%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU657^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:35:59 AM UTC 2026
% Result : Theorem 16.62s 3.71s
% Output : Refutation 16.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 62 ( 54 unt; 0 typ; 0 def)
% Number of atoms : 3031 ( 793 equ; 0 cnn)
% Maximal formula atoms : 175 ( 48 avg)
% Number of connectives : 1971 ( 10 ~; 0 |; 543 &; 688 @)
% ( 0 <=>; 697 =>; 0 <=; 0 <~>)
% Maximal formula depth : 178 ( 21 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 315 ( 310 usr; 181 con; 0-4 aty)
% ( 22 !!; 11 ??; 0 @@+; 0 @@-)
% Number of variables : 97 ( 62 ^; 28 !; 7 ?; 97 :)
% 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_222,type,
sP1: $i > $o ).
thf(func_def_223,type,
sP2: $o > $o ).
thf(func_def_224,type,
sK3: ( $i > $o ) > $i ).
thf(func_def_225,type,
sK4: ( $i > $o ) > $i ).
thf(func_def_226,type,
sK5: ( $i > $o ) > $i ).
thf(func_def_227,type,
sK6: ( $i > $o ) > $i ).
thf(func_def_228,type,
sK7: ( $i > $o ) > $i ).
thf(func_def_229,type,
sK8: $i > $i > $i ).
thf(func_def_230,type,
sK9: $i > $i > $i ).
thf(func_def_231,type,
sK10: $i > $i > $i ).
thf(func_def_232,type,
sK11: $i > ( $i > $i > $o ) > $i ).
thf(func_def_233,type,
sK12: $i > ( $i > $i > $o ) > $i ).
thf(func_def_234,type,
sK13: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_235,type,
sK14: $i > ( $i > $i > $o ) > $i ).
thf(func_def_236,type,
sK15: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_237,type,
sK16: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_238,type,
sK17: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_239,type,
sK18: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_240,type,
sK19: $i > $i ).
thf(func_def_241,type,
sK20: ( $i > $o ) > $i > $i ).
thf(func_def_242,type,
sK21: ( $i > $o ) > $i > $i ).
thf(func_def_243,type,
sK22: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_244,type,
sK23: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_245,type,
sK24: $i > ( $i > $o ) > $i ).
thf(func_def_246,type,
sK25: $i > ( $i > $o ) > $i ).
thf(func_def_247,type,
sK26: $i > ( $i > $o ) > $i ).
thf(func_def_248,type,
sK27: $i > ( $i > $o ) > $i ).
thf(func_def_249,type,
sK28: $i > ( $i > $o ) > $i ).
thf(func_def_250,type,
sK29: $i > ( $i > $o ) > $i ).
thf(func_def_251,type,
sK30: $i > ( $i > $o ) > $i ).
thf(func_def_252,type,
sK31: $i > $i ).
thf(func_def_253,type,
sK32: $i > $i > $i > $i ).
thf(func_def_254,type,
sK33: $i > $i > $i ).
thf(func_def_255,type,
sK34: $i > $i > $i ).
thf(func_def_256,type,
sK35: $i > $i > $i ).
thf(func_def_257,type,
sK36: $i > $i > $i ).
thf(func_def_258,type,
sK37: ( $i > $o ) > $i > $i ).
thf(func_def_259,type,
sK38: ( $i > $o ) > $i > $i ).
thf(func_def_260,type,
sK39: $i > $i > $i ).
thf(func_def_261,type,
sK40: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_262,type,
sK41: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_263,type,
sK42: ( $i > $o ) > $i ).
thf(func_def_264,type,
sK43: $i > ( $i > $o ) > $i ).
thf(func_def_265,type,
sK44: $i > ( $i > $o ) > $i ).
thf(func_def_266,type,
sK45: $i > ( $i > $o ) > $i ).
thf(func_def_267,type,
sK46: $i > ( $i > $o ) > $i ).
thf(func_def_268,type,
sK47: $i > ( $i > $o ) > $i ).
thf(func_def_269,type,
sK48: $i > ( $i > $o ) > $i ).
thf(func_def_270,type,
sK49: $i > ( $i > $o ) > $i ).
thf(func_def_271,type,
sK50: ( $i > $o ) > $i ).
thf(func_def_272,type,
sK51: ( $i > $o ) > $i ).
thf(func_def_273,type,
sK52: ( $i > $o ) > $i ).
thf(func_def_274,type,
sK53: $i > $i ).
thf(func_def_275,type,
sK54: $i > $i ).
thf(func_def_276,type,
sK55: $i > $i > $i ).
thf(func_def_277,type,
sK56: $i > $i > $i ).
thf(func_def_278,type,
sK57: $i > $i ).
thf(func_def_279,type,
sK58: $i > $i > $i ).
thf(func_def_280,type,
sK59: ( $i > $o ) > $i > $i ).
thf(func_def_281,type,
sK60: $i > $i ).
thf(func_def_282,type,
sK61: $i > $i > $i ).
thf(func_def_283,type,
sK62: ( $i > $o ) > $i ).
thf(func_def_284,type,
sK63: ( $i > $o ) > $i > $i ).
thf(func_def_285,type,
sK64: $i > $i > $i ).
thf(func_def_286,type,
sK65: $i > $i > $i ).
thf(func_def_287,type,
sK66: $i > ( $i > $o ) > $i ).
thf(func_def_288,type,
sK67: $i > ( $i > $o ) > $i ).
thf(func_def_289,type,
sK68: $i > ( $i > $o ) > $i ).
thf(func_def_290,type,
sK69: $i > ( $i > $o ) > $i ).
thf(func_def_291,type,
sK70: $i > ( $i > $o ) > $i ).
thf(func_def_294,type,
sK73: $i > $i ).
thf(func_def_295,type,
sK74: $i > $i ).
thf(func_def_296,type,
sK75: ( $i > $o ) > $i ).
thf(func_def_297,type,
sK76: $i > ( $i > $o ) > $i ).
thf(func_def_298,type,
sK77: $i > ( $i > $o ) > $i ).
thf(func_def_299,type,
sK78: ( $i > $o ) > $i > $i ).
thf(func_def_300,type,
sK79: ( $i > $o ) > $i > $i ).
thf(func_def_301,type,
sK80: ( $i > $o ) > $i > $i ).
thf(func_def_302,type,
sK81: ( $i > $o ) > $i > $i ).
thf(func_def_303,type,
sK82: ( $i > $o ) > $i > $i ).
thf(func_def_304,type,
sK83: $i > $i ).
thf(func_def_305,type,
sK84: ( $i > $o ) > $i > $i ).
thf(func_def_306,type,
sK85: ( $i > $o ) > $i ).
thf(func_def_307,type,
sK86: ( $i > $o ) > $i ).
thf(func_def_308,type,
sK87: $i > ( $i > $o ) > $i ).
thf(func_def_309,type,
sK88: $i > $i > ( $i > $o ) > $i ).
thf(func_def_310,type,
sK89: $i > $i > ( $i > $o ) > $i ).
thf(func_def_311,type,
sK90: ( $i > $o ) > $i ).
thf(func_def_312,type,
sK91: ( $i > $o ) > $i > $i ).
thf(func_def_313,type,
sK92: ( $i > $o ) > $i > $i ).
thf(func_def_314,type,
sK93: $i > $i > $i ).
thf(func_def_315,type,
sK94: ( $i > $o ) > $i > $i ).
thf(func_def_316,type,
sK95: $i > $i ).
thf(func_def_317,type,
sK96: $i > $i > $i ).
thf(func_def_318,type,
sK97: $o > $i > $i > $i ).
thf(func_def_319,type,
sK98: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_320,type,
sK99: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_321,type,
sK100: $i > $i > $i > $i ).
thf(func_def_322,type,
sK101: $i > $i > $i > $i ).
thf(func_def_323,type,
sK102: $i > $i > $i ).
thf(func_def_324,type,
sK103: $i > ( $i > $o ) > $i ).
thf(func_def_325,type,
sK104: $i > $i > $i ).
thf(func_def_326,type,
sK105: ( $i > $o ) > $i > $i ).
thf(func_def_327,type,
sK106: $i > $i ).
thf(f3093,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f3092]) ).
thf(f3092,plain,
$false = $true,
inference(backward_demodulation,[status(thm)],[f3090,f3091]) ).
thf(f3091,plain,
( ( sP1 @ ( setadjoin @ ( setadjoin @ sK71 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK71 @ ( setadjoin @ sK72 @ emptyset ) ) @ emptyset ) ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f3089,f1434]) ).
thf(f1434,plain,
! [X2: $i,X1: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= X2 ),
inference(equality_proxy_clausification,[status(thm)],[f1433]) ).
thf(f1433,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( kfst @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= X2 ) ),
inference(beta_eta_normalization,[status(thm)],[f1432]) ).
thf(f1432,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= Y0 )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f1431]) ).
thf(f1431,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= Y0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1430]) ).
thf(f1430,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
= Y1 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f1429]) ).
thf(f1429,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
= Y1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f903]) ).
thf(f903,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst
@ ( ^ [Y2: $i,Y3: $i] : ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
@ Y1
@ Y0 ) )
= Y1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f622,f897]) ).
thf(f897,plain,
( kfstpairEq
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst
@ ( ^ [Y2: $i,Y3: $i] : ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
@ Y1
@ Y0 ) )
= Y1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f549,f548]) ).
thf(f548,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(cnf_transformation,[status(thm)],[f490]) ).
thf(f490,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(fool_elimination,[status(thm)],[f489]) ).
thf(f489,plain,
( ( ^ [X0: $i,X1: $i] : ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= kpair ),
inference(rectify,[status(thm)],[f140]) ).
thf(f140,axiom,
( ( ^ [X1: $i,X2: $i] : ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
= kpair ),
file('/export/starexec/sandbox2/tmp/tmp.UKH9onOzqj/DTF2THF_18632.p',kpair) ).
thf(f549,plain,
( kfstpairEq
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst @ ( kpair @ Y1 @ Y0 ) )
= Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f514]) ).
thf(f514,plain,
( kfstpairEq
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst @ ( kpair @ Y1 @ Y0 ) )
= Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f513]) ).
thf(f513,plain,
! [X0: $i,X1: $i] :
( ( ( kfst @ ( kpair @ X0 @ X1 ) )
= X0 )
= kfstpairEq ),
inference(rectify,[status(thm)],[f168]) ).
thf(f168,axiom,
! [X1: $i,X2: $i] :
( ( ( kfst @ ( kpair @ X1 @ X2 ) )
= X1 )
= kfstpairEq ),
file('/export/starexec/sandbox2/tmp/tmp.UKH9onOzqj/DTF2THF_18632.p',kfstpairEq) ).
thf(f622,plain,
kfstpairEq = $true,
inference(cnf_transformation,[status(thm)],[f540]) ).
thf(f540,plain,
( ( setukpairinjL2 = $true )
& ( in__Cong = $true )
& ( disjointsetsI1 = $true )
& ( emptyset__Cong = $true )
& ( foundationAx = $true )
& ( symdiffI2 = $true )
& ( prop2set2propI = $true )
& ( eqinunit = $true )
& ( symdiffE = $true )
& ( emptyE1 = $true )
& ( powersetsubset = $true )
& ( subsetE2 = $true )
& ( exuI2 = $true )
& ( emptyI = $true )
& ( sepInPowerset = $true )
& ( quantDeMorgan3 = $true )
& ( setadjoinAx = $true )
& ( subPowSU = $true )
& ( noeltsimpempty = $true )
& ( descrp = $true )
& ( dsetconstrI = $true )
& ( upairsubunion = $true )
& ( setadjoinSub = $true )
& ( bs114d = $true )
& ( setbeta = $true )
& ( prop2setI = $true )
& ( notinsingleton = $true )
& ( binunionLsub = $true )
& ( ksndpairEq = $true )
& ( dsetconstr__Cong = $true )
& ( nonemptyI1 = $true )
& ( secondinupair = $true )
& ( omega__Cong = $true )
& ( exuI3 = $true )
& ( exuE3u = $true )
& ( binunionE = $true )
& ( subsetTrans = $true )
& ( quantDeMorgan4 = $true )
& ( binunionEcases = $true )
& ( singletonsswitch = $true )
& ( upairequniteq = $true )
& ( upairset2IR = $true )
& ( subsetI1 = $true )
& ( setoftrueEq = $true )
& ( singletonprop = $true )
& ( exuI1 = $true )
& ( setadjoin__Cong = $true )
& ( subsetE = $true )
& ( exuE3e = $true )
& ( ubforcartprodlem2 = $true )
& ( setukpairIL = $true )
& ( singletoninpowunion = $true )
& ( setadjoinOr = $true )
& ( eqimpsubset1 = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( setminusEL = $true )
& ( notdallE = $true )
& ( symdiffIneg1 = $true )
& ( quantDeMorgan1 = $true )
& ( binintersectEL = $true )
& ( setukpairinjR1 = $true )
& ( emptyInPowerset = $true )
& ( emptysetsubset = $true )
& ( binintersectSubset3 = $true )
& ( setunionE = $true )
& ( setukpairIR = $true )
& ( symdiffIneg2 = $true )
& ( binintersectSubset2 = $true )
& ( ex1I2 = $true )
& ( wellorderingAx = $true )
& ( emptysetAx = $true )
& ( binunionIR = $true )
& ( omegaSAx = $true )
& ( nonemptyE1 = $true )
& ( inCongP = $true )
& ( setukpairinjL1 = $true )
& ( powerset__Cong = $true )
& ( notequalI1 = $true )
& ( cartprodmempair = $true )
& ( binunionRsub = $true )
& ( setextsub = $true )
& ( ex1E1 = $true )
& ( setminusSubset2 = $true )
& ( setminusIRneg = $true )
& ( emptysetE = $true )
& ( upairsetIL = $true )
& ( cartprodpairin = $true )
& ( powersetE = $true )
& ( ubforcartprodlem3 = $true )
& ( kfstsingleton = $true )
& ( upairsetE = $true )
& ( uniqinunit = $true )
& ( notsubsetI = $true )
& ( exu__Cong = $true )
& ( powersetI = $true )
& ( setukpairinjL = $true )
& ( prop2setE = $true )
& ( setunionsingleton2 = $true )
& ( setukpairinjR = $true )
& ( exuEu = $true )
& ( setunionI = $true )
& ( subsetRefl = $true )
& ( kfstpairEq = $true )
& ( setadjoinIL = $true )
& ( powersetE1 = $true )
& ( replAx = $true )
& ( setminusELneg = $true )
& ( setukpairinjR11 = $true )
& ( setminusLsub = $true )
& ( kpairiskpair = $true )
& ( upairinpowunion = $true )
& ( setextAx = $true )
& ( setext = $true )
& ( cartprodmempair1 = $true )
& ( subsetI2 = $true )
& ( dsetconstrEL = $true )
& ( setadjoinE = $true )
& ( omega0Ax = $true )
& ( eqimpsubset2 = $true )
& ( binintersectSubset5 = $true )
& ( setukpairinjR12 = $true )
& ( nonemptyI = $true )
& ( setminusI = $true )
& ( descr__Cong = $true )
& ( binintersectSubset1 = $true )
& ( subsetemptysetimpeq = $true )
& ( upairsetIR = $true )
& ( subset2powerset = $true )
& ( ubforcartprodlem1 = $true )
& ( setminusER = $true )
& ( vacuousDall = $true )
& ( binunionIL = $true )
& ( powersetI1 = $true )
& ( theprop = $true )
& ( setunionE2 = $true )
& ( setminusILneg = $true )
& ( notinemptyset = $true )
& ( setadjoinSub2 = $true )
& ( setminusERneg = $true )
& ( setunion__Cong = $true )
& ( binintersectER = $true )
& ( setunionAx = $true )
& ( singletonsuniq = $true )
& ( setukpairinjR2 = $true )
& ( binintersectRsub = $true )
& ( nonemptyImpWitness = $true )
& ( binintersectI = $true )
& ( sK0
!= ( kpair @ ( kfst @ sK0 ) @ ( ksnd @ sK0 ) ) )
& ( $true
= ( iskpair @ sK0 ) )
& ( emptyinunitempty = $true )
& ( notdexE = $true )
& ( setadjoinIR = $true )
& ( upairset2E = $true )
& ( symdiffI1 = $true )
& ( notequalI2 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectLsub = $true )
& ( ex1I = $true )
& ( ksndsingleton = $true )
& ( setminusSubset1 = $true )
& ( omegaIndAx = $true )
& ( setunionsingleton = $true )
& ( dsetconstrER = $true )
& ( cartprodfstin = $true )
& ( singletoninpowerset = $true )
& ( sepSubset = $true )
& ( powersetAx = $true )
& ( exuE1 = $true )
& ( emptyinPowerset = $true )
& ( inPowerset = $true )
& ( emptysetimpfalse = $true )
& ( setunionsingleton1 = $true )
& ( exuE2 = $true )
& ( quantDeMorgan2 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f538,f539]) ).
thf(f539,plain,
( ? [X0: $i] :
( ( ( kpair @ ( kfst @ X0 ) @ ( ksnd @ X0 ) )
!= X0 )
& ( $true
= ( iskpair @ X0 ) ) )
=> ( ( sK0
!= ( kpair @ ( kfst @ sK0 ) @ ( ksnd @ sK0 ) ) )
& ( $true
= ( iskpair @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f538,plain,
( ( setukpairinjL2 = $true )
& ( in__Cong = $true )
& ( disjointsetsI1 = $true )
& ( emptyset__Cong = $true )
& ( foundationAx = $true )
& ( symdiffI2 = $true )
& ( prop2set2propI = $true )
& ( eqinunit = $true )
& ( symdiffE = $true )
& ( emptyE1 = $true )
& ( powersetsubset = $true )
& ( subsetE2 = $true )
& ( exuI2 = $true )
& ( emptyI = $true )
& ( sepInPowerset = $true )
& ( quantDeMorgan3 = $true )
& ( setadjoinAx = $true )
& ( subPowSU = $true )
& ( noeltsimpempty = $true )
& ( descrp = $true )
& ( dsetconstrI = $true )
& ( upairsubunion = $true )
& ( setadjoinSub = $true )
& ( bs114d = $true )
& ( setbeta = $true )
& ( prop2setI = $true )
& ( notinsingleton = $true )
& ( binunionLsub = $true )
& ( ksndpairEq = $true )
& ( dsetconstr__Cong = $true )
& ( nonemptyI1 = $true )
& ( secondinupair = $true )
& ( omega__Cong = $true )
& ( exuI3 = $true )
& ( exuE3u = $true )
& ( binunionE = $true )
& ( subsetTrans = $true )
& ( quantDeMorgan4 = $true )
& ( binunionEcases = $true )
& ( singletonsswitch = $true )
& ( upairequniteq = $true )
& ( upairset2IR = $true )
& ( subsetI1 = $true )
& ( setoftrueEq = $true )
& ( singletonprop = $true )
& ( exuI1 = $true )
& ( setadjoin__Cong = $true )
& ( subsetE = $true )
& ( exuE3e = $true )
& ( ubforcartprodlem2 = $true )
& ( setukpairIL = $true )
& ( singletoninpowunion = $true )
& ( setadjoinOr = $true )
& ( eqimpsubset1 = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( setminusEL = $true )
& ( notdallE = $true )
& ( symdiffIneg1 = $true )
& ( quantDeMorgan1 = $true )
& ( binintersectEL = $true )
& ( setukpairinjR1 = $true )
& ( emptyInPowerset = $true )
& ( emptysetsubset = $true )
& ( binintersectSubset3 = $true )
& ( setunionE = $true )
& ( setukpairIR = $true )
& ( symdiffIneg2 = $true )
& ( binintersectSubset2 = $true )
& ( ex1I2 = $true )
& ( wellorderingAx = $true )
& ( emptysetAx = $true )
& ( binunionIR = $true )
& ( omegaSAx = $true )
& ( nonemptyE1 = $true )
& ( inCongP = $true )
& ( setukpairinjL1 = $true )
& ( powerset__Cong = $true )
& ( notequalI1 = $true )
& ( cartprodmempair = $true )
& ( binunionRsub = $true )
& ( setextsub = $true )
& ( ex1E1 = $true )
& ( setminusSubset2 = $true )
& ( setminusIRneg = $true )
& ( emptysetE = $true )
& ( upairsetIL = $true )
& ( cartprodpairin = $true )
& ( powersetE = $true )
& ( ubforcartprodlem3 = $true )
& ( kfstsingleton = $true )
& ( upairsetE = $true )
& ( uniqinunit = $true )
& ( notsubsetI = $true )
& ( exu__Cong = $true )
& ( powersetI = $true )
& ( setukpairinjL = $true )
& ( prop2setE = $true )
& ( setunionsingleton2 = $true )
& ( setukpairinjR = $true )
& ( exuEu = $true )
& ( setunionI = $true )
& ( subsetRefl = $true )
& ( kfstpairEq = $true )
& ( setadjoinIL = $true )
& ( powersetE1 = $true )
& ( replAx = $true )
& ( setminusELneg = $true )
& ( setukpairinjR11 = $true )
& ( setminusLsub = $true )
& ( kpairiskpair = $true )
& ( upairinpowunion = $true )
& ( setextAx = $true )
& ( setext = $true )
& ( cartprodmempair1 = $true )
& ( subsetI2 = $true )
& ( dsetconstrEL = $true )
& ( setadjoinE = $true )
& ( omega0Ax = $true )
& ( eqimpsubset2 = $true )
& ( binintersectSubset5 = $true )
& ( setukpairinjR12 = $true )
& ( nonemptyI = $true )
& ( setminusI = $true )
& ( descr__Cong = $true )
& ( binintersectSubset1 = $true )
& ( subsetemptysetimpeq = $true )
& ( upairsetIR = $true )
& ( subset2powerset = $true )
& ( ubforcartprodlem1 = $true )
& ( setminusER = $true )
& ( vacuousDall = $true )
& ( binunionIL = $true )
& ( powersetI1 = $true )
& ( theprop = $true )
& ( setunionE2 = $true )
& ( setminusILneg = $true )
& ( notinemptyset = $true )
& ( setadjoinSub2 = $true )
& ( setminusERneg = $true )
& ( setunion__Cong = $true )
& ( binintersectER = $true )
& ( setunionAx = $true )
& ( singletonsuniq = $true )
& ( setukpairinjR2 = $true )
& ( binintersectRsub = $true )
& ( nonemptyImpWitness = $true )
& ( binintersectI = $true )
& ? [X0: $i] :
( ( ( kpair @ ( kfst @ X0 ) @ ( ksnd @ X0 ) )
!= X0 )
& ( $true
= ( iskpair @ X0 ) ) )
& ( emptyinunitempty = $true )
& ( notdexE = $true )
& ( setadjoinIR = $true )
& ( upairset2E = $true )
& ( symdiffI1 = $true )
& ( notequalI2 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectLsub = $true )
& ( ex1I = $true )
& ( ksndsingleton = $true )
& ( setminusSubset1 = $true )
& ( omegaIndAx = $true )
& ( setunionsingleton = $true )
& ( dsetconstrER = $true )
& ( cartprodfstin = $true )
& ( singletoninpowerset = $true )
& ( sepSubset = $true )
& ( powersetAx = $true )
& ( exuE1 = $true )
& ( emptyinPowerset = $true )
& ( inPowerset = $true )
& ( emptysetimpfalse = $true )
& ( setunionsingleton1 = $true )
& ( exuE2 = $true )
& ( quantDeMorgan2 = $true ) ),
inference(flattening,[status(thm)],[f537]) ).
thf(f537,plain,
( ? [X0: $i] :
( ( ( kpair @ ( kfst @ X0 ) @ ( ksnd @ X0 ) )
!= X0 )
& ( $true
= ( iskpair @ X0 ) ) )
& ( 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)],[f318]) ).
thf(f318,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 )
=> ! [X0: $i] :
( ( $true
= ( iskpair @ X0 ) )
=> ( ( kpair @ ( kfst @ X0 ) @ ( ksnd @ X0 ) )
= X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f317]) ).
thf(f317,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
=> ! [X0: $i] :
( ( iskpair @ X0 )
=> ( ( kpair @ ( kfst @ X0 ) @ ( ksnd @ X0 ) )
= X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f181]) ).
thf(f181,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
=> ! [X10: $i] :
( ( iskpair @ X10 )
=> ( ( kpair @ ( kfst @ X10 ) @ ( ksnd @ X10 ) )
= X10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f180]) ).
thf(f180,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
=> ! [X10: $i] :
( ( iskpair @ X10 )
=> ( ( kpair @ ( kfst @ X10 ) @ ( ksnd @ X10 ) )
= X10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.UKH9onOzqj/DTF2THF_18632.p',kpairsurjEq) ).
thf(f3089,plain,
( $false
= ( sP1 @ ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ sK71 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK71 @ ( setadjoin @ sK72 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ sK71 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK71 @ ( setadjoin @ sK72 @ emptyset ) ) @ emptyset ) ) ) @ ( setadjoin @ sK72 @ emptyset ) ) @ emptyset ) ) ) ),
inference(forward_demodulation,[status(thm)],[f3088,f2851]) ).
thf(f2851,plain,
! [X2: $i,X1: $i] :
( ( ksnd @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= X1 ),
inference(equality_proxy_clausification,[status(thm)],[f2850]) ).
thf(f2850,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( ksnd @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f2849]) ).
thf(f2849,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ksnd @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= X1 )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f2848]) ).
thf(f2848,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ksnd @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2847]) ).
thf(f2847,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ksnd @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
= Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f2846]) ).
thf(f2846,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ksnd @ ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
= Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f962]) ).
thf(f962,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ksnd
@ ( ^ [Y2: $i,Y3: $i] : ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) )
@ Y1
@ Y0 ) )
= Y0 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f779,f697,f548]) ).
thf(f697,plain,
ksndpairEq = $true,
inference(cnf_transformation,[status(thm)],[f540]) ).
thf(f779,plain,
( ksndpairEq
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ksnd @ ( kpair @ Y1 @ Y0 ) )
= Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f316]) ).
thf(f316,plain,
( ksndpairEq
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ksnd @ ( kpair @ Y1 @ Y0 ) )
= Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f315]) ).
thf(f315,plain,
( ksndpairEq
= ( ! [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X0 @ X1 ) )
= X1 ) ) ),
inference(rectify,[status(thm)],[f179]) ).
thf(f179,axiom,
( ksndpairEq
= ( ! [X1: $i,X2: $i] :
( ( ksnd @ ( kpair @ X1 @ X2 ) )
= X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.UKH9onOzqj/DTF2THF_18632.p',ksndpairEq) ).
thf(f3088,plain,
( $false
= ( sP1 @ ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ sK71 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK71 @ ( setadjoin @ sK72 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ sK71 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK71 @ ( setadjoin @ sK72 @ emptyset ) ) @ emptyset ) ) ) @ ( setadjoin @ ( ksnd @ ( setadjoin @ ( setadjoin @ sK71 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK71 @ ( setadjoin @ sK72 @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) ) @ emptyset ) ) ) ),
inference(backward_demodulation,[status(thm)],[f2366,f2307]) ).
thf(f2307,plain,
( sK0
= ( setadjoin @ ( setadjoin @ sK71 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK71 @ ( setadjoin @ sK72 @ emptyset ) ) @ emptyset ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f2306]) ).
thf(f2306,plain,
( $true
= ( ( setadjoin @ ( setadjoin @ sK71 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK71 @ ( setadjoin @ sK72 @ emptyset ) ) @ emptyset ) )
= sK0 ) ),
inference(binary_proxy_clausification,[status(thm)],[f2304]) ).
thf(f2304,plain,
( $true
= ( ( ( setadjoin @ ( setadjoin @ sK71 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK71 @ ( setadjoin @ sK72 @ emptyset ) ) @ emptyset ) )
= sK0 )
& ( in @ sK72 @ ( setunion @ sK0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2303]) ).
thf(f2303,plain,
( $true
= ( ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ sK71 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK71 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
& ( in @ Y0 @ ( setunion @ sK0 ) ) )
@ sK72 ) ),
inference(sigma_clausification,[status(thm)],[f2302]) ).
thf(f2302,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ sK71 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK71 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
& ( in @ Y0 @ ( setunion @ sK0 ) ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f2300]) ).
thf(f2300,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ sK71 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK71 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK0 )
& ( in @ Y0 @ ( setunion @ sK0 ) ) ) )
& ( in @ sK71 @ ( setunion @ sK0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2299]) ).
thf(f2299,plain,
( ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= sK0 )
& ( in @ Y1 @ ( setunion @ sK0 ) ) ) )
& ( in @ Y0 @ ( setunion @ sK0 ) ) )
@ sK71 )
= $true ),
inference(sigma_clausification,[status(thm)],[f2298]) ).
thf(f2298,plain,
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= sK0 )
& ( in @ Y1 @ ( setunion @ sK0 ) ) ) )
& ( in @ Y0 @ ( setunion @ sK0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f906]) ).
thf(f906,plain,
( $true
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ ( setunion @ Y0 ) ) ) )
& ( in @ Y1 @ ( setunion @ Y0 ) ) ) )
@ sK0 ) ),
inference(definition_unfolding,[status(thm)],[f576,f787]) ).
thf(f787,plain,
( iskpair
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ ( setunion @ Y0 ) ) ) )
& ( in @ Y1 @ ( setunion @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f204]) ).
thf(f204,plain,
( iskpair
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ ( setunion @ Y0 ) ) ) )
& ( in @ Y1 @ ( setunion @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f203]) ).
thf(f203,plain,
( iskpair
= ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ ( setunion @ X0 ) )
& ? [X2: $i] :
( ( in @ X2 @ ( setunion @ X0 ) )
& ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f135]) ).
thf(f135,axiom,
( iskpair
= ( ^ [X3: $i] :
? [X1: $i] :
( ( in @ X1 @ ( setunion @ X3 ) )
& ? [X2: $i] :
( ( in @ X2 @ ( setunion @ X3 ) )
& ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= X3 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.UKH9onOzqj/DTF2THF_18632.p',iskpair) ).
thf(f576,plain,
( $true
= ( iskpair @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f540]) ).
thf(f2366,plain,
( ( sP1 @ ( setadjoin @ ( setadjoin @ ( kfst @ sK0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ sK0 ) @ ( setadjoin @ ( ksnd @ sK0 ) @ emptyset ) ) @ emptyset ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f1073]) ).
thf(f1073,plain,
( $false
= ( sP1
@ ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
@ ( kfst @ sK0 )
@ ( ksnd @ sK0 ) ) ) ),
introduced(definition,[new_symbols(naming,[sP1])],[inequality_splitting_name_introduction]) ).
thf(f3090,plain,
( ( sP1 @ ( setadjoin @ ( setadjoin @ sK71 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK71 @ ( setadjoin @ sK72 @ emptyset ) ) @ emptyset ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f1074,f2307]) ).
thf(f1074,plain,
( $true
= ( sP1 @ sK0 ) ),
inference(inequality_splitting,[status(thm)],[f905,f1073]) ).
thf(f905,plain,
( ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
@ ( kfst @ sK0 )
@ ( ksnd @ sK0 ) )
!= sK0 ),
inference(definition_unfolding,[status(thm)],[f577,f548]) ).
thf(f577,plain,
( sK0
!= ( kpair @ ( kfst @ sK0 ) @ ( ksnd @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f540]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU657^1 : TPTP v9.2.1. Released v3.7.0.
% 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n016.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:30:06 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : SEU657^1 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.46 % Domain : Set Theory
% 0.20/0.46 % Problem : Ordered Pairs - Properties of Pairs
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English : (! u:i.iskpair u -> kpair (kfst u) (ksnd u) = u)
% 0.20/0.46
% 0.20/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.20/0.46 % Source : [Bro08]
% 0.20/0.46 % Names : ZFC159g [Bro08]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.50 v8.2.0, 0.54 v8.1.0, 0.27 v7.5.0, 0.29 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v5.1.0, 0.80 v4.1.0, 0.67 v3.7.0
% 0.20/0.46 % Syntax : Number of formulae : 384 ( 179 unt; 204 typ; 179 def)
% 0.20/0.46 % Number of atoms : 947 ( 269 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 175 ( 5 avg)
% 0.20/0.46 % Number of connectives : 1676 ( 47 ~; 7 |; 37 &;1155 @)
% 0.20/0.46 % ( 14 <=>; 416 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 177 ( 2 avg)
% 0.20/0.46 % Number of types : 2 ( 0 usr)
% 0.20/0.46 % Number of type conns : 84 ( 84 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 207 ( 204 usr; 177 con; 0-2 aty)
% 0.20/0.46 % Number of variables : 520 ( 43 ^; 439 !; 38 ?; 520 :)
% 0.20/0.46 % SPC : TH0_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : http://mathgate.info/detsetitem.php?id=426
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(in_type,type,
% 0.20/0.46 in: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(exu_type,type,
% 0.20/0.46 exu: ( $i > $o ) > $o ).
% 0.20/0.46
% 0.20/0.46 thf(exu,definition,
% 0.20/0.46 ( exu
% 0.20/0.46 = ( ^ [Xphi: $i > $o] :
% 0.20/0.46 ? [Xx: $i] :
% 0.20/0.46 ( ( Xphi @ Xx )
% 0.20/0.46 & ! [Xy: $i] :
% 0.20/0.46 ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setextAx_type,type,
% 0.20/0.46 setextAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setextAx,definition,
% 0.20/0.46 ( setextAx
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 <=> ( in @ Xx @ B ) )
% 0.20/0.46 => ( A = B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptyset_type,type,
% 0.20/0.46 emptyset: $i ).
% 0.20/0.46
% 0.20/0.46 thf(emptysetAx_type,type,
% 0.20/0.46 emptysetAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptysetAx,definition,
% 0.20/0.46 ( emptysetAx
% 0.20/0.46 = ( ! [Xx: $i] :
% 0.20/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoin_type,type,
% 0.20/0.46 setadjoin: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinAx_type,type,
% 0.20/0.46 setadjoinAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinAx,definition,
% 0.20/0.46 ( setadjoinAx
% 0.20/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.20/0.46 <=> ( ( Xy = Xx )
% 0.20/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powerset_type,type,
% 0.20/0.46 powerset: $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(powersetAx_type,type,
% 0.20/0.46 powersetAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powersetAx,definition,
% 0.20/0.46 ( powersetAx
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.20/0.46 <=> ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setunion_type,type,
% 0.20/0.46 setunion: $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(setunionAx_type,type,
% 0.20/0.46 setunionAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setunionAx,definition,
% 0.20/0.46 ( setunionAx
% 0.20/0.46 = ( ! [A: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.20/0.46 <=> ? [B: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 & ( in @ B @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(omega_type,type,
% 0.20/0.46 omega: $i ).
% 0.20/0.46
% 0.20/0.46 thf(omega0Ax_type,type,
% 0.20/0.46 omega0Ax: $o ).
% 0.20/0.46
% 0.20/0.46 thf(omega0Ax,definition,
% 0.20/0.46 ( omega0Ax
% 0.20/0.46 = ( in @ emptyset @ omega ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(omegaSAx_type,type,
% 0.20/0.46 omegaSAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(omegaSAx,definition,
% 0.20/0.46 ( omegaSAx
% 0.20/0.46 = ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ omega )
% 0.20/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(omegaIndAx_type,type,
% 0.20/0.46 omegaIndAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(omegaIndAx,definition,
% 0.20/0.46 ( omegaIndAx
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ( ( in @ emptyset @ A )
% 0.20/0.46 & ! [Xx: $i] :
% 0.20/0.46 ( ( ( in @ Xx @ omega )
% 0.20/0.46 & ( in @ Xx @ A ) )
% 0.20/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ omega )
% 0.20/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(replAx_type,type,
% 0.20/0.46 replAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(replAx,definition,
% 0.20/0.46 ( replAx
% 0.20/0.46 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( exu
% 0.20/0.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.20/0.46 => ? [B: $i] :
% 0.20/0.46 ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 <=> ? [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(foundationAx_type,type,
% 0.20/0.46 foundationAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(foundationAx,definition,
% 0.20/0.46 ( foundationAx
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.20/0.46 => ? [B: $i] :
% 0.20/0.46 ( ( in @ B @ A )
% 0.20/0.46 & ~ ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(wellorderingAx_type,type,
% 0.20/0.46 wellorderingAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(wellorderingAx,definition,
% 0.20/0.46 ( wellorderingAx
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ? [B: $i] :
% 0.20/0.46 ( ! [C: $i] :
% 0.20/0.46 ( ( in @ C @ B )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ C )
% 0.20/0.46 => ( in @ Xx @ A ) ) )
% 0.20/0.46 & ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( ( in @ Xx @ A )
% 0.20/0.46 & ( in @ Xy @ A ) )
% 0.20/0.46 => ( ! [C: $i] :
% 0.20/0.46 ( ( in @ C @ B )
% 0.20/0.46 => ( ( in @ Xx @ C )
% 0.20/0.46 <=> ( in @ Xy @ C ) ) )
% 0.20/0.46 => ( Xx = Xy ) ) )
% 0.20/0.46 & ! [C: $i,D: $i] :
% 0.20/0.46 ( ( ( in @ C @ B )
% 0.20/0.46 & ( in @ D @ B ) )
% 0.20/0.46 => ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ C )
% 0.20/0.46 => ( in @ Xx @ D ) )
% 0.20/0.46 | ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ D )
% 0.20/0.46 => ( in @ Xx @ C ) ) ) )
% 0.20/0.46 & ! [C: $i] :
% 0.20/0.46 ( ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ C )
% 0.20/0.46 => ( in @ Xx @ A ) )
% 0.20/0.46 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.20/0.46 => ? [D: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ D @ B )
% 0.20/0.46 & ( in @ Xx @ C )
% 0.20/0.46 & ~ ? [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ D )
% 0.20/0.46 & ( in @ Xy @ C ) )
% 0.20/0.46 & ! [E: $i] :
% 0.20/0.46 ( ( in @ E @ B )
% 0.20/0.46 => ( ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ E )
% 0.20/0.46 => ( in @ Xy @ D ) )
% 0.20/0.46 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(descr_type,type,
% 0.20/0.46 descr: ( $i > $o ) > $i ).
