%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU615^1 : 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 : n008.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 09:35:38 AM UTC 2026
% Result : Theorem 2.42s 1.97s
% Output : Refutation 2.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 9 unt; 0 typ; 2 def)
% Number of atoms : 2948 ( 831 equ; 0 cnn)
% Maximal formula atoms : 134 ( 71 avg)
% Number of connectives : 1652 ( 107 ~; 76 |; 445 &; 322 @)
% ( 6 <=>; 696 =>; 0 <=; 0 <~>)
% Maximal formula depth : 142 ( 32 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 256 ( 253 usr; 142 con; 0-4 aty)
% Number of variables : 94 ( 0 ^; 71 !; 23 ?; 94 :)
% 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_164,type,
sP0: $i > $i > $o ).
thf(func_def_165,type,
sP1: $i > $o ).
thf(func_def_167,type,
sK3: $i > $i ).
thf(func_def_169,type,
sK5: $i > $i ).
thf(func_def_180,type,
sK16: $i > $o ).
thf(func_def_182,type,
sK18: $i > ( $i > $o ) > $i ).
thf(func_def_200,type,
sK36: $i > $i > $i ).
thf(func_def_217,type,
sK53: $i > $o ).
thf(func_def_221,type,
sK57: $i > $o ).
thf(func_def_226,type,
sK62: $i > $i ).
thf(func_def_235,type,
sK71: $i > $i > $i ).
thf(func_def_237,type,
sK73: $i > $i ).
thf(func_def_238,type,
sK74: $i > $i > $i ).
thf(func_def_243,type,
sK79: $i > $i > $i ).
thf(func_def_244,type,
sK80: $i > ( $i > $o ) > $i ).
thf(func_def_245,type,
sK81: $i > $o ).
thf(func_def_248,type,
sK84: $i > $o ).
thf(func_def_253,type,
sK89: $i > ( $i > $o ) > $i ).
thf(func_def_254,type,
sK90: $i > $o ).
thf(func_def_259,type,
sK95: $i > $i > $i ).
thf(func_def_260,type,
sK96: $i > $i > $i ).
thf(func_def_266,type,
sK102: $i > ( $i > $i > $o ) > $i ).
thf(func_def_267,type,
sK103: $i > ( $i > $i > $o ) > $i ).
thf(func_def_268,type,
sK104: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_269,type,
sK105: $i > $i > $o ).
thf(func_def_271,type,
sK107: $i > $i ).
thf(func_def_272,type,
sK108: $i > $i ).
thf(func_def_273,type,
sK109: $i > $o ).
thf(func_def_274,type,
sK110: $i > $i ).
thf(func_def_275,type,
sK111: ( $i > $o ) > $i ).
thf(func_def_278,type,
sK114: $i > $i ).
thf(func_def_303,type,
sK139: $i > $o ).
thf(func_def_307,type,
sK143: $i > $o ).
thf(func_def_311,type,
sK147: $i > $o ).
thf(func_def_314,type,
sK150: $i > $o ).
thf(func_def_316,type,
sK152: ( $i > $o ) > $i ).
thf(func_def_317,type,
sK153: ( $i > $o ) > $i ).
thf(func_def_321,type,
sK157: $i > $o ).
thf(func_def_334,type,
sK170: $i > $o ).
thf(func_def_351,type,
sK187: $i > $i > $i ).
thf(func_def_368,type,
sK204: $o > $i > $i > $i ).
thf(func_def_377,type,
sK213: $i > $o ).
thf(func_def_378,type,
sK214: $i > $i ).
thf(func_def_379,type,
sK215: ( $i > $o ) > $i ).
thf(func_def_380,type,
sK216: $i > $i > $i ).
thf(func_def_387,type,
sK223: $i > $o ).
thf(func_def_389,type,
sK225: ( $i > $o ) > $i > $i ).
thf(func_def_391,type,
sK227: $i > $o ).
thf(func_def_393,type,
sK229: $i > $o ).
thf(func_def_394,type,
sK230: $i > $o ).
