%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU647^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.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 09:35:55 AM UTC 2026
% Result : Theorem 2.53s 1.68s
% Output : Refutation 2.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 2831 ( 743 equ; 0 cnn)
% Maximal formula atoms : 165 ( 74 avg)
% Number of connectives : 1706 ( 39 ~; 25 |; 505 &; 472 @)
% ( 3 <=>; 662 =>; 0 <=; 0 <~>)
% Maximal formula depth : 170 ( 34 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 315 ( 312 usr; 175 con; 0-4 aty)
% Number of variables : 81 ( 0 ^; 54 !; 27 ?; 81 :)
% 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_206,type,
sP0: $i > $i > $o ).
thf(func_def_207,type,
sP1: $i > $o ).
thf(func_def_208,type,
sP2: $i > $i > $o ).
thf(func_def_209,type,
sP3: $i > $i > $o ).
thf(func_def_211,type,
sP5: $o > $i > $i > $i > $o ).
thf(func_def_227,type,
sK21: $i > $i > $i ).
thf(func_def_235,type,
sK29: $o > $i > $i > $i ).
thf(func_def_251,type,
sK45: $i > $o ).
thf(func_def_254,type,
sK48: $i > $o ).
thf(func_def_256,type,
sK50: $i > ( $i > $o ) > $i ).
thf(func_def_257,type,
sK51: $i > $i > $i ).
thf(func_def_258,type,
sK52: $i > $i > $i ).
thf(func_def_259,type,
sK53: $i > $i > $i ).
thf(func_def_260,type,
sK54: $i > $i > $i ).
thf(func_def_261,type,
sK55: $i > $i > $i ).
thf(func_def_262,type,
sK56: $i > $i > $i > $i ).
thf(func_def_263,type,
sK57: $i > $i ).
thf(func_def_264,type,
sK58: $i > $i ).
thf(func_def_265,type,
sK59: $i > $i ).
thf(func_def_266,type,
sK60: $i > $i ).
thf(func_def_267,type,
sK61: $i > $i > $i > $i ).
thf(func_def_268,type,
sK62: $i > $i > $i > $i ).
thf(func_def_269,type,
sK63: $i > $i > $i ).
thf(func_def_270,type,
sK64: $i > $i > $i ).
thf(func_def_271,type,
sK65: $i > $i > $i ).
thf(func_def_272,type,
sK66: $i > $i ).
thf(func_def_274,type,
sK68: $i > $i ).
thf(func_def_275,type,
sK69: $i > $i ).
thf(func_def_279,type,
sK73: $i > $i > $i ).
thf(func_def_285,type,
sK79: $i > $i > $i ).
thf(func_def_290,type,
sK84: $i > $i ).
thf(func_def_293,type,
sK87: $i > $i > $i ).
thf(func_def_312,type,
sK106: $i > $o ).
thf(func_def_319,type,
sK113: $i > $o ).
thf(func_def_325,type,
sK119: ( $i > $o ) > $i > $i ).
thf(func_def_327,type,
sK121: $i > $o ).
thf(func_def_343,type,
sK137: $i > $i ).
thf(func_def_356,type,
sK150: $i > $i > $i ).
thf(func_def_365,type,
sK159: $i > ( $i > $o ) > $i ).
thf(func_def_366,type,
sK160: $i > $o ).
thf(func_def_369,type,
sK163: $i > $o ).
thf(func_def_372,type,
sK166: $i > ( $i > $o ) > $i ).
thf(func_def_373,type,
sK167: $i > ( $i > $o ) > $i ).
thf(func_def_377,type,
sK171: $i > $i > $i > $i ).
thf(func_def_378,type,
sK172: $i > $i > $i > $i ).
thf(func_def_383,type,
sK177: $i > $i > $i ).
thf(func_def_389,type,
sK183: $i > $o ).
thf(func_def_394,type,
sK188: $i > $o ).
thf(func_def_395,type,
sK189: $i > $o ).
thf(func_def_396,type,
sK190: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_397,type,
sK191: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_398,type,
sK192: $i > ( $i > $o ) > $i ).
thf(func_def_399,type,
sK193: $i > $o ).
thf(func_def_411,type,
sK205: $i > $o ).
thf(func_def_413,type,
sK207: ( $i > $o ) > $i ).
thf(func_def_414,type,
sK208: ( $i > $o ) > $i ).
thf(func_def_418,type,
sK212: $i > $o ).
thf(func_def_459,type,
sK253: $i > $o ).
thf(func_def_462,type,
sK256: $i > $o ).
thf(func_def_465,type,
sK259: $i > ( $i > $o ) > $i ).
thf(func_def_485,type,
sK279: $i > $i > $i ).
thf(func_def_493,type,
sK287: $i > $i ).
thf(func_def_495,type,
sK289: $i > $o ).
thf(func_def_496,type,
sK290: $i > $o ).
thf(func_def_497,type,
sK291: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_498,type,
sK292: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_499,type,
sK293: $i > $i ).
thf(func_def_504,type,
sK298: ( $i > $o ) > $i ).
thf(func_def_505,type,
sK299: $i > $o ).
thf(func_def_508,type,
sK302: $i > $i > $i ).
thf(func_def_520,type,
sK314: $i > $o ).
thf(func_def_522,type,
sK316: $i > $o ).
thf(func_def_524,type,
sK318: ( $i > $o ) > $i > $i ).
thf(func_def_525,type,
sK319: ( $i > $o ) > $i > $i ).
thf(func_def_532,type,
sK326: $i > $i > $o ).
thf(func_def_533,type,
sK327: $i > $i ).
thf(func_def_534,type,
sK328: $i > $i ).
thf(func_def_535,type,
sK329: ( $i > $i > $o ) > $i > $i ).
thf(func_def_536,type,
sK330: ( $i > $i > $o ) > $i > $i ).
thf(func_def_537,type,
sK331: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_543,type,
sK337: $i > $o ).
thf(func_def_547,type,
sK341: $i > $o ).
thf(func_def_550,type,
sK344: $i > ( $i > $o ) > $i ).
thf(func_def_568,type,
sK362: $i > $i > $i ).
thf(func_def_569,type,
sK363: $i > $i > $i ).
thf(func_def_572,type,
sK366: $i > $i ).
thf(func_def_573,type,
sK367: $i > $i ).
thf(func_def_575,type,
sK369: $i > $i ).
thf(func_def_576,type,
sK370: $i > $o ).
thf(func_def_577,type,
sK371: $i > $o ).
thf(func_def_578,type,
sK372: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_579,type,
sK373: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_585,type,
sK379: $i > ( $i > $o ) > $i ).
thf(func_def_586,type,
sK380: $i > $o ).
thf(func_def_598,type,
sK392: $i > $o ).
thf(func_def_600,type,
sK394: ( $i > $o ) > $i > $i ).
thf(func_def_602,type,
sK396: $i > $o ).
thf(func_def_607,type,
sK401: ( $i > $o ) > $i ).
thf(func_def_608,type,
sK402: $i > $o ).
thf(func_def_609,type,
sK403: $i > $i ).
thf(func_def_621,type,
sK415: $i > $o ).
thf(func_def_625,type,
sK419: $i > $o ).
thf(func_def_640,type,
sK434: ( $i > $o ) > $i > $i ).
thf(func_def_642,type,
sK436: $i > $o ).
thf(func_def_643,type,
sK437: ( $i > $o ) > $i > $i > $i ).
thf(func_def_646,type,
sK440: $i > $o ).
thf(func_def_653,type,
sK447: ( $i > $o ) > $i ).
thf(func_def_654,type,
sK448: $i > $o ).
thf(func_def_655,type,
sK449: $i > $i ).
thf(func_def_657,type,
sK451: $i > $o ).
thf(func_def_663,type,
ph457:
!>[X0: $tType] : X0 ).
thf(f2549,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f2548]) ).
thf(f2548,plain,
sK441 != sK441,
inference(superposition,[status(thm)],[f2199,f2515]) ).
thf(f2515,plain,
sK441 = sK443,
inference(trivial_inequality_removal,[status(thm)],[f2514]) ).
thf(f2514,plain,
( ( sK441 = sK443 )
| ( $true != $true ) ),
inference(forward_demodulation,[status(thm)],[f2513,f2119]) ).
thf(f2119,plain,
setukpairinjL1 = $true,
inference(cnf_transformation,[status(thm)],[f1456]) ).
thf(f1456,plain,
( ( subsetE2 = $true )
& ( bs114d = $true )
& ( subsetTrans = $true )
& ( setminusIRneg = $true )
& ( cartprodpairin = $true )
& ( ex1E1 = $true )
& ( exu__Cong = $true )
& ( sepSubset = $true )
& ( binintersectSubset4 = $true )
& ( binunionEcases = $true )
& ( setminusELneg = $true )
& ( inCongP = $true )
& ( descr__Cong = $true )
& ( kfstsingleton = $true )
& ( setminusI = $true )
& ( subsetI1 = $true )
& ( notequalI2 = $true )
& ( subsetI2 = $true )
& ( kpairiskpair = $true )
& ( nonemptyI = $true )
& ( vacuousDall = $true )
& ( emptyinunitempty = $true )
& ( replAx = $true )
& ( cartprodfstin = $true )
& ( setminusSubset1 = $true )
& ( exuI1 = $true )
& ( singletoninpowunion = $true )
& ( wellorderingAx = $true )
& ( setadjoin__Cong = $true )
& ( setukpairIR = $true )
& ( setext = $true )
& ( nonemptyImpWitness = $true )
& ( binintersectRsub = $true )
& ( powersetsubset = $true )
& ( singletonsubset = $true )
& ( eqinunit = $true )
& ( upairsetIL = $true )
& ( sepInPowerset = $true )
& ( powersetE = $true )
& ( ex1I2 = $true )
& ( notequalI1 = $true )
& ( setunionI = $true )
& ( binunionIR = $true )
& ( upairsetE = $true )
& ( emptysetsubset = $true )
& ( singletoninpowerset = $true )
& ( omegaIndAx = $true )
& ( notdallE = $true )
& ( in__Cong = $true )
& ( binunionLsub = $true )
& ( symdiffIneg1 = $true )
& ( dsetconstr__Cong = $true )
& ( setunion__Cong = $true )
& ( setminusSubset2 = $true )
& ( quantDeMorgan3 = $true )
& ( notinsingleton = $true )
& ( secondinupair = $true )
& ( setunionE = $true )
& ( emptysetimpfalse = $true )
& ( subset2powerset = $true )
& ( eqimpsubset1 = $true )
& ( kfstpairEq = $true )
& ( exuEu = $true )
& ( omega0Ax = $true )
& ( sK441 != sK443 )
& ( ( setadjoin @ ( setadjoin @ sK443 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK443 @ ( setadjoin @ sK442 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK441 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK441 @ ( setadjoin @ sK444 @ emptyset ) ) @ emptyset ) ) )
& ( setadjoinSub2 = $true )
& ( setoftrueEq = $true )
& ( exuI3 = $true )
& ( subsetE = $true )
& ( binintersectLsub = $true )
& ( prop2set2propI = $true )
& ( emptysetE = $true )
& ( noeltsimpempty = $true )
& ( setadjoinOr = $true )
& ( cartprodmempair = $true )
& ( omegaSAx = $true )
& ( quantDeMorgan1 = $true )
& ( symdiffI2 = $true )
& ( setukpairIL = $true )
& ( quantDeMorgan4 = $true )
& ( powersetAx = $true )
& ( binintersectSubset3 = $true )
& ( omega__Cong = $true )
& ( symdiffIneg2 = $true )
& ( binintersectI = $true )
& ( symdiffI1 = $true )
& ( setadjoinIR = $true )
& ( subPowSU = $true )
& ( emptyE1 = $true )
& ( dsetconstrER = $true )
& ( binintersectER = $true )
& ( binunionRsub = $true )
& ( setextsub = $true )
& ( setadjoinSub = $true )
& ( dsetconstrI = $true )
& ( subsetemptysetimpeq = $true )
& ( setminusILneg = $true )
& ( emptysetAx = $true )
& ( setunionE2 = $true )
& ( kpairp = $true )
& ( setminusER = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( emptyinPowerset = $true )
& ( singletonprop = $true )
& ( exuE1 = $true )
& ( notdexE = $true )
& ( nonemptyE1 = $true )
& ( setunionsingleton = $true )
& ( setunionsingleton2 = $true )
& ( upairset2IR = $true )
& ( ubforcartprodlem1 = $true )
& ( binunionE = $true )
& ( uniqinunit = $true )
& ( prop2setI = $true )
& ( singletonsswitch = $true )
& ( disjointsetsI1 = $true )
& ( upairset2E = $true )
& ( powersetI1 = $true )
& ( setminusLsub = $true )
& ( setunionAx = $true )
& ( ubforcartprodlem2 = $true )
& ( emptyI = $true )
& ( setunionsingleton1 = $true )
& ( cartprodmempair1 = $true )
& ( theprop = $true )
& ( notsubsetI = $true )
& ( quantDeMorgan2 = $true )
& ( ubforcartprodlem3 = $true )
& ( subsetRefl = $true )
& ( exuI2 = $true )
& ( binunionIL = $true )
& ( exuE2 = $true )
& ( setadjoinAx = $true )
& ( dsetconstrEL = $true )
& ( exuE3u = $true )
& ( binintersectSubset2 = $true )
& ( ex1I = $true )
& ( foundationAx = $true )
& ( setadjoinIL = $true )
& ( binintersectSubset1 = $true )
& ( emptyInPowerset = $true )
& ( symdiffE = $true )
& ( setukpairinjL1 = $true )
& ( prop2setE = $true )
& ( powersetI = $true )
& ( eqimpsubset2 = $true )
& ( upairinpowunion = $true )
& ( binintersectEL = $true )
& ( setminusERneg = $true )
& ( descrp = $true )
& ( upairsetIR = $true )
& ( setbeta = $true )
& ( notinemptyset = $true )
& ( setadjoinE = $true )
& ( upairsubunion = $true )
& ( binintersectSubset5 = $true )
& ( emptyset__Cong = $true )
& ( exuE3e = $true )
& ( setextAx = $true )
& ( nonemptyI1 = $true )
& ( powerset__Cong = $true )
& ( setminusEL = $true )
& ( singletonsuniq = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK441,sK442,sK443,sK444])],[f672,f1455]) ).
thf(f1455,plain,
( ? [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 != X2 )
& ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ( sK441 != sK443 )
& ( ( setadjoin @ ( setadjoin @ sK443 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK443 @ ( setadjoin @ sK442 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK441 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK441 @ ( setadjoin @ sK444 @ emptyset ) ) @ emptyset ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f672,plain,
( ( subsetE2 = $true )
& ( bs114d = $true )
& ( subsetTrans = $true )
& ( setminusIRneg = $true )
& ( cartprodpairin = $true )
& ( ex1E1 = $true )
& ( exu__Cong = $true )
& ( sepSubset = $true )
& ( binintersectSubset4 = $true )
& ( binunionEcases = $true )
& ( setminusELneg = $true )
& ( inCongP = $true )
& ( descr__Cong = $true )
& ( kfstsingleton = $true )
& ( setminusI = $true )
& ( subsetI1 = $true )
& ( notequalI2 = $true )
& ( subsetI2 = $true )
& ( kpairiskpair = $true )
& ( nonemptyI = $true )
& ( vacuousDall = $true )
& ( emptyinunitempty = $true )
& ( replAx = $true )
& ( cartprodfstin = $true )
& ( setminusSubset1 = $true )
& ( exuI1 = $true )
& ( singletoninpowunion = $true )
& ( wellorderingAx = $true )
& ( setadjoin__Cong = $true )
& ( setukpairIR = $true )
& ( setext = $true )
& ( nonemptyImpWitness = $true )
& ( binintersectRsub = $true )
& ( powersetsubset = $true )
& ( singletonsubset = $true )
& ( eqinunit = $true )
& ( upairsetIL = $true )
& ( sepInPowerset = $true )
& ( powersetE = $true )
& ( ex1I2 = $true )
& ( notequalI1 = $true )
& ( setunionI = $true )
& ( binunionIR = $true )
& ( upairsetE = $true )
& ( emptysetsubset = $true )
& ( singletoninpowerset = $true )
& ( omegaIndAx = $true )
& ( notdallE = $true )
& ( in__Cong = $true )
& ( binunionLsub = $true )
& ( symdiffIneg1 = $true )
& ( dsetconstr__Cong = $true )
& ( setunion__Cong = $true )
& ( setminusSubset2 = $true )
& ( quantDeMorgan3 = $true )
& ( notinsingleton = $true )
& ( secondinupair = $true )
& ( setunionE = $true )
& ( emptysetimpfalse = $true )
& ( subset2powerset = $true )
& ( eqimpsubset1 = $true )
& ( kfstpairEq = $true )
& ( exuEu = $true )
& ( omega0Ax = $true )
& ? [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 != X2 )
& ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
& ( setadjoinSub2 = $true )
& ( setoftrueEq = $true )
& ( exuI3 = $true )
& ( subsetE = $true )
& ( binintersectLsub = $true )
& ( prop2set2propI = $true )
& ( emptysetE = $true )
& ( noeltsimpempty = $true )
& ( setadjoinOr = $true )
& ( cartprodmempair = $true )
& ( omegaSAx = $true )
& ( quantDeMorgan1 = $true )
& ( symdiffI2 = $true )
& ( setukpairIL = $true )
& ( quantDeMorgan4 = $true )
& ( powersetAx = $true )
& ( binintersectSubset3 = $true )
& ( omega__Cong = $true )
& ( symdiffIneg2 = $true )
& ( binintersectI = $true )
& ( symdiffI1 = $true )
& ( setadjoinIR = $true )
& ( subPowSU = $true )
& ( emptyE1 = $true )
& ( dsetconstrER = $true )
& ( binintersectER = $true )
& ( binunionRsub = $true )
& ( setextsub = $true )
& ( setadjoinSub = $true )
& ( dsetconstrI = $true )
& ( subsetemptysetimpeq = $true )
& ( setminusILneg = $true )
& ( emptysetAx = $true )
& ( setunionE2 = $true )
& ( kpairp = $true )
& ( setminusER = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( emptyinPowerset = $true )
& ( singletonprop = $true )
& ( exuE1 = $true )
& ( notdexE = $true )
& ( nonemptyE1 = $true )
& ( setunionsingleton = $true )
& ( setunionsingleton2 = $true )
& ( upairset2IR = $true )
& ( ubforcartprodlem1 = $true )
& ( binunionE = $true )
& ( uniqinunit = $true )
& ( prop2setI = $true )
& ( singletonsswitch = $true )
& ( disjointsetsI1 = $true )
& ( upairset2E = $true )
& ( powersetI1 = $true )
& ( setminusLsub = $true )
& ( setunionAx = $true )
& ( ubforcartprodlem2 = $true )
& ( emptyI = $true )
& ( setunionsingleton1 = $true )
& ( cartprodmempair1 = $true )
& ( theprop = $true )
& ( notsubsetI = $true )
& ( quantDeMorgan2 = $true )
& ( ubforcartprodlem3 = $true )
& ( subsetRefl = $true )
& ( exuI2 = $true )
& ( binunionIL = $true )
& ( exuE2 = $true )
& ( setadjoinAx = $true )
& ( dsetconstrEL = $true )
& ( exuE3u = $true )
& ( binintersectSubset2 = $true )
& ( ex1I = $true )
& ( foundationAx = $true )
& ( setadjoinIL = $true )
& ( binintersectSubset1 = $true )
& ( emptyInPowerset = $true )
& ( symdiffE = $true )
& ( setukpairinjL1 = $true )
& ( prop2setE = $true )
& ( powersetI = $true )
& ( eqimpsubset2 = $true )
& ( upairinpowunion = $true )
& ( binintersectEL = $true )
& ( setminusERneg = $true )
& ( descrp = $true )
& ( upairsetIR = $true )
& ( setbeta = $true )
& ( notinemptyset = $true )
& ( setadjoinE = $true )
& ( upairsubunion = $true )
& ( binintersectSubset5 = $true )
& ( emptyset__Cong = $true )
& ( exuE3e = $true )
& ( setextAx = $true )
& ( nonemptyI1 = $true )
& ( powerset__Cong = $true )
& ( setminusEL = $true )
& ( singletonsuniq = $true ) ),
inference(flattening,[status(thm)],[f671]) ).
thf(f671,plain,
( ? [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 != X2 )
& ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
& ( 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)],[f226]) ).
thf(f226,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 )
=> ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( X0 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f225]) ).
thf(f225,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
=> ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
=> ( X0 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f171]) ).
thf(f171,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
=> ! [X1: $i,X10: $i,X8: $i,X2: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X8 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) )
=> ( X1 = X8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f170]) ).
thf(f170,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
=> ! [X1: $i,X10: $i,X8: $i,X2: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X8 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) )
=> ( X1 = X8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.VeTrV6L3FZ/DTF2THF_4923.p',setukpairinjL2) ).
thf(f2513,plain,
( ( setukpairinjL1 != $true )
| ( sK441 = sK443 ) ),
inference(trivial_inequality_removal,[status(thm)],[f2500]) ).
thf(f2500,plain,
( ( setukpairinjL1 != $true )
| ( sK441 = sK443 )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1898,f2429]) ).
thf(f2429,plain,
( $true
= ( in @ ( setadjoin @ sK443 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK441 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK441 @ ( setadjoin @ sK444 @ emptyset ) ) @ emptyset ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f2428]) ).
thf(f2428,plain,
( ( $true != $true )
| ( $true
= ( in @ ( setadjoin @ sK443 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK441 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK441 @ ( setadjoin @ sK444 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2422,f2123]) ).
thf(f2123,plain,
setadjoinIL = $true,
inference(cnf_transformation,[status(thm)],[f1456]) ).
thf(f2422,plain,
( ( setadjoinIL != $true )
| ( $true
= ( in @ ( setadjoin @ sK443 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK441 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK441 @ ( setadjoin @ sK444 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(superposition,[status(thm)],[f1816,f2198]) ).
thf(f2198,plain,
( ( setadjoin @ ( setadjoin @ sK443 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK443 @ ( setadjoin @ sK442 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK441 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK441 @ ( setadjoin @ sK444 @ emptyset ) ) @ emptyset ) ) ),
inference(cnf_transformation,[status(thm)],[f1456]) ).
thf(f1816,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
| ( setadjoinIL != $true ) ),
inference(cnf_transformation,[status(thm)],[f1118]) ).
thf(f1118,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ( ( in @ sK241 @ ( setadjoin @ sK241 @ sK240 ) )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK240,sK241])],[f1116,f1117]) ).
thf(f1117,plain,
( ? [X2: $i,X3: $i] :
( $true
!= ( in @ X3 @ ( setadjoin @ X3 @ X2 ) ) )
=> ( ( in @ sK241 @ ( setadjoin @ sK241 @ sK240 ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1116,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ? [X2: $i,X3: $i] :
( $true
!= ( in @ X3 @ ( setadjoin @ X3 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f1115]) ).
thf(f1115,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
| ( setadjoinIL != $true ) )
& ( ( setadjoinIL = $true )
| ? [X0: $i,X1: $i] :
( $true
!= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f309]) ).
thf(f309,plain,
( ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
<=> ( setadjoinIL = $true ) ),
inference(fool_elimination,[status(thm)],[f308]) ).
thf(f308,plain,
! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X1 @ X0 ) )
= setadjoinIL ),
inference(rectify,[status(thm)],[f31]) ).
thf(f31,axiom,
! [X2: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
= setadjoinIL ),
file('/export/starexec/sandbox/tmp/tmp.VeTrV6L3FZ/DTF2THF_4923.p',setadjoinIL) ).
thf(f1898,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
| ( X0 = X1 )
| ( setukpairinjL1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f1215]) ).
thf(f1215,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
| ( X0 = X1 ) )
| ( setukpairinjL1 != $true ) )
& ( ( setukpairinjL1 = $true )
| ( ( $true
= ( in @ ( setadjoin @ sK296 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK295 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK295 @ ( setadjoin @ sK297 @ emptyset ) ) @ emptyset ) ) ) )
& ( sK295 != sK296 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK295,sK296,sK297])],[f1213,f1214]) ).
thf(f1214,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X5 @ emptyset ) ) @ emptyset ) ) )
= $true )
& ( X3 != X4 ) )
=> ( ( $true
= ( in @ ( setadjoin @ sK296 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK295 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK295 @ ( setadjoin @ sK297 @ emptyset ) ) @ emptyset ) ) ) )
& ( sK295 != sK296 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1213,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
| ( X0 = X1 ) )
| ( setukpairinjL1 != $true ) )
& ( ( setukpairinjL1 = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X5 @ emptyset ) ) @ emptyset ) ) )
= $true )
& ( X3 != X4 ) ) ) ),
inference(rectify,[status(thm)],[f1212]) ).
thf(f1212,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
| ( X0 = X1 ) )
| ( setukpairinjL1 != $true ) )
& ( ( setukpairinjL1 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
& ( X0 != X1 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f556]) ).
thf(f556,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
| ( X0 = X1 ) )
<=> ( setukpairinjL1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f455]) ).
thf(f455,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
=> ( X0 = X1 ) )
<=> ( setukpairinjL1 = $true ) ),
inference(fool_elimination,[status(thm)],[f454]) ).
thf(f454,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
=> ( X0 = X1 ) )
= setukpairinjL1 ),
inference(rectify,[status(thm)],[f165]) ).
thf(f165,axiom,
! [X1: $i,X8: $i,X2: $i] :
( ( ( in @ ( setadjoin @ X8 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
=> ( X1 = X8 ) )
= setukpairinjL1 ),
file('/export/starexec/sandbox/tmp/tmp.VeTrV6L3FZ/DTF2THF_4923.p',setukpairinjL1) ).
thf(f2199,plain,
sK441 != sK443,
inference(cnf_transformation,[status(thm)],[f1456]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU647^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n015.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue Feb 24 12:30:16 EST 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.45 thf(spec,logic,$$dhol).
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % File : SEU647^1 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.45 % Domain : Set Theory
% 0.29/0.45 % Problem : Ordered Pairs - Properties of Pairs
% 0.29/0.45 % Version : Especial.
% 0.29/0.45 % English : (! x:i.! y:i.! z:i.! u:i.setadjoin (setadjoin x emptyset)
% 0.29/0.45 % (setadjoin (setadjoin x (setadjoin y emptyset)) emptyset) =
% 0.29/0.45 % setadjoin (setadjoin z emptyset) (setadjoin (setadjoin z
% 0.29/0.45 % (setadjoin u emptyset)) emptyset) -> x = z)
% 0.29/0.45
% 0.29/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.29/0.45 % Source : [Bro08]
% 0.29/0.45 % Names : ZFC149g [Bro08]
% 0.29/0.45
% 0.29/0.45 % Status : Theorem
% 0.29/0.45 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v5.5.0, 0.50 v5.4.0, 0.60 v5.1.0, 0.80 v5.0.0, 0.60 v4.1.0, 0.67 v3.7.0
% 0.29/0.45 % Syntax : Number of formulae : 363 ( 169 unt; 193 typ; 169 def)
% 0.29/0.45 % Number of atoms : 896 ( 241 equ; 0 cnn)
% 0.29/0.45 % Maximal formula atoms : 165 ( 5 avg)
% 0.29/0.45 % Number of connectives : 1566 ( 47 ~; 7 |; 37 &;1065 @)
% 0.29/0.45 % ( 14 <=>; 396 =>; 0 <=; 0 <~>)
% 0.29/0.45 % Maximal formula depth : 169 ( 2 avg)
% 0.29/0.45 % Number of types : 2 ( 0 usr)
% 0.29/0.45 % Number of type conns : 83 ( 83 >; 0 *; 0 +; 0 <<)
% 0.29/0.45 % Number of symbols : 196 ( 193 usr; 167 con; 0-2 aty)
% 0.29/0.45 % Number of variables : 492 ( 42 ^; 412 !; 38 ?; 492 :)
% 0.29/0.45 % SPC : TH0_THM_EQU_NAR
% 0.29/0.45
% 0.29/0.45 % Comments : http://mathgate.info/detsetitem.php?id=204
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 thf(in_type,type,
% 0.29/0.45 in: $i > $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(exu_type,type,
% 0.29/0.45 exu: ( $i > $o ) > $o ).
% 0.29/0.45
% 0.29/0.45 thf(exu,definition,
% 0.29/0.45 ( exu
% 0.29/0.45 = ( ^ [Xphi: $i > $o] :
% 0.29/0.45 ? [Xx: $i] :
% 0.29/0.45 ( ( Xphi @ Xx )
% 0.29/0.45 & ! [Xy: $i] :
% 0.29/0.45 ( ( Xphi @ Xy )
% 0.29/0.45 => ( Xx = Xy ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(setextAx_type,type,
% 0.29/0.45 setextAx: $o ).
