
% 0.35/0.48
% 0.35/0.48 thf(singletoninpowunion,definition,
% 0.35/0.48 ( singletoninpowunion
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(upairset2E_type,type,
% 0.35/0.48 upairset2E: $o ).
% 0.35/0.48
% 0.35/0.48 thf(upairset2E,definition,
% 0.35/0.48 ( upairset2E
% 0.35/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.35/0.48 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.35/0.48 => ( ( Xz = Xx )
% 0.35/0.48 | ( Xz = Xy ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(upairsubunion_type,type,
% 0.35/0.48 upairsubunion: $o ).
% 0.35/0.48
% 0.35/0.48 thf(upairsubunion,definition,
% 0.35/0.48 ( upairsubunion
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ! [Xy: $i] :
% 0.35/0.48 ( ( in @ Xy @ B )
% 0.35/0.48 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(upairinpowunion_type,type,
% 0.35/0.48 upairinpowunion: $o ).
% 0.35/0.48
% 0.35/0.48 thf(upairinpowunion,definition,
% 0.35/0.48 ( upairinpowunion
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ! [Xy: $i] :
% 0.35/0.48 ( ( in @ Xy @ B )
% 0.35/0.48 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(ubforcartprodlem1_type,type,
% 0.35/0.48 ubforcartprodlem1: $o ).
% 0.35/0.48
% 0.35/0.48 thf(ubforcartprodlem1,definition,
% 0.35/0.48 ( ubforcartprodlem1
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ! [Xy: $i] :
% 0.35/0.48 ( ( in @ Xy @ B )
% 0.35/0.48 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(ubforcartprodlem2_type,type,
% 0.35/0.48 ubforcartprodlem2: $o ).
% 0.35/0.48
% 0.35/0.48 thf(ubforcartprodlem2,definition,
% 0.35/0.48 ( ubforcartprodlem2
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ! [Xy: $i] :
% 0.35/0.48 ( ( in @ Xy @ B )
% 0.35/0.48 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(ubforcartprodlem3_type,type,
% 0.35/0.48 ubforcartprodlem3: $o ).
% 0.35/0.48
% 0.35/0.48 thf(ubforcartprodlem3,definition,
% 0.35/0.48 ( ubforcartprodlem3
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ! [Xy: $i] :
% 0.35/0.48 ( ( in @ Xy @ B )
% 0.35/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(cartprodpairin_type,type,
% 0.35/0.48 cartprodpairin: $o ).
% 0.35/0.48
% 0.35/0.48 thf(cartprodpairin,definition,
% 0.35/0.48 ( cartprodpairin
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ! [Xy: $i] :
% 0.35/0.48 ( ( in @ Xy @ B )
% 0.35/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(cartprodmempair1_type,type,
% 0.35/0.48 cartprodmempair1: $o ).
% 0.35/0.48
% 0.35/0.48 thf(cartprodmempair1,definition,
% 0.35/0.48 ( cartprodmempair1
% 0.35/0.48 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.35/0.48 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.35/0.48 => ? [Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 & ? [Xy: $i] :
% 0.35/0.48 ( ( in @ Xy @ B )
% 0.35/0.48 & ( Xu
% 0.35/0.48 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(cartprodmempair_type,type,
% 0.35/0.48 cartprodmempair: $o ).
% 0.35/0.48
% 0.35/0.48 thf(cartprodmempair,definition,
% 0.35/0.48 ( cartprodmempair
% 0.35/0.48 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.35/0.48 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.35/0.48 => ( iskpair @ Xu ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setunionE2_type,type,
% 0.35/0.48 setunionE2: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setunionE2,definition,
% 0.35/0.48 ( setunionE2
% 0.35/0.48 = ( ! [A: $i,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ ( setunion @ A ) )
% 0.35/0.48 => ? [X: $i] :
% 0.35/0.48 ( ( in @ X @ A )
% 0.35/0.48 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setunionsingleton1_type,type,
% 0.35/0.48 setunionsingleton1: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setunionsingleton1,definition,
% 0.35/0.48 ( setunionsingleton1
% 0.35/0.48 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setunionsingleton2_type,type,
% 0.35/0.48 setunionsingleton2: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setunionsingleton2,definition,
% 0.35/0.48 ( setunionsingleton2
% 0.35/0.48 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setunionsingleton_type,type,
% 0.35/0.48 setunionsingleton: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setunionsingleton,definition,
% 0.35/0.48 ( setunionsingleton
% 0.35/0.48 = ( ! [Xx: $i] :
% 0.35/0.48 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.35/0.48 = Xx ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(singleton_type,type,
% 0.35/0.48 singleton: $i > $o ).
% 0.35/0.48
% 0.35/0.48 thf(singleton,definition,
% 0.35/0.48 ( singleton
% 0.35/0.48 = ( ^ [A: $i] :
% 0.35/0.48 ? [Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 & ( A
% 0.35/0.48 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(singletonprop_type,type,
% 0.35/0.48 singletonprop: $o ).
% 0.35/0.48
% 0.35/0.48 thf(singletonprop,definition,
% 0.35/0.48 ( singletonprop
% 0.35/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.35/0.48 ( ! [Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ! [Xy: $i] :
% 0.35/0.48 ( ( in @ Xy @ A )
% 0.35/0.48 => ( ( Xphi @ Xx )
% 0.35/0.48 => ( ( Xphi @ Xy )
% 0.35/0.48 => ( Xx = Xy ) ) ) ) )
% 0.35/0.48 => ( ? [Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 & ( Xphi @ Xx ) )
% 0.35/0.48 => ( singleton
% 0.35/0.48 @ ( dsetconstr @ A
% 0.35/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(ex1_type,type,
% 0.35/0.48 ex1: $i > ( $i > $o ) > $o ).
% 0.35/0.48
% 0.35/0.48 thf(ex1,definition,
% 0.35/0.48 ( ex1
% 0.35/0.48 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.35/0.48 ( singleton
% 0.35/0.48 @ ( dsetconstr @ A
% 0.35/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(ex1E1_type,type,
% 0.35/0.48 ex1E1: $o ).
% 0.35/0.48
% 0.35/0.48 thf(ex1E1,definition,
% 0.35/0.48 ( ex1E1
% 0.35/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.35/0.48 ( ( ex1 @ A
% 0.35/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.35/0.48 => ? [Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(ex1I_type,type,
% 0.35/0.48 ex1I: $o ).
% 0.35/0.48
% 0.35/0.48 thf(ex1I,definition,
% 0.35/0.48 ( ex1I
% 0.35/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ( ( Xphi @ Xx )
% 0.35/0.48 => ( ! [Xy: $i] :
% 0.35/0.48 ( ( in @ Xy @ A )
% 0.35/0.48 => ( ( Xphi @ Xy )
% 0.35/0.48 => ( Xy = Xx ) ) )
% 0.35/0.48 => ( ex1 @ A
% 0.35/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(ex1I2_type,type,
% 0.35/0.48 ex1I2: $o ).
% 0.35/0.48
% 0.35/0.48 thf(ex1I2,definition,
% 0.35/0.48 ( ex1I2
% 0.35/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.35/0.48 ( ! [Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ! [Xy: $i] :
% 0.35/0.48 ( ( in @ Xy @ A )
% 0.35/0.48 => ( ( Xphi @ Xx )
% 0.35/0.48 => ( ( Xphi @ Xy )
% 0.35/0.48 => ( Xx = Xy ) ) ) ) )
% 0.35/0.48 => ( ? [Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 & ( Xphi @ Xx ) )
% 0.35/0.48 => ( ex1 @ A
% 0.35/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(singletonsuniq_type,type,
% 0.35/0.48 singletonsuniq: $o ).
% 0.35/0.48
% 0.35/0.48 thf(singletonsuniq,definition,
% 0.35/0.48 ( singletonsuniq
% 0.35/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.35/0.48 ( ( ( setadjoin @ Xx @ emptyset )
% 0.35/0.48 = ( setadjoin @ Xy @ emptyset ) )
% 0.35/0.48 => ( Xx = Xy ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(atmost1p_type,type,
% 0.35/0.48 atmost1p: $i > $o ).
% 0.35/0.48
% 0.35/0.48 thf(atleast2p_type,type,
% 0.35/0.48 atleast2p: $i > $o ).
% 0.35/0.48
% 0.35/0.48 thf(atmost2p_type,type,
% 0.35/0.48 atmost2p: $i > $o ).
% 0.35/0.48
% 0.35/0.48 thf(upairsetp_type,type,
% 0.35/0.48 upairsetp: $i > $o ).
% 0.35/0.48
% 0.35/0.48 thf(setukpairinjL1_type,type,
% 0.35/0.48 setukpairinjL1: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setukpairinjL1,definition,
% 0.35/0.48 ( setukpairinjL1
% 0.35/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.35/0.48 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.35/0.48 => ( Xx = Xz ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(kfstsingleton_type,type,
% 0.35/0.48 kfstsingleton: $o ).
% 0.35/0.48
% 0.35/0.48 thf(kfstsingleton,definition,
% 0.35/0.48 ( kfstsingleton
% 0.35/0.48 = ( ! [Xu: $i] :
% 0.35/0.48 ( ( iskpair @ Xu )
% 0.35/0.48 => ( singleton
% 0.35/0.48 @ ( dsetconstr @ ( setunion @ Xu )
% 0.35/0.48 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(theprop_type,type,
% 0.35/0.48 theprop: $o ).
% 0.35/0.48
% 0.35/0.48 thf(theprop,definition,
% 0.35/0.48 ( theprop
% 0.35/0.48 = ( ! [X: $i] :
% 0.35/0.48 ( ( singleton @ X )
% 0.35/0.48 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(kfst_type,type,
% 0.35/0.48 kfst: $i > $i ).
% 0.35/0.48
% 0.35/0.48 thf(kfstpairEq_type,type,
% 0.35/0.48 kfstpairEq: $o ).
% 0.35/0.48
% 0.35/0.48 thf(kfstpairEq,definition,
% 0.35/0.48 ( kfstpairEq
% 0.35/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.35/0.48 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.35/0.48 = Xx ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(cartprodfstin_type,type,
% 0.35/0.48 cartprodfstin: $o ).
% 0.35/0.48
% 0.35/0.48 thf(cartprodfstin,definition,
% 0.35/0.48 ( cartprodfstin
% 0.35/0.48 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.35/0.48 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.35/0.48 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setukpairinjL2_type,type,
% 0.35/0.48 setukpairinjL2: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setukpairinjL2,definition,
% 0.35/0.48 ( setukpairinjL2
% 0.35/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.35/0.48 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.35/0.48 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.35/0.48 => ( Xx = Xz ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setukpairinjL_type,type,
% 0.35/0.48 setukpairinjL: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setukpairinjL,definition,
% 0.35/0.48 ( setukpairinjL
% 0.35/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.35/0.48 ( ( ( kpair @ Xx @ Xy )
% 0.35/0.48 = ( kpair @ Xz @ Xu ) )
% 0.35/0.48 => ( Xx = Xz ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setukpairinjR11_type,type,
% 0.35/0.48 setukpairinjR11: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setukpairinjR11,definition,
% 0.35/0.48 ( setukpairinjR11
% 0.35/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.35/0.48 ( ( Xx = Xy )
% 0.35/0.48 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.35/0.48 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setukpairinjR12_type,type,
% 0.35/0.48 setukpairinjR12: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setukpairinjR12,definition,
% 0.35/0.48 ( setukpairinjR12
% 0.35/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.35/0.48 ( ( Xx = Xy )
% 0.35/0.48 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.35/0.48 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setukpairinjR1_type,type,
% 0.35/0.48 setukpairinjR1: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setukpairinjR1,definition,
% 0.35/0.48 ( setukpairinjR1
% 0.35/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.35/0.48 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.35/0.48 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.35/0.48 => ( ( Xz = Xu )
% 0.35/0.48 => ( Xy = Xu ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(upairequniteq_type,type,
% 0.35/0.48 upairequniteq: $o ).
% 0.35/0.48
% 0.35/0.48 thf(upairequniteq,definition,
% 0.35/0.48 ( upairequniteq
% 0.35/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.35/0.48 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.35/0.48 = ( setadjoin @ Xz @ emptyset ) )
% 0.35/0.48 => ( Xx = Xy ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setukpairinjR2_type,type,
% 0.35/0.48 setukpairinjR2: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setukpairinjR2,definition,
% 0.35/0.48 ( setukpairinjR2
% 0.35/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.35/0.48 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.35/0.48 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.35/0.48 => ( Xy = Xu ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setukpairinjR_type,type,
% 0.35/0.48 setukpairinjR: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setukpairinjR,definition,
% 0.35/0.48 ( setukpairinjR
% 0.35/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.35/0.48 ( ( ( kpair @ Xx @ Xy )
% 0.35/0.48 = ( kpair @ Xz @ Xu ) )
% 0.35/0.48 => ( Xy = Xu ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(ksndsingleton_type,type,
% 0.35/0.48 ksndsingleton: $o ).
% 0.35/0.48
% 0.35/0.48 thf(ksndsingleton,definition,
% 0.35/0.48 ( ksndsingleton
% 0.35/0.48 = ( ! [Xu: $i] :
% 0.35/0.48 ( ( iskpair @ Xu )
% 0.35/0.48 => ( singleton
% 0.35/0.48 @ ( dsetconstr @ ( setunion @ Xu )
% 0.35/0.48 @ ^ [Xx: $i] :
% 0.35/0.48 ( Xu
% 0.35/0.48 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(ksnd_type,type,
% 0.35/0.48 ksnd: $i > $i ).
% 0.35/0.48
% 0.35/0.48 thf(ksndpairEq_type,type,
% 0.35/0.48 ksndpairEq: $o ).
% 0.35/0.48
% 0.35/0.48 thf(ksndpairEq,definition,
% 0.35/0.48 ( ksndpairEq
% 0.35/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.35/0.48 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.35/0.48 = Xy ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(kpairsurjEq_type,type,
% 0.35/0.48 kpairsurjEq: $o ).
% 0.35/0.48
% 0.35/0.48 thf(kpairsurjEq,definition,
% 0.35/0.48 ( kpairsurjEq
% 0.35/0.48 = ( ! [Xu: $i] :
% 0.35/0.48 ( ( iskpair @ Xu )
% 0.35/0.48 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.35/0.48 = Xu ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(cartprodsndin_type,type,
% 0.35/0.48 cartprodsndin: $o ).
% 0.35/0.48
% 0.35/0.48 thf(cartprodsndin,definition,
% 0.35/0.48 ( cartprodsndin
% 0.35/0.48 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.35/0.48 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.35/0.48 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(cartprodpairmemEL_type,type,
% 0.35/0.48 cartprodpairmemEL: $o ).
% 0.35/0.48
% 0.35/0.48 thf(cartprodpairmemEL,definition,
% 0.35/0.48 ( cartprodpairmemEL
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.35/0.48 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.35/0.48 => ( in @ Xx @ A ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(cartprodpairmemER_type,type,
% 0.35/0.48 cartprodpairmemER: $o ).
% 0.35/0.48
% 0.35/0.48 thf(cartprodpairmemER,definition,
% 0.35/0.48 ( cartprodpairmemER
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.35/0.48 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.35/0.48 => ( in @ Xy @ B ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(cartprodmempaircEq_type,type,
% 0.35/0.48 cartprodmempaircEq: $o ).
% 0.35/0.48
% 0.35/0.48 thf(cartprodmempaircEq,definition,
% 0.35/0.48 ( cartprodmempaircEq
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ! [Xy: $i] :
% 0.35/0.48 ( ( in @ Xy @ B )
% 0.35/0.48 => ( ( kpair @ Xx @ Xy )
% 0.35/0.48 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(cartprodfstpairEq_type,type,
% 0.35/0.48 cartprodfstpairEq: $o ).
% 0.35/0.48
% 0.35/0.48 thf(cartprodfstpairEq,definition,
% 0.35/0.48 ( cartprodfstpairEq
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ! [Xy: $i] :
% 0.35/0.48 ( ( in @ Xy @ B )
% 0.35/0.48 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.35/0.48 = Xx ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(cartprodsndpairEq_type,type,
% 0.35/0.48 cartprodsndpairEq: $o ).
% 0.35/0.48
% 0.35/0.48 thf(cartprodsndpairEq,definition,
% 0.35/0.48 ( cartprodsndpairEq
% 0.35/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ! [Xy: $i] :
% 0.35/0.48 ( ( in @ Xy @ B )
% 0.35/0.48 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.35/0.48 = Xy ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(cartprodpairsurjEq_type,type,
% 0.35/0.48 cartprodpairsurjEq: $o ).
% 0.35/0.48
% 0.35/0.48 thf(cartprodpairsurjEq,definition,
% 0.35/0.48 ( cartprodpairsurjEq
% 0.35/0.48 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.35/0.48 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.35/0.48 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.35/0.48 = Xu ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(breln_type,type,
% 0.35/0.48 breln: $i > $i > $i > $o ).
% 0.35/0.48
% 0.35/0.48 thf(breln,definition,
% 0.35/0.48 ( breln
% 0.35/0.48 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(dpsetconstr_type,type,
% 0.35/0.48 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.35/0.48
% 0.35/0.48 thf(dpsetconstr,definition,
% 0.35/0.48 ( dpsetconstr
% 0.35/0.48 = ( ^ [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.35/0.48 ( dsetconstr @ ( cartprod @ A @ B )
% 0.35/0.48 @ ^ [Xu: $i] :
% 0.35/0.48 ? [Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 & ? [Xy: $i] :
% 0.35/0.48 ( ( in @ Xy @ B )
% 0.35/0.48 & ( Xphi @ Xx @ Xy )
% 0.35/0.48 & ( Xu
% 0.35/0.48 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(dpsetconstrI_type,type,
% 0.35/0.48 dpsetconstrI: $o ).
% 0.35/0.48
% 0.35/0.48 thf(dpsetconstrI,definition,
% 0.35/0.48 ( dpsetconstrI
% 0.35/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.35/0.48 ( ( in @ Xx @ A )
% 0.35/0.48 => ! [Xy: $i] :
% 0.35/0.48 ( ( in @ Xy @ B )
% 0.35/0.48 => ( ( Xphi @ Xx @ Xy )
% 0.35/0.48 => ( in @ ( kpair @ Xx @ Xy )
% 0.35/0.48 @ ( dpsetconstr @ A @ B
% 0.35/0.48 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(dpsetconstrSub_type,type,
% 0.35/0.48 dpsetconstrSub: $o ).
% 0.35/0.48
% 0.35/0.48 thf(dpsetconstrSub,definition,
% 0.35/0.48 ( dpsetconstrSub
% 0.35/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.35/0.48 ( subset
% 0.35/0.48 @ ( dpsetconstr @ A @ B
% 0.35/0.48 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.35/0.48 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(setOfPairsIsBReln_type,type,
% 0.35/0.48 setOfPairsIsBReln: $o ).
% 0.35/0.48
% 0.35/0.48 thf(setOfPairsIsBReln,definition,
% 0.35/0.48 ( setOfPairsIsBReln
% 0.35/0.48 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.35/0.48 ( breln @ A @ B
% 0.35/0.48 @ ( dpsetconstr @ A @ B
% 0.35/0.48 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.35/0.48
% 0.35/0.48 thf(dpsetconstrERa,conjecture,
% 0.35/0.48 ( setextAx
% 0.35/0.48 => ( emptysetAx
% 0.35/0.48 => ( setadjoinAx
% 0.35/0.48 => ( powersetAx
% 0.35/0.48 => ( setunionAx
% 0.35/0.48 => ( omega0Ax
% 0.35/0.48 => ( omegaSAx
% 0.35/0.48 => ( omegaIndAx
% 0.35/0.48 => ( replAx
% 0.35/0.48 => ( foundationAx
% 0.35/0.48 => ( wellorderingAx
% 0.35/0.48 => ( descrp
% 0.35/0.48 => ( dsetconstrI
% 0.35/0.48 => ( dsetconstrEL
% 0.35/0.48 => ( dsetconstrER
% 0.35/0.48 => ( exuE1
% 0.35/0.48 => ( prop2setE
% 0.35/0.48 => ( emptysetE
% 0.35/0.48 => ( emptysetimpfalse
% 0.35/0.48 => ( notinemptyset
% 0.35/0.48 => ( exuE3e
% 0.35/0.48 => ( setext
% 0.35/0.48 => ( emptyI
% 0.35/0.48 => ( noeltsimpempty
% 0.35/0.48 => ( setbeta
% 0.35/0.48 => ( nonemptyE1
% 0.35/0.48 => ( nonemptyI
% 0.35/0.48 => ( nonemptyI1
% 0.35/0.48 => ( setadjoinIL
% 0.35/0.48 => ( emptyinunitempty
% 0.35/0.48 => ( setadjoinIR
% 0.35/0.48 => ( setadjoinE
% 0.35/0.48 => ( setadjoinOr
% 0.35/0.48 => ( setoftrueEq
% 0.35/0.48 => ( powersetI
% 0.35/0.48 => ( emptyinPowerset
% 0.35/0.48 => ( emptyInPowerset
% 0.35/0.48 => ( powersetE
% 0.35/0.48 => ( setunionI
% 0.35/0.48 => ( setunionE
% 0.35/0.48 => ( subPowSU
% 0.35/0.48 => ( exuE2
% 0.35/0.48 => ( nonemptyImpWitness
% 0.35/0.48 => ( uniqinunit
% 0.35/0.48 => ( notinsingleton
% 0.35/0.48 => ( eqinunit
% 0.35/0.48 => ( singletonsswitch
% 0.35/0.48 => ( upairsetE
% 0.35/0.48 => ( upairsetIL
% 0.35/0.48 => ( upairsetIR
% 0.35/0.48 => ( emptyE1
% 0.35/0.48 => ( vacuousDall
% 0.35/0.48 => ( quantDeMorgan1
% 0.35/0.48 => ( quantDeMorgan2
% 0.35/0.48 => ( quantDeMorgan3
% 0.35/0.48 => ( quantDeMorgan4
% 0.35/0.48 => ( prop2setI
% 0.35/0.48 => ( prop2set2propI
% 0.35/0.48 => ( notdexE
% 0.35/0.48 => ( notdallE
% 0.35/0.48 => ( exuI1
% 0.35/0.48 => ( exuI3
% 0.35/0.48 => ( exuI2
% 0.35/0.48 => ( inCongP
% 0.35/0.48 => ( in__Cong
% 0.35/0.48 => ( exuE3u
% 0.35/0.48 => ( exu__Cong
% 0.35/0.48 => ( emptyset__Cong
% 0.35/0.48 => ( setadjoin__Cong
% 0.35/0.48 => ( powerset__Cong
% 0.35/0.48 => ( setunion__Cong
% 0.35/0.48 => ( omega__Cong
% 0.35/0.48 => ( exuEu
% 0.35/0.48 => ( descr__Cong
% 0.35/0.48 => ( dsetconstr__Cong
% 0.35/0.48 => ( subsetI1
% 0.35/0.48 => ( eqimpsubset2
% 0.35/0.48 => ( eqimpsubset1
% 0.35/0.48 => ( subsetI2
% 0.35/0.48 => ( emptysetsubset
% 0.35/0.48 => ( subsetE
% 0.35/0.48 => ( subsetE2
% 0.35/0.48 => ( notsubsetI
% 0.35/0.48 => ( notequalI1
% 0.35/0.48 => ( notequalI2
% 0.35/0.48 => ( subsetRefl
% 0.35/0.48 => ( subsetTrans
% 0.35/0.48 => ( setadjoinSub
% 0.35/0.48 => ( setadjoinSub2
% 0.35/0.48 => ( subset2powerset
% 0.35/0.48 => ( setextsub
% 0.35/0.48 => ( subsetemptysetimpeq
% 0.35/0.48 => ( powersetI1
% 0.35/0.48 => ( powersetE1
% 0.35/0.48 => ( inPowerset
% 0.35/0.48 => ( powersetsubset
% 0.35/0.48 => ( sepInPowerset
% 0.35/0.48 => ( sepSubset
% 0.35/0.48 => ( binunionIL
% 0.35/0.48 => ( upairset2IR
% 0.35/0.48 => ( binunionIR
% 0.35/0.48 => ( binunionEcases
% 0.35/0.48 => ( binunionE
% 0.35/0.48 => ( binunionLsub
% 0.35/0.48 => ( binunionRsub
% 0.35/0.48 => ( binintersectI
% 0.35/0.48 => ( binintersectSubset5
% 0.35/0.48 => ( binintersectEL
% 0.35/0.48 => ( binintersectLsub
% 0.35/0.48 => ( binintersectSubset2
% 0.35/0.48 => ( binintersectSubset3
% 0.35/0.48 => ( binintersectER
% 0.35/0.48 => ( disjointsetsI1
% 0.35/0.48 => ( binintersectRsub
% 0.35/0.48 => ( binintersectSubset4
% 0.35/0.48 => ( binintersectSubset1
% 0.35/0.48 => ( bs114d
% 0.35/0.48 => ( setminusI
% 0.35/0.48 => ( setminusEL
% 0.35/0.48 => ( setminusER
% 0.35/0.48 => ( setminusSubset2
% 0.35/0.48 => ( setminusERneg
% 0.35/0.48 => ( setminusELneg
% 0.35/0.48 => ( setminusILneg
% 0.35/0.48 => ( setminusIRneg
% 0.35/0.48 => ( setminusLsub
% 0.35/0.49 => ( setminusSubset1
% 0.35/0.49 => ( symdiffE
% 0.35/0.49 => ( symdiffI1
% 0.35/0.49 => ( symdiffI2
% 0.35/0.49 => ( symdiffIneg1
% 0.35/0.49 => ( symdiffIneg2
% 0.35/0.49 => ( secondinupair
% 0.35/0.49 => ( setukpairIL
% 0.35/0.49 => ( setukpairIR
% 0.35/0.49 => ( kpairiskpair
% 0.35/0.49 => ( kpairp
% 0.35/0.49 => ( singletonsubset
% 0.35/0.49 => ( singletoninpowerset
% 0.35/0.49 => ( singletoninpowunion
% 0.35/0.49 => ( upairset2E
% 0.35/0.49 => ( upairsubunion
% 0.35/0.49 => ( upairinpowunion
% 0.35/0.49 => ( ubforcartprodlem1
% 0.35/0.49 => ( ubforcartprodlem2
% 0.35/0.49 => ( ubforcartprodlem3
% 0.35/0.49 => ( cartprodpairin
% 0.35/0.49 => ( cartprodmempair1
% 0.35/0.49 => ( cartprodmempair
% 0.35/0.49 => ( setunionE2
% 0.35/0.49 => ( setunionsingleton1
% 0.35/0.49 => ( setunionsingleton2
% 0.35/0.49 => ( setunionsingleton
% 0.35/0.49 => ( singletonprop
% 0.35/0.49 => ( ex1E1
% 0.35/0.49 => ( ex1I
% 0.35/0.49 => ( ex1I2
% 0.35/0.49 => ( singletonsuniq
% 0.35/0.49 => ( setukpairinjL1
% 0.35/0.49 => ( kfstsingleton
% 0.35/0.49 => ( theprop
% 0.35/0.49 => ( kfstpairEq
% 0.35/0.49 => ( cartprodfstin
% 0.35/0.49 => ( setukpairinjL2
% 0.35/0.49 => ( setukpairinjL
% 0.35/0.49 => ( setukpairinjR11
% 0.35/0.49 => ( setukpairinjR12
% 0.35/0.49 => ( setukpairinjR1
% 0.35/0.49 => ( upairequniteq
% 0.35/0.49 => ( setukpairinjR2
% 0.35/0.49 => ( setukpairinjR
% 0.35/0.49 => ( ksndsingleton
% 0.35/0.49 => ( ksndpairEq
% 0.35/0.49 => ( kpairsurjEq
% 0.35/0.49 => ( cartprodsndin
% 0.35/0.49 => ( cartprodpairmemEL
% 0.35/0.49 => ( cartprodpairmemER
% 0.35/0.49 => ( cartprodmempaircEq
% 0.35/0.49 => ( cartprodfstpairEq
% 0.35/0.49 => ( cartprodsndpairEq
% 0.35/0.49 => ( cartprodpairsurjEq
% 0.35/0.49 => ( dpsetconstrI
% 0.35/0.49 => ( dpsetconstrSub
% 0.35/0.49 => ( setOfPairsIsBReln
% 0.35/0.49 => ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.35/0.49 ( ( in @ Xx @ A )
% 0.35/0.49 => ! [Xy: $i] :
% 0.35/0.49 ( ( in @ Xy @ B )
% 0.35/0.49 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.35/0.49 @ ( dpsetconstr @ A @ B
% 0.35/0.49 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.35/0.49 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.49
% 0.35/0.49 %------------------------------------------------------------------------------
% 0.35/0.49 ------------------------
% 3.01/1.71 ---- Embedded in THF ---
% 3.01/1.71 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.01/1.71 %%% Generated on Tue Feb 24 12:31:06 EST 2026
% 3.01/1.71 %%% using '$$dhol' embedding, version 1.3.0.
% 3.01/1.71 %%% Logic specification used:
% 3.01/1.71 %%% thf(spec, logic, $$dhol).
% 3.01/1.71
% 3.01/1.71 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.pZ9OXiV362/DTF2DTF30834.p
% See solution above
% 3.01/1.71 ------------------------
% 3.01/1.75 ---- Cleaned THF ---
% 3.01/1.75 thf(in_type,type,
% 3.01/1.75 in: $i > $i > $o ).
% 3.01/1.75
% 3.01/1.75 thf(exu_type,type,
% 3.01/1.75 exu: ( $i > $o ) > $o ).
% 3.01/1.75
% 3.01/1.75 thf(exu,definition,
% 3.01/1.75 ( exu
% 3.01/1.75 = ( ^ [Xphi: $i > $o] :
% 3.01/1.75 ? [Xx: $i] :
% 3.01/1.75 ( ( Xphi @ Xx )
% 3.01/1.75 & ! [Xy: $i] :
% 3.01/1.75 ( ( Xphi @ Xy )
% 3.01/1.75 => ( Xx = Xy ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(setextAx_type,type,
% 3.01/1.75 setextAx: $o ).
% 3.01/1.75
% 3.01/1.75 thf(setextAx,definition,
% 3.01/1.75 ( setextAx
% 3.01/1.75 = ( ! [A: $i,B: $i] :
% 3.01/1.75 ( ! [Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ A )
% 3.01/1.75 <=> ( in @ Xx @ B ) )
% 3.01/1.75 => ( A = B ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(emptyset_type,type,
% 3.01/1.75 emptyset: $i ).
% 3.01/1.75
% 3.01/1.75 thf(emptysetAx_type,type,
% 3.01/1.75 emptysetAx: $o ).
% 3.01/1.75
% 3.01/1.75 thf(emptysetAx,definition,
% 3.01/1.75 ( emptysetAx
% 3.01/1.75 = ( ! [Xx: $i] :
% 3.01/1.75 ~ ( in @ Xx @ emptyset ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(setadjoin_type,type,
% 3.01/1.75 setadjoin: $i > $i > $i ).
% 3.01/1.75
% 3.01/1.75 thf(setadjoinAx_type,type,
% 3.01/1.75 setadjoinAx: $o ).
% 3.01/1.75
% 3.01/1.75 thf(setadjoinAx,definition,
% 3.01/1.75 ( setadjoinAx
% 3.01/1.75 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.01/1.75 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.01/1.75 <=> ( ( Xy = Xx )
% 3.01/1.75 | ( in @ Xy @ A ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(powerset_type,type,
% 3.01/1.75 powerset: $i > $i ).
% 3.01/1.75
% 3.01/1.75 thf(powersetAx_type,type,
% 3.01/1.75 powersetAx: $o ).
% 3.01/1.75
% 3.01/1.75 thf(powersetAx,definition,
% 3.01/1.75 ( powersetAx
% 3.01/1.75 = ( ! [A: $i,B: $i] :
% 3.01/1.75 ( ( in @ B @ ( powerset @ A ) )
% 3.01/1.75 <=> ! [Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ B )
% 3.01/1.75 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(setunion_type,type,
% 3.01/1.75 setunion: $i > $i ).
% 3.01/1.75
% 3.01/1.75 thf(setunionAx_type,type,
% 3.01/1.75 setunionAx: $o ).
% 3.01/1.75
% 3.01/1.75 thf(setunionAx,definition,
% 3.01/1.75 ( setunionAx
% 3.01/1.75 = ( ! [A: $i,Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ ( setunion @ A ) )
% 3.01/1.75 <=> ? [B: $i] :
% 3.01/1.75 ( ( in @ Xx @ B )
% 3.01/1.75 & ( in @ B @ A ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(omega_type,type,
% 3.01/1.75 omega: $i ).
% 3.01/1.75
% 3.01/1.75 thf(omega0Ax_type,type,
% 3.01/1.75 omega0Ax: $o ).
% 3.01/1.75
% 3.01/1.75 thf(omega0Ax,definition,
% 3.01/1.75 ( omega0Ax
% 3.01/1.75 = ( in @ emptyset @ omega ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(omegaSAx_type,type,
% 3.01/1.75 omegaSAx: $o ).
% 3.01/1.75
% 3.01/1.75 thf(omegaSAx,definition,
% 3.01/1.75 ( omegaSAx
% 3.01/1.75 = ( ! [Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ omega )
% 3.01/1.75 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(omegaIndAx_type,type,
% 3.01/1.75 omegaIndAx: $o ).
% 3.01/1.75
% 3.01/1.75 thf(omegaIndAx,definition,
% 3.01/1.75 ( omegaIndAx
% 3.01/1.75 = ( ! [A: $i] :
% 3.01/1.75 ( ( ( in @ emptyset @ A )
% 3.01/1.75 & ! [Xx: $i] :
% 3.01/1.75 ( ( ( in @ Xx @ omega )
% 3.01/1.75 & ( in @ Xx @ A ) )
% 3.01/1.75 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 3.01/1.75 => ! [Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ omega )
% 3.01/1.75 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(replAx_type,type,
% 3.01/1.75 replAx: $o ).
% 3.01/1.75
% 3.01/1.75 thf(replAx,definition,
% 3.01/1.75 ( replAx
% 3.01/1.75 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 3.01/1.75 ( ! [Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ A )
% 3.01/1.75 => ( exu
% 3.01/1.75 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 3.01/1.75 => ? [B: $i] :
% 3.01/1.75 ! [Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ B )
% 3.01/1.75 <=> ? [Xy: $i] :
% 3.01/1.75 ( ( in @ Xy @ A )
% 3.01/1.75 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(foundationAx_type,type,
% 3.01/1.75 foundationAx: $o ).
% 3.01/1.75
% 3.01/1.75 thf(foundationAx,definition,
% 3.01/1.75 ( foundationAx
% 3.01/1.75 = ( ! [A: $i] :
% 3.01/1.75 ( ? [Xx: $i] : ( in @ Xx @ A )
% 3.01/1.75 => ? [B: $i] :
% 3.01/1.75 ( ( in @ B @ A )
% 3.01/1.75 & ~ ? [Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ B )
% 3.01/1.75 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(wellorderingAx_type,type,
% 3.01/1.75 wellorderingAx: $o ).