% 0.20/0.46
% 0.20/0.46 thf(descrp_type,type,
% 0.20/0.46 descrp: $o ).
% 0.20/0.46
% 0.20/0.46 thf(descrp,definition,
% 0.20/0.46 ( descrp
% 0.20/0.46 = ( ! [Xphi: $i > $o] :
% 0.20/0.46 ( ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 => ( Xphi
% 0.20/0.46 @ ( descr
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstr_type,type,
% 0.20/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstrI_type,type,
% 0.20/0.46 dsetconstrI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstrI,definition,
% 0.20/0.46 ( dsetconstrI
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( Xphi @ Xx )
% 0.20/0.46 => ( in @ Xx
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstrEL_type,type,
% 0.20/0.46 dsetconstrEL: $o ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstrEL,definition,
% 0.20/0.46 ( dsetconstrEL
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.20/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstrER_type,type,
% 0.20/0.46 dsetconstrER: $o ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstrER,definition,
% 0.20/0.46 ( dsetconstrER
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.20/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(exuE1_type,type,
% 0.20/0.46 exuE1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(exuE1,definition,
% 0.20/0.46 ( exuE1
% 0.20/0.46 = ( ! [Xphi: $i > $o] :
% 0.20/0.46 ( ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 => ? [Xx: $i] :
% 0.20/0.46 ( ( Xphi @ Xx )
% 0.20/0.46 & ! [Xy: $i] :
% 0.20/0.46 ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(prop2set_type,type,
% 0.20/0.46 prop2set: $o > $i ).
% 0.20/0.46
% 0.20/0.46 thf(prop2setE_type,type,
% 0.20/0.46 prop2setE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(prop2setE,definition,
% 0.20/0.46 ( prop2setE
% 0.20/0.46 = ( ! [Xphi: $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.20/0.46 => Xphi ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptysetE_type,type,
% 0.20/0.46 emptysetE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptysetE,definition,
% 0.20/0.46 ( emptysetE
% 0.20/0.46 = ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ emptyset )
% 0.20/0.46 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptysetimpfalse_type,type,
% 0.20/0.46 emptysetimpfalse: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptysetimpfalse,definition,
% 0.20/0.46 ( emptysetimpfalse
% 0.20/0.46 = ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ emptyset )
% 0.20/0.46 => $false ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(notinemptyset_type,type,
% 0.20/0.46 notinemptyset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(notinemptyset,definition,
% 0.20/0.46 ( notinemptyset
% 0.20/0.46 = ( ! [Xx: $i] :
% 0.20/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(exuE3e_type,type,
% 0.20/0.46 exuE3e: $o ).
% 0.20/0.46
% 0.20/0.46 thf(exuE3e,definition,
% 0.20/0.46 ( exuE3e
% 0.20/0.46 = ( ! [Xphi: $i > $o] :
% 0.20/0.46 ( ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setext_type,type,
% 0.20/0.46 setext: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setext,definition,
% 0.20/0.46 ( setext
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xx @ B ) )
% 0.20/0.46 => ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 => ( in @ Xx @ A ) )
% 0.20/0.46 => ( A = B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptyI_type,type,
% 0.20/0.46 emptyI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptyI,definition,
% 0.20/0.46 ( emptyI
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ~ ( in @ Xx @ A )
% 0.20/0.46 => ( A = emptyset ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(noeltsimpempty_type,type,
% 0.20/0.46 noeltsimpempty: $o ).
% 0.20/0.46
% 0.20/0.46 thf(noeltsimpempty,definition,
% 0.20/0.46 ( noeltsimpempty
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ~ ( in @ Xx @ A )
% 0.20/0.46 => ( A = emptyset ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setbeta_type,type,
% 0.20/0.46 setbeta: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setbeta,definition,
% 0.20/0.46 ( setbeta
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.20/0.46 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(nonempty_type,type,
% 0.20/0.46 nonempty: $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(nonempty,definition,
% 0.20/0.46 ( nonempty
% 0.20/0.46 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(nonemptyE1_type,type,
% 0.20/0.46 nonemptyE1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(nonemptyE1,definition,
% 0.20/0.46 ( nonemptyE1
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ( nonempty @ A )
% 0.20/0.46 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(nonemptyI_type,type,
% 0.20/0.46 nonemptyI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(nonemptyI,definition,
% 0.20/0.46 ( nonemptyI
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( Xphi @ Xx )
% 0.20/0.46 => ( nonempty
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(nonemptyI1_type,type,
% 0.20/0.46 nonemptyI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(nonemptyI1,definition,
% 0.20/0.46 ( nonemptyI1
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.20/0.46 => ( nonempty @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinIL_type,type,
% 0.20/0.46 setadjoinIL: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinIL,definition,
% 0.20/0.46 ( setadjoinIL
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptyinunitempty_type,type,
% 0.20/0.46 emptyinunitempty: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptyinunitempty,definition,
% 0.20/0.46 ( emptyinunitempty
% 0.20/0.46 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinIR_type,type,
% 0.20/0.46 setadjoinIR: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinIR,definition,
% 0.20/0.46 ( setadjoinIR
% 0.20/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinE_type,type,
% 0.20/0.46 setadjoinE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinE,definition,
% 0.20/0.46 ( setadjoinE
% 0.20/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.20/0.46 => ! [Xphi: $o] :
% 0.20/0.46 ( ( ( Xy = Xx )
% 0.20/0.46 => Xphi )
% 0.20/0.46 => ( ( ( in @ Xy @ A )
% 0.20/0.46 => Xphi )
% 0.20/0.46 => Xphi ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinOr_type,type,
% 0.20/0.46 setadjoinOr: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinOr,definition,
% 0.20/0.46 ( setadjoinOr
% 0.20/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.20/0.46 => ( ( Xy = Xx )
% 0.20/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setoftrueEq_type,type,
% 0.20/0.46 setoftrueEq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setoftrueEq,definition,
% 0.20/0.46 ( setoftrueEq
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xx: $i] : $true )
% 0.20/0.46 = A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powersetI_type,type,
% 0.20/0.46 powersetI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powersetI,definition,
% 0.20/0.46 ( powersetI
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 => ( in @ Xx @ A ) )
% 0.20/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptyinPowerset_type,type,
% 0.20/0.46 emptyinPowerset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptyinPowerset,definition,
% 0.20/0.46 ( emptyinPowerset
% 0.20/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptyInPowerset_type,type,
% 0.20/0.46 emptyInPowerset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptyInPowerset,definition,
% 0.20/0.46 ( emptyInPowerset
% 0.20/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powersetE_type,type,
% 0.20/0.46 powersetE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powersetE,definition,
% 0.20/0.46 ( powersetE
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.20/0.46 => ( ( in @ Xx @ B )
% 0.20/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setunionI_type,type,
% 0.20/0.46 setunionI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setunionI,definition,
% 0.20/0.46 ( setunionI
% 0.20/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 => ( ( in @ B @ A )
% 0.20/0.46 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setunionE_type,type,
% 0.20/0.46 setunionE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setunionE,definition,
% 0.20/0.46 ( setunionE
% 0.20/0.46 = ( ! [A: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.20/0.46 => ! [Xphi: $o] :
% 0.20/0.46 ( ! [B: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 => ( ( in @ B @ A )
% 0.20/0.46 => Xphi ) )
% 0.20/0.46 => Xphi ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subPowSU_type,type,
% 0.20/0.46 subPowSU: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subPowSU,definition,
% 0.20/0.46 ( subPowSU
% 0.20/0.46 = ( ! [A: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(exuE2_type,type,
% 0.20/0.46 exuE2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(exuE2,definition,
% 0.20/0.46 ( exuE2
% 0.20/0.46 = ( ! [Xphi: $i > $o] :
% 0.20/0.46 ( ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 => ? [Xx: $i] :
% 0.20/0.46 ! [Xy: $i] :
% 0.20/0.46 ( ( Xphi @ Xy )
% 0.20/0.46 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(nonemptyImpWitness_type,type,
% 0.20/0.46 nonemptyImpWitness: $o ).
% 0.20/0.46
% 0.20/0.46 thf(nonemptyImpWitness,definition,
% 0.20/0.46 ( nonemptyImpWitness
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ( nonempty @ A )
% 0.20/0.46 => ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & $true ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(uniqinunit_type,type,
% 0.20/0.46 uniqinunit: $o ).
% 0.20/0.46
% 0.20/0.46 thf(uniqinunit,definition,
% 0.20/0.46 ( uniqinunit
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(notinsingleton_type,type,
% 0.20/0.46 notinsingleton: $o ).
% 0.20/0.46
% 0.20/0.46 thf(notinsingleton,definition,
% 0.20/0.46 ( notinsingleton
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx != Xy )
% 0.20/0.46 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(eqinunit_type,type,
% 0.20/0.46 eqinunit: $o ).
% 0.20/0.46
% 0.20/0.46 thf(eqinunit,definition,
% 0.20/0.46 ( eqinunit
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx = Xy )
% 0.20/0.46 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(singletonsswitch_type,type,
% 0.20/0.46 singletonsswitch: $o ).
% 0.20/0.46
% 0.20/0.46 thf(singletonsswitch,definition,
% 0.20/0.46 ( singletonsswitch
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.20/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(upairsetE_type,type,
% 0.20/0.46 upairsetE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(upairsetE,definition,
% 0.20/0.46 ( upairsetE
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.20/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.20/0.46 => ( ( Xz = Xx )
% 0.20/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(upairsetIL_type,type,
% 0.20/0.46 upairsetIL: $o ).
% 0.20/0.46
% 0.20/0.46 thf(upairsetIL,definition,
% 0.20/0.46 ( upairsetIL
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(upairsetIR_type,type,
% 0.20/0.46 upairsetIR: $o ).
% 0.20/0.46
% 0.20/0.46 thf(upairsetIR,definition,
% 0.20/0.46 ( upairsetIR
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptyE1_type,type,
% 0.20/0.46 emptyE1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptyE1,definition,
% 0.20/0.46 ( emptyE1
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ( Xphi @ Xx ) )
% 0.20/0.46 => ( ( ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 = emptyset )
% 0.20/0.46 => $false ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(vacuousDall_type,type,
% 0.20/0.46 vacuousDall: $o ).
% 0.20/0.46
% 0.20/0.46 thf(vacuousDall,definition,
% 0.20/0.46 ( vacuousDall
% 0.20/0.46 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ emptyset )
% 0.20/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(quantDeMorgan1_type,type,
% 0.20/0.46 quantDeMorgan1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(quantDeMorgan1,definition,
% 0.20/0.46 ( quantDeMorgan1
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ~ ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( Xphi @ Xx ) )
% 0.20/0.46 => ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(quantDeMorgan2_type,type,
% 0.20/0.46 quantDeMorgan2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(quantDeMorgan2,definition,
% 0.20/0.46 ( quantDeMorgan2
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ~ ( Xphi @ Xx ) )
% 0.20/0.46 => ~ ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(quantDeMorgan3_type,type,
% 0.20/0.46 quantDeMorgan3: $o ).
% 0.20/0.46
% 0.20/0.46 thf(quantDeMorgan3,definition,
% 0.20/0.46 ( quantDeMorgan3
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ~ ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ( Xphi @ Xx ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(quantDeMorgan4_type,type,
% 0.20/0.46 quantDeMorgan4: $o ).
% 0.20/0.46
% 0.20/0.46 thf(quantDeMorgan4,definition,
% 0.20/0.46 ( quantDeMorgan4
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ~ ( Xphi @ Xx ) )
% 0.20/0.46 => ~ ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(prop2setI_type,type,
% 0.20/0.46 prop2setI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(prop2setI,definition,
% 0.20/0.46 ( prop2setI
% 0.20/0.46 = ( ! [Xphi: $o] :
% 0.20/0.46 ( Xphi
% 0.20/0.46 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(set2prop_type,type,
% 0.20/0.46 set2prop: $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(prop2set2propI_type,type,
% 0.20/0.46 prop2set2propI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(prop2set2propI,definition,
% 0.20/0.46 ( prop2set2propI
% 0.20/0.46 = ( ! [Xphi: $o] :
% 0.20/0.46 ( Xphi
% 0.20/0.46 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(notdexE_type,type,
% 0.20/0.46 notdexE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(notdexE,definition,
% 0.20/0.46 ( notdexE
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ~ ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ( Xphi @ Xx ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(notdallE_type,type,
% 0.20/0.46 notdallE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(notdallE,definition,
% 0.20/0.46 ( notdallE
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ~ ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( Xphi @ Xx ) )
% 0.20/0.46 => ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(exuI1_type,type,
% 0.20/0.46 exuI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(exuI1,definition,
% 0.20/0.46 ( exuI1
% 0.20/0.46 = ( ! [Xphi: $i > $o] :
% 0.20/0.46 ( ? [Xx: $i] :
% 0.20/0.46 ( ( Xphi @ Xx )
% 0.20/0.46 & ! [Xy: $i] :
% 0.20/0.46 ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xx = Xy ) ) )
% 0.20/0.46 => ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(exuI3_type,type,
% 0.20/0.46 exuI3: $o ).
% 0.20/0.46
% 0.20/0.46 thf(exuI3,definition,
% 0.20/0.46 ( exuI3
% 0.20/0.46 = ( ! [Xphi: $i > $o] :
% 0.20/0.46 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.20/0.46 => ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xphi @ Xx )
% 0.20/0.46 => ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xx = Xy ) ) )
% 0.20/0.46 => ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(exuI2_type,type,
% 0.20/0.46 exuI2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(exuI2,definition,
% 0.20/0.46 ( exuI2
% 0.20/0.46 = ( ! [Xphi: $i > $o] :
% 0.20/0.46 ( ? [Xx: $i] :
% 0.20/0.46 ! [Xy: $i] :
% 0.20/0.46 ( ( Xphi @ Xy )
% 0.20/0.46 <=> ( Xy = Xx ) )
% 0.20/0.46 => ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(inCongP_type,type,
% 0.20/0.46 inCongP: $o ).
% 0.20/0.46
% 0.20/0.46 thf(inCongP,definition,
% 0.20/0.46 ( inCongP
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( A = B )
% 0.20/0.46 => ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx = Xy )
% 0.20/0.46 => ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(in__Cong_type,type,
% 0.20/0.46 in__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(in__Cong,definition,
% 0.20/0.46 ( in__Cong
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( A = B )
% 0.20/0.46 => ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx = Xy )
% 0.20/0.46 => ( ( in @ Xx @ A )
% 0.20/0.46 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(exuE3u_type,type,
% 0.20/0.46 exuE3u: $o ).
% 0.20/0.46
% 0.20/0.46 thf(exuE3u,definition,
% 0.20/0.46 ( exuE3u
% 0.20/0.46 = ( ! [Xphi: $i > $o] :
% 0.20/0.46 ( ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 => ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xphi @ Xx )
% 0.20/0.46 => ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(exu__Cong_type,type,
% 0.20/0.46 exu__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(exu__Cong,definition,
% 0.20/0.46 ( exu__Cong
% 0.20/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.20/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx = Xy )
% 0.20/0.46 => ( ( Xphi @ Xx )
% 0.20/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.20/0.46 => ( ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 <=> ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptyset__Cong_type,type,
% 0.20/0.46 emptyset__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptyset__Cong,definition,
% 0.20/0.46 ( emptyset__Cong
% 0.20/0.46 = ( emptyset = emptyset ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoin__Cong_type,type,
% 0.20/0.46 setadjoin__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoin__Cong,definition,
% 0.20/0.46 ( setadjoin__Cong
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx = Xy )
% 0.20/0.46 => ! [Xz: $i,Xu: $i] :
% 0.20/0.46 ( ( Xz = Xu )
% 0.20/0.46 => ( ( setadjoin @ Xx @ Xz )
% 0.20/0.46 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powerset__Cong_type,type,
% 0.20/0.46 powerset__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powerset__Cong,definition,
% 0.20/0.46 ( powerset__Cong
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( A = B )
% 0.20/0.46 => ( ( powerset @ A )
% 0.20/0.46 = ( powerset @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setunion__Cong_type,type,
% 0.20/0.46 setunion__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setunion__Cong,definition,
% 0.20/0.46 ( setunion__Cong
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( A = B )
% 0.20/0.46 => ( ( setunion @ A )
% 0.20/0.46 = ( setunion @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(omega__Cong_type,type,
% 0.20/0.46 omega__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(omega__Cong,definition,
% 0.20/0.46 ( omega__Cong
% 0.20/0.46 = ( omega = omega ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(exuEu_type,type,
% 0.20/0.46 exuEu: $o ).
% 0.20/0.46
% 0.20/0.46 thf(exuEu,definition,
% 0.20/0.46 ( exuEu
% 0.20/0.46 = ( ! [Xphi: $i > $o] :
% 0.20/0.46 ( ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 => ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xphi @ Xx )
% 0.20/0.46 => ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(descr__Cong_type,type,
% 0.20/0.46 descr__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(descr__Cong,definition,
% 0.20/0.46 ( descr__Cong
% 0.20/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.20/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx = Xy )
% 0.20/0.46 => ( ( Xphi @ Xx )
% 0.20/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.20/0.46 => ( ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 => ( ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.20/0.46 => ( ( descr
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 = ( descr
% 0.20/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstr__Cong_type,type,
% 0.20/0.46 dsetconstr__Cong: $o ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstr__Cong,definition,
% 0.20/0.46 ( dsetconstr__Cong
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( A = B )
% 0.20/0.46 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( ( Xx = Xy )
% 0.20/0.46 => ( ( Xphi @ Xx )
% 0.20/0.46 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.20/0.46 => ( ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 = ( dsetconstr @ B
% 0.20/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subset_type,type,
% 0.20/0.46 subset: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(disjoint_type,type,
% 0.20/0.46 disjoint: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(setsmeet_type,type,
% 0.20/0.46 setsmeet: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetI1_type,type,
% 0.20/0.46 subsetI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetI1,definition,
% 0.20/0.46 ( subsetI1
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xx @ B ) )
% 0.20/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(eqimpsubset2_type,type,
% 0.20/0.46 eqimpsubset2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(eqimpsubset2,definition,
% 0.20/0.46 ( eqimpsubset2
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( A = B )
% 0.20/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(eqimpsubset1_type,type,
% 0.20/0.46 eqimpsubset1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(eqimpsubset1,definition,
% 0.20/0.46 ( eqimpsubset1
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( A = B )
% 0.20/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subsetI2_type,type,
% 0.20/0.46 subsetI2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetI2,definition,
% 0.20/0.46 ( subsetI2
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xx @ B ) )
% 0.20/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptysetsubset_type,type,
% 0.20/0.46 emptysetsubset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptysetsubset,definition,
% 0.20/0.46 ( emptysetsubset
% 0.20/0.46 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subsetE_type,type,
% 0.20/0.46 subsetE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetE,definition,
% 0.20/0.46 ( subsetE
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subsetE2_type,type,
% 0.20/0.46 subsetE2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetE2,definition,
% 0.20/0.46 ( subsetE2
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( ~ ( in @ Xx @ B )
% 0.20/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(notsubsetI_type,type,
% 0.20/0.46 notsubsetI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(notsubsetI,definition,
% 0.20/0.46 ( notsubsetI
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ~ ( in @ Xx @ B )
% 0.20/0.46 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(notequalI1_type,type,
% 0.20/0.46 notequalI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(notequalI1,definition,
% 0.20/0.46 ( notequalI1
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ~ ( subset @ A @ B )
% 0.20/0.46 => ( A != B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(notequalI2_type,type,
% 0.20/0.46 notequalI2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(notequalI2,definition,
% 0.20/0.46 ( notequalI2
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ~ ( in @ Xx @ B )
% 0.20/0.46 => ( A != B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subsetRefl_type,type,
% 0.20/0.46 subsetRefl: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetRefl,definition,
% 0.20/0.46 ( subsetRefl
% 0.20/0.46 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subsetTrans_type,type,
% 0.20/0.46 subsetTrans: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetTrans,definition,
% 0.20/0.46 ( subsetTrans
% 0.20/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( ( subset @ B @ C )
% 0.20/0.46 => ( subset @ A @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinSub_type,type,
% 0.20/0.46 setadjoinSub: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinSub,definition,
% 0.20/0.46 ( setadjoinSub
% 0.20/0.46 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinSub2_type,type,
% 0.20/0.46 setadjoinSub2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinSub2,definition,
% 0.20/0.46 ( setadjoinSub2
% 0.20/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subset2powerset_type,type,
% 0.20/0.46 subset2powerset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subset2powerset,definition,
% 0.20/0.46 ( subset2powerset
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setextsub_type,type,
% 0.20/0.46 setextsub: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setextsub,definition,
% 0.20/0.46 ( setextsub
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( ( subset @ B @ A )
% 0.20/0.46 => ( A = B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subsetemptysetimpeq_type,type,
% 0.20/0.46 subsetemptysetimpeq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subsetemptysetimpeq,definition,
% 0.20/0.46 ( subsetemptysetimpeq
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ( subset @ A @ emptyset )
% 0.20/0.46 => ( A = emptyset ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powersetI1_type,type,
% 0.20/0.46 powersetI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powersetI1,definition,
% 0.20/0.46 ( powersetI1
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( subset @ B @ A )
% 0.20/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powersetE1_type,type,
% 0.20/0.46 powersetE1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powersetE1,definition,
% 0.20/0.46 ( powersetE1
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.20/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(inPowerset_type,type,
% 0.20/0.46 inPowerset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(inPowerset,definition,
% 0.20/0.46 ( inPowerset
% 0.20/0.46 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powersetsubset_type,type,
% 0.20/0.46 powersetsubset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powersetsubset,definition,
% 0.20/0.46 ( powersetsubset
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sepInPowerset_type,type,
% 0.20/0.46 sepInPowerset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(sepInPowerset,definition,
% 0.20/0.46 ( sepInPowerset
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( in
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 @ ( powerset @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sepSubset_type,type,
% 0.20/0.46 sepSubset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(sepSubset,definition,
% 0.20/0.46 ( sepSubset
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( subset
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binunion_type,type,
% 0.20/0.46 binunion: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(binunionIL_type,type,
% 0.20/0.46 binunionIL: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binunionIL,definition,
% 0.20/0.46 ( binunionIL
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(upairset2IR_type,type,
% 0.20/0.46 upairset2IR: $o ).
% 0.20/0.46
% 0.20/0.46 thf(upairset2IR,definition,
% 0.20/0.46 ( upairset2IR
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binunionIR_type,type,
% 0.20/0.46 binunionIR: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binunionIR,definition,
% 0.20/0.46 ( binunionIR
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binunionEcases_type,type,
% 0.20/0.46 binunionEcases: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binunionEcases,definition,
% 0.20/0.46 ( binunionEcases
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.20/0.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.20/0.46 => ( ( ( in @ Xx @ A )
% 0.20/0.46 => Xphi )
% 0.20/0.46 => ( ( ( in @ Xx @ B )
% 0.20/0.46 => Xphi )
% 0.20/0.46 => Xphi ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binunionE_type,type,
% 0.20/0.46 binunionE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binunionE,definition,
% 0.20/0.46 ( binunionE
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.20/0.46 => ( ( in @ Xx @ A )
% 0.20/0.46 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binunionLsub_type,type,
% 0.20/0.46 binunionLsub: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binunionLsub,definition,
% 0.20/0.46 ( binunionLsub
% 0.20/0.46 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binunionRsub_type,type,
% 0.20/0.46 binunionRsub: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binunionRsub,definition,
% 0.20/0.46 ( binunionRsub
% 0.20/0.46 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersect_type,type,
% 0.20/0.46 binintersect: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectI_type,type,
% 0.20/0.46 binintersectI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectI,definition,
% 0.20/0.46 ( binintersectI
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ B )
% 0.20/0.46 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset5_type,type,
% 0.20/0.46 binintersectSubset5: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset5,definition,
% 0.20/0.46 ( binintersectSubset5
% 0.20/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.20/0.46 ( ( subset @ C @ A )
% 0.20/0.46 => ( ( subset @ C @ B )
% 0.20/0.46 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectEL_type,type,
% 0.20/0.46 binintersectEL: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectEL,definition,
% 0.20/0.46 ( binintersectEL
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.20/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectLsub_type,type,
% 0.20/0.46 binintersectLsub: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectLsub,definition,
% 0.20/0.46 ( binintersectLsub
% 0.20/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset2_type,type,
% 0.20/0.46 binintersectSubset2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset2,definition,
% 0.20/0.46 ( binintersectSubset2
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( ( binintersect @ A @ B )
% 0.20/0.46 = A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset3_type,type,
% 0.20/0.46 binintersectSubset3: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset3,definition,
% 0.20/0.46 ( binintersectSubset3
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( ( binintersect @ A @ B )
% 0.20/0.46 = B )
% 0.20/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectER_type,type,
% 0.20/0.46 binintersectER: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectER,definition,
% 0.20/0.46 ( binintersectER
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.20/0.46 => ( in @ Xx @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(disjointsetsI1_type,type,
% 0.20/0.46 disjointsetsI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(disjointsetsI1,definition,
% 0.20/0.46 ( disjointsetsI1
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ~ ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ( in @ Xx @ B ) )
% 0.20/0.46 => ( ( binintersect @ A @ B )
% 0.20/0.46 = emptyset ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectRsub_type,type,
% 0.20/0.46 binintersectRsub: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectRsub,definition,
% 0.20/0.46 ( binintersectRsub
% 0.20/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset4_type,type,
% 0.20/0.46 binintersectSubset4: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset4,definition,
% 0.20/0.46 ( binintersectSubset4
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( subset @ B @ A )
% 0.20/0.46 => ( ( binintersect @ A @ B )
% 0.20/0.46 = B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset1_type,type,
% 0.20/0.46 binintersectSubset1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(binintersectSubset1,definition,
% 0.20/0.46 ( binintersectSubset1
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( ( binintersect @ A @ B )
% 0.20/0.46 = A )
% 0.20/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(bs114d_type,type,
% 0.20/0.46 bs114d: $o ).
% 0.20/0.46
% 0.20/0.46 thf(bs114d,definition,
% 0.20/0.46 ( bs114d
% 0.20/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.20/0.46 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.20/0.46 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(regular_type,type,
% 0.20/0.46 regular: $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminus_type,type,
% 0.20/0.46 setminus: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(setminusI_type,type,
% 0.20/0.46 setminusI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusI,definition,
% 0.20/0.46 ( setminusI
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ~ ( in @ Xx @ B )
% 0.20/0.46 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusEL_type,type,
% 0.20/0.46 setminusEL: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusEL,definition,
% 0.20/0.46 ( setminusEL
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.20/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusER_type,type,
% 0.20/0.46 setminusER: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusER,definition,
% 0.20/0.46 ( setminusER
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.20/0.46 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusSubset2_type,type,
% 0.20/0.46 setminusSubset2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusSubset2,definition,
% 0.20/0.46 ( setminusSubset2
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( subset @ A @ B )
% 0.20/0.46 => ( ( setminus @ A @ B )
% 0.20/0.46 = emptyset ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusERneg_type,type,
% 0.20/0.46 setminusERneg: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusERneg,definition,
% 0.20/0.46 ( setminusERneg
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.20/0.46 => ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusELneg_type,type,
% 0.20/0.46 setminusELneg: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusELneg,definition,
% 0.20/0.46 ( setminusELneg
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.20/0.46 => ( ~ ( in @ Xx @ B )
% 0.20/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusILneg_type,type,
% 0.20/0.46 setminusILneg: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusILneg,definition,
% 0.20/0.46 ( setminusILneg
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ~ ( in @ Xx @ A )
% 0.20/0.46 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusIRneg_type,type,
% 0.20/0.46 setminusIRneg: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusIRneg,definition,
% 0.20/0.46 ( setminusIRneg
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusLsub_type,type,
% 0.20/0.46 setminusLsub: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusLsub,definition,
% 0.20/0.46 ( setminusLsub
% 0.20/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setminusSubset1_type,type,
% 0.20/0.46 setminusSubset1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setminusSubset1,definition,
% 0.20/0.46 ( setminusSubset1
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( ( setminus @ A @ B )
% 0.20/0.46 = emptyset )
% 0.20/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(symdiff_type,type,
% 0.20/0.46 symdiff: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(symdiffE_type,type,
% 0.20/0.46 symdiffE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(symdiffE,definition,
% 0.20/0.46 ( symdiffE
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.20/0.46 => ! [Xphi: $o] :
% 0.20/0.46 ( ( ( in @ Xx @ A )
% 0.20/0.46 => ( ~ ( in @ Xx @ B )
% 0.20/0.46 => Xphi ) )
% 0.20/0.46 => ( ( ~ ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ B )
% 0.20/0.46 => Xphi ) )
% 0.20/0.46 => Xphi ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(symdiffI1_type,type,
% 0.20/0.46 symdiffI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(symdiffI1,definition,
% 0.20/0.46 ( symdiffI1
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ~ ( in @ Xx @ B )
% 0.20/0.46 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(symdiffI2_type,type,
% 0.20/0.46 symdiffI2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(symdiffI2,definition,
% 0.20/0.46 ( symdiffI2
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ~ ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ B )
% 0.20/0.46 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(symdiffIneg1_type,type,
% 0.20/0.46 symdiffIneg1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(symdiffIneg1,definition,
% 0.20/0.46 ( symdiffIneg1
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx @ B )
% 0.20/0.46 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(symdiffIneg2_type,type,
% 0.20/0.46 symdiffIneg2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(symdiffIneg2,definition,
% 0.20/0.46 ( symdiffIneg2
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ~ ( in @ Xx @ A )
% 0.20/0.46 => ( ~ ( in @ Xx @ B )
% 0.20/0.46 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(iskpair_type,type,
% 0.20/0.46 iskpair: $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(iskpair,definition,
% 0.20/0.46 ( iskpair
% 0.20/0.46 = ( ^ [A: $i] :
% 0.20/0.46 ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.20/0.46 & ? [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ ( setunion @ A ) )
% 0.20/0.46 & ( A
% 0.20/0.46 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(secondinupair_type,type,
% 0.20/0.46 secondinupair: $o ).
% 0.20/0.46
% 0.20/0.46 thf(secondinupair,definition,
% 0.20/0.46 ( secondinupair
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairIL_type,type,
% 0.20/0.46 setukpairIL: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairIL,definition,
% 0.20/0.46 ( setukpairIL
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairIR_type,type,
% 0.20/0.46 setukpairIR: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairIR,definition,
% 0.20/0.46 ( setukpairIR
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(kpairiskpair_type,type,
% 0.20/0.46 kpairiskpair: $o ).
% 0.20/0.46
% 0.20/0.46 thf(kpairiskpair,definition,
% 0.20/0.46 ( kpairiskpair
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(kpair_type,type,
% 0.20/0.46 kpair: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(kpair,definition,
% 0.20/0.46 ( kpair
% 0.20/0.46 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(kpairp_type,type,
% 0.20/0.46 kpairp: $o ).
% 0.20/0.46
% 0.20/0.46 thf(kpairp,definition,
% 0.20/0.46 ( kpairp
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(cartprod_type,type,
% 0.20/0.46 cartprod: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(singletonsubset_type,type,
% 0.20/0.46 singletonsubset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(singletonsubset,definition,
% 0.20/0.46 ( singletonsubset
% 0.20/0.46 = ( ! [A: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(singletoninpowerset_type,type,
% 0.20/0.46 singletoninpowerset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(singletoninpowerset,definition,
% 0.20/0.46 ( singletoninpowerset
% 0.20/0.46 = ( ! [A: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(singletoninpowunion_type,type,
% 0.20/0.46 singletoninpowunion: $o ).
% 0.20/0.46
% 0.20/0.46 thf(singletoninpowunion,definition,
% 0.20/0.46 ( singletoninpowunion
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(upairset2E_type,type,
% 0.20/0.46 upairset2E: $o ).
% 0.20/0.46
% 0.20/0.46 thf(upairset2E,definition,
% 0.20/0.46 ( upairset2E
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.20/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.20/0.46 => ( ( Xz = Xx )
% 0.20/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(upairsubunion_type,type,
% 0.20/0.46 upairsubunion: $o ).
% 0.20/0.46
% 0.20/0.46 thf(upairsubunion,definition,
% 0.20/0.46 ( upairsubunion
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(upairinpowunion_type,type,
% 0.20/0.46 upairinpowunion: $o ).
% 0.20/0.46
% 0.20/0.46 thf(upairinpowunion,definition,
% 0.20/0.46 ( upairinpowunion
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ubforcartprodlem1_type,type,
% 0.20/0.46 ubforcartprodlem1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ubforcartprodlem1,definition,
% 0.20/0.46 ( ubforcartprodlem1
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ubforcartprodlem2_type,type,
% 0.20/0.46 ubforcartprodlem2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ubforcartprodlem2,definition,
% 0.20/0.46 ( ubforcartprodlem2
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ubforcartprodlem3_type,type,
% 0.20/0.46 ubforcartprodlem3: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ubforcartprodlem3,definition,
% 0.20/0.46 ( ubforcartprodlem3
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodpairin_type,type,
% 0.20/0.46 cartprodpairin: $o ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodpairin,definition,
% 0.20/0.46 ( cartprodpairin
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodmempair1_type,type,
% 0.20/0.46 cartprodmempair1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodmempair1,definition,
% 0.20/0.46 ( cartprodmempair1
% 0.20/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.20/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.20/0.46 => ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ? [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ B )
% 0.20/0.46 & ( Xu
% 0.20/0.46 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodmempair_type,type,
% 0.20/0.46 cartprodmempair: $o ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodmempair,definition,
% 0.20/0.46 ( cartprodmempair
% 0.20/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.20/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.20/0.46 => ( iskpair @ Xu ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setunionE2_type,type,
% 0.20/0.46 setunionE2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setunionE2,definition,
% 0.20/0.46 ( setunionE2
% 0.20/0.46 = ( ! [A: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.20/0.46 => ? [X: $i] :
% 0.20/0.46 ( ( in @ X @ A )
% 0.20/0.46 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setunionsingleton1_type,type,
% 0.20/0.46 setunionsingleton1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setunionsingleton1,definition,
% 0.20/0.46 ( setunionsingleton1
% 0.20/0.46 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setunionsingleton2_type,type,
% 0.20/0.46 setunionsingleton2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setunionsingleton2,definition,
% 0.20/0.46 ( setunionsingleton2
% 0.20/0.46 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setunionsingleton_type,type,
% 0.20/0.46 setunionsingleton: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setunionsingleton,definition,
% 0.20/0.46 ( setunionsingleton
% 0.20/0.46 = ( ! [Xx: $i] :
% 0.20/0.46 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.20/0.46 = Xx ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(singleton_type,type,
% 0.20/0.46 singleton: $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(singleton,definition,
% 0.20/0.46 ( singleton
% 0.20/0.46 = ( ^ [A: $i] :
% 0.20/0.46 ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ( A
% 0.20/0.46 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(singletonprop_type,type,
% 0.20/0.46 singletonprop: $o ).
% 0.20/0.46
% 0.20/0.46 thf(singletonprop,definition,
% 0.20/0.46 ( singletonprop
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( ( Xphi @ Xx )
% 0.20/0.46 => ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) )
% 0.20/0.46 => ( ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ( Xphi @ Xx ) )
% 0.20/0.46 => ( singleton
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ex1_type,type,
% 0.20/0.46 ex1: $i > ( $i > $o ) > $o ).