% 0.29/0.45
% 0.29/0.45 thf(setextAx,definition,
% 0.29/0.45 ( setextAx
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 <=> ( in @ Xx @ B ) )
% 0.29/0.45 => ( A = B ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(emptyset_type,type,
% 0.29/0.45 emptyset: $i ).
% 0.29/0.45
% 0.29/0.45 thf(emptysetAx_type,type,
% 0.29/0.45 emptysetAx: $o ).
% 0.29/0.45
% 0.29/0.45 thf(emptysetAx,definition,
% 0.29/0.45 ( emptysetAx
% 0.29/0.45 = ( ! [Xx: $i] :
% 0.29/0.45 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(setadjoin_type,type,
% 0.29/0.45 setadjoin: $i > $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(setadjoinAx_type,type,
% 0.29/0.45 setadjoinAx: $o ).
% 0.29/0.45
% 0.29/0.45 thf(setadjoinAx,definition,
% 0.29/0.45 ( setadjoinAx
% 0.29/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.45 <=> ( ( Xy = Xx )
% 0.29/0.45 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(powerset_type,type,
% 0.29/0.45 powerset: $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(powersetAx_type,type,
% 0.29/0.45 powersetAx: $o ).
% 0.29/0.45
% 0.29/0.45 thf(powersetAx,definition,
% 0.29/0.45 ( powersetAx
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.45 <=> ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ B )
% 0.29/0.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(setunion_type,type,
% 0.29/0.45 setunion: $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(setunionAx_type,type,
% 0.29/0.45 setunionAx: $o ).
% 0.29/0.45
% 0.29/0.45 thf(setunionAx,definition,
% 0.29/0.45 ( setunionAx
% 0.29/0.45 = ( ! [A: $i,Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.45 <=> ? [B: $i] :
% 0.29/0.45 ( ( in @ Xx @ B )
% 0.29/0.45 & ( in @ B @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(omega_type,type,
% 0.29/0.45 omega: $i ).
% 0.29/0.45
% 0.29/0.45 thf(omega0Ax_type,type,
% 0.29/0.45 omega0Ax: $o ).
% 0.29/0.45
% 0.29/0.45 thf(omega0Ax,definition,
% 0.29/0.45 ( omega0Ax
% 0.29/0.45 = ( in @ emptyset @ omega ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(omegaSAx_type,type,
% 0.29/0.45 omegaSAx: $o ).
% 0.29/0.45
% 0.29/0.45 thf(omegaSAx,definition,
% 0.29/0.45 ( omegaSAx
% 0.29/0.45 = ( ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ omega )
% 0.29/0.45 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(omegaIndAx_type,type,
% 0.29/0.45 omegaIndAx: $o ).
% 0.29/0.45
% 0.29/0.45 thf(omegaIndAx,definition,
% 0.29/0.45 ( omegaIndAx
% 0.29/0.45 = ( ! [A: $i] :
% 0.29/0.45 ( ( ( in @ emptyset @ A )
% 0.29/0.45 & ! [Xx: $i] :
% 0.29/0.45 ( ( ( in @ Xx @ omega )
% 0.29/0.45 & ( in @ Xx @ A ) )
% 0.29/0.45 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.29/0.45 => ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ omega )
% 0.29/0.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(replAx_type,type,
% 0.29/0.45 replAx: $o ).
% 0.29/0.45
% 0.29/0.45 thf(replAx,definition,
% 0.29/0.45 ( replAx
% 0.29/0.45 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.29/0.45 ( ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 => ( exu
% 0.29/0.45 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.29/0.45 => ? [B: $i] :
% 0.29/0.45 ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ B )
% 0.29/0.45 <=> ? [Xy: $i] :
% 0.29/0.45 ( ( in @ Xy @ A )
% 0.29/0.45 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(foundationAx_type,type,
% 0.29/0.45 foundationAx: $o ).
% 0.29/0.45
% 0.29/0.45 thf(foundationAx,definition,
% 0.29/0.45 ( foundationAx
% 0.29/0.45 = ( ! [A: $i] :
% 0.29/0.45 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.29/0.45 => ? [B: $i] :
% 0.29/0.45 ( ( in @ B @ A )
% 0.29/0.45 & ~ ? [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ B )
% 0.29/0.45 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(wellorderingAx_type,type,
% 0.29/0.45 wellorderingAx: $o ).
% 0.29/0.45
% 0.29/0.45 thf(wellorderingAx,definition,
% 0.29/0.45 ( wellorderingAx
% 0.29/0.45 = ( ! [A: $i] :
% 0.29/0.45 ? [B: $i] :
% 0.29/0.45 ( ! [C: $i] :
% 0.29/0.45 ( ( in @ C @ B )
% 0.29/0.45 => ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ C )
% 0.29/0.45 => ( in @ Xx @ A ) ) )
% 0.29/0.45 & ! [Xx: $i,Xy: $i] :
% 0.29/0.45 ( ( ( in @ Xx @ A )
% 0.29/0.45 & ( in @ Xy @ A ) )
% 0.29/0.45 => ( ! [C: $i] :
% 0.29/0.45 ( ( in @ C @ B )
% 0.29/0.45 => ( ( in @ Xx @ C )
% 0.29/0.45 <=> ( in @ Xy @ C ) ) )
% 0.29/0.45 => ( Xx = Xy ) ) )
% 0.29/0.45 & ! [C: $i,D: $i] :
% 0.29/0.45 ( ( ( in @ C @ B )
% 0.29/0.45 & ( in @ D @ B ) )
% 0.29/0.45 => ( ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ C )
% 0.29/0.45 => ( in @ Xx @ D ) )
% 0.29/0.45 | ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ D )
% 0.29/0.45 => ( in @ Xx @ C ) ) ) )
% 0.29/0.45 & ! [C: $i] :
% 0.29/0.45 ( ( ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ C )
% 0.29/0.45 => ( in @ Xx @ A ) )
% 0.29/0.45 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.29/0.45 => ? [D: $i,Xx: $i] :
% 0.29/0.45 ( ( in @ D @ B )
% 0.29/0.45 & ( in @ Xx @ C )
% 0.29/0.45 & ~ ? [Xy: $i] :
% 0.29/0.45 ( ( in @ Xy @ D )
% 0.29/0.45 & ( in @ Xy @ C ) )
% 0.29/0.45 & ! [E: $i] :
% 0.29/0.45 ( ( in @ E @ B )
% 0.29/0.45 => ( ! [Xy: $i] :
% 0.29/0.45 ( ( in @ Xy @ E )
% 0.29/0.45 => ( in @ Xy @ D ) )
% 0.29/0.45 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(descr_type,type,
% 0.29/0.45 descr: ( $i > $o ) > $i ).
% 0.29/0.45
% 0.29/0.45 thf(descrp_type,type,
% 0.29/0.45 descrp: $o ).
% 0.29/0.45
% 0.29/0.45 thf(descrp,definition,
% 0.29/0.45 ( descrp
% 0.29/0.45 = ( ! [Xphi: $i > $o] :
% 0.29/0.45 ( ( exu
% 0.29/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.45 => ( Xphi
% 0.29/0.45 @ ( descr
% 0.29/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(dsetconstr_type,type,
% 0.29/0.45 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.29/0.45
% 0.29/0.45 thf(dsetconstrI_type,type,
% 0.29/0.45 dsetconstrI: $o ).
% 0.29/0.45
% 0.29/0.45 thf(dsetconstrI,definition,
% 0.29/0.45 ( dsetconstrI
% 0.29/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 => ( ( Xphi @ Xx )
% 0.29/0.45 => ( in @ Xx
% 0.29/0.45 @ ( dsetconstr @ A
% 0.29/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(dsetconstrEL_type,type,
% 0.29/0.45 dsetconstrEL: $o ).
% 0.29/0.45
% 0.29/0.45 thf(dsetconstrEL,definition,
% 0.29/0.45 ( dsetconstrEL
% 0.29/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.45 ( ( in @ Xx
% 0.29/0.45 @ ( dsetconstr @ A
% 0.29/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.45 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(dsetconstrER_type,type,
% 0.29/0.45 dsetconstrER: $o ).
% 0.29/0.45
% 0.29/0.45 thf(dsetconstrER,definition,
% 0.29/0.45 ( dsetconstrER
% 0.29/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.45 ( ( in @ Xx
% 0.29/0.45 @ ( dsetconstr @ A
% 0.29/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.45 => ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(exuE1_type,type,
% 0.29/0.45 exuE1: $o ).
% 0.29/0.45
% 0.29/0.45 thf(exuE1,definition,
% 0.29/0.45 ( exuE1
% 0.29/0.45 = ( ! [Xphi: $i > $o] :
% 0.29/0.45 ( ( exu
% 0.29/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.45 => ? [Xx: $i] :
% 0.29/0.45 ( ( Xphi @ Xx )
% 0.29/0.45 & ! [Xy: $i] :
% 0.29/0.45 ( ( Xphi @ Xy )
% 0.29/0.45 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(prop2set_type,type,
% 0.29/0.45 prop2set: $o > $i ).
% 0.29/0.45
% 0.29/0.45 thf(prop2setE_type,type,
% 0.29/0.45 prop2setE: $o ).
% 0.29/0.45
% 0.29/0.45 thf(prop2setE,definition,
% 0.29/0.45 ( prop2setE
% 0.29/0.45 = ( ! [Xphi: $o,Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.29/0.45 => Xphi ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(emptysetE_type,type,
% 0.29/0.45 emptysetE: $o ).
% 0.29/0.45
% 0.29/0.45 thf(emptysetE,definition,
% 0.29/0.45 ( emptysetE
% 0.29/0.45 = ( ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ emptyset )
% 0.29/0.45 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(emptysetimpfalse_type,type,
% 0.29/0.45 emptysetimpfalse: $o ).
% 0.29/0.45
% 0.29/0.45 thf(emptysetimpfalse,definition,
% 0.29/0.45 ( emptysetimpfalse
% 0.29/0.45 = ( ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ emptyset )
% 0.29/0.45 => $false ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(notinemptyset_type,type,
% 0.29/0.45 notinemptyset: $o ).
% 0.29/0.45
% 0.29/0.45 thf(notinemptyset,definition,
% 0.29/0.45 ( notinemptyset
% 0.29/0.45 = ( ! [Xx: $i] :
% 0.29/0.45 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(exuE3e_type,type,
% 0.29/0.45 exuE3e: $o ).
% 0.29/0.45
% 0.29/0.45 thf(exuE3e,definition,
% 0.29/0.45 ( exuE3e
% 0.29/0.45 = ( ! [Xphi: $i > $o] :
% 0.29/0.45 ( ( exu
% 0.29/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.45 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(setext_type,type,
% 0.29/0.45 setext: $o ).
% 0.29/0.45
% 0.29/0.45 thf(setext,definition,
% 0.29/0.45 ( setext
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 => ( in @ Xx @ B ) )
% 0.29/0.45 => ( ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ B )
% 0.29/0.45 => ( in @ Xx @ A ) )
% 0.29/0.45 => ( A = B ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(emptyI_type,type,
% 0.29/0.45 emptyI: $o ).
% 0.29/0.45
% 0.29/0.45 thf(emptyI,definition,
% 0.29/0.45 ( emptyI
% 0.29/0.45 = ( ! [A: $i] :
% 0.29/0.45 ( ! [Xx: $i] :
% 0.29/0.45 ~ ( in @ Xx @ A )
% 0.29/0.45 => ( A = emptyset ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(noeltsimpempty_type,type,
% 0.29/0.45 noeltsimpempty: $o ).
% 0.29/0.45
% 0.29/0.45 thf(noeltsimpempty,definition,
% 0.29/0.45 ( noeltsimpempty
% 0.29/0.45 = ( ! [A: $i] :
% 0.29/0.45 ( ! [Xx: $i] :
% 0.29/0.45 ~ ( in @ Xx @ A )
% 0.29/0.45 => ( A = emptyset ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(setbeta_type,type,
% 0.29/0.45 setbeta: $o ).
% 0.29/0.45
% 0.29/0.45 thf(setbeta,definition,
% 0.29/0.45 ( setbeta
% 0.29/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 => ( ( in @ Xx
% 0.29/0.45 @ ( dsetconstr @ A
% 0.29/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.45 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(nonempty_type,type,
% 0.29/0.45 nonempty: $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(nonempty,definition,
% 0.29/0.45 ( nonempty
% 0.29/0.45 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(nonemptyE1_type,type,
% 0.29/0.45 nonemptyE1: $o ).
% 0.29/0.45
% 0.29/0.45 thf(nonemptyE1,definition,
% 0.29/0.45 ( nonemptyE1
% 0.29/0.45 = ( ! [A: $i] :
% 0.29/0.45 ( ( nonempty @ A )
% 0.29/0.45 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(nonemptyI_type,type,
% 0.29/0.45 nonemptyI: $o ).
% 0.29/0.45
% 0.29/0.45 thf(nonemptyI,definition,
% 0.29/0.45 ( nonemptyI
% 0.29/0.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 => ( ( Xphi @ Xx )
% 0.29/0.45 => ( nonempty
% 0.29/0.45 @ ( dsetconstr @ A
% 0.29/0.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(nonemptyI1_type,type,
% 0.29/0.45 nonemptyI1: $o ).
% 0.29/0.45
% 0.29/0.45 thf(nonemptyI1,definition,
% 0.29/0.45 ( nonemptyI1
% 0.29/0.45 = ( ! [A: $i] :
% 0.29/0.45 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.29/0.45 => ( nonempty @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(setadjoinIL_type,type,
% 0.29/0.45 setadjoinIL: $o ).
% 0.29/0.45
% 0.29/0.45 thf(setadjoinIL,definition,
% 0.29/0.45 ( setadjoinIL
% 0.29/0.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(emptyinunitempty_type,type,
% 0.29/0.45 emptyinunitempty: $o ).
% 0.29/0.45
% 0.29/0.45 thf(emptyinunitempty,definition,
% 0.29/0.45 ( emptyinunitempty
% 0.29/0.45 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(setadjoinIR_type,type,
% 0.29/0.45 setadjoinIR: $o ).
% 0.29/0.45
% 0.29/0.45 thf(setadjoinIR,definition,
% 0.29/0.45 ( setadjoinIR
% 0.29/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.45 ( ( in @ Xy @ A )
% 0.29/0.45 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(setadjoinE_type,type,
% 0.29/0.45 setadjoinE: $o ).
% 0.29/0.45
% 0.29/0.45 thf(setadjoinE,definition,
% 0.29/0.45 ( setadjoinE
% 0.29/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.45 => ! [Xphi: $o] :
% 0.29/0.45 ( ( ( Xy = Xx )
% 0.29/0.45 => Xphi )
% 0.29/0.45 => ( ( ( in @ Xy @ A )
% 0.29/0.45 => Xphi )
% 0.29/0.45 => Xphi ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(setadjoinOr_type,type,
% 0.29/0.45 setadjoinOr: $o ).
% 0.29/0.45
% 0.29/0.45 thf(setadjoinOr,definition,
% 0.29/0.45 ( setadjoinOr
% 0.29/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.45 => ( ( Xy = Xx )
% 0.29/0.45 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(setoftrueEq_type,type,
% 0.29/0.45 setoftrueEq: $o ).
% 0.29/0.45
% 0.29/0.45 thf(setoftrueEq,definition,
% 0.29/0.45 ( setoftrueEq
% 0.29/0.45 = ( ! [A: $i] :
% 0.29/0.45 ( ( dsetconstr @ A
% 0.29/0.45 @ ^ [Xx: $i] : $true )
% 0.29/0.45 = A ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(powersetI_type,type,
% 0.29/0.45 powersetI: $o ).
% 0.29/0.45
% 0.29/0.45 thf(powersetI,definition,
% 0.29/0.45 ( powersetI
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ B )
% 0.29/0.45 => ( in @ Xx @ A ) )
% 0.29/0.45 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(emptyinPowerset_type,type,
% 0.29/0.45 emptyinPowerset: $o ).
% 0.29/0.45
% 0.29/0.45 thf(emptyinPowerset,definition,
% 0.29/0.45 ( emptyinPowerset
% 0.29/0.45 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(emptyInPowerset_type,type,
% 0.29/0.45 emptyInPowerset: $o ).
% 0.29/0.45
% 0.29/0.45 thf(emptyInPowerset,definition,
% 0.29/0.45 ( emptyInPowerset
% 0.29/0.45 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(powersetE_type,type,
% 0.29/0.45 powersetE: $o ).
% 0.29/0.45
% 0.29/0.45 thf(powersetE,definition,
% 0.29/0.45 ( powersetE
% 0.29/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.45 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.45 => ( ( in @ Xx @ B )
% 0.29/0.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(setunionI_type,type,
% 0.29/0.45 setunionI: $o ).
% 0.29/0.45
% 0.29/0.45 thf(setunionI,definition,
% 0.29/0.45 ( setunionI
% 0.29/0.45 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.29/0.45 ( ( in @ Xx @ B )
% 0.29/0.45 => ( ( in @ B @ A )
% 0.29/0.45 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(setunionE_type,type,
% 0.29/0.45 setunionE: $o ).
% 0.29/0.45
% 0.29/0.45 thf(setunionE,definition,
% 0.29/0.45 ( setunionE
% 0.29/0.45 = ( ! [A: $i,Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.45 => ! [Xphi: $o] :
% 0.29/0.45 ( ! [B: $i] :
% 0.29/0.45 ( ( in @ Xx @ B )
% 0.29/0.45 => ( ( in @ B @ A )
% 0.29/0.45 => Xphi ) )
% 0.29/0.45 => Xphi ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(subPowSU_type,type,
% 0.29/0.45 subPowSU: $o ).
% 0.29/0.45
% 0.29/0.45 thf(subPowSU,definition,
% 0.29/0.45 ( subPowSU
% 0.29/0.45 = ( ! [A: $i,Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(exuE2_type,type,
% 0.29/0.45 exuE2: $o ).
% 0.29/0.45
% 0.29/0.45 thf(exuE2,definition,
% 0.29/0.45 ( exuE2
% 0.29/0.45 = ( ! [Xphi: $i > $o] :
% 0.29/0.45 ( ( exu
% 0.29/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.45 => ? [Xx: $i] :
% 0.29/0.45 ! [Xy: $i] :
% 0.29/0.45 ( ( Xphi @ Xy )
% 0.29/0.45 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(nonemptyImpWitness_type,type,
% 0.29/0.45 nonemptyImpWitness: $o ).
% 0.29/0.45
% 0.29/0.45 thf(nonemptyImpWitness,definition,
% 0.29/0.45 ( nonemptyImpWitness
% 0.29/0.45 = ( ! [A: $i] :
% 0.29/0.45 ( ( nonempty @ A )
% 0.29/0.45 => ? [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 & $true ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(uniqinunit_type,type,
% 0.29/0.45 uniqinunit: $o ).
% 0.29/0.45
% 0.29/0.45 thf(uniqinunit,definition,
% 0.29/0.45 ( uniqinunit
% 0.29/0.45 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.45 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.45 => ( Xx = Xy ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(notinsingleton_type,type,
% 0.29/0.45 notinsingleton: $o ).
% 0.29/0.45
% 0.29/0.45 thf(notinsingleton,definition,
% 0.29/0.45 ( notinsingleton
% 0.29/0.45 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.45 ( ( Xx != Xy )
% 0.29/0.45 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(eqinunit_type,type,
% 0.29/0.45 eqinunit: $o ).
% 0.29/0.45
% 0.29/0.45 thf(eqinunit,definition,
% 0.29/0.45 ( eqinunit
% 0.29/0.45 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.45 ( ( Xx = Xy )
% 0.29/0.45 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(singletonsswitch_type,type,
% 0.29/0.45 singletonsswitch: $o ).
% 0.29/0.45
% 0.29/0.45 thf(singletonsswitch,definition,
% 0.29/0.45 ( singletonsswitch
% 0.29/0.45 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.45 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.45 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(upairsetE_type,type,
% 0.29/0.45 upairsetE: $o ).
% 0.29/0.45
% 0.29/0.45 thf(upairsetE,definition,
% 0.29/0.45 ( upairsetE
% 0.29/0.45 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.29/0.45 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.29/0.45 => ( ( Xz = Xx )
% 0.29/0.45 | ( Xz = Xy ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(upairsetIL_type,type,
% 0.29/0.45 upairsetIL: $o ).
% 0.29/0.45
% 0.29/0.45 thf(upairsetIL,definition,
% 0.29/0.45 ( upairsetIL
% 0.29/0.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(upairsetIR_type,type,
% 0.29/0.45 upairsetIR: $o ).
% 0.29/0.45
% 0.29/0.45 thf(upairsetIR,definition,
% 0.29/0.45 ( upairsetIR
% 0.29/0.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(emptyE1_type,type,
% 0.29/0.45 emptyE1: $o ).
% 0.29/0.45
% 0.29/0.45 thf(emptyE1,definition,
% 0.29/0.45 ( emptyE1
% 0.29/0.45 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.45 ( ? [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 & ( Xphi @ Xx ) )
% 0.29/0.45 => ( ( ( dsetconstr @ A
% 0.29/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.45 = emptyset )
% 0.29/0.45 => $false ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(vacuousDall_type,type,
% 0.29/0.45 vacuousDall: $o ).
% 0.29/0.45
% 0.29/0.45 thf(vacuousDall,definition,
% 0.29/0.45 ( vacuousDall
% 0.29/0.45 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ emptyset )
% 0.29/0.45 => ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(quantDeMorgan1_type,type,
% 0.29/0.45 quantDeMorgan1: $o ).
% 0.29/0.45
% 0.29/0.45 thf(quantDeMorgan1,definition,
% 0.29/0.45 ( quantDeMorgan1
% 0.29/0.45 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.45 ( ~ ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 => ( Xphi @ Xx ) )
% 0.29/0.45 => ? [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(quantDeMorgan2_type,type,
% 0.29/0.45 quantDeMorgan2: $o ).
% 0.29/0.45
% 0.29/0.45 thf(quantDeMorgan2,definition,
% 0.29/0.45 ( quantDeMorgan2
% 0.29/0.45 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.45 ( ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 => ~ ( Xphi @ Xx ) )
% 0.29/0.45 => ~ ? [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(quantDeMorgan3_type,type,
% 0.29/0.45 quantDeMorgan3: $o ).
% 0.29/0.45
% 0.29/0.45 thf(quantDeMorgan3,definition,
% 0.29/0.45 ( quantDeMorgan3
% 0.29/0.45 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.45 ( ~ ? [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 & ( Xphi @ Xx ) )
% 0.29/0.45 => ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(quantDeMorgan4_type,type,
% 0.29/0.45 quantDeMorgan4: $o ).
% 0.29/0.45
% 0.29/0.45 thf(quantDeMorgan4,definition,
% 0.29/0.45 ( quantDeMorgan4
% 0.29/0.45 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.45 ( ? [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 & ~ ( Xphi @ Xx ) )
% 0.29/0.45 => ~ ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(prop2setI_type,type,
% 0.29/0.45 prop2setI: $o ).
% 0.29/0.45
% 0.29/0.45 thf(prop2setI,definition,
% 0.29/0.45 ( prop2setI
% 0.29/0.45 = ( ! [Xphi: $o] :
% 0.29/0.45 ( Xphi
% 0.29/0.45 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(set2prop_type,type,
% 0.29/0.45 set2prop: $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(prop2set2propI_type,type,
% 0.29/0.45 prop2set2propI: $o ).
% 0.29/0.45
% 0.29/0.45 thf(prop2set2propI,definition,
% 0.29/0.45 ( prop2set2propI
% 0.29/0.45 = ( ! [Xphi: $o] :
% 0.29/0.45 ( Xphi
% 0.29/0.45 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(notdexE_type,type,
% 0.29/0.45 notdexE: $o ).
% 0.29/0.45
% 0.29/0.45 thf(notdexE,definition,
% 0.29/0.45 ( notdexE
% 0.29/0.45 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.45 ( ~ ? [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 & ( Xphi @ Xx ) )
% 0.29/0.45 => ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(notdallE_type,type,
% 0.29/0.45 notdallE: $o ).
% 0.29/0.45
% 0.29/0.45 thf(notdallE,definition,
% 0.29/0.45 ( notdallE
% 0.29/0.45 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.45 ( ~ ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 => ( Xphi @ Xx ) )
% 0.29/0.45 => ? [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(exuI1_type,type,
% 0.29/0.45 exuI1: $o ).
% 0.29/0.45
% 0.29/0.45 thf(exuI1,definition,
% 0.29/0.45 ( exuI1
% 0.29/0.45 = ( ! [Xphi: $i > $o] :
% 0.29/0.45 ( ? [Xx: $i] :
% 0.29/0.45 ( ( Xphi @ Xx )
% 0.29/0.45 & ! [Xy: $i] :
% 0.29/0.45 ( ( Xphi @ Xy )
% 0.29/0.45 => ( Xx = Xy ) ) )
% 0.29/0.45 => ( exu
% 0.29/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(exuI3_type,type,
% 0.29/0.45 exuI3: $o ).
% 0.29/0.45
% 0.29/0.45 thf(exuI3,definition,
% 0.29/0.45 ( exuI3
% 0.29/0.45 = ( ! [Xphi: $i > $o] :
% 0.29/0.45 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.29/0.45 => ( ! [Xx: $i,Xy: $i] :
% 0.29/0.45 ( ( Xphi @ Xx )
% 0.29/0.45 => ( ( Xphi @ Xy )
% 0.29/0.45 => ( Xx = Xy ) ) )
% 0.29/0.45 => ( exu
% 0.29/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(exuI2_type,type,
% 0.29/0.45 exuI2: $o ).
% 0.29/0.45
% 0.29/0.45 thf(exuI2,definition,
% 0.29/0.45 ( exuI2
% 0.29/0.45 = ( ! [Xphi: $i > $o] :
% 0.29/0.45 ( ? [Xx: $i] :
% 0.29/0.45 ! [Xy: $i] :
% 0.29/0.45 ( ( Xphi @ Xy )
% 0.29/0.45 <=> ( Xy = Xx ) )
% 0.29/0.45 => ( exu
% 0.29/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(inCongP_type,type,
% 0.29/0.45 inCongP: $o ).
% 0.29/0.45
% 0.29/0.45 thf(inCongP,definition,
% 0.29/0.45 ( inCongP
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ( A = B )
% 0.29/0.45 => ! [Xx: $i,Xy: $i] :
% 0.29/0.45 ( ( Xx = Xy )
% 0.29/0.45 => ( ( in @ Xx @ A )
% 0.29/0.45 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(in__Cong_type,type,
% 0.29/0.45 in__Cong: $o ).
% 0.29/0.45
% 0.29/0.45 thf(in__Cong,definition,
% 0.29/0.45 ( in__Cong
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ( A = B )
% 0.29/0.45 => ! [Xx: $i,Xy: $i] :
% 0.29/0.45 ( ( Xx = Xy )
% 0.29/0.45 => ( ( in @ Xx @ A )
% 0.29/0.45 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(exuE3u_type,type,
% 0.29/0.45 exuE3u: $o ).
% 0.29/0.45
% 0.29/0.45 thf(exuE3u,definition,
% 0.29/0.45 ( exuE3u
% 0.29/0.45 = ( ! [Xphi: $i > $o] :
% 0.29/0.45 ( ( exu
% 0.29/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.45 => ! [Xx: $i,Xy: $i] :
% 0.29/0.45 ( ( Xphi @ Xx )
% 0.29/0.45 => ( ( Xphi @ Xy )
% 0.29/0.45 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(exu__Cong_type,type,
% 0.29/0.45 exu__Cong: $o ).
% 0.29/0.45
% 0.29/0.45 thf(exu__Cong,definition,
% 0.29/0.45 ( exu__Cong
% 0.29/0.45 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.45 ( ! [Xx: $i,Xy: $i] :
% 0.29/0.45 ( ( Xx = Xy )
% 0.29/0.45 => ( ( Xphi @ Xx )
% 0.29/0.45 <=> ( Xpsi @ Xy ) ) )
% 0.29/0.45 => ( ( exu
% 0.29/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.45 <=> ( exu
% 0.29/0.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(emptyset__Cong_type,type,
% 0.29/0.45 emptyset__Cong: $o ).
% 0.29/0.45
% 0.29/0.45 thf(emptyset__Cong,definition,
% 0.29/0.45 ( emptyset__Cong
% 0.29/0.45 = ( emptyset = emptyset ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(setadjoin__Cong_type,type,
% 0.29/0.45 setadjoin__Cong: $o ).