% 3.01/1.75
% 3.01/1.75 thf(wellorderingAx,definition,
% 3.01/1.75 ( wellorderingAx
% 3.01/1.75 = ( ! [A: $i] :
% 3.01/1.75 ? [B: $i] :
% 3.01/1.75 ( ! [C: $i] :
% 3.01/1.75 ( ( in @ C @ B )
% 3.01/1.75 => ! [Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ C )
% 3.01/1.75 => ( in @ Xx @ A ) ) )
% 3.01/1.75 & ! [Xx: $i,Xy: $i] :
% 3.01/1.75 ( ( ( in @ Xx @ A )
% 3.01/1.75 & ( in @ Xy @ A ) )
% 3.01/1.75 => ( ! [C: $i] :
% 3.01/1.75 ( ( in @ C @ B )
% 3.01/1.75 => ( ( in @ Xx @ C )
% 3.01/1.75 <=> ( in @ Xy @ C ) ) )
% 3.01/1.75 => ( Xx = Xy ) ) )
% 3.01/1.75 & ! [C: $i,D: $i] :
% 3.01/1.75 ( ( ( in @ C @ B )
% 3.01/1.75 & ( in @ D @ B ) )
% 3.01/1.75 => ( ! [Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ C )
% 3.01/1.75 => ( in @ Xx @ D ) )
% 3.01/1.75 | ! [Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ D )
% 3.01/1.75 => ( in @ Xx @ C ) ) ) )
% 3.01/1.75 & ! [C: $i] :
% 3.01/1.75 ( ( ! [Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ C )
% 3.01/1.75 => ( in @ Xx @ A ) )
% 3.01/1.75 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 3.01/1.75 => ? [D: $i,Xx: $i] :
% 3.01/1.75 ( ( in @ D @ B )
% 3.01/1.75 & ( in @ Xx @ C )
% 3.01/1.75 & ~ ? [Xy: $i] :
% 3.01/1.75 ( ( in @ Xy @ D )
% 3.01/1.75 & ( in @ Xy @ C ) )
% 3.01/1.75 & ! [E: $i] :
% 3.01/1.75 ( ( in @ E @ B )
% 3.01/1.75 => ( ! [Xy: $i] :
% 3.01/1.75 ( ( in @ Xy @ E )
% 3.01/1.75 => ( in @ Xy @ D ) )
% 3.01/1.75 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(descr_type,type,
% 3.01/1.75 descr: ( $i > $o ) > $i ).
% 3.01/1.75
% 3.01/1.75 thf(descrp_type,type,
% 3.01/1.75 descrp: $o ).
% 3.01/1.75
% 3.01/1.75 thf(descrp,definition,
% 3.01/1.75 ( descrp
% 3.01/1.75 = ( ! [Xphi: $i > $o] :
% 3.01/1.75 ( ( exu
% 3.01/1.75 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.01/1.75 => ( Xphi
% 3.01/1.75 @ ( descr
% 3.01/1.75 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(dsetconstr_type,type,
% 3.01/1.75 dsetconstr: $i > ( $i > $o ) > $i ).
% 3.01/1.75
% 3.01/1.75 thf(dsetconstrI_type,type,
% 3.01/1.75 dsetconstrI: $o ).
% 3.01/1.75
% 3.01/1.75 thf(dsetconstrI,definition,
% 3.01/1.75 ( dsetconstrI
% 3.01/1.75 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ A )
% 3.01/1.75 => ( ( Xphi @ Xx )
% 3.01/1.75 => ( in @ Xx
% 3.01/1.75 @ ( dsetconstr @ A
% 3.01/1.75 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(dsetconstrEL_type,type,
% 3.01/1.75 dsetconstrEL: $o ).
% 3.01/1.75
% 3.01/1.75 thf(dsetconstrEL,definition,
% 3.01/1.75 ( dsetconstrEL
% 3.01/1.75 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.01/1.75 ( ( in @ Xx
% 3.01/1.75 @ ( dsetconstr @ A
% 3.01/1.75 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.01/1.75 => ( in @ Xx @ A ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(dsetconstrER_type,type,
% 3.01/1.75 dsetconstrER: $o ).
% 3.01/1.75
% 3.01/1.75 thf(dsetconstrER,definition,
% 3.01/1.75 ( dsetconstrER
% 3.01/1.75 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.01/1.75 ( ( in @ Xx
% 3.01/1.75 @ ( dsetconstr @ A
% 3.01/1.75 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.01/1.75 => ( Xphi @ Xx ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(exuE1_type,type,
% 3.01/1.75 exuE1: $o ).
% 3.01/1.75
% 3.01/1.75 thf(exuE1,definition,
% 3.01/1.75 ( exuE1
% 3.01/1.75 = ( ! [Xphi: $i > $o] :
% 3.01/1.75 ( ( exu
% 3.01/1.75 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.01/1.75 => ? [Xx: $i] :
% 3.01/1.75 ( ( Xphi @ Xx )
% 3.01/1.75 & ! [Xy: $i] :
% 3.01/1.75 ( ( Xphi @ Xy )
% 3.01/1.75 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(prop2set_type,type,
% 3.01/1.75 prop2set: $o > $i ).
% 3.01/1.75
% 3.01/1.75 thf(prop2setE_type,type,
% 3.01/1.75 prop2setE: $o ).
% 3.01/1.75
% 3.01/1.75 thf(prop2setE,definition,
% 3.01/1.75 ( prop2setE
% 3.01/1.75 = ( ! [Xphi: $o,Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 3.01/1.75 => Xphi ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(emptysetE_type,type,
% 3.01/1.75 emptysetE: $o ).
% 3.01/1.75
% 3.01/1.75 thf(emptysetE,definition,
% 3.01/1.75 ( emptysetE
% 3.01/1.75 = ( ! [Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ emptyset )
% 3.01/1.75 => ! [Xphi: $o] : Xphi ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(emptysetimpfalse_type,type,
% 3.01/1.75 emptysetimpfalse: $o ).
% 3.01/1.75
% 3.01/1.75 thf(emptysetimpfalse,definition,
% 3.01/1.75 ( emptysetimpfalse
% 3.01/1.75 = ( ! [Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ emptyset )
% 3.01/1.75 => $false ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(notinemptyset_type,type,
% 3.01/1.75 notinemptyset: $o ).
% 3.01/1.75
% 3.01/1.75 thf(notinemptyset,definition,
% 3.01/1.75 ( notinemptyset
% 3.01/1.75 = ( ! [Xx: $i] :
% 3.01/1.75 ~ ( in @ Xx @ emptyset ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(exuE3e_type,type,
% 3.01/1.75 exuE3e: $o ).
% 3.01/1.75
% 3.01/1.75 thf(exuE3e,definition,
% 3.01/1.75 ( exuE3e
% 3.01/1.75 = ( ! [Xphi: $i > $o] :
% 3.01/1.75 ( ( exu
% 3.01/1.75 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.01/1.75 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(setext_type,type,
% 3.01/1.75 setext: $o ).
% 3.01/1.75
% 3.01/1.75 thf(setext,definition,
% 3.01/1.75 ( setext
% 3.01/1.75 = ( ! [A: $i,B: $i] :
% 3.01/1.75 ( ! [Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ A )
% 3.01/1.75 => ( in @ Xx @ B ) )
% 3.01/1.75 => ( ! [Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ B )
% 3.01/1.75 => ( in @ Xx @ A ) )
% 3.01/1.75 => ( A = B ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(emptyI_type,type,
% 3.01/1.75 emptyI: $o ).
% 3.01/1.75
% 3.01/1.75 thf(emptyI,definition,
% 3.01/1.75 ( emptyI
% 3.01/1.75 = ( ! [A: $i] :
% 3.01/1.75 ( ! [Xx: $i] :
% 3.01/1.75 ~ ( in @ Xx @ A )
% 3.01/1.75 => ( A = emptyset ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(noeltsimpempty_type,type,
% 3.01/1.75 noeltsimpempty: $o ).
% 3.01/1.75
% 3.01/1.75 thf(noeltsimpempty,definition,
% 3.01/1.75 ( noeltsimpempty
% 3.01/1.75 = ( ! [A: $i] :
% 3.01/1.75 ( ! [Xx: $i] :
% 3.01/1.75 ~ ( in @ Xx @ A )
% 3.01/1.75 => ( A = emptyset ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(setbeta_type,type,
% 3.01/1.75 setbeta: $o ).
% 3.01/1.75
% 3.01/1.75 thf(setbeta,definition,
% 3.01/1.75 ( setbeta
% 3.01/1.75 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ A )
% 3.01/1.75 => ( ( in @ Xx
% 3.01/1.75 @ ( dsetconstr @ A
% 3.01/1.75 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.01/1.75 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(nonempty_type,type,
% 3.01/1.75 nonempty: $i > $o ).
% 3.01/1.75
% 3.01/1.75 thf(nonempty,definition,
% 3.01/1.75 ( nonempty
% 3.01/1.75 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(nonemptyE1_type,type,
% 3.01/1.75 nonemptyE1: $o ).
% 3.01/1.75
% 3.01/1.75 thf(nonemptyE1,definition,
% 3.01/1.75 ( nonemptyE1
% 3.01/1.75 = ( ! [A: $i] :
% 3.01/1.75 ( ( nonempty @ A )
% 3.01/1.75 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(nonemptyI_type,type,
% 3.01/1.75 nonemptyI: $o ).
% 3.01/1.75
% 3.01/1.75 thf(nonemptyI,definition,
% 3.01/1.75 ( nonemptyI
% 3.01/1.75 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ A )
% 3.01/1.75 => ( ( Xphi @ Xx )
% 3.01/1.75 => ( nonempty
% 3.01/1.75 @ ( dsetconstr @ A
% 3.01/1.75 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(nonemptyI1_type,type,
% 3.01/1.75 nonemptyI1: $o ).
% 3.01/1.75
% 3.01/1.75 thf(nonemptyI1,definition,
% 3.01/1.75 ( nonemptyI1
% 3.01/1.75 = ( ! [A: $i] :
% 3.01/1.75 ( ? [Xx: $i] : ( in @ Xx @ A )
% 3.01/1.75 => ( nonempty @ A ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(setadjoinIL_type,type,
% 3.01/1.75 setadjoinIL: $o ).
% 3.01/1.75
% 3.01/1.75 thf(setadjoinIL,definition,
% 3.01/1.75 ( setadjoinIL
% 3.01/1.75 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(emptyinunitempty_type,type,
% 3.01/1.75 emptyinunitempty: $o ).
% 3.01/1.75
% 3.01/1.75 thf(emptyinunitempty,definition,
% 3.01/1.75 ( emptyinunitempty
% 3.01/1.75 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(setadjoinIR_type,type,
% 3.01/1.75 setadjoinIR: $o ).
% 3.01/1.75
% 3.01/1.75 thf(setadjoinIR,definition,
% 3.01/1.75 ( setadjoinIR
% 3.01/1.75 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.01/1.75 ( ( in @ Xy @ A )
% 3.01/1.75 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(setadjoinE_type,type,
% 3.01/1.75 setadjoinE: $o ).
% 3.01/1.75
% 3.01/1.75 thf(setadjoinE,definition,
% 3.01/1.75 ( setadjoinE
% 3.01/1.75 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.01/1.75 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.01/1.75 => ! [Xphi: $o] :
% 3.01/1.75 ( ( ( Xy = Xx )
% 3.01/1.75 => Xphi )
% 3.01/1.75 => ( ( ( in @ Xy @ A )
% 3.01/1.75 => Xphi )
% 3.01/1.75 => Xphi ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(setadjoinOr_type,type,
% 3.01/1.75 setadjoinOr: $o ).
% 3.01/1.75
% 3.01/1.75 thf(setadjoinOr,definition,
% 3.01/1.75 ( setadjoinOr
% 3.01/1.75 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.01/1.75 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.01/1.75 => ( ( Xy = Xx )
% 3.01/1.75 | ( in @ Xy @ A ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(setoftrueEq_type,type,
% 3.01/1.75 setoftrueEq: $o ).
% 3.01/1.75
% 3.01/1.75 thf(setoftrueEq,definition,
% 3.01/1.75 ( setoftrueEq
% 3.01/1.75 = ( ! [A: $i] :
% 3.01/1.75 ( ( dsetconstr @ A
% 3.01/1.75 @ ^ [Xx: $i] : $true )
% 3.01/1.75 = A ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(powersetI_type,type,
% 3.01/1.75 powersetI: $o ).
% 3.01/1.75
% 3.01/1.75 thf(powersetI,definition,
% 3.01/1.75 ( powersetI
% 3.01/1.75 = ( ! [A: $i,B: $i] :
% 3.01/1.75 ( ! [Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ B )
% 3.01/1.75 => ( in @ Xx @ A ) )
% 3.01/1.75 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(emptyinPowerset_type,type,
% 3.01/1.75 emptyinPowerset: $o ).
% 3.01/1.75
% 3.01/1.75 thf(emptyinPowerset,definition,
% 3.01/1.75 ( emptyinPowerset
% 3.01/1.75 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(emptyInPowerset_type,type,
% 3.01/1.75 emptyInPowerset: $o ).
% 3.01/1.75
% 3.01/1.75 thf(emptyInPowerset,definition,
% 3.01/1.75 ( emptyInPowerset
% 3.01/1.75 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(powersetE_type,type,
% 3.01/1.75 powersetE: $o ).
% 3.01/1.75
% 3.01/1.75 thf(powersetE,definition,
% 3.01/1.75 ( powersetE
% 3.01/1.75 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.01/1.75 ( ( in @ B @ ( powerset @ A ) )
% 3.01/1.75 => ( ( in @ Xx @ B )
% 3.01/1.75 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(setunionI_type,type,
% 3.01/1.75 setunionI: $o ).
% 3.01/1.75
% 3.01/1.75 thf(setunionI,definition,
% 3.01/1.75 ( setunionI
% 3.01/1.75 = ( ! [A: $i,Xx: $i,B: $i] :
% 3.01/1.75 ( ( in @ Xx @ B )
% 3.01/1.75 => ( ( in @ B @ A )
% 3.01/1.75 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(setunionE_type,type,
% 3.01/1.75 setunionE: $o ).
% 3.01/1.75
% 3.01/1.75 thf(setunionE,definition,
% 3.01/1.75 ( setunionE
% 3.01/1.75 = ( ! [A: $i,Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ ( setunion @ A ) )
% 3.01/1.75 => ! [Xphi: $o] :
% 3.01/1.75 ( ! [B: $i] :
% 3.01/1.75 ( ( in @ Xx @ B )
% 3.01/1.75 => ( ( in @ B @ A )
% 3.01/1.75 => Xphi ) )
% 3.01/1.75 => Xphi ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(subPowSU_type,type,
% 3.01/1.75 subPowSU: $o ).
% 3.01/1.75
% 3.01/1.75 thf(subPowSU,definition,
% 3.01/1.75 ( subPowSU
% 3.01/1.75 = ( ! [A: $i,Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ A )
% 3.01/1.75 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(exuE2_type,type,
% 3.01/1.75 exuE2: $o ).
% 3.01/1.75
% 3.01/1.75 thf(exuE2,definition,
% 3.01/1.75 ( exuE2
% 3.01/1.75 = ( ! [Xphi: $i > $o] :
% 3.01/1.75 ( ( exu
% 3.01/1.75 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.01/1.75 => ? [Xx: $i] :
% 3.01/1.75 ! [Xy: $i] :
% 3.01/1.75 ( ( Xphi @ Xy )
% 3.01/1.75 <=> ( Xy = Xx ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(nonemptyImpWitness_type,type,
% 3.01/1.75 nonemptyImpWitness: $o ).
% 3.01/1.75
% 3.01/1.75 thf(nonemptyImpWitness,definition,
% 3.01/1.75 ( nonemptyImpWitness
% 3.01/1.75 = ( ! [A: $i] :
% 3.01/1.75 ( ( nonempty @ A )
% 3.01/1.75 => ? [Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ A )
% 3.01/1.75 & $true ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(uniqinunit_type,type,
% 3.01/1.75 uniqinunit: $o ).
% 3.01/1.75
% 3.01/1.75 thf(uniqinunit,definition,
% 3.01/1.75 ( uniqinunit
% 3.01/1.75 = ( ! [Xx: $i,Xy: $i] :
% 3.01/1.75 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.01/1.75 => ( Xx = Xy ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(notinsingleton_type,type,
% 3.01/1.75 notinsingleton: $o ).
% 3.01/1.75
% 3.01/1.75 thf(notinsingleton,definition,
% 3.01/1.75 ( notinsingleton
% 3.01/1.75 = ( ! [Xx: $i,Xy: $i] :
% 3.01/1.75 ( ( Xx != Xy )
% 3.01/1.75 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(eqinunit_type,type,
% 3.01/1.75 eqinunit: $o ).
% 3.01/1.75
% 3.01/1.75 thf(eqinunit,definition,
% 3.01/1.75 ( eqinunit
% 3.01/1.75 = ( ! [Xx: $i,Xy: $i] :
% 3.01/1.75 ( ( Xx = Xy )
% 3.01/1.75 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(singletonsswitch_type,type,
% 3.01/1.75 singletonsswitch: $o ).
% 3.01/1.75
% 3.01/1.75 thf(singletonsswitch,definition,
% 3.01/1.75 ( singletonsswitch
% 3.01/1.75 = ( ! [Xx: $i,Xy: $i] :
% 3.01/1.75 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.01/1.75 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(upairsetE_type,type,
% 3.01/1.75 upairsetE: $o ).
% 3.01/1.75
% 3.01/1.75 thf(upairsetE,definition,
% 3.01/1.75 ( upairsetE
% 3.01/1.75 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.01/1.75 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 3.01/1.75 => ( ( Xz = Xx )
% 3.01/1.75 | ( Xz = Xy ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(upairsetIL_type,type,
% 3.01/1.75 upairsetIL: $o ).
% 3.01/1.75
% 3.01/1.75 thf(upairsetIL,definition,
% 3.01/1.75 ( upairsetIL
% 3.01/1.75 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(upairsetIR_type,type,
% 3.01/1.75 upairsetIR: $o ).
% 3.01/1.75
% 3.01/1.75 thf(upairsetIR,definition,
% 3.01/1.75 ( upairsetIR
% 3.01/1.75 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(emptyE1_type,type,
% 3.01/1.75 emptyE1: $o ).
% 3.01/1.75
% 3.01/1.75 thf(emptyE1,definition,
% 3.01/1.75 ( emptyE1
% 3.01/1.75 = ( ! [A: $i,Xphi: $i > $o] :
% 3.01/1.75 ( ? [Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ A )
% 3.01/1.75 & ( Xphi @ Xx ) )
% 3.01/1.75 => ( ( ( dsetconstr @ A
% 3.01/1.75 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.01/1.75 = emptyset )
% 3.01/1.75 => $false ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(vacuousDall_type,type,
% 3.01/1.75 vacuousDall: $o ).
% 3.01/1.75
% 3.01/1.75 thf(vacuousDall,definition,
% 3.01/1.75 ( vacuousDall
% 3.01/1.75 = ( ! [Xphi: $i > $o,Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ emptyset )
% 3.01/1.75 => ( Xphi @ Xx ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(quantDeMorgan1_type,type,
% 3.01/1.75 quantDeMorgan1: $o ).
% 3.01/1.75
% 3.01/1.75 thf(quantDeMorgan1,definition,
% 3.01/1.75 ( quantDeMorgan1
% 3.01/1.75 = ( ! [A: $i,Xphi: $i > $o] :
% 3.01/1.75 ( ~ ! [Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ A )
% 3.01/1.75 => ( Xphi @ Xx ) )
% 3.01/1.75 => ? [Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ A )
% 3.01/1.75 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(quantDeMorgan2_type,type,
% 3.01/1.75 quantDeMorgan2: $o ).
% 3.01/1.75
% 3.01/1.75 thf(quantDeMorgan2,definition,
% 3.01/1.75 ( quantDeMorgan2
% 3.01/1.75 = ( ! [A: $i,Xphi: $i > $o] :
% 3.01/1.75 ( ! [Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ A )
% 3.01/1.75 => ~ ( Xphi @ Xx ) )
% 3.01/1.75 => ~ ? [Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ A )
% 3.01/1.75 & ( Xphi @ Xx ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(quantDeMorgan3_type,type,
% 3.01/1.75 quantDeMorgan3: $o ).
% 3.01/1.75
% 3.01/1.75 thf(quantDeMorgan3,definition,
% 3.01/1.75 ( quantDeMorgan3
% 3.01/1.75 = ( ! [A: $i,Xphi: $i > $o] :
% 3.01/1.75 ( ~ ? [Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ A )
% 3.01/1.75 & ( Xphi @ Xx ) )
% 3.01/1.75 => ! [Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ A )
% 3.01/1.75 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(quantDeMorgan4_type,type,
% 3.01/1.75 quantDeMorgan4: $o ).
% 3.01/1.75
% 3.01/1.75 thf(quantDeMorgan4,definition,
% 3.01/1.75 ( quantDeMorgan4
% 3.01/1.75 = ( ! [A: $i,Xphi: $i > $o] :
% 3.01/1.75 ( ? [Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ A )
% 3.01/1.75 & ~ ( Xphi @ Xx ) )
% 3.01/1.75 => ~ ! [Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ A )
% 3.01/1.75 => ( Xphi @ Xx ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(prop2setI_type,type,
% 3.01/1.75 prop2setI: $o ).
% 3.01/1.75
% 3.01/1.75 thf(prop2setI,definition,
% 3.01/1.75 ( prop2setI
% 3.01/1.75 = ( ! [Xphi: $o] :
% 3.01/1.75 ( Xphi
% 3.01/1.75 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(set2prop_type,type,
% 3.01/1.75 set2prop: $i > $o ).
% 3.01/1.75
% 3.01/1.75 thf(prop2set2propI_type,type,
% 3.01/1.75 prop2set2propI: $o ).
% 3.01/1.75
% 3.01/1.75 thf(prop2set2propI,definition,
% 3.01/1.75 ( prop2set2propI
% 3.01/1.75 = ( ! [Xphi: $o] :
% 3.01/1.75 ( Xphi
% 3.01/1.75 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(notdexE_type,type,
% 3.01/1.75 notdexE: $o ).
% 3.01/1.75
% 3.01/1.75 thf(notdexE,definition,
% 3.01/1.75 ( notdexE
% 3.01/1.75 = ( ! [A: $i,Xphi: $i > $o] :
% 3.01/1.75 ( ~ ? [Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ A )
% 3.01/1.75 & ( Xphi @ Xx ) )
% 3.01/1.75 => ! [Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ A )
% 3.01/1.75 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(notdallE_type,type,
% 3.01/1.75 notdallE: $o ).
% 3.01/1.75
% 3.01/1.75 thf(notdallE,definition,
% 3.01/1.75 ( notdallE
% 3.01/1.75 = ( ! [A: $i,Xphi: $i > $o] :
% 3.01/1.75 ( ~ ! [Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ A )
% 3.01/1.75 => ( Xphi @ Xx ) )
% 3.01/1.75 => ? [Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ A )
% 3.01/1.75 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(exuI1_type,type,
% 3.01/1.75 exuI1: $o ).
% 3.01/1.75
% 3.01/1.75 thf(exuI1,definition,
% 3.01/1.75 ( exuI1
% 3.01/1.75 = ( ! [Xphi: $i > $o] :
% 3.01/1.75 ( ? [Xx: $i] :
% 3.01/1.75 ( ( Xphi @ Xx )
% 3.01/1.75 & ! [Xy: $i] :
% 3.01/1.75 ( ( Xphi @ Xy )
% 3.01/1.75 => ( Xx = Xy ) ) )
% 3.01/1.75 => ( exu
% 3.01/1.75 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(exuI3_type,type,
% 3.01/1.75 exuI3: $o ).
% 3.01/1.75
% 3.01/1.75 thf(exuI3,definition,
% 3.01/1.75 ( exuI3
% 3.01/1.75 = ( ! [Xphi: $i > $o] :
% 3.01/1.75 ( ? [Xx: $i] : ( Xphi @ Xx )
% 3.01/1.75 => ( ! [Xx: $i,Xy: $i] :
% 3.01/1.75 ( ( Xphi @ Xx )
% 3.01/1.75 => ( ( Xphi @ Xy )
% 3.01/1.75 => ( Xx = Xy ) ) )
% 3.01/1.75 => ( exu
% 3.01/1.75 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(exuI2_type,type,
% 3.01/1.75 exuI2: $o ).
% 3.01/1.75
% 3.01/1.75 thf(exuI2,definition,
% 3.01/1.75 ( exuI2
% 3.01/1.75 = ( ! [Xphi: $i > $o] :
% 3.01/1.75 ( ? [Xx: $i] :
% 3.01/1.75 ! [Xy: $i] :
% 3.01/1.75 ( ( Xphi @ Xy )
% 3.01/1.75 <=> ( Xy = Xx ) )
% 3.01/1.75 => ( exu
% 3.01/1.75 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(inCongP_type,type,
% 3.01/1.75 inCongP: $o ).
% 3.01/1.75
% 3.01/1.75 thf(inCongP,definition,
% 3.01/1.75 ( inCongP
% 3.01/1.75 = ( ! [A: $i,B: $i] :
% 3.01/1.75 ( ( A = B )
% 3.01/1.75 => ! [Xx: $i,Xy: $i] :
% 3.01/1.75 ( ( Xx = Xy )
% 3.01/1.75 => ( ( in @ Xx @ A )
% 3.01/1.75 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(in__Cong_type,type,
% 3.01/1.75 in__Cong: $o ).
% 3.01/1.75
% 3.01/1.75 thf(in__Cong,definition,
% 3.01/1.75 ( in__Cong
% 3.01/1.75 = ( ! [A: $i,B: $i] :
% 3.01/1.75 ( ( A = B )
% 3.01/1.75 => ! [Xx: $i,Xy: $i] :
% 3.01/1.75 ( ( Xx = Xy )
% 3.01/1.75 => ( ( in @ Xx @ A )
% 3.01/1.75 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(exuE3u_type,type,
% 3.01/1.75 exuE3u: $o ).
% 3.01/1.75
% 3.01/1.75 thf(exuE3u,definition,
% 3.01/1.75 ( exuE3u
% 3.01/1.75 = ( ! [Xphi: $i > $o] :
% 3.01/1.75 ( ( exu
% 3.01/1.75 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.01/1.75 => ! [Xx: $i,Xy: $i] :
% 3.01/1.75 ( ( Xphi @ Xx )
% 3.01/1.75 => ( ( Xphi @ Xy )
% 3.01/1.75 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(exu__Cong_type,type,
% 3.01/1.75 exu__Cong: $o ).
% 3.01/1.75
% 3.01/1.75 thf(exu__Cong,definition,
% 3.01/1.75 ( exu__Cong
% 3.01/1.75 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.01/1.75 ( ! [Xx: $i,Xy: $i] :
% 3.01/1.75 ( ( Xx = Xy )
% 3.01/1.75 => ( ( Xphi @ Xx )
% 3.01/1.75 <=> ( Xpsi @ Xy ) ) )
% 3.01/1.75 => ( ( exu
% 3.01/1.75 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.01/1.75 <=> ( exu
% 3.01/1.75 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(emptyset__Cong_type,type,
% 3.01/1.75 emptyset__Cong: $o ).
% 3.01/1.75
% 3.01/1.75 thf(emptyset__Cong,definition,
% 3.01/1.75 ( emptyset__Cong
% 3.01/1.75 = ( emptyset = emptyset ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(setadjoin__Cong_type,type,
% 3.01/1.75 setadjoin__Cong: $o ).
% 3.01/1.75
% 3.01/1.75 thf(setadjoin__Cong,definition,
% 3.01/1.75 ( setadjoin__Cong
% 3.01/1.75 = ( ! [Xx: $i,Xy: $i] :
% 3.01/1.75 ( ( Xx = Xy )
% 3.01/1.75 => ! [Xz: $i,Xu: $i] :
% 3.01/1.75 ( ( Xz = Xu )
% 3.01/1.75 => ( ( setadjoin @ Xx @ Xz )
% 3.01/1.75 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(powerset__Cong_type,type,
% 3.01/1.75 powerset__Cong: $o ).
% 3.01/1.75
% 3.01/1.75 thf(powerset__Cong,definition,
% 3.01/1.75 ( powerset__Cong
% 3.01/1.75 = ( ! [A: $i,B: $i] :
% 3.01/1.75 ( ( A = B )
% 3.01/1.75 => ( ( powerset @ A )
% 3.01/1.75 = ( powerset @ B ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(setunion__Cong_type,type,
% 3.01/1.75 setunion__Cong: $o ).
% 3.01/1.75
% 3.01/1.75 thf(setunion__Cong,definition,
% 3.01/1.75 ( setunion__Cong
% 3.01/1.75 = ( ! [A: $i,B: $i] :
% 3.01/1.75 ( ( A = B )
% 3.01/1.75 => ( ( setunion @ A )
% 3.01/1.75 = ( setunion @ B ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(omega__Cong_type,type,
% 3.01/1.75 omega__Cong: $o ).
% 3.01/1.75
% 3.01/1.75 thf(omega__Cong,definition,
% 3.01/1.75 ( omega__Cong
% 3.01/1.75 = ( omega = omega ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(exuEu_type,type,
% 3.01/1.75 exuEu: $o ).
% 3.01/1.75
% 3.01/1.75 thf(exuEu,definition,
% 3.01/1.75 ( exuEu
% 3.01/1.75 = ( ! [Xphi: $i > $o] :
% 3.01/1.75 ( ( exu
% 3.01/1.75 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.01/1.75 => ! [Xx: $i,Xy: $i] :
% 3.01/1.75 ( ( Xphi @ Xx )
% 3.01/1.75 => ( ( Xphi @ Xy )
% 3.01/1.75 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(descr__Cong_type,type,
% 3.01/1.75 descr__Cong: $o ).
% 3.01/1.75
% 3.01/1.75 thf(descr__Cong,definition,
% 3.01/1.75 ( descr__Cong
% 3.01/1.75 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.01/1.75 ( ! [Xx: $i,Xy: $i] :
% 3.01/1.75 ( ( Xx = Xy )
% 3.01/1.75 => ( ( Xphi @ Xx )
% 3.01/1.75 <=> ( Xpsi @ Xy ) ) )
% 3.01/1.75 => ( ( exu
% 3.01/1.75 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.01/1.75 => ( ( exu
% 3.01/1.75 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 3.01/1.75 => ( ( descr
% 3.01/1.75 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.01/1.75 = ( descr
% 3.01/1.75 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(dsetconstr__Cong_type,type,
% 3.01/1.75 dsetconstr__Cong: $o ).
% 3.01/1.75
% 3.01/1.75 thf(dsetconstr__Cong,definition,
% 3.01/1.75 ( dsetconstr__Cong
% 3.01/1.75 = ( ! [A: $i,B: $i] :
% 3.01/1.75 ( ( A = B )
% 3.01/1.75 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.01/1.75 ( ! [Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ A )
% 3.01/1.75 => ! [Xy: $i] :
% 3.01/1.75 ( ( in @ Xy @ B )
% 3.01/1.75 => ( ( Xx = Xy )
% 3.01/1.75 => ( ( Xphi @ Xx )
% 3.01/1.75 <=> ( Xpsi @ Xy ) ) ) ) )
% 3.01/1.75 => ( ( dsetconstr @ A
% 3.01/1.75 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.01/1.75 = ( dsetconstr @ B
% 3.01/1.75 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(subset_type,type,
% 3.01/1.75 subset: $i > $i > $o ).
% 3.01/1.75
% 3.01/1.75 thf(disjoint_type,type,
% 3.01/1.75 disjoint: $i > $i > $o ).
% 3.01/1.75
% 3.01/1.75 thf(setsmeet_type,type,
% 3.01/1.75 setsmeet: $i > $i > $o ).
% 3.01/1.75
% 3.01/1.75 thf(subsetI1_type,type,
% 3.01/1.75 subsetI1: $o ).
% 3.01/1.75
% 3.01/1.75 thf(subsetI1,definition,
% 3.01/1.75 ( subsetI1
% 3.01/1.75 = ( ! [A: $i,B: $i] :
% 3.01/1.75 ( ! [Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ A )
% 3.01/1.75 => ( in @ Xx @ B ) )
% 3.01/1.75 => ( subset @ A @ B ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(eqimpsubset2_type,type,
% 3.01/1.75 eqimpsubset2: $o ).
% 3.01/1.75
% 3.01/1.75 thf(eqimpsubset2,definition,
% 3.01/1.75 ( eqimpsubset2
% 3.01/1.75 = ( ! [A: $i,B: $i] :
% 3.01/1.75 ( ( A = B )
% 3.01/1.75 => ( subset @ B @ A ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(eqimpsubset1_type,type,
% 3.01/1.75 eqimpsubset1: $o ).
% 3.01/1.75
% 3.01/1.75 thf(eqimpsubset1,definition,
% 3.01/1.75 ( eqimpsubset1
% 3.01/1.75 = ( ! [A: $i,B: $i] :
% 3.01/1.75 ( ( A = B )
% 3.01/1.75 => ( subset @ A @ B ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(subsetI2_type,type,
% 3.01/1.75 subsetI2: $o ).
% 3.01/1.75
% 3.01/1.75 thf(subsetI2,definition,
% 3.01/1.75 ( subsetI2
% 3.01/1.75 = ( ! [A: $i,B: $i] :
% 3.01/1.75 ( ! [Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ A )
% 3.01/1.75 => ( in @ Xx @ B ) )
% 3.01/1.75 => ( subset @ A @ B ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(emptysetsubset_type,type,
% 3.01/1.75 emptysetsubset: $o ).
% 3.01/1.75
% 3.01/1.75 thf(emptysetsubset,definition,
% 3.01/1.75 ( emptysetsubset
% 3.01/1.75 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(subsetE_type,type,
% 3.01/1.75 subsetE: $o ).
% 3.01/1.75
% 3.01/1.75 thf(subsetE,definition,
% 3.01/1.75 ( subsetE
% 3.01/1.75 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.01/1.75 ( ( subset @ A @ B )
% 3.01/1.75 => ( ( in @ Xx @ A )
% 3.01/1.75 => ( in @ Xx @ B ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(subsetE2_type,type,
% 3.01/1.75 subsetE2: $o ).
% 3.01/1.75
% 3.01/1.75 thf(subsetE2,definition,
% 3.01/1.75 ( subsetE2
% 3.01/1.75 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.01/1.75 ( ( subset @ A @ B )
% 3.01/1.75 => ( ~ ( in @ Xx @ B )
% 3.01/1.75 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(notsubsetI_type,type,
% 3.01/1.75 notsubsetI: $o ).
% 3.01/1.75
% 3.01/1.75 thf(notsubsetI,definition,
% 3.01/1.75 ( notsubsetI
% 3.01/1.75 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ A )
% 3.01/1.75 => ( ~ ( in @ Xx @ B )
% 3.01/1.75 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(notequalI1_type,type,
% 3.01/1.75 notequalI1: $o ).