% 0.20/0.46
% 0.20/0.46 thf(ex1,definition,
% 0.20/0.46 ( ex1
% 0.20/0.46 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( singleton
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ex1E1_type,type,
% 0.20/0.46 ex1E1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ex1E1,definition,
% 0.20/0.46 ( ex1E1
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ( ex1 @ A
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 => ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ex1I_type,type,
% 0.20/0.46 ex1I: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ex1I,definition,
% 0.20/0.46 ( ex1I
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( Xphi @ Xx )
% 0.20/0.46 => ( ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xy = Xx ) ) )
% 0.20/0.46 => ( ex1 @ A
% 0.20/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ex1I2_type,type,
% 0.20/0.46 ex1I2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ex1I2,definition,
% 0.20/0.46 ( ex1I2
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( ( Xphi @ Xx )
% 0.20/0.46 => ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) )
% 0.20/0.46 => ( ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & ( Xphi @ Xx ) )
% 0.20/0.46 => ( ex1 @ A
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(singletonsuniq_type,type,
% 0.20/0.46 singletonsuniq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(singletonsuniq,definition,
% 0.20/0.46 ( singletonsuniq
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( ( setadjoin @ Xx @ emptyset )
% 0.20/0.46 = ( setadjoin @ Xy @ emptyset ) )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(atmost1p_type,type,
% 0.20/0.46 atmost1p: $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(atleast2p_type,type,
% 0.20/0.46 atleast2p: $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(atmost2p_type,type,
% 0.20/0.46 atmost2p: $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(upairsetp_type,type,
% 0.20/0.46 upairsetp: $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjL1_type,type,
% 0.20/0.46 setukpairinjL1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjL1,definition,
% 0.20/0.46 ( setukpairinjL1
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.20/0.46 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.20/0.46 => ( Xx = Xz ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(kfstsingleton_type,type,
% 0.20/0.46 kfstsingleton: $o ).
% 0.20/0.46
% 0.20/0.46 thf(kfstsingleton,definition,
% 0.20/0.46 ( kfstsingleton
% 0.20/0.46 = ( ! [Xu: $i] :
% 0.20/0.46 ( ( iskpair @ Xu )
% 0.20/0.46 => ( singleton
% 0.20/0.46 @ ( dsetconstr @ ( setunion @ Xu )
% 0.20/0.46 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(theprop_type,type,
% 0.20/0.46 theprop: $o ).
% 0.20/0.46
% 0.20/0.46 thf(theprop,definition,
% 0.20/0.46 ( theprop
% 0.20/0.46 = ( ! [X: $i] :
% 0.20/0.46 ( ( singleton @ X )
% 0.20/0.46 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(kfst_type,type,
% 0.20/0.46 kfst: $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(kfstpairEq_type,type,
% 0.20/0.46 kfstpairEq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(kfstpairEq,definition,
% 0.20/0.46 ( kfstpairEq
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.20/0.46 = Xx ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodfstin_type,type,
% 0.20/0.46 cartprodfstin: $o ).
% 0.20/0.46
% 0.20/0.46 thf(cartprodfstin,definition,
% 0.20/0.46 ( cartprodfstin
% 0.20/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.20/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.20/0.46 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjL2_type,type,
% 0.20/0.46 setukpairinjL2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjL2,definition,
% 0.20/0.46 ( setukpairinjL2
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.20/0.46 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.20/0.46 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.20/0.46 => ( Xx = Xz ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjL_type,type,
% 0.20/0.46 setukpairinjL: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjL,definition,
% 0.20/0.46 ( setukpairinjL
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.20/0.46 ( ( ( kpair @ Xx @ Xy )
% 0.20/0.46 = ( kpair @ Xz @ Xu ) )
% 0.20/0.46 => ( Xx = Xz ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjR11_type,type,
% 0.20/0.46 setukpairinjR11: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjR11,definition,
% 0.20/0.46 ( setukpairinjR11
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx = Xy )
% 0.20/0.46 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.20/0.46 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjR12_type,type,
% 0.20/0.46 setukpairinjR12: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjR12,definition,
% 0.20/0.46 ( setukpairinjR12
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx = Xy )
% 0.20/0.46 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.20/0.46 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjR1_type,type,
% 0.20/0.46 setukpairinjR1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjR1,definition,
% 0.20/0.46 ( setukpairinjR1
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.20/0.46 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.20/0.46 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.20/0.46 => ( ( Xz = Xu )
% 0.20/0.46 => ( Xy = Xu ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(upairequniteq_type,type,
% 0.20/0.46 upairequniteq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(upairequniteq,definition,
% 0.20/0.46 ( upairequniteq
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.20/0.46 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.20/0.46 = ( setadjoin @ Xz @ emptyset ) )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjR2_type,type,
% 0.20/0.46 setukpairinjR2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjR2,definition,
% 0.20/0.46 ( setukpairinjR2
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.20/0.46 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.20/0.46 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.20/0.46 => ( Xy = Xu ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjR_type,type,
% 0.20/0.46 setukpairinjR: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setukpairinjR,definition,
% 0.20/0.46 ( setukpairinjR
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.20/0.46 ( ( ( kpair @ Xx @ Xy )
% 0.20/0.46 = ( kpair @ Xz @ Xu ) )
% 0.20/0.46 => ( Xy = Xu ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ksndsingleton_type,type,
% 0.20/0.46 ksndsingleton: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ksndsingleton,definition,
% 0.20/0.46 ( ksndsingleton
% 0.20/0.46 = ( ! [Xu: $i] :
% 0.20/0.46 ( ( iskpair @ Xu )
% 0.20/0.46 => ( singleton
% 0.20/0.46 @ ( dsetconstr @ ( setunion @ Xu )
% 0.20/0.46 @ ^ [Xx: $i] :
% 0.20/0.46 ( Xu
% 0.20/0.46 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(ksnd_type,type,
% 0.20/0.46 ksnd: $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(ksndpairEq_type,type,
% 0.20/0.46 ksndpairEq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(ksndpairEq,definition,
% 0.20/0.46 ( ksndpairEq
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.20/0.46 = Xy ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(kpairsurjEq,conjecture,
% 0.20/0.46 ( setextAx
% 0.20/0.46 => ( emptysetAx
% 0.20/0.46 => ( setadjoinAx
% 0.20/0.46 => ( powersetAx
% 0.20/0.46 => ( setunionAx
% 0.20/0.46 => ( omega0Ax
% 0.20/0.46 => ( omegaSAx
% 0.20/0.46 => ( omegaIndAx
% 0.20/0.46 => ( replAx
% 0.20/0.46 => ( foundationAx
% 0.20/0.46 => ( wellorderingAx
% 0.20/0.46 => ( descrp
% 0.20/0.46 => ( dsetconstrI
% 0.20/0.46 => ( dsetconstrEL
% 0.20/0.46 => ( dsetconstrER
% 0.20/0.46 => ( exuE1
% 0.20/0.46 => ( prop2setE
% 0.20/0.46 => ( emptysetE
% 0.20/0.46 => ( emptysetimpfalse
% 0.20/0.46 => ( notinemptyset
% 0.20/0.46 => ( exuE3e
% 0.20/0.46 => ( setext
% 0.20/0.46 => ( emptyI
% 0.20/0.46 => ( noeltsimpempty
% 0.20/0.46 => ( setbeta
% 0.20/0.46 => ( nonemptyE1
% 0.20/0.46 => ( nonemptyI
% 0.20/0.46 => ( nonemptyI1
% 0.20/0.46 => ( setadjoinIL
% 0.20/0.46 => ( emptyinunitempty
% 0.20/0.46 => ( setadjoinIR
% 0.20/0.46 => ( setadjoinE
% 0.20/0.46 => ( setadjoinOr
% 0.20/0.46 => ( setoftrueEq
% 0.20/0.46 => ( powersetI
% 0.20/0.46 => ( emptyinPowerset
% 0.20/0.46 => ( emptyInPowerset
% 0.20/0.46 => ( powersetE
% 0.20/0.46 => ( setunionI
% 0.20/0.46 => ( setunionE
% 0.20/0.46 => ( subPowSU
% 0.20/0.46 => ( exuE2
% 0.20/0.46 => ( nonemptyImpWitness
% 0.20/0.46 => ( uniqinunit
% 0.20/0.46 => ( notinsingleton
% 0.20/0.46 => ( eqinunit
% 0.20/0.46 => ( singletonsswitch
% 0.20/0.46 => ( upairsetE
% 0.20/0.46 => ( upairsetIL
% 0.20/0.46 => ( upairsetIR
% 0.20/0.46 => ( emptyE1
% 0.20/0.46 => ( vacuousDall
% 0.20/0.46 => ( quantDeMorgan1
% 0.20/0.46 => ( quantDeMorgan2
% 0.20/0.46 => ( quantDeMorgan3
% 0.20/0.46 => ( quantDeMorgan4
% 0.20/0.46 => ( prop2setI
% 0.20/0.46 => ( prop2set2propI
% 0.20/0.46 => ( notdexE
% 0.20/0.46 => ( notdallE
% 0.20/0.46 => ( exuI1
% 0.20/0.46 => ( exuI3
% 0.20/0.46 => ( exuI2
% 0.20/0.46 => ( inCongP
% 0.20/0.46 => ( in__Cong
% 0.20/0.46 => ( exuE3u
% 0.20/0.46 => ( exu__Cong
% 0.20/0.46 => ( emptyset__Cong
% 0.20/0.46 => ( setadjoin__Cong
% 0.20/0.46 => ( powerset__Cong
% 0.20/0.46 => ( setunion__Cong
% 0.20/0.46 => ( omega__Cong
% 0.20/0.46 => ( exuEu
% 0.20/0.46 => ( descr__Cong
% 0.20/0.46 => ( dsetconstr__Cong
% 0.20/0.46 => ( subsetI1
% 0.20/0.46 => ( eqimpsubset2
% 0.20/0.46 => ( eqimpsubset1
% 0.20/0.46 => ( subsetI2
% 0.20/0.46 => ( emptysetsubset
% 0.20/0.46 => ( subsetE
% 0.20/0.46 => ( subsetE2
% 0.20/0.46 => ( notsubsetI
% 0.20/0.46 => ( notequalI1
% 0.20/0.46 => ( notequalI2
% 0.20/0.46 => ( subsetRefl
% 0.20/0.46 => ( subsetTrans
% 0.20/0.46 => ( setadjoinSub
% 0.20/0.46 => ( setadjoinSub2
% 0.20/0.46 => ( subset2powerset
% 0.20/0.46 => ( setextsub
% 0.20/0.46 => ( subsetemptysetimpeq
% 0.20/0.46 => ( powersetI1
% 0.20/0.46 => ( powersetE1
% 0.20/0.46 => ( inPowerset
% 0.20/0.46 => ( powersetsubset
% 0.20/0.46 => ( sepInPowerset
% 0.20/0.46 => ( sepSubset
% 0.20/0.46 => ( binunionIL
% 0.20/0.46 => ( upairset2IR
% 0.20/0.46 => ( binunionIR
% 0.20/0.46 => ( binunionEcases
% 0.20/0.46 => ( binunionE
% 0.20/0.46 => ( binunionLsub
% 0.20/0.46 => ( binunionRsub
% 0.20/0.46 => ( binintersectI
% 0.20/0.46 => ( binintersectSubset5
% 0.20/0.46 => ( binintersectEL
% 0.20/0.46 => ( binintersectLsub
% 0.20/0.46 => ( binintersectSubset2
% 0.20/0.46 => ( binintersectSubset3
% 0.20/0.46 => ( binintersectER
% 0.20/0.46 => ( disjointsetsI1
% 0.20/0.46 => ( binintersectRsub
% 0.20/0.46 => ( binintersectSubset4
% 0.20/0.46 => ( binintersectSubset1
% 0.20/0.46 => ( bs114d
% 0.20/0.46 => ( setminusI
% 0.20/0.46 => ( setminusEL
% 0.20/0.46 => ( setminusER
% 0.20/0.46 => ( setminusSubset2
% 0.20/0.46 => ( setminusERneg
% 0.20/0.46 => ( setminusELneg
% 0.20/0.46 => ( setminusILneg
% 0.20/0.46 => ( setminusIRneg
% 0.20/0.46 => ( setminusLsub
% 0.20/0.46 => ( setminusSubset1
% 0.20/0.46 => ( symdiffE
% 0.20/0.46 => ( symdiffI1
% 0.20/0.46 => ( symdiffI2
% 0.20/0.46 => ( symdiffIneg1
% 0.20/0.46 => ( symdiffIneg2
% 0.20/0.46 => ( secondinupair
% 0.20/0.46 => ( setukpairIL
% 0.20/0.46 => ( setukpairIR
% 0.20/0.46 => ( kpairiskpair
% 0.20/0.46 => ( kpairp
% 0.20/0.46 => ( singletonsubset
% 0.20/0.46 => ( singletoninpowerset
% 0.20/0.46 => ( singletoninpowunion
% 0.20/0.46 => ( upairset2E
% 0.20/0.46 => ( upairsubunion
% 0.20/0.46 => ( upairinpowunion
% 0.20/0.46 => ( ubforcartprodlem1
% 0.20/0.46 => ( ubforcartprodlem2
% 0.20/0.46 => ( ubforcartprodlem3
% 0.20/0.46 => ( cartprodpairin
% 0.20/0.46 => ( cartprodmempair1
% 0.20/0.46 => ( cartprodmempair
% 0.20/0.46 => ( setunionE2
% 0.20/0.46 => ( setunionsingleton1
% 0.20/0.46 => ( setunionsingleton2
% 0.20/0.46 => ( setunionsingleton
% 0.20/0.46 => ( singletonprop
% 0.20/0.46 => ( ex1E1
% 0.20/0.46 => ( ex1I
% 0.20/0.46 => ( ex1I2
% 0.20/0.46 => ( singletonsuniq
% 0.20/0.46 => ( setukpairinjL1
% 0.20/0.46 => ( kfstsingleton
% 0.20/0.46 => ( theprop
% 0.20/0.46 => ( kfstpairEq
% 0.20/0.46 => ( cartprodfstin
% 0.20/0.46 => ( setukpairinjL2
% 0.20/0.46 => ( setukpairinjL
% 0.20/0.46 => ( setukpairinjR11
% 0.20/0.46 => ( setukpairinjR12
% 0.20/0.46 => ( setukpairinjR1
% 0.20/0.46 => ( upairequniteq
% 0.20/0.46 => ( setukpairinjR2
% 0.20/0.46 => ( setukpairinjR
% 0.20/0.46 => ( ksndsingleton
% 0.20/0.46 => ( ksndpairEq
% 0.20/0.46 => ! [Xu: $i] :
% 0.20/0.46 ( ( iskpair @ Xu )
% 0.20/0.46 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.20/0.46 = Xu ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 2.38/1.49 ---- Embedded in THF ---
% 2.38/1.49 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.38/1.49 %%% Generated on Tue Feb 24 12:30:07 EST 2026
% 2.38/1.49 %%% using '$$dhol' embedding, version 1.3.0.
% 2.38/1.49 %%% Logic specification used:
% 2.38/1.49 %%% thf(spec, logic, $$dhol).
% 2.38/1.49
% 2.38/1.49 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.UKH9onOzqj/DTF2DTF18632.p
% See solution above
% 2.38/1.50 ------------------------
% 2.62/1.53 ---- Cleaned THF ---
% 2.62/1.53 thf(in_type,type,
% 2.62/1.53 in: $i > $i > $o ).
% 2.62/1.53
% 2.62/1.53 thf(exu_type,type,
% 2.62/1.53 exu: ( $i > $o ) > $o ).
% 2.62/1.53
% 2.62/1.53 thf(exu,definition,
% 2.62/1.53 ( exu
% 2.62/1.53 = ( ^ [Xphi: $i > $o] :
% 2.62/1.53 ? [Xx: $i] :
% 2.62/1.53 ( ( Xphi @ Xx )
% 2.62/1.53 & ! [Xy: $i] :
% 2.62/1.53 ( ( Xphi @ Xy )
% 2.62/1.53 => ( Xx = Xy ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(setextAx_type,type,
% 2.62/1.53 setextAx: $o ).
% 2.62/1.53
% 2.62/1.53 thf(setextAx,definition,
% 2.62/1.53 ( setextAx
% 2.62/1.53 = ( ! [A: $i,B: $i] :
% 2.62/1.53 ( ! [Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ A )
% 2.62/1.53 <=> ( in @ Xx @ B ) )
% 2.62/1.53 => ( A = B ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(emptyset_type,type,
% 2.62/1.53 emptyset: $i ).
% 2.62/1.53
% 2.62/1.53 thf(emptysetAx_type,type,
% 2.62/1.53 emptysetAx: $o ).
% 2.62/1.53
% 2.62/1.53 thf(emptysetAx,definition,
% 2.62/1.53 ( emptysetAx
% 2.62/1.53 = ( ! [Xx: $i] :
% 2.62/1.53 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(setadjoin_type,type,
% 2.62/1.53 setadjoin: $i > $i > $i ).
% 2.62/1.53
% 2.62/1.53 thf(setadjoinAx_type,type,
% 2.62/1.53 setadjoinAx: $o ).
% 2.62/1.53
% 2.62/1.53 thf(setadjoinAx,definition,
% 2.62/1.53 ( setadjoinAx
% 2.62/1.53 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.62/1.53 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.62/1.53 <=> ( ( Xy = Xx )
% 2.62/1.53 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(powerset_type,type,
% 2.62/1.53 powerset: $i > $i ).
% 2.62/1.53
% 2.62/1.53 thf(powersetAx_type,type,
% 2.62/1.53 powersetAx: $o ).
% 2.62/1.53
% 2.62/1.53 thf(powersetAx,definition,
% 2.62/1.53 ( powersetAx
% 2.62/1.53 = ( ! [A: $i,B: $i] :
% 2.62/1.53 ( ( in @ B @ ( powerset @ A ) )
% 2.62/1.53 <=> ! [Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ B )
% 2.62/1.53 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(setunion_type,type,
% 2.62/1.53 setunion: $i > $i ).
% 2.62/1.53
% 2.62/1.53 thf(setunionAx_type,type,
% 2.62/1.53 setunionAx: $o ).
% 2.62/1.53
% 2.62/1.53 thf(setunionAx,definition,
% 2.62/1.53 ( setunionAx
% 2.62/1.53 = ( ! [A: $i,Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ ( setunion @ A ) )
% 2.62/1.53 <=> ? [B: $i] :
% 2.62/1.53 ( ( in @ Xx @ B )
% 2.62/1.53 & ( in @ B @ A ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(omega_type,type,
% 2.62/1.53 omega: $i ).
% 2.62/1.53
% 2.62/1.53 thf(omega0Ax_type,type,
% 2.62/1.53 omega0Ax: $o ).
% 2.62/1.53
% 2.62/1.53 thf(omega0Ax,definition,
% 2.62/1.53 ( omega0Ax
% 2.62/1.53 = ( in @ emptyset @ omega ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(omegaSAx_type,type,
% 2.62/1.53 omegaSAx: $o ).
% 2.62/1.53
% 2.62/1.53 thf(omegaSAx,definition,
% 2.62/1.53 ( omegaSAx
% 2.62/1.53 = ( ! [Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ omega )
% 2.62/1.53 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(omegaIndAx_type,type,
% 2.62/1.53 omegaIndAx: $o ).
% 2.62/1.53
% 2.62/1.53 thf(omegaIndAx,definition,
% 2.62/1.53 ( omegaIndAx
% 2.62/1.53 = ( ! [A: $i] :
% 2.62/1.53 ( ( ( in @ emptyset @ A )
% 2.62/1.53 & ! [Xx: $i] :
% 2.62/1.53 ( ( ( in @ Xx @ omega )
% 2.62/1.53 & ( in @ Xx @ A ) )
% 2.62/1.53 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.62/1.53 => ! [Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ omega )
% 2.62/1.53 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(replAx_type,type,
% 2.62/1.53 replAx: $o ).
% 2.62/1.53
% 2.62/1.53 thf(replAx,definition,
% 2.62/1.53 ( replAx
% 2.62/1.53 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.62/1.53 ( ! [Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ A )
% 2.62/1.53 => ( exu
% 2.62/1.53 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.62/1.53 => ? [B: $i] :
% 2.62/1.53 ! [Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ B )
% 2.62/1.53 <=> ? [Xy: $i] :
% 2.62/1.53 ( ( in @ Xy @ A )
% 2.62/1.53 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(foundationAx_type,type,
% 2.62/1.53 foundationAx: $o ).
% 2.62/1.53
% 2.62/1.53 thf(foundationAx,definition,
% 2.62/1.53 ( foundationAx
% 2.62/1.53 = ( ! [A: $i] :
% 2.62/1.53 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.62/1.53 => ? [B: $i] :
% 2.62/1.53 ( ( in @ B @ A )
% 2.62/1.53 & ~ ? [Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ B )
% 2.62/1.53 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(wellorderingAx_type,type,
% 2.62/1.53 wellorderingAx: $o ).
% 2.62/1.53
% 2.62/1.53 thf(wellorderingAx,definition,
% 2.62/1.53 ( wellorderingAx
% 2.62/1.53 = ( ! [A: $i] :
% 2.62/1.53 ? [B: $i] :
% 2.62/1.53 ( ! [C: $i] :
% 2.62/1.53 ( ( in @ C @ B )
% 2.62/1.53 => ! [Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ C )
% 2.62/1.53 => ( in @ Xx @ A ) ) )
% 2.62/1.53 & ! [Xx: $i,Xy: $i] :
% 2.62/1.53 ( ( ( in @ Xx @ A )
% 2.62/1.53 & ( in @ Xy @ A ) )
% 2.62/1.53 => ( ! [C: $i] :
% 2.62/1.53 ( ( in @ C @ B )
% 2.62/1.53 => ( ( in @ Xx @ C )
% 2.62/1.53 <=> ( in @ Xy @ C ) ) )
% 2.62/1.53 => ( Xx = Xy ) ) )
% 2.62/1.53 & ! [C: $i,D: $i] :
% 2.62/1.53 ( ( ( in @ C @ B )
% 2.62/1.53 & ( in @ D @ B ) )
% 2.62/1.53 => ( ! [Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ C )
% 2.62/1.53 => ( in @ Xx @ D ) )
% 2.62/1.53 | ! [Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ D )
% 2.62/1.53 => ( in @ Xx @ C ) ) ) )
% 2.62/1.53 & ! [C: $i] :
% 2.62/1.53 ( ( ! [Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ C )
% 2.62/1.53 => ( in @ Xx @ A ) )
% 2.62/1.53 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.62/1.53 => ? [D: $i,Xx: $i] :
% 2.62/1.53 ( ( in @ D @ B )
% 2.62/1.53 & ( in @ Xx @ C )
% 2.62/1.53 & ~ ? [Xy: $i] :
% 2.62/1.53 ( ( in @ Xy @ D )
% 2.62/1.53 & ( in @ Xy @ C ) )
% 2.62/1.53 & ! [E: $i] :
% 2.62/1.53 ( ( in @ E @ B )
% 2.62/1.53 => ( ! [Xy: $i] :
% 2.62/1.53 ( ( in @ Xy @ E )
% 2.62/1.53 => ( in @ Xy @ D ) )
% 2.62/1.53 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(descr_type,type,
% 2.62/1.53 descr: ( $i > $o ) > $i ).
% 2.62/1.53
% 2.62/1.53 thf(descrp_type,type,
% 2.62/1.53 descrp: $o ).
% 2.62/1.53
% 2.62/1.53 thf(descrp,definition,
% 2.62/1.53 ( descrp
% 2.62/1.53 = ( ! [Xphi: $i > $o] :
% 2.62/1.53 ( ( exu
% 2.62/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.62/1.53 => ( Xphi
% 2.62/1.53 @ ( descr
% 2.62/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(dsetconstr_type,type,
% 2.62/1.53 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.62/1.53
% 2.62/1.53 thf(dsetconstrI_type,type,
% 2.62/1.53 dsetconstrI: $o ).
% 2.62/1.53
% 2.62/1.53 thf(dsetconstrI,definition,
% 2.62/1.53 ( dsetconstrI
% 2.62/1.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ A )
% 2.62/1.53 => ( ( Xphi @ Xx )
% 2.62/1.53 => ( in @ Xx
% 2.62/1.53 @ ( dsetconstr @ A
% 2.62/1.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(dsetconstrEL_type,type,
% 2.62/1.53 dsetconstrEL: $o ).
% 2.62/1.53
% 2.62/1.53 thf(dsetconstrEL,definition,
% 2.62/1.53 ( dsetconstrEL
% 2.62/1.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.62/1.53 ( ( in @ Xx
% 2.62/1.53 @ ( dsetconstr @ A
% 2.62/1.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.62/1.53 => ( in @ Xx @ A ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(dsetconstrER_type,type,
% 2.62/1.53 dsetconstrER: $o ).
% 2.62/1.53
% 2.62/1.53 thf(dsetconstrER,definition,
% 2.62/1.53 ( dsetconstrER
% 2.62/1.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.62/1.53 ( ( in @ Xx
% 2.62/1.53 @ ( dsetconstr @ A
% 2.62/1.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.62/1.53 => ( Xphi @ Xx ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(exuE1_type,type,
% 2.62/1.53 exuE1: $o ).
% 2.62/1.53
% 2.62/1.53 thf(exuE1,definition,
% 2.62/1.53 ( exuE1
% 2.62/1.53 = ( ! [Xphi: $i > $o] :
% 2.62/1.53 ( ( exu
% 2.62/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.62/1.53 => ? [Xx: $i] :
% 2.62/1.53 ( ( Xphi @ Xx )
% 2.62/1.53 & ! [Xy: $i] :
% 2.62/1.53 ( ( Xphi @ Xy )
% 2.62/1.53 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(prop2set_type,type,
% 2.62/1.53 prop2set: $o > $i ).
% 2.62/1.53
% 2.62/1.53 thf(prop2setE_type,type,
% 2.62/1.53 prop2setE: $o ).
% 2.62/1.53
% 2.62/1.53 thf(prop2setE,definition,
% 2.62/1.53 ( prop2setE
% 2.62/1.53 = ( ! [Xphi: $o,Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.62/1.53 => Xphi ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(emptysetE_type,type,
% 2.62/1.53 emptysetE: $o ).
% 2.62/1.53
% 2.62/1.53 thf(emptysetE,definition,
% 2.62/1.53 ( emptysetE
% 2.62/1.53 = ( ! [Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ emptyset )
% 2.62/1.53 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(emptysetimpfalse_type,type,
% 2.62/1.53 emptysetimpfalse: $o ).
% 2.62/1.53
% 2.62/1.53 thf(emptysetimpfalse,definition,
% 2.62/1.53 ( emptysetimpfalse
% 2.62/1.53 = ( ! [Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ emptyset )
% 2.62/1.53 => $false ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(notinemptyset_type,type,
% 2.62/1.53 notinemptyset: $o ).
% 2.62/1.53
% 2.62/1.53 thf(notinemptyset,definition,
% 2.62/1.53 ( notinemptyset
% 2.62/1.53 = ( ! [Xx: $i] :
% 2.62/1.53 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(exuE3e_type,type,
% 2.62/1.53 exuE3e: $o ).
% 2.62/1.53
% 2.62/1.53 thf(exuE3e,definition,
% 2.62/1.53 ( exuE3e
% 2.62/1.53 = ( ! [Xphi: $i > $o] :
% 2.62/1.53 ( ( exu
% 2.62/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.62/1.53 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(setext_type,type,
% 2.62/1.53 setext: $o ).
% 2.62/1.53
% 2.62/1.53 thf(setext,definition,
% 2.62/1.53 ( setext
% 2.62/1.53 = ( ! [A: $i,B: $i] :
% 2.62/1.53 ( ! [Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ A )
% 2.62/1.53 => ( in @ Xx @ B ) )
% 2.62/1.53 => ( ! [Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ B )
% 2.62/1.53 => ( in @ Xx @ A ) )
% 2.62/1.53 => ( A = B ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(emptyI_type,type,
% 2.62/1.53 emptyI: $o ).
% 2.62/1.53
% 2.62/1.53 thf(emptyI,definition,
% 2.62/1.53 ( emptyI
% 2.62/1.53 = ( ! [A: $i] :
% 2.62/1.53 ( ! [Xx: $i] :
% 2.62/1.53 ~ ( in @ Xx @ A )
% 2.62/1.53 => ( A = emptyset ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(noeltsimpempty_type,type,
% 2.62/1.53 noeltsimpempty: $o ).
% 2.62/1.53
% 2.62/1.53 thf(noeltsimpempty,definition,
% 2.62/1.53 ( noeltsimpempty
% 2.62/1.53 = ( ! [A: $i] :
% 2.62/1.53 ( ! [Xx: $i] :
% 2.62/1.53 ~ ( in @ Xx @ A )
% 2.62/1.53 => ( A = emptyset ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(setbeta_type,type,
% 2.62/1.53 setbeta: $o ).
% 2.62/1.53
% 2.62/1.53 thf(setbeta,definition,
% 2.62/1.53 ( setbeta
% 2.62/1.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ A )
% 2.62/1.53 => ( ( in @ Xx
% 2.62/1.53 @ ( dsetconstr @ A
% 2.62/1.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.62/1.53 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(nonempty_type,type,
% 2.62/1.53 nonempty: $i > $o ).
% 2.62/1.53
% 2.62/1.53 thf(nonempty,definition,
% 2.62/1.53 ( nonempty
% 2.62/1.53 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(nonemptyE1_type,type,
% 2.62/1.53 nonemptyE1: $o ).
% 2.62/1.53
% 2.62/1.53 thf(nonemptyE1,definition,
% 2.62/1.53 ( nonemptyE1
% 2.62/1.53 = ( ! [A: $i] :
% 2.62/1.53 ( ( nonempty @ A )
% 2.62/1.53 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(nonemptyI_type,type,
% 2.62/1.53 nonemptyI: $o ).
% 2.62/1.53
% 2.62/1.53 thf(nonemptyI,definition,
% 2.62/1.53 ( nonemptyI
% 2.62/1.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ A )
% 2.62/1.53 => ( ( Xphi @ Xx )
% 2.62/1.53 => ( nonempty
% 2.62/1.53 @ ( dsetconstr @ A
% 2.62/1.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(nonemptyI1_type,type,
% 2.62/1.53 nonemptyI1: $o ).
% 2.62/1.53
% 2.62/1.53 thf(nonemptyI1,definition,
% 2.62/1.53 ( nonemptyI1
% 2.62/1.53 = ( ! [A: $i] :
% 2.62/1.53 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.62/1.53 => ( nonempty @ A ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(setadjoinIL_type,type,
% 2.62/1.53 setadjoinIL: $o ).
% 2.62/1.53
% 2.62/1.53 thf(setadjoinIL,definition,
% 2.62/1.53 ( setadjoinIL
% 2.62/1.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(emptyinunitempty_type,type,
% 2.62/1.53 emptyinunitempty: $o ).
% 2.62/1.53
% 2.62/1.53 thf(emptyinunitempty,definition,
% 2.62/1.53 ( emptyinunitempty
% 2.62/1.53 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(setadjoinIR_type,type,
% 2.62/1.53 setadjoinIR: $o ).
% 2.62/1.53
% 2.62/1.53 thf(setadjoinIR,definition,
% 2.62/1.53 ( setadjoinIR
% 2.62/1.53 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.62/1.53 ( ( in @ Xy @ A )
% 2.62/1.53 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(setadjoinE_type,type,
% 2.62/1.53 setadjoinE: $o ).
% 2.62/1.53
% 2.62/1.53 thf(setadjoinE,definition,
% 2.62/1.53 ( setadjoinE
% 2.62/1.53 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.62/1.53 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.62/1.53 => ! [Xphi: $o] :
% 2.62/1.53 ( ( ( Xy = Xx )
% 2.62/1.53 => Xphi )
% 2.62/1.53 => ( ( ( in @ Xy @ A )
% 2.62/1.53 => Xphi )
% 2.62/1.53 => Xphi ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(setadjoinOr_type,type,
% 2.62/1.53 setadjoinOr: $o ).
% 2.62/1.53
% 2.62/1.53 thf(setadjoinOr,definition,
% 2.62/1.53 ( setadjoinOr
% 2.62/1.53 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.62/1.53 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.62/1.53 => ( ( Xy = Xx )
% 2.62/1.53 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(setoftrueEq_type,type,
% 2.62/1.53 setoftrueEq: $o ).
% 2.62/1.53
% 2.62/1.53 thf(setoftrueEq,definition,
% 2.62/1.53 ( setoftrueEq
% 2.62/1.53 = ( ! [A: $i] :
% 2.62/1.53 ( ( dsetconstr @ A
% 2.62/1.53 @ ^ [Xx: $i] : $true )
% 2.62/1.53 = A ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(powersetI_type,type,
% 2.62/1.53 powersetI: $o ).
% 2.62/1.53
% 2.62/1.53 thf(powersetI,definition,
% 2.62/1.53 ( powersetI
% 2.62/1.53 = ( ! [A: $i,B: $i] :
% 2.62/1.53 ( ! [Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ B )
% 2.62/1.53 => ( in @ Xx @ A ) )
% 2.62/1.53 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(emptyinPowerset_type,type,
% 2.62/1.53 emptyinPowerset: $o ).
% 2.62/1.53
% 2.62/1.53 thf(emptyinPowerset,definition,
% 2.62/1.53 ( emptyinPowerset
% 2.62/1.53 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(emptyInPowerset_type,type,
% 2.62/1.53 emptyInPowerset: $o ).
% 2.62/1.53
% 2.62/1.53 thf(emptyInPowerset,definition,
% 2.62/1.53 ( emptyInPowerset
% 2.62/1.53 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(powersetE_type,type,
% 2.62/1.53 powersetE: $o ).
% 2.62/1.53
% 2.62/1.53 thf(powersetE,definition,
% 2.62/1.53 ( powersetE
% 2.62/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.62/1.53 ( ( in @ B @ ( powerset @ A ) )
% 2.62/1.53 => ( ( in @ Xx @ B )
% 2.62/1.53 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(setunionI_type,type,
% 2.62/1.53 setunionI: $o ).
% 2.62/1.53
% 2.62/1.53 thf(setunionI,definition,
% 2.62/1.53 ( setunionI
% 2.62/1.53 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.62/1.53 ( ( in @ Xx @ B )
% 2.62/1.53 => ( ( in @ B @ A )
% 2.62/1.53 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(setunionE_type,type,
% 2.62/1.53 setunionE: $o ).
% 2.62/1.53
% 2.62/1.53 thf(setunionE,definition,
% 2.62/1.53 ( setunionE
% 2.62/1.53 = ( ! [A: $i,Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ ( setunion @ A ) )
% 2.62/1.53 => ! [Xphi: $o] :
% 2.62/1.53 ( ! [B: $i] :
% 2.62/1.53 ( ( in @ Xx @ B )
% 2.62/1.53 => ( ( in @ B @ A )
% 2.62/1.53 => Xphi ) )
% 2.62/1.53 => Xphi ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(subPowSU_type,type,
% 2.62/1.53 subPowSU: $o ).
% 2.62/1.53
% 2.62/1.53 thf(subPowSU,definition,
% 2.62/1.53 ( subPowSU
% 2.62/1.53 = ( ! [A: $i,Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ A )
% 2.62/1.53 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(exuE2_type,type,
% 2.62/1.53 exuE2: $o ).
% 2.62/1.53
% 2.62/1.53 thf(exuE2,definition,
% 2.62/1.53 ( exuE2
% 2.62/1.53 = ( ! [Xphi: $i > $o] :
% 2.62/1.53 ( ( exu
% 2.62/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.62/1.53 => ? [Xx: $i] :
% 2.62/1.53 ! [Xy: $i] :
% 2.62/1.53 ( ( Xphi @ Xy )
% 2.62/1.53 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(nonemptyImpWitness_type,type,
% 2.62/1.53 nonemptyImpWitness: $o ).
% 2.62/1.53
% 2.62/1.53 thf(nonemptyImpWitness,definition,
% 2.62/1.53 ( nonemptyImpWitness
% 2.62/1.53 = ( ! [A: $i] :
% 2.62/1.53 ( ( nonempty @ A )
% 2.62/1.53 => ? [Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ A )
% 2.62/1.53 & $true ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(uniqinunit_type,type,
% 2.62/1.53 uniqinunit: $o ).
% 2.62/1.53
% 2.62/1.53 thf(uniqinunit,definition,
% 2.62/1.53 ( uniqinunit
% 2.62/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.62/1.53 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.62/1.53 => ( Xx = Xy ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(notinsingleton_type,type,
% 2.62/1.53 notinsingleton: $o ).
% 2.62/1.53
% 2.62/1.53 thf(notinsingleton,definition,
% 2.62/1.53 ( notinsingleton
% 2.62/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.62/1.53 ( ( Xx != Xy )
% 2.62/1.53 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(eqinunit_type,type,
% 2.62/1.53 eqinunit: $o ).
% 2.62/1.53
% 2.62/1.53 thf(eqinunit,definition,
% 2.62/1.53 ( eqinunit
% 2.62/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.62/1.53 ( ( Xx = Xy )
% 2.62/1.53 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(singletonsswitch_type,type,
% 2.62/1.53 singletonsswitch: $o ).
% 2.62/1.53
% 2.62/1.53 thf(singletonsswitch,definition,
% 2.62/1.53 ( singletonsswitch
% 2.62/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.62/1.53 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.62/1.53 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(upairsetE_type,type,
% 2.62/1.53 upairsetE: $o ).
% 2.62/1.53
% 2.62/1.53 thf(upairsetE,definition,
% 2.62/1.53 ( upairsetE
% 2.62/1.53 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.62/1.53 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.62/1.53 => ( ( Xz = Xx )
% 2.62/1.53 | ( Xz = Xy ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(upairsetIL_type,type,
% 2.62/1.53 upairsetIL: $o ).