% 0.29/0.45
% 0.29/0.45 thf(setadjoin__Cong,definition,
% 0.29/0.45 ( setadjoin__Cong
% 0.29/0.45 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.45 ( ( Xx = Xy )
% 0.29/0.45 => ! [Xz: $i,Xu: $i] :
% 0.29/0.45 ( ( Xz = Xu )
% 0.29/0.45 => ( ( setadjoin @ Xx @ Xz )
% 0.29/0.45 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(powerset__Cong_type,type,
% 0.29/0.45 powerset__Cong: $o ).
% 0.29/0.45
% 0.29/0.45 thf(powerset__Cong,definition,
% 0.29/0.45 ( powerset__Cong
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ( A = B )
% 0.29/0.45 => ( ( powerset @ A )
% 0.29/0.45 = ( powerset @ B ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(setunion__Cong_type,type,
% 0.29/0.45 setunion__Cong: $o ).
% 0.29/0.45
% 0.29/0.45 thf(setunion__Cong,definition,
% 0.29/0.45 ( setunion__Cong
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ( A = B )
% 0.29/0.45 => ( ( setunion @ A )
% 0.29/0.45 = ( setunion @ B ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(omega__Cong_type,type,
% 0.29/0.45 omega__Cong: $o ).
% 0.29/0.45
% 0.29/0.45 thf(omega__Cong,definition,
% 0.29/0.45 ( omega__Cong
% 0.29/0.45 = ( omega = omega ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(exuEu_type,type,
% 0.29/0.45 exuEu: $o ).
% 0.29/0.45
% 0.29/0.45 thf(exuEu,definition,
% 0.29/0.45 ( exuEu
% 0.29/0.45 = ( ! [Xphi: $i > $o] :
% 0.29/0.45 ( ( exu
% 0.29/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.45 => ! [Xx: $i,Xy: $i] :
% 0.29/0.45 ( ( Xphi @ Xx )
% 0.29/0.45 => ( ( Xphi @ Xy )
% 0.29/0.45 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(descr__Cong_type,type,
% 0.29/0.45 descr__Cong: $o ).
% 0.29/0.45
% 0.29/0.45 thf(descr__Cong,definition,
% 0.29/0.45 ( descr__Cong
% 0.29/0.45 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.45 ( ! [Xx: $i,Xy: $i] :
% 0.29/0.45 ( ( Xx = Xy )
% 0.29/0.45 => ( ( Xphi @ Xx )
% 0.29/0.45 <=> ( Xpsi @ Xy ) ) )
% 0.29/0.45 => ( ( exu
% 0.29/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.45 => ( ( exu
% 0.29/0.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.29/0.45 => ( ( descr
% 0.29/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.45 = ( descr
% 0.29/0.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(dsetconstr__Cong_type,type,
% 0.29/0.45 dsetconstr__Cong: $o ).
% 0.29/0.45
% 0.29/0.45 thf(dsetconstr__Cong,definition,
% 0.29/0.45 ( dsetconstr__Cong
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ( A = B )
% 0.29/0.45 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.45 ( ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 => ! [Xy: $i] :
% 0.29/0.45 ( ( in @ Xy @ B )
% 0.29/0.45 => ( ( Xx = Xy )
% 0.29/0.45 => ( ( Xphi @ Xx )
% 0.29/0.45 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.29/0.45 => ( ( dsetconstr @ A
% 0.29/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.45 = ( dsetconstr @ B
% 0.29/0.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(subset_type,type,
% 0.29/0.45 subset: $i > $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(disjoint_type,type,
% 0.29/0.45 disjoint: $i > $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(setsmeet_type,type,
% 0.29/0.45 setsmeet: $i > $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(subsetI1_type,type,
% 0.29/0.45 subsetI1: $o ).
% 0.29/0.45
% 0.29/0.45 thf(subsetI1,definition,
% 0.29/0.45 ( subsetI1
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 => ( in @ Xx @ B ) )
% 0.29/0.45 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(eqimpsubset2_type,type,
% 0.29/0.45 eqimpsubset2: $o ).
% 0.29/0.45
% 0.29/0.45 thf(eqimpsubset2,definition,
% 0.29/0.45 ( eqimpsubset2
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ( A = B )
% 0.29/0.45 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(eqimpsubset1_type,type,
% 0.29/0.45 eqimpsubset1: $o ).
% 0.29/0.45
% 0.29/0.45 thf(eqimpsubset1,definition,
% 0.29/0.45 ( eqimpsubset1
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ( A = B )
% 0.29/0.45 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(subsetI2_type,type,
% 0.29/0.45 subsetI2: $o ).
% 0.29/0.45
% 0.29/0.45 thf(subsetI2,definition,
% 0.29/0.45 ( subsetI2
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ! [Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 => ( in @ Xx @ B ) )
% 0.29/0.45 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(emptysetsubset_type,type,
% 0.29/0.45 emptysetsubset: $o ).
% 0.29/0.45
% 0.29/0.45 thf(emptysetsubset,definition,
% 0.29/0.45 ( emptysetsubset
% 0.29/0.45 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(subsetE_type,type,
% 0.29/0.45 subsetE: $o ).
% 0.29/0.45
% 0.29/0.45 thf(subsetE,definition,
% 0.29/0.45 ( subsetE
% 0.29/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.45 ( ( subset @ A @ B )
% 0.29/0.45 => ( ( in @ Xx @ A )
% 0.29/0.45 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(subsetE2_type,type,
% 0.29/0.45 subsetE2: $o ).
% 0.29/0.45
% 0.29/0.45 thf(subsetE2,definition,
% 0.29/0.45 ( subsetE2
% 0.29/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.45 ( ( subset @ A @ B )
% 0.29/0.45 => ( ~ ( in @ Xx @ B )
% 0.29/0.45 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(notsubsetI_type,type,
% 0.29/0.45 notsubsetI: $o ).
% 0.29/0.45
% 0.29/0.45 thf(notsubsetI,definition,
% 0.29/0.45 ( notsubsetI
% 0.29/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 => ( ~ ( in @ Xx @ B )
% 0.29/0.45 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(notequalI1_type,type,
% 0.29/0.45 notequalI1: $o ).
% 0.29/0.45
% 0.29/0.45 thf(notequalI1,definition,
% 0.29/0.45 ( notequalI1
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ~ ( subset @ A @ B )
% 0.29/0.45 => ( A != B ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(notequalI2_type,type,
% 0.29/0.45 notequalI2: $o ).
% 0.29/0.45
% 0.29/0.45 thf(notequalI2,definition,
% 0.29/0.45 ( notequalI2
% 0.29/0.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.45 ( ( in @ Xx @ A )
% 0.29/0.45 => ( ~ ( in @ Xx @ B )
% 0.29/0.45 => ( A != B ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(subsetRefl_type,type,
% 0.29/0.45 subsetRefl: $o ).
% 0.29/0.45
% 0.29/0.45 thf(subsetRefl,definition,
% 0.29/0.45 ( subsetRefl
% 0.29/0.45 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(subsetTrans_type,type,
% 0.29/0.45 subsetTrans: $o ).
% 0.29/0.45
% 0.29/0.45 thf(subsetTrans,definition,
% 0.29/0.45 ( subsetTrans
% 0.29/0.45 = ( ! [A: $i,B: $i,C: $i] :
% 0.29/0.45 ( ( subset @ A @ B )
% 0.29/0.45 => ( ( subset @ B @ C )
% 0.29/0.45 => ( subset @ A @ C ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(setadjoinSub_type,type,
% 0.29/0.45 setadjoinSub: $o ).
% 0.29/0.45
% 0.29/0.45 thf(setadjoinSub,definition,
% 0.29/0.45 ( setadjoinSub
% 0.29/0.45 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(setadjoinSub2_type,type,
% 0.29/0.45 setadjoinSub2: $o ).
% 0.29/0.45
% 0.29/0.45 thf(setadjoinSub2,definition,
% 0.29/0.45 ( setadjoinSub2
% 0.29/0.45 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.29/0.45 ( ( subset @ A @ B )
% 0.29/0.45 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(subset2powerset_type,type,
% 0.29/0.45 subset2powerset: $o ).
% 0.29/0.45
% 0.29/0.45 thf(subset2powerset,definition,
% 0.29/0.45 ( subset2powerset
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ( subset @ A @ B )
% 0.29/0.45 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(setextsub_type,type,
% 0.29/0.45 setextsub: $o ).
% 0.29/0.45
% 0.29/0.45 thf(setextsub,definition,
% 0.29/0.45 ( setextsub
% 0.29/0.45 = ( ! [A: $i,B: $i] :
% 0.29/0.45 ( ( subset @ A @ B )
% 0.29/0.45 => ( ( subset @ B @ A )
% 0.29/0.45 => ( A = B ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(subsetemptysetimpeq_type,type,
% 0.29/0.45 subsetemptysetimpeq: $o ).
% 0.29/0.45
% 0.29/0.45 thf(subsetemptysetimpeq,definition,
% 0.29/0.45 ( subsetemptysetimpeq
% 0.29/0.45 = ( ! [A: $i] :
% 0.29/0.45 ( ( subset @ A @ emptyset )
% 0.29/0.45 => ( A = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetI1_type,type,
% 0.29/0.46 powersetI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetI1,definition,
% 0.29/0.46 ( powersetI1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ B @ A )
% 0.29/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetE1_type,type,
% 0.29/0.46 powersetE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetE1,definition,
% 0.29/0.46 ( powersetE1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(inPowerset_type,type,
% 0.29/0.46 inPowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(inPowerset,definition,
% 0.29/0.46 ( inPowerset
% 0.29/0.46 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetsubset_type,type,
% 0.29/0.46 powersetsubset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetsubset,definition,
% 0.29/0.46 ( powersetsubset
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sepInPowerset_type,type,
% 0.29/0.46 sepInPowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(sepInPowerset,definition,
% 0.29/0.46 ( sepInPowerset
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( in
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 @ ( powerset @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sepSubset_type,type,
% 0.29/0.46 sepSubset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(sepSubset,definition,
% 0.29/0.46 ( sepSubset
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( subset
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunion_type,type,
% 0.29/0.46 binunion: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(binunionIL_type,type,
% 0.29/0.46 binunionIL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionIL,definition,
% 0.29/0.46 ( binunionIL
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairset2IR_type,type,
% 0.29/0.46 upairset2IR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairset2IR,definition,
% 0.29/0.46 ( upairset2IR
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionIR_type,type,
% 0.29/0.46 binunionIR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionIR,definition,
% 0.29/0.46 ( binunionIR
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionEcases_type,type,
% 0.29/0.46 binunionEcases: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionEcases,definition,
% 0.29/0.46 ( binunionEcases
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.29/0.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.29/0.46 => ( ( ( in @ Xx @ A )
% 0.29/0.46 => Xphi )
% 0.29/0.46 => ( ( ( in @ Xx @ B )
% 0.29/0.46 => Xphi )
% 0.29/0.46 => Xphi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionE_type,type,
% 0.29/0.46 binunionE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionE,definition,
% 0.29/0.46 ( binunionE
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionLsub_type,type,
% 0.29/0.46 binunionLsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionLsub,definition,
% 0.29/0.46 ( binunionLsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionRsub_type,type,
% 0.29/0.46 binunionRsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionRsub,definition,
% 0.29/0.46 ( binunionRsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersect_type,type,
% 0.29/0.46 binintersect: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectI_type,type,
% 0.29/0.46 binintersectI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectI,definition,
% 0.29/0.46 ( binintersectI
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset5_type,type,
% 0.29/0.46 binintersectSubset5: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset5,definition,
% 0.29/0.46 ( binintersectSubset5
% 0.29/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.29/0.46 ( ( subset @ C @ A )
% 0.29/0.46 => ( ( subset @ C @ B )
% 0.29/0.46 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectEL_type,type,
% 0.29/0.46 binintersectEL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectEL,definition,
% 0.29/0.46 ( binintersectEL
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectLsub_type,type,
% 0.29/0.46 binintersectLsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectLsub,definition,
% 0.29/0.46 ( binintersectLsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset2_type,type,
% 0.29/0.46 binintersectSubset2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset2,definition,
% 0.29/0.46 ( binintersectSubset2
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( binintersect @ A @ B )
% 0.29/0.46 = A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset3_type,type,
% 0.29/0.46 binintersectSubset3: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset3,definition,
% 0.29/0.46 ( binintersectSubset3
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( ( binintersect @ A @ B )
% 0.29/0.46 = B )
% 0.29/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectER_type,type,
% 0.29/0.46 binintersectER: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectER,definition,
% 0.29/0.46 ( binintersectER
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.29/0.46 => ( in @ Xx @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(disjointsetsI1_type,type,
% 0.29/0.46 disjointsetsI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(disjointsetsI1,definition,
% 0.29/0.46 ( disjointsetsI1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( in @ Xx @ B ) )
% 0.29/0.46 => ( ( binintersect @ A @ B )
% 0.29/0.46 = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectRsub_type,type,
% 0.29/0.46 binintersectRsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectRsub,definition,
% 0.29/0.46 ( binintersectRsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset4_type,type,
% 0.29/0.46 binintersectSubset4: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset4,definition,
% 0.29/0.46 ( binintersectSubset4
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ B @ A )
% 0.29/0.46 => ( ( binintersect @ A @ B )
% 0.29/0.46 = B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset1_type,type,
% 0.29/0.46 binintersectSubset1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset1,definition,
% 0.29/0.46 ( binintersectSubset1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( ( binintersect @ A @ B )
% 0.29/0.46 = A )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(bs114d_type,type,
% 0.29/0.46 bs114d: $o ).
% 0.29/0.46
% 0.29/0.46 thf(bs114d,definition,
% 0.29/0.46 ( bs114d
% 0.29/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.29/0.46 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.29/0.46 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(regular_type,type,
% 0.29/0.46 regular: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminus_type,type,
% 0.29/0.46 setminus: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(setminusI_type,type,
% 0.29/0.46 setminusI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusI,definition,
% 0.29/0.46 ( setminusI
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusEL_type,type,
% 0.29/0.46 setminusEL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusEL,definition,
% 0.29/0.46 ( setminusEL
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusER_type,type,
% 0.29/0.46 setminusER: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusER,definition,
% 0.29/0.46 ( setminusER
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.46 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusSubset2_type,type,
% 0.29/0.46 setminusSubset2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusSubset2,definition,
% 0.29/0.46 ( setminusSubset2
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( setminus @ A @ B )
% 0.29/0.46 = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusERneg_type,type,
% 0.29/0.46 setminusERneg: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusERneg,definition,
% 0.29/0.46 ( setminusERneg
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusELneg_type,type,
% 0.29/0.46 setminusELneg: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusELneg,definition,
% 0.29/0.46 ( setminusELneg
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusILneg_type,type,
% 0.29/0.46 setminusILneg: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusILneg,definition,
% 0.29/0.46 ( setminusILneg
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ~ ( in @ Xx @ A )
% 0.29/0.46 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusIRneg_type,type,
% 0.29/0.46 setminusIRneg: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusIRneg,definition,
% 0.29/0.46 ( setminusIRneg
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusLsub_type,type,
% 0.29/0.46 setminusLsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusLsub,definition,
% 0.29/0.46 ( setminusLsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusSubset1_type,type,
% 0.29/0.46 setminusSubset1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusSubset1,definition,
% 0.29/0.46 ( setminusSubset1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( ( setminus @ A @ B )
% 0.29/0.46 = emptyset )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(symdiff_type,type,
% 0.29/0.46 symdiff: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffE_type,type,
% 0.29/0.46 symdiffE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffE,definition,
% 0.29/0.46 ( symdiffE
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.29/0.46 => ! [Xphi: $o] :
% 0.29/0.46 ( ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => Xphi ) )
% 0.29/0.46 => ( ( ~ ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ B )
% 0.29/0.46 => Xphi ) )
% 0.29/0.46 => Xphi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffI1_type,type,
% 0.29/0.46 symdiffI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffI1,definition,
% 0.29/0.46 ( symdiffI1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffI2_type,type,
% 0.29/0.46 symdiffI2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffI2,definition,
% 0.29/0.46 ( symdiffI2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ~ ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffIneg1_type,type,
% 0.29/0.46 symdiffIneg1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffIneg1,definition,
% 0.29/0.46 ( symdiffIneg1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ B )
% 0.29/0.46 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffIneg2_type,type,
% 0.29/0.46 symdiffIneg2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffIneg2,definition,
% 0.29/0.46 ( symdiffIneg2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ~ ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(iskpair_type,type,
% 0.29/0.46 iskpair: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(iskpair,definition,
% 0.29/0.46 ( iskpair
% 0.29/0.46 = ( ^ [A: $i] :
% 0.29/0.46 ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.46 & ? [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ ( setunion @ A ) )
% 0.29/0.46 & ( A
% 0.29/0.46 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(secondinupair_type,type,
% 0.29/0.46 secondinupair: $o ).
% 0.29/0.46
% 0.29/0.46 thf(secondinupair,definition,
% 0.29/0.46 ( secondinupair
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairIL_type,type,
% 0.29/0.46 setukpairIL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairIL,definition,
% 0.29/0.46 ( setukpairIL
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairIR_type,type,
% 0.29/0.46 setukpairIR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairIR,definition,
% 0.29/0.46 ( setukpairIR
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(kpairiskpair_type,type,
% 0.29/0.46 kpairiskpair: $o ).
% 0.29/0.46
% 0.29/0.46 thf(kpairiskpair,definition,
% 0.29/0.46 ( kpairiskpair
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(kpair_type,type,
% 0.29/0.46 kpair: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(kpair,definition,
% 0.29/0.46 ( kpair
% 0.29/0.46 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(kpairp_type,type,
% 0.29/0.46 kpairp: $o ).
% 0.29/0.46
% 0.29/0.46 thf(kpairp,definition,
% 0.29/0.46 ( kpairp
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprod_type,type,
% 0.29/0.46 cartprod: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsubset_type,type,
% 0.29/0.46 singletonsubset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsubset,definition,
% 0.29/0.46 ( singletonsubset
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(singletoninpowerset_type,type,
% 0.29/0.46 singletoninpowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletoninpowerset,definition,
% 0.29/0.46 ( singletoninpowerset
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(singletoninpowunion_type,type,
% 0.29/0.46 singletoninpowunion: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletoninpowunion,definition,
% 0.29/0.46 ( singletoninpowunion
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairset2E_type,type,
% 0.29/0.46 upairset2E: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairset2E,definition,
% 0.29/0.46 ( upairset2E
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.29/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.29/0.46 => ( ( Xz = Xx )
% 0.29/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairsubunion_type,type,
% 0.29/0.46 upairsubunion: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairsubunion,definition,
% 0.29/0.46 ( upairsubunion
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairinpowunion_type,type,
% 0.29/0.46 upairinpowunion: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairinpowunion,definition,
% 0.29/0.46 ( upairinpowunion
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ubforcartprodlem1_type,type,
% 0.29/0.46 ubforcartprodlem1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ubforcartprodlem1,definition,
% 0.29/0.46 ( ubforcartprodlem1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ubforcartprodlem2_type,type,
% 0.29/0.46 ubforcartprodlem2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ubforcartprodlem2,definition,
% 0.29/0.46 ( ubforcartprodlem2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ubforcartprodlem3_type,type,
% 0.29/0.46 ubforcartprodlem3: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ubforcartprodlem3,definition,
% 0.29/0.46 ( ubforcartprodlem3
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodpairin_type,type,
% 0.29/0.46 cartprodpairin: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodpairin,definition,
% 0.29/0.46 ( cartprodpairin
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodmempair1_type,type,
% 0.29/0.46 cartprodmempair1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodmempair1,definition,
% 0.29/0.46 ( cartprodmempair1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.29/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ? [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 & ( Xu
% 0.29/0.46 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodmempair_type,type,
% 0.29/0.46 cartprodmempair: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodmempair,definition,
% 0.29/0.46 ( cartprodmempair
% 0.29/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.29/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.29/0.46 => ( iskpair @ Xu ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionE2_type,type,
% 0.29/0.46 setunionE2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionE2,definition,
% 0.29/0.46 ( setunionE2
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.46 => ? [X: $i] :
% 0.29/0.46 ( ( in @ X @ A )
% 0.29/0.46 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionsingleton1_type,type,
% 0.29/0.46 setunionsingleton1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionsingleton1,definition,
% 0.29/0.46 ( setunionsingleton1
% 0.29/0.46 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionsingleton2_type,type,
% 0.29/0.46 setunionsingleton2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionsingleton2,definition,
% 0.29/0.46 ( setunionsingleton2
% 0.29/0.46 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionsingleton_type,type,
% 0.29/0.46 setunionsingleton: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionsingleton,definition,
% 0.29/0.46 ( setunionsingleton
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.29/0.46 = Xx ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(singleton_type,type,
% 0.29/0.46 singleton: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(singleton,definition,
% 0.29/0.46 ( singleton
% 0.29/0.46 = ( ^ [A: $i] :
% 0.29/0.46 ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( A
% 0.29/0.46 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(singletonprop_type,type,
% 0.29/0.46 singletonprop: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletonprop,definition,
% 0.29/0.46 ( singletonprop
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) )
% 0.29/0.46 => ( ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) )
% 0.29/0.46 => ( singleton
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ex1_type,type,
% 0.29/0.46 ex1: $i > ( $i > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(ex1,definition,
% 0.29/0.46 ( ex1
% 0.29/0.46 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( singleton
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ex1E1_type,type,
% 0.29/0.46 ex1E1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ex1E1,definition,
% 0.29/0.46 ( ex1E1
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ( ex1 @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ex1I_type,type,
% 0.29/0.46 ex1I: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ex1I,definition,
% 0.29/0.46 ( ex1I
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xy = Xx ) ) )
% 0.29/0.46 => ( ex1 @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ex1I2_type,type,
% 0.29/0.46 ex1I2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ex1I2,definition,
% 0.29/0.46 ( ex1I2
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) )
% 0.29/0.46 => ( ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) )
% 0.29/0.46 => ( ex1 @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsuniq_type,type,
% 0.29/0.46 singletonsuniq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsuniq,definition,
% 0.29/0.46 ( singletonsuniq
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( ( setadjoin @ Xx @ emptyset )
% 0.29/0.46 = ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(atmost1p_type,type,
% 0.29/0.46 atmost1p: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(atleast2p_type,type,
% 0.29/0.46 atleast2p: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(atmost2p_type,type,
% 0.29/0.46 atmost2p: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetp_type,type,
% 0.29/0.46 upairsetp: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjL1_type,type,
% 0.29/0.46 setukpairinjL1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjL1,definition,
% 0.29/0.46 ( setukpairinjL1
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.29/0.46 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.29/0.46 => ( Xx = Xz ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(kfstsingleton_type,type,
% 0.29/0.46 kfstsingleton: $o ).
% 0.29/0.46
% 0.29/0.46 thf(kfstsingleton,definition,
% 0.29/0.46 ( kfstsingleton
% 0.29/0.46 = ( ! [Xu: $i] :
% 0.29/0.46 ( ( iskpair @ Xu )
% 0.29/0.46 => ( singleton
% 0.29/0.46 @ ( dsetconstr @ ( setunion @ Xu )
% 0.29/0.46 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(theprop_type,type,
% 0.29/0.46 theprop: $o ).
% 0.29/0.46
% 0.29/0.46 thf(theprop,definition,
% 0.29/0.46 ( theprop
% 0.29/0.46 = ( ! [X: $i] :
% 0.29/0.46 ( ( singleton @ X )
% 0.29/0.46 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(kfst_type,type,
% 0.29/0.46 kfst: $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(kfstpairEq_type,type,
% 0.29/0.46 kfstpairEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(kfstpairEq,definition,
% 0.29/0.46 ( kfstpairEq
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.29/0.46 = Xx ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodfstin_type,type,
% 0.29/0.46 cartprodfstin: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodfstin,definition,
% 0.29/0.46 ( cartprodfstin
% 0.29/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.29/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.29/0.46 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjL2,conjecture,
% 0.29/0.46 ( setextAx
% 0.29/0.46 => ( emptysetAx
% 0.29/0.46 => ( setadjoinAx
% 0.29/0.46 => ( powersetAx
% 0.29/0.46 => ( setunionAx
% 0.29/0.46 => ( omega0Ax
% 0.29/0.46 => ( omegaSAx
% 0.29/0.46 => ( omegaIndAx
% 0.29/0.46 => ( replAx
% 0.29/0.46 => ( foundationAx
% 0.29/0.46 => ( wellorderingAx
% 0.29/0.46 => ( descrp
% 0.29/0.46 => ( dsetconstrI
% 0.29/0.46 => ( dsetconstrEL
% 0.29/0.46 => ( dsetconstrER
% 0.29/0.46 => ( exuE1
% 0.29/0.46 => ( prop2setE
% 0.29/0.46 => ( emptysetE
% 0.29/0.46 => ( emptysetimpfalse
% 0.29/0.46 => ( notinemptyset
% 0.29/0.46 => ( exuE3e
% 0.29/0.46 => ( setext
% 0.29/0.46 => ( emptyI
% 0.29/0.46 => ( noeltsimpempty
% 0.29/0.46 => ( setbeta
% 0.29/0.46 => ( nonemptyE1
% 0.29/0.46 => ( nonemptyI
% 0.29/0.46 => ( nonemptyI1
% 0.29/0.46 => ( setadjoinIL
% 0.29/0.46 => ( emptyinunitempty
% 0.29/0.46 => ( setadjoinIR
% 0.29/0.46 => ( setadjoinE
% 0.29/0.46 => ( setadjoinOr
% 0.29/0.46 => ( setoftrueEq
% 0.29/0.46 => ( powersetI
% 0.29/0.46 => ( emptyinPowerset
% 0.29/0.46 => ( emptyInPowerset
% 0.29/0.46 => ( powersetE
% 0.29/0.46 => ( setunionI
% 0.29/0.46 => ( setunionE
% 0.29/0.46 => ( subPowSU
% 0.29/0.46 => ( exuE2
% 0.29/0.46 => ( nonemptyImpWitness
% 0.29/0.46 => ( uniqinunit
% 0.29/0.46 => ( notinsingleton
% 0.29/0.46 => ( eqinunit
% 0.29/0.46 => ( singletonsswitch
% 0.29/0.46 => ( upairsetE
% 0.29/0.46 => ( upairsetIL
% 0.29/0.46 => ( upairsetIR
% 0.29/0.46 => ( emptyE1
% 0.29/0.46 => ( vacuousDall
% 0.29/0.46 => ( quantDeMorgan1
% 0.29/0.46 => ( quantDeMorgan2
% 0.29/0.46 => ( quantDeMorgan3
% 0.29/0.46 => ( quantDeMorgan4
% 0.29/0.46 => ( prop2setI
% 0.29/0.46 => ( prop2set2propI
% 0.29/0.46 => ( notdexE
% 0.29/0.46 => ( notdallE
% 0.29/0.46 => ( exuI1
% 0.29/0.46 => ( exuI3
% 0.29/0.46 => ( exuI2
% 0.29/0.46 => ( inCongP
% 0.29/0.46 => ( in__Cong
% 0.29/0.46 => ( exuE3u
% 0.29/0.46 => ( exu__Cong
% 0.29/0.46 => ( emptyset__Cong
% 0.29/0.46 => ( setadjoin__Cong
% 0.29/0.46 => ( powerset__Cong
% 0.29/0.46 => ( setunion__Cong
% 0.29/0.46 => ( omega__Cong
% 0.29/0.46 => ( exuEu
% 0.29/0.46 => ( descr__Cong
% 0.29/0.46 => ( dsetconstr__Cong
% 0.29/0.46 => ( subsetI1
% 0.29/0.46 => ( eqimpsubset2
% 0.29/0.46 => ( eqimpsubset1
% 0.29/0.46 => ( subsetI2
% 0.29/0.46 => ( emptysetsubset
% 0.29/0.46 => ( subsetE
% 0.29/0.46 => ( subsetE2
% 0.29/0.46 => ( notsubsetI
% 0.29/0.46 => ( notequalI1
% 0.29/0.46 => ( notequalI2
% 0.29/0.46 => ( subsetRefl
% 0.29/0.46 => ( subsetTrans
% 0.29/0.46 => ( setadjoinSub
% 0.29/0.46 => ( setadjoinSub2
% 0.29/0.46 => ( subset2powerset
% 0.29/0.46 => ( setextsub
% 0.29/0.46 => ( subsetemptysetimpeq
% 0.29/0.46 => ( powersetI1
% 0.29/0.46 => ( powersetE1
% 0.29/0.46 => ( inPowerset
% 0.29/0.46 => ( powersetsubset
% 0.29/0.46 => ( sepInPowerset
% 0.29/0.46 => ( sepSubset
% 0.29/0.46 => ( binunionIL
% 0.29/0.46 => ( upairset2IR
% 0.29/0.46 => ( binunionIR
% 0.29/0.46 => ( binunionEcases
% 0.29/0.46 => ( binunionE
% 0.29/0.46 => ( binunionLsub
% 0.29/0.46 => ( binunionRsub
% 0.29/0.46 => ( binintersectI
% 0.29/0.46 => ( binintersectSubset5
% 0.29/0.46 => ( binintersectEL
% 0.29/0.46 => ( binintersectLsub
% 0.29/0.46 => ( binintersectSubset2
% 0.29/0.46 => ( binintersectSubset3
% 0.29/0.46 => ( binintersectER
% 0.29/0.46 => ( disjointsetsI1
% 0.29/0.46 => ( binintersectRsub
% 0.29/0.46 => ( binintersectSubset4
% 0.29/0.46 => ( binintersectSubset1
% 0.29/0.46 => ( bs114d
% 0.29/0.46 => ( setminusI
% 0.29/0.46 => ( setminusEL
% 0.29/0.46 => ( setminusER
% 0.29/0.46 => ( setminusSubset2
% 0.29/0.46 => ( setminusERneg
% 0.29/0.46 => ( setminusELneg
% 0.29/0.46 => ( setminusILneg
% 0.29/0.46 => ( setminusIRneg
% 0.29/0.46 => ( setminusLsub
% 0.29/0.46 => ( setminusSubset1
% 0.29/0.46 => ( symdiffE
% 0.29/0.46 => ( symdiffI1
% 0.29/0.46 => ( symdiffI2
% 0.29/0.46 => ( symdiffIneg1
% 0.29/0.46 => ( symdiffIneg2
% 0.29/0.46 => ( secondinupair
% 0.29/0.46 => ( setukpairIL
% 0.29/0.46 => ( setukpairIR
% 0.29/0.46 => ( kpairiskpair
% 0.29/0.46 => ( kpairp
% 0.29/0.46 => ( singletonsubset
% 0.29/0.46 => ( singletoninpowerset
% 0.29/0.46 => ( singletoninpowunion
% 0.29/0.46 => ( upairset2E
% 0.29/0.46 => ( upairsubunion
% 0.29/0.46 => ( upairinpowunion
% 0.29/0.46 => ( ubforcartprodlem1
% 0.29/0.46 => ( ubforcartprodlem2
% 0.29/0.46 => ( ubforcartprodlem3
% 0.29/0.46 => ( cartprodpairin
% 0.29/0.46 => ( cartprodmempair1
% 0.29/0.46 => ( cartprodmempair
% 0.29/0.46 => ( setunionE2
% 0.29/0.46 => ( setunionsingleton1
% 0.29/0.46 => ( setunionsingleton2
% 0.29/0.46 => ( setunionsingleton
% 0.29/0.46 => ( singletonprop
% 0.29/0.46 => ( ex1E1
% 0.29/0.46 => ( ex1I
% 0.29/0.46 => ( ex1I2
% 0.29/0.46 => ( singletonsuniq
% 0.29/0.46 => ( setukpairinjL1
% 0.29/0.46 => ( kfstsingleton
% 0.29/0.46 => ( theprop
% 0.29/0.46 => ( kfstpairEq
% 0.29/0.46 => ( cartprodfstin
% 0.29/0.46 => ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.29/0.46 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.29/0.46 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.29/0.46 => ( Xx = Xz ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 2.35/1.46 ---- Embedded in THF ---
% 2.35/1.46 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.35/1.46 %%% Generated on Tue Feb 24 12:30:17 EST 2026
% 2.35/1.46 %%% using '$$dhol' embedding, version 1.3.0.