% 3.01/1.75
% 3.01/1.75 thf(notequalI1,definition,
% 3.01/1.75 ( notequalI1
% 3.01/1.75 = ( ! [A: $i,B: $i] :
% 3.01/1.75 ( ~ ( subset @ A @ B )
% 3.01/1.75 => ( A != B ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(notequalI2_type,type,
% 3.01/1.75 notequalI2: $o ).
% 3.01/1.75
% 3.01/1.75 thf(notequalI2,definition,
% 3.01/1.75 ( notequalI2
% 3.01/1.75 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ A )
% 3.01/1.75 => ( ~ ( in @ Xx @ B )
% 3.01/1.75 => ( A != B ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(subsetRefl_type,type,
% 3.01/1.75 subsetRefl: $o ).
% 3.01/1.75
% 3.01/1.75 thf(subsetRefl,definition,
% 3.01/1.75 ( subsetRefl
% 3.01/1.75 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(subsetTrans_type,type,
% 3.01/1.75 subsetTrans: $o ).
% 3.01/1.75
% 3.01/1.75 thf(subsetTrans,definition,
% 3.01/1.75 ( subsetTrans
% 3.01/1.75 = ( ! [A: $i,B: $i,C: $i] :
% 3.01/1.75 ( ( subset @ A @ B )
% 3.01/1.75 => ( ( subset @ B @ C )
% 3.01/1.75 => ( subset @ A @ C ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(setadjoinSub_type,type,
% 3.01/1.75 setadjoinSub: $o ).
% 3.01/1.75
% 3.01/1.75 thf(setadjoinSub,definition,
% 3.01/1.75 ( setadjoinSub
% 3.01/1.75 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(setadjoinSub2_type,type,
% 3.01/1.75 setadjoinSub2: $o ).
% 3.01/1.75
% 3.01/1.75 thf(setadjoinSub2,definition,
% 3.01/1.75 ( setadjoinSub2
% 3.01/1.75 = ( ! [A: $i,Xx: $i,B: $i] :
% 3.01/1.75 ( ( subset @ A @ B )
% 3.01/1.75 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(subset2powerset_type,type,
% 3.01/1.75 subset2powerset: $o ).
% 3.01/1.75
% 3.01/1.75 thf(subset2powerset,definition,
% 3.01/1.75 ( subset2powerset
% 3.01/1.75 = ( ! [A: $i,B: $i] :
% 3.01/1.75 ( ( subset @ A @ B )
% 3.01/1.75 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(setextsub_type,type,
% 3.01/1.75 setextsub: $o ).
% 3.01/1.75
% 3.01/1.75 thf(setextsub,definition,
% 3.01/1.75 ( setextsub
% 3.01/1.75 = ( ! [A: $i,B: $i] :
% 3.01/1.75 ( ( subset @ A @ B )
% 3.01/1.75 => ( ( subset @ B @ A )
% 3.01/1.75 => ( A = B ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(subsetemptysetimpeq_type,type,
% 3.01/1.75 subsetemptysetimpeq: $o ).
% 3.01/1.75
% 3.01/1.75 thf(subsetemptysetimpeq,definition,
% 3.01/1.75 ( subsetemptysetimpeq
% 3.01/1.75 = ( ! [A: $i] :
% 3.01/1.75 ( ( subset @ A @ emptyset )
% 3.01/1.75 => ( A = emptyset ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(powersetI1_type,type,
% 3.01/1.75 powersetI1: $o ).
% 3.01/1.75
% 3.01/1.75 thf(powersetI1,definition,
% 3.01/1.75 ( powersetI1
% 3.01/1.75 = ( ! [A: $i,B: $i] :
% 3.01/1.75 ( ( subset @ B @ A )
% 3.01/1.75 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(powersetE1_type,type,
% 3.01/1.75 powersetE1: $o ).
% 3.01/1.75
% 3.01/1.75 thf(powersetE1,definition,
% 3.01/1.75 ( powersetE1
% 3.01/1.75 = ( ! [A: $i,B: $i] :
% 3.01/1.75 ( ( in @ B @ ( powerset @ A ) )
% 3.01/1.75 => ( subset @ B @ A ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(inPowerset_type,type,
% 3.01/1.75 inPowerset: $o ).
% 3.01/1.75
% 3.01/1.75 thf(inPowerset,definition,
% 3.01/1.75 ( inPowerset
% 3.01/1.75 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(powersetsubset_type,type,
% 3.01/1.75 powersetsubset: $o ).
% 3.01/1.75
% 3.01/1.75 thf(powersetsubset,definition,
% 3.01/1.75 ( powersetsubset
% 3.01/1.75 = ( ! [A: $i,B: $i] :
% 3.01/1.75 ( ( subset @ A @ B )
% 3.01/1.75 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(sepInPowerset_type,type,
% 3.01/1.75 sepInPowerset: $o ).
% 3.01/1.75
% 3.01/1.75 thf(sepInPowerset,definition,
% 3.01/1.75 ( sepInPowerset
% 3.01/1.75 = ( ! [A: $i,Xphi: $i > $o] :
% 3.01/1.75 ( in
% 3.01/1.75 @ ( dsetconstr @ A
% 3.01/1.75 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.01/1.75 @ ( powerset @ A ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(sepSubset_type,type,
% 3.01/1.75 sepSubset: $o ).
% 3.01/1.75
% 3.01/1.75 thf(sepSubset,definition,
% 3.01/1.75 ( sepSubset
% 3.01/1.75 = ( ! [A: $i,Xphi: $i > $o] :
% 3.01/1.75 ( subset
% 3.01/1.75 @ ( dsetconstr @ A
% 3.01/1.75 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.01/1.75 @ A ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(binunion_type,type,
% 3.01/1.75 binunion: $i > $i > $i ).
% 3.01/1.75
% 3.01/1.75 thf(binunionIL_type,type,
% 3.01/1.75 binunionIL: $o ).
% 3.01/1.75
% 3.01/1.75 thf(binunionIL,definition,
% 3.01/1.75 ( binunionIL
% 3.01/1.75 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ A )
% 3.01/1.75 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(upairset2IR_type,type,
% 3.01/1.75 upairset2IR: $o ).
% 3.01/1.75
% 3.01/1.75 thf(upairset2IR,definition,
% 3.01/1.75 ( upairset2IR
% 3.01/1.75 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(binunionIR_type,type,
% 3.01/1.75 binunionIR: $o ).
% 3.01/1.75
% 3.01/1.75 thf(binunionIR,definition,
% 3.01/1.75 ( binunionIR
% 3.01/1.75 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ B )
% 3.01/1.75 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(binunionEcases_type,type,
% 3.01/1.75 binunionEcases: $o ).
% 3.01/1.75
% 3.01/1.75 thf(binunionEcases,definition,
% 3.01/1.75 ( binunionEcases
% 3.01/1.75 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 3.01/1.75 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 3.01/1.75 => ( ( ( in @ Xx @ A )
% 3.01/1.75 => Xphi )
% 3.01/1.75 => ( ( ( in @ Xx @ B )
% 3.01/1.75 => Xphi )
% 3.01/1.75 => Xphi ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(binunionE_type,type,
% 3.01/1.75 binunionE: $o ).
% 3.01/1.75
% 3.01/1.75 thf(binunionE,definition,
% 3.01/1.75 ( binunionE
% 3.01/1.75 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 3.01/1.75 => ( ( in @ Xx @ A )
% 3.01/1.75 | ( in @ Xx @ B ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(binunionLsub_type,type,
% 3.01/1.75 binunionLsub: $o ).
% 3.01/1.75
% 3.01/1.75 thf(binunionLsub,definition,
% 3.01/1.75 ( binunionLsub
% 3.01/1.75 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(binunionRsub_type,type,
% 3.01/1.75 binunionRsub: $o ).
% 3.01/1.75
% 3.01/1.75 thf(binunionRsub,definition,
% 3.01/1.75 ( binunionRsub
% 3.01/1.75 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(binintersect_type,type,
% 3.01/1.75 binintersect: $i > $i > $i ).
% 3.01/1.75
% 3.01/1.75 thf(binintersectI_type,type,
% 3.01/1.75 binintersectI: $o ).
% 3.01/1.75
% 3.01/1.75 thf(binintersectI,definition,
% 3.01/1.75 ( binintersectI
% 3.01/1.75 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ A )
% 3.01/1.75 => ( ( in @ Xx @ B )
% 3.01/1.75 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(binintersectSubset5_type,type,
% 3.01/1.75 binintersectSubset5: $o ).
% 3.01/1.75
% 3.01/1.75 thf(binintersectSubset5,definition,
% 3.01/1.75 ( binintersectSubset5
% 3.01/1.75 = ( ! [A: $i,B: $i,C: $i] :
% 3.01/1.75 ( ( subset @ C @ A )
% 3.01/1.75 => ( ( subset @ C @ B )
% 3.01/1.75 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(binintersectEL_type,type,
% 3.01/1.75 binintersectEL: $o ).
% 3.01/1.75
% 3.01/1.75 thf(binintersectEL,definition,
% 3.01/1.75 ( binintersectEL
% 3.01/1.75 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 3.01/1.75 => ( in @ Xx @ A ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(binintersectLsub_type,type,
% 3.01/1.75 binintersectLsub: $o ).
% 3.01/1.75
% 3.01/1.75 thf(binintersectLsub,definition,
% 3.01/1.75 ( binintersectLsub
% 3.01/1.75 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(binintersectSubset2_type,type,
% 3.01/1.75 binintersectSubset2: $o ).
% 3.01/1.75
% 3.01/1.75 thf(binintersectSubset2,definition,
% 3.01/1.75 ( binintersectSubset2
% 3.01/1.75 = ( ! [A: $i,B: $i] :
% 3.01/1.75 ( ( subset @ A @ B )
% 3.01/1.75 => ( ( binintersect @ A @ B )
% 3.01/1.75 = A ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(binintersectSubset3_type,type,
% 3.01/1.75 binintersectSubset3: $o ).
% 3.01/1.75
% 3.01/1.75 thf(binintersectSubset3,definition,
% 3.01/1.75 ( binintersectSubset3
% 3.01/1.75 = ( ! [A: $i,B: $i] :
% 3.01/1.75 ( ( ( binintersect @ A @ B )
% 3.01/1.75 = B )
% 3.01/1.75 => ( subset @ B @ A ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(binintersectER_type,type,
% 3.01/1.75 binintersectER: $o ).
% 3.01/1.75
% 3.01/1.75 thf(binintersectER,definition,
% 3.01/1.75 ( binintersectER
% 3.01/1.75 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 3.01/1.75 => ( in @ Xx @ B ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(disjointsetsI1_type,type,
% 3.01/1.75 disjointsetsI1: $o ).
% 3.01/1.75
% 3.01/1.75 thf(disjointsetsI1,definition,
% 3.01/1.75 ( disjointsetsI1
% 3.01/1.75 = ( ! [A: $i,B: $i] :
% 3.01/1.75 ( ~ ? [Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ A )
% 3.01/1.75 & ( in @ Xx @ B ) )
% 3.01/1.75 => ( ( binintersect @ A @ B )
% 3.01/1.75 = emptyset ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(binintersectRsub_type,type,
% 3.01/1.75 binintersectRsub: $o ).
% 3.01/1.75
% 3.01/1.75 thf(binintersectRsub,definition,
% 3.01/1.75 ( binintersectRsub
% 3.01/1.75 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(binintersectSubset4_type,type,
% 3.01/1.75 binintersectSubset4: $o ).
% 3.01/1.75
% 3.01/1.75 thf(binintersectSubset4,definition,
% 3.01/1.75 ( binintersectSubset4
% 3.01/1.75 = ( ! [A: $i,B: $i] :
% 3.01/1.75 ( ( subset @ B @ A )
% 3.01/1.75 => ( ( binintersect @ A @ B )
% 3.01/1.75 = B ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(binintersectSubset1_type,type,
% 3.01/1.75 binintersectSubset1: $o ).
% 3.01/1.75
% 3.01/1.75 thf(binintersectSubset1,definition,
% 3.01/1.75 ( binintersectSubset1
% 3.01/1.75 = ( ! [A: $i,B: $i] :
% 3.01/1.75 ( ( ( binintersect @ A @ B )
% 3.01/1.75 = A )
% 3.01/1.75 => ( subset @ A @ B ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(bs114d_type,type,
% 3.01/1.75 bs114d: $o ).
% 3.01/1.75
% 3.01/1.75 thf(bs114d,definition,
% 3.01/1.75 ( bs114d
% 3.01/1.75 = ( ! [A: $i,B: $i,C: $i] :
% 3.01/1.75 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 3.01/1.75 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(regular_type,type,
% 3.01/1.75 regular: $i > $o ).
% 3.01/1.75
% 3.01/1.75 thf(setminus_type,type,
% 3.01/1.75 setminus: $i > $i > $i ).
% 3.01/1.75
% 3.01/1.75 thf(setminusI_type,type,
% 3.01/1.75 setminusI: $o ).
% 3.01/1.75
% 3.01/1.75 thf(setminusI,definition,
% 3.01/1.75 ( setminusI
% 3.01/1.75 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ A )
% 3.01/1.75 => ( ~ ( in @ Xx @ B )
% 3.01/1.75 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(setminusEL_type,type,
% 3.01/1.75 setminusEL: $o ).
% 3.01/1.75
% 3.01/1.75 thf(setminusEL,definition,
% 3.01/1.75 ( setminusEL
% 3.01/1.75 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 3.01/1.75 => ( in @ Xx @ A ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(setminusER_type,type,
% 3.01/1.75 setminusER: $o ).
% 3.01/1.75
% 3.01/1.75 thf(setminusER,definition,
% 3.01/1.75 ( setminusER
% 3.01/1.75 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 3.01/1.75 => ~ ( in @ Xx @ B ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(setminusSubset2_type,type,
% 3.01/1.75 setminusSubset2: $o ).
% 3.01/1.75
% 3.01/1.75 thf(setminusSubset2,definition,
% 3.01/1.75 ( setminusSubset2
% 3.01/1.75 = ( ! [A: $i,B: $i] :
% 3.01/1.75 ( ( subset @ A @ B )
% 3.01/1.75 => ( ( setminus @ A @ B )
% 3.01/1.75 = emptyset ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(setminusERneg_type,type,
% 3.01/1.75 setminusERneg: $o ).
% 3.01/1.75
% 3.01/1.75 thf(setminusERneg,definition,
% 3.01/1.75 ( setminusERneg
% 3.01/1.75 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.01/1.75 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 3.01/1.75 => ( ( in @ Xx @ A )
% 3.01/1.75 => ( in @ Xx @ B ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(setminusELneg_type,type,
% 3.01/1.75 setminusELneg: $o ).
% 3.01/1.75
% 3.01/1.75 thf(setminusELneg,definition,
% 3.01/1.75 ( setminusELneg
% 3.01/1.75 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.01/1.75 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 3.01/1.75 => ( ~ ( in @ Xx @ B )
% 3.01/1.75 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(setminusILneg_type,type,
% 3.01/1.75 setminusILneg: $o ).
% 3.01/1.75
% 3.01/1.75 thf(setminusILneg,definition,
% 3.01/1.75 ( setminusILneg
% 3.01/1.75 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.01/1.75 ( ~ ( in @ Xx @ A )
% 3.01/1.75 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(setminusIRneg_type,type,
% 3.01/1.75 setminusIRneg: $o ).
% 3.01/1.75
% 3.01/1.75 thf(setminusIRneg,definition,
% 3.01/1.75 ( setminusIRneg
% 3.01/1.75 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ B )
% 3.01/1.75 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(setminusLsub_type,type,
% 3.01/1.75 setminusLsub: $o ).
% 3.01/1.75
% 3.01/1.75 thf(setminusLsub,definition,
% 3.01/1.75 ( setminusLsub
% 3.01/1.75 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(setminusSubset1_type,type,
% 3.01/1.75 setminusSubset1: $o ).
% 3.01/1.75
% 3.01/1.75 thf(setminusSubset1,definition,
% 3.01/1.75 ( setminusSubset1
% 3.01/1.75 = ( ! [A: $i,B: $i] :
% 3.01/1.75 ( ( ( setminus @ A @ B )
% 3.01/1.75 = emptyset )
% 3.01/1.75 => ( subset @ A @ B ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(symdiff_type,type,
% 3.01/1.75 symdiff: $i > $i > $i ).
% 3.01/1.75
% 3.01/1.75 thf(symdiffE_type,type,
% 3.01/1.75 symdiffE: $o ).
% 3.01/1.75
% 3.01/1.75 thf(symdiffE,definition,
% 3.01/1.75 ( symdiffE
% 3.01/1.75 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 3.01/1.75 => ! [Xphi: $o] :
% 3.01/1.75 ( ( ( in @ Xx @ A )
% 3.01/1.75 => ( ~ ( in @ Xx @ B )
% 3.01/1.75 => Xphi ) )
% 3.01/1.75 => ( ( ~ ( in @ Xx @ A )
% 3.01/1.75 => ( ( in @ Xx @ B )
% 3.01/1.75 => Xphi ) )
% 3.01/1.75 => Xphi ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(symdiffI1_type,type,
% 3.01/1.75 symdiffI1: $o ).
% 3.01/1.75
% 3.01/1.75 thf(symdiffI1,definition,
% 3.01/1.75 ( symdiffI1
% 3.01/1.75 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ A )
% 3.01/1.75 => ( ~ ( in @ Xx @ B )
% 3.01/1.75 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(symdiffI2_type,type,
% 3.01/1.75 symdiffI2: $o ).
% 3.01/1.75
% 3.01/1.75 thf(symdiffI2,definition,
% 3.01/1.75 ( symdiffI2
% 3.01/1.75 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.01/1.75 ( ~ ( in @ Xx @ A )
% 3.01/1.75 => ( ( in @ Xx @ B )
% 3.01/1.75 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(symdiffIneg1_type,type,
% 3.01/1.75 symdiffIneg1: $o ).
% 3.01/1.75
% 3.01/1.75 thf(symdiffIneg1,definition,
% 3.01/1.75 ( symdiffIneg1
% 3.01/1.75 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.01/1.75 ( ( in @ Xx @ A )
% 3.01/1.75 => ( ( in @ Xx @ B )
% 3.01/1.75 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(symdiffIneg2_type,type,
% 3.01/1.75 symdiffIneg2: $o ).
% 3.01/1.75
% 3.01/1.75 thf(symdiffIneg2,definition,
% 3.01/1.75 ( symdiffIneg2
% 3.01/1.75 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.01/1.75 ( ~ ( in @ Xx @ A )
% 3.01/1.75 => ( ~ ( in @ Xx @ B )
% 3.01/1.75 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.01/1.75
% 3.01/1.75 thf(iskpair_type,type,
% 3.01/1.75 iskpair: $i > $o ).
% 3.01/1.75
% 3.01/1.75 thf(secondinupair_type,type,
% 3.01/1.75 secondinupair: $o ).
% 3.01/1.75
% 3.01/1.76 thf(secondinupair,definition,
% 3.01/1.76 ( secondinupair
% 3.01/1.76 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(setukpairIL_type,type,
% 3.01/1.76 setukpairIL: $o ).
% 3.01/1.76
% 3.01/1.76 thf(setukpairIL,definition,
% 3.01/1.76 ( setukpairIL
% 3.01/1.76 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(setukpairIR_type,type,
% 3.01/1.76 setukpairIR: $o ).
% 3.01/1.76
% 3.01/1.76 thf(setukpairIR,definition,
% 3.01/1.76 ( setukpairIR
% 3.01/1.76 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(kpairiskpair_type,type,
% 3.01/1.76 kpairiskpair: $o ).
% 3.01/1.76
% 3.01/1.76 thf(kpairiskpair,definition,
% 3.01/1.76 ( kpairiskpair
% 3.01/1.76 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(kpair_type,type,
% 3.01/1.76 kpair: $i > $i > $i ).
% 3.01/1.76
% 3.01/1.76 thf(kpairp_type,type,
% 3.01/1.76 kpairp: $o ).
% 3.01/1.76
% 3.01/1.76 thf(kpairp,definition,
% 3.01/1.76 ( kpairp
% 3.01/1.76 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(cartprod_type,type,
% 3.01/1.76 cartprod: $i > $i > $i ).
% 3.01/1.76
% 3.01/1.76 thf(singletonsubset_type,type,
% 3.01/1.76 singletonsubset: $o ).
% 3.01/1.76
% 3.01/1.76 thf(singletonsubset,definition,
% 3.01/1.76 ( singletonsubset
% 3.01/1.76 = ( ! [A: $i,Xx: $i] :
% 3.01/1.76 ( ( in @ Xx @ A )
% 3.01/1.76 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(singletoninpowerset_type,type,
% 3.01/1.76 singletoninpowerset: $o ).
% 3.01/1.76
% 3.01/1.76 thf(singletoninpowerset,definition,
% 3.01/1.76 ( singletoninpowerset
% 3.01/1.76 = ( ! [A: $i,Xx: $i] :
% 3.01/1.76 ( ( in @ Xx @ A )
% 3.01/1.76 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(singletoninpowunion_type,type,
% 3.01/1.76 singletoninpowunion: $o ).
% 3.01/1.76
% 3.01/1.76 thf(singletoninpowunion,definition,
% 3.01/1.76 ( singletoninpowunion
% 3.01/1.76 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.01/1.76 ( ( in @ Xx @ A )
% 3.01/1.76 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(upairset2E_type,type,
% 3.01/1.76 upairset2E: $o ).
% 3.01/1.76
% 3.01/1.76 thf(upairset2E,definition,
% 3.01/1.76 ( upairset2E
% 3.01/1.76 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.01/1.76 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 3.01/1.76 => ( ( Xz = Xx )
% 3.01/1.76 | ( Xz = Xy ) ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(upairsubunion_type,type,
% 3.01/1.76 upairsubunion: $o ).
% 3.01/1.76
% 3.01/1.76 thf(upairsubunion,definition,
% 3.01/1.76 ( upairsubunion
% 3.01/1.76 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.01/1.76 ( ( in @ Xx @ A )
% 3.01/1.76 => ! [Xy: $i] :
% 3.01/1.76 ( ( in @ Xy @ B )
% 3.01/1.76 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(upairinpowunion_type,type,
% 3.01/1.76 upairinpowunion: $o ).
% 3.01/1.76
% 3.01/1.76 thf(upairinpowunion,definition,
% 3.01/1.76 ( upairinpowunion
% 3.01/1.76 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.01/1.76 ( ( in @ Xx @ A )
% 3.01/1.76 => ! [Xy: $i] :
% 3.01/1.76 ( ( in @ Xy @ B )
% 3.01/1.76 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(ubforcartprodlem1_type,type,
% 3.01/1.76 ubforcartprodlem1: $o ).
% 3.01/1.76
% 3.01/1.76 thf(ubforcartprodlem1,definition,
% 3.01/1.76 ( ubforcartprodlem1
% 3.01/1.76 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.01/1.76 ( ( in @ Xx @ A )
% 3.01/1.76 => ! [Xy: $i] :
% 3.01/1.76 ( ( in @ Xy @ B )
% 3.01/1.76 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(ubforcartprodlem2_type,type,
% 3.01/1.76 ubforcartprodlem2: $o ).
% 3.01/1.76
% 3.01/1.76 thf(ubforcartprodlem2,definition,
% 3.01/1.76 ( ubforcartprodlem2
% 3.01/1.76 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.01/1.76 ( ( in @ Xx @ A )
% 3.01/1.76 => ! [Xy: $i] :
% 3.01/1.76 ( ( in @ Xy @ B )
% 3.01/1.76 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(ubforcartprodlem3_type,type,
% 3.01/1.76 ubforcartprodlem3: $o ).
% 3.01/1.76
% 3.01/1.76 thf(ubforcartprodlem3,definition,
% 3.01/1.76 ( ubforcartprodlem3
% 3.01/1.76 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.01/1.76 ( ( in @ Xx @ A )
% 3.01/1.76 => ! [Xy: $i] :
% 3.01/1.76 ( ( in @ Xy @ B )
% 3.01/1.76 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(cartprodpairin_type,type,
% 3.01/1.76 cartprodpairin: $o ).
% 3.01/1.76
% 3.01/1.76 thf(cartprodpairin,definition,
% 3.01/1.76 ( cartprodpairin
% 3.01/1.76 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.01/1.76 ( ( in @ Xx @ A )
% 3.01/1.76 => ! [Xy: $i] :
% 3.01/1.76 ( ( in @ Xy @ B )
% 3.01/1.76 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(cartprodmempair1_type,type,
% 3.01/1.76 cartprodmempair1: $o ).
% 3.01/1.76
% 3.01/1.76 thf(cartprodmempair1,definition,
% 3.01/1.76 ( cartprodmempair1
% 3.01/1.76 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.01/1.76 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.01/1.76 => ? [Xx: $i] :
% 3.01/1.76 ( ( in @ Xx @ A )
% 3.01/1.76 & ? [Xy: $i] :
% 3.01/1.76 ( ( in @ Xy @ B )
% 3.01/1.76 & ( Xu
% 3.01/1.76 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(cartprodmempair_type,type,
% 3.01/1.76 cartprodmempair: $o ).
% 3.01/1.76
% 3.01/1.76 thf(cartprodmempair,definition,
% 3.01/1.76 ( cartprodmempair
% 3.01/1.76 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.01/1.76 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.01/1.76 => ( iskpair @ Xu ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(setunionE2_type,type,
% 3.01/1.76 setunionE2: $o ).
% 3.01/1.76
% 3.01/1.76 thf(setunionE2,definition,
% 3.01/1.76 ( setunionE2
% 3.01/1.76 = ( ! [A: $i,Xx: $i] :
% 3.01/1.76 ( ( in @ Xx @ ( setunion @ A ) )
% 3.01/1.76 => ? [X: $i] :
% 3.01/1.76 ( ( in @ X @ A )
% 3.01/1.76 & ( in @ Xx @ X ) ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(setunionsingleton1_type,type,
% 3.01/1.76 setunionsingleton1: $o ).
% 3.01/1.76
% 3.01/1.76 thf(setunionsingleton1,definition,
% 3.01/1.76 ( setunionsingleton1
% 3.01/1.76 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(setunionsingleton2_type,type,
% 3.01/1.76 setunionsingleton2: $o ).
% 3.01/1.76
% 3.01/1.76 thf(setunionsingleton2,definition,
% 3.01/1.76 ( setunionsingleton2
% 3.01/1.76 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(setunionsingleton_type,type,
% 3.01/1.76 setunionsingleton: $o ).
% 3.01/1.76
% 3.01/1.76 thf(setunionsingleton,definition,
% 3.01/1.76 ( setunionsingleton
% 3.01/1.76 = ( ! [Xx: $i] :
% 3.01/1.76 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 3.01/1.76 = Xx ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(singleton_type,type,
% 3.01/1.76 singleton: $i > $o ).
% 3.01/1.76
% 3.01/1.76 thf(singleton,definition,
% 3.01/1.76 ( singleton
% 3.01/1.76 = ( ^ [A: $i] :
% 3.01/1.76 ? [Xx: $i] :
% 3.01/1.76 ( ( in @ Xx @ A )
% 3.01/1.76 & ( A
% 3.01/1.76 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(singletonprop_type,type,
% 3.01/1.76 singletonprop: $o ).
% 3.01/1.76
% 3.01/1.76 thf(singletonprop,definition,
% 3.01/1.76 ( singletonprop
% 3.01/1.76 = ( ! [A: $i,Xphi: $i > $o] :
% 3.01/1.76 ( ! [Xx: $i] :
% 3.01/1.76 ( ( in @ Xx @ A )
% 3.01/1.76 => ! [Xy: $i] :
% 3.01/1.76 ( ( in @ Xy @ A )
% 3.01/1.76 => ( ( Xphi @ Xx )
% 3.01/1.76 => ( ( Xphi @ Xy )
% 3.01/1.76 => ( Xx = Xy ) ) ) ) )
% 3.01/1.76 => ( ? [Xx: $i] :
% 3.01/1.76 ( ( in @ Xx @ A )
% 3.01/1.76 & ( Xphi @ Xx ) )
% 3.01/1.76 => ( singleton
% 3.01/1.76 @ ( dsetconstr @ A
% 3.01/1.76 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(ex1_type,type,
% 3.01/1.76 ex1: $i > ( $i > $o ) > $o ).
% 3.01/1.76
% 3.01/1.76 thf(ex1,definition,
% 3.01/1.76 ( ex1
% 3.01/1.76 = ( ^ [A: $i,Xphi: $i > $o] :
% 3.01/1.76 ( singleton
% 3.01/1.76 @ ( dsetconstr @ A
% 3.01/1.76 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(ex1E1_type,type,
% 3.01/1.76 ex1E1: $o ).
% 3.01/1.76
% 3.01/1.76 thf(ex1E1,definition,
% 3.01/1.76 ( ex1E1
% 3.01/1.76 = ( ! [A: $i,Xphi: $i > $o] :
% 3.01/1.76 ( ( ex1 @ A
% 3.01/1.76 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.01/1.76 => ? [Xx: $i] :
% 3.01/1.76 ( ( in @ Xx @ A )
% 3.01/1.76 & ( Xphi @ Xx ) ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(ex1I_type,type,
% 3.01/1.76 ex1I: $o ).
% 3.01/1.76
% 3.01/1.76 thf(ex1I,definition,
% 3.01/1.76 ( ex1I
% 3.01/1.76 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.01/1.76 ( ( in @ Xx @ A )
% 3.01/1.76 => ( ( Xphi @ Xx )
% 3.01/1.76 => ( ! [Xy: $i] :
% 3.01/1.76 ( ( in @ Xy @ A )
% 3.01/1.76 => ( ( Xphi @ Xy )
% 3.01/1.76 => ( Xy = Xx ) ) )
% 3.01/1.76 => ( ex1 @ A
% 3.01/1.76 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(ex1I2_type,type,
% 3.01/1.76 ex1I2: $o ).
% 3.01/1.76
% 3.01/1.76 thf(ex1I2,definition,
% 3.01/1.76 ( ex1I2
% 3.01/1.76 = ( ! [A: $i,Xphi: $i > $o] :
% 3.01/1.76 ( ! [Xx: $i] :
% 3.01/1.76 ( ( in @ Xx @ A )
% 3.01/1.76 => ! [Xy: $i] :
% 3.01/1.76 ( ( in @ Xy @ A )
% 3.01/1.76 => ( ( Xphi @ Xx )
% 3.01/1.76 => ( ( Xphi @ Xy )
% 3.01/1.76 => ( Xx = Xy ) ) ) ) )
% 3.01/1.76 => ( ? [Xx: $i] :
% 3.01/1.76 ( ( in @ Xx @ A )
% 3.01/1.76 & ( Xphi @ Xx ) )
% 3.01/1.76 => ( ex1 @ A
% 3.01/1.76 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(singletonsuniq_type,type,
% 3.01/1.76 singletonsuniq: $o ).
% 3.01/1.76
% 3.01/1.76 thf(singletonsuniq,definition,
% 3.01/1.76 ( singletonsuniq
% 3.01/1.76 = ( ! [Xx: $i,Xy: $i] :
% 3.01/1.76 ( ( ( setadjoin @ Xx @ emptyset )
% 3.01/1.76 = ( setadjoin @ Xy @ emptyset ) )
% 3.01/1.76 => ( Xx = Xy ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(atmost1p_type,type,
% 3.01/1.76 atmost1p: $i > $o ).
% 3.01/1.76
% 3.01/1.76 thf(atleast2p_type,type,
% 3.01/1.76 atleast2p: $i > $o ).
% 3.01/1.76
% 3.01/1.76 thf(atmost2p_type,type,
% 3.01/1.76 atmost2p: $i > $o ).
% 3.01/1.76
% 3.01/1.76 thf(upairsetp_type,type,
% 3.01/1.76 upairsetp: $i > $o ).
% 3.01/1.76
% 3.01/1.76 thf(setukpairinjL1_type,type,
% 3.01/1.76 setukpairinjL1: $o ).
% 3.01/1.76
% 3.01/1.76 thf(setukpairinjL1,definition,
% 3.01/1.76 ( setukpairinjL1
% 3.01/1.76 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.01/1.76 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 3.01/1.76 => ( Xx = Xz ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(kfstsingleton_type,type,
% 3.01/1.76 kfstsingleton: $o ).
% 3.01/1.76
% 3.01/1.76 thf(kfstsingleton,definition,
% 3.01/1.76 ( kfstsingleton
% 3.01/1.76 = ( ! [Xu: $i] :
% 3.01/1.76 ( ( iskpair @ Xu )
% 3.01/1.76 => ( singleton
% 3.01/1.76 @ ( dsetconstr @ ( setunion @ Xu )
% 3.01/1.76 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(theprop_type,type,
% 3.01/1.76 theprop: $o ).
% 3.01/1.76
% 3.01/1.76 thf(theprop,definition,
% 3.01/1.76 ( theprop
% 3.01/1.76 = ( ! [X: $i] :
% 3.01/1.76 ( ( singleton @ X )
% 3.01/1.76 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(kfst_type,type,
% 3.01/1.76 kfst: $i > $i ).
% 3.01/1.76
% 3.01/1.76 thf(kfstpairEq_type,type,
% 3.01/1.76 kfstpairEq: $o ).
% 3.01/1.76
% 3.01/1.76 thf(kfstpairEq,definition,
% 3.01/1.76 ( kfstpairEq
% 3.01/1.76 = ( ! [Xx: $i,Xy: $i] :
% 3.01/1.76 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 3.01/1.76 = Xx ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(cartprodfstin_type,type,
% 3.01/1.76 cartprodfstin: $o ).
% 3.01/1.76
% 3.01/1.76 thf(cartprodfstin,definition,
% 3.01/1.76 ( cartprodfstin
% 3.01/1.76 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.01/1.76 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.01/1.76 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(setukpairinjL2_type,type,
% 3.01/1.76 setukpairinjL2: $o ).
% 3.01/1.76
% 3.01/1.76 thf(setukpairinjL2,definition,
% 3.01/1.76 ( setukpairinjL2
% 3.01/1.76 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.01/1.76 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.01/1.76 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.01/1.76 => ( Xx = Xz ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(setukpairinjL_type,type,
% 3.01/1.76 setukpairinjL: $o ).
% 3.01/1.76
% 3.01/1.76 thf(setukpairinjL,definition,
% 3.01/1.76 ( setukpairinjL
% 3.01/1.76 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.01/1.76 ( ( ( kpair @ Xx @ Xy )
% 3.01/1.76 = ( kpair @ Xz @ Xu ) )
% 3.01/1.76 => ( Xx = Xz ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(setukpairinjR11_type,type,
% 3.01/1.76 setukpairinjR11: $o ).
% 3.01/1.76
% 3.01/1.76 thf(setukpairinjR11,definition,
% 3.01/1.76 ( setukpairinjR11
% 3.01/1.76 = ( ! [Xx: $i,Xy: $i] :
% 3.01/1.76 ( ( Xx = Xy )
% 3.01/1.76 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.01/1.76 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(setukpairinjR12_type,type,
% 3.01/1.76 setukpairinjR12: $o ).