thf(func_def_395,type,
sK231: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_396,type,
sK232: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_402,type,
sK238: $i > ( $i > $o ) > $i ).
thf(func_def_403,type,
sK239: $i > $o ).
thf(func_def_419,type,
sK255: $i > $i > $i ).
thf(func_def_423,type,
sK259: $i > ( $i > $o ) > $i ).
thf(func_def_424,type,
sK260: $i > $o ).
thf(func_def_427,type,
sK263: $i > $i ).
thf(func_def_436,type,
sK272: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_437,type,
sK273: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_440,type,
sK276: $i > $o ).
thf(func_def_441,type,
sK277: $i > $o ).
thf(func_def_444,type,
sK280: $i > $o ).
thf(func_def_451,type,
sK287: $i > $i ).
thf(func_def_452,type,
sK288: $i > $i ).
thf(func_def_453,type,
sK289: $i > $i ).
thf(func_def_454,type,
sK290: $i > $i ).
thf(func_def_455,type,
sK291: $i > $i > $i ).
thf(func_def_456,type,
sK292: $i > $i > $i ).
thf(func_def_457,type,
sK293: $i > $i > $i > $i ).
thf(func_def_458,type,
sK294: $i > $i > $i > $i ).
thf(func_def_459,type,
sK295: $i > $i > $i > $i ).
thf(func_def_460,type,
sK296: $i > $i > $i ).
thf(func_def_461,type,
sK297: $i > $i > $i ).
thf(func_def_462,type,
sK298: $i > $i > $i ).
thf(func_def_463,type,
sK299: $i > $i ).
thf(func_def_464,type,
sK300: $i > $i > $i > $i ).
thf(func_def_466,type,
sK302: $i > $i ).
thf(func_def_467,type,
sK303: $i > $i ).
thf(func_def_468,type,
sK304: $i > $i ).
thf(func_def_469,type,
sK305: $i > $i ).
thf(func_def_470,type,
sK306: ( $i > $o ) > $i > $i ).
thf(func_def_472,type,
sK308: $i > $o ).
thf(func_def_475,type,
sK311: $i > $i ).
thf(func_def_484,type,
sK320: $i > $o ).
thf(func_def_486,type,
sK322: $i > $o ).
thf(func_def_491,type,
sK327: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_492,type,
sK328: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_493,type,
sK329: $i > $o ).
thf(func_def_494,type,
sK330: $i > $o ).
thf(func_def_501,type,
sK337: $i > $o ).
thf(func_def_502,type,
sK338: ( $i > $o ) > $i ).
thf(func_def_519,type,
sK355: $i > $o ).
thf(func_def_522,type,
sK358: $i > ( $i > $o ) > $i ).
thf(func_def_524,type,
ph360:
!>[X0: $tType] : X0 ).
thf(f2684,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f2590,f2661,f2680]) ).
thf(f2680,plain,
~ spl359_2,
inference(avatar_contradiction_clause,[status(thm)],[f2679]) ).
thf(f2679,plain,
( $false
| ~ spl359_2 ),
inference(trivial_inequality_removal,[status(thm)],[f2669]) ).
thf(f2669,plain,
( ( $true != $true )
| ~ spl359_2 ),
inference(superposition,[status(thm)],[f1282,f2581]) ).
thf(f2581,plain,
( ! [X3: $o] : ( $true = X3 )
| ~ spl359_2 ),
inference(avatar_component_clause,[status(thm)],[f2580]) ).
thf(f2580,definition,
( spl359_2
<=> ! [X3: $o] : ( $true = X3 ) ),
introduced(definition,[new_symbols(naming,[spl359_2])],[avatar_definition]) ).
thf(f1282,plain,
( $true
!= ( in @ sK51 @ sK50 ) ),
inference(cnf_transformation,[status(thm)],[f672]) ).