% 2.35/1.46 %%% Logic specification used:
% 2.35/1.46 %%% thf(spec, logic, $$dhol).
% 2.35/1.46
% 2.35/1.46 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.VeTrV6L3FZ/DTF2DTF4923.p
% See solution above
% 2.35/1.46 ------------------------
% 2.35/1.49 ---- Cleaned THF ---
% 2.35/1.49 thf(in_type,type,
% 2.35/1.49 in: $i > $i > $o ).
% 2.35/1.49
% 2.35/1.49 thf(exu_type,type,
% 2.35/1.49 exu: ( $i > $o ) > $o ).
% 2.35/1.49
% 2.35/1.49 thf(exu,definition,
% 2.35/1.49 ( exu
% 2.35/1.49 = ( ^ [Xphi: $i > $o] :
% 2.35/1.49 ? [Xx: $i] :
% 2.35/1.49 ( ( Xphi @ Xx )
% 2.35/1.49 & ! [Xy: $i] :
% 2.35/1.49 ( ( Xphi @ Xy )
% 2.35/1.49 => ( Xx = Xy ) ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(setextAx_type,type,
% 2.35/1.49 setextAx: $o ).
% 2.35/1.49
% 2.35/1.49 thf(setextAx,definition,
% 2.35/1.49 ( setextAx
% 2.35/1.49 = ( ! [A: $i,B: $i] :
% 2.35/1.49 ( ! [Xx: $i] :
% 2.35/1.49 ( ( in @ Xx @ A )
% 2.35/1.49 <=> ( in @ Xx @ B ) )
% 2.35/1.49 => ( A = B ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(emptyset_type,type,
% 2.35/1.49 emptyset: $i ).
% 2.35/1.49
% 2.35/1.49 thf(emptysetAx_type,type,
% 2.35/1.49 emptysetAx: $o ).
% 2.35/1.49
% 2.35/1.49 thf(emptysetAx,definition,
% 2.35/1.49 ( emptysetAx
% 2.35/1.49 = ( ! [Xx: $i] :
% 2.35/1.49 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(setadjoin_type,type,
% 2.35/1.49 setadjoin: $i > $i > $i ).
% 2.35/1.49
% 2.35/1.49 thf(setadjoinAx_type,type,
% 2.35/1.49 setadjoinAx: $o ).
% 2.35/1.49
% 2.35/1.49 thf(setadjoinAx,definition,
% 2.35/1.49 ( setadjoinAx
% 2.35/1.49 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.35/1.49 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.35/1.49 <=> ( ( Xy = Xx )
% 2.35/1.49 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(powerset_type,type,
% 2.35/1.49 powerset: $i > $i ).
% 2.35/1.49
% 2.35/1.49 thf(powersetAx_type,type,
% 2.35/1.49 powersetAx: $o ).
% 2.35/1.49
% 2.35/1.49 thf(powersetAx,definition,
% 2.35/1.49 ( powersetAx
% 2.35/1.49 = ( ! [A: $i,B: $i] :
% 2.35/1.49 ( ( in @ B @ ( powerset @ A ) )
% 2.35/1.49 <=> ! [Xx: $i] :
% 2.35/1.49 ( ( in @ Xx @ B )
% 2.35/1.49 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(setunion_type,type,
% 2.35/1.49 setunion: $i > $i ).
% 2.35/1.49
% 2.35/1.49 thf(setunionAx_type,type,
% 2.35/1.49 setunionAx: $o ).
% 2.35/1.49
% 2.35/1.49 thf(setunionAx,definition,
% 2.35/1.49 ( setunionAx
% 2.35/1.49 = ( ! [A: $i,Xx: $i] :
% 2.35/1.49 ( ( in @ Xx @ ( setunion @ A ) )
% 2.35/1.49 <=> ? [B: $i] :
% 2.35/1.49 ( ( in @ Xx @ B )
% 2.35/1.49 & ( in @ B @ A ) ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(omega_type,type,
% 2.35/1.49 omega: $i ).
% 2.35/1.49
% 2.35/1.49 thf(omega0Ax_type,type,
% 2.35/1.49 omega0Ax: $o ).
% 2.35/1.49
% 2.35/1.49 thf(omega0Ax,definition,
% 2.35/1.49 ( omega0Ax
% 2.35/1.49 = ( in @ emptyset @ omega ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(omegaSAx_type,type,
% 2.35/1.49 omegaSAx: $o ).
% 2.35/1.49
% 2.35/1.49 thf(omegaSAx,definition,
% 2.35/1.49 ( omegaSAx
% 2.35/1.49 = ( ! [Xx: $i] :
% 2.35/1.49 ( ( in @ Xx @ omega )
% 2.35/1.49 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(omegaIndAx_type,type,
% 2.35/1.49 omegaIndAx: $o ).
% 2.35/1.49
% 2.35/1.49 thf(omegaIndAx,definition,
% 2.35/1.49 ( omegaIndAx
% 2.35/1.49 = ( ! [A: $i] :
% 2.35/1.49 ( ( ( in @ emptyset @ A )
% 2.35/1.49 & ! [Xx: $i] :
% 2.35/1.49 ( ( ( in @ Xx @ omega )
% 2.35/1.49 & ( in @ Xx @ A ) )
% 2.35/1.49 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.35/1.49 => ! [Xx: $i] :
% 2.35/1.49 ( ( in @ Xx @ omega )
% 2.35/1.49 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(replAx_type,type,
% 2.35/1.49 replAx: $o ).
% 2.35/1.49
% 2.35/1.49 thf(replAx,definition,
% 2.35/1.49 ( replAx
% 2.35/1.49 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.35/1.49 ( ! [Xx: $i] :
% 2.35/1.49 ( ( in @ Xx @ A )
% 2.35/1.49 => ( exu
% 2.35/1.49 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.35/1.49 => ? [B: $i] :
% 2.35/1.49 ! [Xx: $i] :
% 2.35/1.49 ( ( in @ Xx @ B )
% 2.35/1.49 <=> ? [Xy: $i] :
% 2.35/1.49 ( ( in @ Xy @ A )
% 2.35/1.49 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(foundationAx_type,type,
% 2.35/1.49 foundationAx: $o ).
% 2.35/1.49
% 2.35/1.49 thf(foundationAx,definition,
% 2.35/1.49 ( foundationAx
% 2.35/1.49 = ( ! [A: $i] :
% 2.35/1.49 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.35/1.49 => ? [B: $i] :
% 2.35/1.49 ( ( in @ B @ A )
% 2.35/1.49 & ~ ? [Xx: $i] :
% 2.35/1.49 ( ( in @ Xx @ B )
% 2.35/1.49 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(wellorderingAx_type,type,
% 2.35/1.49 wellorderingAx: $o ).
% 2.35/1.49
% 2.35/1.49 thf(wellorderingAx,definition,
% 2.35/1.49 ( wellorderingAx
% 2.35/1.49 = ( ! [A: $i] :
% 2.35/1.49 ? [B: $i] :
% 2.35/1.49 ( ! [C: $i] :
% 2.35/1.49 ( ( in @ C @ B )
% 2.35/1.49 => ! [Xx: $i] :
% 2.35/1.49 ( ( in @ Xx @ C )
% 2.35/1.49 => ( in @ Xx @ A ) ) )
% 2.35/1.49 & ! [Xx: $i,Xy: $i] :
% 2.35/1.49 ( ( ( in @ Xx @ A )
% 2.35/1.49 & ( in @ Xy @ A ) )
% 2.35/1.49 => ( ! [C: $i] :
% 2.35/1.49 ( ( in @ C @ B )
% 2.35/1.49 => ( ( in @ Xx @ C )
% 2.35/1.49 <=> ( in @ Xy @ C ) ) )
% 2.35/1.49 => ( Xx = Xy ) ) )
% 2.35/1.49 & ! [C: $i,D: $i] :
% 2.35/1.49 ( ( ( in @ C @ B )
% 2.35/1.49 & ( in @ D @ B ) )
% 2.35/1.49 => ( ! [Xx: $i] :
% 2.35/1.49 ( ( in @ Xx @ C )
% 2.35/1.49 => ( in @ Xx @ D ) )
% 2.35/1.49 | ! [Xx: $i] :
% 2.35/1.49 ( ( in @ Xx @ D )
% 2.35/1.49 => ( in @ Xx @ C ) ) ) )
% 2.35/1.49 & ! [C: $i] :
% 2.35/1.49 ( ( ! [Xx: $i] :
% 2.35/1.49 ( ( in @ Xx @ C )
% 2.35/1.49 => ( in @ Xx @ A ) )
% 2.35/1.49 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.35/1.49 => ? [D: $i,Xx: $i] :
% 2.35/1.49 ( ( in @ D @ B )
% 2.35/1.49 & ( in @ Xx @ C )
% 2.35/1.49 & ~ ? [Xy: $i] :
% 2.35/1.49 ( ( in @ Xy @ D )
% 2.35/1.49 & ( in @ Xy @ C ) )
% 2.35/1.49 & ! [E: $i] :
% 2.35/1.49 ( ( in @ E @ B )
% 2.35/1.49 => ( ! [Xy: $i] :
% 2.35/1.49 ( ( in @ Xy @ E )
% 2.35/1.49 => ( in @ Xy @ D ) )
% 2.35/1.49 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(descr_type,type,
% 2.35/1.49 descr: ( $i > $o ) > $i ).
% 2.35/1.49
% 2.35/1.49 thf(descrp_type,type,
% 2.35/1.49 descrp: $o ).
% 2.35/1.49
% 2.35/1.49 thf(descrp,definition,
% 2.35/1.49 ( descrp
% 2.35/1.49 = ( ! [Xphi: $i > $o] :
% 2.35/1.49 ( ( exu
% 2.35/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.35/1.49 => ( Xphi
% 2.35/1.49 @ ( descr
% 2.35/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(dsetconstr_type,type,
% 2.35/1.49 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.35/1.49
% 2.35/1.49 thf(dsetconstrI_type,type,
% 2.35/1.49 dsetconstrI: $o ).
% 2.35/1.49
% 2.35/1.49 thf(dsetconstrI,definition,
% 2.35/1.49 ( dsetconstrI
% 2.35/1.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.35/1.49 ( ( in @ Xx @ A )
% 2.35/1.49 => ( ( Xphi @ Xx )
% 2.35/1.49 => ( in @ Xx
% 2.35/1.49 @ ( dsetconstr @ A
% 2.35/1.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(dsetconstrEL_type,type,
% 2.35/1.49 dsetconstrEL: $o ).
% 2.35/1.49
% 2.35/1.49 thf(dsetconstrEL,definition,
% 2.35/1.49 ( dsetconstrEL
% 2.35/1.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.35/1.49 ( ( in @ Xx
% 2.35/1.49 @ ( dsetconstr @ A
% 2.35/1.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.35/1.49 => ( in @ Xx @ A ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(dsetconstrER_type,type,
% 2.35/1.49 dsetconstrER: $o ).
% 2.35/1.49
% 2.35/1.49 thf(dsetconstrER,definition,
% 2.35/1.49 ( dsetconstrER
% 2.35/1.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.35/1.49 ( ( in @ Xx
% 2.35/1.49 @ ( dsetconstr @ A
% 2.35/1.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.35/1.49 => ( Xphi @ Xx ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(exuE1_type,type,
% 2.35/1.49 exuE1: $o ).
% 2.35/1.49
% 2.35/1.49 thf(exuE1,definition,
% 2.35/1.49 ( exuE1
% 2.35/1.49 = ( ! [Xphi: $i > $o] :
% 2.35/1.49 ( ( exu
% 2.35/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.35/1.49 => ? [Xx: $i] :
% 2.35/1.49 ( ( Xphi @ Xx )
% 2.35/1.49 & ! [Xy: $i] :
% 2.35/1.49 ( ( Xphi @ Xy )
% 2.35/1.49 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(prop2set_type,type,
% 2.35/1.49 prop2set: $o > $i ).
% 2.35/1.49
% 2.35/1.49 thf(prop2setE_type,type,
% 2.35/1.49 prop2setE: $o ).
% 2.35/1.49
% 2.35/1.49 thf(prop2setE,definition,
% 2.35/1.49 ( prop2setE
% 2.35/1.49 = ( ! [Xphi: $o,Xx: $i] :
% 2.35/1.49 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.35/1.49 => Xphi ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(emptysetE_type,type,
% 2.35/1.49 emptysetE: $o ).
% 2.35/1.49
% 2.35/1.49 thf(emptysetE,definition,
% 2.35/1.49 ( emptysetE
% 2.35/1.49 = ( ! [Xx: $i] :
% 2.35/1.49 ( ( in @ Xx @ emptyset )
% 2.35/1.49 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(emptysetimpfalse_type,type,
% 2.35/1.49 emptysetimpfalse: $o ).
% 2.35/1.49
% 2.35/1.49 thf(emptysetimpfalse,definition,
% 2.35/1.49 ( emptysetimpfalse
% 2.35/1.49 = ( ! [Xx: $i] :
% 2.35/1.49 ( ( in @ Xx @ emptyset )
% 2.35/1.49 => $false ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(notinemptyset_type,type,
% 2.35/1.49 notinemptyset: $o ).
% 2.35/1.49
% 2.35/1.49 thf(notinemptyset,definition,
% 2.35/1.49 ( notinemptyset
% 2.35/1.49 = ( ! [Xx: $i] :
% 2.35/1.49 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(exuE3e_type,type,
% 2.35/1.49 exuE3e: $o ).
% 2.35/1.49
% 2.35/1.49 thf(exuE3e,definition,
% 2.35/1.49 ( exuE3e
% 2.35/1.49 = ( ! [Xphi: $i > $o] :
% 2.35/1.49 ( ( exu
% 2.35/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.35/1.49 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(setext_type,type,
% 2.35/1.49 setext: $o ).
% 2.35/1.49
% 2.35/1.49 thf(setext,definition,
% 2.35/1.49 ( setext
% 2.35/1.49 = ( ! [A: $i,B: $i] :
% 2.35/1.49 ( ! [Xx: $i] :
% 2.35/1.49 ( ( in @ Xx @ A )
% 2.35/1.49 => ( in @ Xx @ B ) )
% 2.35/1.49 => ( ! [Xx: $i] :
% 2.35/1.49 ( ( in @ Xx @ B )
% 2.35/1.49 => ( in @ Xx @ A ) )
% 2.35/1.49 => ( A = B ) ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(emptyI_type,type,
% 2.35/1.49 emptyI: $o ).
% 2.35/1.49
% 2.35/1.49 thf(emptyI,definition,
% 2.35/1.49 ( emptyI
% 2.35/1.49 = ( ! [A: $i] :
% 2.35/1.49 ( ! [Xx: $i] :
% 2.35/1.49 ~ ( in @ Xx @ A )
% 2.35/1.49 => ( A = emptyset ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(noeltsimpempty_type,type,
% 2.35/1.49 noeltsimpempty: $o ).
% 2.35/1.49
% 2.35/1.49 thf(noeltsimpempty,definition,
% 2.35/1.49 ( noeltsimpempty
% 2.35/1.49 = ( ! [A: $i] :
% 2.35/1.49 ( ! [Xx: $i] :
% 2.35/1.49 ~ ( in @ Xx @ A )
% 2.35/1.49 => ( A = emptyset ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(setbeta_type,type,
% 2.35/1.49 setbeta: $o ).
% 2.35/1.49
% 2.35/1.49 thf(setbeta,definition,
% 2.35/1.49 ( setbeta
% 2.35/1.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.35/1.49 ( ( in @ Xx @ A )
% 2.35/1.49 => ( ( in @ Xx
% 2.35/1.49 @ ( dsetconstr @ A
% 2.35/1.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.35/1.49 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(nonempty_type,type,
% 2.35/1.49 nonempty: $i > $o ).
% 2.35/1.49
% 2.35/1.49 thf(nonempty,definition,
% 2.35/1.49 ( nonempty
% 2.35/1.49 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(nonemptyE1_type,type,
% 2.35/1.49 nonemptyE1: $o ).
% 2.35/1.49
% 2.35/1.49 thf(nonemptyE1,definition,
% 2.35/1.49 ( nonemptyE1
% 2.35/1.49 = ( ! [A: $i] :
% 2.35/1.49 ( ( nonempty @ A )
% 2.35/1.49 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(nonemptyI_type,type,
% 2.35/1.49 nonemptyI: $o ).
% 2.35/1.49
% 2.35/1.49 thf(nonemptyI,definition,
% 2.35/1.49 ( nonemptyI
% 2.35/1.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.35/1.49 ( ( in @ Xx @ A )
% 2.35/1.49 => ( ( Xphi @ Xx )
% 2.35/1.49 => ( nonempty
% 2.35/1.49 @ ( dsetconstr @ A
% 2.35/1.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(nonemptyI1_type,type,
% 2.35/1.49 nonemptyI1: $o ).
% 2.35/1.49
% 2.35/1.49 thf(nonemptyI1,definition,
% 2.35/1.49 ( nonemptyI1
% 2.35/1.49 = ( ! [A: $i] :
% 2.35/1.49 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.35/1.49 => ( nonempty @ A ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(setadjoinIL_type,type,
% 2.35/1.49 setadjoinIL: $o ).
% 2.35/1.49
% 2.35/1.49 thf(setadjoinIL,definition,
% 2.35/1.49 ( setadjoinIL
% 2.35/1.49 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(emptyinunitempty_type,type,
% 2.35/1.49 emptyinunitempty: $o ).
% 2.35/1.49
% 2.35/1.49 thf(emptyinunitempty,definition,
% 2.35/1.49 ( emptyinunitempty
% 2.35/1.49 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(setadjoinIR_type,type,
% 2.35/1.49 setadjoinIR: $o ).
% 2.35/1.49
% 2.35/1.49 thf(setadjoinIR,definition,
% 2.35/1.49 ( setadjoinIR
% 2.35/1.49 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.35/1.49 ( ( in @ Xy @ A )
% 2.35/1.49 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(setadjoinE_type,type,
% 2.35/1.49 setadjoinE: $o ).
% 2.35/1.49
% 2.35/1.49 thf(setadjoinE,definition,
% 2.35/1.49 ( setadjoinE
% 2.35/1.49 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.35/1.49 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.35/1.49 => ! [Xphi: $o] :
% 2.35/1.49 ( ( ( Xy = Xx )
% 2.35/1.49 => Xphi )
% 2.35/1.49 => ( ( ( in @ Xy @ A )
% 2.35/1.49 => Xphi )
% 2.35/1.49 => Xphi ) ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(setadjoinOr_type,type,
% 2.35/1.49 setadjoinOr: $o ).
% 2.35/1.49
% 2.35/1.49 thf(setadjoinOr,definition,
% 2.35/1.49 ( setadjoinOr
% 2.35/1.49 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.35/1.49 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.35/1.49 => ( ( Xy = Xx )
% 2.35/1.49 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(setoftrueEq_type,type,
% 2.35/1.49 setoftrueEq: $o ).
% 2.35/1.49
% 2.35/1.49 thf(setoftrueEq,definition,
% 2.35/1.49 ( setoftrueEq
% 2.35/1.49 = ( ! [A: $i] :
% 2.35/1.49 ( ( dsetconstr @ A
% 2.35/1.49 @ ^ [Xx: $i] : $true )
% 2.35/1.49 = A ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(powersetI_type,type,
% 2.35/1.49 powersetI: $o ).
% 2.35/1.49
% 2.35/1.49 thf(powersetI,definition,
% 2.35/1.49 ( powersetI
% 2.35/1.49 = ( ! [A: $i,B: $i] :
% 2.35/1.49 ( ! [Xx: $i] :
% 2.35/1.49 ( ( in @ Xx @ B )
% 2.35/1.49 => ( in @ Xx @ A ) )
% 2.35/1.49 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(emptyinPowerset_type,type,
% 2.35/1.49 emptyinPowerset: $o ).
% 2.35/1.49
% 2.35/1.49 thf(emptyinPowerset,definition,
% 2.35/1.49 ( emptyinPowerset
% 2.35/1.49 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(emptyInPowerset_type,type,
% 2.35/1.49 emptyInPowerset: $o ).
% 2.35/1.49
% 2.35/1.49 thf(emptyInPowerset,definition,
% 2.35/1.49 ( emptyInPowerset
% 2.35/1.49 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(powersetE_type,type,
% 2.35/1.49 powersetE: $o ).
% 2.35/1.49
% 2.35/1.49 thf(powersetE,definition,
% 2.35/1.49 ( powersetE
% 2.35/1.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.49 ( ( in @ B @ ( powerset @ A ) )
% 2.35/1.49 => ( ( in @ Xx @ B )
% 2.35/1.49 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(setunionI_type,type,
% 2.35/1.49 setunionI: $o ).
% 2.35/1.49
% 2.35/1.49 thf(setunionI,definition,
% 2.35/1.49 ( setunionI
% 2.35/1.49 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.35/1.49 ( ( in @ Xx @ B )
% 2.35/1.49 => ( ( in @ B @ A )
% 2.35/1.49 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(setunionE_type,type,
% 2.35/1.49 setunionE: $o ).
% 2.35/1.49
% 2.35/1.49 thf(setunionE,definition,
% 2.35/1.49 ( setunionE
% 2.35/1.49 = ( ! [A: $i,Xx: $i] :
% 2.35/1.49 ( ( in @ Xx @ ( setunion @ A ) )
% 2.35/1.49 => ! [Xphi: $o] :
% 2.35/1.49 ( ! [B: $i] :
% 2.35/1.49 ( ( in @ Xx @ B )
% 2.35/1.49 => ( ( in @ B @ A )
% 2.35/1.49 => Xphi ) )
% 2.35/1.49 => Xphi ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(subPowSU_type,type,
% 2.35/1.49 subPowSU: $o ).
% 2.35/1.49
% 2.35/1.49 thf(subPowSU,definition,
% 2.35/1.49 ( subPowSU
% 2.35/1.49 = ( ! [A: $i,Xx: $i] :
% 2.35/1.49 ( ( in @ Xx @ A )
% 2.35/1.49 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(exuE2_type,type,
% 2.35/1.49 exuE2: $o ).
% 2.35/1.49
% 2.35/1.49 thf(exuE2,definition,
% 2.35/1.49 ( exuE2
% 2.35/1.49 = ( ! [Xphi: $i > $o] :
% 2.35/1.49 ( ( exu
% 2.35/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.35/1.49 => ? [Xx: $i] :
% 2.35/1.49 ! [Xy: $i] :
% 2.35/1.49 ( ( Xphi @ Xy )
% 2.35/1.49 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(nonemptyImpWitness_type,type,
% 2.35/1.49 nonemptyImpWitness: $o ).
% 2.35/1.49
% 2.35/1.49 thf(nonemptyImpWitness,definition,
% 2.35/1.49 ( nonemptyImpWitness
% 2.35/1.49 = ( ! [A: $i] :
% 2.35/1.49 ( ( nonempty @ A )
% 2.35/1.49 => ? [Xx: $i] :
% 2.35/1.49 ( ( in @ Xx @ A )
% 2.35/1.49 & $true ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(uniqinunit_type,type,
% 2.35/1.49 uniqinunit: $o ).
% 2.35/1.49
% 2.35/1.49 thf(uniqinunit,definition,
% 2.35/1.49 ( uniqinunit
% 2.35/1.49 = ( ! [Xx: $i,Xy: $i] :
% 2.35/1.49 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.35/1.49 => ( Xx = Xy ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(notinsingleton_type,type,
% 2.35/1.49 notinsingleton: $o ).
% 2.35/1.49
% 2.35/1.49 thf(notinsingleton,definition,
% 2.35/1.49 ( notinsingleton
% 2.35/1.49 = ( ! [Xx: $i,Xy: $i] :
% 2.35/1.49 ( ( Xx != Xy )
% 2.35/1.49 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(eqinunit_type,type,
% 2.35/1.49 eqinunit: $o ).
% 2.35/1.49
% 2.35/1.49 thf(eqinunit,definition,
% 2.35/1.49 ( eqinunit
% 2.35/1.49 = ( ! [Xx: $i,Xy: $i] :
% 2.35/1.49 ( ( Xx = Xy )
% 2.35/1.49 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(singletonsswitch_type,type,
% 2.35/1.49 singletonsswitch: $o ).
% 2.35/1.49
% 2.35/1.49 thf(singletonsswitch,definition,
% 2.35/1.49 ( singletonsswitch
% 2.35/1.49 = ( ! [Xx: $i,Xy: $i] :
% 2.35/1.49 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.35/1.49 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(upairsetE_type,type,
% 2.35/1.49 upairsetE: $o ).
% 2.35/1.49
% 2.35/1.49 thf(upairsetE,definition,
% 2.35/1.49 ( upairsetE
% 2.35/1.49 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.35/1.49 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.35/1.49 => ( ( Xz = Xx )
% 2.35/1.49 | ( Xz = Xy ) ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(upairsetIL_type,type,
% 2.35/1.49 upairsetIL: $o ).