% 3.01/1.76
% 3.01/1.76 thf(setukpairinjR12,definition,
% 3.01/1.76 ( setukpairinjR12
% 3.01/1.76 = ( ! [Xx: $i,Xy: $i] :
% 3.01/1.76 ( ( Xx = Xy )
% 3.01/1.76 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.01/1.76 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(setukpairinjR1_type,type,
% 3.01/1.76 setukpairinjR1: $o ).
% 3.01/1.76
% 3.01/1.76 thf(setukpairinjR1,definition,
% 3.01/1.76 ( setukpairinjR1
% 3.01/1.76 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.01/1.76 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.01/1.76 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.01/1.76 => ( ( Xz = Xu )
% 3.01/1.76 => ( Xy = Xu ) ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(upairequniteq_type,type,
% 3.01/1.76 upairequniteq: $o ).
% 3.01/1.76
% 3.01/1.76 thf(upairequniteq,definition,
% 3.01/1.76 ( upairequniteq
% 3.01/1.76 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.01/1.76 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.01/1.76 = ( setadjoin @ Xz @ emptyset ) )
% 3.01/1.76 => ( Xx = Xy ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(setukpairinjR2_type,type,
% 3.01/1.76 setukpairinjR2: $o ).
% 3.01/1.76
% 3.01/1.76 thf(setukpairinjR2,definition,
% 3.01/1.76 ( setukpairinjR2
% 3.01/1.76 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.01/1.76 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.01/1.76 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.01/1.76 => ( Xy = Xu ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(setukpairinjR_type,type,
% 3.01/1.76 setukpairinjR: $o ).
% 3.01/1.76
% 3.01/1.76 thf(setukpairinjR,definition,
% 3.01/1.76 ( setukpairinjR
% 3.01/1.76 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.01/1.76 ( ( ( kpair @ Xx @ Xy )
% 3.01/1.76 = ( kpair @ Xz @ Xu ) )
% 3.01/1.76 => ( Xy = Xu ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(ksndsingleton_type,type,
% 3.01/1.76 ksndsingleton: $o ).
% 3.01/1.76
% 3.01/1.76 thf(ksndsingleton,definition,
% 3.01/1.76 ( ksndsingleton
% 3.01/1.76 = ( ! [Xu: $i] :
% 3.01/1.76 ( ( iskpair @ Xu )
% 3.01/1.76 => ( singleton
% 3.01/1.76 @ ( dsetconstr @ ( setunion @ Xu )
% 3.01/1.76 @ ^ [Xx: $i] :
% 3.01/1.76 ( Xu
% 3.01/1.76 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(ksnd_type,type,
% 3.01/1.76 ksnd: $i > $i ).
% 3.01/1.76
% 3.01/1.76 thf(ksndpairEq_type,type,
% 3.01/1.76 ksndpairEq: $o ).
% 3.01/1.76
% 3.01/1.76 thf(ksndpairEq,definition,
% 3.01/1.76 ( ksndpairEq
% 3.01/1.76 = ( ! [Xx: $i,Xy: $i] :
% 3.01/1.76 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 3.01/1.76 = Xy ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(kpairsurjEq_type,type,
% 3.01/1.76 kpairsurjEq: $o ).
% 3.01/1.76
% 3.01/1.76 thf(kpairsurjEq,definition,
% 3.01/1.76 ( kpairsurjEq
% 3.01/1.76 = ( ! [Xu: $i] :
% 3.01/1.76 ( ( iskpair @ Xu )
% 3.01/1.76 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 3.01/1.76 = Xu ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(cartprodsndin_type,type,
% 3.01/1.76 cartprodsndin: $o ).
% 3.01/1.76
% 3.01/1.76 thf(cartprodsndin,definition,
% 3.01/1.76 ( cartprodsndin
% 3.01/1.76 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.01/1.76 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.01/1.76 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(cartprodpairmemEL_type,type,
% 3.01/1.76 cartprodpairmemEL: $o ).
% 3.01/1.76
% 3.01/1.76 thf(cartprodpairmemEL,definition,
% 3.01/1.76 ( cartprodpairmemEL
% 3.01/1.76 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 3.01/1.76 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 3.01/1.76 => ( in @ Xx @ A ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(cartprodpairmemER_type,type,
% 3.01/1.76 cartprodpairmemER: $o ).
% 3.01/1.76
% 3.01/1.76 thf(cartprodpairmemER,definition,
% 3.01/1.76 ( cartprodpairmemER
% 3.01/1.76 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 3.01/1.76 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 3.01/1.76 => ( in @ Xy @ B ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(cartprodmempaircEq_type,type,
% 3.01/1.76 cartprodmempaircEq: $o ).
% 3.01/1.76
% 3.01/1.76 thf(cartprodmempaircEq,definition,
% 3.01/1.76 ( cartprodmempaircEq
% 3.01/1.76 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.01/1.76 ( ( in @ Xx @ A )
% 3.01/1.76 => ! [Xy: $i] :
% 3.01/1.76 ( ( in @ Xy @ B )
% 3.01/1.76 => ( ( kpair @ Xx @ Xy )
% 3.01/1.76 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(cartprodfstpairEq_type,type,
% 3.01/1.76 cartprodfstpairEq: $o ).
% 3.01/1.76
% 3.01/1.76 thf(cartprodfstpairEq,definition,
% 3.01/1.76 ( cartprodfstpairEq
% 3.01/1.76 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.01/1.76 ( ( in @ Xx @ A )
% 3.01/1.76 => ! [Xy: $i] :
% 3.01/1.76 ( ( in @ Xy @ B )
% 3.01/1.76 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 3.01/1.76 = Xx ) ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(cartprodsndpairEq_type,type,
% 3.01/1.76 cartprodsndpairEq: $o ).
% 3.01/1.76
% 3.01/1.76 thf(cartprodsndpairEq,definition,
% 3.01/1.76 ( cartprodsndpairEq
% 3.01/1.76 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.01/1.76 ( ( in @ Xx @ A )
% 3.01/1.76 => ! [Xy: $i] :
% 3.01/1.76 ( ( in @ Xy @ B )
% 3.01/1.76 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 3.01/1.76 = Xy ) ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(cartprodpairsurjEq_type,type,
% 3.01/1.76 cartprodpairsurjEq: $o ).
% 3.01/1.76
% 3.01/1.76 thf(cartprodpairsurjEq,definition,
% 3.01/1.76 ( cartprodpairsurjEq
% 3.01/1.76 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.01/1.76 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.01/1.76 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 3.01/1.76 = Xu ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(breln_type,type,
% 3.01/1.76 breln: $i > $i > $i > $o ).
% 3.01/1.76
% 3.01/1.76 thf(breln,definition,
% 3.01/1.76 ( breln
% 3.01/1.76 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(dpsetconstr_type,type,
% 3.01/1.76 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 3.01/1.76
% 3.01/1.76 thf(dpsetconstr,definition,
% 3.01/1.76 ( dpsetconstr
% 3.01/1.76 = ( ^ [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.01/1.76 ( dsetconstr @ ( cartprod @ A @ B )
% 3.01/1.76 @ ^ [Xu: $i] :
% 3.01/1.76 ? [Xx: $i] :
% 3.01/1.76 ( ( in @ Xx @ A )
% 3.01/1.76 & ? [Xy: $i] :
% 3.01/1.76 ( ( in @ Xy @ B )
% 3.01/1.76 & ( Xphi @ Xx @ Xy )
% 3.01/1.76 & ( Xu
% 3.01/1.76 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(dpsetconstrI_type,type,
% 3.01/1.76 dpsetconstrI: $o ).
% 3.01/1.76
% 3.01/1.76 thf(dpsetconstrI,definition,
% 3.01/1.76 ( dpsetconstrI
% 3.01/1.76 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 3.01/1.76 ( ( in @ Xx @ A )
% 3.01/1.76 => ! [Xy: $i] :
% 3.01/1.76 ( ( in @ Xy @ B )
% 3.01/1.76 => ( ( Xphi @ Xx @ Xy )
% 3.01/1.76 => ( in @ ( kpair @ Xx @ Xy )
% 3.01/1.76 @ ( dpsetconstr @ A @ B
% 3.01/1.76 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(dpsetconstrSub_type,type,
% 3.01/1.76 dpsetconstrSub: $o ).
% 3.01/1.76
% 3.01/1.76 thf(dpsetconstrSub,definition,
% 3.01/1.76 ( dpsetconstrSub
% 3.01/1.76 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.01/1.76 ( subset
% 3.01/1.76 @ ( dpsetconstr @ A @ B
% 3.01/1.76 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 3.01/1.76 @ ( cartprod @ A @ B ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(setOfPairsIsBReln_type,type,
% 3.01/1.76 setOfPairsIsBReln: $o ).
% 3.01/1.76
% 3.01/1.76 thf(setOfPairsIsBReln,definition,
% 3.01/1.76 ( setOfPairsIsBReln
% 3.01/1.76 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.01/1.76 ( breln @ A @ B
% 3.01/1.76 @ ( dpsetconstr @ A @ B
% 3.01/1.76 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 3.01/1.76
% 3.01/1.76 thf(dpsetconstrERa,conjecture,
% 3.01/1.76 ( setextAx
% 3.01/1.76 => ( emptysetAx
% 3.01/1.76 => ( setadjoinAx
% 3.01/1.76 => ( powersetAx
% 3.01/1.76 => ( setunionAx
% 3.01/1.76 => ( omega0Ax
% 3.01/1.76 => ( omegaSAx
% 3.01/1.76 => ( omegaIndAx
% 3.01/1.76 => ( replAx
% 3.01/1.76 => ( foundationAx
% 3.01/1.76 => ( wellorderingAx
% 3.01/1.76 => ( descrp
% 3.01/1.76 => ( dsetconstrI
% 3.01/1.76 => ( dsetconstrEL
% 3.01/1.76 => ( dsetconstrER
% 3.01/1.76 => ( exuE1
% 3.01/1.76 => ( prop2setE
% 3.01/1.76 => ( emptysetE
% 3.01/1.76 => ( emptysetimpfalse
% 3.01/1.76 => ( notinemptyset
% 3.01/1.76 => ( exuE3e
% 3.01/1.76 => ( setext
% 3.01/1.76 => ( emptyI
% 3.01/1.76 => ( noeltsimpempty
% 3.01/1.76 => ( setbeta
% 3.01/1.76 => ( nonemptyE1
% 3.01/1.76 => ( nonemptyI
% 3.01/1.76 => ( nonemptyI1
% 3.01/1.76 => ( setadjoinIL
% 3.01/1.76 => ( emptyinunitempty
% 3.01/1.76 => ( setadjoinIR
% 3.01/1.76 => ( setadjoinE
% 3.01/1.76 => ( setadjoinOr
% 3.01/1.76 => ( setoftrueEq
% 3.01/1.76 => ( powersetI
% 3.01/1.76 => ( emptyinPowerset
% 3.01/1.76 => ( emptyInPowerset
% 3.01/1.76 => ( powersetE
% 3.01/1.76 => ( setunionI
% 3.01/1.76 => ( setunionE
% 3.01/1.76 => ( subPowSU
% 3.01/1.76 => ( exuE2
% 3.01/1.76 => ( nonemptyImpWitness
% 3.01/1.76 => ( uniqinunit
% 3.01/1.76 => ( notinsingleton
% 3.01/1.76 => ( eqinunit
% 3.01/1.76 => ( singletonsswitch
% 3.01/1.76 => ( upairsetE
% 3.01/1.76 => ( upairsetIL
% 3.01/1.76 => ( upairsetIR
% 3.01/1.76 => ( emptyE1
% 3.01/1.76 => ( vacuousDall
% 3.01/1.76 => ( quantDeMorgan1
% 3.01/1.76 => ( quantDeMorgan2
% 3.01/1.76 => ( quantDeMorgan3
% 3.01/1.76 => ( quantDeMorgan4
% 3.01/1.76 => ( prop2setI
% 3.01/1.76 => ( prop2set2propI
% 3.01/1.76 => ( notdexE
% 3.01/1.76 => ( notdallE
% 3.01/1.76 => ( exuI1
% 3.01/1.76 => ( exuI3
% 3.01/1.76 => ( exuI2
% 3.01/1.76 => ( inCongP
% 3.01/1.76 => ( in__Cong
% 3.01/1.76 => ( exuE3u
% 3.01/1.76 => ( exu__Cong
% 3.01/1.76 => ( emptyset__Cong
% 3.01/1.76 => ( setadjoin__Cong
% 3.01/1.76 => ( powerset__Cong
% 3.01/1.76 => ( setunion__Cong
% 3.01/1.76 => ( omega__Cong
% 3.01/1.76 => ( exuEu
% 3.01/1.76 => ( descr__Cong
% 3.01/1.76 => ( dsetconstr__Cong
% 3.01/1.76 => ( subsetI1
% 3.01/1.76 => ( eqimpsubset2
% 3.01/1.76 => ( eqimpsubset1
% 3.01/1.76 => ( subsetI2
% 3.01/1.76 => ( emptysetsubset
% 3.01/1.76 => ( subsetE
% 3.01/1.76 => ( subsetE2
% 3.01/1.76 => ( notsubsetI
% 3.01/1.76 => ( notequalI1
% 3.01/1.76 => ( notequalI2
% 3.01/1.76 => ( subsetRefl
% 3.01/1.76 => ( subsetTrans
% 3.01/1.76 => ( setadjoinSub
% 3.01/1.76 => ( setadjoinSub2
% 3.01/1.76 => ( subset2powerset
% 3.01/1.76 => ( setextsub
% 3.01/1.76 => ( subsetemptysetimpeq
% 3.01/1.76 => ( powersetI1
% 3.01/1.76 => ( powersetE1
% 3.01/1.76 => ( inPowerset
% 3.01/1.76 => ( powersetsubset
% 3.01/1.76 => ( sepInPowerset
% 3.01/1.76 => ( sepSubset
% 3.01/1.76 => ( binunionIL
% 3.01/1.76 => ( upairset2IR
% 3.01/1.76 => ( binunionIR
% 3.01/1.76 => ( binunionEcases
% 3.01/1.76 => ( binunionE
% 3.01/1.76 => ( binunionLsub
% 3.01/1.76 => ( binunionRsub
% 3.01/1.76 => ( binintersectI
% 3.01/1.76 => ( binintersectSubset5
% 3.01/1.76 => ( binintersectEL
% 3.01/1.76 => ( binintersectLsub
% 3.01/1.76 => ( binintersectSubset2
% 3.01/1.76 => ( binintersectSubset3
% 3.01/1.76 => ( binintersectER
% 3.01/1.76 => ( disjointsetsI1
% 3.01/1.76 => ( binintersectRsub
% 3.01/1.76 => ( binintersectSubset4
% 3.01/1.76 => ( binintersectSubset1
% 3.01/1.76 => ( bs114d
% 3.01/1.76 => ( setminusI
% 3.01/1.76 => ( setminusEL
% 3.01/1.76 => ( setminusER
% 3.01/1.76 => ( setminusSubset2
% 3.01/1.76 => ( setminusERneg
% 3.01/1.76 => ( setminusELneg
% 3.01/1.76 => ( setminusILneg
% 3.01/1.76 => ( setminusIRneg
% 3.01/1.76 => ( setminusLsub
% 3.01/1.76 => ( setminusSubset1
% 3.01/1.76 => ( symdiffE
% 3.01/1.76 => ( symdiffI1
% 3.01/1.76 => ( symdiffI2
% 3.01/1.76 => ( symdiffIneg1
% 3.01/1.76 => ( symdiffIneg2
% 3.01/1.76 => ( secondinupair
% 3.01/1.76 => ( setukpairIL
% 3.01/1.76 => ( setukpairIR
% 3.01/1.76 => ( kpairiskpair
% 3.01/1.76 => ( kpairp
% 3.01/1.76 => ( singletonsubset
% 3.01/1.76 => ( singletoninpowerset
% 3.01/1.76 => ( singletoninpowunion
% 3.01/1.76 => ( upairset2E
% 3.01/1.76 => ( upairsubunion
% 3.01/1.76 => ( upairinpowunion
% 3.01/1.76 => ( ubforcartprodlem1
% 3.01/1.76 => ( ubforcartprodlem2
% 3.01/1.76 => ( ubforcartprodlem3
% 3.01/1.76 => ( cartprodpairin
% 3.01/1.76 => ( cartprodmempair1
% 3.01/1.76 => ( cartprodmempair
% 3.01/1.76 => ( setunionE2
% 3.01/1.76 => ( setunionsingleton1
% 3.01/1.76 => ( setunionsingleton2
% 3.01/1.76 => ( setunionsingleton
% 3.01/1.76 => ( singletonprop
% 3.01/1.76 => ( ex1E1
% 3.01/1.76 => ( ex1I
% 3.01/1.76 => ( ex1I2
% 3.01/1.76 => ( singletonsuniq
% 3.01/1.76 => ( setukpairinjL1
% 3.01/1.76 => ( kfstsingleton
% 3.01/1.76 => ( theprop
% 3.01/1.76 => ( kfstpairEq
% 3.01/1.76 => ( cartprodfstin
% 3.01/1.76 => ( setukpairinjL2
% 3.01/1.76 => ( setukpairinjL
% 3.01/1.76 => ( setukpairinjR11
% 3.01/1.76 => ( setukpairinjR12
% 3.01/1.76 => ( setukpairinjR1
% 3.01/1.76 => ( upairequniteq
% 3.01/1.76 => ( setukpairinjR2
% 3.01/1.76 => ( setukpairinjR
% 3.01/1.76 => ( ksndsingleton
% 3.01/1.76 => ( ksndpairEq
% 3.01/1.76 => ( kpairsurjEq
% 3.01/1.76 => ( cartprodsndin
% 3.01/1.76 => ( cartprodpairmemEL
% 3.01/1.76 => ( cartprodpairmemER
% 3.01/1.76 => ( cartprodmempaircEq
% 3.01/1.76 => ( cartprodfstpairEq
% 3.01/1.76 => ( cartprodsndpairEq
% 3.01/1.76 => ( cartprodpairsurjEq
% 3.01/1.76 => ( dpsetconstrI
% 3.01/1.76 => ( dpsetconstrSub
% 3.01/1.76 => ( setOfPairsIsBReln
% 3.01/1.76 => ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 3.01/1.76 ( ( in @ Xx @ A )
% 3.01/1.76 => ! [Xy: $i] :
% 3.01/1.76 ( ( in @ Xy @ B )
% 3.01/1.76 => ( ( in @ ( kpair @ Xx @ Xy )
% 3.01/1.76 @ ( dpsetconstr @ A @ B
% 3.01/1.76 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.01/1.76 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.01/1.76 ------------------------
% 3.01/1.79 % (30943)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_30834 for (2999ds/27Mi)
% 3.01/1.79 % (30941)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30834 for (2999ds/183Mi)
% 3.01/1.79 % (30947)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30834 for (2999ds/18Mi)
% 3.01/1.79 % (30944)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30834 for (2999ds/2Mi)
% 3.01/1.79 % (30946)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_30834 for (2999ds/275Mi)
% 3.01/1.79 % (30945)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_30834 for (2999ds/2Mi)
% 3.01/1.79 % (30942)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_30834 for (2999ds/4Mi)
% 3.01/1.79 % (30944)Instruction limit reached!
% 3.01/1.79 % (30944)------------------------------
% 3.01/1.79 % (30944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.01/1.79 % (30944)Termination reason: Unknown
% 3.01/1.79 % (30944)Termination phase: shuffling
% 3.01/1.79
% 3.01/1.79 % (30944)Memory used [KB]: 1407
% 3.01/1.79 % (30944)Time elapsed: 0.004 s
% 3.01/1.79 % (30944)Instructions burned: 3 (million)
% 3.01/1.79 % (30944)------------------------------
% 3.01/1.79 % (30944)------------------------------
% 3.01/1.79 % (30945)Instruction limit reached!
% 3.01/1.79 % (30945)------------------------------
% 3.01/1.79 % (30945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.01/1.79 % (30945)Termination reason: Unknown
% 3.01/1.79 % (30945)Termination phase: shuffling
% 3.01/1.79
% 3.01/1.79 % (30945)Memory used [KB]: 1279
% 3.01/1.79 % (30945)Time elapsed: 0.004 s
% 3.01/1.79 % (30945)Instructions burned: 4 (million)
% 3.01/1.79 % (30945)------------------------------
% 3.01/1.79 % (30945)------------------------------
% 3.01/1.79 % (30942)Instruction limit reached!
% 3.01/1.79 % (30942)------------------------------
% 3.01/1.79 % (30942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.01/1.79 % (30942)Termination reason: Unknown
% 3.01/1.79 % (30942)Termination phase: shuffling
% 3.01/1.79
% 3.01/1.79 % (30942)Memory used [KB]: 1407
% 3.01/1.79 % (30942)Time elapsed: 0.004 s
% 3.01/1.79 % (30942)Instructions burned: 5 (million)
% 3.01/1.79 % (30942)------------------------------
% 3.01/1.79 % (30942)------------------------------
% 3.08/1.80 % (30947)Instruction limit reached!
% 3.08/1.80 % (30947)------------------------------
% 3.08/1.80 % (30947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.80 % (30947)Termination reason: Unknown
% 3.08/1.80 % (30947)Termination phase: Property scanning
% 3.08/1.80
% 3.08/1.80 % (30947)Memory used [KB]: 1663
% 3.08/1.80 % (30947)Time elapsed: 0.012 s
% 3.08/1.80 % (30947)Instructions burned: 18 (million)
% 3.08/1.80 % (30947)------------------------------
% 3.08/1.80 % (30947)------------------------------
% 3.08/1.80 % (30943)Instruction limit reached!
% 3.08/1.80 % (30943)------------------------------
% 3.08/1.80 % (30943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.80 % (30943)Termination reason: Unknown
% 3.08/1.80 % (30943)Termination phase: shuffling
% 3.08/1.80
% 3.08/1.80 % (30943)Memory used [KB]: 1918
% 3.08/1.80 % (30943)Time elapsed: 0.014 s
% 3.08/1.80 % (30943)Instructions burned: 27 (million)
% 3.08/1.80 % (30943)------------------------------
% 3.08/1.80 % (30943)------------------------------
% 3.08/1.81 % (30950)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_30834 for (2999ds/15Mi)
% 3.08/1.81 % (30948)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30834 for (2999ds/3Mi)
% 3.08/1.81 % (30949)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_30834 for (2999ds/37Mi)
% 3.08/1.81 % (30948)Instruction limit reached!
% 3.08/1.81 % (30948)------------------------------
% 3.08/1.81 % (30948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.81 % (30948)Termination reason: Unknown
% 3.08/1.81 % (30948)Termination phase: shuffling
% 3.08/1.81
% 3.08/1.81 % (30948)Memory used [KB]: 1407
% 3.08/1.81 % (30948)Time elapsed: 0.004 s
% 3.08/1.81 % (30948)Instructions burned: 4 (million)
% 3.08/1.81 % (30948)------------------------------
% 3.08/1.81 % (30948)------------------------------
% 3.08/1.81 % (30951)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_30834 for (2999ds/3Mi)
% 3.08/1.81 % (30950)Instruction limit reached!
% 3.08/1.81 % (30950)------------------------------
% 3.08/1.81 % (30950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.81 % (30950)Termination reason: Unknown
% 3.08/1.81 % (30950)Termination phase: shuffling
% 3.08/1.81
% 3.08/1.81 % (30950)Memory used [KB]: 1663
% 3.08/1.81 % (30950)Time elapsed: 0.010 s
% 3.08/1.81 % (30950)Instructions burned: 16 (million)
% 3.08/1.81 % (30950)------------------------------
% 3.08/1.81 % (30950)------------------------------
% 3.08/1.82 % (30951)Instruction limit reached!
% 3.08/1.82 % (30951)------------------------------
% 3.08/1.82 % (30951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.82 % (30951)Termination reason: Unknown
% 3.08/1.82 % (30951)Termination phase: shuffling
% 3.08/1.82
% 3.08/1.82 % (30951)Memory used [KB]: 1279
% 3.08/1.82 % (30951)Time elapsed: 0.003 s
% 3.08/1.82 % (30951)Instructions burned: 3 (million)
% 3.08/1.82 % (30951)------------------------------
% 3.08/1.82 % (30951)------------------------------
% 3.08/1.82 % (30952)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_30834 for (2999ds/1041Mi)
% 3.08/1.82 % (30949)Instruction limit reached!
% 3.08/1.82 % (30949)------------------------------
% 3.08/1.82 % (30949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.82 % (30949)Termination reason: Unknown
% 3.08/1.82 % (30949)Termination phase: Property scanning
% 3.08/1.82
% 3.08/1.82 % (30949)Memory used [KB]: 1918
% 3.08/1.82 % (30949)Time elapsed: 0.019 s
% 3.08/1.82 % (30949)Instructions burned: 38 (million)
% 3.08/1.82 % (30949)------------------------------
% 3.08/1.82 % (30949)------------------------------
% 3.08/1.83 % (30953)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_30834 for (2999ds/7Mi)
% 3.08/1.83 % (30953)Instruction limit reached!
% 3.08/1.83 % (30953)------------------------------
% 3.08/1.83 % (30953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.83 % (30953)Termination reason: Unknown
% 3.08/1.83 % (30953)Termination phase: shuffling
% 3.08/1.83
% 3.08/1.83 % (30953)Memory used [KB]: 1407
% 3.08/1.83 % (30953)Time elapsed: 0.006 s
% 3.08/1.83 % (30953)Instructions burned: 9 (million)
% 3.08/1.83 % (30953)------------------------------
% 3.08/1.83 % (30953)------------------------------
% 3.08/1.83 % (30954)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_30834 for (2999ds/16Mi)
% 3.08/1.83 % (30955)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_30834 for (2999ds/3Mi)
% 3.08/1.83 % (30955)Instruction limit reached!
% 3.08/1.83 % (30955)------------------------------
% 3.08/1.83 % (30955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.83 % (30955)Termination reason: Unknown
% 3.08/1.83 % (30955)Termination phase: shuffling
% 3.08/1.83
% 3.08/1.83 % (30955)Memory used [KB]: 1279
% 3.08/1.83 % (30955)Time elapsed: 0.003 s
% 3.08/1.83 % (30955)Instructions burned: 3 (million)
% 3.08/1.83 % (30955)------------------------------
% 3.08/1.83 % (30955)------------------------------
% 3.08/1.84 % (30954)Instruction limit reached!
% 3.08/1.84 % (30954)------------------------------
% 3.08/1.84 % (30954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.84 % (30954)Termination reason: Unknown
% 3.08/1.84 % (30954)Termination phase: shuffling
% 3.08/1.84
% 3.08/1.84 % (30954)Memory used [KB]: 1663
% 3.08/1.84 % (30954)Time elapsed: 0.009 s
% 3.08/1.84 % (30954)Instructions burned: 16 (million)
% 3.08/1.84 % (30954)------------------------------
% 3.08/1.84 % (30954)------------------------------
% 3.08/1.84 % (30956)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_30834 for (2999ds/3Mi)
% 3.08/1.84 % (30956)Instruction limit reached!
% 3.08/1.84 % (30956)------------------------------
% 3.08/1.84 % (30956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.84 % (30956)Termination reason: Unknown
% 3.08/1.84 % (30956)Termination phase: shuffling
% 3.08/1.84
% 3.08/1.84 % (30956)Memory used [KB]: 1279
% 3.08/1.84 % (30956)Time elapsed: 0.003 s
% 3.08/1.84 % (30956)Instructions burned: 3 (million)
% 3.08/1.84 % (30956)------------------------------
% 3.08/1.84 % (30956)------------------------------
% 3.08/1.85 % (30957)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_30834 for (2999ds/7Mi)
% 3.08/1.85 % (30957)Instruction limit reached!
% 3.08/1.85 % (30957)------------------------------
% 3.08/1.85 % (30957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.85 % (30957)Termination reason: Unknown
% 3.08/1.85 % (30957)Termination phase: shuffling
% 3.08/1.85
% 3.08/1.85 % (30958)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_30834 for (2999ds/3Mi)
% 3.08/1.85 % (30957)Memory used [KB]: 1407
% 3.08/1.85 % (30957)Time elapsed: 0.005 s
% 3.08/1.85 % (30957)Instructions burned: 7 (million)
% 3.08/1.85 % (30957)------------------------------
% 3.08/1.85 % (30957)------------------------------
% 3.08/1.85 % (30958)Instruction limit reached!
% 3.08/1.85 % (30958)------------------------------
% 3.08/1.85 % (30958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.85 % (30958)Termination reason: Unknown
% 3.08/1.85 % (30958)Termination phase: shuffling
% 3.08/1.85
% 3.08/1.85 % (30958)Memory used [KB]: 1279
% 3.08/1.85 % (30958)Time elapsed: 0.003 s
% 3.08/1.85 % (30958)Instructions burned: 3 (million)
% 3.08/1.85 % (30958)------------------------------
% 3.08/1.85 % (30958)------------------------------
% 3.08/1.85 % (30959)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_30834 for (2999ds/4Mi)
% 3.08/1.86 % (30959)Instruction limit reached!
% 3.08/1.86 % (30959)------------------------------
% 3.08/1.86 % (30959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.86 % (30959)Termination reason: Unknown
% 3.08/1.86 % (30959)Termination phase: shuffling
% 3.08/1.86
% 3.08/1.86 % (30959)Memory used [KB]: 1407
% 3.08/1.86 % (30959)Time elapsed: 0.004 s
% 3.08/1.86 % (30959)Instructions burned: 5 (million)
% 3.08/1.86 % (30959)------------------------------
% 3.08/1.86 % (30959)------------------------------
% 3.08/1.86 % (30960)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_30834 for (2999ds/18Mi)
% 3.08/1.87 % (30961)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_30834 for (2999ds/710Mi)
% 3.08/1.87 % (30960)Instruction limit reached!
% 3.08/1.87 % (30960)------------------------------
% 3.08/1.87 % (30960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.87 % (30960)Termination reason: Unknown
% 3.08/1.87 % (30960)Termination phase: shuffling
% 3.08/1.87
% 3.08/1.87 % (30960)Memory used [KB]: 1663
% 3.08/1.87 % (30960)Time elapsed: 0.010 s
% 3.08/1.87 % (30960)Instructions burned: 18 (million)
% 3.08/1.87 % (30962)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_30834 for (2999ds/6Mi)
% 3.08/1.87 % (30960)------------------------------
% 3.08/1.87 % (30960)------------------------------
% 3.08/1.87 % (30962)Instruction limit reached!
% 3.08/1.87 % (30962)------------------------------
% 3.08/1.87 % (30962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.87 % (30962)Termination reason: Unknown
% 3.08/1.87 % (30962)Termination phase: shuffling
% 3.08/1.87
% 3.08/1.87 % (30962)Memory used [KB]: 1407
% 3.08/1.87 % (30962)Time elapsed: 0.005 s
% 3.08/1.87 % (30962)Instructions burned: 6 (million)
% 3.08/1.87 % (30962)------------------------------
% 3.08/1.87 % (30962)------------------------------
% 3.08/1.87 % (30941)Instruction limit reached!
% 3.08/1.87 % (30941)------------------------------
% 3.08/1.87 % (30941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.87 % (30941)Termination reason: Unknown
% 3.08/1.87 % (30941)Termination phase: Saturation
% 3.08/1.87
% 3.08/1.87 % (30941)Memory used [KB]: 7419
% 3.08/1.87 % (30941)Time elapsed: 0.084 s
% 3.08/1.87 % (30941)Instructions burned: 184 (million)
% 3.08/1.87 % (30941)------------------------------
% 3.08/1.87 % (30941)------------------------------
% 3.08/1.87 % (30963)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_30834 for (2999ds/902Mi)
% 3.08/1.88 % (30964)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_30834 for (2999ds/21Mi)
% 3.08/1.88 % (30965)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_30834 for (2998ds/5Mi)
% 3.08/1.89 % (30966)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_30834 for (2998ds/6Mi)
% 3.08/1.89 % (30965)Instruction limit reached!
% 3.08/1.89 % (30965)------------------------------
% 3.08/1.89 % (30965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.89 % (30965)Termination reason: Unknown
% 3.08/1.89 % (30965)Termination phase: shuffling
% 3.08/1.89
% 3.08/1.89 % (30965)Memory used [KB]: 1407
% 3.08/1.89 % (30965)Time elapsed: 0.004 s
% 3.08/1.89 % (30965)Instructions burned: 5 (million)
% 3.08/1.89 % (30965)------------------------------
% 3.08/1.89 % (30965)------------------------------
% 3.08/1.89 % (30966)Instruction limit reached!
% 3.08/1.89 % (30966)------------------------------
% 3.08/1.89 % (30966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.89 % (30966)Termination reason: Unknown
% 3.08/1.89 % (30966)Termination phase: shuffling
% 3.08/1.89
% 3.08/1.89 % (30966)Memory used [KB]: 1407
% 3.08/1.89 % (30966)Time elapsed: 0.005 s
% 3.08/1.89 % (30966)Instructions burned: 7 (million)
% 3.08/1.89 % (30966)------------------------------
% 3.08/1.89 % (30966)------------------------------
% 3.08/1.89 % (30964)Instruction limit reached!
% 3.08/1.89 % (30964)------------------------------
% 3.08/1.89 % (30964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.89 % (30964)Termination reason: Unknown
% 3.08/1.89 % (30964)Termination phase: shuffling
% 3.08/1.89
% 3.08/1.89 % (30964)Memory used [KB]: 1791
% 3.08/1.89 % (30964)Time elapsed: 0.012 s
% 3.08/1.89 % (30964)Instructions burned: 21 (million)
% 3.08/1.89 % (30964)------------------------------
% 3.08/1.89 % (30964)------------------------------
% 3.08/1.90 % (30967)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_30834 for (2998ds/377Mi)
% 3.08/1.91 % (30968)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_30834 for (2998ds/779Mi)
% 3.08/1.91 % (30969)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_30834 for (2998ds/19Mi)
% 3.08/1.92 % (30969)Instruction limit reached!
% 3.08/1.92 % (30969)------------------------------
% 3.08/1.92 % (30969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.92 % (30969)Termination reason: Unknown
% 3.08/1.92 % (30969)Termination phase: shuffling
% 3.08/1.92
% 3.08/1.92 % (30969)Memory used [KB]: 1791
% 3.08/1.92 % (30969)Time elapsed: 0.011 s
% 3.08/1.92 % (30969)Instructions burned: 20 (million)
% 3.08/1.92 % (30969)------------------------------
% 3.08/1.92 % (30969)------------------------------
% 3.08/1.92 % (30946)Instruction limit reached!