% 2.62/1.53
% 2.62/1.53 thf(upairsetIL,definition,
% 2.62/1.53 ( upairsetIL
% 2.62/1.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(upairsetIR_type,type,
% 2.62/1.53 upairsetIR: $o ).
% 2.62/1.53
% 2.62/1.53 thf(upairsetIR,definition,
% 2.62/1.53 ( upairsetIR
% 2.62/1.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(emptyE1_type,type,
% 2.62/1.53 emptyE1: $o ).
% 2.62/1.53
% 2.62/1.53 thf(emptyE1,definition,
% 2.62/1.53 ( emptyE1
% 2.62/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.62/1.53 ( ? [Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ A )
% 2.62/1.53 & ( Xphi @ Xx ) )
% 2.62/1.53 => ( ( ( dsetconstr @ A
% 2.62/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.62/1.53 = emptyset )
% 2.62/1.53 => $false ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(vacuousDall_type,type,
% 2.62/1.53 vacuousDall: $o ).
% 2.62/1.53
% 2.62/1.53 thf(vacuousDall,definition,
% 2.62/1.53 ( vacuousDall
% 2.62/1.53 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ emptyset )
% 2.62/1.53 => ( Xphi @ Xx ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(quantDeMorgan1_type,type,
% 2.62/1.53 quantDeMorgan1: $o ).
% 2.62/1.53
% 2.62/1.53 thf(quantDeMorgan1,definition,
% 2.62/1.53 ( quantDeMorgan1
% 2.62/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.62/1.53 ( ~ ! [Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ A )
% 2.62/1.53 => ( Xphi @ Xx ) )
% 2.62/1.53 => ? [Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ A )
% 2.62/1.53 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(quantDeMorgan2_type,type,
% 2.62/1.53 quantDeMorgan2: $o ).
% 2.62/1.53
% 2.62/1.53 thf(quantDeMorgan2,definition,
% 2.62/1.53 ( quantDeMorgan2
% 2.62/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.62/1.53 ( ! [Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ A )
% 2.62/1.53 => ~ ( Xphi @ Xx ) )
% 2.62/1.53 => ~ ? [Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ A )
% 2.62/1.53 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(quantDeMorgan3_type,type,
% 2.62/1.53 quantDeMorgan3: $o ).
% 2.62/1.53
% 2.62/1.53 thf(quantDeMorgan3,definition,
% 2.62/1.53 ( quantDeMorgan3
% 2.62/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.62/1.53 ( ~ ? [Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ A )
% 2.62/1.53 & ( Xphi @ Xx ) )
% 2.62/1.53 => ! [Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ A )
% 2.62/1.53 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(quantDeMorgan4_type,type,
% 2.62/1.53 quantDeMorgan4: $o ).
% 2.62/1.53
% 2.62/1.53 thf(quantDeMorgan4,definition,
% 2.62/1.53 ( quantDeMorgan4
% 2.62/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.62/1.53 ( ? [Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ A )
% 2.62/1.53 & ~ ( Xphi @ Xx ) )
% 2.62/1.53 => ~ ! [Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ A )
% 2.62/1.53 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(prop2setI_type,type,
% 2.62/1.53 prop2setI: $o ).
% 2.62/1.53
% 2.62/1.53 thf(prop2setI,definition,
% 2.62/1.53 ( prop2setI
% 2.62/1.53 = ( ! [Xphi: $o] :
% 2.62/1.53 ( Xphi
% 2.62/1.53 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(set2prop_type,type,
% 2.62/1.53 set2prop: $i > $o ).
% 2.62/1.53
% 2.62/1.53 thf(prop2set2propI_type,type,
% 2.62/1.53 prop2set2propI: $o ).
% 2.62/1.53
% 2.62/1.53 thf(prop2set2propI,definition,
% 2.62/1.53 ( prop2set2propI
% 2.62/1.53 = ( ! [Xphi: $o] :
% 2.62/1.53 ( Xphi
% 2.62/1.53 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(notdexE_type,type,
% 2.62/1.53 notdexE: $o ).
% 2.62/1.53
% 2.62/1.53 thf(notdexE,definition,
% 2.62/1.53 ( notdexE
% 2.62/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.62/1.53 ( ~ ? [Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ A )
% 2.62/1.53 & ( Xphi @ Xx ) )
% 2.62/1.53 => ! [Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ A )
% 2.62/1.53 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(notdallE_type,type,
% 2.62/1.53 notdallE: $o ).
% 2.62/1.53
% 2.62/1.53 thf(notdallE,definition,
% 2.62/1.53 ( notdallE
% 2.62/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.62/1.53 ( ~ ! [Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ A )
% 2.62/1.53 => ( Xphi @ Xx ) )
% 2.62/1.53 => ? [Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ A )
% 2.62/1.53 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(exuI1_type,type,
% 2.62/1.53 exuI1: $o ).
% 2.62/1.53
% 2.62/1.53 thf(exuI1,definition,
% 2.62/1.53 ( exuI1
% 2.62/1.53 = ( ! [Xphi: $i > $o] :
% 2.62/1.53 ( ? [Xx: $i] :
% 2.62/1.53 ( ( Xphi @ Xx )
% 2.62/1.53 & ! [Xy: $i] :
% 2.62/1.53 ( ( Xphi @ Xy )
% 2.62/1.53 => ( Xx = Xy ) ) )
% 2.62/1.53 => ( exu
% 2.62/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(exuI3_type,type,
% 2.62/1.53 exuI3: $o ).
% 2.62/1.53
% 2.62/1.53 thf(exuI3,definition,
% 2.62/1.53 ( exuI3
% 2.62/1.53 = ( ! [Xphi: $i > $o] :
% 2.62/1.53 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.62/1.53 => ( ! [Xx: $i,Xy: $i] :
% 2.62/1.53 ( ( Xphi @ Xx )
% 2.62/1.53 => ( ( Xphi @ Xy )
% 2.62/1.53 => ( Xx = Xy ) ) )
% 2.62/1.53 => ( exu
% 2.62/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(exuI2_type,type,
% 2.62/1.53 exuI2: $o ).
% 2.62/1.53
% 2.62/1.53 thf(exuI2,definition,
% 2.62/1.53 ( exuI2
% 2.62/1.53 = ( ! [Xphi: $i > $o] :
% 2.62/1.53 ( ? [Xx: $i] :
% 2.62/1.53 ! [Xy: $i] :
% 2.62/1.53 ( ( Xphi @ Xy )
% 2.62/1.53 <=> ( Xy = Xx ) )
% 2.62/1.53 => ( exu
% 2.62/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(inCongP_type,type,
% 2.62/1.53 inCongP: $o ).
% 2.62/1.53
% 2.62/1.53 thf(inCongP,definition,
% 2.62/1.53 ( inCongP
% 2.62/1.53 = ( ! [A: $i,B: $i] :
% 2.62/1.53 ( ( A = B )
% 2.62/1.53 => ! [Xx: $i,Xy: $i] :
% 2.62/1.53 ( ( Xx = Xy )
% 2.62/1.53 => ( ( in @ Xx @ A )
% 2.62/1.53 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(in__Cong_type,type,
% 2.62/1.53 in__Cong: $o ).
% 2.62/1.53
% 2.62/1.53 thf(in__Cong,definition,
% 2.62/1.53 ( in__Cong
% 2.62/1.53 = ( ! [A: $i,B: $i] :
% 2.62/1.53 ( ( A = B )
% 2.62/1.53 => ! [Xx: $i,Xy: $i] :
% 2.62/1.53 ( ( Xx = Xy )
% 2.62/1.53 => ( ( in @ Xx @ A )
% 2.62/1.53 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(exuE3u_type,type,
% 2.62/1.53 exuE3u: $o ).
% 2.62/1.53
% 2.62/1.53 thf(exuE3u,definition,
% 2.62/1.53 ( exuE3u
% 2.62/1.53 = ( ! [Xphi: $i > $o] :
% 2.62/1.53 ( ( exu
% 2.62/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.62/1.53 => ! [Xx: $i,Xy: $i] :
% 2.62/1.53 ( ( Xphi @ Xx )
% 2.62/1.53 => ( ( Xphi @ Xy )
% 2.62/1.53 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(exu__Cong_type,type,
% 2.62/1.53 exu__Cong: $o ).
% 2.62/1.53
% 2.62/1.53 thf(exu__Cong,definition,
% 2.62/1.53 ( exu__Cong
% 2.62/1.53 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.62/1.53 ( ! [Xx: $i,Xy: $i] :
% 2.62/1.53 ( ( Xx = Xy )
% 2.62/1.53 => ( ( Xphi @ Xx )
% 2.62/1.53 <=> ( Xpsi @ Xy ) ) )
% 2.62/1.53 => ( ( exu
% 2.62/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.62/1.53 <=> ( exu
% 2.62/1.53 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(emptyset__Cong_type,type,
% 2.62/1.53 emptyset__Cong: $o ).
% 2.62/1.53
% 2.62/1.53 thf(emptyset__Cong,definition,
% 2.62/1.53 ( emptyset__Cong
% 2.62/1.53 = ( emptyset = emptyset ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(setadjoin__Cong_type,type,
% 2.62/1.53 setadjoin__Cong: $o ).
% 2.62/1.53
% 2.62/1.53 thf(setadjoin__Cong,definition,
% 2.62/1.53 ( setadjoin__Cong
% 2.62/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.62/1.53 ( ( Xx = Xy )
% 2.62/1.53 => ! [Xz: $i,Xu: $i] :
% 2.62/1.53 ( ( Xz = Xu )
% 2.62/1.53 => ( ( setadjoin @ Xx @ Xz )
% 2.62/1.53 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(powerset__Cong_type,type,
% 2.62/1.53 powerset__Cong: $o ).
% 2.62/1.53
% 2.62/1.53 thf(powerset__Cong,definition,
% 2.62/1.53 ( powerset__Cong
% 2.62/1.53 = ( ! [A: $i,B: $i] :
% 2.62/1.53 ( ( A = B )
% 2.62/1.53 => ( ( powerset @ A )
% 2.62/1.53 = ( powerset @ B ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(setunion__Cong_type,type,
% 2.62/1.53 setunion__Cong: $o ).
% 2.62/1.53
% 2.62/1.53 thf(setunion__Cong,definition,
% 2.62/1.53 ( setunion__Cong
% 2.62/1.53 = ( ! [A: $i,B: $i] :
% 2.62/1.53 ( ( A = B )
% 2.62/1.53 => ( ( setunion @ A )
% 2.62/1.53 = ( setunion @ B ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(omega__Cong_type,type,
% 2.62/1.53 omega__Cong: $o ).
% 2.62/1.53
% 2.62/1.53 thf(omega__Cong,definition,
% 2.62/1.53 ( omega__Cong
% 2.62/1.53 = ( omega = omega ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(exuEu_type,type,
% 2.62/1.53 exuEu: $o ).
% 2.62/1.53
% 2.62/1.53 thf(exuEu,definition,
% 2.62/1.53 ( exuEu
% 2.62/1.53 = ( ! [Xphi: $i > $o] :
% 2.62/1.53 ( ( exu
% 2.62/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.62/1.53 => ! [Xx: $i,Xy: $i] :
% 2.62/1.53 ( ( Xphi @ Xx )
% 2.62/1.53 => ( ( Xphi @ Xy )
% 2.62/1.53 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(descr__Cong_type,type,
% 2.62/1.53 descr__Cong: $o ).
% 2.62/1.53
% 2.62/1.53 thf(descr__Cong,definition,
% 2.62/1.53 ( descr__Cong
% 2.62/1.53 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.62/1.53 ( ! [Xx: $i,Xy: $i] :
% 2.62/1.53 ( ( Xx = Xy )
% 2.62/1.53 => ( ( Xphi @ Xx )
% 2.62/1.53 <=> ( Xpsi @ Xy ) ) )
% 2.62/1.53 => ( ( exu
% 2.62/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.62/1.53 => ( ( exu
% 2.62/1.53 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.62/1.53 => ( ( descr
% 2.62/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.62/1.53 = ( descr
% 2.62/1.53 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(dsetconstr__Cong_type,type,
% 2.62/1.53 dsetconstr__Cong: $o ).
% 2.62/1.53
% 2.62/1.53 thf(dsetconstr__Cong,definition,
% 2.62/1.53 ( dsetconstr__Cong
% 2.62/1.53 = ( ! [A: $i,B: $i] :
% 2.62/1.53 ( ( A = B )
% 2.62/1.53 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.62/1.53 ( ! [Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ A )
% 2.62/1.53 => ! [Xy: $i] :
% 2.62/1.53 ( ( in @ Xy @ B )
% 2.62/1.53 => ( ( Xx = Xy )
% 2.62/1.53 => ( ( Xphi @ Xx )
% 2.62/1.53 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.62/1.53 => ( ( dsetconstr @ A
% 2.62/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.62/1.53 = ( dsetconstr @ B
% 2.62/1.53 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(subset_type,type,
% 2.62/1.53 subset: $i > $i > $o ).
% 2.62/1.53
% 2.62/1.53 thf(disjoint_type,type,
% 2.62/1.53 disjoint: $i > $i > $o ).
% 2.62/1.53
% 2.62/1.53 thf(setsmeet_type,type,
% 2.62/1.53 setsmeet: $i > $i > $o ).
% 2.62/1.53
% 2.62/1.53 thf(subsetI1_type,type,
% 2.62/1.53 subsetI1: $o ).
% 2.62/1.53
% 2.62/1.53 thf(subsetI1,definition,
% 2.62/1.53 ( subsetI1
% 2.62/1.53 = ( ! [A: $i,B: $i] :
% 2.62/1.53 ( ! [Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ A )
% 2.62/1.53 => ( in @ Xx @ B ) )
% 2.62/1.53 => ( subset @ A @ B ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(eqimpsubset2_type,type,
% 2.62/1.53 eqimpsubset2: $o ).
% 2.62/1.53
% 2.62/1.53 thf(eqimpsubset2,definition,
% 2.62/1.53 ( eqimpsubset2
% 2.62/1.53 = ( ! [A: $i,B: $i] :
% 2.62/1.53 ( ( A = B )
% 2.62/1.53 => ( subset @ B @ A ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(eqimpsubset1_type,type,
% 2.62/1.53 eqimpsubset1: $o ).
% 2.62/1.53
% 2.62/1.53 thf(eqimpsubset1,definition,
% 2.62/1.53 ( eqimpsubset1
% 2.62/1.53 = ( ! [A: $i,B: $i] :
% 2.62/1.53 ( ( A = B )
% 2.62/1.53 => ( subset @ A @ B ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(subsetI2_type,type,
% 2.62/1.53 subsetI2: $o ).
% 2.62/1.53
% 2.62/1.53 thf(subsetI2,definition,
% 2.62/1.53 ( subsetI2
% 2.62/1.53 = ( ! [A: $i,B: $i] :
% 2.62/1.53 ( ! [Xx: $i] :
% 2.62/1.53 ( ( in @ Xx @ A )
% 2.62/1.53 => ( in @ Xx @ B ) )
% 2.62/1.53 => ( subset @ A @ B ) ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(emptysetsubset_type,type,
% 2.62/1.53 emptysetsubset: $o ).
% 2.62/1.53
% 2.62/1.53 thf(emptysetsubset,definition,
% 2.62/1.53 ( emptysetsubset
% 2.62/1.53 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.62/1.53
% 2.62/1.53 thf(subsetE_type,type,
% 2.62/1.53 subsetE: $o ).
% 2.62/1.53
% 2.62/1.53 thf(subsetE,definition,
% 2.62/1.53 ( subsetE
% 2.62/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.62/1.53 ( ( subset @ A @ B )
% 2.62/1.53 => ( ( in @ Xx @ A )
% 2.62/1.54 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(subsetE2_type,type,
% 2.62/1.54 subsetE2: $o ).
% 2.62/1.54
% 2.62/1.54 thf(subsetE2,definition,
% 2.62/1.54 ( subsetE2
% 2.62/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.62/1.54 ( ( subset @ A @ B )
% 2.62/1.54 => ( ~ ( in @ Xx @ B )
% 2.62/1.54 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(notsubsetI_type,type,
% 2.62/1.54 notsubsetI: $o ).
% 2.62/1.54
% 2.62/1.54 thf(notsubsetI,definition,
% 2.62/1.54 ( notsubsetI
% 2.62/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ A )
% 2.62/1.54 => ( ~ ( in @ Xx @ B )
% 2.62/1.54 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(notequalI1_type,type,
% 2.62/1.54 notequalI1: $o ).
% 2.62/1.54
% 2.62/1.54 thf(notequalI1,definition,
% 2.62/1.54 ( notequalI1
% 2.62/1.54 = ( ! [A: $i,B: $i] :
% 2.62/1.54 ( ~ ( subset @ A @ B )
% 2.62/1.54 => ( A != B ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(notequalI2_type,type,
% 2.62/1.54 notequalI2: $o ).
% 2.62/1.54
% 2.62/1.54 thf(notequalI2,definition,
% 2.62/1.54 ( notequalI2
% 2.62/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ A )
% 2.62/1.54 => ( ~ ( in @ Xx @ B )
% 2.62/1.54 => ( A != B ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(subsetRefl_type,type,
% 2.62/1.54 subsetRefl: $o ).
% 2.62/1.54
% 2.62/1.54 thf(subsetRefl,definition,
% 2.62/1.54 ( subsetRefl
% 2.62/1.54 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(subsetTrans_type,type,
% 2.62/1.54 subsetTrans: $o ).
% 2.62/1.54
% 2.62/1.54 thf(subsetTrans,definition,
% 2.62/1.54 ( subsetTrans
% 2.62/1.54 = ( ! [A: $i,B: $i,C: $i] :
% 2.62/1.54 ( ( subset @ A @ B )
% 2.62/1.54 => ( ( subset @ B @ C )
% 2.62/1.54 => ( subset @ A @ C ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(setadjoinSub_type,type,
% 2.62/1.54 setadjoinSub: $o ).
% 2.62/1.54
% 2.62/1.54 thf(setadjoinSub,definition,
% 2.62/1.54 ( setadjoinSub
% 2.62/1.54 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(setadjoinSub2_type,type,
% 2.62/1.54 setadjoinSub2: $o ).
% 2.62/1.54
% 2.62/1.54 thf(setadjoinSub2,definition,
% 2.62/1.54 ( setadjoinSub2
% 2.62/1.54 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.62/1.54 ( ( subset @ A @ B )
% 2.62/1.54 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(subset2powerset_type,type,
% 2.62/1.54 subset2powerset: $o ).
% 2.62/1.54
% 2.62/1.54 thf(subset2powerset,definition,
% 2.62/1.54 ( subset2powerset
% 2.62/1.54 = ( ! [A: $i,B: $i] :
% 2.62/1.54 ( ( subset @ A @ B )
% 2.62/1.54 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(setextsub_type,type,
% 2.62/1.54 setextsub: $o ).
% 2.62/1.54
% 2.62/1.54 thf(setextsub,definition,
% 2.62/1.54 ( setextsub
% 2.62/1.54 = ( ! [A: $i,B: $i] :
% 2.62/1.54 ( ( subset @ A @ B )
% 2.62/1.54 => ( ( subset @ B @ A )
% 2.62/1.54 => ( A = B ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(subsetemptysetimpeq_type,type,
% 2.62/1.54 subsetemptysetimpeq: $o ).
% 2.62/1.54
% 2.62/1.54 thf(subsetemptysetimpeq,definition,
% 2.62/1.54 ( subsetemptysetimpeq
% 2.62/1.54 = ( ! [A: $i] :
% 2.62/1.54 ( ( subset @ A @ emptyset )
% 2.62/1.54 => ( A = emptyset ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(powersetI1_type,type,
% 2.62/1.54 powersetI1: $o ).
% 2.62/1.54
% 2.62/1.54 thf(powersetI1,definition,
% 2.62/1.54 ( powersetI1
% 2.62/1.54 = ( ! [A: $i,B: $i] :
% 2.62/1.54 ( ( subset @ B @ A )
% 2.62/1.54 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(powersetE1_type,type,
% 2.62/1.54 powersetE1: $o ).
% 2.62/1.54
% 2.62/1.54 thf(powersetE1,definition,
% 2.62/1.54 ( powersetE1
% 2.62/1.54 = ( ! [A: $i,B: $i] :
% 2.62/1.54 ( ( in @ B @ ( powerset @ A ) )
% 2.62/1.54 => ( subset @ B @ A ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(inPowerset_type,type,
% 2.62/1.54 inPowerset: $o ).
% 2.62/1.54
% 2.62/1.54 thf(inPowerset,definition,
% 2.62/1.54 ( inPowerset
% 2.62/1.54 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(powersetsubset_type,type,
% 2.62/1.54 powersetsubset: $o ).
% 2.62/1.54
% 2.62/1.54 thf(powersetsubset,definition,
% 2.62/1.54 ( powersetsubset
% 2.62/1.54 = ( ! [A: $i,B: $i] :
% 2.62/1.54 ( ( subset @ A @ B )
% 2.62/1.54 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(sepInPowerset_type,type,
% 2.62/1.54 sepInPowerset: $o ).
% 2.62/1.54
% 2.62/1.54 thf(sepInPowerset,definition,
% 2.62/1.54 ( sepInPowerset
% 2.62/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 2.62/1.54 ( in
% 2.62/1.54 @ ( dsetconstr @ A
% 2.62/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.62/1.54 @ ( powerset @ A ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(sepSubset_type,type,
% 2.62/1.54 sepSubset: $o ).
% 2.62/1.54
% 2.62/1.54 thf(sepSubset,definition,
% 2.62/1.54 ( sepSubset
% 2.62/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 2.62/1.54 ( subset
% 2.62/1.54 @ ( dsetconstr @ A
% 2.62/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.62/1.54 @ A ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(binunion_type,type,
% 2.62/1.54 binunion: $i > $i > $i ).
% 2.62/1.54
% 2.62/1.54 thf(binunionIL_type,type,
% 2.62/1.54 binunionIL: $o ).
% 2.62/1.54
% 2.62/1.54 thf(binunionIL,definition,
% 2.62/1.54 ( binunionIL
% 2.62/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ A )
% 2.62/1.54 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(upairset2IR_type,type,
% 2.62/1.54 upairset2IR: $o ).
% 2.62/1.54
% 2.62/1.54 thf(upairset2IR,definition,
% 2.62/1.54 ( upairset2IR
% 2.62/1.54 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(binunionIR_type,type,
% 2.62/1.54 binunionIR: $o ).
% 2.62/1.54
% 2.62/1.54 thf(binunionIR,definition,
% 2.62/1.54 ( binunionIR
% 2.62/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ B )
% 2.62/1.54 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(binunionEcases_type,type,
% 2.62/1.54 binunionEcases: $o ).
% 2.62/1.54
% 2.62/1.54 thf(binunionEcases,definition,
% 2.62/1.54 ( binunionEcases
% 2.62/1.54 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.62/1.54 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.62/1.54 => ( ( ( in @ Xx @ A )
% 2.62/1.54 => Xphi )
% 2.62/1.54 => ( ( ( in @ Xx @ B )
% 2.62/1.54 => Xphi )
% 2.62/1.54 => Xphi ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(binunionE_type,type,
% 2.62/1.54 binunionE: $o ).
% 2.62/1.54
% 2.62/1.54 thf(binunionE,definition,
% 2.62/1.54 ( binunionE
% 2.62/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.62/1.54 => ( ( in @ Xx @ A )
% 2.62/1.54 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(binunionLsub_type,type,
% 2.62/1.54 binunionLsub: $o ).
% 2.62/1.54
% 2.62/1.54 thf(binunionLsub,definition,
% 2.62/1.54 ( binunionLsub
% 2.62/1.54 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(binunionRsub_type,type,
% 2.62/1.54 binunionRsub: $o ).
% 2.62/1.54
% 2.62/1.54 thf(binunionRsub,definition,
% 2.62/1.54 ( binunionRsub
% 2.62/1.54 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(binintersect_type,type,
% 2.62/1.54 binintersect: $i > $i > $i ).
% 2.62/1.54
% 2.62/1.54 thf(binintersectI_type,type,
% 2.62/1.54 binintersectI: $o ).
% 2.62/1.54
% 2.62/1.54 thf(binintersectI,definition,
% 2.62/1.54 ( binintersectI
% 2.62/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ A )
% 2.62/1.54 => ( ( in @ Xx @ B )
% 2.62/1.54 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(binintersectSubset5_type,type,
% 2.62/1.54 binintersectSubset5: $o ).
% 2.62/1.54
% 2.62/1.54 thf(binintersectSubset5,definition,
% 2.62/1.54 ( binintersectSubset5
% 2.62/1.54 = ( ! [A: $i,B: $i,C: $i] :
% 2.62/1.54 ( ( subset @ C @ A )
% 2.62/1.54 => ( ( subset @ C @ B )
% 2.62/1.54 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(binintersectEL_type,type,
% 2.62/1.54 binintersectEL: $o ).
% 2.62/1.54
% 2.62/1.54 thf(binintersectEL,definition,
% 2.62/1.54 ( binintersectEL
% 2.62/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.62/1.54 => ( in @ Xx @ A ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(binintersectLsub_type,type,
% 2.62/1.54 binintersectLsub: $o ).
% 2.62/1.54
% 2.62/1.54 thf(binintersectLsub,definition,
% 2.62/1.54 ( binintersectLsub
% 2.62/1.54 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(binintersectSubset2_type,type,
% 2.62/1.54 binintersectSubset2: $o ).
% 2.62/1.54
% 2.62/1.54 thf(binintersectSubset2,definition,
% 2.62/1.54 ( binintersectSubset2
% 2.62/1.54 = ( ! [A: $i,B: $i] :
% 2.62/1.54 ( ( subset @ A @ B )
% 2.62/1.54 => ( ( binintersect @ A @ B )
% 2.62/1.54 = A ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(binintersectSubset3_type,type,
% 2.62/1.54 binintersectSubset3: $o ).
% 2.62/1.54
% 2.62/1.54 thf(binintersectSubset3,definition,
% 2.62/1.54 ( binintersectSubset3
% 2.62/1.54 = ( ! [A: $i,B: $i] :
% 2.62/1.54 ( ( ( binintersect @ A @ B )
% 2.62/1.54 = B )
% 2.62/1.54 => ( subset @ B @ A ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(binintersectER_type,type,
% 2.62/1.54 binintersectER: $o ).
% 2.62/1.54
% 2.62/1.54 thf(binintersectER,definition,
% 2.62/1.54 ( binintersectER
% 2.62/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.62/1.54 => ( in @ Xx @ B ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(disjointsetsI1_type,type,
% 2.62/1.54 disjointsetsI1: $o ).
% 2.62/1.54
% 2.62/1.54 thf(disjointsetsI1,definition,
% 2.62/1.54 ( disjointsetsI1
% 2.62/1.54 = ( ! [A: $i,B: $i] :
% 2.62/1.54 ( ~ ? [Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ A )
% 2.62/1.54 & ( in @ Xx @ B ) )
% 2.62/1.54 => ( ( binintersect @ A @ B )
% 2.62/1.54 = emptyset ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(binintersectRsub_type,type,
% 2.62/1.54 binintersectRsub: $o ).
% 2.62/1.54
% 2.62/1.54 thf(binintersectRsub,definition,
% 2.62/1.54 ( binintersectRsub
% 2.62/1.54 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(binintersectSubset4_type,type,
% 2.62/1.54 binintersectSubset4: $o ).
% 2.62/1.54
% 2.62/1.54 thf(binintersectSubset4,definition,
% 2.62/1.54 ( binintersectSubset4
% 2.62/1.54 = ( ! [A: $i,B: $i] :
% 2.62/1.54 ( ( subset @ B @ A )
% 2.62/1.54 => ( ( binintersect @ A @ B )
% 2.62/1.54 = B ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(binintersectSubset1_type,type,
% 2.62/1.54 binintersectSubset1: $o ).
% 2.62/1.54
% 2.62/1.54 thf(binintersectSubset1,definition,
% 2.62/1.54 ( binintersectSubset1
% 2.62/1.54 = ( ! [A: $i,B: $i] :
% 2.62/1.54 ( ( ( binintersect @ A @ B )
% 2.62/1.54 = A )
% 2.62/1.54 => ( subset @ A @ B ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(bs114d_type,type,
% 2.62/1.54 bs114d: $o ).
% 2.62/1.54
% 2.62/1.54 thf(bs114d,definition,
% 2.62/1.54 ( bs114d
% 2.62/1.54 = ( ! [A: $i,B: $i,C: $i] :
% 2.62/1.54 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.62/1.54 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(regular_type,type,
% 2.62/1.54 regular: $i > $o ).
% 2.62/1.54
% 2.62/1.54 thf(setminus_type,type,
% 2.62/1.54 setminus: $i > $i > $i ).
% 2.62/1.54
% 2.62/1.54 thf(setminusI_type,type,
% 2.62/1.54 setminusI: $o ).
% 2.62/1.54
% 2.62/1.54 thf(setminusI,definition,
% 2.62/1.54 ( setminusI
% 2.62/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ A )
% 2.62/1.54 => ( ~ ( in @ Xx @ B )
% 2.62/1.54 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(setminusEL_type,type,
% 2.62/1.54 setminusEL: $o ).
% 2.62/1.54
% 2.62/1.54 thf(setminusEL,definition,
% 2.62/1.54 ( setminusEL
% 2.62/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.62/1.54 => ( in @ Xx @ A ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(setminusER_type,type,
% 2.62/1.54 setminusER: $o ).
% 2.62/1.54
% 2.62/1.54 thf(setminusER,definition,
% 2.62/1.54 ( setminusER
% 2.62/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.62/1.54 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(setminusSubset2_type,type,
% 2.62/1.54 setminusSubset2: $o ).
% 2.62/1.54
% 2.62/1.54 thf(setminusSubset2,definition,
% 2.62/1.54 ( setminusSubset2
% 2.62/1.54 = ( ! [A: $i,B: $i] :
% 2.62/1.54 ( ( subset @ A @ B )
% 2.62/1.54 => ( ( setminus @ A @ B )
% 2.62/1.54 = emptyset ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(setminusERneg_type,type,
% 2.62/1.54 setminusERneg: $o ).
% 2.62/1.54
% 2.62/1.54 thf(setminusERneg,definition,
% 2.62/1.54 ( setminusERneg
% 2.62/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.62/1.54 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.62/1.54 => ( ( in @ Xx @ A )
% 2.62/1.54 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(setminusELneg_type,type,
% 2.62/1.54 setminusELneg: $o ).
% 2.62/1.54
% 2.62/1.54 thf(setminusELneg,definition,
% 2.62/1.54 ( setminusELneg
% 2.62/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.62/1.54 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.62/1.54 => ( ~ ( in @ Xx @ B )
% 2.62/1.54 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(setminusILneg_type,type,
% 2.62/1.54 setminusILneg: $o ).
% 2.62/1.54
% 2.62/1.54 thf(setminusILneg,definition,
% 2.62/1.54 ( setminusILneg
% 2.62/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.62/1.54 ( ~ ( in @ Xx @ A )
% 2.62/1.54 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(setminusIRneg_type,type,
% 2.62/1.54 setminusIRneg: $o ).
% 2.62/1.54
% 2.62/1.54 thf(setminusIRneg,definition,
% 2.62/1.54 ( setminusIRneg
% 2.62/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ B )
% 2.62/1.54 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(setminusLsub_type,type,
% 2.62/1.54 setminusLsub: $o ).
% 2.62/1.54
% 2.62/1.54 thf(setminusLsub,definition,
% 2.62/1.54 ( setminusLsub
% 2.62/1.54 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(setminusSubset1_type,type,
% 2.62/1.54 setminusSubset1: $o ).
% 2.62/1.54
% 2.62/1.54 thf(setminusSubset1,definition,
% 2.62/1.54 ( setminusSubset1
% 2.62/1.54 = ( ! [A: $i,B: $i] :
% 2.62/1.54 ( ( ( setminus @ A @ B )
% 2.62/1.54 = emptyset )
% 2.62/1.54 => ( subset @ A @ B ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(symdiff_type,type,
% 2.62/1.54 symdiff: $i > $i > $i ).
% 2.62/1.54
% 2.62/1.54 thf(symdiffE_type,type,
% 2.62/1.54 symdiffE: $o ).
% 2.62/1.54
% 2.62/1.54 thf(symdiffE,definition,
% 2.62/1.54 ( symdiffE
% 2.62/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.62/1.54 => ! [Xphi: $o] :
% 2.62/1.54 ( ( ( in @ Xx @ A )
% 2.62/1.54 => ( ~ ( in @ Xx @ B )
% 2.62/1.54 => Xphi ) )
% 2.62/1.54 => ( ( ~ ( in @ Xx @ A )
% 2.62/1.54 => ( ( in @ Xx @ B )
% 2.62/1.54 => Xphi ) )
% 2.62/1.54 => Xphi ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(symdiffI1_type,type,
% 2.62/1.54 symdiffI1: $o ).
% 2.62/1.54
% 2.62/1.54 thf(symdiffI1,definition,
% 2.62/1.54 ( symdiffI1
% 2.62/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ A )
% 2.62/1.54 => ( ~ ( in @ Xx @ B )
% 2.62/1.54 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(symdiffI2_type,type,
% 2.62/1.54 symdiffI2: $o ).
% 2.62/1.54
% 2.62/1.54 thf(symdiffI2,definition,
% 2.62/1.54 ( symdiffI2
% 2.62/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.62/1.54 ( ~ ( in @ Xx @ A )
% 2.62/1.54 => ( ( in @ Xx @ B )
% 2.62/1.54 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(symdiffIneg1_type,type,
% 2.62/1.54 symdiffIneg1: $o ).
% 2.62/1.54
% 2.62/1.54 thf(symdiffIneg1,definition,
% 2.62/1.54 ( symdiffIneg1
% 2.62/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ A )
% 2.62/1.54 => ( ( in @ Xx @ B )
% 2.62/1.54 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(symdiffIneg2_type,type,
% 2.62/1.54 symdiffIneg2: $o ).
% 2.62/1.54
% 2.62/1.54 thf(symdiffIneg2,definition,
% 2.62/1.54 ( symdiffIneg2
% 2.62/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.62/1.54 ( ~ ( in @ Xx @ A )
% 2.62/1.54 => ( ~ ( in @ Xx @ B )
% 2.62/1.54 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(iskpair_type,type,
% 2.62/1.54 iskpair: $i > $o ).
% 2.62/1.54
% 2.62/1.54 thf(iskpair,definition,
% 2.62/1.54 ( iskpair
% 2.62/1.54 = ( ^ [A: $i] :
% 2.62/1.54 ? [Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ ( setunion @ A ) )
% 2.62/1.54 & ? [Xy: $i] :
% 2.62/1.54 ( ( in @ Xy @ ( setunion @ A ) )
% 2.62/1.54 & ( A
% 2.62/1.54 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(secondinupair_type,type,
% 2.62/1.54 secondinupair: $o ).
% 2.62/1.54
% 2.62/1.54 thf(secondinupair,definition,
% 2.62/1.54 ( secondinupair
% 2.62/1.54 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(setukpairIL_type,type,
% 2.62/1.54 setukpairIL: $o ).
% 2.62/1.54
% 2.62/1.54 thf(setukpairIL,definition,
% 2.62/1.54 ( setukpairIL
% 2.62/1.54 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(setukpairIR_type,type,
% 2.62/1.54 setukpairIR: $o ).
% 2.62/1.54
% 2.62/1.54 thf(setukpairIR,definition,
% 2.62/1.54 ( setukpairIR
% 2.62/1.54 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(kpairiskpair_type,type,
% 2.62/1.54 kpairiskpair: $o ).
% 2.62/1.54
% 2.62/1.54 thf(kpairiskpair,definition,
% 2.62/1.54 ( kpairiskpair
% 2.62/1.54 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(kpair_type,type,
% 2.62/1.54 kpair: $i > $i > $i ).
% 2.62/1.54
% 2.62/1.54 thf(kpair,definition,
% 2.62/1.54 ( kpair
% 2.62/1.54 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(kpairp_type,type,
% 2.62/1.54 kpairp: $o ).
% 2.62/1.54
% 2.62/1.54 thf(kpairp,definition,
% 2.62/1.54 ( kpairp
% 2.62/1.54 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(cartprod_type,type,
% 2.62/1.54 cartprod: $i > $i > $i ).
% 2.62/1.54
% 2.62/1.54 thf(singletonsubset_type,type,
% 2.62/1.54 singletonsubset: $o ).
% 2.62/1.54
% 2.62/1.54 thf(singletonsubset,definition,
% 2.62/1.54 ( singletonsubset
% 2.62/1.54 = ( ! [A: $i,Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ A )
% 2.62/1.54 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(singletoninpowerset_type,type,
% 2.62/1.54 singletoninpowerset: $o ).
% 2.62/1.54
% 2.62/1.54 thf(singletoninpowerset,definition,
% 2.62/1.54 ( singletoninpowerset
% 2.62/1.54 = ( ! [A: $i,Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ A )
% 2.62/1.54 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(singletoninpowunion_type,type,
% 2.62/1.54 singletoninpowunion: $o ).