% 2.35/1.49
% 2.35/1.49 thf(upairsetIL,definition,
% 2.35/1.49 ( upairsetIL
% 2.35/1.49 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.35/1.49
% 2.35/1.49 thf(upairsetIR_type,type,
% 2.35/1.49 upairsetIR: $o ).
% 2.35/1.49
% 2.35/1.49 thf(upairsetIR,definition,
% 2.35/1.49 ( upairsetIR
% 2.35/1.49 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(emptyE1_type,type,
% 2.35/1.50 emptyE1: $o ).
% 2.35/1.50
% 2.35/1.50 thf(emptyE1,definition,
% 2.35/1.50 ( emptyE1
% 2.35/1.50 = ( ! [A: $i,Xphi: $i > $o] :
% 2.35/1.50 ( ? [Xx: $i] :
% 2.35/1.50 ( ( in @ Xx @ A )
% 2.35/1.50 & ( Xphi @ Xx ) )
% 2.35/1.50 => ( ( ( dsetconstr @ A
% 2.35/1.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.35/1.50 = emptyset )
% 2.35/1.50 => $false ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(vacuousDall_type,type,
% 2.35/1.50 vacuousDall: $o ).
% 2.35/1.50
% 2.35/1.50 thf(vacuousDall,definition,
% 2.35/1.50 ( vacuousDall
% 2.35/1.50 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.35/1.50 ( ( in @ Xx @ emptyset )
% 2.35/1.50 => ( Xphi @ Xx ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(quantDeMorgan1_type,type,
% 2.35/1.50 quantDeMorgan1: $o ).
% 2.35/1.50
% 2.35/1.50 thf(quantDeMorgan1,definition,
% 2.35/1.50 ( quantDeMorgan1
% 2.35/1.50 = ( ! [A: $i,Xphi: $i > $o] :
% 2.35/1.50 ( ~ ! [Xx: $i] :
% 2.35/1.50 ( ( in @ Xx @ A )
% 2.35/1.50 => ( Xphi @ Xx ) )
% 2.35/1.50 => ? [Xx: $i] :
% 2.35/1.50 ( ( in @ Xx @ A )
% 2.35/1.50 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(quantDeMorgan2_type,type,
% 2.35/1.50 quantDeMorgan2: $o ).
% 2.35/1.50
% 2.35/1.50 thf(quantDeMorgan2,definition,
% 2.35/1.50 ( quantDeMorgan2
% 2.35/1.50 = ( ! [A: $i,Xphi: $i > $o] :
% 2.35/1.50 ( ! [Xx: $i] :
% 2.35/1.50 ( ( in @ Xx @ A )
% 2.35/1.50 => ~ ( Xphi @ Xx ) )
% 2.35/1.50 => ~ ? [Xx: $i] :
% 2.35/1.50 ( ( in @ Xx @ A )
% 2.35/1.50 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(quantDeMorgan3_type,type,
% 2.35/1.50 quantDeMorgan3: $o ).
% 2.35/1.50
% 2.35/1.50 thf(quantDeMorgan3,definition,
% 2.35/1.50 ( quantDeMorgan3
% 2.35/1.50 = ( ! [A: $i,Xphi: $i > $o] :
% 2.35/1.50 ( ~ ? [Xx: $i] :
% 2.35/1.50 ( ( in @ Xx @ A )
% 2.35/1.50 & ( Xphi @ Xx ) )
% 2.35/1.50 => ! [Xx: $i] :
% 2.35/1.50 ( ( in @ Xx @ A )
% 2.35/1.50 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(quantDeMorgan4_type,type,
% 2.35/1.50 quantDeMorgan4: $o ).
% 2.35/1.50
% 2.35/1.50 thf(quantDeMorgan4,definition,
% 2.35/1.50 ( quantDeMorgan4
% 2.35/1.50 = ( ! [A: $i,Xphi: $i > $o] :
% 2.35/1.50 ( ? [Xx: $i] :
% 2.35/1.50 ( ( in @ Xx @ A )
% 2.35/1.50 & ~ ( Xphi @ Xx ) )
% 2.35/1.50 => ~ ! [Xx: $i] :
% 2.35/1.50 ( ( in @ Xx @ A )
% 2.35/1.50 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(prop2setI_type,type,
% 2.35/1.50 prop2setI: $o ).
% 2.35/1.50
% 2.35/1.50 thf(prop2setI,definition,
% 2.35/1.50 ( prop2setI
% 2.35/1.50 = ( ! [Xphi: $o] :
% 2.35/1.50 ( Xphi
% 2.35/1.50 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(set2prop_type,type,
% 2.35/1.50 set2prop: $i > $o ).
% 2.35/1.50
% 2.35/1.50 thf(prop2set2propI_type,type,
% 2.35/1.50 prop2set2propI: $o ).
% 2.35/1.50
% 2.35/1.50 thf(prop2set2propI,definition,
% 2.35/1.50 ( prop2set2propI
% 2.35/1.50 = ( ! [Xphi: $o] :
% 2.35/1.50 ( Xphi
% 2.35/1.50 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(notdexE_type,type,
% 2.35/1.50 notdexE: $o ).
% 2.35/1.50
% 2.35/1.50 thf(notdexE,definition,
% 2.35/1.50 ( notdexE
% 2.35/1.50 = ( ! [A: $i,Xphi: $i > $o] :
% 2.35/1.50 ( ~ ? [Xx: $i] :
% 2.35/1.50 ( ( in @ Xx @ A )
% 2.35/1.50 & ( Xphi @ Xx ) )
% 2.35/1.50 => ! [Xx: $i] :
% 2.35/1.50 ( ( in @ Xx @ A )
% 2.35/1.50 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(notdallE_type,type,
% 2.35/1.50 notdallE: $o ).
% 2.35/1.50
% 2.35/1.50 thf(notdallE,definition,
% 2.35/1.50 ( notdallE
% 2.35/1.50 = ( ! [A: $i,Xphi: $i > $o] :
% 2.35/1.50 ( ~ ! [Xx: $i] :
% 2.35/1.50 ( ( in @ Xx @ A )
% 2.35/1.50 => ( Xphi @ Xx ) )
% 2.35/1.50 => ? [Xx: $i] :
% 2.35/1.50 ( ( in @ Xx @ A )
% 2.35/1.50 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(exuI1_type,type,
% 2.35/1.50 exuI1: $o ).
% 2.35/1.50
% 2.35/1.50 thf(exuI1,definition,
% 2.35/1.50 ( exuI1
% 2.35/1.50 = ( ! [Xphi: $i > $o] :
% 2.35/1.50 ( ? [Xx: $i] :
% 2.35/1.50 ( ( Xphi @ Xx )
% 2.35/1.50 & ! [Xy: $i] :
% 2.35/1.50 ( ( Xphi @ Xy )
% 2.35/1.50 => ( Xx = Xy ) ) )
% 2.35/1.50 => ( exu
% 2.35/1.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(exuI3_type,type,
% 2.35/1.50 exuI3: $o ).
% 2.35/1.50
% 2.35/1.50 thf(exuI3,definition,
% 2.35/1.50 ( exuI3
% 2.35/1.50 = ( ! [Xphi: $i > $o] :
% 2.35/1.50 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.35/1.50 => ( ! [Xx: $i,Xy: $i] :
% 2.35/1.50 ( ( Xphi @ Xx )
% 2.35/1.50 => ( ( Xphi @ Xy )
% 2.35/1.50 => ( Xx = Xy ) ) )
% 2.35/1.50 => ( exu
% 2.35/1.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(exuI2_type,type,
% 2.35/1.50 exuI2: $o ).
% 2.35/1.50
% 2.35/1.50 thf(exuI2,definition,
% 2.35/1.50 ( exuI2
% 2.35/1.50 = ( ! [Xphi: $i > $o] :
% 2.35/1.50 ( ? [Xx: $i] :
% 2.35/1.50 ! [Xy: $i] :
% 2.35/1.50 ( ( Xphi @ Xy )
% 2.35/1.50 <=> ( Xy = Xx ) )
% 2.35/1.50 => ( exu
% 2.35/1.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(inCongP_type,type,
% 2.35/1.50 inCongP: $o ).
% 2.35/1.50
% 2.35/1.50 thf(inCongP,definition,
% 2.35/1.50 ( inCongP
% 2.35/1.50 = ( ! [A: $i,B: $i] :
% 2.35/1.50 ( ( A = B )
% 2.35/1.50 => ! [Xx: $i,Xy: $i] :
% 2.35/1.50 ( ( Xx = Xy )
% 2.35/1.50 => ( ( in @ Xx @ A )
% 2.35/1.50 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(in__Cong_type,type,
% 2.35/1.50 in__Cong: $o ).
% 2.35/1.50
% 2.35/1.50 thf(in__Cong,definition,
% 2.35/1.50 ( in__Cong
% 2.35/1.50 = ( ! [A: $i,B: $i] :
% 2.35/1.50 ( ( A = B )
% 2.35/1.50 => ! [Xx: $i,Xy: $i] :
% 2.35/1.50 ( ( Xx = Xy )
% 2.35/1.50 => ( ( in @ Xx @ A )
% 2.35/1.50 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(exuE3u_type,type,
% 2.35/1.50 exuE3u: $o ).
% 2.35/1.50
% 2.35/1.50 thf(exuE3u,definition,
% 2.35/1.50 ( exuE3u
% 2.35/1.50 = ( ! [Xphi: $i > $o] :
% 2.35/1.50 ( ( exu
% 2.35/1.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.35/1.50 => ! [Xx: $i,Xy: $i] :
% 2.35/1.50 ( ( Xphi @ Xx )
% 2.35/1.50 => ( ( Xphi @ Xy )
% 2.35/1.50 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(exu__Cong_type,type,
% 2.35/1.50 exu__Cong: $o ).
% 2.35/1.50
% 2.35/1.50 thf(exu__Cong,definition,
% 2.35/1.50 ( exu__Cong
% 2.35/1.50 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.35/1.50 ( ! [Xx: $i,Xy: $i] :
% 2.35/1.50 ( ( Xx = Xy )
% 2.35/1.50 => ( ( Xphi @ Xx )
% 2.35/1.50 <=> ( Xpsi @ Xy ) ) )
% 2.35/1.50 => ( ( exu
% 2.35/1.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.35/1.50 <=> ( exu
% 2.35/1.50 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(emptyset__Cong_type,type,
% 2.35/1.50 emptyset__Cong: $o ).
% 2.35/1.50
% 2.35/1.50 thf(emptyset__Cong,definition,
% 2.35/1.50 ( emptyset__Cong
% 2.35/1.50 = ( emptyset = emptyset ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(setadjoin__Cong_type,type,
% 2.35/1.50 setadjoin__Cong: $o ).
% 2.35/1.50
% 2.35/1.50 thf(setadjoin__Cong,definition,
% 2.35/1.50 ( setadjoin__Cong
% 2.35/1.50 = ( ! [Xx: $i,Xy: $i] :
% 2.35/1.50 ( ( Xx = Xy )
% 2.35/1.50 => ! [Xz: $i,Xu: $i] :
% 2.35/1.50 ( ( Xz = Xu )
% 2.35/1.50 => ( ( setadjoin @ Xx @ Xz )
% 2.35/1.50 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(powerset__Cong_type,type,
% 2.35/1.50 powerset__Cong: $o ).
% 2.35/1.50
% 2.35/1.50 thf(powerset__Cong,definition,
% 2.35/1.50 ( powerset__Cong
% 2.35/1.50 = ( ! [A: $i,B: $i] :
% 2.35/1.50 ( ( A = B )
% 2.35/1.50 => ( ( powerset @ A )
% 2.35/1.50 = ( powerset @ B ) ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(setunion__Cong_type,type,
% 2.35/1.50 setunion__Cong: $o ).
% 2.35/1.50
% 2.35/1.50 thf(setunion__Cong,definition,
% 2.35/1.50 ( setunion__Cong
% 2.35/1.50 = ( ! [A: $i,B: $i] :
% 2.35/1.50 ( ( A = B )
% 2.35/1.50 => ( ( setunion @ A )
% 2.35/1.50 = ( setunion @ B ) ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(omega__Cong_type,type,
% 2.35/1.50 omega__Cong: $o ).
% 2.35/1.50
% 2.35/1.50 thf(omega__Cong,definition,
% 2.35/1.50 ( omega__Cong
% 2.35/1.50 = ( omega = omega ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(exuEu_type,type,
% 2.35/1.50 exuEu: $o ).
% 2.35/1.50
% 2.35/1.50 thf(exuEu,definition,
% 2.35/1.50 ( exuEu
% 2.35/1.50 = ( ! [Xphi: $i > $o] :
% 2.35/1.50 ( ( exu
% 2.35/1.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.35/1.50 => ! [Xx: $i,Xy: $i] :
% 2.35/1.50 ( ( Xphi @ Xx )
% 2.35/1.50 => ( ( Xphi @ Xy )
% 2.35/1.50 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(descr__Cong_type,type,
% 2.35/1.50 descr__Cong: $o ).
% 2.35/1.50
% 2.35/1.50 thf(descr__Cong,definition,
% 2.35/1.50 ( descr__Cong
% 2.35/1.50 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.35/1.50 ( ! [Xx: $i,Xy: $i] :
% 2.35/1.50 ( ( Xx = Xy )
% 2.35/1.50 => ( ( Xphi @ Xx )
% 2.35/1.50 <=> ( Xpsi @ Xy ) ) )
% 2.35/1.50 => ( ( exu
% 2.35/1.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.35/1.50 => ( ( exu
% 2.35/1.50 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.35/1.50 => ( ( descr
% 2.35/1.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.35/1.50 = ( descr
% 2.35/1.50 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(dsetconstr__Cong_type,type,
% 2.35/1.50 dsetconstr__Cong: $o ).
% 2.35/1.50
% 2.35/1.50 thf(dsetconstr__Cong,definition,
% 2.35/1.50 ( dsetconstr__Cong
% 2.35/1.50 = ( ! [A: $i,B: $i] :
% 2.35/1.50 ( ( A = B )
% 2.35/1.50 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.35/1.50 ( ! [Xx: $i] :
% 2.35/1.50 ( ( in @ Xx @ A )
% 2.35/1.50 => ! [Xy: $i] :
% 2.35/1.50 ( ( in @ Xy @ B )
% 2.35/1.50 => ( ( Xx = Xy )
% 2.35/1.50 => ( ( Xphi @ Xx )
% 2.35/1.50 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.35/1.50 => ( ( dsetconstr @ A
% 2.35/1.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.35/1.50 = ( dsetconstr @ B
% 2.35/1.50 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(subset_type,type,
% 2.35/1.50 subset: $i > $i > $o ).
% 2.35/1.50
% 2.35/1.50 thf(disjoint_type,type,
% 2.35/1.50 disjoint: $i > $i > $o ).
% 2.35/1.50
% 2.35/1.50 thf(setsmeet_type,type,
% 2.35/1.50 setsmeet: $i > $i > $o ).
% 2.35/1.50
% 2.35/1.50 thf(subsetI1_type,type,
% 2.35/1.50 subsetI1: $o ).
% 2.35/1.50
% 2.35/1.50 thf(subsetI1,definition,
% 2.35/1.50 ( subsetI1
% 2.35/1.50 = ( ! [A: $i,B: $i] :
% 2.35/1.50 ( ! [Xx: $i] :
% 2.35/1.50 ( ( in @ Xx @ A )
% 2.35/1.50 => ( in @ Xx @ B ) )
% 2.35/1.50 => ( subset @ A @ B ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(eqimpsubset2_type,type,
% 2.35/1.50 eqimpsubset2: $o ).
% 2.35/1.50
% 2.35/1.50 thf(eqimpsubset2,definition,
% 2.35/1.50 ( eqimpsubset2
% 2.35/1.50 = ( ! [A: $i,B: $i] :
% 2.35/1.50 ( ( A = B )
% 2.35/1.50 => ( subset @ B @ A ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(eqimpsubset1_type,type,
% 2.35/1.50 eqimpsubset1: $o ).
% 2.35/1.50
% 2.35/1.50 thf(eqimpsubset1,definition,
% 2.35/1.50 ( eqimpsubset1
% 2.35/1.50 = ( ! [A: $i,B: $i] :
% 2.35/1.50 ( ( A = B )
% 2.35/1.50 => ( subset @ A @ B ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(subsetI2_type,type,
% 2.35/1.50 subsetI2: $o ).
% 2.35/1.50
% 2.35/1.50 thf(subsetI2,definition,
% 2.35/1.50 ( subsetI2
% 2.35/1.50 = ( ! [A: $i,B: $i] :
% 2.35/1.50 ( ! [Xx: $i] :
% 2.35/1.50 ( ( in @ Xx @ A )
% 2.35/1.50 => ( in @ Xx @ B ) )
% 2.35/1.50 => ( subset @ A @ B ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(emptysetsubset_type,type,
% 2.35/1.50 emptysetsubset: $o ).
% 2.35/1.50
% 2.35/1.50 thf(emptysetsubset,definition,
% 2.35/1.50 ( emptysetsubset
% 2.35/1.50 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(subsetE_type,type,
% 2.35/1.50 subsetE: $o ).
% 2.35/1.50
% 2.35/1.50 thf(subsetE,definition,
% 2.35/1.50 ( subsetE
% 2.35/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.50 ( ( subset @ A @ B )
% 2.35/1.50 => ( ( in @ Xx @ A )
% 2.35/1.50 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(subsetE2_type,type,
% 2.35/1.50 subsetE2: $o ).
% 2.35/1.50
% 2.35/1.50 thf(subsetE2,definition,
% 2.35/1.50 ( subsetE2
% 2.35/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.50 ( ( subset @ A @ B )
% 2.35/1.50 => ( ~ ( in @ Xx @ B )
% 2.35/1.50 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(notsubsetI_type,type,
% 2.35/1.50 notsubsetI: $o ).
% 2.35/1.50
% 2.35/1.50 thf(notsubsetI,definition,
% 2.35/1.50 ( notsubsetI
% 2.35/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.50 ( ( in @ Xx @ A )
% 2.35/1.50 => ( ~ ( in @ Xx @ B )
% 2.35/1.50 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(notequalI1_type,type,
% 2.35/1.50 notequalI1: $o ).
% 2.35/1.50
% 2.35/1.50 thf(notequalI1,definition,
% 2.35/1.50 ( notequalI1
% 2.35/1.50 = ( ! [A: $i,B: $i] :
% 2.35/1.50 ( ~ ( subset @ A @ B )
% 2.35/1.50 => ( A != B ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(notequalI2_type,type,
% 2.35/1.50 notequalI2: $o ).
% 2.35/1.50
% 2.35/1.50 thf(notequalI2,definition,
% 2.35/1.50 ( notequalI2
% 2.35/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.50 ( ( in @ Xx @ A )
% 2.35/1.50 => ( ~ ( in @ Xx @ B )
% 2.35/1.50 => ( A != B ) ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(subsetRefl_type,type,
% 2.35/1.50 subsetRefl: $o ).
% 2.35/1.50
% 2.35/1.50 thf(subsetRefl,definition,
% 2.35/1.50 ( subsetRefl
% 2.35/1.50 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(subsetTrans_type,type,
% 2.35/1.50 subsetTrans: $o ).
% 2.35/1.50
% 2.35/1.50 thf(subsetTrans,definition,
% 2.35/1.50 ( subsetTrans
% 2.35/1.50 = ( ! [A: $i,B: $i,C: $i] :
% 2.35/1.50 ( ( subset @ A @ B )
% 2.35/1.50 => ( ( subset @ B @ C )
% 2.35/1.50 => ( subset @ A @ C ) ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(setadjoinSub_type,type,
% 2.35/1.50 setadjoinSub: $o ).
% 2.35/1.50
% 2.35/1.50 thf(setadjoinSub,definition,
% 2.35/1.50 ( setadjoinSub
% 2.35/1.50 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(setadjoinSub2_type,type,
% 2.35/1.50 setadjoinSub2: $o ).
% 2.35/1.50
% 2.35/1.50 thf(setadjoinSub2,definition,
% 2.35/1.50 ( setadjoinSub2
% 2.35/1.50 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.35/1.50 ( ( subset @ A @ B )
% 2.35/1.50 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(subset2powerset_type,type,
% 2.35/1.50 subset2powerset: $o ).
% 2.35/1.50
% 2.35/1.50 thf(subset2powerset,definition,
% 2.35/1.50 ( subset2powerset
% 2.35/1.50 = ( ! [A: $i,B: $i] :
% 2.35/1.50 ( ( subset @ A @ B )
% 2.35/1.50 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.35/1.50
% 2.35/1.50 thf(setextsub_type,type,
% 2.35/1.50 setextsub: $o ).
% 2.35/1.50
% 2.35/1.50 thf(setextsub,definition,
% 2.35/1.50 ( setextsub
% 2.35/1.50 = ( ! [A: $i,B: $i] :
% 2.35/1.50 ( ( subset @ A @ B )
% 2.53/1.50 => ( ( subset @ B @ A )
% 2.53/1.50 => ( A = B ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(subsetemptysetimpeq_type,type,
% 2.53/1.50 subsetemptysetimpeq: $o ).
% 2.53/1.50
% 2.53/1.50 thf(subsetemptysetimpeq,definition,
% 2.53/1.50 ( subsetemptysetimpeq
% 2.53/1.50 = ( ! [A: $i] :
% 2.53/1.50 ( ( subset @ A @ emptyset )
% 2.53/1.50 => ( A = emptyset ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(powersetI1_type,type,
% 2.53/1.50 powersetI1: $o ).
% 2.53/1.50
% 2.53/1.50 thf(powersetI1,definition,
% 2.53/1.50 ( powersetI1
% 2.53/1.50 = ( ! [A: $i,B: $i] :
% 2.53/1.50 ( ( subset @ B @ A )
% 2.53/1.50 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(powersetE1_type,type,
% 2.53/1.50 powersetE1: $o ).
% 2.53/1.50
% 2.53/1.50 thf(powersetE1,definition,
% 2.53/1.50 ( powersetE1
% 2.53/1.50 = ( ! [A: $i,B: $i] :
% 2.53/1.50 ( ( in @ B @ ( powerset @ A ) )
% 2.53/1.50 => ( subset @ B @ A ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(inPowerset_type,type,
% 2.53/1.50 inPowerset: $o ).
% 2.53/1.50
% 2.53/1.50 thf(inPowerset,definition,
% 2.53/1.50 ( inPowerset
% 2.53/1.50 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(powersetsubset_type,type,
% 2.53/1.50 powersetsubset: $o ).
% 2.53/1.50
% 2.53/1.50 thf(powersetsubset,definition,
% 2.53/1.50 ( powersetsubset
% 2.53/1.50 = ( ! [A: $i,B: $i] :
% 2.53/1.50 ( ( subset @ A @ B )
% 2.53/1.50 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(sepInPowerset_type,type,
% 2.53/1.50 sepInPowerset: $o ).
% 2.53/1.50
% 2.53/1.50 thf(sepInPowerset,definition,
% 2.53/1.50 ( sepInPowerset
% 2.53/1.50 = ( ! [A: $i,Xphi: $i > $o] :
% 2.53/1.50 ( in
% 2.53/1.50 @ ( dsetconstr @ A
% 2.53/1.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.53/1.50 @ ( powerset @ A ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(sepSubset_type,type,
% 2.53/1.50 sepSubset: $o ).
% 2.53/1.50
% 2.53/1.50 thf(sepSubset,definition,
% 2.53/1.50 ( sepSubset
% 2.53/1.50 = ( ! [A: $i,Xphi: $i > $o] :
% 2.53/1.50 ( subset
% 2.53/1.50 @ ( dsetconstr @ A
% 2.53/1.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.53/1.50 @ A ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(binunion_type,type,
% 2.53/1.50 binunion: $i > $i > $i ).
% 2.53/1.50
% 2.53/1.50 thf(binunionIL_type,type,
% 2.53/1.50 binunionIL: $o ).
% 2.53/1.50
% 2.53/1.50 thf(binunionIL,definition,
% 2.53/1.50 ( binunionIL
% 2.53/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.53/1.50 ( ( in @ Xx @ A )
% 2.53/1.50 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(upairset2IR_type,type,
% 2.53/1.50 upairset2IR: $o ).
% 2.53/1.50
% 2.53/1.50 thf(upairset2IR,definition,
% 2.53/1.50 ( upairset2IR
% 2.53/1.50 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(binunionIR_type,type,
% 2.53/1.50 binunionIR: $o ).
% 2.53/1.50
% 2.53/1.50 thf(binunionIR,definition,
% 2.53/1.50 ( binunionIR
% 2.53/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.53/1.50 ( ( in @ Xx @ B )
% 2.53/1.50 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(binunionEcases_type,type,
% 2.53/1.50 binunionEcases: $o ).
% 2.53/1.50
% 2.53/1.50 thf(binunionEcases,definition,
% 2.53/1.50 ( binunionEcases
% 2.53/1.50 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.53/1.50 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.53/1.50 => ( ( ( in @ Xx @ A )
% 2.53/1.50 => Xphi )
% 2.53/1.50 => ( ( ( in @ Xx @ B )
% 2.53/1.50 => Xphi )
% 2.53/1.50 => Xphi ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(binunionE_type,type,
% 2.53/1.50 binunionE: $o ).
% 2.53/1.50
% 2.53/1.50 thf(binunionE,definition,
% 2.53/1.50 ( binunionE
% 2.53/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.53/1.50 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.53/1.50 => ( ( in @ Xx @ A )
% 2.53/1.50 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(binunionLsub_type,type,
% 2.53/1.50 binunionLsub: $o ).
% 2.53/1.50
% 2.53/1.50 thf(binunionLsub,definition,
% 2.53/1.50 ( binunionLsub
% 2.53/1.50 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(binunionRsub_type,type,
% 2.53/1.50 binunionRsub: $o ).
% 2.53/1.50
% 2.53/1.50 thf(binunionRsub,definition,
% 2.53/1.50 ( binunionRsub
% 2.53/1.50 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(binintersect_type,type,
% 2.53/1.50 binintersect: $i > $i > $i ).
% 2.53/1.50
% 2.53/1.50 thf(binintersectI_type,type,
% 2.53/1.50 binintersectI: $o ).
% 2.53/1.50
% 2.53/1.50 thf(binintersectI,definition,
% 2.53/1.50 ( binintersectI
% 2.53/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.53/1.50 ( ( in @ Xx @ A )
% 2.53/1.50 => ( ( in @ Xx @ B )
% 2.53/1.50 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(binintersectSubset5_type,type,
% 2.53/1.50 binintersectSubset5: $o ).
% 2.53/1.50
% 2.53/1.50 thf(binintersectSubset5,definition,
% 2.53/1.50 ( binintersectSubset5
% 2.53/1.50 = ( ! [A: $i,B: $i,C: $i] :
% 2.53/1.50 ( ( subset @ C @ A )
% 2.53/1.50 => ( ( subset @ C @ B )
% 2.53/1.50 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(binintersectEL_type,type,
% 2.53/1.50 binintersectEL: $o ).
% 2.53/1.50
% 2.53/1.50 thf(binintersectEL,definition,
% 2.53/1.50 ( binintersectEL
% 2.53/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.53/1.50 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.53/1.50 => ( in @ Xx @ A ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(binintersectLsub_type,type,
% 2.53/1.50 binintersectLsub: $o ).
% 2.53/1.50
% 2.53/1.50 thf(binintersectLsub,definition,
% 2.53/1.50 ( binintersectLsub
% 2.53/1.50 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(binintersectSubset2_type,type,
% 2.53/1.50 binintersectSubset2: $o ).
% 2.53/1.50
% 2.53/1.50 thf(binintersectSubset2,definition,
% 2.53/1.50 ( binintersectSubset2
% 2.53/1.50 = ( ! [A: $i,B: $i] :
% 2.53/1.50 ( ( subset @ A @ B )
% 2.53/1.50 => ( ( binintersect @ A @ B )
% 2.53/1.50 = A ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(binintersectSubset3_type,type,
% 2.53/1.50 binintersectSubset3: $o ).
% 2.53/1.50
% 2.53/1.50 thf(binintersectSubset3,definition,
% 2.53/1.50 ( binintersectSubset3
% 2.53/1.50 = ( ! [A: $i,B: $i] :
% 2.53/1.50 ( ( ( binintersect @ A @ B )
% 2.53/1.50 = B )
% 2.53/1.50 => ( subset @ B @ A ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(binintersectER_type,type,
% 2.53/1.50 binintersectER: $o ).
% 2.53/1.50
% 2.53/1.50 thf(binintersectER,definition,
% 2.53/1.50 ( binintersectER
% 2.53/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.53/1.50 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.53/1.50 => ( in @ Xx @ B ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(disjointsetsI1_type,type,
% 2.53/1.50 disjointsetsI1: $o ).