% 3.08/1.92 % (30946)------------------------------
% 3.08/1.92 % (30946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.92 % (30946)Termination reason: Unknown
% 3.08/1.92 % (30946)Termination phase: Saturation
% 3.08/1.92
% 3.08/1.92 % (30946)Memory used [KB]: 8443
% 3.08/1.92 % (30946)Time elapsed: 0.138 s
% 3.08/1.92 % (30946)Instructions burned: 276 (million)
% 3.08/1.92 % (30946)------------------------------
% 3.08/1.92 % (30946)------------------------------
% 3.08/1.94 % (30970)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_30834 for (2998ds/879Mi)
% 3.08/1.94 % (30971)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_30834 for (2998ds/17Mi)
% 3.08/1.95 % (30971)Instruction limit reached!
% 3.08/1.95 % (30971)------------------------------
% 3.08/1.95 % (30971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.95 % (30971)Termination reason: Unknown
% 3.08/1.95 % (30971)Termination phase: shuffling
% 3.08/1.95
% 3.08/1.95 % (30971)Memory used [KB]: 1663
% 3.08/1.95 % (30971)Time elapsed: 0.010 s
% 3.08/1.95 % (30971)Instructions burned: 17 (million)
% 3.08/1.95 % (30971)------------------------------
% 3.08/1.95 % (30971)------------------------------
% 3.08/1.97 % (30972)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_30834 for (2998ds/3Mi)
% 3.08/1.97 % (30972)Instruction limit reached!
% 3.08/1.97 % (30972)------------------------------
% 3.08/1.97 % (30972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.97 % (30972)Termination reason: Unknown
% 3.08/1.97 % (30972)Termination phase: shuffling
% 3.08/1.97
% 3.08/1.97 % (30972)Memory used [KB]: 1279
% 3.08/1.97 % (30972)Time elapsed: 0.004 s
% 3.08/1.97 % (30972)Instructions burned: 3 (million)
% 3.08/1.97 % (30972)------------------------------
% 3.08/1.97 % (30972)------------------------------
% 3.08/1.98 % (30963)Refutation not found, incomplete strategy
% 3.08/1.98 % (30963)------------------------------
% 3.08/1.98 % (30963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/1.98 % (30963)Termination reason: Refutation not found, incomplete strategy
% 3.08/1.98
% 3.08/1.98
% 3.08/1.98 % (30963)Memory used [KB]: 8315
% 3.08/1.98 % (30963)Time elapsed: 0.106 s
% 3.08/1.98 % (30963)Instructions burned: 210 (million)
% 3.08/1.98 % (30963)------------------------------
% 3.08/1.98 % (30963)------------------------------
% 3.08/1.98 % (30973)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_30834 for (2998ds/30Mi)
% 3.08/2.00 % (30974)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_30834 for (2997ds/127Mi)
% 3.08/2.00 % (30973)Instruction limit reached!
% 3.08/2.00 % (30973)------------------------------
% 3.08/2.00 % (30973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.08/2.00 % (30973)Termination reason: Unknown
% 3.08/2.00 % (30973)Termination phase: Property scanning
% 3.08/2.00
% 3.08/2.00 % (30973)Memory used [KB]: 1918
% 3.08/2.00 % (30973)Time elapsed: 0.016 s
% 3.08/2.00 % (30973)Instructions burned: 30 (million)
% 3.08/2.00 % (30973)------------------------------
% 3.08/2.00 % (30973)------------------------------
% 3.08/2.02 % (30976)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_30834 for (2997ds/100Mi)
% 4.77/2.05 % (30974)Instruction limit reached!
% 4.77/2.05 % (30974)------------------------------
% 4.77/2.05 % (30974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.77/2.05 % (30974)Termination reason: Unknown
% 4.77/2.05 % (30974)Termination phase: Saturation
% 4.77/2.05
% 4.77/2.05 % (30974)Memory used [KB]: 6908
% 4.77/2.05 % (30974)Time elapsed: 0.059 s
% 4.77/2.05 % (30974)Instructions burned: 128 (million)
% 4.77/2.05 % (30974)------------------------------
% 4.77/2.05 % (30974)------------------------------
% 4.77/2.06 % (30976)Instruction limit reached!
% 4.77/2.06 % (30976)------------------------------
% 4.77/2.06 % (30976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.77/2.06 % (30976)Termination reason: Unknown
% 4.77/2.06 % (30976)Termination phase: Saturation
% 4.77/2.06
% 4.77/2.06 % (30976)Memory used [KB]: 6524
% 4.77/2.06 % (30976)Time elapsed: 0.047 s
% 4.77/2.06 % (30976)Instructions burned: 100 (million)
% 4.77/2.06 % (30976)------------------------------
% 4.77/2.06 % (30976)------------------------------
% 4.77/2.07 % (30977)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_30834 for (2997ds/3Mi)
% 4.77/2.07 % (30977)Instruction limit reached!
% 4.77/2.07 % (30977)------------------------------
% 4.77/2.07 % (30977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.77/2.07 % (30977)Termination reason: Unknown
% 4.77/2.07 % (30977)Termination phase: shuffling
% 4.77/2.07
% 4.77/2.07 % (30977)Memory used [KB]: 1279
% 4.77/2.07 % (30977)Time elapsed: 0.003 s
% 4.77/2.07 % (30977)Instructions burned: 3 (million)
% 4.77/2.07 % (30977)------------------------------
% 4.77/2.07 % (30977)------------------------------
% 4.77/2.08 % (30978)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_30834 for (2997ds/20Mi)
% 4.77/2.08 % (30967)Instruction limit reached!
% 4.77/2.08 % (30967)------------------------------
% 4.77/2.08 % (30967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.77/2.08 % (30967)Termination reason: Unknown
% 4.77/2.08 % (30967)Termination phase: Saturation
% 4.77/2.09
% 4.77/2.09 % (30967)Memory used [KB]: 8187
% 4.77/2.09 % (30967)Time elapsed: 0.183 s
% 4.77/2.09 % (30967)Instructions burned: 378 (million)
% 4.77/2.09 % (30967)------------------------------
% 4.77/2.09 % (30967)------------------------------
% 4.77/2.09 % (30978)Instruction limit reached!
% 4.77/2.09 % (30978)------------------------------
% 4.77/2.09 % (30978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.77/2.09 % (30978)Termination reason: Unknown
% 4.77/2.09 % (30978)Termination phase: Property scanning
% 4.77/2.09
% 4.77/2.09 % (30978)Memory used [KB]: 1663
% 4.77/2.09 % (30978)Time elapsed: 0.012 s
% 4.77/2.09 % (30978)Instructions burned: 20 (million)
% 4.77/2.09 % (30978)------------------------------
% 4.77/2.09 % (30978)------------------------------
% 4.77/2.09 % (30979)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_30834 for (2997ds/86Mi)
% 4.77/2.10 % (30980)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_30834 for (2996ds/107Mi)
% 4.77/2.10 % (30981)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_30834 for (2996ds/39Mi)
% 4.77/2.12 % (30981)Instruction limit reached!
% 4.77/2.12 % (30981)------------------------------
% 4.77/2.12 % (30981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.77/2.12 % (30981)Termination reason: Unknown
% 4.77/2.12 % (30981)Termination phase: Property scanning
% 4.77/2.12
% 4.77/2.12 % (30981)Memory used [KB]: 1918
% 4.77/2.12 % (30981)Time elapsed: 0.019 s
% 4.77/2.12 % (30981)Instructions burned: 39 (million)
% 4.77/2.12 % (30981)------------------------------
% 4.77/2.12 % (30981)------------------------------
% 4.77/2.13 % (30979)Instruction limit reached!
% 4.77/2.13 % (30979)------------------------------
% 4.77/2.13 % (30979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.77/2.13 % (30979)Termination reason: Unknown
% 4.77/2.13 % (30979)Termination phase: Property scanning
% 4.77/2.13
% 4.77/2.13 % (30979)Memory used [KB]: 2046
% 4.77/2.13 % (30979)Time elapsed: 0.040 s
% 4.77/2.13 % (30979)Instructions burned: 86 (million)
% 4.77/2.13 % (30979)------------------------------
% 4.77/2.13 % (30979)------------------------------
% 5.43/2.14 % (30982)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_30834 for (2996ds/448Mi)
% 5.43/2.14 % (30983)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_30834 for (2996ds/46Mi)
% 5.43/2.15 % (30980)Instruction limit reached!
% 5.43/2.15 % (30980)------------------------------
% 5.43/2.15 % (30980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.43/2.15 % (30980)Termination reason: Unknown
% 5.43/2.15 % (30980)Termination phase: Saturation
% 5.43/2.15
% 5.43/2.15 % (30980)Memory used [KB]: 6652
% 5.43/2.15 % (30980)Time elapsed: 0.049 s
% 5.43/2.15 % (30980)Instructions burned: 108 (million)
% 5.43/2.15 % (30980)------------------------------
% 5.43/2.15 % (30980)------------------------------
% 5.43/2.17 % (30983)Instruction limit reached!
% 5.43/2.17 % (30983)------------------------------
% 5.43/2.17 % (30983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.43/2.17 % (30983)Termination reason: Unknown
% 5.43/2.17 % (30983)Termination phase: Property scanning
% 5.43/2.17
% 5.43/2.17 % (30983)Memory used [KB]: 1918
% 5.43/2.17 % (30983)Time elapsed: 0.023 s
% 5.43/2.17 % (30983)Instructions burned: 46 (million)
% 5.43/2.17 % (30983)------------------------------
% 5.43/2.17 % (30983)------------------------------
% 5.43/2.17 % (30984)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_30834 for (2996ds/98Mi)
% 5.43/2.18 % (30985)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_30834 for (2995ds/507Mi)
% 5.43/2.19 % (30968)Instruction limit reached!
% 5.43/2.19 % (30968)------------------------------
% 5.43/2.19 % (30968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.43/2.19 % (30968)Termination reason: Unknown
% 5.43/2.19 % (30968)Termination phase: Saturation
% 5.43/2.19
% 5.43/2.19 % (30968)Memory used [KB]: 6908
% 5.43/2.19 % (30968)Time elapsed: 0.290 s
% 5.43/2.19 % (30968)Instructions burned: 779 (million)
% 5.43/2.19 % (30968)------------------------------
% 5.43/2.19 % (30968)------------------------------
% 5.87/2.21 % (30952)Instruction limit reached!
% 5.87/2.21 % (30952)------------------------------
% 5.87/2.21 % (30952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.87/2.21 % (30984)Instruction limit reached!
% 5.87/2.21 % (30984)------------------------------
% 5.87/2.21 % (30984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.87/2.21 % (30984)Termination reason: Unknown
% 5.87/2.21 % (30984)Termination phase: Saturation
% 5.87/2.21
% 5.87/2.21 % (30984)Memory used [KB]: 2174
% 5.87/2.21 % (30984)Time elapsed: 0.045 s
% 5.87/2.21 % (30984)Instructions burned: 98 (million)
% 5.87/2.21 % (30984)------------------------------
% 5.87/2.21 % (30984)------------------------------
% 5.87/2.21 % (30952)Termination reason: Unknown
% 5.87/2.21 % (30952)Termination phase: Saturation
% 5.87/2.21
% 5.87/2.21 % (30952)Memory used [KB]: 11001
% 5.87/2.21 % (30952)Time elapsed: 0.394 s
% 5.87/2.21 % (30952)Instructions burned: 1041 (million)
% 5.87/2.21 % (30952)------------------------------
% 5.87/2.21 % (30952)------------------------------
% 5.87/2.21 % (30986)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_30834 for (2995ds/149Mi)
% 5.87/2.23 % (30988)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_30834 for (2995ds/6Mi)
% 5.87/2.23 % (30987)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_30834 for (2995ds/39Mi)
% 5.87/2.23 % (30961)Instruction limit reached!
% 5.87/2.23 % (30961)------------------------------
% 5.87/2.23 % (30961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.87/2.23 % (30961)Termination reason: Unknown
% 5.87/2.23 % (30961)Termination phase: Saturation
% 5.87/2.23
% 5.87/2.23 % (30961)Memory used [KB]: 9338
% 5.87/2.23 % (30961)Time elapsed: 0.365 s
% 5.87/2.23 % (30961)Instructions burned: 711 (million)
% 5.87/2.23 % (30961)------------------------------
% 5.87/2.23 % (30961)------------------------------
% 5.87/2.23 % (30988)Instruction limit reached!
% 5.87/2.23 % (30988)------------------------------
% 5.87/2.23 % (30988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.87/2.23 % (30988)Termination reason: Unknown
% 5.87/2.23 % (30988)Termination phase: shuffling
% 5.87/2.23
% 5.87/2.23 % (30988)Memory used [KB]: 1407
% 5.87/2.23 % (30988)Time elapsed: 0.005 s
% 5.87/2.23 % (30988)Instructions burned: 8 (million)
% 5.87/2.23 % (30988)------------------------------
% 5.87/2.23 % (30988)------------------------------
% 5.87/2.24 % (30987)Instruction limit reached!
% 5.87/2.24 % (30987)------------------------------
% 5.87/2.24 % (30987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.87/2.24 % (30987)Termination reason: Unknown
% 5.87/2.24 % (30987)Termination phase: Property scanning
% 5.87/2.24
% 5.87/2.24 % (30987)Memory used [KB]: 1918
% 5.87/2.24 % (30987)Time elapsed: 0.019 s
% 5.87/2.24 % (30987)Instructions burned: 39 (million)
% 5.87/2.24 % (30987)------------------------------
% 5.87/2.24 % (30987)------------------------------
% 5.87/2.25 % (30990)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_30834 for (2995ds/47Mi)
% 5.87/2.25 % (30989)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_30834 for (2995ds/1087Mi)
% 5.87/2.26 % (30991)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_30834 for (2995ds/44Mi)
% 5.87/2.27 % (30990)Instruction limit reached!
% 5.87/2.27 % (30990)------------------------------
% 5.87/2.27 % (30990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.87/2.27 % (30990)Termination reason: Unknown
% 5.87/2.27 % (30990)Termination phase: Preprocessing 3
% 5.87/2.27
% 5.87/2.27 % (30990)Memory used [KB]: 2046
% 5.87/2.27 % (30990)Time elapsed: 0.023 s
% 5.87/2.27 % (30990)Instructions burned: 47 (million)
% 5.87/2.27 % (30990)------------------------------
% 5.87/2.27 % (30990)------------------------------
% 5.87/2.28 % (30991)Instruction limit reached!
% 5.87/2.28 % (30991)------------------------------
% 5.87/2.28 % (30991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.87/2.28 % (30991)Termination reason: Unknown
% 5.87/2.28 % (30991)Termination phase: Property scanning
% 5.87/2.28
% 5.87/2.28 % (30991)Memory used [KB]: 1918
% 5.87/2.28 % (30991)Time elapsed: 0.022 s
% 5.87/2.28 % (30991)Instructions burned: 44 (million)
% 5.87/2.28 % (30991)------------------------------
% 5.87/2.28 % (30991)------------------------------
% 5.87/2.28 % (30986)Instruction limit reached!
% 5.87/2.28 % (30986)------------------------------
% 5.87/2.28 % (30986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.87/2.28 % (30986)Termination reason: Unknown
% 5.87/2.28 % (30986)Termination phase: Saturation
% 5.87/2.28
% 5.87/2.28 % (30986)Memory used [KB]: 7419
% 5.87/2.28 % (30986)Time elapsed: 0.070 s
% 5.87/2.28 % (30986)Instructions burned: 149 (million)
% 5.87/2.28 % (30986)------------------------------
% 5.87/2.28 % (30986)------------------------------
% 5.87/2.28 % (30992)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_30834 for (2994ds/432Mi)
% 5.87/2.29 % (30993)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_30834 for (2994ds/62Mi)
% 6.31/2.30 % (30994)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_30834 for (2994ds/31Mi)
% 6.31/2.31 % (30982)Instruction limit reached!
% 6.31/2.31 % (30982)------------------------------
% 6.31/2.31 % (30982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.31/2.31 % (30982)Termination reason: Unknown
% 6.31/2.31 % (30982)Termination phase: Saturation
% 6.31/2.31
% 6.31/2.31 % (30982)Memory used [KB]: 6780
% 6.31/2.31 % (30982)Time elapsed: 0.172 s
% 6.31/2.31 % (30982)Instructions burned: 449 (million)
% 6.31/2.31 % (30982)------------------------------
% 6.31/2.31 % (30982)------------------------------
% 6.31/2.31 % (30994)Instruction limit reached!
% 6.31/2.31 % (30994)------------------------------
% 6.31/2.31 % (30994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.31/2.31 % (30994)Termination reason: Unknown
% 6.31/2.31 % (30994)Termination phase: Property scanning
% 6.31/2.31
% 6.31/2.31 % (30994)Memory used [KB]: 1918
% 6.31/2.31 % (30994)Time elapsed: 0.016 s
% 6.31/2.31 % (30994)Instructions burned: 31 (million)
% 6.31/2.31 % (30994)------------------------------
% 6.31/2.31 % (30994)------------------------------
% 6.31/2.32 % (30993)Instruction limit reached!
% 6.31/2.32 % (30993)------------------------------
% 6.31/2.32 % (30993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.31/2.32 % (30993)Termination reason: Unknown
% 6.31/2.32 % (30993)Termination phase: Property scanning
% 6.31/2.32
% 6.31/2.32 % (30993)Memory used [KB]: 1918
% 6.31/2.32 % (30993)Time elapsed: 0.030 s
% 6.31/2.32 % (30993)Instructions burned: 62 (million)
% 6.31/2.32 % (30993)------------------------------
% 6.31/2.32 % (30993)------------------------------
% 6.31/2.32 % (30995)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_30834 for (2994ds/96Mi)
% 6.31/2.33 % (30996)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_30834 for (2994ds/453Mi)
% 6.31/2.34 % (30997)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_30834 for (2994ds/71Mi)
% 6.31/2.37 % (30995)Instruction limit reached!
% 6.31/2.37 % (30995)------------------------------
% 6.31/2.37 % (30995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.31/2.37 % (30995)Termination reason: Unknown
% 6.31/2.37 % (30995)Termination phase: Saturation
% 6.31/2.37
% 6.31/2.37 % (30995)Memory used [KB]: 6780
% 6.31/2.37 % (30995)Time elapsed: 0.046 s
% 6.31/2.37 % (30995)Instructions burned: 97 (million)
% 6.31/2.37 % (30995)------------------------------
% 6.31/2.37 % (30995)------------------------------
% 6.31/2.37 % (30997)Instruction limit reached!
% 6.31/2.37 % (30997)------------------------------
% 6.31/2.37 % (30997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.31/2.37 % (30997)Termination reason: Unknown
% 6.31/2.37 % (30997)Termination phase: Property scanning
% 6.31/2.37
% 6.31/2.37 % (30997)Memory used [KB]: 2046
% 6.31/2.37 % (30997)Time elapsed: 0.034 s
% 6.31/2.37 % (30997)Instructions burned: 71 (million)
% 6.31/2.37 % (30997)------------------------------
% 6.31/2.37 % (30997)------------------------------
% 6.31/2.37 % (30970)Instruction limit reached!
% 6.31/2.37 % (30970)------------------------------
% 6.31/2.37 % (30970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.31/2.37 % (30970)Termination reason: Unknown
% 6.31/2.37 % (30970)Termination phase: Saturation
% 6.31/2.37
% 6.31/2.37 % (30970)Memory used [KB]: 8571
% 6.31/2.37 % (30970)Time elapsed: 0.438 s
% 6.31/2.37 % (30970)Instructions burned: 879 (million)
% 6.31/2.37 % (30970)------------------------------
% 6.31/2.37 % (30970)------------------------------
% 6.31/2.38 % (30998)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_30834 for (2993ds/83Mi)
% 6.31/2.39 % (30999)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_30834 for (2993ds/11Mi)
% 6.31/2.39 % (31000)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_30834 for (2993ds/41Mi)
% 6.31/2.39 % (30999)Instruction limit reached!
% 6.31/2.39 % (30999)------------------------------
% 6.31/2.39 % (30999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.31/2.39 % (30999)Termination reason: Unknown
% 6.31/2.39 % (30999)Termination phase: shuffling
% 6.31/2.39
% 6.31/2.39 % (30999)Memory used [KB]: 1535
% 6.31/2.39 % (30999)Time elapsed: 0.007 s
% 6.31/2.39 % (30999)Instructions burned: 12 (million)
% 6.31/2.39 % (30999)------------------------------
% 6.31/2.39 % (30999)------------------------------
% 6.79/2.41 % (31000)Instruction limit reached!
% 6.79/2.41 % (31000)------------------------------
% 6.79/2.41 % (31000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.79/2.41 % (31000)Termination reason: Unknown
% 6.79/2.41 % (31000)Termination phase: Property scanning
% 6.79/2.41
% 6.79/2.41 % (31000)Memory used [KB]: 1918
% 6.79/2.41 % (31000)Time elapsed: 0.020 s
% 6.79/2.41 % (31000)Instructions burned: 41 (million)
% 6.79/2.41 % (31000)------------------------------
% 6.79/2.41 % (31000)------------------------------
% 6.79/2.41 % (31001)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_30834 for (2993ds/6Mi)
% 6.79/2.41 % (31001)Instruction limit reached!
% 6.79/2.41 % (31001)------------------------------
% 6.79/2.41 % (31001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.79/2.41 % (31001)Termination reason: Unknown
% 6.79/2.41 % (31001)Termination phase: shuffling
% 6.79/2.41
% 6.79/2.41 % (31001)Memory used [KB]: 1407
% 6.79/2.41 % (31001)Time elapsed: 0.005 s
% 6.79/2.41 % (31001)Instructions burned: 6 (million)
% 6.79/2.41 % (31001)------------------------------
% 6.79/2.41 % (31001)------------------------------
% 6.79/2.42 % (30998)Instruction limit reached!
% 6.79/2.42 % (30998)------------------------------
% 6.79/2.42 % (30998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.79/2.42 % (30998)Termination reason: Unknown
% 6.79/2.42 % (30998)Termination phase: Property scanning
% 6.79/2.42
% 6.79/2.42 % (30998)Memory used [KB]: 2046
% 6.79/2.42 % (30998)Time elapsed: 0.039 s
% 6.79/2.42 % (30998)Instructions burned: 83 (million)
% 6.79/2.42 % (30998)------------------------------
% 6.79/2.42 % (30998)------------------------------
% 6.79/2.42 % (31002)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_30834 for (2993ds/150Mi)
% 6.79/2.43 % (30985)Instruction limit reached!
% 6.79/2.43 % (30985)------------------------------
% 6.79/2.43 % (30985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.79/2.43 % (30985)Termination reason: Unknown
% 6.79/2.43 % (30985)Termination phase: Saturation
% 6.79/2.43
% 6.79/2.43 % (30985)Memory used [KB]: 7547
% 6.79/2.43 % (30985)Time elapsed: 0.247 s
% 6.79/2.43 % (30985)Instructions burned: 508 (million)
% 6.79/2.43 % (30985)------------------------------
% 6.79/2.43 % (30985)------------------------------
% 6.79/2.43 % (31003)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_30834 for (2993ds/343Mi)
% 6.79/2.44 % (31004)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_30834 for (2993ds/109Mi)
% 6.79/2.44 % (31005)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_30834 for (2993ds/253Mi)
% 6.79/2.45 % (30992)Instruction limit reached!
% 6.79/2.45 % (30992)------------------------------
% 6.79/2.45 % (30992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.79/2.45 % (30992)Termination reason: Unknown
% 6.79/2.45 % (30992)Termination phase: Saturation
% 6.79/2.45
% 6.79/2.45 % (30992)Memory used [KB]: 3070
% 6.79/2.45 % (30992)Time elapsed: 0.172 s
% 6.79/2.45 % (30992)Instructions burned: 433 (million)
% 6.79/2.45 % (30992)------------------------------
% 6.79/2.45 % (30992)------------------------------
% 6.79/2.47 % (31006)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_30834 for (2993ds/140Mi)
% 6.79/2.49 % (31004)Instruction limit reached!
% 6.79/2.49 % (31004)------------------------------
% 6.79/2.49 % (31004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.79/2.49 % (31004)Termination reason: Unknown
% 6.79/2.49 % (31004)Termination phase: Saturation
% 6.79/2.49
% 6.79/2.49 % (31004)Memory used [KB]: 6780
% 6.79/2.49 % (31004)Time elapsed: 0.050 s
% 6.79/2.49 % (31004)Instructions burned: 110 (million)
% 6.79/2.49 % (31004)------------------------------
% 6.79/2.49 % (31004)------------------------------
% 6.79/2.49 % (31002)Instruction limit reached!
% 6.79/2.49 % (31002)------------------------------
% 6.79/2.49 % (31002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.79/2.49 % (31002)Termination reason: Unknown
% 6.79/2.49 % (31002)Termination phase: Saturation
% 6.79/2.49
% 6.79/2.49 % (31002)Memory used [KB]: 8059
% 6.79/2.49 % (31002)Time elapsed: 0.074 s
% 6.79/2.49 % (31002)Instructions burned: 150 (million)
% 6.79/2.49 % (31002)------------------------------
% 6.79/2.49 % (31002)------------------------------
% 7.49/2.50 % (30996)Instruction limit reached!
% 7.49/2.50 % (30996)------------------------------
% 7.49/2.50 % (30996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.50 % (30996)Termination reason: Unknown
% 7.49/2.50 % (30996)Termination phase: Saturation
% 7.49/2.50
% 7.49/2.50 % (30996)Memory used [KB]: 6908
% 7.49/2.50 % (30996)Time elapsed: 0.175 s
% 7.49/2.50 % (30996)Instructions burned: 455 (million)
% 7.49/2.50 % (30996)------------------------------
% 7.49/2.50 % (30996)------------------------------
% 7.49/2.50 % (31007)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_30834 for (2992ds/614Mi)
% 7.49/2.51 % (31008)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_30834 for (2992ds/202Mi)
% 7.49/2.52 % (31009)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_30834 for (2992ds/339Mi)
% 7.49/2.53 % (31006)Instruction limit reached!
% 7.49/2.53 % (31006)------------------------------
% 7.49/2.53 % (31006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.53 % (31006)Termination reason: Unknown
% 7.49/2.53 % (31006)Termination phase: Saturation
% 7.49/2.53
% 7.49/2.53 % (31006)Memory used [KB]: 6908
% 7.49/2.53 % (31006)Time elapsed: 0.065 s
% 7.49/2.53 % (31006)Instructions burned: 141 (million)
% 7.49/2.53 % (31006)------------------------------
% 7.49/2.53 % (31006)------------------------------
% 7.49/2.55 % (31010)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_30834 for (2992ds/283Mi)
% 7.49/2.57 % (31005)Instruction limit reached!
% 7.49/2.57 % (31005)------------------------------
% 7.49/2.57 % (31005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.57 % (31005)Termination reason: Unknown
% 7.49/2.57 % (31005)Termination phase: Saturation
% 7.49/2.57
% 7.49/2.57 % (31005)Memory used [KB]: 8315
% 7.49/2.57 % (31005)Time elapsed: 0.126 s
% 7.49/2.57 % (31005)Instructions burned: 253 (million)
% 7.49/2.57 % (31005)------------------------------
% 7.49/2.57 % (31005)------------------------------
% 7.49/2.59 % (31011)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_30834 for (2992ds/134Mi)
% 7.49/2.59 % (31003)Instruction limit reached!
% 7.49/2.59 % (31003)------------------------------
% 7.49/2.59 % (31003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.59 % (31003)Termination reason: Unknown
% 7.49/2.59 % (31003)Termination phase: Saturation
% 7.49/2.59
% 7.49/2.59 % (31003)Memory used [KB]: 7931
% 7.49/2.59 % (31003)Time elapsed: 0.161 s
% 7.49/2.59 % (31003)Instructions burned: 344 (million)
% 7.49/2.59 % (31003)------------------------------
% 7.49/2.59 % (31003)------------------------------
% 8.08/2.61 % (31012)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_30834 for (2991ds/298Mi)
% 8.08/2.61 % (31008)Instruction limit reached!
% 8.08/2.61 % (31008)------------------------------
% 8.08/2.61 % (31008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.08/2.61 % (31008)Termination reason: Unknown
% 8.08/2.61 % (31008)Termination phase: Saturation
% 8.08/2.61
% 8.08/2.61 % (31008)Memory used [KB]: 8827
% 8.08/2.61 % (31008)Time elapsed: 0.101 s
% 8.08/2.61 % (31008)Instructions burned: 202 (million)
% 8.08/2.61 % (31008)------------------------------
% 8.08/2.61 % (31008)------------------------------
% 8.08/2.63 % (31013)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_30834 for (2991ds/192Mi)
% 8.08/2.65 % (31011)Instruction limit reached!
% 8.08/2.65 % (31011)------------------------------
% 8.08/2.65 % (31011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.08/2.65 % (31011)Termination reason: Unknown
% 8.08/2.65 % (31011)Termination phase: Saturation
% 8.08/2.65
% 8.08/2.65 % (31011)Memory used [KB]: 7036
% 8.08/2.65 % (31011)Time elapsed: 0.062 s
% 8.08/2.65 % (31011)Instructions burned: 134 (million)
% 8.08/2.65 % (31011)------------------------------
% 8.08/2.65 % (31011)------------------------------
% 8.08/2.66 % (31014)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_30834 for (2991ds/258Mi)
% 8.08/2.66 % (31010)Instruction limit reached!
% 8.08/2.66 % (31010)------------------------------
% 8.08/2.66 % (31010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.08/2.66 % (31010)Termination reason: Unknown
% 8.08/2.66 % (31010)Termination phase: Saturation
% 8.08/2.66
% 8.08/2.66 % (31010)Memory used [KB]: 7291
% 8.08/2.66 % (31010)Time elapsed: 0.114 s
% 8.08/2.66 % (31010)Instructions burned: 284 (million)
% 8.08/2.66 % (31010)------------------------------
% 8.08/2.66 % (31010)------------------------------
% 8.08/2.68 % (31009)Instruction limit reached!
% 8.08/2.68 % (31009)------------------------------
% 8.08/2.68 % (31009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.08/2.68 % (31009)Termination reason: Unknown
% 8.08/2.68 % (31009)Termination phase: Saturation
% 8.08/2.68
% 8.08/2.68 % (31009)Memory used [KB]: 7803
% 8.08/2.68 % (31009)Time elapsed: 0.160 s
% 8.08/2.68 % (31009)Instructions burned: 340 (million)
% 8.08/2.68 % (31009)------------------------------
% 8.08/2.68 % (31009)------------------------------
% 8.08/2.68 % (31015)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_30834 for (2991ds/90Mi)
% 8.08/2.69 % (31016)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_30834 for (2991ds/231Mi)
% 8.58/2.72 % (31013)Instruction limit reached!
% 8.58/2.72 % (31013)------------------------------
% 8.58/2.72 % (31013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.58/2.72 % (31013)Termination reason: Unknown
% 8.58/2.72 % (31013)Termination phase: Saturation
% 8.58/2.72
% 8.58/2.72 % (31013)Memory used [KB]: 7419
% 8.58/2.72 % (31013)Time elapsed: 0.089 s
% 8.58/2.72 % (31013)Instructions burned: 192 (million)
% 8.58/2.72 % (31013)------------------------------
% 8.58/2.72 % (31013)------------------------------
% 8.58/2.72 % (31015)Instruction limit reached!
% 8.58/2.72 % (31015)------------------------------
% 8.58/2.72 % (31015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.58/2.72 % (31015)Termination reason: Unknown
% 8.58/2.72 % (31015)Termination phase: Property scanning
% 8.58/2.72
% 8.58/2.72 % (31015)Memory used [KB]: 2686
% 8.58/2.72 % (31015)Time elapsed: 0.043 s
% 8.58/2.72 % (31015)Instructions burned: 91 (million)
% 8.58/2.72 % (31015)------------------------------
% 8.58/2.72 % (31015)------------------------------
% 8.58/2.73 % (31012)Instruction limit reached!
% 8.58/2.73 % (31012)------------------------------
% 8.58/2.73 % (31012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.58/2.73 % (31012)Termination reason: Unknown
% 8.58/2.73 % (31012)Termination phase: Saturation
% 8.58/2.73
% 8.58/2.73 % (31012)Memory used [KB]: 6780
% 8.58/2.73 % (31012)Time elapsed: 0.126 s
% 8.58/2.73 % (31012)Instructions burned: 300 (million)
% 8.58/2.73 % (31012)------------------------------
% 8.58/2.73 % (31012)------------------------------
% 8.58/2.73 % (31017)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_30834 for (2990ds/458Mi)
% 8.58/2.74 % (31018)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_30834 for (2990ds/31Mi)
% 8.58/2.75 % (31019)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_30834 for (2990ds/297Mi)
% 8.58/2.75 % (31018)Instruction limit reached!
% 8.58/2.75 % (31018)------------------------------
% 8.58/2.75 % (31018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.58/2.75 % (31018)Termination reason: Unknown
% 8.58/2.75 % (31018)Termination phase: Property scanning
% 8.58/2.75
% 8.58/2.75 % (31018)Memory used [KB]: 1918
% 8.58/2.75 % (31018)Time elapsed: 0.017 s
% 8.58/2.75 % (31018)Instructions burned: 33 (million)
% 8.58/2.75 % (31018)------------------------------
% 8.58/2.75 % (31018)------------------------------
% 8.58/2.77 % (31020)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_30834 for (2990ds/987Mi)
% 8.58/2.78 % (31014)Instruction limit reached!
% 8.58/2.78 % (31014)------------------------------
% 8.58/2.78 % (31014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.58/2.78 % (31014)Termination reason: Unknown
% 8.58/2.78 % (31014)Termination phase: Saturation
% 8.58/2.78
% 8.58/2.78 % (31014)Memory used [KB]: 7675
% 8.58/2.78 % (31014)Time elapsed: 0.120 s
% 8.58/2.78 % (31014)Instructions burned: 258 (million)
% 8.58/2.78 % (31014)------------------------------
% 8.58/2.78 % (31014)------------------------------
% 9.05/2.80 % (31007)Instruction limit reached!
% 9.05/2.80 % (31007)------------------------------
% 9.05/2.80 % (31007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.05/2.80 % (31007)Termination reason: Unknown
% 9.05/2.80 % (31007)Termination phase: Saturation
% 9.05/2.80
% 9.05/2.80 % (31007)Memory used [KB]: 8571
% 9.05/2.80 % (31007)Time elapsed: 0.296 s
% 9.05/2.80 % (31007)Instructions burned: 616 (million)
% 9.05/2.80 % (31007)------------------------------
% 9.05/2.80 % (31007)------------------------------
% 9.05/2.80 % (30989)Instruction limit reached!
% 9.05/2.80 % (30989)------------------------------
% 9.05/2.80 % (30989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.05/2.80 % (30989)Termination reason: Unknown
% 9.05/2.80 % (30989)Termination phase: Saturation
% 9.05/2.80
% 9.05/2.80 % (30989)Memory used [KB]: 10618
% 9.05/2.80 % (30989)Time elapsed: 0.555 s
% 9.05/2.80 % (30989)Instructions burned: 1087 (million)
% 9.05/2.80 % (30989)------------------------------
% 9.05/2.80 % (30989)------------------------------
% 9.05/2.80 % (31021)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_30834 for (2989ds/182Mi)
% 9.05/2.80 % (31016)Instruction limit reached!