% 2.62/1.54
% 2.62/1.54 thf(singletoninpowunion,definition,
% 2.62/1.54 ( singletoninpowunion
% 2.62/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ A )
% 2.62/1.54 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(upairset2E_type,type,
% 2.62/1.54 upairset2E: $o ).
% 2.62/1.54
% 2.62/1.54 thf(upairset2E,definition,
% 2.62/1.54 ( upairset2E
% 2.62/1.54 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.62/1.54 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.62/1.54 => ( ( Xz = Xx )
% 2.62/1.54 | ( Xz = Xy ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(upairsubunion_type,type,
% 2.62/1.54 upairsubunion: $o ).
% 2.62/1.54
% 2.62/1.54 thf(upairsubunion,definition,
% 2.62/1.54 ( upairsubunion
% 2.62/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ A )
% 2.62/1.54 => ! [Xy: $i] :
% 2.62/1.54 ( ( in @ Xy @ B )
% 2.62/1.54 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(upairinpowunion_type,type,
% 2.62/1.54 upairinpowunion: $o ).
% 2.62/1.54
% 2.62/1.54 thf(upairinpowunion,definition,
% 2.62/1.54 ( upairinpowunion
% 2.62/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ A )
% 2.62/1.54 => ! [Xy: $i] :
% 2.62/1.54 ( ( in @ Xy @ B )
% 2.62/1.54 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(ubforcartprodlem1_type,type,
% 2.62/1.54 ubforcartprodlem1: $o ).
% 2.62/1.54
% 2.62/1.54 thf(ubforcartprodlem1,definition,
% 2.62/1.54 ( ubforcartprodlem1
% 2.62/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ A )
% 2.62/1.54 => ! [Xy: $i] :
% 2.62/1.54 ( ( in @ Xy @ B )
% 2.62/1.54 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(ubforcartprodlem2_type,type,
% 2.62/1.54 ubforcartprodlem2: $o ).
% 2.62/1.54
% 2.62/1.54 thf(ubforcartprodlem2,definition,
% 2.62/1.54 ( ubforcartprodlem2
% 2.62/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ A )
% 2.62/1.54 => ! [Xy: $i] :
% 2.62/1.54 ( ( in @ Xy @ B )
% 2.62/1.54 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(ubforcartprodlem3_type,type,
% 2.62/1.54 ubforcartprodlem3: $o ).
% 2.62/1.54
% 2.62/1.54 thf(ubforcartprodlem3,definition,
% 2.62/1.54 ( ubforcartprodlem3
% 2.62/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ A )
% 2.62/1.54 => ! [Xy: $i] :
% 2.62/1.54 ( ( in @ Xy @ B )
% 2.62/1.54 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(cartprodpairin_type,type,
% 2.62/1.54 cartprodpairin: $o ).
% 2.62/1.54
% 2.62/1.54 thf(cartprodpairin,definition,
% 2.62/1.54 ( cartprodpairin
% 2.62/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ A )
% 2.62/1.54 => ! [Xy: $i] :
% 2.62/1.54 ( ( in @ Xy @ B )
% 2.62/1.54 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(cartprodmempair1_type,type,
% 2.62/1.54 cartprodmempair1: $o ).
% 2.62/1.54
% 2.62/1.54 thf(cartprodmempair1,definition,
% 2.62/1.54 ( cartprodmempair1
% 2.62/1.54 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.62/1.54 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.62/1.54 => ? [Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ A )
% 2.62/1.54 & ? [Xy: $i] :
% 2.62/1.54 ( ( in @ Xy @ B )
% 2.62/1.54 & ( Xu
% 2.62/1.54 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(cartprodmempair_type,type,
% 2.62/1.54 cartprodmempair: $o ).
% 2.62/1.54
% 2.62/1.54 thf(cartprodmempair,definition,
% 2.62/1.54 ( cartprodmempair
% 2.62/1.54 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.62/1.54 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.62/1.54 => ( iskpair @ Xu ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(setunionE2_type,type,
% 2.62/1.54 setunionE2: $o ).
% 2.62/1.54
% 2.62/1.54 thf(setunionE2,definition,
% 2.62/1.54 ( setunionE2
% 2.62/1.54 = ( ! [A: $i,Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ ( setunion @ A ) )
% 2.62/1.54 => ? [X: $i] :
% 2.62/1.54 ( ( in @ X @ A )
% 2.62/1.54 & ( in @ Xx @ X ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(setunionsingleton1_type,type,
% 2.62/1.54 setunionsingleton1: $o ).
% 2.62/1.54
% 2.62/1.54 thf(setunionsingleton1,definition,
% 2.62/1.54 ( setunionsingleton1
% 2.62/1.54 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(setunionsingleton2_type,type,
% 2.62/1.54 setunionsingleton2: $o ).
% 2.62/1.54
% 2.62/1.54 thf(setunionsingleton2,definition,
% 2.62/1.54 ( setunionsingleton2
% 2.62/1.54 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(setunionsingleton_type,type,
% 2.62/1.54 setunionsingleton: $o ).
% 2.62/1.54
% 2.62/1.54 thf(setunionsingleton,definition,
% 2.62/1.54 ( setunionsingleton
% 2.62/1.54 = ( ! [Xx: $i] :
% 2.62/1.54 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 2.62/1.54 = Xx ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(singleton_type,type,
% 2.62/1.54 singleton: $i > $o ).
% 2.62/1.54
% 2.62/1.54 thf(singleton,definition,
% 2.62/1.54 ( singleton
% 2.62/1.54 = ( ^ [A: $i] :
% 2.62/1.54 ? [Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ A )
% 2.62/1.54 & ( A
% 2.62/1.54 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(singletonprop_type,type,
% 2.62/1.54 singletonprop: $o ).
% 2.62/1.54
% 2.62/1.54 thf(singletonprop,definition,
% 2.62/1.54 ( singletonprop
% 2.62/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 2.62/1.54 ( ! [Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ A )
% 2.62/1.54 => ! [Xy: $i] :
% 2.62/1.54 ( ( in @ Xy @ A )
% 2.62/1.54 => ( ( Xphi @ Xx )
% 2.62/1.54 => ( ( Xphi @ Xy )
% 2.62/1.54 => ( Xx = Xy ) ) ) ) )
% 2.62/1.54 => ( ? [Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ A )
% 2.62/1.54 & ( Xphi @ Xx ) )
% 2.62/1.54 => ( singleton
% 2.62/1.54 @ ( dsetconstr @ A
% 2.62/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(ex1_type,type,
% 2.62/1.54 ex1: $i > ( $i > $o ) > $o ).
% 2.62/1.54
% 2.62/1.54 thf(ex1,definition,
% 2.62/1.54 ( ex1
% 2.62/1.54 = ( ^ [A: $i,Xphi: $i > $o] :
% 2.62/1.54 ( singleton
% 2.62/1.54 @ ( dsetconstr @ A
% 2.62/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(ex1E1_type,type,
% 2.62/1.54 ex1E1: $o ).
% 2.62/1.54
% 2.62/1.54 thf(ex1E1,definition,
% 2.62/1.54 ( ex1E1
% 2.62/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 2.62/1.54 ( ( ex1 @ A
% 2.62/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.62/1.54 => ? [Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ A )
% 2.62/1.54 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(ex1I_type,type,
% 2.62/1.54 ex1I: $o ).
% 2.62/1.54
% 2.62/1.54 thf(ex1I,definition,
% 2.62/1.54 ( ex1I
% 2.62/1.54 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ A )
% 2.62/1.54 => ( ( Xphi @ Xx )
% 2.62/1.54 => ( ! [Xy: $i] :
% 2.62/1.54 ( ( in @ Xy @ A )
% 2.62/1.54 => ( ( Xphi @ Xy )
% 2.62/1.54 => ( Xy = Xx ) ) )
% 2.62/1.54 => ( ex1 @ A
% 2.62/1.54 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(ex1I2_type,type,
% 2.62/1.54 ex1I2: $o ).
% 2.62/1.54
% 2.62/1.54 thf(ex1I2,definition,
% 2.62/1.54 ( ex1I2
% 2.62/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 2.62/1.54 ( ! [Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ A )
% 2.62/1.54 => ! [Xy: $i] :
% 2.62/1.54 ( ( in @ Xy @ A )
% 2.62/1.54 => ( ( Xphi @ Xx )
% 2.62/1.54 => ( ( Xphi @ Xy )
% 2.62/1.54 => ( Xx = Xy ) ) ) ) )
% 2.62/1.54 => ( ? [Xx: $i] :
% 2.62/1.54 ( ( in @ Xx @ A )
% 2.62/1.54 & ( Xphi @ Xx ) )
% 2.62/1.54 => ( ex1 @ A
% 2.62/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(singletonsuniq_type,type,
% 2.62/1.54 singletonsuniq: $o ).
% 2.62/1.54
% 2.62/1.54 thf(singletonsuniq,definition,
% 2.62/1.54 ( singletonsuniq
% 2.62/1.54 = ( ! [Xx: $i,Xy: $i] :
% 2.62/1.54 ( ( ( setadjoin @ Xx @ emptyset )
% 2.62/1.54 = ( setadjoin @ Xy @ emptyset ) )
% 2.62/1.54 => ( Xx = Xy ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(atmost1p_type,type,
% 2.62/1.54 atmost1p: $i > $o ).
% 2.62/1.54
% 2.62/1.54 thf(atleast2p_type,type,
% 2.62/1.54 atleast2p: $i > $o ).
% 2.62/1.54
% 2.62/1.54 thf(atmost2p_type,type,
% 2.62/1.54 atmost2p: $i > $o ).
% 2.62/1.54
% 2.62/1.54 thf(upairsetp_type,type,
% 2.62/1.54 upairsetp: $i > $o ).
% 2.62/1.54
% 2.62/1.54 thf(setukpairinjL1_type,type,
% 2.62/1.54 setukpairinjL1: $o ).
% 2.62/1.54
% 2.62/1.54 thf(setukpairinjL1,definition,
% 2.62/1.54 ( setukpairinjL1
% 2.62/1.54 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.62/1.54 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 2.62/1.54 => ( Xx = Xz ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(kfstsingleton_type,type,
% 2.62/1.54 kfstsingleton: $o ).
% 2.62/1.54
% 2.62/1.54 thf(kfstsingleton,definition,
% 2.62/1.54 ( kfstsingleton
% 2.62/1.54 = ( ! [Xu: $i] :
% 2.62/1.54 ( ( iskpair @ Xu )
% 2.62/1.54 => ( singleton
% 2.62/1.54 @ ( dsetconstr @ ( setunion @ Xu )
% 2.62/1.54 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(theprop_type,type,
% 2.62/1.54 theprop: $o ).
% 2.62/1.54
% 2.62/1.54 thf(theprop,definition,
% 2.62/1.54 ( theprop
% 2.62/1.54 = ( ! [X: $i] :
% 2.62/1.54 ( ( singleton @ X )
% 2.62/1.54 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(kfst_type,type,
% 2.62/1.54 kfst: $i > $i ).
% 2.62/1.54
% 2.62/1.54 thf(kfstpairEq_type,type,
% 2.62/1.54 kfstpairEq: $o ).
% 2.62/1.54
% 2.62/1.54 thf(kfstpairEq,definition,
% 2.62/1.54 ( kfstpairEq
% 2.62/1.54 = ( ! [Xx: $i,Xy: $i] :
% 2.62/1.54 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.62/1.54 = Xx ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(cartprodfstin_type,type,
% 2.62/1.54 cartprodfstin: $o ).
% 2.62/1.54
% 2.62/1.54 thf(cartprodfstin,definition,
% 2.62/1.54 ( cartprodfstin
% 2.62/1.54 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.62/1.54 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.62/1.54 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(setukpairinjL2_type,type,
% 2.62/1.54 setukpairinjL2: $o ).
% 2.62/1.54
% 2.62/1.54 thf(setukpairinjL2,definition,
% 2.62/1.54 ( setukpairinjL2
% 2.62/1.54 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.62/1.54 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.62/1.54 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.62/1.54 => ( Xx = Xz ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(setukpairinjL_type,type,
% 2.62/1.54 setukpairinjL: $o ).
% 2.62/1.54
% 2.62/1.54 thf(setukpairinjL,definition,
% 2.62/1.54 ( setukpairinjL
% 2.62/1.54 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.62/1.54 ( ( ( kpair @ Xx @ Xy )
% 2.62/1.54 = ( kpair @ Xz @ Xu ) )
% 2.62/1.54 => ( Xx = Xz ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(setukpairinjR11_type,type,
% 2.62/1.54 setukpairinjR11: $o ).
% 2.62/1.54
% 2.62/1.54 thf(setukpairinjR11,definition,
% 2.62/1.54 ( setukpairinjR11
% 2.62/1.54 = ( ! [Xx: $i,Xy: $i] :
% 2.62/1.54 ( ( Xx = Xy )
% 2.62/1.54 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.62/1.54 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(setukpairinjR12_type,type,
% 2.62/1.54 setukpairinjR12: $o ).
% 2.62/1.54
% 2.62/1.54 thf(setukpairinjR12,definition,
% 2.62/1.54 ( setukpairinjR12
% 2.62/1.54 = ( ! [Xx: $i,Xy: $i] :
% 2.62/1.54 ( ( Xx = Xy )
% 2.62/1.54 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.62/1.54 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(setukpairinjR1_type,type,
% 2.62/1.54 setukpairinjR1: $o ).
% 2.62/1.54
% 2.62/1.54 thf(setukpairinjR1,definition,
% 2.62/1.54 ( setukpairinjR1
% 2.62/1.54 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.62/1.54 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.62/1.54 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.62/1.54 => ( ( Xz = Xu )
% 2.62/1.54 => ( Xy = Xu ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(upairequniteq_type,type,
% 2.62/1.54 upairequniteq: $o ).
% 2.62/1.54
% 2.62/1.54 thf(upairequniteq,definition,
% 2.62/1.54 ( upairequniteq
% 2.62/1.54 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.62/1.54 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.62/1.54 = ( setadjoin @ Xz @ emptyset ) )
% 2.62/1.54 => ( Xx = Xy ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(setukpairinjR2_type,type,
% 2.62/1.54 setukpairinjR2: $o ).
% 2.62/1.54
% 2.62/1.54 thf(setukpairinjR2,definition,
% 2.62/1.54 ( setukpairinjR2
% 2.62/1.54 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.62/1.54 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.62/1.54 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.62/1.54 => ( Xy = Xu ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(setukpairinjR_type,type,
% 2.62/1.54 setukpairinjR: $o ).
% 2.62/1.54
% 2.62/1.54 thf(setukpairinjR,definition,
% 2.62/1.54 ( setukpairinjR
% 2.62/1.54 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.62/1.54 ( ( ( kpair @ Xx @ Xy )
% 2.62/1.54 = ( kpair @ Xz @ Xu ) )
% 2.62/1.54 => ( Xy = Xu ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(ksndsingleton_type,type,
% 2.62/1.54 ksndsingleton: $o ).
% 2.62/1.54
% 2.62/1.54 thf(ksndsingleton,definition,
% 2.62/1.54 ( ksndsingleton
% 2.62/1.54 = ( ! [Xu: $i] :
% 2.62/1.54 ( ( iskpair @ Xu )
% 2.62/1.54 => ( singleton
% 2.62/1.54 @ ( dsetconstr @ ( setunion @ Xu )
% 2.62/1.54 @ ^ [Xx: $i] :
% 2.62/1.54 ( Xu
% 2.62/1.54 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(ksnd_type,type,
% 2.62/1.54 ksnd: $i > $i ).
% 2.62/1.54
% 2.62/1.54 thf(ksndpairEq_type,type,
% 2.62/1.54 ksndpairEq: $o ).
% 2.62/1.54
% 2.62/1.54 thf(ksndpairEq,definition,
% 2.62/1.54 ( ksndpairEq
% 2.62/1.54 = ( ! [Xx: $i,Xy: $i] :
% 2.62/1.54 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.62/1.54 = Xy ) ) ) ).
% 2.62/1.54
% 2.62/1.54 thf(kpairsurjEq,conjecture,
% 2.62/1.54 ( setextAx
% 2.62/1.54 => ( emptysetAx
% 2.62/1.54 => ( setadjoinAx
% 2.62/1.54 => ( powersetAx
% 2.62/1.54 => ( setunionAx
% 2.62/1.54 => ( omega0Ax
% 2.62/1.54 => ( omegaSAx
% 2.62/1.54 => ( omegaIndAx
% 2.62/1.54 => ( replAx
% 2.62/1.54 => ( foundationAx
% 2.62/1.54 => ( wellorderingAx
% 2.62/1.54 => ( descrp
% 2.62/1.54 => ( dsetconstrI
% 2.62/1.54 => ( dsetconstrEL
% 2.62/1.54 => ( dsetconstrER
% 2.62/1.54 => ( exuE1
% 2.62/1.54 => ( prop2setE
% 2.62/1.54 => ( emptysetE
% 2.62/1.54 => ( emptysetimpfalse
% 2.62/1.54 => ( notinemptyset
% 2.62/1.54 => ( exuE3e
% 2.62/1.54 => ( setext
% 2.62/1.54 => ( emptyI
% 2.62/1.54 => ( noeltsimpempty
% 2.62/1.54 => ( setbeta
% 2.62/1.54 => ( nonemptyE1
% 2.62/1.54 => ( nonemptyI
% 2.62/1.54 => ( nonemptyI1
% 2.62/1.54 => ( setadjoinIL
% 2.62/1.54 => ( emptyinunitempty
% 2.62/1.54 => ( setadjoinIR
% 2.62/1.54 => ( setadjoinE
% 2.62/1.54 => ( setadjoinOr
% 2.62/1.54 => ( setoftrueEq
% 2.62/1.54 => ( powersetI
% 2.62/1.54 => ( emptyinPowerset
% 2.62/1.54 => ( emptyInPowerset
% 2.62/1.54 => ( powersetE
% 2.62/1.54 => ( setunionI
% 2.62/1.54 => ( setunionE
% 2.62/1.54 => ( subPowSU
% 2.62/1.54 => ( exuE2
% 2.62/1.54 => ( nonemptyImpWitness
% 2.62/1.54 => ( uniqinunit
% 2.62/1.54 => ( notinsingleton
% 2.62/1.54 => ( eqinunit
% 2.62/1.54 => ( singletonsswitch
% 2.62/1.54 => ( upairsetE
% 2.62/1.54 => ( upairsetIL
% 2.62/1.54 => ( upairsetIR
% 2.62/1.54 => ( emptyE1
% 2.62/1.54 => ( vacuousDall
% 2.62/1.54 => ( quantDeMorgan1
% 2.62/1.54 => ( quantDeMorgan2
% 2.62/1.54 => ( quantDeMorgan3
% 2.62/1.54 => ( quantDeMorgan4
% 2.62/1.54 => ( prop2setI
% 2.62/1.54 => ( prop2set2propI
% 2.62/1.54 => ( notdexE
% 2.62/1.54 => ( notdallE
% 2.62/1.54 => ( exuI1
% 2.62/1.54 => ( exuI3
% 2.62/1.54 => ( exuI2
% 2.62/1.54 => ( inCongP
% 2.62/1.54 => ( in__Cong
% 2.62/1.54 => ( exuE3u
% 2.62/1.54 => ( exu__Cong
% 2.62/1.54 => ( emptyset__Cong
% 2.62/1.54 => ( setadjoin__Cong
% 2.62/1.54 => ( powerset__Cong
% 2.62/1.54 => ( setunion__Cong
% 2.62/1.54 => ( omega__Cong
% 2.62/1.54 => ( exuEu
% 2.62/1.54 => ( descr__Cong
% 2.62/1.54 => ( dsetconstr__Cong
% 2.62/1.54 => ( subsetI1
% 2.62/1.54 => ( eqimpsubset2
% 2.62/1.54 => ( eqimpsubset1
% 2.62/1.54 => ( subsetI2
% 2.62/1.54 => ( emptysetsubset
% 2.62/1.54 => ( subsetE
% 2.62/1.54 => ( subsetE2
% 2.62/1.54 => ( notsubsetI
% 2.62/1.54 => ( notequalI1
% 2.62/1.54 => ( notequalI2
% 2.62/1.54 => ( subsetRefl
% 2.62/1.54 => ( subsetTrans
% 2.62/1.54 => ( setadjoinSub
% 2.62/1.54 => ( setadjoinSub2
% 2.62/1.54 => ( subset2powerset
% 2.62/1.54 => ( setextsub
% 2.62/1.54 => ( subsetemptysetimpeq
% 2.62/1.54 => ( powersetI1
% 2.62/1.54 => ( powersetE1
% 2.62/1.54 => ( inPowerset
% 2.62/1.54 => ( powersetsubset
% 2.62/1.54 => ( sepInPowerset
% 2.62/1.54 => ( sepSubset
% 2.62/1.54 => ( binunionIL
% 2.62/1.54 => ( upairset2IR
% 2.62/1.54 => ( binunionIR
% 2.62/1.54 => ( binunionEcases
% 2.62/1.54 => ( binunionE
% 2.62/1.54 => ( binunionLsub
% 2.62/1.54 => ( binunionRsub
% 2.62/1.54 => ( binintersectI
% 2.62/1.54 => ( binintersectSubset5
% 2.62/1.54 => ( binintersectEL
% 2.62/1.54 => ( binintersectLsub
% 2.62/1.54 => ( binintersectSubset2
% 2.62/1.54 => ( binintersectSubset3
% 2.62/1.54 => ( binintersectER
% 2.62/1.54 => ( disjointsetsI1
% 2.62/1.54 => ( binintersectRsub
% 2.62/1.54 => ( binintersectSubset4
% 2.62/1.54 => ( binintersectSubset1
% 2.62/1.54 => ( bs114d
% 2.62/1.54 => ( setminusI
% 2.62/1.54 => ( setminusEL
% 2.62/1.54 => ( setminusER
% 2.62/1.54 => ( setminusSubset2
% 2.62/1.54 => ( setminusERneg
% 2.62/1.54 => ( setminusELneg
% 2.62/1.54 => ( setminusILneg
% 2.62/1.54 => ( setminusIRneg
% 2.62/1.54 => ( setminusLsub
% 2.62/1.54 => ( setminusSubset1
% 2.62/1.54 => ( symdiffE
% 2.62/1.54 => ( symdiffI1
% 2.62/1.54 => ( symdiffI2
% 2.62/1.54 => ( symdiffIneg1
% 2.62/1.54 => ( symdiffIneg2
% 2.62/1.54 => ( secondinupair
% 2.62/1.54 => ( setukpairIL
% 2.62/1.54 => ( setukpairIR
% 2.62/1.54 => ( kpairiskpair
% 2.62/1.54 => ( kpairp
% 2.62/1.54 => ( singletonsubset
% 2.62/1.54 => ( singletoninpowerset
% 2.62/1.54 => ( singletoninpowunion
% 2.62/1.54 => ( upairset2E
% 2.62/1.54 => ( upairsubunion
% 2.62/1.54 => ( upairinpowunion
% 2.62/1.54 => ( ubforcartprodlem1
% 2.62/1.54 => ( ubforcartprodlem2
% 2.62/1.54 => ( ubforcartprodlem3
% 2.62/1.54 => ( cartprodpairin
% 2.62/1.54 => ( cartprodmempair1
% 2.62/1.54 => ( cartprodmempair
% 2.62/1.54 => ( setunionE2
% 2.62/1.54 => ( setunionsingleton1
% 2.62/1.54 => ( setunionsingleton2
% 2.62/1.54 => ( setunionsingleton
% 2.62/1.54 => ( singletonprop
% 2.62/1.54 => ( ex1E1
% 2.62/1.54 => ( ex1I
% 2.62/1.54 => ( ex1I2
% 2.62/1.54 => ( singletonsuniq
% 2.62/1.54 => ( setukpairinjL1
% 2.62/1.54 => ( kfstsingleton
% 2.62/1.54 => ( theprop
% 2.62/1.54 => ( kfstpairEq
% 2.62/1.54 => ( cartprodfstin
% 2.62/1.54 => ( setukpairinjL2
% 2.62/1.54 => ( setukpairinjL
% 2.62/1.54 => ( setukpairinjR11
% 2.62/1.54 => ( setukpairinjR12
% 2.62/1.54 => ( setukpairinjR1
% 2.62/1.54 => ( upairequniteq
% 2.62/1.54 => ( setukpairinjR2
% 2.62/1.54 => ( setukpairinjR
% 2.62/1.54 => ( ksndsingleton
% 2.62/1.54 => ( ksndpairEq
% 2.62/1.54 => ! [Xu: $i] :
% 2.62/1.54 ( ( iskpair @ Xu )
% 2.62/1.54 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.62/1.54 = Xu ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.62/1.54 ------------------------
% 2.62/1.55 % (18858)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_18632 for (2999ds/2Mi)
% 2.62/1.55 % (18858)Instruction limit reached!
% 2.62/1.55 % (18858)------------------------------
% 2.62/1.55 % (18858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.55 % (18858)Termination reason: Unknown
% 2.62/1.55 % (18858)Termination phase: shuffling
% 2.62/1.55
% 2.62/1.55 % (18858)Memory used [KB]: 1279
% 2.62/1.55 % (18858)Time elapsed: 0.002 s
% 2.62/1.55 % (18858)Instructions burned: 2 (million)
% 2.62/1.55 % (18858)------------------------------
% 2.62/1.55 % (18858)------------------------------
% 2.62/1.56 % (18854)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18632 for (2999ds/183Mi)
% 2.62/1.56 % (18855)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_18632 for (2999ds/4Mi)
% 2.62/1.56 % (18856)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_18632 for (2999ds/27Mi)
% 2.62/1.56 % (18857)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_18632 for (2999ds/2Mi)
% 2.62/1.56 % (18859)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_18632 for (2999ds/275Mi)
% 2.62/1.56 % (18860)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_18632 for (2999ds/18Mi)
% 2.62/1.56 % (18857)Instruction limit reached!
% 2.62/1.56 % (18857)------------------------------
% 2.62/1.56 % (18857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.56 % (18857)Termination reason: Unknown
% 2.62/1.56 % (18857)Termination phase: shuffling
% 2.62/1.56
% 2.62/1.56 % (18857)Memory used [KB]: 1279
% 2.62/1.56 % (18857)Time elapsed: 0.003 s
% 2.62/1.56 % (18857)Instructions burned: 2 (million)
% 2.62/1.56 % (18857)------------------------------
% 2.62/1.56 % (18857)------------------------------
% 2.62/1.56 % (18855)Instruction limit reached!
% 2.62/1.56 % (18855)------------------------------
% 2.62/1.56 % (18855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.56 % (18855)Termination reason: Unknown
% 2.62/1.56 % (18855)Termination phase: shuffling
% 2.62/1.56
% 2.62/1.56 % (18855)Memory used [KB]: 1279
% 2.62/1.56 % (18855)Time elapsed: 0.004 s
% 2.62/1.56 % (18855)Instructions burned: 4 (million)
% 2.62/1.56 % (18855)------------------------------
% 2.62/1.56 % (18855)------------------------------
% 2.62/1.56 % (18871)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_18632 for (2999ds/3Mi)
% 2.62/1.57 % (18871)Instruction limit reached!
% 2.62/1.57 % (18871)------------------------------
% 2.62/1.57 % (18871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.57 % (18871)Termination reason: Unknown
% 2.62/1.57 % (18871)Termination phase: shuffling
% 2.62/1.57
% 2.62/1.57 % (18871)Memory used [KB]: 1407
% 2.62/1.57 % (18871)Time elapsed: 0.003 s
% 2.62/1.57 % (18871)Instructions burned: 6 (million)
% 2.62/1.57 % (18871)------------------------------
% 2.62/1.57 % (18871)------------------------------
% 2.62/1.57 % (18860)Instruction limit reached!
% 2.62/1.57 % (18860)------------------------------
% 2.62/1.57 % (18860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.57 % (18860)Termination reason: Unknown
% 2.62/1.57 % (18860)Termination phase: Property scanning
% 2.62/1.57
% 2.62/1.57 % (18860)Memory used [KB]: 1663
% 2.62/1.57 % (18860)Time elapsed: 0.013 s
% 2.62/1.57 % (18860)Instructions burned: 19 (million)
% 2.62/1.57 % (18860)------------------------------
% 2.62/1.57 % (18860)------------------------------
% 2.62/1.57 % (18856)Instruction limit reached!
% 2.62/1.57 % (18856)------------------------------
% 2.62/1.57 % (18856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.57 % (18856)Termination reason: Unknown
% 2.62/1.57 % (18856)Termination phase: Property scanning
% 2.62/1.57
% 2.62/1.57 % (18856)Memory used [KB]: 1791
% 2.62/1.57 % (18856)Time elapsed: 0.016 s
% 2.62/1.57 % (18856)Instructions burned: 27 (million)
% 2.62/1.57 % (18856)------------------------------
% 2.62/1.57 % (18856)------------------------------
% 2.62/1.58 % (18880)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_18632 for (2999ds/3Mi)
% 2.62/1.58 % (18880)Instruction limit reached!
% 2.62/1.58 % (18880)------------------------------
% 2.62/1.58 % (18880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.58 % (18880)Termination reason: Unknown
% 2.62/1.58 % (18880)Termination phase: shuffling
% 2.62/1.58
% 2.62/1.58 % (18880)Memory used [KB]: 1279
% 2.62/1.58 % (18880)Time elapsed: 0.002 s
% 2.62/1.58 % (18880)Instructions burned: 3 (million)
% 2.62/1.58 % (18880)------------------------------
% 2.62/1.58 % (18880)------------------------------
% 2.62/1.58 % (18875)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_18632 for (2999ds/37Mi)
% 2.62/1.58 % (18876)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_18632 for (2999ds/15Mi)
% 2.62/1.59 % (18885)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_18632 for (2999ds/16Mi)
% 2.62/1.59 % (18876)Instruction limit reached!
% 2.62/1.59 % (18876)------------------------------
% 2.62/1.59 % (18876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.59 % (18876)Termination reason: Unknown
% 2.62/1.59 % (18876)Termination phase: shuffling
% 2.62/1.59
% 2.62/1.59 % (18883)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_18632 for (2999ds/1041Mi)
% 2.62/1.59 % (18876)Memory used [KB]: 1663
% 2.62/1.59 % (18876)Time elapsed: 0.011 s
% 2.62/1.59 % (18876)Instructions burned: 15 (million)
% 2.62/1.59 % (18876)------------------------------
% 2.62/1.59 % (18876)------------------------------
% 2.62/1.59 % (18885)Instruction limit reached!
% 2.62/1.59 % (18885)------------------------------
% 2.62/1.59 % (18885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.62/1.59 % (18885)Termination reason: Unknown
% 2.62/1.59 % (18885)Termination phase: shuffling
% 2.62/1.59
% 2.62/1.59 % (18885)Memory used [KB]: 1663
% 2.62/1.59 % (18885)Time elapsed: 0.007 s
% 2.62/1.59 % (18885)Instructions burned: 19 (million)
% 2.62/1.59 % (18885)------------------------------
% 2.62/1.59 % (18885)------------------------------
% 2.62/1.59 % (18884)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_18632 for (2999ds/7Mi)
% 2.66/1.60 % (18884)Instruction limit reached!
% 2.66/1.60 % (18884)------------------------------
% 2.66/1.60 % (18884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.60 % (18884)Termination reason: Unknown
% 2.66/1.60 % (18884)Termination phase: shuffling
% 2.66/1.60
% 2.66/1.60 % (18884)Memory used [KB]: 1407
% 2.66/1.60 % (18884)Time elapsed: 0.005 s
% 2.66/1.60 % (18884)Instructions burned: 7 (million)
% 2.66/1.60 % (18884)------------------------------
% 2.66/1.60 % (18884)------------------------------
% 2.66/1.60 % (18875)Instruction limit reached!
% 2.66/1.60 % (18875)------------------------------
% 2.66/1.60 % (18875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.60 % (18875)Termination reason: Unknown
% 2.66/1.60 % (18875)Termination phase: Property scanning
% 2.66/1.60
% 2.66/1.60 % (18875)Memory used [KB]: 1791
% 2.66/1.60 % (18875)Time elapsed: 0.020 s
% 2.66/1.60 % (18875)Instructions burned: 38 (million)
% 2.66/1.60 % (18875)------------------------------
% 2.66/1.60 % (18875)------------------------------
% 2.66/1.60 % (18895)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_18632 for (2999ds/3Mi)
% 2.66/1.60 % (18895)Instruction limit reached!
% 2.66/1.60 % (18895)------------------------------
% 2.66/1.60 % (18895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.60 % (18895)Termination reason: Unknown
% 2.66/1.60 % (18895)Termination phase: shuffling
% 2.66/1.60
% 2.66/1.60 % (18895)Memory used [KB]: 1407
% 2.66/1.60 % (18895)Time elapsed: 0.003 s
% 2.66/1.60 % (18895)Instructions burned: 6 (million)
% 2.66/1.60 % (18895)------------------------------
% 2.66/1.60 % (18895)------------------------------
% 2.66/1.61 % (18892)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_18632 for (2999ds/3Mi)
% 2.66/1.61 % (18892)Instruction limit reached!
% 2.66/1.61 % (18892)------------------------------
% 2.66/1.61 % (18892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.61 % (18892)Termination reason: Unknown
% 2.66/1.61 % (18892)Termination phase: shuffling
% 2.66/1.61
% 2.66/1.61 % (18892)Memory used [KB]: 1279
% 2.66/1.61 % (18892)Time elapsed: 0.003 s
% 2.66/1.61 % (18892)Instructions burned: 3 (million)
% 2.66/1.61 % (18892)------------------------------
% 2.66/1.61 % (18892)------------------------------
% 2.66/1.61 % (18906)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_18632 for (2999ds/4Mi)
% 2.66/1.61 % (18906)Instruction limit reached!
% 2.66/1.61 % (18906)------------------------------
% 2.66/1.61 % (18906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.61 % (18906)Termination reason: Unknown
% 2.66/1.61 % (18906)Termination phase: shuffling
% 2.66/1.61
% 2.66/1.61 % (18906)Memory used [KB]: 1407
% 2.66/1.61 % (18906)Time elapsed: 0.003 s
% 2.66/1.61 % (18906)Instructions burned: 7 (million)
% 2.66/1.61 % (18906)------------------------------
% 2.66/1.61 % (18906)------------------------------
% 2.66/1.61 % (18899)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_18632 for (2999ds/7Mi)
% 2.66/1.62 % (18902)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_18632 for (2999ds/3Mi)
% 2.66/1.62 % (18902)Instruction limit reached!
% 2.66/1.62 % (18902)------------------------------
% 2.66/1.62 % (18902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.62 % (18902)Termination reason: Unknown
% 2.66/1.62 % (18902)Termination phase: shuffling
% 2.66/1.62
% 2.66/1.62 % (18902)Memory used [KB]: 1279
% 2.66/1.62 % (18902)Time elapsed: 0.003 s
% 2.66/1.62 % (18902)Instructions burned: 4 (million)
% 2.66/1.62 % (18902)------------------------------
% 2.66/1.62 % (18902)------------------------------
% 2.66/1.62 % (18899)Instruction limit reached!
% 2.66/1.62 % (18899)------------------------------
% 2.66/1.62 % (18899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.62 % (18899)Termination reason: Unknown
% 2.66/1.62 % (18899)Termination phase: shuffling
% 2.66/1.62
% 2.66/1.62 % (18899)Memory used [KB]: 1407
% 2.66/1.62 % (18899)Time elapsed: 0.005 s
% 2.66/1.62 % (18899)Instructions burned: 7 (million)
% 2.66/1.62 % (18899)------------------------------
% 2.66/1.62 % (18899)------------------------------
% 2.66/1.62 % (18915)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_18632 for (2999ds/710Mi)
% 2.66/1.63 % (18911)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_18632 for (2999ds/18Mi)
% 2.66/1.63 % (18918)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_18632 for (2999ds/6Mi)
% 2.66/1.63 % (18918)Instruction limit reached!
% 2.66/1.63 % (18918)------------------------------
% 2.66/1.63 % (18918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.63 % (18918)Termination reason: Unknown
% 2.66/1.63 % (18918)Termination phase: shuffling
% 2.66/1.63
% 2.66/1.63 % (18918)Memory used [KB]: 1407
% 2.66/1.63 % (18918)Time elapsed: 0.004 s
% 2.66/1.63 % (18918)Instructions burned: 7 (million)
% 2.66/1.63 % (18918)------------------------------
% 2.66/1.63 % (18918)------------------------------
% 2.66/1.63 % (18919)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_18632 for (2999ds/902Mi)
% 2.66/1.64 % (18911)Instruction limit reached!