% 2.53/1.50
% 2.53/1.50 thf(disjointsetsI1,definition,
% 2.53/1.50 ( disjointsetsI1
% 2.53/1.50 = ( ! [A: $i,B: $i] :
% 2.53/1.50 ( ~ ? [Xx: $i] :
% 2.53/1.50 ( ( in @ Xx @ A )
% 2.53/1.50 & ( in @ Xx @ B ) )
% 2.53/1.50 => ( ( binintersect @ A @ B )
% 2.53/1.50 = emptyset ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(binintersectRsub_type,type,
% 2.53/1.50 binintersectRsub: $o ).
% 2.53/1.50
% 2.53/1.50 thf(binintersectRsub,definition,
% 2.53/1.50 ( binintersectRsub
% 2.53/1.50 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(binintersectSubset4_type,type,
% 2.53/1.50 binintersectSubset4: $o ).
% 2.53/1.50
% 2.53/1.50 thf(binintersectSubset4,definition,
% 2.53/1.50 ( binintersectSubset4
% 2.53/1.50 = ( ! [A: $i,B: $i] :
% 2.53/1.50 ( ( subset @ B @ A )
% 2.53/1.50 => ( ( binintersect @ A @ B )
% 2.53/1.50 = B ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(binintersectSubset1_type,type,
% 2.53/1.50 binintersectSubset1: $o ).
% 2.53/1.50
% 2.53/1.50 thf(binintersectSubset1,definition,
% 2.53/1.50 ( binintersectSubset1
% 2.53/1.50 = ( ! [A: $i,B: $i] :
% 2.53/1.50 ( ( ( binintersect @ A @ B )
% 2.53/1.50 = A )
% 2.53/1.50 => ( subset @ A @ B ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(bs114d_type,type,
% 2.53/1.50 bs114d: $o ).
% 2.53/1.50
% 2.53/1.50 thf(bs114d,definition,
% 2.53/1.50 ( bs114d
% 2.53/1.50 = ( ! [A: $i,B: $i,C: $i] :
% 2.53/1.50 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.53/1.50 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(regular_type,type,
% 2.53/1.50 regular: $i > $o ).
% 2.53/1.50
% 2.53/1.50 thf(setminus_type,type,
% 2.53/1.50 setminus: $i > $i > $i ).
% 2.53/1.50
% 2.53/1.50 thf(setminusI_type,type,
% 2.53/1.50 setminusI: $o ).
% 2.53/1.50
% 2.53/1.50 thf(setminusI,definition,
% 2.53/1.50 ( setminusI
% 2.53/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.53/1.50 ( ( in @ Xx @ A )
% 2.53/1.50 => ( ~ ( in @ Xx @ B )
% 2.53/1.50 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(setminusEL_type,type,
% 2.53/1.50 setminusEL: $o ).
% 2.53/1.50
% 2.53/1.50 thf(setminusEL,definition,
% 2.53/1.50 ( setminusEL
% 2.53/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.53/1.50 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.53/1.50 => ( in @ Xx @ A ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(setminusER_type,type,
% 2.53/1.50 setminusER: $o ).
% 2.53/1.50
% 2.53/1.50 thf(setminusER,definition,
% 2.53/1.50 ( setminusER
% 2.53/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.53/1.50 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.53/1.50 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(setminusSubset2_type,type,
% 2.53/1.50 setminusSubset2: $o ).
% 2.53/1.50
% 2.53/1.50 thf(setminusSubset2,definition,
% 2.53/1.50 ( setminusSubset2
% 2.53/1.50 = ( ! [A: $i,B: $i] :
% 2.53/1.50 ( ( subset @ A @ B )
% 2.53/1.50 => ( ( setminus @ A @ B )
% 2.53/1.50 = emptyset ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(setminusERneg_type,type,
% 2.53/1.50 setminusERneg: $o ).
% 2.53/1.50
% 2.53/1.50 thf(setminusERneg,definition,
% 2.53/1.50 ( setminusERneg
% 2.53/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.53/1.50 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.53/1.50 => ( ( in @ Xx @ A )
% 2.53/1.50 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(setminusELneg_type,type,
% 2.53/1.50 setminusELneg: $o ).
% 2.53/1.50
% 2.53/1.50 thf(setminusELneg,definition,
% 2.53/1.50 ( setminusELneg
% 2.53/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.53/1.50 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.53/1.50 => ( ~ ( in @ Xx @ B )
% 2.53/1.50 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(setminusILneg_type,type,
% 2.53/1.50 setminusILneg: $o ).
% 2.53/1.50
% 2.53/1.50 thf(setminusILneg,definition,
% 2.53/1.50 ( setminusILneg
% 2.53/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.53/1.50 ( ~ ( in @ Xx @ A )
% 2.53/1.50 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(setminusIRneg_type,type,
% 2.53/1.50 setminusIRneg: $o ).
% 2.53/1.50
% 2.53/1.50 thf(setminusIRneg,definition,
% 2.53/1.50 ( setminusIRneg
% 2.53/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.53/1.50 ( ( in @ Xx @ B )
% 2.53/1.50 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(setminusLsub_type,type,
% 2.53/1.50 setminusLsub: $o ).
% 2.53/1.50
% 2.53/1.50 thf(setminusLsub,definition,
% 2.53/1.50 ( setminusLsub
% 2.53/1.50 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(setminusSubset1_type,type,
% 2.53/1.50 setminusSubset1: $o ).
% 2.53/1.50
% 2.53/1.50 thf(setminusSubset1,definition,
% 2.53/1.50 ( setminusSubset1
% 2.53/1.50 = ( ! [A: $i,B: $i] :
% 2.53/1.50 ( ( ( setminus @ A @ B )
% 2.53/1.50 = emptyset )
% 2.53/1.50 => ( subset @ A @ B ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(symdiff_type,type,
% 2.53/1.50 symdiff: $i > $i > $i ).
% 2.53/1.50
% 2.53/1.50 thf(symdiffE_type,type,
% 2.53/1.50 symdiffE: $o ).
% 2.53/1.50
% 2.53/1.50 thf(symdiffE,definition,
% 2.53/1.50 ( symdiffE
% 2.53/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.53/1.50 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.53/1.50 => ! [Xphi: $o] :
% 2.53/1.50 ( ( ( in @ Xx @ A )
% 2.53/1.50 => ( ~ ( in @ Xx @ B )
% 2.53/1.50 => Xphi ) )
% 2.53/1.50 => ( ( ~ ( in @ Xx @ A )
% 2.53/1.50 => ( ( in @ Xx @ B )
% 2.53/1.50 => Xphi ) )
% 2.53/1.50 => Xphi ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(symdiffI1_type,type,
% 2.53/1.50 symdiffI1: $o ).
% 2.53/1.50
% 2.53/1.50 thf(symdiffI1,definition,
% 2.53/1.50 ( symdiffI1
% 2.53/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.53/1.50 ( ( in @ Xx @ A )
% 2.53/1.50 => ( ~ ( in @ Xx @ B )
% 2.53/1.50 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(symdiffI2_type,type,
% 2.53/1.50 symdiffI2: $o ).
% 2.53/1.50
% 2.53/1.50 thf(symdiffI2,definition,
% 2.53/1.50 ( symdiffI2
% 2.53/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.53/1.50 ( ~ ( in @ Xx @ A )
% 2.53/1.50 => ( ( in @ Xx @ B )
% 2.53/1.50 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(symdiffIneg1_type,type,
% 2.53/1.50 symdiffIneg1: $o ).
% 2.53/1.50
% 2.53/1.50 thf(symdiffIneg1,definition,
% 2.53/1.50 ( symdiffIneg1
% 2.53/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.53/1.50 ( ( in @ Xx @ A )
% 2.53/1.50 => ( ( in @ Xx @ B )
% 2.53/1.50 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(symdiffIneg2_type,type,
% 2.53/1.50 symdiffIneg2: $o ).
% 2.53/1.50
% 2.53/1.50 thf(symdiffIneg2,definition,
% 2.53/1.50 ( symdiffIneg2
% 2.53/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.53/1.50 ( ~ ( in @ Xx @ A )
% 2.53/1.50 => ( ~ ( in @ Xx @ B )
% 2.53/1.50 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(iskpair_type,type,
% 2.53/1.50 iskpair: $i > $o ).
% 2.53/1.50
% 2.53/1.50 thf(iskpair,definition,
% 2.53/1.50 ( iskpair
% 2.53/1.50 = ( ^ [A: $i] :
% 2.53/1.50 ? [Xx: $i] :
% 2.53/1.50 ( ( in @ Xx @ ( setunion @ A ) )
% 2.53/1.50 & ? [Xy: $i] :
% 2.53/1.50 ( ( in @ Xy @ ( setunion @ A ) )
% 2.53/1.50 & ( A
% 2.53/1.50 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(secondinupair_type,type,
% 2.53/1.50 secondinupair: $o ).
% 2.53/1.50
% 2.53/1.50 thf(secondinupair,definition,
% 2.53/1.50 ( secondinupair
% 2.53/1.50 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(setukpairIL_type,type,
% 2.53/1.50 setukpairIL: $o ).
% 2.53/1.50
% 2.53/1.50 thf(setukpairIL,definition,
% 2.53/1.50 ( setukpairIL
% 2.53/1.50 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(setukpairIR_type,type,
% 2.53/1.50 setukpairIR: $o ).
% 2.53/1.50
% 2.53/1.50 thf(setukpairIR,definition,
% 2.53/1.50 ( setukpairIR
% 2.53/1.50 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(kpairiskpair_type,type,
% 2.53/1.50 kpairiskpair: $o ).
% 2.53/1.50
% 2.53/1.50 thf(kpairiskpair,definition,
% 2.53/1.50 ( kpairiskpair
% 2.53/1.50 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(kpair_type,type,
% 2.53/1.50 kpair: $i > $i > $i ).
% 2.53/1.50
% 2.53/1.50 thf(kpair,definition,
% 2.53/1.50 ( kpair
% 2.53/1.50 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(kpairp_type,type,
% 2.53/1.50 kpairp: $o ).
% 2.53/1.50
% 2.53/1.50 thf(kpairp,definition,
% 2.53/1.50 ( kpairp
% 2.53/1.50 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(cartprod_type,type,
% 2.53/1.50 cartprod: $i > $i > $i ).
% 2.53/1.50
% 2.53/1.50 thf(singletonsubset_type,type,
% 2.53/1.50 singletonsubset: $o ).
% 2.53/1.50
% 2.53/1.50 thf(singletonsubset,definition,
% 2.53/1.50 ( singletonsubset
% 2.53/1.50 = ( ! [A: $i,Xx: $i] :
% 2.53/1.50 ( ( in @ Xx @ A )
% 2.53/1.50 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(singletoninpowerset_type,type,
% 2.53/1.50 singletoninpowerset: $o ).
% 2.53/1.50
% 2.53/1.50 thf(singletoninpowerset,definition,
% 2.53/1.50 ( singletoninpowerset
% 2.53/1.50 = ( ! [A: $i,Xx: $i] :
% 2.53/1.50 ( ( in @ Xx @ A )
% 2.53/1.50 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(singletoninpowunion_type,type,
% 2.53/1.50 singletoninpowunion: $o ).
% 2.53/1.50
% 2.53/1.50 thf(singletoninpowunion,definition,
% 2.53/1.50 ( singletoninpowunion
% 2.53/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.53/1.50 ( ( in @ Xx @ A )
% 2.53/1.50 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(upairset2E_type,type,
% 2.53/1.50 upairset2E: $o ).
% 2.53/1.50
% 2.53/1.50 thf(upairset2E,definition,
% 2.53/1.50 ( upairset2E
% 2.53/1.50 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.53/1.50 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.53/1.50 => ( ( Xz = Xx )
% 2.53/1.50 | ( Xz = Xy ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(upairsubunion_type,type,
% 2.53/1.50 upairsubunion: $o ).
% 2.53/1.50
% 2.53/1.50 thf(upairsubunion,definition,
% 2.53/1.50 ( upairsubunion
% 2.53/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.53/1.50 ( ( in @ Xx @ A )
% 2.53/1.50 => ! [Xy: $i] :
% 2.53/1.50 ( ( in @ Xy @ B )
% 2.53/1.50 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(upairinpowunion_type,type,
% 2.53/1.50 upairinpowunion: $o ).
% 2.53/1.50
% 2.53/1.50 thf(upairinpowunion,definition,
% 2.53/1.50 ( upairinpowunion
% 2.53/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.53/1.50 ( ( in @ Xx @ A )
% 2.53/1.50 => ! [Xy: $i] :
% 2.53/1.50 ( ( in @ Xy @ B )
% 2.53/1.50 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(ubforcartprodlem1_type,type,
% 2.53/1.50 ubforcartprodlem1: $o ).
% 2.53/1.50
% 2.53/1.50 thf(ubforcartprodlem1,definition,
% 2.53/1.50 ( ubforcartprodlem1
% 2.53/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.53/1.50 ( ( in @ Xx @ A )
% 2.53/1.50 => ! [Xy: $i] :
% 2.53/1.50 ( ( in @ Xy @ B )
% 2.53/1.50 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(ubforcartprodlem2_type,type,
% 2.53/1.50 ubforcartprodlem2: $o ).
% 2.53/1.50
% 2.53/1.50 thf(ubforcartprodlem2,definition,
% 2.53/1.50 ( ubforcartprodlem2
% 2.53/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.53/1.50 ( ( in @ Xx @ A )
% 2.53/1.50 => ! [Xy: $i] :
% 2.53/1.50 ( ( in @ Xy @ B )
% 2.53/1.50 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(ubforcartprodlem3_type,type,
% 2.53/1.50 ubforcartprodlem3: $o ).
% 2.53/1.50
% 2.53/1.50 thf(ubforcartprodlem3,definition,
% 2.53/1.50 ( ubforcartprodlem3
% 2.53/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.53/1.50 ( ( in @ Xx @ A )
% 2.53/1.50 => ! [Xy: $i] :
% 2.53/1.50 ( ( in @ Xy @ B )
% 2.53/1.50 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(cartprodpairin_type,type,
% 2.53/1.50 cartprodpairin: $o ).
% 2.53/1.50
% 2.53/1.50 thf(cartprodpairin,definition,
% 2.53/1.50 ( cartprodpairin
% 2.53/1.50 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.53/1.50 ( ( in @ Xx @ A )
% 2.53/1.50 => ! [Xy: $i] :
% 2.53/1.50 ( ( in @ Xy @ B )
% 2.53/1.50 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(cartprodmempair1_type,type,
% 2.53/1.50 cartprodmempair1: $o ).
% 2.53/1.50
% 2.53/1.50 thf(cartprodmempair1,definition,
% 2.53/1.50 ( cartprodmempair1
% 2.53/1.50 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.53/1.50 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.53/1.50 => ? [Xx: $i] :
% 2.53/1.50 ( ( in @ Xx @ A )
% 2.53/1.50 & ? [Xy: $i] :
% 2.53/1.50 ( ( in @ Xy @ B )
% 2.53/1.50 & ( Xu
% 2.53/1.50 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(cartprodmempair_type,type,
% 2.53/1.50 cartprodmempair: $o ).
% 2.53/1.50
% 2.53/1.50 thf(cartprodmempair,definition,
% 2.53/1.50 ( cartprodmempair
% 2.53/1.50 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.53/1.50 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.53/1.50 => ( iskpair @ Xu ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(setunionE2_type,type,
% 2.53/1.50 setunionE2: $o ).
% 2.53/1.50
% 2.53/1.50 thf(setunionE2,definition,
% 2.53/1.50 ( setunionE2
% 2.53/1.50 = ( ! [A: $i,Xx: $i] :
% 2.53/1.50 ( ( in @ Xx @ ( setunion @ A ) )
% 2.53/1.50 => ? [X: $i] :
% 2.53/1.50 ( ( in @ X @ A )
% 2.53/1.50 & ( in @ Xx @ X ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(setunionsingleton1_type,type,
% 2.53/1.50 setunionsingleton1: $o ).
% 2.53/1.50
% 2.53/1.50 thf(setunionsingleton1,definition,
% 2.53/1.50 ( setunionsingleton1
% 2.53/1.50 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(setunionsingleton2_type,type,
% 2.53/1.50 setunionsingleton2: $o ).
% 2.53/1.50
% 2.53/1.50 thf(setunionsingleton2,definition,
% 2.53/1.50 ( setunionsingleton2
% 2.53/1.50 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(setunionsingleton_type,type,
% 2.53/1.50 setunionsingleton: $o ).
% 2.53/1.50
% 2.53/1.50 thf(setunionsingleton,definition,
% 2.53/1.50 ( setunionsingleton
% 2.53/1.50 = ( ! [Xx: $i] :
% 2.53/1.50 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 2.53/1.50 = Xx ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(singleton_type,type,
% 2.53/1.50 singleton: $i > $o ).
% 2.53/1.50
% 2.53/1.50 thf(singleton,definition,
% 2.53/1.50 ( singleton
% 2.53/1.50 = ( ^ [A: $i] :
% 2.53/1.50 ? [Xx: $i] :
% 2.53/1.50 ( ( in @ Xx @ A )
% 2.53/1.50 & ( A
% 2.53/1.50 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(singletonprop_type,type,
% 2.53/1.50 singletonprop: $o ).
% 2.53/1.50
% 2.53/1.50 thf(singletonprop,definition,
% 2.53/1.50 ( singletonprop
% 2.53/1.50 = ( ! [A: $i,Xphi: $i > $o] :
% 2.53/1.50 ( ! [Xx: $i] :
% 2.53/1.50 ( ( in @ Xx @ A )
% 2.53/1.50 => ! [Xy: $i] :
% 2.53/1.50 ( ( in @ Xy @ A )
% 2.53/1.50 => ( ( Xphi @ Xx )
% 2.53/1.50 => ( ( Xphi @ Xy )
% 2.53/1.50 => ( Xx = Xy ) ) ) ) )
% 2.53/1.50 => ( ? [Xx: $i] :
% 2.53/1.50 ( ( in @ Xx @ A )
% 2.53/1.50 & ( Xphi @ Xx ) )
% 2.53/1.50 => ( singleton
% 2.53/1.50 @ ( dsetconstr @ A
% 2.53/1.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(ex1_type,type,
% 2.53/1.50 ex1: $i > ( $i > $o ) > $o ).
% 2.53/1.50
% 2.53/1.50 thf(ex1,definition,
% 2.53/1.50 ( ex1
% 2.53/1.50 = ( ^ [A: $i,Xphi: $i > $o] :
% 2.53/1.50 ( singleton
% 2.53/1.50 @ ( dsetconstr @ A
% 2.53/1.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(ex1E1_type,type,
% 2.53/1.50 ex1E1: $o ).
% 2.53/1.50
% 2.53/1.50 thf(ex1E1,definition,
% 2.53/1.50 ( ex1E1
% 2.53/1.50 = ( ! [A: $i,Xphi: $i > $o] :
% 2.53/1.50 ( ( ex1 @ A
% 2.53/1.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.53/1.50 => ? [Xx: $i] :
% 2.53/1.50 ( ( in @ Xx @ A )
% 2.53/1.50 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(ex1I_type,type,
% 2.53/1.50 ex1I: $o ).
% 2.53/1.50
% 2.53/1.50 thf(ex1I,definition,
% 2.53/1.50 ( ex1I
% 2.53/1.50 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.53/1.50 ( ( in @ Xx @ A )
% 2.53/1.50 => ( ( Xphi @ Xx )
% 2.53/1.50 => ( ! [Xy: $i] :
% 2.53/1.50 ( ( in @ Xy @ A )
% 2.53/1.50 => ( ( Xphi @ Xy )
% 2.53/1.50 => ( Xy = Xx ) ) )
% 2.53/1.50 => ( ex1 @ A
% 2.53/1.50 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(ex1I2_type,type,
% 2.53/1.50 ex1I2: $o ).
% 2.53/1.50
% 2.53/1.50 thf(ex1I2,definition,
% 2.53/1.50 ( ex1I2
% 2.53/1.50 = ( ! [A: $i,Xphi: $i > $o] :
% 2.53/1.50 ( ! [Xx: $i] :
% 2.53/1.50 ( ( in @ Xx @ A )
% 2.53/1.50 => ! [Xy: $i] :
% 2.53/1.50 ( ( in @ Xy @ A )
% 2.53/1.50 => ( ( Xphi @ Xx )
% 2.53/1.50 => ( ( Xphi @ Xy )
% 2.53/1.50 => ( Xx = Xy ) ) ) ) )
% 2.53/1.50 => ( ? [Xx: $i] :
% 2.53/1.50 ( ( in @ Xx @ A )
% 2.53/1.50 & ( Xphi @ Xx ) )
% 2.53/1.50 => ( ex1 @ A
% 2.53/1.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(singletonsuniq_type,type,
% 2.53/1.50 singletonsuniq: $o ).
% 2.53/1.50
% 2.53/1.50 thf(singletonsuniq,definition,
% 2.53/1.50 ( singletonsuniq
% 2.53/1.50 = ( ! [Xx: $i,Xy: $i] :
% 2.53/1.50 ( ( ( setadjoin @ Xx @ emptyset )
% 2.53/1.50 = ( setadjoin @ Xy @ emptyset ) )
% 2.53/1.50 => ( Xx = Xy ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(atmost1p_type,type,
% 2.53/1.50 atmost1p: $i > $o ).
% 2.53/1.50
% 2.53/1.50 thf(atleast2p_type,type,
% 2.53/1.50 atleast2p: $i > $o ).
% 2.53/1.50
% 2.53/1.50 thf(atmost2p_type,type,
% 2.53/1.50 atmost2p: $i > $o ).
% 2.53/1.50
% 2.53/1.50 thf(upairsetp_type,type,
% 2.53/1.50 upairsetp: $i > $o ).
% 2.53/1.50
% 2.53/1.50 thf(setukpairinjL1_type,type,
% 2.53/1.50 setukpairinjL1: $o ).
% 2.53/1.50
% 2.53/1.50 thf(setukpairinjL1,definition,
% 2.53/1.50 ( setukpairinjL1
% 2.53/1.50 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.53/1.50 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 2.53/1.50 => ( Xx = Xz ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(kfstsingleton_type,type,
% 2.53/1.50 kfstsingleton: $o ).
% 2.53/1.50
% 2.53/1.50 thf(kfstsingleton,definition,
% 2.53/1.50 ( kfstsingleton
% 2.53/1.50 = ( ! [Xu: $i] :
% 2.53/1.50 ( ( iskpair @ Xu )
% 2.53/1.50 => ( singleton
% 2.53/1.50 @ ( dsetconstr @ ( setunion @ Xu )
% 2.53/1.50 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(theprop_type,type,
% 2.53/1.50 theprop: $o ).
% 2.53/1.50
% 2.53/1.50 thf(theprop,definition,
% 2.53/1.50 ( theprop
% 2.53/1.50 = ( ! [X: $i] :
% 2.53/1.50 ( ( singleton @ X )
% 2.53/1.50 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(kfst_type,type,
% 2.53/1.50 kfst: $i > $i ).
% 2.53/1.50
% 2.53/1.50 thf(kfstpairEq_type,type,
% 2.53/1.50 kfstpairEq: $o ).
% 2.53/1.50
% 2.53/1.50 thf(kfstpairEq,definition,
% 2.53/1.50 ( kfstpairEq
% 2.53/1.50 = ( ! [Xx: $i,Xy: $i] :
% 2.53/1.50 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.53/1.50 = Xx ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(cartprodfstin_type,type,
% 2.53/1.50 cartprodfstin: $o ).
% 2.53/1.50
% 2.53/1.50 thf(cartprodfstin,definition,
% 2.53/1.50 ( cartprodfstin
% 2.53/1.50 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.53/1.50 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.53/1.50 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 2.53/1.50
% 2.53/1.50 thf(setukpairinjL2,conjecture,
% 2.53/1.50 ( setextAx
% 2.53/1.50 => ( emptysetAx
% 2.53/1.50 => ( setadjoinAx
% 2.53/1.50 => ( powersetAx
% 2.53/1.50 => ( setunionAx
% 2.53/1.50 => ( omega0Ax
% 2.53/1.50 => ( omegaSAx
% 2.53/1.50 => ( omegaIndAx
% 2.53/1.50 => ( replAx
% 2.53/1.50 => ( foundationAx
% 2.53/1.50 => ( wellorderingAx
% 2.53/1.50 => ( descrp
% 2.53/1.50 => ( dsetconstrI
% 2.53/1.50 => ( dsetconstrEL
% 2.53/1.50 => ( dsetconstrER
% 2.53/1.50 => ( exuE1
% 2.53/1.50 => ( prop2setE
% 2.53/1.50 => ( emptysetE
% 2.53/1.50 => ( emptysetimpfalse
% 2.53/1.50 => ( notinemptyset
% 2.53/1.50 => ( exuE3e
% 2.53/1.50 => ( setext
% 2.53/1.50 => ( emptyI
% 2.53/1.50 => ( noeltsimpempty
% 2.53/1.50 => ( setbeta
% 2.53/1.50 => ( nonemptyE1
% 2.53/1.50 => ( nonemptyI
% 2.53/1.50 => ( nonemptyI1
% 2.53/1.50 => ( setadjoinIL
% 2.53/1.50 => ( emptyinunitempty
% 2.53/1.50 => ( setadjoinIR
% 2.53/1.50 => ( setadjoinE
% 2.53/1.50 => ( setadjoinOr
% 2.53/1.50 => ( setoftrueEq
% 2.53/1.50 => ( powersetI
% 2.53/1.50 => ( emptyinPowerset
% 2.53/1.50 => ( emptyInPowerset
% 2.53/1.50 => ( powersetE
% 2.53/1.50 => ( setunionI
% 2.53/1.50 => ( setunionE
% 2.53/1.50 => ( subPowSU
% 2.53/1.50 => ( exuE2
% 2.53/1.50 => ( nonemptyImpWitness
% 2.53/1.50 => ( uniqinunit
% 2.53/1.50 => ( notinsingleton
% 2.53/1.50 => ( eqinunit
% 2.53/1.50 => ( singletonsswitch
% 2.53/1.50 => ( upairsetE
% 2.53/1.50 => ( upairsetIL
% 2.53/1.50 => ( upairsetIR
% 2.53/1.50 => ( emptyE1
% 2.53/1.50 => ( vacuousDall
% 2.53/1.50 => ( quantDeMorgan1
% 2.53/1.50 => ( quantDeMorgan2
% 2.53/1.50 => ( quantDeMorgan3
% 2.53/1.50 => ( quantDeMorgan4
% 2.53/1.50 => ( prop2setI
% 2.53/1.50 => ( prop2set2propI
% 2.53/1.50 => ( notdexE
% 2.53/1.50 => ( notdallE
% 2.53/1.50 => ( exuI1
% 2.53/1.50 => ( exuI3
% 2.53/1.50 => ( exuI2
% 2.53/1.50 => ( inCongP
% 2.53/1.50 => ( in__Cong
% 2.53/1.50 => ( exuE3u
% 2.53/1.50 => ( exu__Cong
% 2.53/1.50 => ( emptyset__Cong
% 2.53/1.50 => ( setadjoin__Cong
% 2.53/1.50 => ( powerset__Cong
% 2.53/1.50 => ( setunion__Cong
% 2.53/1.50 => ( omega__Cong
% 2.53/1.50 => ( exuEu
% 2.53/1.50 => ( descr__Cong
% 2.53/1.50 => ( dsetconstr__Cong
% 2.53/1.50 => ( subsetI1
% 2.53/1.50 => ( eqimpsubset2
% 2.53/1.50 => ( eqimpsubset1
% 2.53/1.50 => ( subsetI2
% 2.53/1.50 => ( emptysetsubset
% 2.53/1.50 => ( subsetE
% 2.53/1.50 => ( subsetE2
% 2.53/1.50 => ( notsubsetI
% 2.53/1.50 => ( notequalI1
% 2.53/1.50 => ( notequalI2
% 2.53/1.50 => ( subsetRefl
% 2.53/1.50 => ( subsetTrans
% 2.53/1.50 => ( setadjoinSub
% 2.53/1.50 => ( setadjoinSub2
% 2.53/1.50 => ( subset2powerset
% 2.53/1.50 => ( setextsub
% 2.53/1.50 => ( subsetemptysetimpeq
% 2.53/1.50 => ( powersetI1
% 2.53/1.50 => ( powersetE1
% 2.53/1.50 => ( inPowerset
% 2.53/1.50 => ( powersetsubset
% 2.53/1.50 => ( sepInPowerset
% 2.53/1.50 => ( sepSubset
% 2.53/1.50 => ( binunionIL
% 2.53/1.50 => ( upairset2IR
% 2.53/1.50 => ( binunionIR
% 2.53/1.50 => ( binunionEcases
% 2.53/1.50 => ( binunionE
% 2.53/1.50 => ( binunionLsub
% 2.53/1.50 => ( binunionRsub
% 2.53/1.50 => ( binintersectI
% 2.53/1.50 => ( binintersectSubset5
% 2.53/1.50 => ( binintersectEL
% 2.53/1.50 => ( binintersectLsub
% 2.53/1.50 => ( binintersectSubset2
% 2.53/1.50 => ( binintersectSubset3
% 2.53/1.50 => ( binintersectER
% 2.53/1.50 => ( disjointsetsI1
% 2.53/1.50 => ( binintersectRsub
% 2.53/1.50 => ( binintersectSubset4
% 2.53/1.50 => ( binintersectSubset1
% 2.53/1.50 => ( bs114d
% 2.53/1.50 => ( setminusI
% 2.53/1.50 => ( setminusEL
% 2.53/1.50 => ( setminusER
% 2.53/1.50 => ( setminusSubset2
% 2.53/1.50 => ( setminusERneg
% 2.53/1.50 => ( setminusELneg
% 2.53/1.50 => ( setminusILneg
% 2.53/1.50 => ( setminusIRneg
% 2.53/1.50 => ( setminusLsub
% 2.53/1.50 => ( setminusSubset1
% 2.53/1.50 => ( symdiffE
% 2.53/1.50 => ( symdiffI1
% 2.53/1.50 => ( symdiffI2
% 2.53/1.50 => ( symdiffIneg1
% 2.53/1.50 => ( symdiffIneg2
% 2.53/1.50 => ( secondinupair
% 2.53/1.50 => ( setukpairIL
% 2.53/1.50 => ( setukpairIR
% 2.53/1.50 => ( kpairiskpair
% 2.53/1.50 => ( kpairp
% 2.53/1.50 => ( singletonsubset
% 2.53/1.50 => ( singletoninpowerset
% 2.53/1.50 => ( singletoninpowunion
% 2.53/1.50 => ( upairset2E
% 2.53/1.50 => ( upairsubunion
% 2.53/1.50 => ( upairinpowunion
% 2.53/1.50 => ( ubforcartprodlem1
% 2.53/1.50 => ( ubforcartprodlem2
% 2.53/1.50 => ( ubforcartprodlem3
% 2.53/1.50 => ( cartprodpairin
% 2.53/1.50 => ( cartprodmempair1
% 2.53/1.50 => ( cartprodmempair
% 2.53/1.50 => ( setunionE2
% 2.53/1.50 => ( setunionsingleton1
% 2.53/1.50 => ( setunionsingleton2
% 2.53/1.50 => ( setunionsingleton
% 2.53/1.50 => ( singletonprop
% 2.53/1.50 => ( ex1E1
% 2.53/1.50 => ( ex1I
% 2.53/1.50 => ( ex1I2
% 2.53/1.50 => ( singletonsuniq
% 2.53/1.50 => ( setukpairinjL1
% 2.53/1.50 => ( kfstsingleton
% 2.53/1.50 => ( theprop
% 2.53/1.50 => ( kfstpairEq
% 2.53/1.50 => ( cartprodfstin
% 2.53/1.50 => ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.53/1.50 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.53/1.50 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.53/1.50 => ( Xx = Xz ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.53/1.50 ------------------------
% 2.53/1.52 % (5213)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_4923 for (2999ds/2Mi)
% 2.53/1.52 % (5214)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_4923 for (2999ds/275Mi)
% 2.53/1.52 % (5209)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4923 for (2999ds/183Mi)
% 2.53/1.52 % (5213)Instruction limit reached!