thf(f672,plain,
( ( noeltsimpempty = $true )
& ( setunionI = $true )
& ( emptyinunitempty = $true )
& ( setextAx = $true )
& ( dsetconstrER = $true )
& ( emptyinPowerset = $true )
& ( prop2setE = $true )
& ( omegaSAx = $true )
& ( subsetE = $true )
& ( sepInPowerset = $true )
& ( subsetE2 = $true )
& ( omegaIndAx = $true )
& ( setadjoinIL = $true )
& ( prop2set2propI = $true )
& ( symdiffI1 = $true )
& ( binintersectER = $true )
& ( notequalI2 = $true )
& ( setminusEL = $true )
& ( exu__Cong = $true )
& ( binunionLsub = $true )
& ( setadjoinE = $true )
& ( binunionRsub = $true )
& ( symdiffIneg1 = $true )
& ( quantDeMorgan1 = $true )
& ( emptysetsubset = $true )
& ( setbeta = $true )
& ( powersetE1 = $true )
& ( nonemptyImpWitness = $true )
& ( binunionE = $true )
& ( binintersectSubset5 = $true )
& ( binintersectSubset4 = $true )
& ( exuE3u = $true )
& ( binintersectRsub = $true )
& ( binintersectEL = $true )
& ( setminusSubset2 = $true )
& ( setadjoinSub2 = $true )
& ( eqinunit = $true )
& ( upairsetIR = $true )
& ( setadjoinOr = $true )
& ( notdallE = $true )
& ( eqimpsubset2 = $true )
& ( omega__Cong = $true )
& ( exuI2 = $true )
& ( setminusILneg = $true )
& ( binunionEcases = $true )
& ( in__Cong = $true )
& ( quantDeMorgan2 = $true )
& ( emptysetimpfalse = $true )
& ( emptyInPowerset = $true )
& ( emptyI = $true )
& ( powersetsubset = $true )
& ( binunionIL = $true )
& ( prop2setI = $true )
& ( exuE3e = $true )
& ( setoftrueEq = $true )
& ( setunionAx = $true )
& ( notinemptyset = $true )
& ( inCongP = $true )
& ( powersetI1 = $true )
& ( setminusELneg = $true )
& ( setadjoin__Cong = $true )
& ( notdexE = $true )
& ( setminusIRneg = $true )
& ( setadjoinAx = $true )
& ( notinsingleton = $true )
& ( setunionE = $true )
& ( exuE2 = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( powersetI = $true )
& ( emptysetE = $true )
& ( powersetE = $true )
& ( setextsub = $true )
& ( descr__Cong = $true )
& ( sepSubset = $true )
& ( upairsetE = $true )
& ( subsetTrans = $true )
& ( binunionIR = $true )
& ( exuEu = $true )
& ( nonemptyI = $true )
& ( subPowSU = $true )
& ( setminusERneg = $true )
& ( eqimpsubset1 = $true )
& ( symdiffI2 = $true )
& ( notsubsetI = $true )
& ( setadjoinSub = $true )
& ( setminusER = $true )
& ( binintersectI = $true )
& ( emptyE1 = $true )
& ( dsetconstr__Cong = $true )
& ( bs114d = $true )
& ( setunion__Cong = $true )
& ( exuI1 = $true )
& ( setminusSubset1 = $true )
& ( subsetI1 = $true )
& ( binintersectSubset1 = $true )
& ( disjointsetsI1 = $true )
& ( nonemptyE1 = $true )
& ( powerset__Cong = $true )
& ( exuE1 = $true )
& ( vacuousDall = $true )
& ( $true
!= ( in @ sK51 @ sK52 ) )
& ( ( in @ sK51 @ ( symdiff @ sK52 @ sK50 ) )
= $true )
& ( $true
!= ( in @ sK51 @ sK50 ) )
& ( nonemptyI1 = $true )
& ( symdiffE = $true )
& ( binintersectLsub = $true )
& ( setminusI = $true )
& ( dsetconstrEL = $true )
& ( subsetRefl = $true )
& ( binintersectSubset3 = $true )
& ( notequalI1 = $true )
& ( emptysetAx = $true )
& ( replAx = $true )
& ( powersetAx = $true )
& ( omega0Ax = $true )
& ( subsetemptysetimpeq = $true )
& ( descrp = $true )
& ( emptyset__Cong = $true )
& ( setadjoinIR = $true )
& ( inPowerset = $true )
& ( setext = $true )
& ( upairsetIL = $true )
& ( subsetI2 = $true )
& ( upairset2IR = $true )
& ( setminusLsub = $true )
& ( binintersectSubset2 = $true )
& ( foundationAx = $true )
& ( singletonsswitch = $true )
& ( dsetconstrI = $true )
& ( subset2powerset = $true )
& ( uniqinunit = $true )
& ( exuI3 = $true )
& ( wellorderingAx = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK50,sK51,sK52])],[f482,f671]) ).