% 2.66/1.64 % (18911)------------------------------
% 2.66/1.64 % (18911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.64 % (18911)Termination reason: Unknown
% 2.66/1.64 % (18911)Termination phase: shuffling
% 2.66/1.64
% 2.66/1.64 % (18911)Memory used [KB]: 1663
% 2.66/1.64 % (18911)Time elapsed: 0.010 s
% 2.66/1.64 % (18911)Instructions burned: 19 (million)
% 2.66/1.64 % (18911)------------------------------
% 2.66/1.64 % (18911)------------------------------
% 2.66/1.64 % (18920)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_18632 for (2999ds/21Mi)
% 2.66/1.65 % (18922)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_18632 for (2999ds/5Mi)
% 2.66/1.65 % (18922)Instruction limit reached!
% 2.66/1.65 % (18922)------------------------------
% 2.66/1.65 % (18922)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.65 % (18922)Termination reason: Unknown
% 2.66/1.65 % (18922)Termination phase: shuffling
% 2.66/1.65
% 2.66/1.65 % (18922)Memory used [KB]: 1407
% 2.66/1.65 % (18922)Time elapsed: 0.003 s
% 2.66/1.65 % (18922)Instructions burned: 6 (million)
% 2.66/1.65 % (18922)------------------------------
% 2.66/1.65 % (18922)------------------------------
% 2.66/1.65 % (18920)Instruction limit reached!
% 2.66/1.65 % (18920)------------------------------
% 2.66/1.65 % (18920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.65 % (18920)Termination reason: Unknown
% 2.66/1.65 % (18920)Termination phase: shuffling
% 2.66/1.65
% 2.66/1.65 % (18920)Memory used [KB]: 1791
% 2.66/1.65 % (18920)Time elapsed: 0.008 s
% 2.66/1.65 % (18920)Instructions burned: 23 (million)
% 2.66/1.65 % (18920)------------------------------
% 2.66/1.65 % (18920)------------------------------
% 2.66/1.65 % (18854)Instruction limit reached!
% 2.66/1.65 % (18854)------------------------------
% 2.66/1.65 % (18854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.65 % (18854)Termination reason: Unknown
% 2.66/1.65 % (18854)Termination phase: Saturation
% 2.66/1.65
% 2.66/1.65 % (18854)Memory used [KB]: 7419
% 2.66/1.65 % (18854)Time elapsed: 0.094 s
% 2.66/1.65 % (18854)Instructions burned: 184 (million)
% 2.66/1.65 % (18854)------------------------------
% 2.66/1.65 % (18854)------------------------------
% 2.66/1.66 % (18936)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_18632 for (2998ds/6Mi)
% 2.66/1.66 % (18936)Instruction limit reached!
% 2.66/1.66 % (18936)------------------------------
% 2.66/1.66 % (18936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.66 % (18936)Termination reason: Unknown
% 2.66/1.66 % (18936)Termination phase: shuffling
% 2.66/1.66
% 2.66/1.66 % (18936)Memory used [KB]: 1407
% 2.66/1.66 % (18936)Time elapsed: 0.003 s
% 2.66/1.66 % (18936)Instructions burned: 6 (million)
% 2.66/1.66 % (18936)------------------------------
% 2.66/1.66 % (18936)------------------------------
% 2.66/1.66 % (18938)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_18632 for (2998ds/377Mi)
% 2.66/1.67 % (18939)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_18632 for (2998ds/779Mi)
% 2.66/1.67 % (18941)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_18632 for (2998ds/19Mi)
% 2.66/1.68 % (18941)Instruction limit reached!
% 2.66/1.68 % (18941)------------------------------
% 2.66/1.68 % (18941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.68 % (18941)Termination reason: Unknown
% 2.66/1.68 % (18941)Termination phase: shuffling
% 2.66/1.68
% 2.66/1.68 % (18941)Memory used [KB]: 1791
% 2.66/1.68 % (18941)Time elapsed: 0.007 s
% 2.66/1.68 % (18941)Instructions burned: 21 (million)
% 2.66/1.68 % (18941)------------------------------
% 2.66/1.68 % (18941)------------------------------
% 2.66/1.69 % (18950)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_18632 for (2998ds/879Mi)
% 2.66/1.69 % (18919)Refutation not found, incomplete strategy
% 2.66/1.69 % (18919)------------------------------
% 2.66/1.69 % (18919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.69 % (18919)Termination reason: Refutation not found, incomplete strategy
% 2.66/1.69
% 2.66/1.69
% 2.66/1.69 % (18919)Memory used [KB]: 8059
% 2.66/1.69 % (18919)Time elapsed: 0.058 s
% 2.66/1.69 % (18919)Instructions burned: 187 (million)
% 2.66/1.69 % (18919)------------------------------
% 2.66/1.69 % (18919)------------------------------
% 2.66/1.70 % (18957)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_18632 for (2998ds/17Mi)
% 2.66/1.70 % (18859)Instruction limit reached!
% 2.66/1.70 % (18859)------------------------------
% 2.66/1.70 % (18859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.70 % (18859)Termination reason: Unknown
% 2.66/1.70 % (18859)Termination phase: Saturation
% 2.66/1.70
% 2.66/1.70 % (18859)Memory used [KB]: 8187
% 2.66/1.70 % (18859)Time elapsed: 0.143 s
% 2.66/1.70 % (18859)Instructions burned: 275 (million)
% 2.66/1.70 % (18859)------------------------------
% 2.66/1.70 % (18859)------------------------------
% 2.66/1.71 % (18957)Instruction limit reached!
% 2.66/1.71 % (18957)------------------------------
% 2.66/1.71 % (18957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.71 % (18957)Termination reason: Unknown
% 2.66/1.71 % (18957)Termination phase: shuffling
% 2.66/1.71
% 2.66/1.71 % (18957)Memory used [KB]: 1663
% 2.66/1.71 % (18957)Time elapsed: 0.006 s
% 2.66/1.71 % (18957)Instructions burned: 17 (million)
% 2.66/1.71 % (18957)------------------------------
% 2.66/1.71 % (18957)------------------------------
% 2.66/1.71 % (18961)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_18632 for (2998ds/3Mi)
% 2.66/1.71 % (18961)Instruction limit reached!
% 2.66/1.71 % (18961)------------------------------
% 2.66/1.71 % (18961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.71 % (18961)Termination reason: Unknown
% 2.66/1.71 % (18961)Termination phase: shuffling
% 2.66/1.71
% 2.66/1.71 % (18961)Memory used [KB]: 1279
% 2.66/1.71 % (18961)Time elapsed: 0.002 s
% 2.66/1.71 % (18961)Instructions burned: 3 (million)
% 2.66/1.71 % (18961)------------------------------
% 2.66/1.71 % (18961)------------------------------
% 2.66/1.72 % (18963)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_18632 for (2998ds/30Mi)
% 2.66/1.72 % (18963)Instruction limit reached!
% 2.66/1.72 % (18963)------------------------------
% 2.66/1.72 % (18963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.72 % (18963)Termination reason: Unknown
% 2.66/1.72 % (18963)Termination phase: Property scanning
% 2.66/1.72
% 2.66/1.72 % (18963)Memory used [KB]: 1918
% 2.66/1.72 % (18963)Time elapsed: 0.010 s
% 2.66/1.72 % (18963)Instructions burned: 30 (million)
% 2.66/1.72 % (18963)------------------------------
% 2.66/1.72 % (18963)------------------------------
% 2.66/1.72 % (18967)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_18632 for (2998ds/127Mi)
% 2.66/1.73 % (18971)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_18632 for (2998ds/100Mi)
% 2.66/1.76 % (18971)Instruction limit reached!
% 2.66/1.76 % (18971)------------------------------
% 2.66/1.76 % (18971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.76 % (18971)Termination reason: Unknown
% 2.66/1.76 % (18971)Termination phase: Saturation
% 2.66/1.76
% 2.66/1.76 % (18971)Memory used [KB]: 6780
% 2.66/1.76 % (18971)Time elapsed: 0.027 s
% 2.66/1.76 % (18971)Instructions burned: 102 (million)
% 2.66/1.76 % (18971)------------------------------
% 2.66/1.76 % (18971)------------------------------
% 2.66/1.76 % (18967)Instruction limit reached!
% 2.66/1.76 % (18967)------------------------------
% 2.66/1.76 % (18967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.76 % (18967)Termination reason: Unknown
% 2.66/1.76 % (18967)Termination phase: Saturation
% 2.66/1.76
% 2.66/1.76 % (18967)Memory used [KB]: 6908
% 2.66/1.76 % (18967)Time elapsed: 0.037 s
% 2.66/1.76 % (18967)Instructions burned: 128 (million)
% 2.66/1.76 % (18967)------------------------------
% 2.66/1.76 % (18967)------------------------------
% 2.66/1.77 % (18986)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_18632 for (2997ds/3Mi)
% 2.66/1.77 % (18986)Instruction limit reached!
% 2.66/1.77 % (18986)------------------------------
% 2.66/1.77 % (18986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.77 % (18986)Termination reason: Unknown
% 2.66/1.77 % (18986)Termination phase: shuffling
% 2.66/1.77
% 2.66/1.77 % (18986)Memory used [KB]: 1279
% 2.66/1.77 % (18986)Time elapsed: 0.002 s
% 2.66/1.77 % (18986)Instructions burned: 3 (million)
% 2.66/1.77 % (18986)------------------------------
% 2.66/1.77 % (18986)------------------------------
% 2.66/1.77 % (18987)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_18632 for (2997ds/20Mi)
% 2.66/1.78 % (18987)Instruction limit reached!
% 2.66/1.78 % (18987)------------------------------
% 2.66/1.78 % (18987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.78 % (18987)Termination reason: Unknown
% 2.66/1.78 % (18987)Termination phase: Property scanning
% 2.66/1.78
% 2.66/1.78 % (18987)Memory used [KB]: 1663
% 2.66/1.78 % (18987)Time elapsed: 0.008 s
% 2.66/1.78 % (18987)Instructions burned: 22 (million)
% 2.66/1.78 % (18987)------------------------------
% 2.66/1.78 % (18987)------------------------------
% 2.66/1.78 % (18991)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_18632 for (2997ds/86Mi)
% 2.66/1.78 % (18938)Instruction limit reached!
% 2.66/1.78 % (18938)------------------------------
% 2.66/1.78 % (18938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.78 % (18938)Termination reason: Unknown
% 2.66/1.78 % (18938)Termination phase: Saturation
% 2.66/1.78
% 2.66/1.78 % (18938)Memory used [KB]: 8187
% 2.66/1.78 % (18938)Time elapsed: 0.120 s
% 2.66/1.78 % (18938)Instructions burned: 379 (million)
% 2.66/1.78 % (18938)------------------------------
% 2.66/1.78 % (18938)------------------------------
% 2.66/1.79 % (18994)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_18632 for (2997ds/107Mi)
% 2.66/1.79 % (18996)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_18632 for (2997ds/39Mi)
% 2.66/1.80 % (18991)Instruction limit reached!
% 2.66/1.80 % (18991)------------------------------
% 2.66/1.80 % (18991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.80 % (18991)Termination reason: Unknown
% 2.66/1.80 % (18991)Termination phase: Saturation
% 2.66/1.80
% 2.66/1.80 % (18991)Memory used [KB]: 6652
% 2.66/1.80 % (18991)Time elapsed: 0.023 s
% 2.66/1.80 % (18991)Instructions burned: 86 (million)
% 2.66/1.80 % (18991)------------------------------
% 2.66/1.80 % (18991)------------------------------
% 2.66/1.80 % (18996)Instruction limit reached!
% 2.66/1.80 % (18996)------------------------------
% 2.66/1.80 % (18996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.80 % (18996)Termination reason: Unknown
% 2.66/1.80 % (18996)Termination phase: Property scanning
% 2.66/1.80
% 2.66/1.80 % (18996)Memory used [KB]: 1918
% 2.66/1.80 % (18996)Time elapsed: 0.012 s
% 2.66/1.80 % (18996)Instructions burned: 40 (million)
% 2.66/1.80 % (18996)------------------------------
% 2.66/1.80 % (18996)------------------------------
% 2.66/1.81 % (19001)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_18632 for (2997ds/448Mi)
% 2.66/1.81 % (19002)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_18632 for (2997ds/46Mi)
% 2.66/1.82 % (18994)Instruction limit reached!
% 2.66/1.82 % (18994)------------------------------
% 2.66/1.82 % (18994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.82 % (18994)Termination reason: Unknown
% 2.66/1.82 % (18994)Termination phase: Saturation
% 2.66/1.82
% 2.66/1.82 % (18994)Memory used [KB]: 6780
% 2.66/1.82 % (18994)Time elapsed: 0.031 s
% 2.66/1.82 % (18994)Instructions burned: 109 (million)
% 2.66/1.82 % (18994)------------------------------
% 2.66/1.82 % (18994)------------------------------
% 2.66/1.83 % (19002)Instruction limit reached!
% 2.66/1.83 % (19002)------------------------------
% 2.66/1.83 % (19002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.83 % (19002)Termination reason: Unknown
% 2.66/1.83 % (19002)Termination phase: SInE selection
% 2.66/1.83
% 2.66/1.83 % (19002)Memory used [KB]: 1918
% 2.66/1.83 % (19002)Time elapsed: 0.014 s
% 2.66/1.83 % (19002)Instructions burned: 47 (million)
% 2.66/1.83 % (19002)------------------------------
% 2.66/1.83 % (19002)------------------------------
% 2.66/1.83 % (19009)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_18632 for (2997ds/98Mi)
% 2.66/1.84 % (19012)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_18632 for (2997ds/507Mi)
% 2.66/1.84 % (18915)Instruction limit reached!
% 2.66/1.84 % (18915)------------------------------
% 2.66/1.84 % (18915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.84 % (18915)Termination reason: Unknown
% 2.66/1.84 % (18915)Termination phase: Saturation
% 2.66/1.84
% 2.66/1.84 % (18915)Memory used [KB]: 9466
% 2.66/1.84 % (18915)Time elapsed: 0.222 s
% 2.66/1.84 % (18915)Instructions burned: 710 (million)
% 2.66/1.84 % (18915)------------------------------
% 2.66/1.84 % (18915)------------------------------
% 2.66/1.85 % (19019)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_18632 for (2996ds/149Mi)
% 2.66/1.86 % (19009)Instruction limit reached!
% 2.66/1.86 % (19009)------------------------------
% 2.66/1.86 % (19009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.86 % (19009)Termination reason: Unknown
% 2.66/1.86 % (19009)Termination phase: Saturation
% 2.66/1.86
% 2.66/1.86 % (19009)Memory used [KB]: 2174
% 2.66/1.86 % (19009)Time elapsed: 0.028 s
% 2.66/1.86 % (19009)Instructions burned: 101 (million)
% 2.66/1.86 % (19009)------------------------------
% 2.66/1.86 % (19009)------------------------------
% 2.66/1.87 % (19023)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_18632 for (2996ds/39Mi)
% 2.66/1.87 % (18939)Instruction limit reached!
% 2.66/1.87 % (18939)------------------------------
% 2.66/1.87 % (18939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.87 % (18939)Termination reason: Unknown
% 2.66/1.87 % (18939)Termination phase: Saturation
% 2.66/1.87
% 2.66/1.87 % (18939)Memory used [KB]: 6908
% 2.66/1.87 % (18939)Time elapsed: 0.201 s
% 2.66/1.87 % (18939)Instructions burned: 780 (million)
% 2.66/1.87 % (18939)------------------------------
% 2.66/1.87 % (18939)------------------------------
% 2.66/1.88 % (19023)Instruction limit reached!
% 2.66/1.88 % (19023)------------------------------
% 2.66/1.88 % (19023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.88 % (19023)Termination reason: Unknown
% 2.66/1.88 % (19023)Termination phase: Property scanning
% 2.66/1.88
% 2.66/1.88 % (19023)Memory used [KB]: 1918
% 2.66/1.88 % (19023)Time elapsed: 0.013 s
% 2.66/1.88 % (19023)Instructions burned: 42 (million)
% 2.66/1.88 % (19023)------------------------------
% 2.66/1.88 % (19023)------------------------------
% 2.66/1.88 % (19026)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_18632 for (2996ds/6Mi)
% 2.66/1.88 % (19026)Instruction limit reached!
% 2.66/1.88 % (19026)------------------------------
% 2.66/1.88 % (19026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.88 % (19026)Termination reason: Unknown
% 2.66/1.88 % (19026)Termination phase: shuffling
% 2.66/1.88
% 2.66/1.88 % (19026)Memory used [KB]: 1407
% 2.66/1.88 % (19026)Time elapsed: 0.003 s
% 2.66/1.88 % (19026)Instructions burned: 6 (million)
% 2.66/1.88 % (19026)------------------------------
% 2.66/1.88 % (19026)------------------------------
% 2.66/1.89 % (19032)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_18632 for (2996ds/1087Mi)
% 2.66/1.89 % (19035)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_18632 for (2996ds/47Mi)
% 2.66/1.89 % (18883)Instruction limit reached!
% 2.66/1.89 % (18883)------------------------------
% 2.66/1.89 % (18883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.89 % (18883)Termination reason: Unknown
% 2.66/1.89 % (18883)Termination phase: Saturation
% 2.66/1.89
% 2.66/1.89 % (18883)Memory used [KB]: 10362
% 2.66/1.89 % (18883)Time elapsed: 0.306 s
% 2.66/1.89 % (18883)Instructions burned: 1041 (million)
% 2.66/1.89 % (18883)------------------------------
% 2.66/1.89 % (18883)------------------------------
% 2.66/1.90 % (19019)Instruction limit reached!
% 2.66/1.90 % (19019)------------------------------
% 2.66/1.90 % (19019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.90 % (19019)Termination reason: Unknown
% 2.66/1.90 % (19019)Termination phase: Saturation
% 2.66/1.90
% 2.66/1.90 % (19019)Memory used [KB]: 7291
% 2.66/1.90 % (19019)Time elapsed: 0.043 s
% 2.66/1.90 % (19019)Instructions burned: 150 (million)
% 2.66/1.90 % (19019)------------------------------
% 2.66/1.90 % (19019)------------------------------
% 2.66/1.90 % (19035)Instruction limit reached!
% 2.66/1.90 % (19035)------------------------------
% 2.66/1.90 % (19035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.90 % (19035)Termination reason: Unknown
% 2.66/1.90 % (19035)Termination phase: Property scanning
% 2.66/1.90
% 2.66/1.90 % (19035)Memory used [KB]: 1918
% 2.66/1.90 % (19035)Time elapsed: 0.014 s
% 2.66/1.90 % (19035)Instructions burned: 50 (million)
% 2.66/1.90 % (19035)------------------------------
% 2.66/1.90 % (19035)------------------------------
% 2.66/1.91 % (19046)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_18632 for (2996ds/432Mi)
% 2.66/1.91 % (19045)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_18632 for (2996ds/44Mi)
% 2.66/1.91 % (19052)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_18632 for (2996ds/62Mi)
% 2.66/1.92 % (19001)Instruction limit reached!
% 2.66/1.92 % (19001)------------------------------
% 2.66/1.92 % (19001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.92 % (19001)Termination reason: Unknown
% 2.66/1.92 % (19001)Termination phase: Saturation
% 2.66/1.92
% 2.66/1.92 % (19001)Memory used [KB]: 6780
% 2.66/1.92 % (19001)Time elapsed: 0.108 s
% 2.66/1.92 % (19001)Instructions burned: 450 (million)
% 2.66/1.92 % (19001)------------------------------
% 2.66/1.92 % (19001)------------------------------
% 2.66/1.92 % (19045)Instruction limit reached!
% 2.66/1.92 % (19045)------------------------------
% 2.66/1.92 % (19045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.92 % (19045)Termination reason: Unknown
% 2.66/1.92 % (19045)Termination phase: SInE selection
% 2.66/1.92
% 2.66/1.92 % (19045)Memory used [KB]: 1918
% 2.66/1.92 % (19045)Time elapsed: 0.014 s
% 2.66/1.92 % (19045)Instructions burned: 46 (million)
% 2.66/1.92 % (19045)------------------------------
% 2.66/1.92 % (19045)------------------------------
% 2.66/1.93 % (19063)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_18632 for (2996ds/31Mi)
% 2.66/1.93 % (19052)Instruction limit reached!
% 2.66/1.93 % (19052)------------------------------
% 2.66/1.93 % (19052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.93 % (19052)Termination reason: Unknown
% 2.66/1.93 % (19052)Termination phase: Property scanning
% 2.66/1.93
% 2.66/1.93 % (19052)Memory used [KB]: 1918
% 2.66/1.93 % (19052)Time elapsed: 0.017 s
% 2.66/1.93 % (19052)Instructions burned: 62 (million)
% 2.66/1.93 % (19052)------------------------------
% 2.66/1.93 % (19052)------------------------------
% 2.66/1.93 % (19064)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_18632 for (2996ds/96Mi)
% 2.66/1.94 % (19063)Instruction limit reached!
% 2.66/1.94 % (19063)------------------------------
% 2.66/1.94 % (19063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.94 % (19063)Termination reason: Unknown
% 2.66/1.94 % (19063)Termination phase: Property scanning
% 2.66/1.94
% 2.66/1.94 % (19063)Memory used [KB]: 1791
% 2.66/1.94 % (19063)Time elapsed: 0.010 s
% 2.66/1.94 % (19063)Instructions burned: 31 (million)
% 2.66/1.94 % (19063)------------------------------
% 2.66/1.94 % (19063)------------------------------
% 2.66/1.94 % (19067)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_18632 for (2996ds/453Mi)
% 2.66/1.95 % (19072)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_18632 for (2996ds/71Mi)
% 2.66/1.96 % (19064)Instruction limit reached!
% 2.66/1.96 % (19064)------------------------------
% 2.66/1.96 % (19064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.96 % (19064)Termination reason: Unknown
% 2.66/1.96 % (19064)Termination phase: Saturation
% 2.66/1.96
% 2.66/1.96 % (19064)Memory used [KB]: 6780
% 2.66/1.96 % (19064)Time elapsed: 0.029 s
% 2.66/1.96 % (19064)Instructions burned: 97 (million)
% 2.66/1.96 % (19064)------------------------------
% 2.66/1.96 % (19064)------------------------------
% 2.66/1.96 % (19072)Instruction limit reached!
% 2.66/1.96 % (19072)------------------------------
% 2.66/1.96 % (19072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.96 % (19072)Termination reason: Unknown
% 2.66/1.96 % (19072)Termination phase: Property scanning
% 2.66/1.96
% 2.66/1.96 % (19072)Memory used [KB]: 2046
% 2.66/1.96 % (19072)Time elapsed: 0.020 s
% 2.66/1.96 % (19072)Instructions burned: 74 (million)
% 2.66/1.96 % (19072)------------------------------
% 2.66/1.96 % (19072)------------------------------
% 2.66/1.97 % (19074)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_18632 for (2995ds/83Mi)
% 2.66/1.97 % (19075)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_18632 for (2995ds/11Mi)
% 2.66/1.98 % (19075)Instruction limit reached!
% 2.66/1.98 % (19075)------------------------------
% 2.66/1.98 % (19075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.98 % (19075)Termination reason: Unknown
% 2.66/1.98 % (19075)Termination phase: shuffling
% 2.66/1.98
% 2.66/1.98 % (19075)Memory used [KB]: 1535
% 2.66/1.98 % (19075)Time elapsed: 0.005 s
% 2.66/1.98 % (19075)Instructions burned: 13 (million)
% 2.66/1.98 % (19075)------------------------------
% 2.66/1.98 % (19075)------------------------------
% 2.66/1.98 % (18950)Instruction limit reached!
% 2.66/1.98 % (18950)------------------------------
% 2.66/1.98 % (18950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.98 % (18950)Termination reason: Unknown
% 2.66/1.98 % (18950)Termination phase: Saturation
% 2.66/1.98
% 2.66/1.98 % (18950)Memory used [KB]: 8443
% 2.66/1.98 % (18950)Time elapsed: 0.314 s
% 2.66/1.98 % (18950)Instructions burned: 879 (million)
% 2.66/1.98 % (18950)------------------------------
% 2.66/1.98 % (18950)------------------------------
% 2.66/1.99 % (19076)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_18632 for (2995ds/41Mi)
% 2.66/1.99 % (19077)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_18632 for (2995ds/6Mi)
% 2.66/1.99 % (19074)Instruction limit reached!
% 2.66/1.99 % (19074)------------------------------
% 2.66/1.99 % (19074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.99 % (19074)Termination reason: Unknown
% 2.66/1.99 % (19074)Termination phase: Function definition elimination
% 2.66/1.99
% 2.66/1.99 % (19074)Memory used [KB]: 2046
% 2.66/1.99 % (19074)Time elapsed: 0.024 s
% 2.66/1.99 % (19074)Instructions burned: 83 (million)
% 2.66/1.99 % (19074)------------------------------
% 2.66/1.99 % (19074)------------------------------
% 2.66/1.99 % (19077)Instruction limit reached!
% 2.66/1.99 % (19077)------------------------------
% 2.66/1.99 % (19077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.99 % (19077)Termination reason: Unknown
% 2.66/1.99 % (19077)Termination phase: shuffling
% 2.66/1.99
% 2.66/1.99 % (19077)Memory used [KB]: 1407
% 2.66/1.99 % (19077)Time elapsed: 0.004 s
% 2.66/1.99 % (19077)Instructions burned: 9 (million)
% 2.66/1.99 % (19077)------------------------------
% 2.66/1.99 % (19077)------------------------------
% 2.66/1.99 % (19012)Instruction limit reached!
% 2.66/1.99 % (19012)------------------------------
% 2.66/1.99 % (19012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.99 % (19012)Termination reason: Unknown
% 2.66/1.99 % (19012)Termination phase: Saturation
% 2.66/1.99
% 2.66/1.99 % (19012)Memory used [KB]: 7547
% 2.66/1.99 % (19012)Time elapsed: 0.160 s
% 2.66/1.99 % (19012)Instructions burned: 509 (million)
% 2.66/1.99 % (19012)------------------------------
% 2.66/1.99 % (19012)------------------------------
% 2.66/2.00 % (19076)Instruction limit reached!
% 2.66/2.00 % (19076)------------------------------
% 2.66/2.00 % (19076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/2.00 % (19076)Termination reason: Unknown
% 2.66/2.00 % (19076)Termination phase: Property scanning
% 2.66/2.00
% 2.66/2.00 % (19076)Memory used [KB]: 1918
% 2.66/2.00 % (19076)Time elapsed: 0.012 s
% 2.66/2.00 % (19076)Instructions burned: 43 (million)
% 2.66/2.00 % (19076)------------------------------
% 2.66/2.00 % (19076)------------------------------
% 2.66/2.00 % (19080)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_18632 for (2995ds/343Mi)
% 2.66/2.00 % (19081)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_18632 for (2995ds/109Mi)
% 2.66/2.01 % (19079)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_18632 for (2995ds/150Mi)
% 2.66/2.01 % (19082)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_18632 for (2995ds/253Mi)
% 2.66/2.01 % (19046)Instruction limit reached!
% 2.66/2.01 % (19046)------------------------------
% 2.66/2.01 % (19046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/2.01 % (19046)Termination reason: Unknown
% 2.66/2.01 % (19046)Termination phase: Saturation
% 2.66/2.01
% 2.66/2.01 % (19046)Memory used [KB]: 3070
% 2.66/2.01 % (19046)Time elapsed: 0.107 s
% 2.66/2.01 % (19046)Instructions burned: 432 (million)
% 2.66/2.01 % (19046)------------------------------
% 2.66/2.01 % (19046)------------------------------
% 5.86/2.02 % (19083)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_18632 for (2995ds/140Mi)
% 5.86/2.03 % (19081)Instruction limit reached!
% 5.86/2.03 % (19081)------------------------------
% 5.86/2.03 % (19081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.86/2.03 % (19081)Termination reason: Unknown
% 5.86/2.03 % (19081)Termination phase: Saturation
% 5.86/2.03
% 5.86/2.03 % (19081)Memory used [KB]: 6780
% 5.86/2.03 % (19081)Time elapsed: 0.029 s
% 5.86/2.03 % (19081)Instructions burned: 110 (million)
% 5.86/2.03 % (19081)------------------------------
% 5.86/2.03 % (19081)------------------------------
% 5.86/2.04 % (19084)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_18632 for (2995ds/614Mi)
% 5.86/2.05 % (19067)Instruction limit reached!
% 5.86/2.05 % (19067)------------------------------
% 5.86/2.05 % (19067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.86/2.05 % (19067)Termination reason: Unknown
% 5.86/2.05 % (19067)Termination phase: Saturation
% 5.86/2.05
% 5.86/2.05 % (19067)Memory used [KB]: 6780
% 5.86/2.05 % (19067)Time elapsed: 0.110 s
% 5.86/2.05 % (19067)Instructions burned: 456 (million)
% 5.86/2.05 % (19067)------------------------------
% 5.86/2.05 % (19067)------------------------------
% 5.86/2.06 % (19085)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_18632 for (2994ds/202Mi)
% 5.86/2.06 % (19083)Instruction limit reached!
% 5.86/2.06 % (19083)------------------------------
% 5.86/2.06 % (19083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.86/2.06 % (19083)Termination reason: Unknown
% 5.86/2.06 % (19083)Termination phase: Saturation
% 5.86/2.06
% 5.86/2.06 % (19083)Memory used [KB]: 6780
% 5.86/2.06 % (19083)Time elapsed: 0.038 s
% 5.86/2.06 % (19083)Instructions burned: 140 (million)
% 5.86/2.06 % (19083)------------------------------
% 5.86/2.06 % (19083)------------------------------
% 5.86/2.07 % (19086)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_18632 for (2994ds/339Mi)
% 5.86/2.08 % (19082)Instruction limit reached!
% 5.86/2.08 % (19082)------------------------------
% 5.86/2.08 % (19082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.86/2.08 % (19082)Termination reason: Unknown
% 5.86/2.08 % (19082)Termination phase: Saturation
% 5.86/2.08
% 5.86/2.08 % (19082)Memory used [KB]: 8315
% 5.86/2.08 % (19082)Time elapsed: 0.077 s
% 5.86/2.08 % (19082)Instructions burned: 255 (million)
% 5.86/2.08 % (19082)------------------------------
% 5.86/2.08 % (19082)------------------------------
% 5.86/2.09 % (19079)Instruction limit reached!
% 5.86/2.09 % (19079)------------------------------
% 5.86/2.09 % (19079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.86/2.09 % (19079)Termination reason: Unknown
% 5.86/2.09 % (19079)Termination phase: Saturation
% 5.86/2.09
% 5.86/2.09 % (19079)Memory used [KB]: 7931
% 5.86/2.09 % (19079)Time elapsed: 0.084 s
% 5.86/2.09 % (19079)Instructions burned: 150 (million)
% 5.86/2.09 % (19079)------------------------------
% 5.86/2.09 % (19079)------------------------------
% 5.86/2.09 % (19087)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_18632 for (2994ds/283Mi)
% 5.86/2.10 % (19080)Instruction limit reached!
% 5.86/2.10 % (19080)------------------------------
% 5.86/2.10 % (19080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.86/2.10 % (19080)Termination reason: Unknown
% 5.86/2.10 % (19080)Termination phase: Saturation
% 5.86/2.10
% 5.86/2.10 % (19080)Memory used [KB]: 7931
% 5.86/2.10 % (19080)Time elapsed: 0.098 s
% 5.86/2.10 % (19080)Instructions burned: 345 (million)
% 5.86/2.10 % (19080)------------------------------
% 5.86/2.10 % (19080)------------------------------
% 5.86/2.11 % (19088)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_18632 for (2994ds/134Mi)
% 5.86/2.11 % (19089)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_18632 for (2994ds/298Mi)
% 6.37/2.12 % (19085)Instruction limit reached!
% 6.37/2.12 % (19085)------------------------------
% 6.37/2.12 % (19085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.37/2.12 % (19085)Termination reason: Unknown
% 6.37/2.12 % (19085)Termination phase: Saturation
% 6.37/2.12
% 6.37/2.12 % (19085)Memory used [KB]: 8827
% 6.37/2.12 % (19085)Time elapsed: 0.060 s
% 6.37/2.12 % (19085)Instructions burned: 202 (million)
% 6.37/2.12 % (19085)------------------------------
% 6.37/2.12 % (19085)------------------------------
% 6.37/2.13 % (19090)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_18632 for (2994ds/192Mi)
% 6.37/2.15 % (19088)Instruction limit reached!
% 6.37/2.15 % (19088)------------------------------
% 6.37/2.15 % (19088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.37/2.15 % (19088)Termination reason: Unknown
% 6.37/2.15 % (19088)Termination phase: Saturation
% 6.37/2.15
% 6.37/2.15 % (19088)Memory used [KB]: 6908
% 6.37/2.15 % (19088)Time elapsed: 0.043 s
% 6.37/2.15 % (19088)Instructions burned: 134 (million)
% 6.37/2.15 % (19088)------------------------------
% 6.37/2.15 % (19088)------------------------------
% 6.37/2.16 % (19091)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_18632 for (2994ds/258Mi)
% 6.37/2.16 % (19087)Instruction limit reached!
% 6.37/2.16 % (19087)------------------------------
% 6.37/2.16 % (19087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.37/2.16 % (19087)Termination reason: Unknown
% 6.37/2.16 % (19087)Termination phase: Saturation
% 6.37/2.16
% 6.37/2.16 % (19087)Memory used [KB]: 8827
% 6.37/2.16 % (19087)Time elapsed: 0.071 s
% 6.37/2.16 % (19087)Instructions burned: 283 (million)
% 6.37/2.16 % (19087)------------------------------
% 6.37/2.16 % (19087)------------------------------
% 6.37/2.16 % (19086)Instruction limit reached!
% 6.37/2.16 % (19086)------------------------------
% 6.37/2.16 % (19086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.37/2.16 % (19086)Termination reason: Unknown
% 6.37/2.16 % (19086)Termination phase: Saturation
% 6.37/2.16
% 6.37/2.16 % (19086)Memory used [KB]: 7931
% 6.37/2.16 % (19086)Time elapsed: 0.098 s
% 6.37/2.16 % (19086)Instructions burned: 341 (million)
% 6.37/2.16 % (19086)------------------------------
% 6.37/2.16 % (19086)------------------------------
% 6.37/2.17 % (19092)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_18632 for (2993ds/90Mi)
% 6.37/2.17 % (19093)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_18632 for (2993ds/231Mi)
% 6.37/2.18 % (19090)Instruction limit reached!
% 6.37/2.18 % (19090)------------------------------
% 6.37/2.18 % (19090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.37/2.18 % (19090)Termination reason: Unknown
% 6.37/2.18 % (19090)Termination phase: Saturation
% 6.37/2.18
% 6.37/2.18 % (19090)Memory used [KB]: 7547
% 6.37/2.18 % (19090)Time elapsed: 0.053 s
% 6.37/2.18 % (19090)Instructions burned: 194 (million)
% 6.37/2.18 % (19090)------------------------------
% 6.37/2.18 % (19090)------------------------------
% 6.37/2.18 % (19089)Instruction limit reached!
% 6.37/2.18 % (19089)------------------------------
% 6.37/2.18 % (19089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.37/2.18 % (19089)Termination reason: Unknown
% 6.37/2.18 % (19089)Termination phase: Saturation
% 6.37/2.18
% 6.37/2.18 % (19089)Memory used [KB]: 6780
% 6.37/2.18 % (19089)Time elapsed: 0.076 s
% 6.37/2.18 % (19089)Instructions burned: 299 (million)
% 6.37/2.18 % (19089)------------------------------
% 6.37/2.18 % (19089)------------------------------
% 6.37/2.19 % (19094)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_18632 for (2993ds/458Mi)
% 6.37/2.19 % (19095)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_18632 for (2993ds/31Mi)
% 6.90/2.20 % (19092)Instruction limit reached!
% 6.90/2.20 % (19092)------------------------------
% 6.90/2.20 % (19092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.20 % (19092)Termination reason: Unknown
% 6.90/2.20 % (19092)Termination phase: Property scanning
% 6.90/2.20
% 6.90/2.20 % (19092)Memory used [KB]: 2558
% 6.90/2.20 % (19092)Time elapsed: 0.026 s
% 6.90/2.20 % (19092)Instructions burned: 93 (million)
% 6.90/2.20 % (19092)------------------------------
% 6.90/2.20 % (19092)------------------------------
% 6.90/2.20 % (19095)Instruction limit reached!
% 6.90/2.20 % (19095)------------------------------
% 6.90/2.20 % (19095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.20 % (19095)Termination reason: Unknown
% 6.90/2.20 % (19095)Termination phase: Property scanning
% 6.90/2.20
% 6.90/2.20 % (19095)Memory used [KB]: 1791
% 6.90/2.20 % (19095)Time elapsed: 0.010 s
% 6.90/2.20 % (19095)Instructions burned: 33 (million)
% 6.90/2.20 % (19095)------------------------------
% 6.90/2.20 % (19095)------------------------------
% 6.90/2.21 % (19096)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_18632 for (2993ds/297Mi)
% 6.90/2.21 % (19097)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_18632 for (2993ds/987Mi)
% 6.90/2.23 % (19084)Instruction limit reached!