% 2.53/1.52 % (5213)------------------------------
% 2.53/1.52 % (5213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.52 % (5213)Termination reason: Unknown
% 2.53/1.52 % (5213)Termination phase: shuffling
% 2.53/1.52
% 2.53/1.52 % (5213)Memory used [KB]: 1279
% 2.53/1.52 % (5213)Time elapsed: 0.002 s
% 2.53/1.52 % (5213)Instructions burned: 2 (million)
% 2.53/1.52 % (5213)------------------------------
% 2.53/1.52 % (5213)------------------------------
% 2.53/1.53 % (5210)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_4923 for (2999ds/4Mi)
% 2.53/1.53 % (5211)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_4923 for (2999ds/27Mi)
% 2.53/1.53 % (5212)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4923 for (2999ds/2Mi)
% 2.53/1.53 % (5215)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4923 for (2999ds/18Mi)
% 2.53/1.53 % (5212)Instruction limit reached!
% 2.53/1.53 % (5212)------------------------------
% 2.53/1.53 % (5212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.53 % (5212)Termination reason: Unknown
% 2.53/1.53 % (5212)Termination phase: shuffling
% 2.53/1.53
% 2.53/1.53 % (5212)Memory used [KB]: 1279
% 2.53/1.53 % (5212)Time elapsed: 0.004 s
% 2.53/1.53 % (5212)Instructions burned: 3 (million)
% 2.53/1.53 % (5212)------------------------------
% 2.53/1.53 % (5212)------------------------------
% 2.53/1.53 % (5210)Instruction limit reached!
% 2.53/1.53 % (5210)------------------------------
% 2.53/1.53 % (5210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.53 % (5210)Termination reason: Unknown
% 2.53/1.53 % (5210)Termination phase: shuffling
% 2.53/1.53
% 2.53/1.53 % (5216)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_4923 for (2999ds/3Mi)
% 2.53/1.53 % (5210)Memory used [KB]: 1407
% 2.53/1.53 % (5210)Time elapsed: 0.005 s
% 2.53/1.53 % (5210)Instructions burned: 5 (million)
% 2.53/1.53 % (5210)------------------------------
% 2.53/1.53 % (5210)------------------------------
% 2.53/1.53 % (5216)Instruction limit reached!
% 2.53/1.53 % (5216)------------------------------
% 2.53/1.53 % (5216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.53 % (5216)Termination reason: Unknown
% 2.53/1.53 % (5216)Termination phase: shuffling
% 2.53/1.53
% 2.53/1.53 % (5216)Memory used [KB]: 1407
% 2.53/1.53 % (5216)Time elapsed: 0.003 s
% 2.53/1.53 % (5216)Instructions burned: 6 (million)
% 2.53/1.53 % (5216)------------------------------
% 2.53/1.53 % (5216)------------------------------
% 2.53/1.54 % (5215)Instruction limit reached!
% 2.53/1.54 % (5215)------------------------------
% 2.53/1.54 % (5215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.54 % (5215)Termination reason: Unknown
% 2.53/1.54 % (5215)Termination phase: Property scanning
% 2.53/1.54
% 2.53/1.54 % (5215)Memory used [KB]: 1535
% 2.53/1.54 % (5215)Time elapsed: 0.013 s
% 2.53/1.54 % (5215)Instructions burned: 18 (million)
% 2.53/1.54 % (5215)------------------------------
% 2.53/1.54 % (5215)------------------------------
% 2.53/1.54 % (5219)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_4923 for (2999ds/3Mi)
% 2.53/1.54 % (5211)Instruction limit reached!
% 2.53/1.54 % (5211)------------------------------
% 2.53/1.54 % (5211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.54 % (5211)Termination reason: Unknown
% 2.53/1.54 % (5211)Termination phase: Property scanning
% 2.53/1.54
% 2.53/1.54 % (5211)Memory used [KB]: 1791
% 2.53/1.54 % (5211)Time elapsed: 0.016 s
% 2.53/1.54 % (5211)Instructions burned: 27 (million)
% 2.53/1.54 % (5211)------------------------------
% 2.53/1.54 % (5211)------------------------------
% 2.53/1.54 % (5219)Instruction limit reached!
% 2.53/1.54 % (5219)------------------------------
% 2.53/1.54 % (5219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.54 % (5219)Termination reason: Unknown
% 2.53/1.54 % (5219)Termination phase: shuffling
% 2.53/1.54
% 2.53/1.54 % (5219)Memory used [KB]: 1279
% 2.53/1.54 % (5219)Time elapsed: 0.002 s
% 2.53/1.54 % (5219)Instructions burned: 3 (million)
% 2.53/1.54 % (5219)------------------------------
% 2.53/1.54 % (5219)------------------------------
% 2.53/1.55 % (5217)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_4923 for (2999ds/37Mi)
% 2.53/1.55 % (5218)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_4923 for (2999ds/15Mi)
% 2.53/1.55 % (5222)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_4923 for (2999ds/16Mi)
% 2.53/1.56 % (5220)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_4923 for (2999ds/1041Mi)
% 2.53/1.56 % (5222)Instruction limit reached!
% 2.53/1.56 % (5222)------------------------------
% 2.53/1.56 % (5222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.56 % (5222)Termination reason: Unknown
% 2.53/1.56 % (5222)Termination phase: shuffling
% 2.53/1.56
% 2.53/1.56 % (5222)Memory used [KB]: 1663
% 2.53/1.56 % (5222)Time elapsed: 0.006 s
% 2.53/1.56 % (5222)Instructions burned: 18 (million)
% 2.53/1.56 % (5222)------------------------------
% 2.53/1.56 % (5222)------------------------------
% 2.53/1.56 % (5218)Instruction limit reached!
% 2.53/1.56 % (5218)------------------------------
% 2.53/1.56 % (5218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.56 % (5218)Termination reason: Unknown
% 2.53/1.56 % (5218)Termination phase: Property scanning
% 2.53/1.56
% 2.53/1.56 % (5218)Memory used [KB]: 1535
% 2.53/1.56 % (5218)Time elapsed: 0.011 s
% 2.53/1.56 % (5218)Instructions burned: 15 (million)
% 2.53/1.56 % (5218)------------------------------
% 2.53/1.56 % (5218)------------------------------
% 2.53/1.56 % (5221)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_4923 for (2999ds/7Mi)
% 2.53/1.56 % (5221)Instruction limit reached!
% 2.53/1.56 % (5221)------------------------------
% 2.53/1.56 % (5221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.56 % (5221)Termination reason: Unknown
% 2.53/1.56 % (5221)Termination phase: shuffling
% 2.53/1.56
% 2.53/1.56 % (5221)Memory used [KB]: 1407
% 2.53/1.56 % (5221)Time elapsed: 0.006 s
% 2.53/1.56 % (5221)Instructions burned: 8 (million)
% 2.53/1.56 % (5221)------------------------------
% 2.53/1.56 % (5221)------------------------------
% 2.53/1.57 % (5217)Instruction limit reached!
% 2.53/1.57 % (5217)------------------------------
% 2.53/1.57 % (5217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.57 % (5217)Termination reason: Unknown
% 2.53/1.57 % (5217)Termination phase: Property scanning
% 2.53/1.57
% 2.53/1.57 % (5217)Memory used [KB]: 1791
% 2.53/1.57 % (5217)Time elapsed: 0.020 s
% 2.53/1.57 % (5217)Instructions burned: 37 (million)
% 2.53/1.57 % (5217)------------------------------
% 2.53/1.57 % (5217)------------------------------
% 2.53/1.57 % (5223)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_4923 for (2999ds/3Mi)
% 2.53/1.57 % (5223)Instruction limit reached!
% 2.53/1.57 % (5223)------------------------------
% 2.53/1.57 % (5223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.57 % (5223)Termination reason: Unknown
% 2.53/1.57 % (5223)Termination phase: shuffling
% 2.53/1.57
% 2.53/1.57 % (5223)Memory used [KB]: 1279
% 2.53/1.57 % (5223)Time elapsed: 0.002 s
% 2.53/1.57 % (5223)Instructions burned: 3 (million)
% 2.53/1.57 % (5223)------------------------------
% 2.53/1.57 % (5223)------------------------------
% 2.53/1.57 % (5209)Instruction limit reached!
% 2.53/1.57 % (5209)------------------------------
% 2.53/1.57 % (5209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.57 % (5209)Termination reason: Unknown
% 2.53/1.57 % (5209)Termination phase: Saturation
% 2.53/1.57
% 2.53/1.57 % (5209)Memory used [KB]: 7419
% 2.53/1.57 % (5209)Time elapsed: 0.054 s
% 2.53/1.57 % (5209)Instructions burned: 183 (million)
% 2.53/1.57 % (5209)------------------------------
% 2.53/1.57 % (5209)------------------------------
% 2.53/1.58 % (5224)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_4923 for (2999ds/3Mi)
% 2.53/1.58 % (5224)Instruction limit reached!
% 2.53/1.58 % (5224)------------------------------
% 2.53/1.58 % (5224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.58 % (5224)Termination reason: Unknown
% 2.53/1.58 % (5224)Termination phase: shuffling
% 2.53/1.58
% 2.53/1.58 % (5224)Memory used [KB]: 1279
% 2.53/1.58 % (5224)Time elapsed: 0.003 s
% 2.53/1.58 % (5224)Instructions burned: 3 (million)
% 2.53/1.58 % (5224)------------------------------
% 2.53/1.58 % (5224)------------------------------
% 2.53/1.58 % (5227)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_4923 for (2999ds/4Mi)
% 2.53/1.58 % (5227)Instruction limit reached!
% 2.53/1.58 % (5227)------------------------------
% 2.53/1.58 % (5227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.58 % (5227)Termination reason: Unknown
% 2.53/1.58 % (5227)Termination phase: shuffling
% 2.53/1.58
% 2.53/1.58 % (5227)Memory used [KB]: 1279
% 2.53/1.58 % (5227)Time elapsed: 0.002 s
% 2.53/1.58 % (5227)Instructions burned: 4 (million)
% 2.53/1.58 % (5227)------------------------------
% 2.53/1.58 % (5227)------------------------------
% 2.53/1.58 % (5225)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_4923 for (2999ds/7Mi)
% 2.53/1.58 % (5226)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_4923 for (2999ds/3Mi)
% 2.53/1.59 % (5228)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_4923 for (2999ds/18Mi)
% 2.53/1.59 % (5225)Instruction limit reached!
% 2.53/1.59 % (5225)------------------------------
% 2.53/1.59 % (5225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.59 % (5225)Termination reason: Unknown
% 2.53/1.59 % (5225)Termination phase: shuffling
% 2.53/1.59
% 2.53/1.59 % (5225)Memory used [KB]: 1407
% 2.53/1.59 % (5225)Time elapsed: 0.006 s
% 2.53/1.59 % (5225)Instructions burned: 8 (million)
% 2.53/1.59 % (5225)------------------------------
% 2.53/1.59 % (5225)------------------------------
% 2.53/1.59 % (5226)Instruction limit reached!
% 2.53/1.59 % (5226)------------------------------
% 2.53/1.59 % (5226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.59 % (5226)Termination reason: Unknown
% 2.53/1.59 % (5226)Termination phase: shuffling
% 2.53/1.59
% 2.53/1.59 % (5226)Memory used [KB]: 1279
% 2.53/1.59 % (5226)Time elapsed: 0.004 s
% 2.53/1.59 % (5226)Instructions burned: 4 (million)
% 2.53/1.59 % (5226)------------------------------
% 2.53/1.59 % (5226)------------------------------
% 2.53/1.59 % (5230)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_4923 for (2999ds/6Mi)
% 2.53/1.59 % (5229)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_4923 for (2999ds/710Mi)
% 2.53/1.59 % (5230)Instruction limit reached!
% 2.53/1.59 % (5230)------------------------------
% 2.53/1.59 % (5230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.59 % (5230)Termination reason: Unknown
% 2.53/1.59 % (5230)Termination phase: shuffling
% 2.53/1.59
% 2.53/1.59 % (5230)Memory used [KB]: 1407
% 2.53/1.59 % (5230)Time elapsed: 0.003 s
% 2.53/1.59 % (5230)Instructions burned: 8 (million)
% 2.53/1.59 % (5230)------------------------------
% 2.53/1.59 % (5230)------------------------------
% 2.53/1.59 % (5228)Instruction limit reached!
% 2.53/1.59 % (5228)------------------------------
% 2.53/1.59 % (5228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.59 % (5228)Termination reason: Unknown
% 2.53/1.59 % (5228)Termination phase: shuffling
% 2.53/1.59
% 2.53/1.59 % (5228)Memory used [KB]: 1663
% 2.53/1.59 % (5228)Time elapsed: 0.007 s
% 2.53/1.59 % (5228)Instructions burned: 18 (million)
% 2.53/1.59 % (5228)------------------------------
% 2.53/1.59 % (5228)------------------------------
% 2.53/1.60 % (5233)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_4923 for (2999ds/5Mi)
% 2.53/1.60 % (5234)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_4923 for (2999ds/6Mi)
% 2.53/1.60 % (5233)Instruction limit reached!
% 2.53/1.60 % (5233)------------------------------
% 2.53/1.60 % (5233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.60 % (5233)Termination reason: Unknown
% 2.53/1.60 % (5233)Termination phase: shuffling
% 2.53/1.60
% 2.53/1.60 % (5233)Memory used [KB]: 1407
% 2.53/1.60 % (5233)Time elapsed: 0.003 s
% 2.53/1.60 % (5233)Instructions burned: 7 (million)
% 2.53/1.60 % (5233)------------------------------
% 2.53/1.60 % (5233)------------------------------
% 2.53/1.60 % (5234)Instruction limit reached!
% 2.53/1.60 % (5234)------------------------------
% 2.53/1.60 % (5234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.60 % (5234)Termination reason: Unknown
% 2.53/1.60 % (5234)Termination phase: shuffling
% 2.53/1.60
% 2.53/1.60 % (5234)Memory used [KB]: 1407
% 2.53/1.60 % (5234)Time elapsed: 0.004 s
% 2.53/1.60 % (5234)Instructions burned: 8 (million)
% 2.53/1.60 % (5234)------------------------------
% 2.53/1.60 % (5234)------------------------------
% 2.53/1.60 % (5231)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_4923 for (2999ds/902Mi)
% 2.53/1.60 % (5232)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_4923 for (2999ds/21Mi)
% 2.53/1.61 % (5214)Instruction limit reached!
% 2.53/1.61 % (5214)------------------------------
% 2.53/1.61 % (5214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.61 % (5214)Termination reason: Unknown
% 2.53/1.61 % (5214)Termination phase: Saturation
% 2.53/1.61
% 2.53/1.61 % (5214)Memory used [KB]: 8187
% 2.53/1.61 % (5214)Time elapsed: 0.085 s
% 2.53/1.61 % (5214)Instructions burned: 275 (million)
% 2.53/1.61 % (5214)------------------------------
% 2.53/1.61 % (5214)------------------------------
% 2.53/1.61 % (5235)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_4923 for (2999ds/377Mi)
% 2.53/1.61 % (5236)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_4923 for (2999ds/779Mi)
% 2.53/1.61 % (5232)Instruction limit reached!
% 2.53/1.61 % (5232)------------------------------
% 2.53/1.61 % (5232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.61 % (5232)Termination reason: Unknown
% 2.53/1.61 % (5232)Termination phase: shuffling
% 2.53/1.61
% 2.53/1.61 % (5232)Memory used [KB]: 1791
% 2.53/1.61 % (5232)Time elapsed: 0.013 s
% 2.53/1.61 % (5232)Instructions burned: 21 (million)
% 2.53/1.61 % (5232)------------------------------
% 2.53/1.61 % (5232)------------------------------
% 2.53/1.61 % (5237)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_4923 for (2999ds/19Mi)
% 2.53/1.62 % (5237)Instruction limit reached!
% 2.53/1.62 % (5237)------------------------------
% 2.53/1.62 % (5237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.62 % (5237)Termination reason: Unknown
% 2.53/1.62 % (5237)Termination phase: shuffling
% 2.53/1.62
% 2.53/1.62 % (5237)Memory used [KB]: 1663
% 2.53/1.62 % (5237)Time elapsed: 0.006 s
% 2.53/1.62 % (5237)Instructions burned: 19 (million)
% 2.53/1.62 % (5237)------------------------------
% 2.53/1.62 % (5237)------------------------------
% 2.53/1.63 % (5239)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_4923 for (2998ds/17Mi)
% 2.53/1.63 % (5238)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_4923 for (2998ds/879Mi)
% 2.53/1.63 % (5239)Instruction limit reached!
% 2.53/1.63 % (5239)------------------------------
% 2.53/1.63 % (5239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.63 % (5239)Termination reason: Unknown
% 2.53/1.63 % (5239)Termination phase: shuffling
% 2.53/1.63
% 2.53/1.63 % (5239)Memory used [KB]: 1663
% 2.53/1.63 % (5239)Time elapsed: 0.006 s
% 2.53/1.63 % (5239)Instructions burned: 18 (million)
% 2.53/1.63 % (5239)------------------------------
% 2.53/1.63 % (5239)------------------------------
% 2.53/1.64 % (5240)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_4923 for (2998ds/3Mi)
% 2.53/1.65 % (5240)Instruction limit reached!
% 2.53/1.65 % (5240)------------------------------
% 2.53/1.65 % (5240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.65 % (5240)Termination reason: Unknown
% 2.53/1.65 % (5240)Termination phase: shuffling
% 2.53/1.65
% 2.53/1.65 % (5240)Memory used [KB]: 1407
% 2.53/1.65 % (5240)Time elapsed: 0.003 s
% 2.53/1.65 % (5240)Instructions burned: 6 (million)
% 2.53/1.65 % (5240)------------------------------
% 2.53/1.65 % (5240)------------------------------
% 2.53/1.65 % (5241)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_4923 for (2998ds/30Mi)
% 2.53/1.66 % (5241)Instruction limit reached!
% 2.53/1.66 % (5241)------------------------------
% 2.53/1.66 % (5241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.66 % (5241)Termination reason: Unknown
% 2.53/1.66 % (5241)Termination phase: Property scanning
% 2.53/1.66
% 2.53/1.66 % (5241)Memory used [KB]: 1791
% 2.53/1.66 % (5241)Time elapsed: 0.009 s
% 2.53/1.66 % (5241)Instructions burned: 30 (million)
% 2.53/1.66 % (5241)------------------------------
% 2.53/1.66 % (5241)------------------------------
% 2.53/1.67 % (5242)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_4923 for (2998ds/127Mi)
% 2.53/1.68 % (5231)First to succeed.
% 2.53/1.68 % (5231)Refutation found. Thanks to Tanya!
% 2.53/1.68 % SZS status Theorem for DTF2THF_4923
% 2.53/1.68 % SZS output start Proof for DTF2THF_4923
% 2.53/1.68 thf(func_def_0, type, in: $i > $i > $o).
% 2.53/1.68 thf(func_def_1, type, exu: ($i > $o) > $o).
% 2.53/1.68 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 2.53/1.68 thf(func_def_8, type, powerset: $i > $i).
% 2.53/1.68 thf(func_def_10, type, setunion: $i > $i).
% 2.53/1.68 thf(func_def_19, type, descr: ($i > $o) > $i).
% 2.53/1.68 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 2.53/1.68 thf(func_def_26, type, prop2set: $o > $i).
% 2.53/1.68 thf(func_def_36, type, nonempty: $i > $o).
% 2.53/1.68 thf(func_def_69, type, set2prop: $i > $o).
% 2.53/1.68 thf(func_def_88, type, subset: $i > $i > $o).
% 2.53/1.68 thf(func_def_89, type, disjoint: $i > $i > $o).
% 2.53/1.68 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 2.53/1.68 thf(func_def_114, type, binunion: $i > $i > $i).
% 2.53/1.68 thf(func_def_122, type, binintersect: $i > $i > $i).
% 2.53/1.68 thf(func_def_135, type, regular: $i > $o).
% 2.53/1.68 thf(func_def_136, type, setminus: $i > $i > $i).
% 2.53/1.68 thf(func_def_147, type, symdiff: $i > $i > $i).
% 2.53/1.68 thf(func_def_153, type, iskpair: $i > $o).
% 2.53/1.68 thf(func_def_158, type, kpair: $i > $i > $i).
% 2.53/1.68 thf(func_def_160, type, cartprod: $i > $i > $i).
% 2.53/1.68 thf(func_def_177, type, singleton: $i > $o).
% 2.53/1.68 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 2.53/1.68 thf(func_def_184, type, atmost1p: $i > $o).
% 2.53/1.68 thf(func_def_185, type, atleast2p: $i > $o).
% 2.53/1.68 thf(func_def_186, type, atmost2p: $i > $o).
% 2.53/1.68 thf(func_def_187, type, upairsetp: $i > $o).
% 2.53/1.68 thf(func_def_191, type, kfst: $i > $i).
% 2.53/1.68 thf(func_def_206, type, sP0: $i > $i > $o).
% 2.53/1.68 thf(func_def_207, type, sP1: $i > $o).
% 2.53/1.68 thf(func_def_208, type, sP2: $i > $i > $o).
% 2.53/1.68 thf(func_def_209, type, sP3: $i > $i > $o).
% 2.53/1.68 thf(func_def_211, type, sP5: $o > $i > $i > $i > $o).
% 2.53/1.68 thf(func_def_227, type, sK21: $i > $i > $i).
% 2.53/1.68 thf(func_def_235, type, sK29: $o > $i > $i > $i).
% 2.53/1.68 thf(func_def_251, type, sK45: $i > $o).
% 2.53/1.68 thf(func_def_254, type, sK48: $i > $o).
% 2.53/1.68 thf(func_def_256, type, sK50: $i > ($i > $o) > $i).
% 2.53/1.68 thf(func_def_257, type, sK51: $i > $i > $i).
% 2.53/1.68 thf(func_def_258, type, sK52: $i > $i > $i).
% 2.53/1.68 thf(func_def_259, type, sK53: $i > $i > $i).
% 2.53/1.68 thf(func_def_260, type, sK54: $i > $i > $i).
% 2.53/1.68 thf(func_def_261, type, sK55: $i > $i > $i).
% 2.53/1.68 thf(func_def_262, type, sK56: $i > $i > $i > $i).
% 2.53/1.68 thf(func_def_263, type, sK57: $i > $i).
% 2.53/1.68 thf(func_def_264, type, sK58: $i > $i).
% 2.53/1.68 thf(func_def_265, type, sK59: $i > $i).
% 2.53/1.68 thf(func_def_266, type, sK60: $i > $i).
% 2.53/1.68 thf(func_def_267, type, sK61: $i > $i > $i > $i).
% 2.53/1.68 thf(func_def_268, type, sK62: $i > $i > $i > $i).
% 2.53/1.68 thf(func_def_269, type, sK63: $i > $i > $i).
% 2.53/1.68 thf(func_def_270, type, sK64: $i > $i > $i).
% 2.53/1.68 thf(func_def_271, type, sK65: $i > $i > $i).
% 2.53/1.68 thf(func_def_272, type, sK66: $i > $i).
% 2.53/1.68 thf(func_def_274, type, sK68: $i > $i).
% 2.53/1.68 thf(func_def_275, type, sK69: $i > $i).
% 2.53/1.68 thf(func_def_279, type, sK73: $i > $i > $i).
% 2.53/1.68 thf(func_def_285, type, sK79: $i > $i > $i).
% 2.53/1.68 thf(func_def_290, type, sK84: $i > $i).
% 2.53/1.68 thf(func_def_293, type, sK87: $i > $i > $i).
% 2.53/1.68 thf(func_def_312, type, sK106: $i > $o).
% 2.53/1.68 thf(func_def_319, type, sK113: $i > $o).
% 2.53/1.68 thf(func_def_325, type, sK119: ($i > $o) > $i > $i).
% 2.53/1.68 thf(func_def_327, type, sK121: $i > $o).
% 2.53/1.68 thf(func_def_343, type, sK137: $i > $i).
% 2.53/1.68 thf(func_def_356, type, sK150: $i > $i > $i).
% 2.53/1.68 thf(func_def_365, type, sK159: $i > ($i > $o) > $i).
% 2.53/1.68 thf(func_def_366, type, sK160: $i > $o).
% 2.53/1.68 thf(func_def_369, type, sK163: $i > $o).
% 2.53/1.68 thf(func_def_372, type, sK166: $i > ($i > $o) > $i).
% 2.53/1.68 thf(func_def_373, type, sK167: $i > ($i > $o) > $i).
% 2.53/1.68 thf(func_def_377, type, sK171: $i > $i > $i > $i).
% 2.53/1.68 thf(func_def_378, type, sK172: $i > $i > $i > $i).
% 2.53/1.68 thf(func_def_383, type, sK177: $i > $i > $i).
% 2.53/1.68 thf(func_def_389, type, sK183: $i > $o).
% 2.53/1.68 thf(func_def_394, type, sK188: $i > $o).