thf(f671,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ X2 ) )
& ( ( in @ X1 @ ( symdiff @ X2 @ X0 ) )
= $true )
& ( ( in @ X1 @ X0 )
!= $true ) )
=> ( ( $true
!= ( in @ sK51 @ sK52 ) )
& ( ( in @ sK51 @ ( symdiff @ sK52 @ sK50 ) )
= $true )
& ( $true
!= ( in @ sK51 @ sK50 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f482,plain,
( ( noeltsimpempty = $true )
& ( setunionI = $true )
& ( emptyinunitempty = $true )
& ( setextAx = $true )
& ( dsetconstrER = $true )
& ( emptyinPowerset = $true )
& ( prop2setE = $true )
& ( omegaSAx = $true )
& ( subsetE = $true )
& ( sepInPowerset = $true )
& ( subsetE2 = $true )
& ( omegaIndAx = $true )
& ( setadjoinIL = $true )
& ( prop2set2propI = $true )
& ( symdiffI1 = $true )
& ( binintersectER = $true )
& ( notequalI2 = $true )
& ( setminusEL = $true )
& ( exu__Cong = $true )
& ( binunionLsub = $true )
& ( setadjoinE = $true )
& ( binunionRsub = $true )
& ( symdiffIneg1 = $true )
& ( quantDeMorgan1 = $true )
& ( emptysetsubset = $true )
& ( setbeta = $true )
& ( powersetE1 = $true )
& ( nonemptyImpWitness = $true )
& ( binunionE = $true )
& ( binintersectSubset5 = $true )
& ( binintersectSubset4 = $true )
& ( exuE3u = $true )
& ( binintersectRsub = $true )
& ( binintersectEL = $true )
& ( setminusSubset2 = $true )
& ( setadjoinSub2 = $true )
& ( eqinunit = $true )
& ( upairsetIR = $true )
& ( setadjoinOr = $true )
& ( notdallE = $true )
& ( eqimpsubset2 = $true )
& ( omega__Cong = $true )
& ( exuI2 = $true )
& ( setminusILneg = $true )
& ( binunionEcases = $true )
& ( in__Cong = $true )
& ( quantDeMorgan2 = $true )
& ( emptysetimpfalse = $true )
& ( emptyInPowerset = $true )
& ( emptyI = $true )
& ( powersetsubset = $true )
& ( binunionIL = $true )
& ( prop2setI = $true )
& ( exuE3e = $true )
& ( setoftrueEq = $true )
& ( setunionAx = $true )
& ( notinemptyset = $true )
& ( inCongP = $true )
& ( powersetI1 = $true )
& ( setminusELneg = $true )
& ( setadjoin__Cong = $true )
& ( notdexE = $true )
& ( setminusIRneg = $true )
& ( setadjoinAx = $true )
& ( notinsingleton = $true )
& ( setunionE = $true )
& ( exuE2 = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( powersetI = $true )
& ( emptysetE = $true )
& ( powersetE = $true )
& ( setextsub = $true )
& ( descr__Cong = $true )
& ( sepSubset = $true )
& ( upairsetE = $true )
& ( subsetTrans = $true )
& ( binunionIR = $true )
& ( exuEu = $true )
& ( nonemptyI = $true )
& ( subPowSU = $true )
& ( setminusERneg = $true )
& ( eqimpsubset1 = $true )
& ( symdiffI2 = $true )
& ( notsubsetI = $true )
& ( setadjoinSub = $true )
& ( setminusER = $true )
& ( binintersectI = $true )
& ( emptyE1 = $true )
& ( dsetconstr__Cong = $true )
& ( bs114d = $true )
& ( setunion__Cong = $true )
& ( exuI1 = $true )
& ( setminusSubset1 = $true )
& ( subsetI1 = $true )