% 6.90/2.23 % (19084)------------------------------
% 6.90/2.23 % (19084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.23 % (19084)Termination reason: Unknown
% 6.90/2.23 % (19084)Termination phase: Saturation
% 6.90/2.23
% 6.90/2.23 % (19084)Memory used [KB]: 8699
% 6.90/2.23 % (19084)Time elapsed: 0.188 s
% 6.90/2.23 % (19084)Instructions burned: 614 (million)
% 6.90/2.23 % (19084)------------------------------
% 6.90/2.23 % (19084)------------------------------
% 6.90/2.23 % (19091)Instruction limit reached!
% 6.90/2.23 % (19091)------------------------------
% 6.90/2.23 % (19091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.23 % (19091)Termination reason: Unknown
% 6.90/2.23 % (19091)Termination phase: Saturation
% 6.90/2.23
% 6.90/2.23 % (19091)Memory used [KB]: 7547
% 6.90/2.23 % (19091)Time elapsed: 0.078 s
% 6.90/2.23 % (19091)Instructions burned: 259 (million)
% 6.90/2.23 % (19091)------------------------------
% 6.90/2.23 % (19091)------------------------------
% 6.90/2.24 % (19098)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_18632 for (2993ds/182Mi)
% 6.90/2.24 % (19093)Instruction limit reached!
% 6.90/2.24 % (19093)------------------------------
% 6.90/2.24 % (19093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.24 % (19093)Termination reason: Unknown
% 6.90/2.24 % (19093)Termination phase: Saturation
% 6.90/2.24
% 6.90/2.24 % (19093)Memory used [KB]: 11129
% 6.90/2.24 % (19093)Time elapsed: 0.091 s
% 6.90/2.24 % (19093)Instructions burned: 232 (million)
% 6.90/2.24 % (19093)------------------------------
% 6.90/2.24 % (19093)------------------------------
% 6.90/2.24 % (19032)Instruction limit reached!
% 6.90/2.24 % (19032)------------------------------
% 6.90/2.24 % (19032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.24 % (19032)Termination reason: Unknown
% 6.90/2.24 % (19032)Termination phase: Saturation
% 6.90/2.24
% 6.90/2.24 % (19032)Memory used [KB]: 10106
% 6.90/2.24 % (19032)Time elapsed: 0.355 s
% 6.90/2.24 % (19032)Instructions burned: 1087 (million)
% 6.90/2.24 % (19032)------------------------------
% 6.90/2.24 % (19032)------------------------------
% 6.90/2.25 % (19099)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_18632 for (2992ds/182Mi)
% 6.90/2.25 % (19100)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_18632 for (2992ds/154Mi)
% 6.90/2.25 % (19101)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_18632 for (2992ds/79Mi)
% 6.90/2.27 % (19101)Instruction limit reached!
% 6.90/2.27 % (19101)------------------------------
% 6.90/2.27 % (19101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.27 % (19101)Termination reason: Unknown
% 6.90/2.27 % (19101)Termination phase: Property scanning
% 6.90/2.27
% 6.90/2.27 % (19101)Memory used [KB]: 2046
% 6.90/2.27 % (19101)Time elapsed: 0.023 s
% 6.90/2.27 % (19101)Instructions burned: 82 (million)
% 6.90/2.27 % (19101)------------------------------
% 6.90/2.27 % (19101)------------------------------
% 6.90/2.28 % (19096)Instruction limit reached!
% 6.90/2.28 % (19096)------------------------------
% 6.90/2.28 % (19096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.28 % (19096)Termination reason: Unknown
% 6.90/2.28 % (19096)Termination phase: Saturation
% 6.90/2.28
% 6.90/2.28 % (19096)Memory used [KB]: 8827
% 6.90/2.28 % (19096)Time elapsed: 0.100 s
% 6.90/2.28 % (19096)Instructions burned: 300 (million)
% 6.90/2.28 % (19096)------------------------------
% 6.90/2.28 % (19096)------------------------------
% 6.90/2.28 % (19102)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_18632 for (2992ds/216Mi)
% 6.90/2.29 % (19098)Instruction limit reached!
% 6.90/2.29 % (19098)------------------------------
% 6.90/2.29 % (19098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.29 % (19098)Termination reason: Unknown
% 6.90/2.29 % (19098)Termination phase: Saturation
% 6.90/2.29
% 6.90/2.29 % (19098)Memory used [KB]: 7419
% 6.90/2.29 % (19098)Time elapsed: 0.051 s
% 6.90/2.29 % (19098)Instructions burned: 184 (million)
% 6.90/2.29 % (19098)------------------------------
% 6.90/2.29 % (19098)------------------------------
% 6.90/2.29 % (19100)Instruction limit reached!
% 6.90/2.29 % (19100)------------------------------
% 6.90/2.29 % (19100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.29 % (19100)Termination reason: Unknown
% 6.90/2.29 % (19100)Termination phase: Saturation
% 6.90/2.29
% 6.90/2.29 % (19100)Memory used [KB]: 6652
% 6.90/2.29 % (19100)Time elapsed: 0.041 s
% 6.90/2.29 % (19100)Instructions burned: 154 (million)
% 6.90/2.29 % (19100)------------------------------
% 6.90/2.29 % (19100)------------------------------
% 6.90/2.29 % (19103)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_18632 for (2992ds/114Mi)
% 7.61/2.30 % (19104)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_18632 for (2992ds/922Mi)
% 7.61/2.30 % (19105)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_18632 for (2992ds/182Mi)
% 7.61/2.30 % (19099)Instruction limit reached!
% 7.61/2.30 % (19099)------------------------------
% 7.61/2.30 % (19099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.61/2.30 % (19099)Termination reason: Unknown
% 7.61/2.30 % (19099)Termination phase: Saturation
% 7.61/2.30
% 7.61/2.30 % (19099)Memory used [KB]: 9850
% 7.61/2.30 % (19099)Time elapsed: 0.059 s
% 7.61/2.30 % (19099)Instructions burned: 185 (million)
% 7.61/2.30 % (19099)------------------------------
% 7.61/2.30 % (19099)------------------------------
% 7.61/2.31 % (19106)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_18632 for (2992ds/164Mi)
% 7.61/2.32 % (19103)Instruction limit reached!
% 7.61/2.32 % (19103)------------------------------
% 7.61/2.32 % (19103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.61/2.32 % (19103)Termination reason: Unknown
% 7.61/2.32 % (19103)Termination phase: Saturation
% 7.61/2.32
% 7.61/2.32 % (19103)Memory used [KB]: 6908
% 7.61/2.32 % (19103)Time elapsed: 0.031 s
% 7.61/2.32 % (19103)Instructions burned: 116 (million)
% 7.61/2.32 % (19103)------------------------------
% 7.61/2.32 % (19103)------------------------------
% 7.61/2.32 % (19094)Instruction limit reached!
% 7.61/2.32 % (19094)------------------------------
% 7.61/2.32 % (19094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.61/2.32 % (19094)Termination reason: Unknown
% 7.61/2.32 % (19094)Termination phase: Saturation
% 7.61/2.32
% 7.61/2.32 % (19094)Memory used [KB]: 8315
% 7.61/2.32 % (19094)Time elapsed: 0.162 s
% 7.61/2.32 % (19094)Instructions burned: 459 (million)
% 7.61/2.32 % (19094)------------------------------
% 7.61/2.32 % (19094)------------------------------
% 7.61/2.33 % (19107)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_18632 for (2992ds/50Mi)
% 7.61/2.33 % (19108)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_18632 for (2992ds/368Mi)
% 7.61/2.34 % (19102)Instruction limit reached!
% 7.61/2.34 % (19102)------------------------------
% 7.61/2.34 % (19102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.61/2.34 % (19102)Termination reason: Unknown
% 7.61/2.34 % (19102)Termination phase: Saturation
% 7.61/2.34
% 7.61/2.34 % (19102)Memory used [KB]: 6780
% 7.61/2.34 % (19102)Time elapsed: 0.055 s
% 7.61/2.34 % (19102)Instructions burned: 218 (million)
% 7.61/2.34 % (19102)------------------------------
% 7.61/2.34 % (19102)------------------------------
% 7.61/2.35 % (19105)Instruction limit reached!
% 7.61/2.35 % (19105)------------------------------
% 7.61/2.35 % (19105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.61/2.35 % (19105)Termination reason: Unknown
% 7.61/2.35 % (19105)Termination phase: Saturation
% 7.61/2.35
% 7.61/2.35 % (19105)Memory used [KB]: 6780
% 7.61/2.35 % (19105)Time elapsed: 0.047 s
% 7.61/2.35 % (19105)Instructions burned: 184 (million)
% 7.61/2.35 % (19105)------------------------------
% 7.61/2.35 % (19105)------------------------------
% 7.61/2.35 % (19107)Instruction limit reached!
% 7.61/2.35 % (19107)------------------------------
% 7.61/2.35 % (19107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.61/2.35 % (19107)Termination reason: Unknown
% 7.61/2.35 % (19107)Termination phase: Property scanning
% 7.61/2.35
% 7.61/2.35 % (19107)Memory used [KB]: 1918
% 7.61/2.35 % (19107)Time elapsed: 0.014 s
% 7.61/2.35 % (19107)Instructions burned: 50 (million)
% 7.61/2.35 % (19107)------------------------------
% 7.61/2.35 % (19107)------------------------------
% 7.61/2.35 % (19109)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_18632 for (2992ds/1021Mi)
% 7.61/2.36 % (19110)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_18632 for (2991ds/267Mi)
% 7.61/2.36 % (19111)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_18632 for (2991ds/204Mi)
% 7.61/2.36 % (19106)Instruction limit reached!
% 7.61/2.36 % (19106)------------------------------
% 7.61/2.36 % (19106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.61/2.36 % (19106)Termination reason: Unknown
% 7.61/2.36 % (19106)Termination phase: Saturation
% 7.61/2.36
% 7.61/2.36 % (19106)Memory used [KB]: 2430
% 7.61/2.36 % (19106)Time elapsed: 0.048 s
% 7.61/2.36 % (19106)Instructions burned: 164 (million)
% 7.61/2.36 % (19106)------------------------------
% 7.61/2.36 % (19106)------------------------------
% 7.61/2.37 % (19112)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_18632 for (2991ds/26Mi)
% 7.61/2.38 % (19112)Instruction limit reached!
% 7.61/2.38 % (19112)------------------------------
% 7.61/2.38 % (19112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.61/2.38 % (19112)Termination reason: Unknown
% 7.61/2.38 % (19112)Termination phase: shuffling
% 7.61/2.38
% 7.61/2.38 % (19112)Memory used [KB]: 1918
% 7.61/2.38 % (19112)Time elapsed: 0.009 s
% 7.61/2.38 % (19112)Instructions burned: 27 (million)
% 7.61/2.38 % (19112)------------------------------
% 7.61/2.38 % (19112)------------------------------
% 7.61/2.39 % (19113)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_18632 for (2991ds/53Mi)
% 8.08/2.40 % (19113)Instruction limit reached!
% 8.08/2.40 % (19113)------------------------------
% 8.08/2.40 % (19113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.08/2.40 % (19113)Termination reason: Unknown
% 8.08/2.40 % (19113)Termination phase: Property scanning
% 8.08/2.40
% 8.08/2.40 % (19113)Memory used [KB]: 1918
% 8.08/2.40 % (19113)Time elapsed: 0.016 s
% 8.08/2.40 % (19113)Instructions burned: 55 (million)
% 8.08/2.40 % (19113)------------------------------
% 8.08/2.40 % (19113)------------------------------
% 8.08/2.41 % (19111)Instruction limit reached!
% 8.08/2.41 % (19111)------------------------------
% 8.08/2.41 % (19111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.08/2.41 % (19111)Termination reason: Unknown
% 8.08/2.41 % (19111)Termination phase: Saturation
% 8.08/2.41
% 8.08/2.41 % (19111)Memory used [KB]: 7419
% 8.08/2.41 % (19111)Time elapsed: 0.055 s
% 8.08/2.41 % (19111)Instructions burned: 204 (million)
% 8.08/2.41 % (19111)------------------------------
% 8.08/2.41 % (19111)------------------------------
% 8.08/2.42 % (19114)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_18632 for (2991ds/4436Mi)
% 8.08/2.42 % (19115)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_18632 for (2991ds/1539Mi)
% 8.08/2.42 % (19110)Instruction limit reached!
% 8.08/2.42 % (19110)------------------------------
% 8.08/2.42 % (19110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.08/2.42 % (19110)Termination reason: Unknown
% 8.08/2.42 % (19110)Termination phase: Saturation
% 8.08/2.42
% 8.08/2.42 % (19110)Memory used [KB]: 7931
% 8.08/2.42 % (19110)Time elapsed: 0.068 s
% 8.08/2.42 % (19110)Instructions burned: 270 (million)
% 8.08/2.42 % (19110)------------------------------
% 8.08/2.42 % (19110)------------------------------
% 8.08/2.43 % (19116)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_18632 for (2991ds/408Mi)
% 8.08/2.44 % (19108)Instruction limit reached!
% 8.08/2.44 % (19108)------------------------------
% 8.08/2.44 % (19108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.08/2.44 % (19108)Termination reason: Unknown
% 8.08/2.44 % (19108)Termination phase: Saturation
% 8.08/2.44
% 8.08/2.44 % (19108)Memory used [KB]: 8059
% 8.08/2.44 % (19108)Time elapsed: 0.109 s
% 8.08/2.44 % (19108)Instructions burned: 368 (million)
% 8.08/2.44 % (19108)------------------------------
% 8.08/2.44 % (19108)------------------------------
% 8.08/2.45 % (19117)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_18632 for (2991ds/5205Mi)
% 8.08/2.45 % (19097)Instruction limit reached!
% 8.08/2.45 % (19097)------------------------------
% 8.08/2.45 % (19097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.08/2.45 % (19097)Termination reason: Unknown
% 8.08/2.45 % (19097)Termination phase: Saturation
% 8.08/2.45
% 8.08/2.45 % (19097)Memory used [KB]: 10234
% 8.08/2.45 % (19097)Time elapsed: 0.242 s
% 8.08/2.45 % (19097)Instructions burned: 989 (million)
% 8.08/2.45 % (19097)------------------------------
% 8.08/2.45 % (19097)------------------------------
% 8.08/2.46 % (19118)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_18632 for (2990ds/1913Mi)
% 8.61/2.56 % (19116)Instruction limit reached!
% 8.61/2.56 % (19116)------------------------------
% 8.61/2.56 % (19116)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.61/2.56 % (19116)Termination reason: Unknown
% 8.61/2.56 % (19116)Termination phase: Saturation
% 8.61/2.56
% 8.61/2.56 % (19116)Memory used [KB]: 9466
% 8.61/2.56 % (19116)Time elapsed: 0.130 s
% 8.61/2.56 % (19116)Instructions burned: 410 (million)
% 8.61/2.56 % (19116)------------------------------
% 8.61/2.56 % (19116)------------------------------
% 8.61/2.57 % (19119)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_18632 for (2989ds/4350Mi)
% 8.61/2.59 % (19104)Instruction limit reached!
% 8.61/2.59 % (19104)------------------------------
% 8.61/2.59 % (19104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.61/2.59 % (19104)Termination reason: Unknown
% 8.61/2.59 % (19104)Termination phase: Saturation
% 8.61/2.59
% 8.61/2.59 % (19104)Memory used [KB]: 9722
% 8.61/2.59 % (19104)Time elapsed: 0.290 s
% 8.61/2.59 % (19104)Instructions burned: 924 (million)
% 8.61/2.59 % (19104)------------------------------
% 8.61/2.59 % (19104)------------------------------
% 9.05/2.60 % (19120)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_18632 for (2989ds/68Mi)
% 9.05/2.61 % (19120)Instruction limit reached!
% 9.05/2.61 % (19120)------------------------------
% 9.05/2.61 % (19120)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.05/2.61 % (19120)Termination reason: Unknown
% 9.05/2.61 % (19120)Termination phase: Property scanning
% 9.05/2.61
% 9.05/2.61 % (19120)Memory used [KB]: 2046
% 9.05/2.61 % (19120)Time elapsed: 0.019 s
% 9.05/2.61 % (19120)Instructions burned: 70 (million)
% 9.05/2.61 % (19120)------------------------------
% 9.05/2.61 % (19120)------------------------------
% 9.05/2.62 % (19121)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_18632 for (2989ds/358Mi)
% 9.05/2.67 % (19109)Instruction limit reached!
% 9.05/2.67 % (19109)------------------------------
% 9.05/2.67 % (19109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.05/2.67 % (19109)Termination reason: Unknown
% 9.05/2.67 % (19109)Termination phase: Saturation
% 9.05/2.67
% 9.05/2.67 % (19109)Memory used [KB]: 10362
% 9.05/2.67 % (19109)Time elapsed: 0.324 s
% 9.05/2.67 % (19109)Instructions burned: 1022 (million)
% 9.05/2.67 % (19109)------------------------------
% 9.05/2.67 % (19109)------------------------------
% 9.05/2.68 % (19122)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_18632 for (2988ds/31Mi)
% 9.05/2.69 % (19122)Instruction limit reached!
% 9.05/2.69 % (19122)------------------------------
% 9.05/2.69 % (19122)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.05/2.69 % (19122)Termination reason: Unknown
% 9.05/2.69 % (19122)Termination phase: Property scanning
% 9.05/2.69
% 9.05/2.69 % (19122)Memory used [KB]: 1791
% 9.05/2.69 % (19122)Time elapsed: 0.010 s
% 9.05/2.69 % (19122)Instructions burned: 32 (million)
% 9.05/2.69 % (19122)------------------------------
% 9.05/2.69 % (19122)------------------------------
% 9.45/2.70 % (19123)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_18632 for (2988ds/279Mi)
% 9.45/2.73 % (19121)Instruction limit reached!
% 9.45/2.73 % (19121)------------------------------
% 9.45/2.73 % (19121)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.45/2.73 % (19121)Termination reason: Unknown
% 9.45/2.73 % (19121)Termination phase: Saturation
% 9.45/2.73
% 9.45/2.73 % (19121)Memory used [KB]: 7803
% 9.45/2.73 % (19121)Time elapsed: 0.105 s
% 9.45/2.73 % (19121)Instructions burned: 358 (million)
% 9.45/2.73 % (19121)------------------------------
% 9.45/2.73 % (19121)------------------------------
% 9.45/2.74 % (19124)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_18632 for (2988ds/258Mi)
% 9.45/2.77 % (19123)Instruction limit reached!
% 9.45/2.77 % (19123)------------------------------
% 9.45/2.77 % (19123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.45/2.77 % (19123)Termination reason: Unknown
% 9.45/2.77 % (19123)Termination phase: Saturation
% 9.45/2.77
% 9.45/2.77 % (19123)Memory used [KB]: 6780
% 9.45/2.77 % (19123)Time elapsed: 0.069 s
% 9.45/2.77 % (19123)Instructions burned: 282 (million)
% 9.45/2.77 % (19123)------------------------------
% 9.45/2.77 % (19123)------------------------------
% 9.45/2.78 % (19125)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_18632 for (2987ds/26Mi)
% 9.45/2.78 % (19125)Instruction limit reached!
% 9.45/2.78 % (19125)------------------------------
% 9.45/2.78 % (19125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.45/2.78 % (19125)Termination reason: Unknown
% 9.45/2.78 % (19125)Termination phase: shuffling
% 9.45/2.78
% 9.45/2.78 % (19125)Memory used [KB]: 1791
% 9.45/2.78 % (19125)Time elapsed: 0.008 s
% 9.45/2.78 % (19125)Instructions burned: 26 (million)
% 9.45/2.78 % (19125)------------------------------
% 9.45/2.78 % (19125)------------------------------
% 9.45/2.79 % (19126)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_18632 for (2987ds/995Mi)
% 9.66/2.81 % (19124)Instruction limit reached!
% 9.66/2.81 % (19124)------------------------------
% 9.66/2.81 % (19124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.66/2.81 % (19124)Termination reason: Unknown
% 9.66/2.81 % (19124)Termination phase: Saturation
% 9.66/2.81
% 9.66/2.81 % (19124)Memory used [KB]: 8059
% 9.66/2.81 % (19124)Time elapsed: 0.071 s
% 9.66/2.81 % (19124)Instructions burned: 259 (million)
% 9.66/2.81 % (19124)------------------------------
% 9.66/2.81 % (19124)------------------------------
% 9.66/2.82 % (19127)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_18632 for (2987ds/373Mi)
% 9.74/2.90 % (19115)Instruction limit reached!
% 9.74/2.90 % (19115)------------------------------
% 9.74/2.90 % (19115)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.74/2.90 % (19115)Termination reason: Unknown
% 9.74/2.90 % (19115)Termination phase: Saturation
% 9.74/2.90
% 9.74/2.90 % (19115)Memory used [KB]: 9338
% 9.74/2.90 % (19115)Time elapsed: 0.484 s
% 9.74/2.90 % (19115)Instructions burned: 1541 (million)
% 9.74/2.90 % (19115)------------------------------
% 9.74/2.90 % (19115)------------------------------
% 9.74/2.91 % (19128)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_18632 for (2986ds/253Mi)
% 9.74/2.93 % (19127)Instruction limit reached!
% 9.74/2.93 % (19127)------------------------------
% 9.74/2.93 % (19127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.74/2.93 % (19127)Termination reason: Unknown
% 9.74/2.93 % (19127)Termination phase: Saturation
% 9.74/2.93
% 9.74/2.93 % (19127)Memory used [KB]: 7931
% 9.74/2.93 % (19127)Time elapsed: 0.115 s
% 9.74/2.93 % (19127)Instructions burned: 374 (million)
% 9.74/2.93 % (19127)------------------------------
% 9.74/2.93 % (19127)------------------------------
% 9.74/2.94 % (19129)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_18632 for (2986ds/832Mi)
% 9.74/2.97 % (19128)Instruction limit reached!
% 9.74/2.97 % (19128)------------------------------
% 9.74/2.97 % (19128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.74/2.97 % (19128)Termination reason: Unknown
% 9.74/2.97 % (19128)Termination phase: Saturation
% 9.74/2.97
% 9.74/2.97 % (19128)Memory used [KB]: 6908
% 9.74/2.97 % (19128)Time elapsed: 0.063 s
% 9.74/2.97 % (19128)Instructions burned: 254 (million)
% 9.74/2.97 % (19128)------------------------------
% 9.74/2.97 % (19128)------------------------------
% 9.74/2.98 % (19130)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_18632 for (2985ds/668Mi)
% 9.74/3.00 % (19129)Refutation not found, incomplete strategy
% 9.74/3.00 % (19129)------------------------------
% 9.74/3.00 % (19129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.74/3.00 % (19129)Termination reason: Refutation not found, incomplete strategy
% 9.74/3.00
% 9.74/3.00
% 9.74/3.00 % (19129)Memory used [KB]: 8443
% 9.74/3.00 % (19129)Time elapsed: 0.084 s
% 9.74/3.00 % (19129)Instructions burned: 205 (million)
% 9.74/3.00 % (19129)------------------------------
% 9.74/3.00 % (19129)------------------------------
% 9.74/3.01 % (19131)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_18632 for (2985ds/40Mi)
% 12.96/3.02 % (19131)Instruction limit reached!
% 12.96/3.02 % (19131)------------------------------
% 12.96/3.02 % (19131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.96/3.02 % (19131)Termination reason: Unknown
% 12.96/3.02 % (19131)Termination phase: Property scanning
% 12.96/3.02
% 12.96/3.02 % (19131)Memory used [KB]: 1918
% 12.96/3.02 % (19131)Time elapsed: 0.012 s
% 12.96/3.02 % (19131)Instructions burned: 42 (million)
% 12.96/3.02 % (19131)------------------------------
% 12.96/3.02 % (19131)------------------------------
% 12.96/3.03 % (19132)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_18632 for (2985ds/294Mi)
% 12.96/3.04 % (19126)Instruction limit reached!
% 12.96/3.04 % (19126)------------------------------
% 12.96/3.04 % (19126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.96/3.04 % (19126)Termination reason: Unknown
% 12.96/3.04 % (19126)Termination phase: Saturation
% 12.96/3.04
% 12.96/3.04 % (19126)Memory used [KB]: 9978
% 12.96/3.04 % (19126)Time elapsed: 0.246 s
% 12.96/3.04 % (19126)Instructions burned: 995 (million)
% 12.96/3.04 % (19126)------------------------------
% 12.96/3.04 % (19126)------------------------------
% 12.96/3.05 % (19133)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_18632 for (2984ds/187Mi)
% 12.96/3.06 % (19118)Instruction limit reached!
% 12.96/3.06 % (19118)------------------------------
% 12.96/3.06 % (19118)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.96/3.06 % (19118)Termination reason: Unknown
% 12.96/3.06 % (19118)Termination phase: Saturation
% 12.96/3.06
% 12.96/3.06 % (19118)Memory used [KB]: 4349
% 12.96/3.06 % (19118)Time elapsed: 0.596 s
% 12.96/3.06 % (19118)Instructions burned: 1913 (million)
% 12.96/3.06 % (19118)------------------------------
% 12.96/3.06 % (19118)------------------------------
% 12.96/3.07 % (19134)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_18632 for (2984ds/371Mi)
% 12.96/3.10 % (19133)Instruction limit reached!
% 12.96/3.10 % (19133)------------------------------
% 12.96/3.10 % (19133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.96/3.10 % (19133)Termination reason: Unknown
% 12.96/3.10 % (19133)Termination phase: Saturation
% 12.96/3.10
% 12.96/3.10 % (19133)Memory used [KB]: 7419
% 12.96/3.10 % (19133)Time elapsed: 0.051 s
% 12.96/3.10 % (19133)Instructions burned: 188 (million)
% 12.96/3.10 % (19133)------------------------------
% 12.96/3.10 % (19133)------------------------------
% 12.96/3.11 % (19132)Instruction limit reached!
% 12.96/3.11 % (19132)------------------------------
% 12.96/3.11 % (19132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.96/3.11 % (19132)Termination reason: Unknown
% 12.96/3.11 % (19132)Termination phase: Saturation
% 12.96/3.11
% 12.96/3.11 % (19132)Memory used [KB]: 6652
% 12.96/3.11 % (19132)Time elapsed: 0.074 s
% 12.96/3.11 % (19132)Instructions burned: 296 (million)
% 12.96/3.11 % (19132)------------------------------
% 12.96/3.11 % (19132)------------------------------
% 12.96/3.11 % (19135)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_18632 for (2984ds/1827Mi)
% 12.96/3.12 % (19136)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_18632 for (2984ds/70Mi)
% 13.60/3.14 % (19136)Instruction limit reached!
% 13.60/3.14 % (19136)------------------------------
% 13.60/3.14 % (19136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.60/3.14 % (19136)Termination reason: Unknown
% 13.60/3.14 % (19136)Termination phase: Property scanning
% 13.60/3.14
% 13.60/3.14 % (19136)Memory used [KB]: 2174
% 13.60/3.14 % (19136)Time elapsed: 0.020 s
% 13.60/3.14 % (19136)Instructions burned: 72 (million)
% 13.60/3.14 % (19136)------------------------------
% 13.60/3.14 % (19136)------------------------------
% 13.60/3.14 % (19137)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_18632 for (2984ds/316Mi)
% 13.60/3.15 % (19130)Instruction limit reached!
% 13.60/3.15 % (19130)------------------------------
% 13.60/3.15 % (19130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.60/3.15 % (19130)Termination reason: Unknown
% 13.60/3.15 % (19130)Termination phase: Saturation
% 13.60/3.15
% 13.60/3.15 % (19130)Memory used [KB]: 14583
% 13.60/3.15 % (19130)Time elapsed: 0.164 s
% 13.60/3.15 % (19130)Instructions burned: 671 (million)
% 13.60/3.15 % (19130)------------------------------
% 13.60/3.15 % (19130)------------------------------
% 13.60/3.16 % (19138)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_18632 for (2983ds/932Mi)
% 13.60/3.17 % (19134)Instruction limit reached!
% 13.60/3.17 % (19134)------------------------------
% 13.60/3.17 % (19134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.60/3.17 % (19134)Termination reason: Unknown
% 13.60/3.17 % (19134)Termination phase: Saturation
% 13.60/3.17
% 13.60/3.17 % (19134)Memory used [KB]: 8059
% 13.60/3.17 % (19134)Time elapsed: 0.109 s
% 13.60/3.17 % (19134)Instructions burned: 373 (million)
% 13.60/3.17 % (19134)------------------------------
% 13.60/3.17 % (19134)------------------------------
% 13.60/3.18 % (19139)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_18632 for (2983ds/4714Mi)
% 14.01/3.22 % (19137)Instruction limit reached!
% 14.01/3.22 % (19137)------------------------------
% 14.01/3.22 % (19137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.01/3.22 % (19137)Termination reason: Unknown
% 14.01/3.22 % (19137)Termination phase: Saturation
% 14.01/3.22
% 14.01/3.22 % (19137)Memory used [KB]: 7291
% 14.01/3.22 % (19137)Time elapsed: 0.079 s
% 14.01/3.22 % (19137)Instructions burned: 317 (million)
% 14.01/3.22 % (19137)------------------------------
% 14.01/3.22 % (19137)------------------------------
% 14.01/3.23 % (19140)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_18632 for (2983ds/8250Mi)
% 14.39/3.39 % (19138)Instruction limit reached!
% 14.39/3.39 % (19138)------------------------------
% 14.39/3.39 % (19138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.39/3.39 % (19138)Termination reason: Unknown
% 14.39/3.39 % (19138)Termination phase: Saturation
% 14.39/3.39
% 14.39/3.39 % (19138)Memory used [KB]: 11129
% 14.39/3.39 % (19138)Time elapsed: 0.238 s
% 14.39/3.39 % (19138)Instructions burned: 934 (million)
% 14.39/3.39 % (19138)------------------------------
% 14.39/3.39 % (19138)------------------------------
% 14.95/3.40 % (19141)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_18632 for (2981ds/770Mi)
% 15.55/3.62 % (19141)Instruction limit reached!
% 15.55/3.62 % (19141)------------------------------
% 15.55/3.62 % (19141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.55/3.62 % (19141)Termination reason: Unknown
% 15.55/3.62 % (19141)Termination phase: Saturation
% 15.55/3.62
% 15.55/3.62 % (19141)Memory used [KB]: 6908
% 15.55/3.62 % (19141)Time elapsed: 0.213 s
% 15.55/3.62 % (19141)Instructions burned: 773 (million)
% 15.55/3.62 % (19141)------------------------------
% 15.55/3.62 % (19141)------------------------------
% 15.55/3.63 % (19142)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_18632 for (2979ds/794Mi)
% 15.55/3.65 % (19135)Instruction limit reached!
% 15.55/3.65 % (19135)------------------------------
% 15.55/3.65 % (19135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.55/3.65 % (19135)Termination reason: Unknown
% 15.55/3.65 % (19135)Termination phase: Saturation
% 15.55/3.65
% 15.55/3.65 % (19135)Memory used [KB]: 16119
% 15.55/3.65 % (19135)Time elapsed: 0.549 s
% 15.55/3.65 % (19135)Instructions burned: 1828 (million)
% 15.55/3.65 % (19135)------------------------------
% 15.55/3.65 % (19135)------------------------------
% 15.55/3.67 % (19143)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_18632 for (2978ds/464Mi)
% 15.55/3.68 % (19117)Instruction limit reached!
% 15.55/3.68 % (19117)------------------------------
% 15.55/3.68 % (19117)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.55/3.68 % (19117)Termination reason: Unknown
% 15.55/3.68 % (19117)Termination phase: Saturation
% 15.55/3.68
% 15.55/3.68 % (19117)Memory used [KB]: 10490
% 15.55/3.68 % (19117)Time elapsed: 1.234 s
% 15.55/3.68 % (19117)Instructions burned: 5208 (million)
% 15.55/3.68 % (19117)------------------------------
% 15.55/3.68 % (19117)------------------------------
% 15.55/3.69 % (19144)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_18632 for (2978ds/1376Mi)
% 16.62/3.71 % (19142)First to succeed.
% 16.62/3.71 % (19142)Refutation found. Thanks to Tanya!
% 16.62/3.71 % SZS status Theorem for DTF2THF_18632
% 16.62/3.71 % SZS output start Proof for DTF2THF_18632
% 16.62/3.71 thf(func_def_0, type, in: $i > $i > $o).
% 16.62/3.71 thf(func_def_1, type, exu: ($i > $o) > $o).
% 16.62/3.71 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 16.62/3.71 thf(func_def_8, type, powerset: $i > $i).
% 16.62/3.71 thf(func_def_10, type, setunion: $i > $i).
% 16.62/3.71 thf(func_def_19, type, descr: ($i > $o) > $i).
% 16.62/3.71 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 16.62/3.71 thf(func_def_26, type, prop2set: $o > $i).
% 16.62/3.71 thf(func_def_36, type, nonempty: $i > $o).
% 16.62/3.71 thf(func_def_69, type, set2prop: $i > $o).
% 16.62/3.71 thf(func_def_88, type, subset: $i > $i > $o).
% 16.62/3.71 thf(func_def_89, type, disjoint: $i > $i > $o).
% 16.62/3.71 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 16.62/3.71 thf(func_def_114, type, binunion: $i > $i > $i).
% 16.62/3.71 thf(func_def_122, type, binintersect: $i > $i > $i).
% 16.62/3.71 thf(func_def_135, type, regular: $i > $o).
% 16.62/3.71 thf(func_def_136, type, setminus: $i > $i > $i).
% 16.62/3.71 thf(func_def_147, type, symdiff: $i > $i > $i).
% 16.62/3.71 thf(func_def_153, type, iskpair: $i > $o).
% 16.62/3.71 thf(func_def_158, type, kpair: $i > $i > $i).
% 16.62/3.71 thf(func_def_160, type, cartprod: $i > $i > $i).
% 16.62/3.71 thf(func_def_177, type, singleton: $i > $o).
% 16.62/3.71 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 16.62/3.71 thf(func_def_184, type, atmost1p: $i > $o).
% 16.62/3.71 thf(func_def_185, type, atleast2p: $i > $o).
% 16.62/3.71 thf(func_def_186, type, atmost2p: $i > $o).
% 16.62/3.71 thf(func_def_187, type, upairsetp: $i > $o).
% 16.62/3.71 thf(func_def_191, type, kfst: $i > $i).
% 16.62/3.71 thf(func_def_203, type, ksnd: $i > $i).
% 16.62/3.71 thf(func_def_222, type, sP1: $i > $o).
% 16.62/3.71 thf(func_def_223, type, sP2: $o > $o).
% 16.62/3.71 thf(func_def_224, type, sK3: ($i > $o) > $i).
% 16.62/3.71 thf(func_def_225, type, sK4: ($i > $o) > $i).
% 16.62/3.71 thf(func_def_226, type, sK5: ($i > $o) > $i).
% 16.62/3.71 thf(func_def_227, type, sK6: ($i > $o) > $i).
% 16.62/3.71 thf(func_def_228, type, sK7: ($i > $o) > $i).
% 16.62/3.71 thf(func_def_229, type, sK8: $i > $i > $i).
% 16.62/3.71 thf(func_def_230, type, sK9: $i > $i > $i).
% 16.62/3.71 thf(func_def_231, type, sK10: $i > $i > $i).
% 16.62/3.71 thf(func_def_232, type, sK11: $i > ($i > $i > $o) > $i).
% 16.62/3.71 thf(func_def_233, type, sK12: $i > ($i > $i > $o) > $i).
% 16.62/3.71 thf(func_def_234, type, sK13: $i > $i > ($i > $i > $o) > $i).
% 16.62/3.71 thf(func_def_235, type, sK14: $i > ($i > $i > $o) > $i).
% 16.62/3.71 thf(func_def_236, type, sK15: $i > $i > ($i > $i > $o) > $i).
% 16.62/3.71 thf(func_def_237, type, sK16: $i > $i > ($i > $i > $o) > $i).
% 16.62/3.71 thf(func_def_238, type, sK17: $i > $i > ($i > $i > $o) > $i).
% 16.62/3.71 thf(func_def_239, type, sK18: $i > $i > ($i > $i > $o) > $i).
% 16.62/3.71 thf(func_def_240, type, sK19: $i > $i).
% 16.62/3.71 thf(func_def_241, type, sK20: ($i > $o) > $i > $i).
% 16.62/3.71 thf(func_def_242, type, sK21: ($i > $o) > $i > $i).
% 16.62/3.71 thf(func_def_243, type, sK22: ($i > $o) > ($i > $o) > $i).
% 16.62/3.71 thf(func_def_244, type, sK23: ($i > $o) > ($i > $o) > $i).
% 16.62/3.71 thf(func_def_245, type, sK24: $i > ($i > $o) > $i).
% 16.62/3.71 thf(func_def_246, type, sK25: $i > ($i > $o) > $i).
% 16.62/3.71 thf(func_def_247, type, sK26: $i > ($i > $o) > $i).
% 16.62/3.71 thf(func_def_248, type, sK27: $i > ($i > $o) > $i).
% 16.62/3.71 thf(func_def_249, type, sK28: $i > ($i > $o) > $i).