% 9.05/2.80 % (31016)------------------------------
% 9.05/2.80 % (31016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.05/2.80 % (31016)Termination reason: Unknown
% 9.05/2.80 % (31016)Termination phase: Saturation
% 9.05/2.80
% 9.05/2.80 % (31016)Memory used [KB]: 12025
% 9.05/2.80 % (31016)Time elapsed: 0.133 s
% 9.05/2.80 % (31016)Instructions burned: 232 (million)
% 9.05/2.80 % (31016)------------------------------
% 9.05/2.80 % (31016)------------------------------
% 9.05/2.81 % (31022)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_30834 for (2989ds/182Mi)
% 9.05/2.82 % (31023)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_30834 for (2989ds/154Mi)
% 9.05/2.82 % (31024)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_30834 for (2989ds/79Mi)
% 9.05/2.86 % (31024)Instruction limit reached!
% 9.05/2.86 % (31024)------------------------------
% 9.05/2.86 % (31024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.05/2.86 % (31024)Termination reason: Unknown
% 9.05/2.86 % (31024)Termination phase: Property scanning
% 9.05/2.86
% 9.05/2.86 % (31024)Memory used [KB]: 2174
% 9.05/2.86 % (31024)Time elapsed: 0.037 s
% 9.05/2.86 % (31024)Instructions burned: 79 (million)
% 9.05/2.86 % (31024)------------------------------
% 9.05/2.86 % (31024)------------------------------
% 9.05/2.87 % (31019)Instruction limit reached!
% 9.05/2.87 % (31019)------------------------------
% 9.05/2.87 % (31019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.05/2.87 % (31019)Termination reason: Unknown
% 9.05/2.87 % (31019)Termination phase: Saturation
% 9.05/2.87
% 9.05/2.87 % (31019)Memory used [KB]: 8699
% 9.05/2.87 % (31019)Time elapsed: 0.122 s
% 9.05/2.87 % (31019)Instructions burned: 298 (million)
% 9.05/2.87 % (31019)------------------------------
% 9.05/2.87 % (31019)------------------------------
% 9.05/2.87 % (31025)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_30834 for (2989ds/216Mi)
% 9.05/2.88 % (31023)Instruction limit reached!
% 9.05/2.88 % (31023)------------------------------
% 9.05/2.88 % (31023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.05/2.88 % (31023)Termination reason: Unknown
% 9.05/2.88 % (31023)Termination phase: Saturation
% 9.05/2.88
% 9.05/2.88 % (31023)Memory used [KB]: 6780
% 9.05/2.88 % (31023)Time elapsed: 0.067 s
% 9.05/2.88 % (31023)Instructions burned: 155 (million)
% 9.05/2.88 % (31023)------------------------------
% 9.05/2.88 % (31023)------------------------------
% 9.05/2.88 % (31021)Instruction limit reached!
% 9.05/2.88 % (31021)------------------------------
% 9.05/2.88 % (31021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.05/2.88 % (31021)Termination reason: Unknown
% 9.05/2.88 % (31021)Termination phase: Saturation
% 9.05/2.88
% 9.05/2.88 % (31021)Memory used [KB]: 7419
% 9.05/2.88 % (31021)Time elapsed: 0.085 s
% 9.05/2.88 % (31021)Instructions burned: 183 (million)
% 9.05/2.88 % (31021)------------------------------
% 9.05/2.88 % (31021)------------------------------
% 9.05/2.88 % (31026)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_30834 for (2988ds/114Mi)
% 10.43/2.90 % (31027)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_30834 for (2988ds/922Mi)
% 10.43/2.90 % (31028)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_30834 for (2988ds/182Mi)
% 10.43/2.90 % (31022)Instruction limit reached!
% 10.43/2.90 % (31022)------------------------------
% 10.43/2.90 % (31022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.43/2.90 % (31022)Termination reason: Unknown
% 10.43/2.90 % (31022)Termination phase: Saturation
% 10.43/2.90
% 10.43/2.90 % (31022)Memory used [KB]: 9978
% 10.43/2.90 % (31022)Time elapsed: 0.091 s
% 10.43/2.90 % (31022)Instructions burned: 184 (million)
% 10.43/2.90 % (31022)------------------------------
% 10.43/2.90 % (31022)------------------------------
% 10.43/2.92 % (31029)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_30834 for (2988ds/164Mi)
% 10.43/2.93 % (31026)Instruction limit reached!
% 10.43/2.93 % (31026)------------------------------
% 10.43/2.93 % (31026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.43/2.93 % (31026)Termination reason: Unknown
% 10.43/2.93 % (31026)Termination phase: Saturation
% 10.43/2.93
% 10.43/2.93 % (31026)Memory used [KB]: 6908
% 10.43/2.93 % (31026)Time elapsed: 0.052 s
% 10.43/2.93 % (31026)Instructions burned: 114 (million)
% 10.43/2.93 % (31026)------------------------------
% 10.43/2.93 % (31026)------------------------------
% 10.43/2.95 % (31017)Instruction limit reached!
% 10.43/2.95 % (31017)------------------------------
% 10.43/2.95 % (31017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.43/2.95 % (31017)Termination reason: Unknown
% 10.43/2.95 % (31017)Termination phase: Saturation
% 10.43/2.95
% 10.43/2.95 % (31017)Memory used [KB]: 8187
% 10.43/2.95 % (31017)Time elapsed: 0.219 s
% 10.43/2.95 % (31017)Instructions burned: 458 (million)
% 10.43/2.95 % (31017)------------------------------
% 10.43/2.95 % (31017)------------------------------
% 10.43/2.95 % (31030)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_30834 for (2988ds/50Mi)
% 10.43/2.96 % (31025)Instruction limit reached!
% 10.43/2.96 % (31025)------------------------------
% 10.43/2.96 % (31025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.43/2.96 % (31025)Termination reason: Unknown
% 10.43/2.96 % (31025)Termination phase: Saturation
% 10.43/2.96
% 10.43/2.96 % (31025)Memory used [KB]: 6780
% 10.43/2.96 % (31025)Time elapsed: 0.091 s
% 10.43/2.96 % (31025)Instructions burned: 217 (million)
% 10.43/2.96 % (31025)------------------------------
% 10.43/2.96 % (31025)------------------------------
% 10.43/2.97 % (31031)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_30834 for (2988ds/368Mi)
% 10.43/2.97 % (31030)Instruction limit reached!
% 10.43/2.97 % (31030)------------------------------
% 10.43/2.97 % (31030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.43/2.97 % (31030)Termination reason: Unknown
% 10.43/2.97 % (31030)Termination phase: Property scanning
% 10.43/2.97
% 10.43/2.97 % (31030)Memory used [KB]: 1918
% 10.43/2.97 % (31030)Time elapsed: 0.024 s
% 10.43/2.97 % (31030)Instructions burned: 50 (million)
% 10.43/2.97 % (31030)------------------------------
% 10.43/2.97 % (31030)------------------------------
% 10.43/2.98 % (31028)Instruction limit reached!
% 10.43/2.98 % (31028)------------------------------
% 10.43/2.98 % (31028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.43/2.98 % (31028)Termination reason: Unknown
% 10.43/2.98 % (31028)Termination phase: Saturation
% 10.43/2.98
% 10.43/2.98 % (31028)Memory used [KB]: 6780
% 10.43/2.98 % (31028)Time elapsed: 0.078 s
% 10.43/2.98 % (31028)Instructions burned: 183 (million)
% 10.43/2.98 % (31028)------------------------------
% 10.43/2.98 % (31028)------------------------------
% 10.43/2.98 % (31032)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_30834 for (2988ds/1021Mi)
% 10.43/2.99 % (31033)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_30834 for (2987ds/267Mi)
% 10.43/2.99 % (31034)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_30834 for (2987ds/204Mi)
% 10.43/3.00 % (31029)Instruction limit reached!
% 10.43/3.00 % (31029)------------------------------
% 10.43/3.00 % (31029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.43/3.00 % (31029)Termination reason: Unknown
% 10.43/3.00 % (31029)Termination phase: Saturation
% 10.43/3.00
% 10.43/3.00 % (31029)Memory used [KB]: 2430
% 10.43/3.00 % (31029)Time elapsed: 0.075 s
% 10.43/3.00 % (31029)Instructions burned: 165 (million)
% 10.43/3.00 % (31029)------------------------------
% 10.43/3.00 % (31029)------------------------------
% 10.43/3.01 % (31035)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_30834 for (2987ds/26Mi)
% 10.43/3.02 % (31035)Instruction limit reached!
% 10.43/3.02 % (31035)------------------------------
% 10.43/3.02 % (31035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.43/3.02 % (31035)Termination reason: Unknown
% 10.43/3.02 % (31035)Termination phase: shuffling
% 10.43/3.02
% 10.43/3.02 % (31035)Memory used [KB]: 1791
% 10.43/3.02 % (31035)Time elapsed: 0.014 s
% 10.43/3.02 % (31035)Instructions burned: 26 (million)
% 10.43/3.02 % (31035)------------------------------
% 10.43/3.02 % (31035)------------------------------
% 11.76/3.04 % (31036)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_30834 for (2987ds/53Mi)
% 11.76/3.07 % (31036)Instruction limit reached!
% 11.76/3.07 % (31036)------------------------------
% 11.76/3.07 % (31036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.76/3.07 % (31036)Termination reason: Unknown
% 11.76/3.07 % (31036)Termination phase: Property scanning
% 11.76/3.07
% 11.76/3.07 % (31036)Memory used [KB]: 1918
% 11.76/3.07 % (31036)Time elapsed: 0.026 s
% 11.76/3.07 % (31036)Instructions burned: 53 (million)
% 11.76/3.07 % (31036)------------------------------
% 11.76/3.07 % (31036)------------------------------
% 11.76/3.08 % (31034)Instruction limit reached!
% 11.76/3.08 % (31034)------------------------------
% 11.76/3.08 % (31034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.76/3.08 % (31034)Termination reason: Unknown
% 11.76/3.08 % (31034)Termination phase: Saturation
% 11.76/3.08
% 11.76/3.08 % (31034)Memory used [KB]: 7419
% 11.76/3.08 % (31034)Time elapsed: 0.092 s
% 11.76/3.08 % (31034)Instructions burned: 205 (million)
% 11.76/3.08 % (31034)------------------------------
% 11.76/3.08 % (31034)------------------------------
% 11.76/3.08 % (31037)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_30834 for (2987ds/4436Mi)
% 11.76/3.10 % (31033)Instruction limit reached!
% 11.76/3.10 % (31033)------------------------------
% 11.76/3.10 % (31033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.76/3.10 % (31033)Termination reason: Unknown
% 11.76/3.10 % (31033)Termination phase: Saturation
% 11.76/3.10
% 11.76/3.10 % (31033)Memory used [KB]: 6908
% 11.76/3.10 % (31033)Time elapsed: 0.110 s
% 11.76/3.10 % (31033)Instructions burned: 268 (million)
% 11.76/3.10 % (31033)------------------------------
% 11.76/3.10 % (31033)------------------------------
% 11.76/3.10 % (31038)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_30834 for (2986ds/1539Mi)
% 11.76/3.12 % (31039)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_30834 for (2986ds/408Mi)
% 12.39/3.15 % (31031)Instruction limit reached!
% 12.39/3.15 % (31031)------------------------------
% 12.39/3.15 % (31031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.39/3.15 % (31031)Termination reason: Unknown
% 12.39/3.15 % (31031)Termination phase: Saturation
% 12.39/3.15
% 12.39/3.15 % (31031)Memory used [KB]: 8187
% 12.39/3.15 % (31031)Time elapsed: 0.180 s
% 12.39/3.15 % (31031)Instructions burned: 369 (million)
% 12.39/3.15 % (31031)------------------------------
% 12.39/3.15 % (31031)------------------------------
% 12.39/3.15 % (31020)Instruction limit reached!
% 12.39/3.15 % (31020)------------------------------
% 12.39/3.15 % (31020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.39/3.15 % (31020)Termination reason: Unknown
% 12.39/3.15 % (31020)Termination phase: Saturation
% 12.39/3.15
% 12.39/3.15 % (31020)Memory used [KB]: 10362
% 12.39/3.15 % (31020)Time elapsed: 0.399 s
% 12.39/3.15 % (31020)Instructions burned: 989 (million)
% 12.39/3.15 % (31020)------------------------------
% 12.39/3.15 % (31020)------------------------------
% 12.39/3.16 % (31041)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_30834 for (2986ds/1913Mi)
% 12.39/3.16 % (31040)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_30834 for (2986ds/5205Mi)
% 12.79/3.33 % (31039)Instruction limit reached!
% 12.79/3.33 % (31039)------------------------------
% 12.79/3.33 % (31039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.79/3.33 % (31039)Termination reason: Unknown
% 12.79/3.33 % (31039)Termination phase: Saturation
% 12.79/3.33
% 12.79/3.33 % (31039)Memory used [KB]: 9722
% 12.79/3.33 % (31039)Time elapsed: 0.213 s
% 12.79/3.33 % (31039)Instructions burned: 408 (million)
% 12.79/3.33 % (31039)------------------------------
% 12.79/3.33 % (31039)------------------------------
% 12.79/3.35 % (31044)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_30834 for (2984ds/4350Mi)
% 12.79/3.36 % (31027)Instruction limit reached!
% 12.79/3.36 % (31027)------------------------------
% 12.79/3.36 % (31027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.79/3.36 % (31027)Termination reason: Unknown
% 12.79/3.36 % (31027)Termination phase: Saturation
% 12.79/3.36
% 12.79/3.36 % (31027)Memory used [KB]: 9850
% 12.79/3.36 % (31027)Time elapsed: 0.466 s
% 12.79/3.36 % (31027)Instructions burned: 923 (million)
% 12.79/3.36 % (31027)------------------------------
% 12.79/3.36 % (31027)------------------------------
% 12.79/3.38 % (31045)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_30834 for (2984ds/68Mi)
% 13.19/3.41 % (31045)Instruction limit reached!
% 13.19/3.41 % (31045)------------------------------
% 13.19/3.41 % (31045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.19/3.41 % (31045)Termination reason: Unknown
% 13.19/3.41 % (31045)Termination phase: Property scanning
% 13.19/3.41
% 13.19/3.41 % (31045)Memory used [KB]: 2046
% 13.19/3.41 % (31045)Time elapsed: 0.032 s
% 13.19/3.41 % (31045)Instructions burned: 70 (million)
% 13.19/3.41 % (31045)------------------------------
% 13.19/3.41 % (31045)------------------------------
% 13.19/3.43 % (31046)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_30834 for (2983ds/358Mi)
% 13.35/3.50 % (31032)Instruction limit reached!
% 13.35/3.50 % (31032)------------------------------
% 13.35/3.50 % (31032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.35/3.50 % (31032)Termination reason: Unknown
% 13.35/3.50 % (31032)Termination phase: Saturation
% 13.35/3.50
% 13.35/3.50 % (31032)Memory used [KB]: 10618
% 13.35/3.50 % (31032)Time elapsed: 0.522 s
% 13.35/3.50 % (31032)Instructions burned: 1022 (million)
% 13.35/3.50 % (31032)------------------------------
% 13.35/3.50 % (31032)------------------------------
% 13.35/3.52 % (31047)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_30834 for (2982ds/31Mi)
% 13.35/3.54 % (31047)Instruction limit reached!
% 13.35/3.54 % (31047)------------------------------
% 13.35/3.54 % (31047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.35/3.54 % (31047)Termination reason: Unknown
% 13.35/3.54 % (31047)Termination phase: Property scanning
% 13.35/3.54
% 13.35/3.54 % (31047)Memory used [KB]: 1918
% 13.35/3.54 % (31047)Time elapsed: 0.017 s
% 13.35/3.54 % (31047)Instructions burned: 33 (million)
% 13.35/3.54 % (31047)------------------------------
% 13.35/3.54 % (31047)------------------------------
% 13.35/3.55 % (31048)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_30834 for (2982ds/279Mi)
% 13.35/3.59 % (31046)Instruction limit reached!
% 13.35/3.59 % (31046)------------------------------
% 13.35/3.59 % (31046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.35/3.59 % (31046)Termination reason: Unknown
% 13.35/3.59 % (31046)Termination phase: Saturation
% 13.35/3.59
% 13.35/3.59 % (31046)Memory used [KB]: 7931
% 13.35/3.59 % (31046)Time elapsed: 0.169 s
% 13.35/3.59 % (31046)Instructions burned: 358 (million)
% 13.35/3.60 % (31046)------------------------------
% 13.35/3.60 % (31046)------------------------------
% 13.58/3.61 % (31049)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_30834 for (2981ds/258Mi)
% 13.58/3.67 % (31048)Instruction limit reached!
% 13.58/3.67 % (31048)------------------------------
% 13.58/3.67 % (31048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.58/3.67 % (31048)Termination reason: Unknown
% 13.58/3.67 % (31048)Termination phase: Saturation
% 13.58/3.67
% 13.58/3.67 % (31048)Memory used [KB]: 6908
% 13.58/3.67 % (31048)Time elapsed: 0.114 s
% 13.58/3.67 % (31048)Instructions burned: 280 (million)
% 13.58/3.67 % (31048)------------------------------
% 13.58/3.67 % (31048)------------------------------
% 13.58/3.68 % (31050)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_30834 for (2981ds/26Mi)
% 13.72/3.70 % (31050)Instruction limit reached!
% 13.72/3.70 % (31050)------------------------------
% 13.72/3.70 % (31050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.72/3.70 % (31050)Termination reason: Unknown
% 13.72/3.70 % (31050)Termination phase: shuffling
% 13.72/3.70
% 13.72/3.70 % (31050)Memory used [KB]: 1791
% 13.72/3.70 % (31050)Time elapsed: 0.014 s
% 13.72/3.70 % (31050)Instructions burned: 27 (million)
% 13.72/3.70 % (31050)------------------------------
% 13.72/3.70 % (31050)------------------------------
% 13.72/3.71 % (31051)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_30834 for (2980ds/995Mi)
% 13.72/3.73 % (31049)Instruction limit reached!
% 13.72/3.73 % (31049)------------------------------
% 13.72/3.73 % (31049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.72/3.73 % (31049)Termination reason: Unknown
% 13.72/3.73 % (31049)Termination phase: Saturation
% 13.72/3.73
% 13.72/3.73 % (31049)Memory used [KB]: 7803
% 13.72/3.73 % (31049)Time elapsed: 0.118 s
% 13.72/3.73 % (31049)Instructions burned: 258 (million)
% 13.72/3.73 % (31049)------------------------------
% 13.72/3.73 % (31049)------------------------------
% 13.72/3.75 % (31052)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_30834 for (2980ds/373Mi)
% 13.87/3.86 % (31038)Instruction limit reached!
% 13.87/3.86 % (31038)------------------------------
% 13.87/3.86 % (31038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.87/3.86 % (31038)Termination reason: Unknown
% 13.87/3.86 % (31038)Termination phase: Saturation
% 13.87/3.86
% 13.87/3.86 % (31038)Memory used [KB]: 9210
% 13.87/3.86 % (31038)Time elapsed: 0.765 s
% 13.87/3.86 % (31038)Instructions burned: 1540 (million)
% 13.87/3.86 % (31038)------------------------------
% 13.87/3.86 % (31038)------------------------------
% 13.87/3.88 % (31053)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_30834 for (2979ds/253Mi)
% 14.66/3.92 % (31052)Instruction limit reached!
% 14.66/3.92 % (31052)------------------------------
% 14.66/3.92 % (31052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.66/3.92 % (31052)Termination reason: Unknown
% 14.66/3.92 % (31052)Termination phase: Saturation
% 14.66/3.92
% 14.66/3.92 % (31052)Memory used [KB]: 8059
% 14.66/3.92 % (31052)Time elapsed: 0.201 s
% 14.66/3.92 % (31052)Instructions burned: 374 (million)
% 14.66/3.92 % (31052)------------------------------
% 14.66/3.92 % (31052)------------------------------
% 14.66/3.94 % (31054)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_30834 for (2978ds/832Mi)
% 14.66/3.98 % (31053)Instruction limit reached!
% 14.66/3.98 % (31053)------------------------------
% 14.66/3.98 % (31053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.66/3.98 % (31053)Termination reason: Unknown
% 14.66/3.98 % (31053)Termination phase: Saturation
% 14.66/3.98
% 14.66/3.98 % (31053)Memory used [KB]: 7036
% 14.66/3.98 % (31053)Time elapsed: 0.105 s
% 14.66/3.98 % (31053)Instructions burned: 253 (million)
% 14.66/3.98 % (31053)------------------------------
% 14.66/3.98 % (31053)------------------------------
% 14.66/4.00 % (31055)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_30834 for (2977ds/668Mi)
% 18.79/4.06 % (31054)Refutation not found, incomplete strategy
% 18.79/4.06 % (31054)------------------------------
% 18.79/4.06 % (31054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.79/4.06 % (31054)Termination reason: Refutation not found, incomplete strategy
% 18.79/4.06
% 18.79/4.06
% 18.79/4.06 % (31054)Memory used [KB]: 8699
% 18.79/4.06 % (31054)Time elapsed: 0.141 s
% 18.79/4.06 % (31054)Instructions burned: 228 (million)
% 18.79/4.06 % (31054)------------------------------
% 18.79/4.06 % (31054)------------------------------
% 18.79/4.08 % (31056)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_30834 for (2977ds/40Mi)
% 18.79/4.09 % (31056)Instruction limit reached!
% 18.79/4.09 % (31056)------------------------------
% 18.79/4.09 % (31056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.79/4.09 % (31056)Termination reason: Unknown
% 18.79/4.09 % (31056)Termination phase: Property scanning
% 18.79/4.09
% 18.79/4.09 % (31056)Memory used [KB]: 1918
% 18.79/4.09 % (31056)Time elapsed: 0.020 s
% 18.79/4.09 % (31056)Instructions burned: 40 (million)
% 18.79/4.09 % (31056)------------------------------
% 18.79/4.09 % (31056)------------------------------
% 18.79/4.10 % (31041)Instruction limit reached!
% 18.79/4.10 % (31041)------------------------------
% 18.79/4.10 % (31041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.79/4.10 % (31041)Termination reason: Unknown
% 18.79/4.10 % (31041)Termination phase: Saturation
% 18.79/4.10
% 18.79/4.10 % (31041)Memory used [KB]: 4477
% 18.79/4.10 % (31041)Time elapsed: 0.933 s
% 18.79/4.10 % (31041)Instructions burned: 1913 (million)
% 18.79/4.10 % (31041)------------------------------
% 18.79/4.10 % (31041)------------------------------
% 18.79/4.10 % (31051)Instruction limit reached!
% 18.79/4.10 % (31051)------------------------------
% 18.79/4.10 % (31051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.79/4.10 % (31051)Termination reason: Unknown
% 18.79/4.10 % (31051)Termination phase: Saturation
% 18.79/4.10
% 18.79/4.10 % (31051)Memory used [KB]: 10362
% 18.79/4.10 % (31051)Time elapsed: 0.387 s
% 18.79/4.10 % (31051)Instructions burned: 996 (million)
% 18.79/4.10 % (31051)------------------------------
% 18.79/4.10 % (31051)------------------------------
% 18.79/4.11 % (31057)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_30834 for (2976ds/294Mi)
% 18.79/4.11 % (31058)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_30834 for (2976ds/187Mi)
% 18.79/4.12 % (31059)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_30834 for (2976ds/371Mi)
% 19.72/4.20 % (31058)Instruction limit reached!
% 19.72/4.20 % (31058)------------------------------
% 19.72/4.20 % (31058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.72/4.20 % (31058)Termination reason: Unknown
% 19.72/4.20 % (31058)Termination phase: Saturation
% 19.72/4.20
% 19.72/4.20 % (31058)Memory used [KB]: 7419
% 19.72/4.20 % (31058)Time elapsed: 0.087 s
% 19.72/4.20 % (31058)Instructions burned: 187 (million)
% 19.72/4.20 % (31058)------------------------------
% 19.72/4.20 % (31058)------------------------------
% 19.72/4.22 % (31060)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_30834 for (2975ds/1827Mi)
% 19.72/4.24 % (31057)Instruction limit reached!
% 19.72/4.24 % (31057)------------------------------
% 19.72/4.24 % (31057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.72/4.24 % (31057)Termination reason: Unknown
% 19.72/4.24 % (31057)Termination phase: Saturation
% 19.72/4.24
% 19.72/4.24 % (31057)Memory used [KB]: 6780
% 19.72/4.24 % (31057)Time elapsed: 0.125 s
% 19.72/4.24 % (31057)Instructions burned: 296 (million)
% 19.72/4.24 % (31057)------------------------------
% 19.72/4.24 % (31057)------------------------------
% 19.72/4.25 % (31061)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_30834 for (2975ds/70Mi)
% 19.72/4.26 % (31055)Instruction limit reached!
% 19.72/4.26 % (31055)------------------------------
% 19.72/4.26 % (31055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.72/4.26 % (31055)Termination reason: Unknown
% 19.72/4.26 % (31055)Termination phase: Saturation
% 19.72/4.26
% 19.72/4.26 % (31055)Memory used [KB]: 15223
% 19.72/4.26 % (31055)Time elapsed: 0.287 s
% 19.72/4.26 % (31055)Instructions burned: 668 (million)
% 19.72/4.26 % (31055)------------------------------
% 19.72/4.26 % (31055)------------------------------
% 19.72/4.27 % (31061)Instruction limit reached!
% 19.72/4.27 % (31061)------------------------------
% 19.72/4.27 % (31061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.72/4.27 % (31061)Termination reason: Unknown
% 19.72/4.27 % (31061)Termination phase: Function definition elimination
% 19.72/4.27
% 19.72/4.27 % (31061)Memory used [KB]: 1918
% 19.72/4.27 % (31061)Time elapsed: 0.026 s
% 19.72/4.27 % (31061)Instructions burned: 72 (million)
% 19.72/4.27 % (31061)------------------------------
% 19.72/4.27 % (31061)------------------------------
% 19.72/4.28 % (31062)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_30834 for (2975ds/316Mi)
% 19.72/4.29 % (31063)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_30834 for (2974ds/932Mi)
% 19.72/4.29 % (31059)Instruction limit reached!
% 19.72/4.29 % (31059)------------------------------
% 19.72/4.29 % (31059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.72/4.29 % (31059)Termination reason: Unknown
% 19.72/4.29 % (31059)Termination phase: Saturation
% 19.72/4.29
% 19.72/4.29 % (31059)Memory used [KB]: 8059
% 19.72/4.29 % (31059)Time elapsed: 0.178 s
% 19.72/4.29 % (31059)Instructions burned: 371 (million)
% 19.72/4.29 % (31059)------------------------------
% 19.72/4.29 % (31059)------------------------------
% 20.56/4.31 % (31064)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_30834 for (2974ds/4714Mi)
% 20.86/4.41 % (31062)Instruction limit reached!
% 20.86/4.41 % (31062)------------------------------
% 20.86/4.41 % (31062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.86/4.41 % (31062)Termination reason: Unknown
% 20.86/4.41 % (31062)Termination phase: Saturation
% 20.86/4.41
% 20.86/4.41 % (31062)Memory used [KB]: 7164
% 20.86/4.41 % (31062)Time elapsed: 0.128 s
% 20.86/4.41 % (31062)Instructions burned: 316 (million)
% 20.86/4.41 % (31062)------------------------------
% 20.86/4.41 % (31062)------------------------------
% 20.86/4.43 % (31065)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_30834 for (2973ds/8250Mi)
% 21.59/4.66 % (31063)Instruction limit reached!
% 21.59/4.66 % (31063)------------------------------
% 21.59/4.66 % (31063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.59/4.66 % (31063)Termination reason: Unknown
% 21.59/4.66 % (31063)Termination phase: Saturation
% 21.59/4.66
% 21.59/4.66 % (31063)Memory used [KB]: 11897
% 21.59/4.66 % (31063)Time elapsed: 0.373 s
% 21.59/4.66 % (31063)Instructions burned: 933 (million)
% 21.59/4.66 % (31063)------------------------------
% 21.59/4.66 % (31063)------------------------------
% 21.59/4.68 % (31067)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_30834 for (2971ds/770Mi)
% 22.88/5.02 % (31067)Instruction limit reached!
% 22.88/5.02 % (31067)------------------------------
% 22.88/5.02 % (31067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.88/5.02 % (31067)Termination reason: Unknown
% 22.88/5.02 % (31067)Termination phase: Saturation
% 22.88/5.02
% 22.88/5.02 % (31067)Memory used [KB]: 7036
% 22.88/5.02 % (31067)Time elapsed: 0.343 s
% 22.88/5.02 % (31067)Instructions burned: 770 (million)
% 22.88/5.02 % (31067)------------------------------
% 22.88/5.02 % (31067)------------------------------
% 25.78/5.04 % (31068)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_30834 for (2967ds/794Mi)
% 25.78/5.11 % (31060)Instruction limit reached!
% 25.78/5.11 % (31060)------------------------------
% 25.78/5.11 % (31060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.78/5.11 % (31060)Termination reason: Unknown
% 25.78/5.11 % (31060)Termination phase: Saturation
% 25.78/5.11
% 25.78/5.11 % (31060)Memory used [KB]: 16502
% 25.78/5.11 % (31060)Time elapsed: 0.896 s
% 25.78/5.11 % (31060)Instructions burned: 1828 (million)
% 25.78/5.11 % (31060)------------------------------
% 25.78/5.11 % (31060)------------------------------
% 25.78/5.12 % (31040)Instruction limit reached!
% 25.78/5.12 % (31040)------------------------------
% 25.78/5.12 % (31040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.78/5.12 % (31040)Termination reason: Unknown
% 25.78/5.12 % (31040)Termination phase: Saturation
% 25.78/5.12
% 25.78/5.12 % (31040)Memory used [KB]: 11257
% 25.78/5.12 % (31040)Time elapsed: 1.953 s
% 25.78/5.12 % (31040)Instructions burned: 5206 (million)
% 25.78/5.12 % (31040)------------------------------
% 25.78/5.12 % (31040)------------------------------
% 25.78/5.12 % (31069)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_30834 for (2966ds/464Mi)
% 26.36/5.13 % (31071)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_30834 for (2966ds/1376Mi)
% 27.02/5.34 % (31069)Instruction limit reached!
% 27.02/5.34 % (31069)------------------------------
% 27.02/5.34 % (31069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.02/5.34 % (31069)Termination reason: Unknown
% 27.02/5.34 % (31069)Termination phase: Saturation
% 27.02/5.34
% 27.02/5.34 % (31069)Memory used [KB]: 8187
% 27.02/5.34 % (31069)Time elapsed: 0.217 s
% 27.02/5.34 % (31069)Instructions burned: 464 (million)
% 27.02/5.34 % (31069)------------------------------
% 27.02/5.34 % (31069)------------------------------
% 27.02/5.35 % (31037)Instruction limit reached!
% 27.02/5.35 % (31037)------------------------------
% 27.02/5.35 % (31037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.02/5.35 % (31037)Termination reason: Unknown
% 27.02/5.35 % (31037)Termination phase: Saturation
% 27.02/5.35
% 27.02/5.35 % (31037)Memory used [KB]: 17014
% 27.02/5.35 % (31037)Time elapsed: 2.268 s
% 27.02/5.35 % (31037)Instructions burned: 4437 (million)
% 27.02/5.35 % (31037)------------------------------
% 27.02/5.35 % (31037)------------------------------
% 27.02/5.35 % (31072)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_30834 for (2964ds/906Mi)
% 27.02/5.38 % (31073)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_30834 for (2964ds/434Mi)
% 27.63/5.43 % (31068)Instruction limit reached!
% 27.63/5.43 % (31068)------------------------------
% 27.63/5.43 % (31068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.63/5.43 % (31068)Termination reason: Unknown
% 27.63/5.43 % (31068)Termination phase: Saturation
% 27.63/5.43
% 27.63/5.43 % (31068)Memory used [KB]: 4349
% 27.63/5.43 % (31068)Time elapsed: 0.396 s
% 27.63/5.43 % (31068)Instructions burned: 795 (million)
% 27.63/5.43 % (31068)------------------------------
% 27.63/5.43 % (31068)------------------------------
% 27.63/5.45 % (31074)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_30834 for (2963ds/865Mi)
% 28.35/5.52 % (31044)Instruction limit reached!
% 28.35/5.52 % (31044)------------------------------
% 28.35/5.52 % (31044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.35/5.52 % (31044)Termination reason: Unknown
% 28.35/5.52 % (31044)Termination phase: Saturation
% 28.35/5.52
% 28.35/5.52 % (31044)Memory used [KB]: 11257
% 28.35/5.52 % (31044)Time elapsed: 2.172 s
% 28.35/5.52 % (31044)Instructions burned: 4350 (million)
% 28.35/5.52 % (31044)------------------------------
% 28.35/5.52 % (31044)------------------------------
% 28.35/5.54 % (31075)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_30834 for (2962ds/593Mi)
% 28.35/5.57 % (31073)Refutation not found, non-redundant clauses discarded% (31073)------------------------------
% 28.35/5.57 % (31073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.35/5.57 % (31073)Termination reason: Refutation not found, non-redundant clauses discarded
% 28.35/5.57
% 28.35/5.57 % (31073)Memory used [KB]: 9210
% 28.35/5.57 % (31073)Time elapsed: 0.218 s
% 28.35/5.57 % (31073)Instructions burned: 408 (million)
% 28.35/5.57 % (31073)------------------------------
% 28.35/5.57 % (31073)------------------------------
% 28.35/5.59 % (31076)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_30834 for (2962ds/443Mi)
% 28.77/5.69 % (31071)Instruction limit reached!
% 28.77/5.69 % (31071)------------------------------
% 28.77/5.69 % (31071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.77/5.69 % (31071)Termination reason: Unknown
% 28.77/5.69 % (31071)Termination phase: Saturation
% 28.77/5.69
% 28.77/5.69 % (31071)Memory used [KB]: 8187
% 28.77/5.69 % (31071)Time elapsed: 0.554 s
% 28.77/5.69 % (31071)Instructions burned: 1378 (million)
% 28.77/5.69 % (31071)------------------------------
% 28.77/5.69 % (31071)------------------------------
% 29.55/5.70 % (31077)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_30834 for (2960ds/594Mi)
% 29.55/5.76 % (31075)Instruction limit reached!
% 29.55/5.76 % (31075)------------------------------
% 29.55/5.76 % (31075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.55/5.76 % (31075)Termination reason: Unknown
% 29.55/5.76 % (31075)Termination phase: Saturation
% 29.55/5.76
% 29.55/5.76 % (31075)Memory used [KB]: 6908
% 29.55/5.76 % (31075)Time elapsed: 0.224 s
% 29.55/5.76 % (31075)Instructions burned: 594 (million)
% 29.55/5.76 % (31075)------------------------------
% 29.55/5.76 % (31075)------------------------------
% 29.55/5.78 % (31079)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_30834 for (2960ds/327Mi)
% 29.55/5.80 % (31072)Instruction limit reached!