& ( binintersectSubset1 = $true )
& ( disjointsetsI1 = $true )
& ( nonemptyE1 = $true )
& ( powerset__Cong = $true )
& ( exuE1 = $true )
& ( vacuousDall = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ X2 ) )
& ( ( in @ X1 @ ( symdiff @ X2 @ X0 ) )
= $true )
& ( ( in @ X1 @ X0 )
!= $true ) )
& ( nonemptyI1 = $true )
& ( symdiffE = $true )
& ( binintersectLsub = $true )
& ( setminusI = $true )
& ( dsetconstrEL = $true )
& ( subsetRefl = $true )
& ( binintersectSubset3 = $true )
& ( notequalI1 = $true )
& ( emptysetAx = $true )
& ( replAx = $true )
& ( powersetAx = $true )
& ( omega0Ax = $true )
& ( subsetemptysetimpeq = $true )
& ( descrp = $true )
& ( emptyset__Cong = $true )
& ( setadjoinIR = $true )
& ( inPowerset = $true )
& ( setext = $true )
& ( upairsetIL = $true )
& ( subsetI2 = $true )
& ( upairset2IR = $true )
& ( setminusLsub = $true )
& ( binintersectSubset2 = $true )
& ( foundationAx = $true )
& ( singletonsswitch = $true )
& ( dsetconstrI = $true )
& ( subset2powerset = $true )
& ( uniqinunit = $true )
& ( exuI3 = $true )
& ( wellorderingAx = $true ) ),
inference(flattening,[status(thm)],[f481]) ).
thf(f481,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( symdiff @ X2 @ X0 ) )
= $true )
& ( ( in @ X1 @ X0 )
!= $true )
& ( $true
!= ( in @ X1 @ X2 ) ) )
& ( 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)],[f426]) ).
thf(f426,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ X2 ) )
=> ( ( ( in @ X1 @ X0 )
!= $true )
=> ( ( in @ X1 @ ( symdiff @ X2 @ X0 ) )
!= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f307]) ).
thf(f307,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ X2 ) )
=> ( ( ( in @ X1 @ X0 )
!= $true )
=> ( ( in @ X1 @ ( symdiff @ X2 @ X0 ) )
!= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f306]) ).
thf(f306,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X1 @ X2 )
=> ( ~ ( in @ X1 @ X0 )
=> ~ ( in @ X1 @ ( symdiff @ X2 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f135]) ).
thf(f135,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
=> ! [X4: $i,X1: $i,X3: $i] :
( ~ ( in @ X1 @ X3 )
=> ( ~ ( in @ X1 @ X4 )
=> ~ ( in @ X1 @ ( symdiff @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f134]) ).
thf(f134,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
=> ! [X4: $i,X1: $i,X3: $i] :
( ~ ( in @ X1 @ X3 )
=> ( ~ ( in @ X1 @ X4 )
=> ~ ( in @ X1 @ ( symdiff @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.75Z7m6xG9f/DTF2THF_28853.p',symdiffIneg2) ).
thf(f2661,plain,
~ spl359_4,
inference(avatar_contradiction_clause,[status(thm)],[f2660]) ).
thf(f2660,plain,
( $false
| ~ spl359_4 ),
inference(subsumption_resolution,[status(thm)],[f2659,f1282]) ).
thf(f2659,plain,
( ( $true
= ( in @ sK51 @ sK50 ) )
| ~ spl359_4 ),
inference(subsumption_resolution,[status(thm)],[f2657,f1284]) ).