% 2.53/1.68 thf(func_def_395, type, sK189: $i > $o).
% 2.53/1.68 thf(func_def_396, type, sK190: ($i > $o) > ($i > $o) > $i > $i > $i).
% 2.53/1.68 thf(func_def_397, type, sK191: ($i > $o) > ($i > $o) > $i > $i > $i).
% 2.53/1.68 thf(func_def_398, type, sK192: $i > ($i > $o) > $i).
% 2.53/1.68 thf(func_def_399, type, sK193: $i > $o).
% 2.53/1.68 thf(func_def_411, type, sK205: $i > $o).
% 2.53/1.68 thf(func_def_413, type, sK207: ($i > $o) > $i).
% 2.53/1.68 thf(func_def_414, type, sK208: ($i > $o) > $i).
% 2.53/1.68 thf(func_def_418, type, sK212: $i > $o).
% 2.53/1.68 thf(func_def_459, type, sK253: $i > $o).
% 2.53/1.68 thf(func_def_462, type, sK256: $i > $o).
% 2.53/1.68 thf(func_def_465, type, sK259: $i > ($i > $o) > $i).
% 2.53/1.68 thf(func_def_485, type, sK279: $i > $i > $i).
% 2.53/1.68 thf(func_def_493, type, sK287: $i > $i).
% 2.53/1.68 thf(func_def_495, type, sK289: $i > $o).
% 2.53/1.68 thf(func_def_496, type, sK290: $i > $o).
% 2.53/1.68 thf(func_def_497, type, sK291: ($i > $o) > ($i > $o) > $i).
% 2.53/1.68 thf(func_def_498, type, sK292: ($i > $o) > ($i > $o) > $i).
% 2.53/1.68 thf(func_def_499, type, sK293: $i > $i).
% 2.53/1.68 thf(func_def_504, type, sK298: ($i > $o) > $i).
% 2.53/1.68 thf(func_def_505, type, sK299: $i > $o).
% 2.53/1.68 thf(func_def_508, type, sK302: $i > $i > $i).
% 2.53/1.68 thf(func_def_520, type, sK314: $i > $o).
% 2.53/1.68 thf(func_def_522, type, sK316: $i > $o).
% 2.53/1.68 thf(func_def_524, type, sK318: ($i > $o) > $i > $i).
% 2.53/1.68 thf(func_def_525, type, sK319: ($i > $o) > $i > $i).
% 2.53/1.68 thf(func_def_532, type, sK326: $i > $i > $o).
% 2.53/1.68 thf(func_def_533, type, sK327: $i > $i).
% 2.53/1.68 thf(func_def_534, type, sK328: $i > $i).
% 2.53/1.68 thf(func_def_535, type, sK329: ($i > $i > $o) > $i > $i).
% 2.53/1.68 thf(func_def_536, type, sK330: ($i > $i > $o) > $i > $i).
% 2.53/1.68 thf(func_def_537, type, sK331: $i > ($i > $i > $o) > $i > $i).
% 2.53/1.68 thf(func_def_543, type, sK337: $i > $o).
% 2.53/1.68 thf(func_def_547, type, sK341: $i > $o).
% 2.53/1.68 thf(func_def_550, type, sK344: $i > ($i > $o) > $i).
% 2.53/1.68 thf(func_def_568, type, sK362: $i > $i > $i).
% 2.53/1.68 thf(func_def_569, type, sK363: $i > $i > $i).
% 2.53/1.68 thf(func_def_572, type, sK366: $i > $i).
% 2.53/1.68 thf(func_def_573, type, sK367: $i > $i).
% 2.53/1.68 thf(func_def_575, type, sK369: $i > $i).
% 2.53/1.68 thf(func_def_576, type, sK370: $i > $o).
% 2.53/1.68 thf(func_def_577, type, sK371: $i > $o).
% 2.53/1.68 thf(func_def_578, type, sK372: ($i > $o) > ($i > $o) > $i).
% 2.53/1.68 thf(func_def_579, type, sK373: ($i > $o) > ($i > $o) > $i).
% 2.53/1.68 thf(func_def_585, type, sK379: $i > ($i > $o) > $i).
% 2.53/1.68 thf(func_def_586, type, sK380: $i > $o).
% 2.53/1.68 thf(func_def_598, type, sK392: $i > $o).
% 2.53/1.68 thf(func_def_600, type, sK394: ($i > $o) > $i > $i).
% 2.53/1.68 thf(func_def_602, type, sK396: $i > $o).
% 2.53/1.68 thf(func_def_607, type, sK401: ($i > $o) > $i).
% 2.53/1.68 thf(func_def_608, type, sK402: $i > $o).
% 2.53/1.68 thf(func_def_609, type, sK403: $i > $i).
% 2.53/1.68 thf(func_def_621, type, sK415: $i > $o).
% 2.53/1.68 thf(func_def_625, type, sK419: $i > $o).
% 2.53/1.68 thf(func_def_640, type, sK434: ($i > $o) > $i > $i).
% 2.53/1.68 thf(func_def_642, type, sK436: $i > $o).
% 2.53/1.68 thf(func_def_643, type, sK437: ($i > $o) > $i > $i > $i).
% 2.53/1.68 thf(func_def_646, type, sK440: $i > $o).
% 2.53/1.68 thf(func_def_653, type, sK447: ($i > $o) > $i).
% 2.53/1.68 thf(func_def_654, type, sK448: $i > $o).
% 2.53/1.68 thf(func_def_655, type, sK449: $i > $i).
% 2.53/1.68 thf(func_def_657, type, sK451: $i > $o).
% 2.53/1.68 thf(func_def_663, type, ph457: !>[X0: $tType]:(X0)).
% 2.53/1.68 thf(f2549,plain,(
% 2.53/1.68 $false),
% 2.53/1.68 inference(trivial_inequality_removal,[status(thm)],[f2548])).
% 2.53/1.68 thf(f2548,plain,(
% 2.53/1.68 (sK441 != sK441)),
% 2.53/1.68 inference(superposition,[status(thm)],[f2199,f2515])).
% 2.53/1.68 thf(f2515,plain,(
% 2.53/1.68 (sK441 = sK443)),
% 2.53/1.68 inference(trivial_inequality_removal,[status(thm)],[f2514])).
% 2.53/1.68 thf(f2514,plain,(
% 2.53/1.68 (sK441 = sK443) | ($true != $true)),
% 2.53/1.68 inference(forward_demodulation,[status(thm)],[f2513,f2119])).
% 2.53/1.68 thf(f2119,plain,(
% 2.53/1.68 (setukpairinjL1 = $true)),
% 2.53/1.68 inference(cnf_transformation,[status(thm)],[f1456])).
% 2.53/1.68 thf(f1456,plain,(
% 2.53/1.68 (subsetE2 = $true) & (bs114d = $true) & (subsetTrans = $true) & (setminusIRneg = $true) & (cartprodpairin = $true) & (ex1E1 = $true) & (exu__Cong = $true) & (sepSubset = $true) & (binintersectSubset4 = $true) & (binunionEcases = $true) & (setminusELneg = $true) & (inCongP = $true) & (descr__Cong = $true) & (kfstsingleton = $true) & (setminusI = $true) & (subsetI1 = $true) & (notequalI2 = $true) & (subsetI2 = $true) & (kpairiskpair = $true) & (nonemptyI = $true) & (vacuousDall = $true) & (emptyinunitempty = $true) & (replAx = $true) & (cartprodfstin = $true) & (setminusSubset1 = $true) & (exuI1 = $true) & (singletoninpowunion = $true) & (wellorderingAx = $true) & (setadjoin__Cong = $true) & (setukpairIR = $true) & (setext = $true) & (nonemptyImpWitness = $true) & (binintersectRsub = $true) & (powersetsubset = $true) & (singletonsubset = $true) & (eqinunit = $true) & (upairsetIL = $true) & (sepInPowerset = $true) & (powersetE = $true) & (ex1I2 = $true) & (notequalI1 = $true) & (setunionI = $true) & (binunionIR = $true) & (upairsetE = $true) & (emptysetsubset = $true) & (singletoninpowerset = $true) & (omegaIndAx = $true) & (notdallE = $true) & (in__Cong = $true) & (binunionLsub = $true) & (symdiffIneg1 = $true) & (dsetconstr__Cong = $true) & (setunion__Cong = $true) & (setminusSubset2 = $true) & (quantDeMorgan3 = $true) & (notinsingleton = $true) & (secondinupair = $true) & (setunionE = $true) & (emptysetimpfalse = $true) & (subset2powerset = $true) & (eqimpsubset1 = $true) & (kfstpairEq = $true) & (exuEu = $true) & (omega0Ax = $true) & ((sK441 != sK443) & ((setadjoin @ (setadjoin @ sK443 @ emptyset) @ (setadjoin @ (setadjoin @ sK443 @ (setadjoin @ sK442 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK441 @ emptyset) @ (setadjoin @ (setadjoin @ sK441 @ (setadjoin @ sK444 @ emptyset)) @ emptyset)))) & (setadjoinSub2 = $true) & (setoftrueEq = $true) & (exuI3 = $true) & (subsetE = $true) & (binintersectLsub = $true) & (prop2set2propI = $true) & (emptysetE = $true) & (noeltsimpempty = $true) & (setadjoinOr = $true) & (cartprodmempair = $true) & (omegaSAx = $true) & (quantDeMorgan1 = $true) & (symdiffI2 = $true) & (setukpairIL = $true) & (quantDeMorgan4 = $true) & (powersetAx = $true) & (binintersectSubset3 = $true) & (omega__Cong = $true) & (symdiffIneg2 = $true) & (binintersectI = $true) & (symdiffI1 = $true) & (setadjoinIR = $true) & (subPowSU = $true) & (emptyE1 = $true) & (dsetconstrER = $true) & (binintersectER = $true) & (binunionRsub = $true) & (setextsub = $true) & (setadjoinSub = $true) & (dsetconstrI = $true) & (subsetemptysetimpeq = $true) & (setminusILneg = $true) & (emptysetAx = $true) & (setunionE2 = $true) & (kpairp = $true) & (setminusER = $true) & (inPowerset = $true) & (powersetE1 = $true) & (emptyinPowerset = $true) & (singletonprop = $true) & (exuE1 = $true) & (notdexE = $true) & (nonemptyE1 = $true) & (setunionsingleton = $true) & (setunionsingleton2 = $true) & (upairset2IR = $true) & (ubforcartprodlem1 = $true) & (binunionE = $true) & (uniqinunit = $true) & (prop2setI = $true) & (singletonsswitch = $true) & (disjointsetsI1 = $true) & (upairset2E = $true) & (powersetI1 = $true) & (setminusLsub = $true) & (setunionAx = $true) & (ubforcartprodlem2 = $true) & (emptyI = $true) & (setunionsingleton1 = $true) & (cartprodmempair1 = $true) & (theprop = $true) & (notsubsetI = $true) & (quantDeMorgan2 = $true) & (ubforcartprodlem3 = $true) & (subsetRefl = $true) & (exuI2 = $true) & (binunionIL = $true) & (exuE2 = $true) & (setadjoinAx = $true) & (dsetconstrEL = $true) & (exuE3u = $true) & (binintersectSubset2 = $true) & (ex1I = $true) & (foundationAx = $true) & (setadjoinIL = $true) & (binintersectSubset1 = $true) & (emptyInPowerset = $true) & (symdiffE = $true) & (setukpairinjL1 = $true) & (prop2setE = $true) & (powersetI = $true) & (eqimpsubset2 = $true) & (upairinpowunion = $true) & (binintersectEL = $true) & (setminusERneg = $true) & (descrp = $true) & (upairsetIR = $true) & (setbeta = $true) & (notinemptyset = $true) & (setadjoinE = $true) & (upairsubunion = $true) & (binintersectSubset5 = $true) & (emptyset__Cong = $true) & (exuE3e = $true) & (setextAx = $true) & (nonemptyI1 = $true) & (powerset__Cong = $true) & (setminusEL = $true) & (singletonsuniq = $true)),
% 2.53/1.68 inference(skolemisation,[status(esa),new_symbols(skolem,[sK441,sK442,sK443,sK444])],[f672,f1455])).
% 2.53/1.68 thf(f1455,plain,(
% 2.53/1.68 ? [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((X0 != X2) & ((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))) => ((sK441 != sK443) & ((setadjoin @ (setadjoin @ sK443 @ emptyset) @ (setadjoin @ (setadjoin @ sK443 @ (setadjoin @ sK442 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK441 @ emptyset) @ (setadjoin @ (setadjoin @ sK441 @ (setadjoin @ sK444 @ emptyset)) @ emptyset))))),
% 2.53/1.68 introduced(definition,[],[choice_axiom])).
% 2.53/1.68 thf(f672,plain,(
% 2.53/1.68 (subsetE2 = $true) & (bs114d = $true) & (subsetTrans = $true) & (setminusIRneg = $true) & (cartprodpairin = $true) & (ex1E1 = $true) & (exu__Cong = $true) & (sepSubset = $true) & (binintersectSubset4 = $true) & (binunionEcases = $true) & (setminusELneg = $true) & (inCongP = $true) & (descr__Cong = $true) & (kfstsingleton = $true) & (setminusI = $true) & (subsetI1 = $true) & (notequalI2 = $true) & (subsetI2 = $true) & (kpairiskpair = $true) & (nonemptyI = $true) & (vacuousDall = $true) & (emptyinunitempty = $true) & (replAx = $true) & (cartprodfstin = $true) & (setminusSubset1 = $true) & (exuI1 = $true) & (singletoninpowunion = $true) & (wellorderingAx = $true) & (setadjoin__Cong = $true) & (setukpairIR = $true) & (setext = $true) & (nonemptyImpWitness = $true) & (binintersectRsub = $true) & (powersetsubset = $true) & (singletonsubset = $true) & (eqinunit = $true) & (upairsetIL = $true) & (sepInPowerset = $true) & (powersetE = $true) & (ex1I2 = $true) & (notequalI1 = $true) & (setunionI = $true) & (binunionIR = $true) & (upairsetE = $true) & (emptysetsubset = $true) & (singletoninpowerset = $true) & (omegaIndAx = $true) & (notdallE = $true) & (in__Cong = $true) & (binunionLsub = $true) & (symdiffIneg1 = $true) & (dsetconstr__Cong = $true) & (setunion__Cong = $true) & (setminusSubset2 = $true) & (quantDeMorgan3 = $true) & (notinsingleton = $true) & (secondinupair = $true) & (setunionE = $true) & (emptysetimpfalse = $true) & (subset2powerset = $true) & (eqimpsubset1 = $true) & (kfstpairEq = $true) & (exuEu = $true) & (omega0Ax = $true) & ? [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((X0 != X2) & ((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))) & (setadjoinSub2 = $true) & (setoftrueEq = $true) & (exuI3 = $true) & (subsetE = $true) & (binintersectLsub = $true) & (prop2set2propI = $true) & (emptysetE = $true) & (noeltsimpempty = $true) & (setadjoinOr = $true) & (cartprodmempair = $true) & (omegaSAx = $true) & (quantDeMorgan1 = $true) & (symdiffI2 = $true) & (setukpairIL = $true) & (quantDeMorgan4 = $true) & (powersetAx = $true) & (binintersectSubset3 = $true) & (omega__Cong = $true) & (symdiffIneg2 = $true) & (binintersectI = $true) & (symdiffI1 = $true) & (setadjoinIR = $true) & (subPowSU = $true) & (emptyE1 = $true) & (dsetconstrER = $true) & (binintersectER = $true) & (binunionRsub = $true) & (setextsub = $true) & (setadjoinSub = $true) & (dsetconstrI = $true) & (subsetemptysetimpeq = $true) & (setminusILneg = $true) & (emptysetAx = $true) & (setunionE2 = $true) & (kpairp = $true) & (setminusER = $true) & (inPowerset = $true) & (powersetE1 = $true) & (emptyinPowerset = $true) & (singletonprop = $true) & (exuE1 = $true) & (notdexE = $true) & (nonemptyE1 = $true) & (setunionsingleton = $true) & (setunionsingleton2 = $true) & (upairset2IR = $true) & (ubforcartprodlem1 = $true) & (binunionE = $true) & (uniqinunit = $true) & (prop2setI = $true) & (singletonsswitch = $true) & (disjointsetsI1 = $true) & (upairset2E = $true) & (powersetI1 = $true) & (setminusLsub = $true) & (setunionAx = $true) & (ubforcartprodlem2 = $true) & (emptyI = $true) & (setunionsingleton1 = $true) & (cartprodmempair1 = $true) & (theprop = $true) & (notsubsetI = $true) & (quantDeMorgan2 = $true) & (ubforcartprodlem3 = $true) & (subsetRefl = $true) & (exuI2 = $true) & (binunionIL = $true) & (exuE2 = $true) & (setadjoinAx = $true) & (dsetconstrEL = $true) & (exuE3u = $true) & (binintersectSubset2 = $true) & (ex1I = $true) & (foundationAx = $true) & (setadjoinIL = $true) & (binintersectSubset1 = $true) & (emptyInPowerset = $true) & (symdiffE = $true) & (setukpairinjL1 = $true) & (prop2setE = $true) & (powersetI = $true) & (eqimpsubset2 = $true) & (upairinpowunion = $true) & (binintersectEL = $true) & (setminusERneg = $true) & (descrp = $true) & (upairsetIR = $true) & (setbeta = $true) & (notinemptyset = $true) & (setadjoinE = $true) & (upairsubunion = $true) & (binintersectSubset5 = $true) & (emptyset__Cong = $true) & (exuE3e = $true) & (setextAx = $true) & (nonemptyI1 = $true) & (powerset__Cong = $true) & (setminusEL = $true) & (singletonsuniq = $true)),
% 2.53/1.68 inference(flattening,[status(thm)],[f671])).
% 2.53/1.68 thf(f671,plain,(
% 2.53/1.68 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((X0 != X2) & ((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))) & (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)),
% 2.53/1.68 inference(ennf_transformation,[status(thm)],[f226])).
% 2.53/1.68 thf(f226,plain,(
% 2.53/1.68 ~((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) => ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) => (X0 = X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.53/1.68 inference(fool_elimination,[status(thm)],[f225])).
% 2.53/1.68 thf(f225,plain,(
% 2.53/1.68 ~(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 => ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) => (X0 = X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.53/1.68 inference(rectify,[status(thm)],[f171])).
% 2.53/1.68 thf(f171,negated_conjecture,(
% 2.53/1.68 ~(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 => ! [X1 : $i,X10 : $i,X8 : $i,X2 : $i] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X8 @ emptyset) @ (setadjoin @ (setadjoin @ X8 @ (setadjoin @ X10 @ emptyset)) @ emptyset))) => (X1 = X8)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.53/1.68 inference(negated_conjecture,[status(cth)],[f170])).
% 2.53/1.68 thf(f170,conjecture,(
% 2.53/1.68 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 => ! [X1 : $i,X10 : $i,X8 : $i,X2 : $i] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X8 @ emptyset) @ (setadjoin @ (setadjoin @ X8 @ (setadjoin @ X10 @ emptyset)) @ emptyset))) => (X1 = X8))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.53/1.68 file('/export/starexec/sandbox/tmp/tmp.VeTrV6L3FZ/DTF2THF_4923.p',setukpairinjL2)).
% 2.53/1.68 thf(f2513,plain,(
% 2.53/1.68 (setukpairinjL1 != $true) | (sK441 = sK443)),
% 2.53/1.68 inference(trivial_inequality_removal,[status(thm)],[f2500])).
% 2.53/1.68 thf(f2500,plain,(
% 2.53/1.68 (setukpairinjL1 != $true) | (sK441 = sK443) | ($true != $true)),
% 2.53/1.68 inference(superposition,[status(thm)],[f1898,f2429])).
% 2.53/1.68 thf(f2429,plain,(
% 2.53/1.68 ($true = (in @ (setadjoin @ sK443 @ emptyset) @ (setadjoin @ (setadjoin @ sK441 @ emptyset) @ (setadjoin @ (setadjoin @ sK441 @ (setadjoin @ sK444 @ emptyset)) @ emptyset))))),
% 2.53/1.68 inference(trivial_inequality_removal,[status(thm)],[f2428])).
% 2.53/1.68 thf(f2428,plain,(
% 2.53/1.68 ($true != $true) | ($true = (in @ (setadjoin @ sK443 @ emptyset) @ (setadjoin @ (setadjoin @ sK441 @ emptyset) @ (setadjoin @ (setadjoin @ sK441 @ (setadjoin @ sK444 @ emptyset)) @ emptyset))))),
% 2.53/1.68 inference(forward_demodulation,[status(thm)],[f2422,f2123])).
% 2.53/1.68 thf(f2123,plain,(
% 2.53/1.68 (setadjoinIL = $true)),
% 2.53/1.68 inference(cnf_transformation,[status(thm)],[f1456])).
% 2.53/1.68 thf(f2422,plain,(
% 2.53/1.68 (setadjoinIL != $true) | ($true = (in @ (setadjoin @ sK443 @ emptyset) @ (setadjoin @ (setadjoin @ sK441 @ emptyset) @ (setadjoin @ (setadjoin @ sK441 @ (setadjoin @ sK444 @ emptyset)) @ emptyset))))),
% 2.53/1.68 inference(superposition,[status(thm)],[f1816,f2198])).
% 2.53/1.68 thf(f2198,plain,(
% 2.53/1.68 ((setadjoin @ (setadjoin @ sK443 @ emptyset) @ (setadjoin @ (setadjoin @ sK443 @ (setadjoin @ sK442 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK441 @ emptyset) @ (setadjoin @ (setadjoin @ sK441 @ (setadjoin @ sK444 @ emptyset)) @ emptyset)))),
% 2.53/1.68 inference(cnf_transformation,[status(thm)],[f1456])).
% 2.53/1.68 thf(f1816,plain,(
% 2.53/1.68 ( ! [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (setadjoin @ X1 @ X0))) | (setadjoinIL != $true)) )),
% 2.53/1.68 inference(cnf_transformation,[status(thm)],[f1118])).
% 2.53/1.68 thf(f1118,plain,(
% 2.53/1.68 (! [X0 : $i,X1 : $i] : ($true = (in @ X1 @ (setadjoin @ X1 @ X0))) | (setadjoinIL != $true)) & ((setadjoinIL = $true) | ((in @ sK241 @ (setadjoin @ sK241 @ sK240)) != $true))),
% 2.53/1.68 inference(skolemisation,[status(esa),new_symbols(skolem,[sK240,sK241])],[f1116,f1117])).
% 2.53/1.68 thf(f1117,plain,(
% 2.53/1.68 ? [X2 : $i,X3 : $i] : ($true != (in @ X3 @ (setadjoin @ X3 @ X2))) => ((in @ sK241 @ (setadjoin @ sK241 @ sK240)) != $true)),
% 2.53/1.68 introduced(definition,[],[choice_axiom])).
% 2.53/1.68 thf(f1116,plain,(
% 2.53/1.68 (! [X0 : $i,X1 : $i] : ($true = (in @ X1 @ (setadjoin @ X1 @ X0))) | (setadjoinIL != $true)) & ((setadjoinIL = $true) | ? [X2 : $i,X3 : $i] : ($true != (in @ X3 @ (setadjoin @ X3 @ X2))))),
% 2.53/1.68 inference(rectify,[status(thm)],[f1115])).
% 2.53/1.68 thf(f1115,plain,(
% 2.53/1.68 (! [X0 : $i,X1 : $i] : ($true = (in @ X1 @ (setadjoin @ X1 @ X0))) | (setadjoinIL != $true)) & ((setadjoinIL = $true) | ? [X0 : $i,X1 : $i] : ($true != (in @ X1 @ (setadjoin @ X1 @ X0))))),
% 2.53/1.68 inference(nnf_transformation,[status(thm)],[f309])).
% 2.53/1.68 thf(f309,plain,(
% 2.53/1.68 ! [X0 : $i,X1 : $i] : ($true = (in @ X1 @ (setadjoin @ X1 @ X0))) <=> (setadjoinIL = $true)),
% 2.53/1.68 inference(fool_elimination,[status(thm)],[f308])).
% 2.53/1.68 thf(f308,plain,(
% 2.53/1.68 (! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X1 @ X0)) = setadjoinIL)),
% 2.53/1.68 inference(rectify,[status(thm)],[f31])).
% 2.53/1.68 thf(f31,axiom,(
% 2.53/1.68 (! [X2 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X1 @ X2)) = setadjoinIL)),
% 2.53/1.68 file('/export/starexec/sandbox/tmp/tmp.VeTrV6L3FZ/DTF2THF_4923.p',setadjoinIL)).
% 2.53/1.68 thf(f1898,plain,(
% 2.53/1.68 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))) | (X0 = X1) | (setukpairinjL1 != $true)) )),
% 2.53/1.68 inference(cnf_transformation,[status(thm)],[f1215])).
% 2.53/1.68 thf(f1215,plain,(
% 2.53/1.68 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))) | (X0 = X1)) | (setukpairinjL1 != $true)) & ((setukpairinjL1 = $true) | (($true = (in @ (setadjoin @ sK296 @ emptyset) @ (setadjoin @ (setadjoin @ sK295 @ emptyset) @ (setadjoin @ (setadjoin @ sK295 @ (setadjoin @ sK297 @ emptyset)) @ emptyset)))) & (sK295 != sK296)))),
% 2.53/1.68 inference(skolemisation,[status(esa),new_symbols(skolem,[sK295,sK296,sK297])],[f1213,f1214])).
% 2.53/1.68 thf(f1214,plain,(
% 2.53/1.68 ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ (setadjoin @ X4 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X5 @ emptyset)) @ emptyset))) = $true) & (X3 != X4)) => (($true = (in @ (setadjoin @ sK296 @ emptyset) @ (setadjoin @ (setadjoin @ sK295 @ emptyset) @ (setadjoin @ (setadjoin @ sK295 @ (setadjoin @ sK297 @ emptyset)) @ emptyset)))) & (sK295 != sK296))),
% 2.53/1.68 introduced(definition,[],[choice_axiom])).
% 2.53/1.68 thf(f1213,plain,(
% 2.53/1.68 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))) | (X0 = X1)) | (setukpairinjL1 != $true)) & ((setukpairinjL1 = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ (setadjoin @ X4 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X5 @ emptyset)) @ emptyset))) = $true) & (X3 != X4)))),
% 2.53/1.68 inference(rectify,[status(thm)],[f1212])).
% 2.53/1.68 thf(f1212,plain,(
% 2.53/1.68 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))) | (X0 = X1)) | (setukpairinjL1 != $true)) & ((setukpairinjL1 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))) & (X0 != X1)))),
% 2.53/1.68 inference(nnf_transformation,[status(thm)],[f556])).
% 2.53/1.68 thf(f556,plain,(
% 2.53/1.68 ! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))) | (X0 = X1)) <=> (setukpairinjL1 = $true)),
% 2.53/1.68 inference(ennf_transformation,[status(thm)],[f455])).
% 2.53/1.68 thf(f455,plain,(
% 2.53/1.68 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))) => (X0 = X1)) <=> (setukpairinjL1 = $true)),
% 2.53/1.68 inference(fool_elimination,[status(thm)],[f454])).
% 2.53/1.68 thf(f454,plain,(
% 2.53/1.68 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X2 @ emptyset)) @ emptyset))) => (X0 = X1)) = setukpairinjL1)),
% 2.53/1.68 inference(rectify,[status(thm)],[f165])).
% 2.53/1.68 thf(f165,axiom,(
% 2.53/1.68 (! [X1 : $i,X8 : $i,X2 : $i] : ((in @ (setadjoin @ X8 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset))) => (X1 = X8)) = setukpairinjL1)),
% 2.53/1.68 file('/export/starexec/sandbox/tmp/tmp.VeTrV6L3FZ/DTF2THF_4923.p',setukpairinjL1)).
% 2.53/1.68 thf(f2199,plain,(
% 2.53/1.68 (sK441 != sK443)),
% 2.53/1.68 inference(cnf_transformation,[status(thm)],[f1456])).
% 2.53/1.68 % SZS output end Proof for DTF2THF_4923
% 2.53/1.68 % (5231)------------------------------
% 2.53/1.68 % (5231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.53/1.68 % (5231)Termination reason: Refutation
% 2.53/1.68
% 2.53/1.68 % (5231)Memory used [KB]: 8315
% 2.53/1.68 % (5231)Time elapsed: 0.079 s
% 2.53/1.68 % (5231)Instructions burned: 204 (million)
% 2.53/1.68 % (5231)------------------------------
% 2.53/1.68 % (5231)------------------------------
% 2.53/1.68 % (5208)Success in time 0.167 s
%------------------------------------------------------------------------------