% 29.55/5.80 % (31072)------------------------------
% 29.55/5.80 % (31072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.55/5.80 % (31072)Termination reason: Unknown
% 29.55/5.80 % (31072)Termination phase: Saturation
% 29.55/5.80
% 29.55/5.80 % (31072)Memory used [KB]: 9722
% 29.55/5.80 % (31072)Time elapsed: 0.443 s
% 29.55/5.80 % (31072)Instructions burned: 906 (million)
% 29.55/5.80 % (31072)------------------------------
% 29.55/5.80 % (31072)------------------------------
% 29.99/5.80 % (31076)Instruction limit reached!
% 29.99/5.80 % (31076)------------------------------
% 29.99/5.80 % (31076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.99/5.80 % (31076)Termination reason: Unknown
% 29.99/5.80 % (31076)Termination phase: Saturation
% 29.99/5.80
% 29.99/5.80 % (31076)Memory used [KB]: 8187
% 29.99/5.80 % (31076)Time elapsed: 0.215 s
% 29.99/5.80 % (31076)Instructions burned: 443 (million)
% 29.99/5.80 % (31076)------------------------------
% 29.99/5.80 % (31076)------------------------------
% 29.99/5.81 % (31080)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_30834 for (2959ds/5411Mi)
% 29.99/5.82 % (31074)Instruction limit reached!
% 29.99/5.82 % (31074)------------------------------
% 29.99/5.82 % (31074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.99/5.82 % (31074)Termination reason: Unknown
% 29.99/5.82 % (31074)Termination phase: Saturation
% 29.99/5.82
% 29.99/5.82 % (31074)Memory used [KB]: 7803
% 29.99/5.82 % (31074)Time elapsed: 0.367 s
% 29.99/5.82 % (31074)Instructions burned: 865 (million)
% 29.99/5.82 % (31074)------------------------------
% 29.99/5.82 % (31074)------------------------------
% 29.99/5.82 % (31081)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_30834 for (2959ds/1762Mi)
% 29.99/5.83 % (31082)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_30834 for (2959ds/96Mi)
% 29.99/5.87 % (31082)Instruction limit reached!
% 29.99/5.87 % (31082)------------------------------
% 29.99/5.87 % (31082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.99/5.87 % (31082)Termination reason: Unknown
% 29.99/5.87 % (31082)Termination phase: Saturation
% 29.99/5.87
% 29.99/5.87 % (31082)Memory used [KB]: 6652
% 29.99/5.87 % (31082)Time elapsed: 0.044 s
% 29.99/5.87 % (31082)Instructions burned: 97 (million)
% 29.99/5.87 % (31082)------------------------------
% 29.99/5.87 % (31082)------------------------------
% 29.99/5.89 % (31083)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_30834 for (2959ds/503Mi)
% 31.30/5.94 % (31079)Instruction limit reached!
% 31.30/5.94 % (31079)------------------------------
% 31.30/5.94 % (31079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.30/5.94 % (31079)Termination reason: Unknown
% 31.30/5.94 % (31079)Termination phase: Saturation
% 31.30/5.94
% 31.30/5.94 % (31079)Memory used [KB]: 9722
% 31.30/5.94 % (31079)Time elapsed: 0.168 s
% 31.30/5.94 % (31079)Instructions burned: 327 (million)
% 31.30/5.94 % (31079)------------------------------
% 31.30/5.94 % (31079)------------------------------
% 31.30/5.96 % (31084)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_30834 for (2958ds/90Mi)
% 31.30/5.98 % (31064)Refutation not found, non-redundant clauses discarded% (31064)------------------------------
% 31.30/5.98 % (31064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.30/5.98 % (31064)Termination reason: Refutation not found, non-redundant clauses discarded
% 31.30/5.98
% 31.30/5.98 % (31064)Memory used [KB]: 7547
% 31.30/5.98 % (31064)Time elapsed: 1.677 s
% 31.30/5.98 % (31064)Instructions burned: 4533 (million)
% 31.30/5.98 % (31064)------------------------------
% 31.30/5.98 % (31064)------------------------------
% 31.30/5.99 % (31077)Instruction limit reached!
% 31.30/5.99 % (31077)------------------------------
% 31.30/5.99 % (31077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.30/5.99 % (31077)Termination reason: Unknown
% 31.30/5.99 % (31077)Termination phase: Saturation
% 31.30/5.99
% 31.30/5.99 % (31077)Memory used [KB]: 8315
% 31.30/5.99 % (31077)Time elapsed: 0.291 s
% 31.30/5.99 % (31077)Instructions burned: 594 (million)
% 31.30/5.99 % (31077)------------------------------
% 31.30/5.99 % (31077)------------------------------
% 31.30/6.00 % (31084)Instruction limit reached!
% 31.30/6.00 % (31084)------------------------------
% 31.30/6.00 % (31084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.30/6.00 % (31084)Termination reason: Unknown
% 31.30/6.00 % (31084)Termination phase: Twee Goal Transformation
% 31.30/6.00
% 31.30/6.00 % (31084)Memory used [KB]: 2558
% 31.30/6.00 % (31084)Time elapsed: 0.043 s
% 31.30/6.00 % (31084)Instructions burned: 90 (million)
% 31.30/6.00 % (31084)------------------------------
% 31.30/6.00 % (31084)------------------------------
% 31.30/6.00 % (31085)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_30834 for (2957ds/593Mi)
% 31.30/6.01 % (31086)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_30834 for (2957ds/1512Mi)
% 31.30/6.02 % (31087)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_30834 for (2957ds/569Mi)
% 33.31/6.14 % (31083)Instruction limit reached!
% 33.31/6.14 % (31083)------------------------------
% 33.31/6.14 % (31083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.31/6.14 % (31083)Termination reason: Unknown
% 33.31/6.14 % (31083)Termination phase: Saturation
% 33.31/6.14
% 33.31/6.14 % (31083)Memory used [KB]: 8315
% 33.31/6.14 % (31083)Time elapsed: 0.266 s
% 33.31/6.14 % (31083)Instructions burned: 504 (million)
% 33.31/6.14 % (31083)------------------------------
% 33.31/6.14 % (31083)------------------------------
% 33.31/6.14 % (31086)Refutation not found, incomplete strategy
% 33.31/6.14 % (31086)------------------------------
% 33.31/6.14 % (31086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.31/6.14 % (31086)Termination reason: Refutation not found, incomplete strategy
% 33.31/6.14
% 33.31/6.14
% 33.31/6.14 % (31086)Memory used [KB]: 8699
% 33.31/6.14 % (31086)Time elapsed: 0.148 s
% 33.31/6.14 % (31086)Instructions burned: 247 (million)
% 33.31/6.14 % (31086)------------------------------
% 33.31/6.14 % (31086)------------------------------
% 33.31/6.15 % (31088)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_30834 for (2956ds/501Mi)
% 33.31/6.15 % (31089)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_30834 for (2956ds/562Mi)
% 33.63/6.24 % (31087)Instruction limit reached!
% 33.63/6.24 % (31087)------------------------------
% 33.63/6.24 % (31087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.63/6.24 % (31087)Termination reason: Unknown
% 33.63/6.24 % (31087)Termination phase: Saturation
% 33.63/6.24
% 33.63/6.24 % (31087)Memory used [KB]: 10234
% 33.63/6.24 % (31087)Time elapsed: 0.225 s
% 33.63/6.24 % (31087)Instructions burned: 571 (million)
% 33.63/6.24 % (31087)------------------------------
% 33.63/6.24 % (31087)------------------------------
% 33.63/6.26 % (31090)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_30834 for (2955ds/406Mi)
% 33.63/6.29 % (31085)Instruction limit reached!
% 33.63/6.29 % (31085)------------------------------
% 33.63/6.29 % (31085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.63/6.29 % (31085)Termination reason: Unknown
% 33.63/6.29 % (31085)Termination phase: Saturation
% 33.63/6.29
% 33.63/6.29 % (31085)Memory used [KB]: 8315
% 33.63/6.29 % (31085)Time elapsed: 0.313 s
% 33.63/6.29 % (31085)Instructions burned: 593 (million)
% 33.63/6.29 % (31085)------------------------------
% 33.63/6.29 % (31085)------------------------------
% 34.28/6.31 % (31091)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_30834 for (2954ds/582Mi)
% 34.28/6.38 % (31089)Instruction limit reached!
% 34.28/6.38 % (31089)------------------------------
% 34.28/6.38 % (31089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.28/6.38 % (31089)Termination reason: Unknown
% 34.28/6.38 % (31089)Termination phase: Saturation
% 34.28/6.38
% 34.28/6.38 % (31089)Memory used [KB]: 7036
% 34.28/6.38 % (31089)Time elapsed: 0.228 s
% 34.28/6.38 % (31089)Instructions burned: 562 (million)
% 34.28/6.38 % (31089)------------------------------
% 34.28/6.38 % (31089)------------------------------
% 34.82/6.40 % (31092)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_30834 for (2953ds/456Mi)
% 34.82/6.40 % (31088)Instruction limit reached!
% 34.82/6.40 % (31088)------------------------------
% 34.82/6.40 % (31088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.82/6.40 % (31088)Termination reason: Unknown
% 34.82/6.40 % (31088)Termination phase: Saturation
% 34.82/6.40
% 34.82/6.40 % (31088)Memory used [KB]: 9083
% 34.82/6.40 % (31088)Time elapsed: 0.271 s
% 34.82/6.40 % (31088)Instructions burned: 501 (million)
% 34.82/6.40 % (31088)------------------------------
% 34.82/6.40 % (31088)------------------------------
% 34.82/6.42 % (31093)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_30834 for (2953ds/393Mi)
% 34.82/6.44 % (31090)Instruction limit reached!
% 34.82/6.44 % (31090)------------------------------
% 34.82/6.44 % (31090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.82/6.44 % (31090)Termination reason: Unknown
% 34.82/6.44 % (31090)Termination phase: Saturation
% 34.82/6.44
% 34.82/6.44 % (31090)Memory used [KB]: 7164
% 34.82/6.44 % (31090)Time elapsed: 0.185 s
% 34.82/6.44 % (31090)Instructions burned: 406 (million)
% 34.82/6.44 % (31090)------------------------------
% 34.82/6.44 % (31090)------------------------------
% 34.82/6.46 % (31094)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_30834 for (2953ds/1335Mi)
% 35.58/6.50 % (31081)Instruction limit reached!
% 35.58/6.50 % (31081)------------------------------
% 35.58/6.50 % (31081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.58/6.50 % (31081)Termination reason: Unknown
% 35.58/6.50 % (31081)Termination phase: Saturation
% 35.58/6.50
% 35.58/6.50 % (31081)Memory used [KB]: 14583
% 35.58/6.50 % (31081)Time elapsed: 0.683 s
% 35.58/6.50 % (31081)Instructions burned: 1762 (million)
% 35.58/6.50 % (31081)------------------------------
% 35.58/6.50 % (31081)------------------------------
% 35.58/6.52 % (31095)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_30834 for (2952ds/3373Mi)
% 35.80/6.61 % (31091)Instruction limit reached!
% 35.80/6.61 % (31091)------------------------------
% 35.80/6.61 % (31091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.80/6.61 % (31091)Termination reason: Unknown
% 35.80/6.61 % (31091)Termination phase: Saturation
% 35.80/6.61
% 35.80/6.61 % (31091)Memory used [KB]: 9338
% 35.80/6.61 % (31091)Time elapsed: 0.296 s
% 35.80/6.61 % (31091)Instructions burned: 583 (million)
% 35.80/6.61 % (31091)------------------------------
% 35.80/6.61 % (31091)------------------------------
% 35.80/6.61 % (31093)Instruction limit reached!
% 35.80/6.61 % (31093)------------------------------
% 35.80/6.61 % (31093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.80/6.61 % (31093)Termination reason: Unknown
% 35.80/6.61 % (31093)Termination phase: Saturation
% 35.80/6.61
% 35.80/6.61 % (31093)Memory used [KB]: 8955
% 35.80/6.61 % (31093)Time elapsed: 0.195 s
% 35.80/6.61 % (31093)Instructions burned: 394 (million)
% 35.80/6.61 % (31093)------------------------------
% 35.80/6.61 % (31093)------------------------------
% 35.80/6.61 % (31092)Instruction limit reached!
% 35.80/6.61 % (31092)------------------------------
% 35.80/6.61 % (31092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.80/6.61 % (31092)Termination reason: Unknown
% 35.80/6.61 % (31092)Termination phase: Saturation
% 35.80/6.61
% 35.80/6.62 % (31092)Memory used [KB]: 8315
% 35.80/6.62 % (31092)Time elapsed: 0.220 s
% 35.80/6.62 % (31092)Instructions burned: 456 (million)
% 35.80/6.62 % (31092)------------------------------
% 35.80/6.62 % (31092)------------------------------
% 35.80/6.62 % (31096)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_30834 for (2951ds/474Mi)
% 35.80/6.63 % (31097)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_30834 for (2951ds/157Mi)
% 35.80/6.63 % (31098)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_30834 for (2951ds/590Mi)
% 35.80/6.69 % (31097)Instruction limit reached!
% 35.80/6.69 % (31097)------------------------------
% 35.80/6.69 % (31097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.80/6.69 % (31097)Termination reason: Unknown
% 35.80/6.69 % (31097)Termination phase: Saturation
% 35.80/6.69
% 35.80/6.69 % (31097)Memory used [KB]: 6780
% 35.80/6.69 % (31097)Time elapsed: 0.068 s
% 35.80/6.69 % (31097)Instructions burned: 157 (million)
% 35.80/6.69 % (31097)------------------------------
% 35.80/6.69 % (31097)------------------------------
% 36.83/6.71 % (31099)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_30834 for (2950ds/104Mi)
% 36.83/6.76 % (31099)Instruction limit reached!
% 36.83/6.76 % (31099)------------------------------
% 36.83/6.76 % (31099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.83/6.76 % (31099)Termination reason: Unknown
% 36.83/6.76 % (31099)Termination phase: Saturation
% 36.83/6.76
% 36.83/6.76 % (31099)Memory used [KB]: 6908
% 36.83/6.76 % (31099)Time elapsed: 0.048 s
% 36.83/6.76 % (31099)Instructions burned: 105 (million)
% 36.83/6.76 % (31099)------------------------------
% 36.83/6.76 % (31099)------------------------------
% 36.83/6.77 % (31100)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_30834 for (2950ds/414Mi)
% 37.11/6.81 % (31096)Instruction limit reached!
% 37.11/6.81 % (31096)------------------------------
% 37.11/6.81 % (31096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.11/6.81 % (31096)Termination reason: Unknown
% 37.11/6.81 % (31096)Termination phase: Saturation
% 37.11/6.81
% 37.11/6.81 % (31096)Memory used [KB]: 10362
% 37.11/6.81 % (31096)Time elapsed: 0.186 s
% 37.11/6.81 % (31096)Instructions burned: 475 (million)
% 37.11/6.81 % (31096)------------------------------
% 37.11/6.81 % (31096)------------------------------
% 37.11/6.83 % (31101)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_30834 for (2949ds/715Mi)
% 37.51/6.91 % (31098)Instruction limit reached!
% 37.51/6.91 % (31098)------------------------------
% 37.51/6.91 % (31098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.51/6.91 % (31098)Termination reason: Unknown
% 37.51/6.91 % (31098)Termination phase: Saturation
% 37.51/6.91
% 37.51/6.91 % (31098)Memory used [KB]: 9466
% 37.51/6.91 % (31098)Time elapsed: 0.277 s
% 37.51/6.91 % (31098)Instructions burned: 590 (million)
% 37.51/6.91 % (31098)------------------------------
% 37.51/6.91 % (31098)------------------------------
% 37.51/6.93 % (31102)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_30834 for (2948ds/961Mi)
% 37.51/6.94 % (31100)Instruction limit reached!
% 37.51/6.94 % (31100)------------------------------
% 37.51/6.94 % (31100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.51/6.94 % (31100)Termination reason: Unknown
% 37.51/6.94 % (31100)Termination phase: Saturation
% 37.51/6.94
% 37.51/6.94 % (31100)Memory used [KB]: 6908
% 37.51/6.94 % (31100)Time elapsed: 0.163 s
% 37.51/6.94 % (31100)Instructions burned: 416 (million)
% 37.51/6.94 % (31100)------------------------------
% 37.51/6.94 % (31100)------------------------------
% 37.51/6.95 % (31103)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_30834 for (2948ds/1213Mi)
% 39.69/7.11 % (31094)Instruction limit reached!
% 39.69/7.11 % (31094)------------------------------
% 39.69/7.11 % (31094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.69/7.11 % (31094)Termination reason: Unknown
% 39.69/7.11 % (31094)Termination phase: Saturation
% 39.69/7.11
% 39.69/7.11 % (31094)Memory used [KB]: 8571
% 39.69/7.11 % (31094)Time elapsed: 0.655 s
% 39.69/7.11 % (31094)Instructions burned: 1335 (million)
% 39.69/7.11 % (31094)------------------------------
% 39.69/7.11 % (31094)------------------------------
% 40.39/7.13 % (31105)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_30834 for (2946ds/1979Mi)
% 40.39/7.19 % (31101)Instruction limit reached!
% 40.39/7.19 % (31101)------------------------------
% 40.39/7.19 % (31101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.39/7.19 % (31101)Termination reason: Unknown
% 40.39/7.19 % (31101)Termination phase: Saturation
% 40.39/7.19
% 40.39/7.19 % (31101)Memory used [KB]: 4093
% 40.39/7.19 % (31101)Time elapsed: 0.352 s
% 40.39/7.19 % (31101)Instructions burned: 716 (million)
% 40.39/7.19 % (31101)------------------------------
% 40.39/7.19 % (31101)------------------------------
% 40.81/7.20 % (31106)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_30834 for (2945ds/481Mi)
% 41.31/7.39 % (31106)Instruction limit reached!
% 41.31/7.39 % (31106)------------------------------
% 41.31/7.39 % (31106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.31/7.39 % (31106)Termination reason: Unknown
% 41.31/7.39 % (31106)Termination phase: Saturation
% 41.31/7.39
% 41.31/7.39 % (31106)Memory used [KB]: 10362
% 41.31/7.39 % (31106)Time elapsed: 0.187 s
% 41.31/7.39 % (31106)Instructions burned: 481 (million)
% 41.31/7.39 % (31106)------------------------------
% 41.31/7.39 % (31106)------------------------------
% 41.31/7.39 % (31102)Instruction limit reached!
% 41.31/7.39 % (31102)------------------------------
% 41.31/7.39 % (31102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.31/7.39 % (31102)Termination reason: Unknown
% 41.31/7.39 % (31102)Termination phase: Saturation
% 41.31/7.39
% 41.31/7.39 % (31102)Memory used [KB]: 8571
% 41.31/7.39 % (31102)Time elapsed: 0.468 s
% 41.31/7.39 % (31102)Instructions burned: 962 (million)
% 41.31/7.39 % (31102)------------------------------
% 41.31/7.39 % (31102)------------------------------
% 42.03/7.41 % (31108)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_30834 for (2943ds/432Mi)
% 42.03/7.41 % (31107)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_30834 for (2943ds/783Mi)
% 42.44/7.56 % (31103)Instruction limit reached!
% 42.44/7.56 % (31103)------------------------------
% 42.44/7.56 % (31103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.44/7.56 % (31103)Termination reason: Unknown
% 42.44/7.56 % (31103)Termination phase: Saturation
% 42.44/7.56
% 42.44/7.56 % (31103)Memory used [KB]: 11769
% 42.44/7.56 % (31103)Time elapsed: 0.611 s
% 42.44/7.56 % (31103)Instructions burned: 1214 (million)
% 42.44/7.56 % (31103)------------------------------
% 42.44/7.56 % (31103)------------------------------
% 42.44/7.58 % (31109)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_30834 for (2942ds/1670Mi)
% 42.82/7.62 % (31108)Instruction limit reached!
% 42.82/7.62 % (31108)------------------------------
% 42.82/7.62 % (31108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.82/7.62 % (31108)Termination reason: Unknown
% 42.82/7.62 % (31108)Termination phase: Saturation
% 42.82/7.62
% 42.82/7.62 % (31108)Memory used [KB]: 8187
% 42.82/7.62 % (31108)Time elapsed: 0.210 s
% 42.82/7.62 % (31108)Instructions burned: 433 (million)
% 42.82/7.62 % (31108)------------------------------
% 42.82/7.62 % (31108)------------------------------
% 42.82/7.63 % (31110)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_30834 for (2941ds/90Mi)
% 42.82/7.66 % (31095)First to succeed.
% 42.82/7.67 % (31095)Refutation found. Thanks to Tanya!
% 42.82/7.67 % SZS status Theorem for DTF2THF_30834
% 42.82/7.67 % SZS output start Proof for DTF2THF_30834
% 42.82/7.67 thf(func_def_0, type, in: $i > $i > $o).
% 42.82/7.67 thf(func_def_1, type, exu: ($i > $o) > $o).
% 42.82/7.67 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 42.82/7.67 thf(func_def_8, type, powerset: $i > $i).
% 42.82/7.67 thf(func_def_10, type, setunion: $i > $i).
% 42.82/7.67 thf(func_def_19, type, descr: ($i > $o) > $i).
% 42.82/7.67 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 42.82/7.67 thf(func_def_26, type, prop2set: $o > $i).
% 42.82/7.67 thf(func_def_36, type, nonempty: $i > $o).
% 42.82/7.67 thf(func_def_69, type, set2prop: $i > $o).
% 42.82/7.67 thf(func_def_88, type, subset: $i > $i > $o).
% 42.82/7.67 thf(func_def_89, type, disjoint: $i > $i > $o).
% 42.82/7.67 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 42.82/7.67 thf(func_def_114, type, binunion: $i > $i > $i).
% 42.82/7.67 thf(func_def_122, type, binintersect: $i > $i > $i).
% 42.82/7.67 thf(func_def_135, type, regular: $i > $o).
% 42.82/7.67 thf(func_def_136, type, setminus: $i > $i > $i).
% 42.82/7.67 thf(func_def_147, type, symdiff: $i > $i > $i).
% 42.82/7.67 thf(func_def_153, type, iskpair: $i > $o).
% 42.82/7.67 thf(func_def_158, type, kpair: $i > $i > $i).
% 42.82/7.67 thf(func_def_160, type, cartprod: $i > $i > $i).
% 42.82/7.67 thf(func_def_177, type, singleton: $i > $o).
% 42.82/7.67 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 42.82/7.67 thf(func_def_184, type, atmost1p: $i > $o).
% 42.82/7.67 thf(func_def_185, type, atleast2p: $i > $o).
% 42.82/7.67 thf(func_def_186, type, atmost2p: $i > $o).
% 42.82/7.67 thf(func_def_187, type, upairsetp: $i > $o).
% 42.82/7.67 thf(func_def_191, type, kfst: $i > $i).
% 42.82/7.67 thf(func_def_203, type, ksnd: $i > $i).
% 42.82/7.67 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 42.82/7.67 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 42.82/7.67 thf(func_def_235, type, sK1: $i > $i > $o).
% 42.82/7.67 thf(func_def_240, type, sK6: $i > $i).
% 42.82/7.67 thf(func_def_241, type, sK7: $o > $i > $i > $i).
% 42.82/7.67 thf(func_def_245, type, sK8: $i > $i).
% 42.82/7.67 thf(func_def_246, type, sK9: $i > ($i > $o) > $i).
% 42.82/7.67 thf(func_def_247, type, sK10: $i > $i).
% 42.82/7.67 thf(func_def_248, type, sK11: $i > $i > $i).
% 42.82/7.67 thf(func_def_249, type, sK12: $i > $i).
% 42.82/7.67 thf(func_def_250, type, sK13: ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_251, type, sK14: ($i > $o) > $i).
% 42.82/7.67 thf(func_def_252, type, sK15: ($i > $o) > $i).
% 42.82/7.67 thf(func_def_253, type, sK16: ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_254, type, sK17: $i > ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_255, type, sK18: $i > ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_256, type, sK19: ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_257, type, sK20: ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_258, type, sK21: ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_259, type, sK22: ($i > $o) > $i).
% 42.82/7.67 thf(func_def_260, type, sK23: ($i > $o) > $i).
% 42.82/7.67 thf(func_def_261, type, sK24: ($i > $o) > $i).
% 42.82/7.67 thf(func_def_262, type, sK25: ($i > $o) > $i).
% 42.82/7.67 thf(func_def_263, type, sK26: $i > $i > $i).
% 42.82/7.67 thf(func_def_264, type, sK27: ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_265, type, sK28: ($i > $o) > $i).
% 42.82/7.67 thf(func_def_266, type, sK29: ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_267, type, sK30: $i > $i > $i).
% 42.82/7.67 thf(func_def_268, type, sK31: $i > $i > $i).
% 42.82/7.67 thf(func_def_269, type, sK32: $i > $i > $i).
% 42.82/7.67 thf(func_def_270, type, sK33: $i > $i > $i).
% 42.82/7.67 thf(func_def_271, type, sK34: ($i > $o) > $i).
% 42.82/7.67 thf(func_def_272, type, sK35: ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_273, type, sK36: $i > $i > $i).
% 42.82/7.67 thf(func_def_274, type, sK37: $i > $i > $i).
% 42.82/7.67 thf(func_def_275, type, sK38: $i > $i > $i).
% 42.82/7.67 thf(func_def_276, type, sK39: $i > $i > $i).
% 42.82/7.67 thf(func_def_277, type, sK40: $i > $i).
% 42.82/7.67 thf(func_def_278, type, sK41: ($i > $o) > ($i > $o) > $i > $i > $i).
% 42.82/7.67 thf(func_def_279, type, sK42: $i > $i > ($i > $o) > ($i > $o) > $i).
% 42.82/7.67 thf(func_def_280, type, sK43: $i > $i).
% 42.82/7.67 thf(func_def_281, type, sK44: $i > $i > $i).
% 42.82/7.67 thf(func_def_282, type, sK45: $i > $i > $i).
% 42.82/7.67 thf(func_def_283, type, sK46: $i > $i > $i).
% 42.82/7.67 thf(func_def_284, type, sK47: $i > $i > $i).
% 42.82/7.67 thf(func_def_285, type, sK48: $i > $i > $i).
% 42.82/7.67 thf(func_def_286, type, sK49: $i > $i > $i).
% 42.82/7.67 thf(func_def_287, type, sK50: $i > $i > $i > $i).
% 42.82/7.67 thf(func_def_288, type, sK51: $i > $i).
% 42.82/7.67 thf(func_def_289, type, sK52: $i > ($i > $o) > $i).
% 42.82/7.67 thf(func_def_290, type, sK53: $i > ($i > $o) > $i).
% 42.82/7.67 thf(func_def_291, type, sK54: $i > ($i > $o) > $i).
% 42.82/7.67 thf(func_def_292, type, sK55: $i > ($i > $o) > $i).
% 42.82/7.67 thf(func_def_293, type, sK56: ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_294, type, sK57: ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_295, type, sK58: ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_296, type, sK59: ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_297, type, sK60: ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_298, type, sK61: ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_299, type, sK62: ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_300, type, sK63: $i > ($i > $o) > $i).
% 42.82/7.67 thf(func_def_301, type, sK64: ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_302, type, sK65: $i > $i).
% 42.82/7.67 thf(func_def_303, type, sK66: $i > $i > $i > $i).
% 42.82/7.67 thf(func_def_304, type, sK67: $i > $i > $i > $i).
% 42.82/7.67 thf(func_def_305, type, sK68: $i > $i > $i).
% 42.82/7.67 thf(func_def_306, type, sK69: ($i > $o) > ($i > $o) > $i).
% 42.82/7.67 thf(func_def_307, type, sK70: ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_308, type, sK71: ($i > $o) > ($i > $o) > $i).
% 42.82/7.67 thf(func_def_309, type, sK72: ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_310, type, sK73: ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_311, type, sK74: ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_312, type, sK75: ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_313, type, sK76: $i > $i).
% 42.82/7.67 thf(func_def_315, type, sK77: ($i > $i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_316, type, sK78: ($i > $i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_317, type, sK79: ($i > $i > $o) > $i > $i > $i).
% 42.82/7.67 thf(func_def_318, type, sK80: ($i > $i > $o) > $i > $i > $i).
% 42.82/7.67 thf(func_def_319, type, sK81: ($i > $i > $o) > $i > $i > $i).
% 42.82/7.67 thf(func_def_320, type, sK82: ($i > $i > $o) > $i > $i > $i).
% 42.82/7.67 thf(func_def_321, type, sK83: $i > ($i > $o) > $i).
% 42.82/7.67 thf(func_def_322, type, sK84: ($i > $o) > $i).
% 42.82/7.67 thf(func_def_323, type, sK85: ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_324, type, sK86: ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_325, type, sK87: ($i > $o) > ($i > $o) > $i).
% 42.82/7.67 thf(func_def_326, type, sK88: ($i > $o) > ($i > $o) > $i).
% 42.82/7.67 thf(func_def_327, type, sK89: ($i > $o) > $i).
% 42.82/7.67 thf(func_def_328, type, sK90: ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_329, type, sK91: ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_330, type, sK92: ($i > $o) > $i).
% 42.82/7.67 thf(func_def_331, type, sK93: ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_332, type, sK94: ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_333, type, sK95: ($i > $o) > $i).
% 42.82/7.67 thf(func_def_334, type, sK96: ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_335, type, sK97: ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_336, type, sK98: ($i > $o) > ($i > $o) > $i).
% 42.82/7.67 thf(func_def_337, type, sK99: ($i > $o) > $i).
% 42.82/7.67 thf(func_def_338, type, sK100: ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_339, type, sK101: ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_340, type, sK102: ($i > $o) > $i).
% 42.82/7.67 thf(func_def_341, type, sK103: ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_342, type, sK104: ($i > $o) > $i).
% 42.82/7.67 thf(func_def_343, type, sK105: ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_344, type, sK106: ($i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_345, type, ph107: !>[X0: $tType]:(X0)).
% 42.82/7.67 thf(func_def_346, type, sK108: $i > $i > $i > ($i > $i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_347, type, sK109: $i > $i > $i > ($i > $i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_352, type, sK114: $i > $i > $i > ($i > $i > $o) > $i > $i).
% 42.82/7.67 thf(func_def_353, type, sK115: $i > $i > $i > ($i > $i > $o) > $i > $i).
% 42.82/7.67 thf(f8370,plain,(
% 42.82/7.67 $false),
% 42.82/7.67 inference(avatar_sat_refutation,[status(thm)],[f3305,f3333,f7097,f7107,f8359,f8367,f8368])).
% 42.82/7.67 thf(f8368,plain,(
% 42.82/7.67 (sK112 != sK0) | (sK113 != sK4) | ($true != (sK1 @ sK112 @ sK113)) | ($true = (sK1 @ sK0 @ sK4))),
% 42.82/7.67 introduced(definition,[],[theory_tautology_sat_conflict])).
% 42.82/7.67 thf(f8367,plain,(
% 42.82/7.67 spl5_35 | ~spl5_25),
% 42.82/7.67 inference(avatar_split_clause,[status(thm)],[f8366,f7094,f8362])).
% 42.82/7.67 thf(f8362,definition,(
% 42.82/7.67 spl5_35 <=> (sK112 = sK0)),
% 42.82/7.67 introduced(definition,[new_symbols(naming,[spl5_35])],[avatar_definition])).
% 42.82/7.67 thf(f7094,definition,(
% 42.82/7.67 spl5_25 <=> ((kpair @ sK112 @ sK113) = (kpair @ sK0 @ sK4))),
% 42.82/7.67 introduced(definition,[new_symbols(naming,[spl5_25])],[avatar_definition])).
% 42.82/7.67 thf(f8366,plain,(
% 42.82/7.67 (sK112 = sK0) | ~spl5_25),
% 42.82/7.67 inference(forward_demodulation,[status(thm)],[f8345,f3241])).
% 42.82/7.67 thf(f3241,plain,(
% 42.82/7.67 ( ! [X2 : $i,X1 : $i] : (((kfst @ (kpair @ X2 @ X1)) = X2)) )),
% 42.82/7.67 inference(equality_proxy_clausification,[status(thm)],[f3240])).
% 42.82/7.67 thf(f3240,plain,(
% 42.82/7.67 ( ! [X2 : $i,X1 : $i] : ((((kfst @ (kpair @ X2 @ X1)) = X2) = $true)) )),
% 42.82/7.67 inference(beta_eta_normalization,[status(thm)],[f3239])).
% 42.82/7.67 thf(f3239,plain,(
% 42.82/7.67 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((kfst @ (kpair @ Y0 @ X1)) = Y0)) @ X2) = $true)) )),
% 42.82/7.67 inference(pi_clausification,[status(thm)],[f3238])).
% 42.82/7.67 thf(f3238,plain,(
% 42.82/7.67 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((kfst @ (kpair @ Y0 @ X1)) = Y0))) = $true)) )),
% 42.82/7.67 inference(beta_eta_normalization,[status(thm)],[f3237])).
% 42.82/7.67 thf(f3237,plain,(
% 42.82/7.67 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y1 @ Y0)) = Y1)))) @ X1) = $true)) )),
% 42.82/7.67 inference(pi_clausification,[status(thm)],[f1060])).
% 42.82/7.67 thf(f1060,plain,(
% 42.82/7.67 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y1 @ Y0)) = Y1))))))),
% 42.82/7.67 inference(definition_unfolding,[status(thm)],[f866,f620])).
% 42.82/7.67 thf(f620,plain,(
% 42.82/7.67 (kfstpairEq = $true)),
% 42.82/7.67 inference(cnf_transformation,[status(thm)],[f574])).