thf(f1284,plain,
( $true
!= ( in @ sK51 @ sK52 ) ),
inference(cnf_transformation,[status(thm)],[f672]) ).
thf(f2657,plain,
( ( $true
= ( in @ sK51 @ sK52 ) )
| ( $true
= ( in @ sK51 @ sK50 ) )
| ~ spl359_4 ),
inference(trivial_inequality_removal,[status(thm)],[f2655]) ).
thf(f2655,plain,
( ( $true
= ( in @ sK51 @ sK52 ) )
| ( $true
= ( in @ sK51 @ sK50 ) )
| ( $true != $true )
| ~ spl359_4 ),
inference(superposition,[status(thm)],[f2589,f1283]) ).
thf(f1283,plain,
( ( in @ sK51 @ ( symdiff @ sK52 @ sK50 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f672]) ).
thf(f2589,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( symdiff @ X1 @ X2 ) )
!= $true )
| ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ X2 )
= $true ) )
| ~ spl359_4 ),
inference(avatar_component_clause,[status(thm)],[f2588]) ).
thf(f2588,definition,
( spl359_4
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X0 @ ( symdiff @ X1 @ X2 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl359_4])],[avatar_definition]) ).
thf(f2590,plain,
( spl359_2
| spl359_4 ),
inference(avatar_split_clause,[status(thm)],[f2426,f2588,f2580]) ).
thf(f2426,plain,
! [X2: $i,X3: $o,X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ ( symdiff @ X1 @ X2 ) )
!= $true )
| ( $true = X3 )
| ( ( in @ X0 @ X2 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f2006]) ).
thf(f2006,plain,
! [X2: $i,X3: $o,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( symdiff @ X1 @ X2 ) )
!= $true )
| ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ X2 )
= $true )
| ( $true != $true )
| ( $true = X3 ) ),
inference(definition_unfolding,[status(thm)],[f1487,f1280]) ).
thf(f1280,plain,
symdiffE = $true,
inference(cnf_transformation,[status(thm)],[f672]) ).
thf(f1487,plain,
! [X2: $i,X3: $o,X0: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
| ( ( in @ X0 @ X2 )
= $true )
| ( $true = X3 )
| ( ( in @ X0 @ ( symdiff @ X1 @ X2 ) )
!= $true )
| ( symdiffE != $true ) ),
inference(cnf_transformation,[status(thm)],[f788]) ).
thf(f788,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $o] :
( ( ( ( in @ X0 @ X2 )
!= $true )
& ( ( in @ X0 @ X1 )
= $true )
& ( $true != X3 ) )
| ( ( ( in @ X0 @ X1 )
!= $true )
& ( $true != X3 )
& ( ( in @ X0 @ X2 )
= $true ) )
| ( $true = X3 ) )
| ( ( in @ X0 @ ( symdiff @ X1 @ X2 ) )
!= $true ) )
| ( symdiffE != $true ) )
& ( ( symdiffE = $true )
| ( ( ( $true
= ( in @ sK118 @ sK120 ) )
| ( ( in @ sK118 @ sK119 )
!= $true )
| ( sK121 = $true ) )
& ( ( ( in @ sK118 @ sK119 )
= $true )
| ( sK121 = $true )
| ( $true
!= ( in @ sK118 @ sK120 ) ) )
& ( sK121 != $true )
& ( $true
= ( in @ sK118 @ ( symdiff @ sK119 @ sK120 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK118,sK119,sK120,sK121])],[f785,f787,f786]) ).