% 16.62/3.71 thf(func_def_250, type, sK29: $i > ($i > $o) > $i).
% 16.62/3.71 thf(func_def_251, type, sK30: $i > ($i > $o) > $i).
% 16.62/3.71 thf(func_def_252, type, sK31: $i > $i).
% 16.62/3.71 thf(func_def_253, type, sK32: $i > $i > $i > $i).
% 16.62/3.71 thf(func_def_254, type, sK33: $i > $i > $i).
% 16.62/3.71 thf(func_def_255, type, sK34: $i > $i > $i).
% 16.62/3.71 thf(func_def_256, type, sK35: $i > $i > $i).
% 16.62/3.71 thf(func_def_257, type, sK36: $i > $i > $i).
% 16.62/3.71 thf(func_def_258, type, sK37: ($i > $o) > $i > $i).
% 16.62/3.71 thf(func_def_259, type, sK38: ($i > $o) > $i > $i).
% 16.62/3.71 thf(func_def_260, type, sK39: $i > $i > $i).
% 16.62/3.71 thf(func_def_261, type, sK40: ($i > $o) > ($i > $o) > $i).
% 16.62/3.71 thf(func_def_262, type, sK41: ($i > $o) > ($i > $o) > $i).
% 16.62/3.71 thf(func_def_263, type, sK42: ($i > $o) > $i).
% 16.62/3.71 thf(func_def_264, type, sK43: $i > ($i > $o) > $i).
% 16.62/3.71 thf(func_def_265, type, sK44: $i > ($i > $o) > $i).
% 16.62/3.71 thf(func_def_266, type, sK45: $i > ($i > $o) > $i).
% 16.62/3.71 thf(func_def_267, type, sK46: $i > ($i > $o) > $i).
% 16.62/3.71 thf(func_def_268, type, sK47: $i > ($i > $o) > $i).
% 16.62/3.71 thf(func_def_269, type, sK48: $i > ($i > $o) > $i).
% 16.62/3.71 thf(func_def_270, type, sK49: $i > ($i > $o) > $i).
% 16.62/3.71 thf(func_def_271, type, sK50: ($i > $o) > $i).
% 16.62/3.71 thf(func_def_272, type, sK51: ($i > $o) > $i).
% 16.62/3.71 thf(func_def_273, type, sK52: ($i > $o) > $i).
% 16.62/3.71 thf(func_def_274, type, sK53: $i > $i).
% 16.62/3.71 thf(func_def_275, type, sK54: $i > $i).
% 16.62/3.71 thf(func_def_276, type, sK55: $i > $i > $i).
% 16.62/3.71 thf(func_def_277, type, sK56: $i > $i > $i).
% 16.62/3.71 thf(func_def_278, type, sK57: $i > $i).
% 16.62/3.71 thf(func_def_279, type, sK58: $i > $i > $i).
% 16.62/3.71 thf(func_def_280, type, sK59: ($i > $o) > $i > $i).
% 16.62/3.71 thf(func_def_281, type, sK60: $i > $i).
% 16.62/3.71 thf(func_def_282, type, sK61: $i > $i > $i).
% 16.62/3.71 thf(func_def_283, type, sK62: ($i > $o) > $i).
% 16.62/3.71 thf(func_def_284, type, sK63: ($i > $o) > $i > $i).
% 16.62/3.71 thf(func_def_285, type, sK64: $i > $i > $i).
% 16.62/3.71 thf(func_def_286, type, sK65: $i > $i > $i).
% 16.62/3.71 thf(func_def_287, type, sK66: $i > ($i > $o) > $i).
% 16.62/3.71 thf(func_def_288, type, sK67: $i > ($i > $o) > $i).
% 16.62/3.71 thf(func_def_289, type, sK68: $i > ($i > $o) > $i).
% 16.62/3.71 thf(func_def_290, type, sK69: $i > ($i > $o) > $i).
% 16.62/3.71 thf(func_def_291, type, sK70: $i > ($i > $o) > $i).
% 16.62/3.71 thf(func_def_294, type, sK73: $i > $i).
% 16.62/3.71 thf(func_def_295, type, sK74: $i > $i).
% 16.62/3.71 thf(func_def_296, type, sK75: ($i > $o) > $i).
% 16.62/3.71 thf(func_def_297, type, sK76: $i > ($i > $o) > $i).
% 16.62/3.71 thf(func_def_298, type, sK77: $i > ($i > $o) > $i).
% 16.62/3.71 thf(func_def_299, type, sK78: ($i > $o) > $i > $i).
% 16.62/3.71 thf(func_def_300, type, sK79: ($i > $o) > $i > $i).
% 16.62/3.71 thf(func_def_301, type, sK80: ($i > $o) > $i > $i).
% 16.62/3.71 thf(func_def_302, type, sK81: ($i > $o) > $i > $i).
% 16.62/3.71 thf(func_def_303, type, sK82: ($i > $o) > $i > $i).
% 16.62/3.71 thf(func_def_304, type, sK83: $i > $i).
% 16.62/3.71 thf(func_def_305, type, sK84: ($i > $o) > $i > $i).
% 16.62/3.71 thf(func_def_306, type, sK85: ($i > $o) > $i).
% 16.62/3.71 thf(func_def_307, type, sK86: ($i > $o) > $i).
% 16.62/3.71 thf(func_def_308, type, sK87: $i > ($i > $o) > $i).
% 16.62/3.71 thf(func_def_309, type, sK88: $i > $i > ($i > $o) > $i).
% 16.62/3.71 thf(func_def_310, type, sK89: $i > $i > ($i > $o) > $i).
% 16.62/3.71 thf(func_def_311, type, sK90: ($i > $o) > $i).
% 16.62/3.71 thf(func_def_312, type, sK91: ($i > $o) > $i > $i).
% 16.62/3.71 thf(func_def_313, type, sK92: ($i > $o) > $i > $i).
% 16.62/3.71 thf(func_def_314, type, sK93: $i > $i > $i).
% 16.62/3.71 thf(func_def_315, type, sK94: ($i > $o) > $i > $i).
% 16.62/3.71 thf(func_def_316, type, sK95: $i > $i).
% 16.62/3.71 thf(func_def_317, type, sK96: $i > $i > $i).
% 16.62/3.71 thf(func_def_318, type, sK97: $o > $i > $i > $i).
% 16.62/3.71 thf(func_def_319, type, sK98: ($i > $o) > ($i > $o) > $i > $i > $i).
% 16.62/3.71 thf(func_def_320, type, sK99: $i > $i > ($i > $o) > ($i > $o) > $i).
% 16.62/3.71 thf(func_def_321, type, sK100: $i > $i > $i > $i).
% 16.62/3.71 thf(func_def_322, type, sK101: $i > $i > $i > $i).
% 16.62/3.71 thf(func_def_323, type, sK102: $i > $i > $i).
% 16.62/3.71 thf(func_def_324, type, sK103: $i > ($i > $o) > $i).
% 16.62/3.71 thf(func_def_325, type, sK104: $i > $i > $i).
% 16.62/3.71 thf(func_def_326, type, sK105: ($i > $o) > $i > $i).
% 16.62/3.71 thf(func_def_327, type, sK106: $i > $i).
% 16.62/3.71 thf(f3093,plain,(
% 16.62/3.71 $false),
% 16.62/3.71 inference(trivial_inequality_removal,[status(thm)],[f3092])).
% 16.62/3.71 thf(f3092,plain,(
% 16.62/3.71 ($false = $true)),
% 16.62/3.71 inference(backward_demodulation,[status(thm)],[f3090,f3091])).
% 16.62/3.71 thf(f3091,plain,(
% 16.62/3.71 ((sP1 @ (setadjoin @ (setadjoin @ sK71 @ emptyset) @ (setadjoin @ (setadjoin @ sK71 @ (setadjoin @ sK72 @ emptyset)) @ emptyset))) = $false)),
% 16.62/3.71 inference(backward_demodulation,[status(thm)],[f3089,f1434])).
% 16.62/3.71 thf(f1434,plain,(
% 16.62/3.71 ( ! [X2 : $i,X1 : $i] : (((kfst @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = X2)) )),
% 16.62/3.71 inference(equality_proxy_clausification,[status(thm)],[f1433])).
% 16.62/3.71 thf(f1433,plain,(
% 16.62/3.71 ( ! [X2 : $i,X1 : $i] : (($true = ((kfst @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = X2))) )),
% 16.62/3.71 inference(beta_eta_normalization,[status(thm)],[f1432])).
% 16.62/3.71 thf(f1432,plain,(
% 16.62/3.71 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((kfst @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = Y0)) @ X2))) )),
% 16.62/3.71 inference(pi_clausification,[status(thm)],[f1431])).
% 16.62/3.71 thf(f1431,plain,(
% 16.62/3.71 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((kfst @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = Y0))))) )),
% 16.62/3.71 inference(beta_eta_normalization,[status(thm)],[f1430])).
% 16.62/3.71 thf(f1430,plain,(
% 16.62/3.71 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) = Y1)))) @ X1))) )),
% 16.62/3.71 inference(pi_clausification,[status(thm)],[f1429])).
% 16.62/3.71 thf(f1429,plain,(
% 16.62/3.71 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) = Y1))))))),
% 16.62/3.71 inference(beta_eta_normalization,[status(thm)],[f903])).
% 16.62/3.71 thf(f903,plain,(
% 16.62/3.71 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ ((^[Y2 : $i]: ((^[Y3 : $i]: (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))))) @ Y1 @ Y0)) = Y1))))))),
% 16.62/3.71 inference(definition_unfolding,[status(thm)],[f622,f897])).
% 16.62/3.71 thf(f897,plain,(
% 16.62/3.71 (kfstpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ ((^[Y2 : $i]: ((^[Y3 : $i]: (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))))) @ Y1 @ Y0)) = Y1))))))),
% 16.62/3.71 inference(definition_unfolding,[status(thm)],[f549,f548])).
% 16.62/3.71 thf(f548,plain,(
% 16.62/3.71 (kpair = (^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))),
% 16.62/3.71 inference(cnf_transformation,[status(thm)],[f490])).
% 16.62/3.71 thf(f490,plain,(
% 16.62/3.71 (kpair = (^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))),
% 16.62/3.71 inference(fool_elimination,[status(thm)],[f489])).
% 16.62/3.71 thf(f489,plain,(
% 16.62/3.71 ((^[X0 : $i, X1 : $i] : (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = kpair)),
% 16.62/3.71 inference(rectify,[status(thm)],[f140])).
% 16.62/3.71 thf(f140,axiom,(
% 16.62/3.71 ((^[X1 : $i, X2 : $i] : (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset))) = kpair)),
% 16.62/3.71 file('/export/starexec/sandbox2/tmp/tmp.UKH9onOzqj/DTF2THF_18632.p',kpair)).
% 16.62/3.71 thf(f549,plain,(
% 16.62/3.71 (kfstpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y1 @ Y0)) = Y1))))))),
% 16.62/3.71 inference(cnf_transformation,[status(thm)],[f514])).
% 16.62/3.71 thf(f514,plain,(
% 16.62/3.71 (kfstpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y1 @ Y0)) = Y1))))))),
% 16.62/3.71 inference(fool_elimination,[status(thm)],[f513])).
% 16.62/3.71 thf(f513,plain,(
% 16.62/3.71 (! [X0 : $i,X1 : $i] : ((kfst @ (kpair @ X0 @ X1)) = X0) = kfstpairEq)),
% 16.62/3.71 inference(rectify,[status(thm)],[f168])).
% 16.62/3.71 thf(f168,axiom,(
% 16.62/3.71 (! [X1 : $i,X2 : $i] : ((kfst @ (kpair @ X1 @ X2)) = X1) = kfstpairEq)),
% 16.62/3.71 file('/export/starexec/sandbox2/tmp/tmp.UKH9onOzqj/DTF2THF_18632.p',kfstpairEq)).
% 16.62/3.71 thf(f622,plain,(
% 16.62/3.71 (kfstpairEq = $true)),
% 16.62/3.71 inference(cnf_transformation,[status(thm)],[f540])).
% 16.62/3.71 thf(f540,plain,(
% 16.62/3.71 (setukpairinjL2 = $true) & (in__Cong = $true) & (disjointsetsI1 = $true) & (emptyset__Cong = $true) & (foundationAx = $true) & (symdiffI2 = $true) & (prop2set2propI = $true) & (eqinunit = $true) & (symdiffE = $true) & (emptyE1 = $true) & (powersetsubset = $true) & (subsetE2 = $true) & (exuI2 = $true) & (emptyI = $true) & (sepInPowerset = $true) & (quantDeMorgan3 = $true) & (setadjoinAx = $true) & (subPowSU = $true) & (noeltsimpempty = $true) & (descrp = $true) & (dsetconstrI = $true) & (upairsubunion = $true) & (setadjoinSub = $true) & (bs114d = $true) & (setbeta = $true) & (prop2setI = $true) & (notinsingleton = $true) & (binunionLsub = $true) & (ksndpairEq = $true) & (dsetconstr__Cong = $true) & (nonemptyI1 = $true) & (secondinupair = $true) & (omega__Cong = $true) & (exuI3 = $true) & (exuE3u = $true) & (binunionE = $true) & (subsetTrans = $true) & (quantDeMorgan4 = $true) & (binunionEcases = $true) & (singletonsswitch = $true) & (upairequniteq = $true) & (upairset2IR = $true) & (subsetI1 = $true) & (setoftrueEq = $true) & (singletonprop = $true) & (exuI1 = $true) & (setadjoin__Cong = $true) & (subsetE = $true) & (exuE3e = $true) & (ubforcartprodlem2 = $true) & (setukpairIL = $true) & (singletoninpowunion = $true) & (setadjoinOr = $true) & (eqimpsubset1 = $true) & (singletonsubset = $true) & (kpairp = $true) & (setminusEL = $true) & (notdallE = $true) & (symdiffIneg1 = $true) & (quantDeMorgan1 = $true) & (binintersectEL = $true) & (setukpairinjR1 = $true) & (emptyInPowerset = $true) & (emptysetsubset = $true) & (binintersectSubset3 = $true) & (setunionE = $true) & (setukpairIR = $true) & (symdiffIneg2 = $true) & (binintersectSubset2 = $true) & (ex1I2 = $true) & (wellorderingAx = $true) & (emptysetAx = $true) & (binunionIR = $true) & (omegaSAx = $true) & (nonemptyE1 = $true) & (inCongP = $true) & (setukpairinjL1 = $true) & (powerset__Cong = $true) & (notequalI1 = $true) & (cartprodmempair = $true) & (binunionRsub = $true) & (setextsub = $true) & (ex1E1 = $true) & (setminusSubset2 = $true) & (setminusIRneg = $true) & (emptysetE = $true) & (upairsetIL = $true) & (cartprodpairin = $true) & (powersetE = $true) & (ubforcartprodlem3 = $true) & (kfstsingleton = $true) & (upairsetE = $true) & (uniqinunit = $true) & (notsubsetI = $true) & (exu__Cong = $true) & (powersetI = $true) & (setukpairinjL = $true) & (prop2setE = $true) & (setunionsingleton2 = $true) & (setukpairinjR = $true) & (exuEu = $true) & (setunionI = $true) & (subsetRefl = $true) & (kfstpairEq = $true) & (setadjoinIL = $true) & (powersetE1 = $true) & (replAx = $true) & (setminusELneg = $true) & (setukpairinjR11 = $true) & (setminusLsub = $true) & (kpairiskpair = $true) & (upairinpowunion = $true) & (setextAx = $true) & (setext = $true) & (cartprodmempair1 = $true) & (subsetI2 = $true) & (dsetconstrEL = $true) & (setadjoinE = $true) & (omega0Ax = $true) & (eqimpsubset2 = $true) & (binintersectSubset5 = $true) & (setukpairinjR12 = $true) & (nonemptyI = $true) & (setminusI = $true) & (descr__Cong = $true) & (binintersectSubset1 = $true) & (subsetemptysetimpeq = $true) & (upairsetIR = $true) & (subset2powerset = $true) & (ubforcartprodlem1 = $true) & (setminusER = $true) & (vacuousDall = $true) & (binunionIL = $true) & (powersetI1 = $true) & (theprop = $true) & (setunionE2 = $true) & (setminusILneg = $true) & (notinemptyset = $true) & (setadjoinSub2 = $true) & (setminusERneg = $true) & (setunion__Cong = $true) & (binintersectER = $true) & (setunionAx = $true) & (singletonsuniq = $true) & (setukpairinjR2 = $true) & (binintersectRsub = $true) & (nonemptyImpWitness = $true) & (binintersectI = $true) & ((sK0 != (kpair @ (kfst @ sK0) @ (ksnd @ sK0))) & ($true = (iskpair @ sK0))) & (emptyinunitempty = $true) & (notdexE = $true) & (setadjoinIR = $true) & (upairset2E = $true) & (symdiffI1 = $true) & (notequalI2 = $true) & (binintersectSubset4 = $true) & (binintersectLsub = $true) & (ex1I = $true) & (ksndsingleton = $true) & (setminusSubset1 = $true) & (omegaIndAx = $true) & (setunionsingleton = $true) & (dsetconstrER = $true) & (cartprodfstin = $true) & (singletoninpowerset = $true) & (sepSubset = $true) & (powersetAx = $true) & (exuE1 = $true) & (emptyinPowerset = $true) & (inPowerset = $true) & (emptysetimpfalse = $true) & (setunionsingleton1 = $true) & (exuE2 = $true) & (quantDeMorgan2 = $true)),
% 16.62/3.71 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f538,f539])).
% 16.62/3.71 thf(f539,plain,(
% 16.62/3.71 ? [X0 : $i] : (((kpair @ (kfst @ X0) @ (ksnd @ X0)) != X0) & ($true = (iskpair @ X0))) => ((sK0 != (kpair @ (kfst @ sK0) @ (ksnd @ sK0))) & ($true = (iskpair @ sK0)))),
% 16.62/3.71 introduced(definition,[],[choice_axiom])).
% 16.62/3.71 thf(f538,plain,(
% 16.62/3.71 (setukpairinjL2 = $true) & (in__Cong = $true) & (disjointsetsI1 = $true) & (emptyset__Cong = $true) & (foundationAx = $true) & (symdiffI2 = $true) & (prop2set2propI = $true) & (eqinunit = $true) & (symdiffE = $true) & (emptyE1 = $true) & (powersetsubset = $true) & (subsetE2 = $true) & (exuI2 = $true) & (emptyI = $true) & (sepInPowerset = $true) & (quantDeMorgan3 = $true) & (setadjoinAx = $true) & (subPowSU = $true) & (noeltsimpempty = $true) & (descrp = $true) & (dsetconstrI = $true) & (upairsubunion = $true) & (setadjoinSub = $true) & (bs114d = $true) & (setbeta = $true) & (prop2setI = $true) & (notinsingleton = $true) & (binunionLsub = $true) & (ksndpairEq = $true) & (dsetconstr__Cong = $true) & (nonemptyI1 = $true) & (secondinupair = $true) & (omega__Cong = $true) & (exuI3 = $true) & (exuE3u = $true) & (binunionE = $true) & (subsetTrans = $true) & (quantDeMorgan4 = $true) & (binunionEcases = $true) & (singletonsswitch = $true) & (upairequniteq = $true) & (upairset2IR = $true) & (subsetI1 = $true) & (setoftrueEq = $true) & (singletonprop = $true) & (exuI1 = $true) & (setadjoin__Cong = $true) & (subsetE = $true) & (exuE3e = $true) & (ubforcartprodlem2 = $true) & (setukpairIL = $true) & (singletoninpowunion = $true) & (setadjoinOr = $true) & (eqimpsubset1 = $true) & (singletonsubset = $true) & (kpairp = $true) & (setminusEL = $true) & (notdallE = $true) & (symdiffIneg1 = $true) & (quantDeMorgan1 = $true) & (binintersectEL = $true) & (setukpairinjR1 = $true) & (emptyInPowerset = $true) & (emptysetsubset = $true) & (binintersectSubset3 = $true) & (setunionE = $true) & (setukpairIR = $true) & (symdiffIneg2 = $true) & (binintersectSubset2 = $true) & (ex1I2 = $true) & (wellorderingAx = $true) & (emptysetAx = $true) & (binunionIR = $true) & (omegaSAx = $true) & (nonemptyE1 = $true) & (inCongP = $true) & (setukpairinjL1 = $true) & (powerset__Cong = $true) & (notequalI1 = $true) & (cartprodmempair = $true) & (binunionRsub = $true) & (setextsub = $true) & (ex1E1 = $true) & (setminusSubset2 = $true) & (setminusIRneg = $true) & (emptysetE = $true) & (upairsetIL = $true) & (cartprodpairin = $true) & (powersetE = $true) & (ubforcartprodlem3 = $true) & (kfstsingleton = $true) & (upairsetE = $true) & (uniqinunit = $true) & (notsubsetI = $true) & (exu__Cong = $true) & (powersetI = $true) & (setukpairinjL = $true) & (prop2setE = $true) & (setunionsingleton2 = $true) & (setukpairinjR = $true) & (exuEu = $true) & (setunionI = $true) & (subsetRefl = $true) & (kfstpairEq = $true) & (setadjoinIL = $true) & (powersetE1 = $true) & (replAx = $true) & (setminusELneg = $true) & (setukpairinjR11 = $true) & (setminusLsub = $true) & (kpairiskpair = $true) & (upairinpowunion = $true) & (setextAx = $true) & (setext = $true) & (cartprodmempair1 = $true) & (subsetI2 = $true) & (dsetconstrEL = $true) & (setadjoinE = $true) & (omega0Ax = $true) & (eqimpsubset2 = $true) & (binintersectSubset5 = $true) & (setukpairinjR12 = $true) & (nonemptyI = $true) & (setminusI = $true) & (descr__Cong = $true) & (binintersectSubset1 = $true) & (subsetemptysetimpeq = $true) & (upairsetIR = $true) & (subset2powerset = $true) & (ubforcartprodlem1 = $true) & (setminusER = $true) & (vacuousDall = $true) & (binunionIL = $true) & (powersetI1 = $true) & (theprop = $true) & (setunionE2 = $true) & (setminusILneg = $true) & (notinemptyset = $true) & (setadjoinSub2 = $true) & (setminusERneg = $true) & (setunion__Cong = $true) & (binintersectER = $true) & (setunionAx = $true) & (singletonsuniq = $true) & (setukpairinjR2 = $true) & (binintersectRsub = $true) & (nonemptyImpWitness = $true) & (binintersectI = $true) & ? [X0 : $i] : (((kpair @ (kfst @ X0) @ (ksnd @ X0)) != X0) & ($true = (iskpair @ X0))) & (emptyinunitempty = $true) & (notdexE = $true) & (setadjoinIR = $true) & (upairset2E = $true) & (symdiffI1 = $true) & (notequalI2 = $true) & (binintersectSubset4 = $true) & (binintersectLsub = $true) & (ex1I = $true) & (ksndsingleton = $true) & (setminusSubset1 = $true) & (omegaIndAx = $true) & (setunionsingleton = $true) & (dsetconstrER = $true) & (cartprodfstin = $true) & (singletoninpowerset = $true) & (sepSubset = $true) & (powersetAx = $true) & (exuE1 = $true) & (emptyinPowerset = $true) & (inPowerset = $true) & (emptysetimpfalse = $true) & (setunionsingleton1 = $true) & (exuE2 = $true) & (quantDeMorgan2 = $true)),
% 16.62/3.71 inference(flattening,[status(thm)],[f537])).
% 16.62/3.71 thf(f537,plain,(
% 16.62/3.71 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i] : (((kpair @ (kfst @ X0) @ (ksnd @ X0)) != X0) & ($true = (iskpair @ X0))) & (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)),
% 16.62/3.71 inference(ennf_transformation,[status(thm)],[f318])).
% 16.62/3.71 thf(f318,plain,(
% 16.62/3.71 ~((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) => ! [X0 : $i] : (($true = (iskpair @ X0)) => ((kpair @ (kfst @ X0) @ (ksnd @ X0)) = X0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 16.62/3.71 inference(fool_elimination,[status(thm)],[f317])).
% 16.62/3.71 thf(f317,plain,(
% 16.62/3.71 ~(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 => ! [X0 : $i] : ((iskpair @ X0) => ((kpair @ (kfst @ X0) @ (ksnd @ X0)) = X0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 16.62/3.71 inference(rectify,[status(thm)],[f181])).
% 16.62/3.71 thf(f181,negated_conjecture,(
% 16.62/3.71 ~(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 => ! [X10 : $i] : ((iskpair @ X10) => ((kpair @ (kfst @ X10) @ (ksnd @ X10)) = X10)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 16.62/3.71 inference(negated_conjecture,[status(cth)],[f180])).
% 16.62/3.71 thf(f180,conjecture,(
% 16.62/3.71 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 => ! [X10 : $i] : ((iskpair @ X10) => ((kpair @ (kfst @ X10) @ (ksnd @ X10)) = X10))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 16.62/3.71 file('/export/starexec/sandbox2/tmp/tmp.UKH9onOzqj/DTF2THF_18632.p',kpairsurjEq)).
% 16.62/3.71 thf(f3089,plain,(
% 16.62/3.71 ($false = (sP1 @ (setadjoin @ (setadjoin @ (kfst @ (setadjoin @ (setadjoin @ sK71 @ emptyset) @ (setadjoin @ (setadjoin @ sK71 @ (setadjoin @ sK72 @ emptyset)) @ emptyset))) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ (setadjoin @ (setadjoin @ sK71 @ emptyset) @ (setadjoin @ (setadjoin @ sK71 @ (setadjoin @ sK72 @ emptyset)) @ emptyset))) @ (setadjoin @ sK72 @ emptyset)) @ emptyset))))),
% 16.62/3.71 inference(forward_demodulation,[status(thm)],[f3088,f2851])).
% 16.62/3.71 thf(f2851,plain,(
% 16.62/3.71 ( ! [X2 : $i,X1 : $i] : (((ksnd @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = X1)) )),
% 16.62/3.71 inference(equality_proxy_clausification,[status(thm)],[f2850])).
% 16.62/3.71 thf(f2850,plain,(
% 16.62/3.71 ( ! [X2 : $i,X1 : $i] : (($true = ((ksnd @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = X1))) )),
% 16.62/3.71 inference(beta_eta_normalization,[status(thm)],[f2849])).
% 16.62/3.71 thf(f2849,plain,(
% 16.62/3.71 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((ksnd @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = X1)) @ X2))) )),
% 16.62/3.71 inference(pi_clausification,[status(thm)],[f2848])).
% 16.62/3.71 thf(f2848,plain,(
% 16.62/3.71 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((ksnd @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = X1))))) )),
% 16.62/3.71 inference(beta_eta_normalization,[status(thm)],[f2847])).
% 16.62/3.71 thf(f2847,plain,(
% 16.62/3.71 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) = Y0)))) @ X1))) )),
% 16.62/3.71 inference(pi_clausification,[status(thm)],[f2846])).
% 16.62/3.71 thf(f2846,plain,(
% 16.62/3.71 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) = Y0))))))),
% 16.62/3.71 inference(beta_eta_normalization,[status(thm)],[f962])).
% 16.62/3.71 thf(f962,plain,(
% 16.62/3.71 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ ((^[Y2 : $i]: ((^[Y3 : $i]: (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))))) @ Y1 @ Y0)) = Y0))))))),
% 16.62/3.71 inference(definition_unfolding,[status(thm)],[f779,f697,f548])).
% 16.62/3.71 thf(f697,plain,(
% 16.62/3.71 (ksndpairEq = $true)),
% 16.62/3.71 inference(cnf_transformation,[status(thm)],[f540])).
% 16.62/3.71 thf(f779,plain,(
% 16.62/3.71 (ksndpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y1 @ Y0)) = Y0))))))),
% 16.62/3.71 inference(cnf_transformation,[status(thm)],[f316])).
% 16.62/3.71 thf(f316,plain,(
% 16.62/3.71 (ksndpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y1 @ Y0)) = Y0))))))),
% 16.62/3.71 inference(fool_elimination,[status(thm)],[f315])).
% 16.62/3.71 thf(f315,plain,(
% 16.62/3.71 (ksndpairEq = ! [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X0 @ X1)) = X1))),
% 16.62/3.71 inference(rectify,[status(thm)],[f179])).
% 16.62/3.71 thf(f179,axiom,(
% 16.62/3.71 (ksndpairEq = ! [X1 : $i,X2 : $i] : ((ksnd @ (kpair @ X1 @ X2)) = X2))),
% 16.62/3.71 file('/export/starexec/sandbox2/tmp/tmp.UKH9onOzqj/DTF2THF_18632.p',ksndpairEq)).
% 16.62/3.71 thf(f3088,plain,(
% 16.62/3.71 ($false = (sP1 @ (setadjoin @ (setadjoin @ (kfst @ (setadjoin @ (setadjoin @ sK71 @ emptyset) @ (setadjoin @ (setadjoin @ sK71 @ (setadjoin @ sK72 @ emptyset)) @ emptyset))) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ (setadjoin @ (setadjoin @ sK71 @ emptyset) @ (setadjoin @ (setadjoin @ sK71 @ (setadjoin @ sK72 @ emptyset)) @ emptyset))) @ (setadjoin @ (ksnd @ (setadjoin @ (setadjoin @ sK71 @ emptyset) @ (setadjoin @ (setadjoin @ sK71 @ (setadjoin @ sK72 @ emptyset)) @ emptyset))) @ emptyset)) @ emptyset))))),
% 16.62/3.71 inference(backward_demodulation,[status(thm)],[f2366,f2307])).
% 16.62/3.71 thf(f2307,plain,(
% 16.62/3.71 (sK0 = (setadjoin @ (setadjoin @ sK71 @ emptyset) @ (setadjoin @ (setadjoin @ sK71 @ (setadjoin @ sK72 @ emptyset)) @ emptyset)))),
% 16.62/3.71 inference(equality_proxy_clausification,[status(thm)],[f2306])).
% 16.62/3.71 thf(f2306,plain,(
% 16.62/3.71 ($true = ((setadjoin @ (setadjoin @ sK71 @ emptyset) @ (setadjoin @ (setadjoin @ sK71 @ (setadjoin @ sK72 @ emptyset)) @ emptyset)) = sK0))),
% 16.62/3.71 inference(binary_proxy_clausification,[status(thm)],[f2304])).
% 16.62/3.71 thf(f2304,plain,(
% 16.62/3.71 ($true = (((setadjoin @ (setadjoin @ sK71 @ emptyset) @ (setadjoin @ (setadjoin @ sK71 @ (setadjoin @ sK72 @ emptyset)) @ emptyset)) = sK0) & (in @ sK72 @ (setunion @ sK0))))),
% 16.62/3.71 inference(beta_eta_normalization,[status(thm)],[f2303])).
% 16.62/3.71 thf(f2303,plain,(
% 16.62/3.71 ($true = ((^[Y0 : $i]: (((setadjoin @ (setadjoin @ sK71 @ emptyset) @ (setadjoin @ (setadjoin @ sK71 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK0) & (in @ Y0 @ (setunion @ sK0)))) @ sK72))),
% 16.62/3.71 inference(sigma_clausification,[status(thm)],[f2302])).
% 16.62/3.71 thf(f2302,plain,(
% 16.62/3.71 ((?? @ $i @ (^[Y0 : $i]: (((setadjoin @ (setadjoin @ sK71 @ emptyset) @ (setadjoin @ (setadjoin @ sK71 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK0) & (in @ Y0 @ (setunion @ sK0))))) = $true)),
% 16.62/3.71 inference(binary_proxy_clausification,[status(thm)],[f2300])).
% 16.62/3.71 thf(f2300,plain,(
% 16.62/3.71 (((?? @ $i @ (^[Y0 : $i]: (((setadjoin @ (setadjoin @ sK71 @ emptyset) @ (setadjoin @ (setadjoin @ sK71 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK0) & (in @ Y0 @ (setunion @ sK0))))) & (in @ sK71 @ (setunion @ sK0))) = $true)),
% 16.62/3.71 inference(beta_eta_normalization,[status(thm)],[f2299])).
% 16.62/3.71 thf(f2299,plain,(
% 16.62/3.71 (((^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = sK0) & (in @ Y1 @ (setunion @ sK0))))) & (in @ Y0 @ (setunion @ sK0)))) @ sK71) = $true)),
% 16.62/3.71 inference(sigma_clausification,[status(thm)],[f2298])).
% 16.62/3.71 thf(f2298,plain,(
% 16.62/3.71 ($true = (?? @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = sK0) & (in @ Y1 @ (setunion @ sK0))))) & (in @ Y0 @ (setunion @ sK0))))))),
% 16.62/3.71 inference(beta_eta_normalization,[status(thm)],[f906])).
% 16.62/3.71 thf(f906,plain,(
% 16.62/3.71 ($true = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ (setunion @ Y0))))) & (in @ Y1 @ (setunion @ Y0)))))) @ sK0))),
% 16.62/3.71 inference(definition_unfolding,[status(thm)],[f576,f787])).
% 16.62/3.71 thf(f787,plain,(
% 16.62/3.71 (iskpair = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ (setunion @ Y0))))) & (in @ Y1 @ (setunion @ Y0)))))))),
% 16.62/3.71 inference(cnf_transformation,[status(thm)],[f204])).
% 16.62/3.71 thf(f204,plain,(
% 16.62/3.71 (iskpair = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ (setunion @ Y0))))) & (in @ Y1 @ (setunion @ Y0)))))))),
% 16.62/3.71 inference(fool_elimination,[status(thm)],[f203])).
% 16.62/3.71 thf(f203,plain,(
% 16.62/3.71 (iskpair = (^[X0 : $i] : (? [X1 : $i] : ((in @ X1 @ (setunion @ X0)) & ? [X2 : $i] : ((in @ X2 @ (setunion @ X0)) & ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = X0))))))),
% 16.62/3.71 inference(rectify,[status(thm)],[f135])).
% 16.62/3.71 thf(f135,axiom,(
% 16.62/3.71 (iskpair = (^[X3 : $i] : (? [X1 : $i] : ((in @ X1 @ (setunion @ X3)) & ? [X2 : $i] : ((in @ X2 @ (setunion @ X3)) & ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = X3))))))),
% 16.62/3.71 file('/export/starexec/sandbox2/tmp/tmp.UKH9onOzqj/DTF2THF_18632.p',iskpair)).
% 16.62/3.71 thf(f576,plain,(
% 16.62/3.71 ($true = (iskpair @ sK0))),
% 16.62/3.71 inference(cnf_transformation,[status(thm)],[f540])).
% 16.62/3.71 thf(f2366,plain,(
% 16.62/3.71 ((sP1 @ (setadjoin @ (setadjoin @ (kfst @ sK0) @ emptyset) @ (setadjoin @ (setadjoin @ (kfst @ sK0) @ (setadjoin @ (ksnd @ sK0) @ emptyset)) @ emptyset))) = $false)),
% 16.62/3.71 inference(beta_eta_normalization,[status(thm)],[f1073])).
% 16.62/3.71 thf(f1073,plain,(
% 16.62/3.71 ($false = (sP1 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))) @ (kfst @ sK0) @ (ksnd @ sK0))))),
% 16.62/3.71 introduced(definition,[new_symbols(naming,[sP1])],[inequality_splitting_name_introduction])).
% 16.62/3.71 thf(f3090,plain,(
% 16.62/3.71 ((sP1 @ (setadjoin @ (setadjoin @ sK71 @ emptyset) @ (setadjoin @ (setadjoin @ sK71 @ (setadjoin @ sK72 @ emptyset)) @ emptyset))) = $true)),
% 16.62/3.71 inference(forward_demodulation,[status(thm)],[f1074,f2307])).
% 16.62/3.71 thf(f1074,plain,(
% 16.62/3.71 ($true = (sP1 @ sK0))),
% 16.62/3.71 inference(inequality_splitting,[status(thm)],[f905,f1073])).
% 16.62/3.71 thf(f905,plain,(
% 16.62/3.71 (((^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))) @ (kfst @ sK0) @ (ksnd @ sK0)) != sK0)),
% 16.62/3.71 inference(definition_unfolding,[status(thm)],[f577,f548])).
% 16.62/3.71 thf(f577,plain,(
% 16.62/3.71 (sK0 != (kpair @ (kfst @ sK0) @ (ksnd @ sK0)))),
% 16.62/3.71 inference(cnf_transformation,[status(thm)],[f540])).
% 16.62/3.71 % SZS output end Proof for DTF2THF_18632
% 16.62/3.71 % (19142)------------------------------
% 16.62/3.71 % (19142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.62/3.71 % (19142)Termination reason: Refutation
% 16.62/3.71
% 16.62/3.71 % (19142)Memory used [KB]: 3582
% 16.62/3.71 % (19142)Time elapsed: 0.088 s
% 16.62/3.71 % (19142)Instructions burned: 295 (million)
% 16.62/3.71 % (19142)------------------------------
% 16.62/3.71 % (19142)------------------------------
% 16.62/3.71 % (18851)Success in time 2.173 s
%------------------------------------------------------------------------------