% 42.82/7.67 thf(f574,plain,(
% 42.82/7.67 (setextsub = $true) & (subsetemptysetimpeq = $true) & (binintersectSubset4 = $true) & (singletoninpowunion = $true) & (setadjoin__Cong = $true) & (upairset2IR = $true) & (setadjoinOr = $true) & (dsetconstr__Cong = $true) & (omegaSAx = $true) & (setminusEL = $true) & (ex1I2 = $true) & (binintersectSubset1 = $true) & (exuE1 = $true) & (symdiffI1 = $true) & (binintersectI = $true) & (exuE3e = $true) & (prop2setI = $true) & (descrp = $true) & (setunionAx = $true) & (subset2powerset = $true) & (subPowSU = $true) & (notequalI2 = $true) & (subsetE = $true) & (inPowerset = $true) & (cartprodfstpairEq = $true) & (binunionE = $true) & (upairequniteq = $true) & (exu__Cong = $true) & (setminusELneg = $true) & (cartprodmempair = $true) & (setminusI = $true) & (binunionLsub = $true) & (setunionI = $true) & (binintersectLsub = $true) & (foundationAx = $true) & (setminusSubset1 = $true) & (theprop = $true) & (bs114d = $true) & (exuEu = $true) & (subsetRefl = $true) & (subsetI2 = $true) & (singletoninpowerset = $true) & (setukpairinjL = $true) & ((((in @ sK4 @ sK2) = $true) & ($true != (sK1 @ sK0 @ sK4)) & ((in @ (kpair @ sK0 @ sK4) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK1 @ Y0 @ Y1)))))) = $true)) & ($true = (in @ sK0 @ sK3))) & (subsetTrans = $true) & (upairinpowunion = $true) & (cartprodmempaircEq = $true) & (cartprodpairsurjEq = $true) & (singletonsuniq = $true) & (dpsetconstrSub = $true) & (binintersectEL = $true) & (emptysetAx = $true) & (omegaIndAx = $true) & (symdiffIneg2 = $true) & (kpairsurjEq = $true) & (setunionsingleton2 = $true) & (ubforcartprodlem3 = $true) & (dsetconstrI = $true) & (binintersectRsub = $true) & (uniqinunit = $true) & (nonemptyI1 = $true) & (quantDeMorgan1 = $true) & (setminusLsub = $true) & (setunionsingleton1 = $true) & (setextAx = $true) & (notsubsetI = $true) & (powersetE = $true) & (exuI1 = $true) & (upairset2E = $true) & (secondinupair = $true) & (singletonprop = $true) & (notequalI1 = $true) & (cartprodsndin = $true) & (in__Cong = $true) & (descr__Cong = $true) & (powersetI = $true) & (subsetE2 = $true) & (setukpairinjR1 = $true) & (eqimpsubset1 = $true) & (sepSubset = $true) & (setminusILneg = $true) & (eqimpsubset2 = $true) & (dsetconstrEL = $true) & (dsetconstrER = $true) & (sepInPowerset = $true) & (ex1I = $true) & (binunionEcases = $true) & (exuE2 = $true) & (binintersectSubset3 = $true) & (prop2setE = $true) & (upairsetE = $true) & (setukpairinjR = $true) & (setadjoinIL = $true) & (binunionIR = $true) & (quantDeMorgan3 = $true) & (disjointsetsI1 = $true) & (cartprodsndpairEq = $true) & (emptyset__Cong = $true) & (setoftrueEq = $true) & (notinemptyset = $true) & (setunionsingleton = $true) & (symdiffI2 = $true) & (cartprodpairmemEL = $true) & (setminusIRneg = $true) & (setunion__Cong = $true) & (wellorderingAx = $true) & (singletonsswitch = $true) & (ksndpairEq = $true) & (upairsetIR = $true) & (replAx = $true) & (powersetAx = $true) & (singletonsubset = $true) & (inCongP = $true) & (cartprodmempair1 = $true) & (binunionRsub = $true) & (setukpairinjR2 = $true) & (emptyE1 = $true) & (quantDeMorgan2 = $true) & (notinsingleton = $true) & (setunionE2 = $true) & (powersetE1 = $true) & (setukpairinjL1 = $true) & (binintersectER = $true) & (setadjoinE = $true) & (binunionIL = $true) & (exuI3 = $true) & (setext = $true) & (powersetsubset = $true) & (omega0Ax = $true) & (kfstsingleton = $true) & (eqinunit = $true) & (ubforcartprodlem2 = $true) & (setadjoinSub = $true) & (ex1E1 = $true) & (setukpairIL = $true) & (emptysetE = $true) & (subsetI1 = $true) & (binintersectSubset2 = $true) & (kpairp = $true) & (emptyI = $true) & (setukpairinjL2 = $true) & (setminusERneg = $true) & (cartprodpairmemER = $true) & (ksndsingleton = $true) & (nonemptyI = $true) & (omega__Cong = $true) & (powersetI1 = $true) & (exuI2 = $true) & (prop2set2propI = $true) & (setukpairinjR11 = $true) & (powerset__Cong = $true) & (ubforcartprodlem1 = $true) & (binintersectSubset5 = $true) & (nonemptyE1 = $true) & (symdiffE = $true) & (notdallE = $true) & (setadjoinAx = $true) & (exuE3u = $true) & (emptysetimpfalse = $true) & (cartprodpairin = $true) & (emptyinunitempty = $true) & (setminusSubset2 = $true) & (symdiffIneg1 = $true) & (quantDeMorgan4 = $true) & (setukpairIR = $true) & (setunionE = $true) & (setadjoinSub2 = $true) & (kpairiskpair = $true) & (dpsetconstrI = $true) & (emptyInPowerset = $true) & (emptysetsubset = $true) & (setadjoinIR = $true) & (vacuousDall = $true) & (setminusER = $true) & (kfstpairEq = $true) & (upairsetIL = $true) & (setbeta = $true) & (notdexE = $true) & (setukpairinjR12 = $true) & (setOfPairsIsBReln = $true) & (emptyinPowerset = $true) & (nonemptyImpWitness = $true) & (cartprodfstin = $true) & (noeltsimpempty = $true) & (upairsubunion = $true)),
% 42.82/7.67 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f571,f573,f572])).
% 42.82/7.67 thf(f572,plain,(
% 42.82/7.67 ? [X0 : $i,X1 : $i > $i > $o,X2 : $i,X3 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ X2)) & ($true != (X1 @ X0 @ X4)) & ($true = (in @ (kpair @ X0 @ X4) @ (dpsetconstr @ X3 @ X2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1)))))))) & ((in @ X0 @ X3) = $true)) => (? [X4 : $i] : (($true = (in @ X4 @ sK2)) & ($true != (sK1 @ sK0 @ X4)) & ((in @ (kpair @ sK0 @ X4) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK1 @ Y0 @ Y1)))))) = $true)) & ($true = (in @ sK0 @ sK3)))),
% 42.82/7.67 introduced(definition,[],[choice_axiom])).
% 42.82/7.67 thf(f573,plain,(
% 42.82/7.67 ? [X4 : $i] : (($true = (in @ X4 @ sK2)) & ($true != (sK1 @ sK0 @ X4)) & ((in @ (kpair @ sK0 @ X4) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK1 @ Y0 @ Y1)))))) = $true)) => (((in @ sK4 @ sK2) = $true) & ($true != (sK1 @ sK0 @ sK4)) & ((in @ (kpair @ sK0 @ sK4) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK1 @ Y0 @ Y1)))))) = $true))),
% 42.82/7.67 introduced(definition,[],[choice_axiom])).
% 42.82/7.67 thf(f571,plain,(
% 42.82/7.67 (setextsub = $true) & (subsetemptysetimpeq = $true) & (binintersectSubset4 = $true) & (singletoninpowunion = $true) & (setadjoin__Cong = $true) & (upairset2IR = $true) & (setadjoinOr = $true) & (dsetconstr__Cong = $true) & (omegaSAx = $true) & (setminusEL = $true) & (ex1I2 = $true) & (binintersectSubset1 = $true) & (exuE1 = $true) & (symdiffI1 = $true) & (binintersectI = $true) & (exuE3e = $true) & (prop2setI = $true) & (descrp = $true) & (setunionAx = $true) & (subset2powerset = $true) & (subPowSU = $true) & (notequalI2 = $true) & (subsetE = $true) & (inPowerset = $true) & (cartprodfstpairEq = $true) & (binunionE = $true) & (upairequniteq = $true) & (exu__Cong = $true) & (setminusELneg = $true) & (cartprodmempair = $true) & (setminusI = $true) & (binunionLsub = $true) & (setunionI = $true) & (binintersectLsub = $true) & (foundationAx = $true) & (setminusSubset1 = $true) & (theprop = $true) & (bs114d = $true) & (exuEu = $true) & (subsetRefl = $true) & (subsetI2 = $true) & (singletoninpowerset = $true) & (setukpairinjL = $true) & ? [X0 : $i,X1 : $i > $i > $o,X2 : $i,X3 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ X2)) & ($true != (X1 @ X0 @ X4)) & ($true = (in @ (kpair @ X0 @ X4) @ (dpsetconstr @ X3 @ X2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1)))))))) & ((in @ X0 @ X3) = $true)) & (subsetTrans = $true) & (upairinpowunion = $true) & (cartprodmempaircEq = $true) & (cartprodpairsurjEq = $true) & (singletonsuniq = $true) & (dpsetconstrSub = $true) & (binintersectEL = $true) & (emptysetAx = $true) & (omegaIndAx = $true) & (symdiffIneg2 = $true) & (kpairsurjEq = $true) & (setunionsingleton2 = $true) & (ubforcartprodlem3 = $true) & (dsetconstrI = $true) & (binintersectRsub = $true) & (uniqinunit = $true) & (nonemptyI1 = $true) & (quantDeMorgan1 = $true) & (setminusLsub = $true) & (setunionsingleton1 = $true) & (setextAx = $true) & (notsubsetI = $true) & (powersetE = $true) & (exuI1 = $true) & (upairset2E = $true) & (secondinupair = $true) & (singletonprop = $true) & (notequalI1 = $true) & (cartprodsndin = $true) & (in__Cong = $true) & (descr__Cong = $true) & (powersetI = $true) & (subsetE2 = $true) & (setukpairinjR1 = $true) & (eqimpsubset1 = $true) & (sepSubset = $true) & (setminusILneg = $true) & (eqimpsubset2 = $true) & (dsetconstrEL = $true) & (dsetconstrER = $true) & (sepInPowerset = $true) & (ex1I = $true) & (binunionEcases = $true) & (exuE2 = $true) & (binintersectSubset3 = $true) & (prop2setE = $true) & (upairsetE = $true) & (setukpairinjR = $true) & (setadjoinIL = $true) & (binunionIR = $true) & (quantDeMorgan3 = $true) & (disjointsetsI1 = $true) & (cartprodsndpairEq = $true) & (emptyset__Cong = $true) & (setoftrueEq = $true) & (notinemptyset = $true) & (setunionsingleton = $true) & (symdiffI2 = $true) & (cartprodpairmemEL = $true) & (setminusIRneg = $true) & (setunion__Cong = $true) & (wellorderingAx = $true) & (singletonsswitch = $true) & (ksndpairEq = $true) & (upairsetIR = $true) & (replAx = $true) & (powersetAx = $true) & (singletonsubset = $true) & (inCongP = $true) & (cartprodmempair1 = $true) & (binunionRsub = $true) & (setukpairinjR2 = $true) & (emptyE1 = $true) & (quantDeMorgan2 = $true) & (notinsingleton = $true) & (setunionE2 = $true) & (powersetE1 = $true) & (setukpairinjL1 = $true) & (binintersectER = $true) & (setadjoinE = $true) & (binunionIL = $true) & (exuI3 = $true) & (setext = $true) & (powersetsubset = $true) & (omega0Ax = $true) & (kfstsingleton = $true) & (eqinunit = $true) & (ubforcartprodlem2 = $true) & (setadjoinSub = $true) & (ex1E1 = $true) & (setukpairIL = $true) & (emptysetE = $true) & (subsetI1 = $true) & (binintersectSubset2 = $true) & (kpairp = $true) & (emptyI = $true) & (setukpairinjL2 = $true) & (setminusERneg = $true) & (cartprodpairmemER = $true) & (ksndsingleton = $true) & (nonemptyI = $true) & (omega__Cong = $true) & (powersetI1 = $true) & (exuI2 = $true) & (prop2set2propI = $true) & (setukpairinjR11 = $true) & (powerset__Cong = $true) & (ubforcartprodlem1 = $true) & (binintersectSubset5 = $true) & (nonemptyE1 = $true) & (symdiffE = $true) & (notdallE = $true) & (setadjoinAx = $true) & (exuE3u = $true) & (emptysetimpfalse = $true) & (cartprodpairin = $true) & (emptyinunitempty = $true) & (setminusSubset2 = $true) & (symdiffIneg1 = $true) & (quantDeMorgan4 = $true) & (setukpairIR = $true) & (setunionE = $true) & (setadjoinSub2 = $true) & (kpairiskpair = $true) & (dpsetconstrI = $true) & (emptyInPowerset = $true) & (emptysetsubset = $true) & (setadjoinIR = $true) & (vacuousDall = $true) & (setminusER = $true) & (kfstpairEq = $true) & (upairsetIL = $true) & (setbeta = $true) & (notdexE = $true) & (setukpairinjR12 = $true) & (setOfPairsIsBReln = $true) & (emptyinPowerset = $true) & (nonemptyImpWitness = $true) & (cartprodfstin = $true) & (noeltsimpempty = $true) & (upairsubunion = $true)),
% 42.82/7.67 inference(flattening,[status(thm)],[f570])).
% 42.82/7.67 thf(f570,plain,(
% 42.82/7.67 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i > $i > $o,X2 : $i,X3 : $i] : (? [X4 : $i] : ((($true != (X1 @ X0 @ X4)) & ($true = (in @ (kpair @ X0 @ X4) @ (dpsetconstr @ X3 @ X2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1)))))))) & ($true = (in @ X4 @ X2))) & ((in @ X0 @ X3) = $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)),
% 42.82/7.67 inference(ennf_transformation,[status(thm)],[f555])).
% 42.82/7.67 thf(f555,plain,(
% 42.82/7.67 ~((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) => ! [X0 : $i,X1 : $i > $i > $o,X2 : $i,X3 : $i] : (((in @ X0 @ X3) = $true) => ! [X4 : $i] : (($true = (in @ X4 @ X2)) => (($true = (in @ (kpair @ X0 @ X4) @ (dpsetconstr @ X3 @ X2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1))))))) => ($true = (X1 @ X0 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 42.82/7.67 inference(fool_elimination,[status(thm)],[f554])).
% 42.82/7.67 thf(f554,plain,(
% 42.82/7.67 ~(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 => ! [X0 : $i,X1 : $i > $i > $o,X2 : $i,X3 : $i] : ((in @ X0 @ X3) => ! [X4 : $i] : ((in @ X4 @ X2) => ((in @ (kpair @ X0 @ X4) @ (dpsetconstr @ X3 @ X2 @ (^[X5 : $i, X6 : $i] : (X1 @ X5 @ X6)))) => (X1 @ X0 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 42.82/7.67 inference(rectify,[status(thm)],[f192])).
% 42.82/7.67 thf(f192,negated_conjecture,(
% 42.82/7.67 ~(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 => ! [X1 : $i,X0 : $i > $i > $o,X4 : $i,X3 : $i] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X4) => ((in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X3 @ X4 @ (^[X8 : $i, X10 : $i] : (X0 @ X8 @ X10)))) => (X0 @ X1 @ X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 42.82/7.67 inference(negated_conjecture,[status(cth)],[f191])).
% 42.82/7.67 thf(f191,conjecture,(
% 42.82/7.67 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 => ! [X1 : $i,X0 : $i > $i > $o,X4 : $i,X3 : $i] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X4) => ((in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X3 @ X4 @ (^[X8 : $i, X10 : $i] : (X0 @ X8 @ X10)))) => (X0 @ X1 @ X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 42.82/7.67 file('/export/starexec/sandbox/tmp/tmp.pZ9OXiV362/DTF2THF_30834.p',dpsetconstrERa)).
% 42.82/7.67 thf(f866,plain,(
% 42.82/7.67 (kfstpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y1 @ Y0)) = Y1))))))),
% 42.82/7.67 inference(cnf_transformation,[status(thm)],[f215])).
% 42.82/7.67 thf(f215,plain,(
% 42.82/7.67 (kfstpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y1 @ Y0)) = Y1))))))),
% 42.82/7.67 inference(fool_elimination,[status(thm)],[f214])).
% 42.82/7.67 thf(f214,plain,(
% 42.82/7.67 (! [X0 : $i,X1 : $i] : ((kfst @ (kpair @ X0 @ X1)) = X0) = kfstpairEq)),
% 42.82/7.67 inference(rectify,[status(thm)],[f166])).
% 42.82/7.67 thf(f166,axiom,(
% 42.82/7.67 (! [X1 : $i,X2 : $i] : ((kfst @ (kpair @ X1 @ X2)) = X1) = kfstpairEq)),
% 42.82/7.67 file('/export/starexec/sandbox/tmp/tmp.pZ9OXiV362/DTF2THF_30834.p',kfstpairEq)).
% 42.82/7.67 thf(f8345,plain,(
% 42.82/7.67 ((kfst @ (kpair @ sK0 @ sK4)) = sK112) | ~spl5_25),
% 42.82/7.67 inference(superposition,[status(thm)],[f3241,f7096])).
% 42.82/7.67 thf(f7096,plain,(
% 42.82/7.67 ((kpair @ sK112 @ sK113) = (kpair @ sK0 @ sK4)) | ~spl5_25),
% 42.82/7.67 inference(avatar_component_clause,[status(thm)],[f7094])).
% 42.82/7.67 thf(f8359,plain,(
% 42.82/7.67 spl5_34 | ~spl5_25),
% 42.82/7.67 inference(avatar_split_clause,[status(thm)],[f8358,f7094,f8354])).
% 42.82/7.67 thf(f8354,definition,(
% 42.82/7.67 spl5_34 <=> (sK113 = sK4)),
% 42.82/7.67 introduced(definition,[new_symbols(naming,[spl5_34])],[avatar_definition])).
% 42.82/7.67 thf(f8358,plain,(
% 42.82/7.67 (sK113 = sK4) | ~spl5_25),
% 42.82/7.67 inference(forward_demodulation,[status(thm)],[f8338,f1805])).
% 42.82/7.67 thf(f1805,plain,(
% 42.82/7.67 ( ! [X2 : $i,X1 : $i] : (((ksnd @ (kpair @ X2 @ X1)) = X1)) )),
% 42.82/7.67 inference(equality_proxy_clausification,[status(thm)],[f1804])).
% 42.82/7.67 thf(f1804,plain,(
% 42.82/7.67 ( ! [X2 : $i,X1 : $i] : ((((ksnd @ (kpair @ X2 @ X1)) = X1) = $true)) )),
% 42.82/7.67 inference(beta_eta_normalization,[status(thm)],[f1803])).
% 42.82/7.67 thf(f1803,plain,(
% 42.82/7.67 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((ksnd @ (kpair @ Y0 @ X1)) = X1)) @ X2))) )),
% 42.82/7.67 inference(pi_clausification,[status(thm)],[f1802])).
% 42.82/7.67 thf(f1802,plain,(
% 42.82/7.67 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((ksnd @ (kpair @ Y0 @ X1)) = X1))) = $true)) )),
% 42.82/7.67 inference(beta_eta_normalization,[status(thm)],[f1801])).
% 42.82/7.67 thf(f1801,plain,(
% 42.82/7.67 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y1 @ Y0)) = Y0)))) @ X1) = $true)) )),
% 42.82/7.67 inference(pi_clausification,[status(thm)],[f1139])).
% 42.82/7.67 thf(f1139,plain,(
% 42.82/7.67 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y1 @ Y0)) = Y0))))) = $true)),
% 42.82/7.67 inference(definition_unfolding,[status(thm)],[f947,f687])).
% 42.82/7.67 thf(f687,plain,(
% 42.82/7.67 (ksndpairEq = $true)),
% 42.82/7.67 inference(cnf_transformation,[status(thm)],[f574])).
% 42.82/7.67 thf(f947,plain,(
% 42.82/7.67 (ksndpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y1 @ Y0)) = Y0))))))),
% 42.82/7.67 inference(cnf_transformation,[status(thm)],[f415])).
% 42.82/7.67 thf(f415,plain,(
% 42.82/7.67 (ksndpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y1 @ Y0)) = Y0))))))),
% 42.82/7.67 inference(fool_elimination,[status(thm)],[f414])).
% 42.82/7.67 thf(f414,plain,(
% 42.82/7.67 (ksndpairEq = ! [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X0 @ X1)) = X1))),
% 42.82/7.67 inference(rectify,[status(thm)],[f177])).
% 42.82/7.67 thf(f177,axiom,(
% 42.82/7.67 (ksndpairEq = ! [X1 : $i,X2 : $i] : ((ksnd @ (kpair @ X1 @ X2)) = X2))),
% 42.82/7.67 file('/export/starexec/sandbox/tmp/tmp.pZ9OXiV362/DTF2THF_30834.p',ksndpairEq)).
% 42.82/7.67 thf(f8338,plain,(
% 42.82/7.67 (sK113 = (ksnd @ (kpair @ sK0 @ sK4))) | ~spl5_25),
% 42.82/7.67 inference(superposition,[status(thm)],[f1805,f7096])).
% 42.82/7.67 thf(f7107,plain,(
% 42.82/7.67 spl5_27 | ~spl5_21),
% 42.82/7.67 inference(avatar_split_clause,[status(thm)],[f7068,f3330,f7104])).
% 42.82/7.67 thf(f7104,definition,(
% 42.82/7.67 spl5_27 <=> ($true = (sK1 @ sK112 @ sK113))),
% 42.82/7.67 introduced(definition,[new_symbols(naming,[spl5_27])],[avatar_definition])).
% 42.82/7.67 thf(f3330,definition,(
% 42.82/7.67 spl5_21 <=> ($true = (in @ (kpair @ sK0 @ sK4) @ (dsetconstr @ (cartprod @ sK3 @ sK2) @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((sK1 @ Y1 @ Y2) & (in @ Y2 @ sK2)) & ((kpair @ Y1 @ Y2) = Y0)))) & (in @ Y1 @ sK3))))))))),
% 42.82/7.67 introduced(definition,[new_symbols(naming,[spl5_21])],[avatar_definition])).
% 42.82/7.67 thf(f7068,plain,(
% 42.82/7.67 ($true = (sK1 @ sK112 @ sK113)) | ~spl5_21),
% 42.82/7.67 inference(binary_proxy_clausification,[status(thm)],[f7066])).
% 42.82/7.67 thf(f7066,plain,(
% 42.82/7.67 ($true = ((sK1 @ sK112 @ sK113) & (in @ sK113 @ sK2))) | ~spl5_21),
% 42.82/7.67 inference(binary_proxy_clausification,[status(thm)],[f7064])).
% 42.82/7.67 thf(f7064,plain,(
% 42.82/7.67 ($true = (((sK1 @ sK112 @ sK113) & (in @ sK113 @ sK2)) & ((kpair @ sK112 @ sK113) = (kpair @ sK0 @ sK4)))) | ~spl5_21),
% 42.82/7.67 inference(beta_eta_normalization,[status(thm)],[f7063])).
% 42.82/7.67 thf(f7063,plain,(
% 42.82/7.67 (((^[Y0 : $i]: (((sK1 @ sK112 @ Y0) & (in @ Y0 @ sK2)) & ((kpair @ sK112 @ Y0) = (kpair @ sK0 @ sK4)))) @ sK113) = $true) | ~spl5_21),
% 42.82/7.67 inference(sigma_clausification,[status(thm)],[f7062])).
% 42.82/7.67 thf(f7062,plain,(
% 42.82/7.67 ($true = (?? @ $i @ (^[Y0 : $i]: (((sK1 @ sK112 @ Y0) & (in @ Y0 @ sK2)) & ((kpair @ sK112 @ Y0) = (kpair @ sK0 @ sK4)))))) | ~spl5_21),
% 42.82/7.67 inference(binary_proxy_clausification,[status(thm)],[f7060])).
% 42.82/7.67 thf(f7060,plain,(
% 42.82/7.67 (((?? @ $i @ (^[Y0 : $i]: (((sK1 @ sK112 @ Y0) & (in @ Y0 @ sK2)) & ((kpair @ sK112 @ Y0) = (kpair @ sK0 @ sK4))))) & (in @ sK112 @ sK3)) = $true) | ~spl5_21),
% 42.82/7.67 inference(beta_eta_normalization,[status(thm)],[f7059])).
% 42.82/7.67 thf(f7059,plain,(
% 42.82/7.67 (((^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((sK1 @ Y0 @ Y1) & (in @ Y1 @ sK2)) & ((kpair @ Y0 @ Y1) = (kpair @ sK0 @ sK4))))) & (in @ Y0 @ sK3))) @ sK112) = $true) | ~spl5_21),
% 42.82/7.67 inference(sigma_clausification,[status(thm)],[f7058])).
% 42.82/7.67 thf(f7058,plain,(
% 42.82/7.67 ($true = (?? @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((sK1 @ Y0 @ Y1) & (in @ Y1 @ sK2)) & ((kpair @ Y0 @ Y1) = (kpair @ sK0 @ sK4))))) & (in @ Y0 @ sK3))))) | ~spl5_21),
% 42.82/7.67 inference(beta_eta_normalization,[status(thm)],[f7057])).
% 42.82/7.67 thf(f7057,plain,(
% 42.82/7.67 (((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((sK1 @ Y1 @ Y2) & (in @ Y2 @ sK2)) & ((kpair @ Y1 @ Y2) = Y0)))) & (in @ Y1 @ sK3))))) @ (kpair @ sK0 @ sK4)) = $true) | ~spl5_21),
% 42.82/7.67 inference(trivial_inequality_removal,[status(thm)],[f7012])).
% 42.82/7.67 thf(f7012,plain,(
% 42.82/7.67 ($true = $false) | (((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((sK1 @ Y1 @ Y2) & (in @ Y2 @ sK2)) & ((kpair @ Y1 @ Y2) = Y0)))) & (in @ Y1 @ sK3))))) @ (kpair @ sK0 @ sK4)) = $true) | ~spl5_21),
% 42.82/7.67 inference(superposition,[status(thm)],[f3332,f2569])).
% 42.82/7.67 thf(f2569,plain,(
% 42.82/7.67 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (((in @ X3 @ (dsetconstr @ X1 @ X2)) = $false) | ($true = (X2 @ X3))) )),
% 42.82/7.67 inference(binary_proxy_clausification,[status(thm)],[f2568])).
% 42.82/7.67 thf(f2568,plain,(
% 42.82/7.67 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : ((((in @ X3 @ (dsetconstr @ X1 @ X2)) => (X2 @ X3)) = $true)) )),
% 42.82/7.67 inference(beta_eta_normalization,[status(thm)],[f2567])).
% 42.82/7.67 thf(f2567,plain,(
% 42.82/7.67 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ X1 @ X2)) => (X2 @ Y0))) @ X3))) )),
% 42.82/7.67 inference(pi_clausification,[status(thm)],[f2566])).
% 42.82/7.67 thf(f2566,plain,(
% 42.82/7.67 ( ! [X2 : $i > $o,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ X1 @ X2)) => (X2 @ Y0)))) = $true)) )),
% 42.82/7.67 inference(beta_eta_normalization,[status(thm)],[f2565])).
% 42.82/7.67 thf(f2565,plain,(
% 42.82/7.67 ( ! [X2 : $i > $o,X1 : $i] : ((((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ X1 @ Y0)) => (Y0 @ Y1))))) @ X2) = $true)) )),
% 42.82/7.67 inference(pi_clausification,[status(thm)],[f2564])).
% 42.82/7.67 thf(f2564,plain,(
% 42.82/7.67 ( ! [X1 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ X1 @ Y0)) => (Y0 @ Y1)))))))) )),
% 42.82/7.67 inference(beta_eta_normalization,[status(thm)],[f2563])).
% 42.82/7.67 thf(f2563,plain,(
% 42.82/7.67 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (Y1 @ Y2))))))) @ X1) = $true)) )),
% 42.82/7.67 inference(pi_clausification,[status(thm)],[f2562])).
% 42.82/7.67 thf(f2562,plain,(
% 42.82/7.67 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (Y1 @ Y2)))))))))),
% 42.82/7.67 inference(beta_eta_normalization,[status(thm)],[f971])).
% 42.82/7.67 thf(f971,plain,(
% 42.82/7.67 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (Y1 @ Y2)))))))))),
% 42.82/7.67 inference(definition_unfolding,[status(thm)],[f711,f581])).
% 42.82/7.67 thf(f581,plain,(
% 42.82/7.67 (dsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (Y1 @ Y2)))))))))),
% 42.82/7.67 inference(cnf_transformation,[status(thm)],[f350])).
% 42.82/7.67 thf(f350,plain,(
% 42.82/7.67 (dsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (Y1 @ Y2)))))))))),
% 42.82/7.67 inference(fool_elimination,[status(thm)],[f349])).
% 42.82/7.67 thf(f349,plain,(
% 42.82/7.67 (dsetconstrER = ! [X0 : $i,X1 : $i > $o,X2 : $i] : ((in @ X0 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X0)))),
% 42.82/7.67 inference(rectify,[status(thm)],[f16])).
% 42.82/7.67 thf(f16,axiom,(
% 42.82/7.67 (dsetconstrER = ! [X1 : $i,X0 : $i > $o,X3 : $i] : ((in @ X1 @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))) => (X0 @ X1)))),
% 42.82/7.67 file('/export/starexec/sandbox/tmp/tmp.pZ9OXiV362/DTF2THF_30834.p',dsetconstrER)).
% 42.82/7.67 thf(f711,plain,(
% 42.82/7.67 (dsetconstrER = $true)),
% 42.82/7.67 inference(cnf_transformation,[status(thm)],[f574])).
% 42.82/7.67 thf(f3332,plain,(
% 42.82/7.67 ($true = (in @ (kpair @ sK0 @ sK4) @ (dsetconstr @ (cartprod @ sK3 @ sK2) @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((sK1 @ Y1 @ Y2) & (in @ Y2 @ sK2)) & ((kpair @ Y1 @ Y2) = Y0)))) & (in @ Y1 @ sK3)))))))) | ~spl5_21),
% 42.82/7.67 inference(avatar_component_clause,[status(thm)],[f3330])).
% 42.82/7.67 thf(f7097,plain,(
% 42.82/7.67 spl5_25 | ~spl5_21),
% 42.82/7.67 inference(avatar_split_clause,[status(thm)],[f7069,f3330,f7094])).
% 42.82/7.67 thf(f7069,plain,(
% 42.82/7.67 ((kpair @ sK112 @ sK113) = (kpair @ sK0 @ sK4)) | ~spl5_21),
% 42.82/7.67 inference(equality_proxy_clausification,[status(thm)],[f7065])).
% 42.82/7.67 thf(f7065,plain,(
% 42.82/7.67 ($true = ((kpair @ sK112 @ sK113) = (kpair @ sK0 @ sK4))) | ~spl5_21),
% 42.82/7.67 inference(binary_proxy_clausification,[status(thm)],[f7064])).
% 42.82/7.67 thf(f3333,plain,(
% 42.82/7.67 spl5_21),
% 42.82/7.67 inference(avatar_split_clause,[status(thm)],[f1340,f3330])).
% 42.82/7.67 thf(f1340,plain,(
% 42.82/7.67 ($true = (in @ (kpair @ sK0 @ sK4) @ (dsetconstr @ (cartprod @ sK3 @ sK2) @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((sK1 @ Y1 @ Y2) & (in @ Y2 @ sK2)) & ((kpair @ Y1 @ Y2) = Y0)))) & (in @ Y1 @ sK3))))))))),
% 42.82/7.67 inference(beta_eta_normalization,[status(thm)],[f966])).
% 42.82/7.67 thf(f966,plain,(
% 42.82/7.67 ($true = (in @ (kpair @ sK0 @ sK4) @ ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((?? @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y5) & (in @ Y5 @ Y1)) & ((kpair @ Y4 @ Y5) = Y3)))) & (in @ Y4 @ Y0))))))))))) @ sK3 @ sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK1 @ Y0 @ Y1)))))))),
% 42.82/7.67 inference(definition_unfolding,[status(thm)],[f752,f843])).
% 42.82/7.67 thf(f843,plain,(
% 42.82/7.67 (dpsetconstr = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((?? @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y5) & (in @ Y5 @ Y1)) & ((kpair @ Y4 @ Y5) = Y3)))) & (in @ Y4 @ Y0))))))))))))),
% 42.82/7.67 inference(cnf_transformation,[status(thm)],[f467])).
% 42.82/7.67 thf(f467,plain,(
% 42.82/7.67 (dpsetconstr = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((?? @ $i @ (^[Y5 : $i]: (((Y2 @ Y4 @ Y5) & (in @ Y5 @ Y1)) & ((kpair @ Y4 @ Y5) = Y3)))) & (in @ Y4 @ Y0))))))))))))),
% 42.82/7.67 inference(fool_elimination,[status(thm)],[f466])).
% 42.82/7.67 thf(f466,plain,(
% 42.82/7.67 (dpsetconstr = (^[X0 : $i, X1 : $i, X2 : $i > $i > $o] : (dsetconstr @ (cartprod @ X0 @ X1) @ (^[X3 : $i] : (? [X4 : $i] : ((in @ X4 @ X0) & ? [X5 : $i] : (((kpair @ X4 @ X5) = X3) & (in @ X5 @ X1) & (X2 @ X4 @ X5))))))))),
% 42.82/7.67 inference(rectify,[status(thm)],[f187])).
% 42.82/7.67 thf(f187,axiom,(
% 42.82/7.67 (dpsetconstr = (^[X3 : $i, X4 : $i, X0 : $i > $i > $o] : (dsetconstr @ (cartprod @ X3 @ X4) @ (^[X10 : $i] : (? [X1 : $i] : ((in @ X1 @ X3) & ? [X2 : $i] : (((kpair @ X1 @ X2) = X10) & (in @ X2 @ X4) & (X0 @ X1 @ X2))))))))),
% 42.82/7.67 file('/export/starexec/sandbox/tmp/tmp.pZ9OXiV362/DTF2THF_30834.p',dpsetconstr)).
% 42.82/7.67 thf(f752,plain,(
% 42.82/7.67 ((in @ (kpair @ sK0 @ sK4) @ (dpsetconstr @ sK3 @ sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK1 @ Y0 @ Y1)))))) = $true)),
% 42.82/7.67 inference(cnf_transformation,[status(thm)],[f574])).
% 42.82/7.67 thf(f3305,plain,(
% 42.82/7.67 ~spl5_15),
% 42.82/7.67 inference(avatar_split_clause,[status(thm)],[f753,f3302])).
% 42.82/7.67 thf(f3302,definition,(
% 42.82/7.67 spl5_15 <=> ($true = (sK1 @ sK0 @ sK4))),
% 42.82/7.67 introduced(definition,[new_symbols(naming,[spl5_15])],[avatar_definition])).
% 42.82/7.67 thf(f753,plain,(
% 42.82/7.67 ($true != (sK1 @ sK0 @ sK4))),
% 42.82/7.67 inference(cnf_transformation,[status(thm)],[f574])).
% 42.82/7.67 % SZS output end Proof for DTF2THF_30834
% 42.82/7.67 % (31095)------------------------------
% 42.82/7.67 % (31095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.82/7.67 % (31095)Termination reason: Refutation
% 42.82/7.67
% 42.82/7.67 % (31095)Memory used [KB]: 10874
% 42.82/7.67 % (31095)Time elapsed: 1.150 s
% 42.82/7.67 % (31095)Instructions burned: 2384 (million)
% 42.82/7.67 % (31095)------------------------------
% 42.82/7.67 % (31095)------------------------------
% 42.82/7.67 % (30940)Success in time 5.9 s
%------------------------------------------------------------------------------