thf(f786,plain,
( ? [X4: $i,X5: $i,X6: $i] :
( ? [X7: $o] :
( ( ( ( in @ X4 @ X6 )
= $true )
| ( $true
!= ( in @ X4 @ X5 ) )
| ( $true = X7 ) )
& ( ( $true
= ( in @ X4 @ X5 ) )
| ( $true = X7 )
| ( ( in @ X4 @ X6 )
!= $true ) )
& ( $true != X7 ) )
& ( $true
= ( in @ X4 @ ( symdiff @ X5 @ X6 ) ) ) )
=> ( ? [X7: $o] :
( ( ( $true
= ( in @ sK118 @ sK120 ) )
| ( ( in @ sK118 @ sK119 )
!= $true )
| ( $true = X7 ) )
& ( ( ( in @ sK118 @ sK119 )
= $true )
| ( $true = X7 )
| ( $true
!= ( in @ sK118 @ sK120 ) ) )
& ( $true != X7 ) )
& ( $true
= ( in @ sK118 @ ( symdiff @ sK119 @ sK120 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f787,plain,
( ? [X7: $o] :
( ( ( $true
= ( in @ sK118 @ sK120 ) )
| ( ( in @ sK118 @ sK119 )
!= $true )
| ( $true = X7 ) )
& ( ( ( in @ sK118 @ sK119 )
= $true )
| ( $true = X7 )
| ( $true
!= ( in @ sK118 @ sK120 ) ) )
& ( $true != X7 ) )
=> ( ( ( $true
= ( in @ sK118 @ sK120 ) )
| ( ( in @ sK118 @ sK119 )
!= $true )
| ( sK121 = $true ) )
& ( ( ( in @ sK118 @ sK119 )
= $true )
| ( sK121 = $true )
| ( $true
!= ( in @ sK118 @ sK120 ) ) )
& ( sK121 != $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f785,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $o] :
( ( ( ( in @ X0 @ X2 )
!= $true )
& ( ( in @ X0 @ X1 )
= $true )
& ( $true != X3 ) )
| ( ( ( in @ X0 @ X1 )
!= $true )
& ( $true != X3 )
& ( ( in @ X0 @ X2 )
= $true ) )
| ( $true = X3 ) )
| ( ( in @ X0 @ ( symdiff @ X1 @ X2 ) )
!= $true ) )
| ( symdiffE != $true ) )
& ( ( symdiffE = $true )
| ? [X4: $i,X5: $i,X6: $i] :
( ? [X7: $o] :
( ( ( ( in @ X4 @ X6 )
= $true )
| ( $true
!= ( in @ X4 @ X5 ) )
| ( $true = X7 ) )
& ( ( $true
= ( in @ X4 @ X5 ) )
| ( $true = X7 )
| ( ( in @ X4 @ X6 )
!= $true ) )
& ( $true != X7 ) )
& ( $true
= ( in @ X4 @ ( symdiff @ X5 @ X6 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f784]) ).
thf(f784,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $o] :
( ( ( ( in @ X0 @ X2 )
!= $true )
& ( ( in @ X0 @ X1 )
= $true )
& ( $true != X3 ) )
| ( ( ( in @ X0 @ X1 )
!= $true )
& ( $true != X3 )
& ( ( in @ X0 @ X2 )
= $true ) )
| ( $true = X3 ) )
| ( ( in @ X0 @ ( symdiff @ X1 @ X2 ) )
!= $true ) )
| ( symdiffE != $true ) )
& ( ( symdiffE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $o] :
( ( ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X0 @ X1 )
!= $true )
| ( $true = X3 ) )
& ( ( ( in @ X0 @ X1 )
= $true )
| ( $true = X3 )
| ( ( in @ X0 @ X2 )
!= $true ) )
& ( $true != X3 ) )
& ( ( in @ X0 @ ( symdiff @ X1 @ X2 ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f447]) ).
thf(f447,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $o] :
( ( ( ( in @ X0 @ X2 )
!= $true )
& ( ( in @ X0 @ X1 )
= $true )
& ( $true != X3 ) )
| ( ( ( in @ X0 @ X1 )
!= $true )
& ( $true != X3 )
& ( ( in @ X0 @ X2 )
= $true ) )
| ( $true = X3 ) )
| ( ( in @ X0 @ ( symdiff @ X1 @ X2 ) )
!= $true ) )
<=> ( symdiffE = $true ) ),
inference(flattening,[status(thm)],[f446]) ).
thf(f446,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $o] :
( ( $true = X3 )
| ( ( $true != X3 )
& ( ( in @ X0 @ X2 )
= $true )
& ( ( in @ X0 @ X1 )
!= $true ) )
| ( ( $true != X3 )
& ( ( in @ X0 @ X2 )
!= $true )
& ( ( in @ X0 @ X1 )
= $true ) ) )
| ( ( in @ X0 @ ( symdiff @ X1 @ X2 ) )
!= $true ) )
<=> ( symdiffE = $true ) ),
inference(ennf_transformation,[status(thm)],[f430]) ).
thf(f430,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( symdiff @ X1 @ X2 ) )
= $true )
=> ! [X3: $o] :
( ( ( ( in @ X0 @ X1 )
= $true )
=> ( ( ( in @ X0 @ X2 )
!= $true )
=> ( $true = X3 ) ) )
=> ( ( ( ( in @ X0 @ X1 )
!= $true )
=> ( ( ( in @ X0 @ X2 )
= $true )
=> ( $true = X3 ) ) )
=> ( $true = X3 ) ) ) )
<=> ( symdiffE = $true ) ),
inference(flattening,[status(thm)],[f323]) ).
thf(f323,plain,
( ( symdiffE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( symdiff @ X1 @ X2 ) )
= $true )
=> ! [X3: $o] :
( ( ( ( in @ X0 @ X1 )
= $true )
=> ( ( ( in @ X0 @ X2 )
!= $true )
=> ( $true = X3 ) ) )
=> ( ( ( ( in @ X0 @ X1 )
!= $true )
=> ( ( ( in @ X0 @ X2 )
= $true )
=> ( $true = X3 ) ) )
=> ( $true = X3 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f322]) ).
thf(f322,plain,
( symdiffE
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ ( symdiff @ X1 @ X2 ) )
=> ! [X3: $o] :
( ( ( in @ X0 @ X1 )
=> ( ~ ( in @ X0 @ X2 )
=> X3 ) )
=> ( ( ~ ( in @ X0 @ X1 )
=> ( ( in @ X0 @ X2 )
=> X3 ) )
=> X3 ) ) ) ) ),
inference(rectify,[status(thm)],[f130]) ).
thf(f130,axiom,
( symdiffE
= ( ! [X1: $i,X3: $i,X4: $i] :
( ( in @ X1 @ ( symdiff @ X3 @ X4 ) )
=> ! [X0: $o] :
( ( ( in @ X1 @ X3 )
=> ( ~ ( in @ X1 @ X4 )
=> X0 ) )
=> ( ( ~ ( in @ X1 @ X3 )
=> ( ( in @ X1 @ X4 )
=> X0 ) )
=> X0 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.75Z7m6xG9f/DTF2THF_28853.p',symdiffE) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU615^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n008.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:29:09 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SEU615^1 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.46 % Domain : Set Theory
% 0.30/0.46 % Problem : Preliminary Notions - Operations on Sets - Symmetric Difference
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English : (! A:i.! B:i.! x:i.~(in x A) -> ~(in x B) -> ~(in x
% 0.30/0.46 % (symdiff A B)))
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.30/0.46 % Source : [Bro08]
% 0.30/0.46 % Names : ZFC117g [Bro08]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.18 v7.5.0, 0.29 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.60 v6.2.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v5.2.0, 1.00 v5.0.0, 0.80 v4.1.0, 0.67 v3.7.0
% 0.30/0.46 % Syntax : Number of formulae : 285 ( 133 unt; 151 typ; 133 def)
% 0.30/0.46 % Number of atoms : 713 ( 190 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 134 ( 5 avg)
% 0.30/0.46 % Number of connectives : 1151 ( 47 ~; 6 |; 28 &; 735 @)
% 0.30/0.46 % ( 14 <=>; 321 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 141 ( 2 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 64 ( 64 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 154 ( 151 usr; 135 con; 0-2 aty)
% 0.30/0.46 % Number of variables : 386 ( 30 ^; 327 !; 29 ?; 386 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : http://mathgate.info/detsetitem.php?id=493
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(in_type,type,
% 0.30/0.46 in: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(exu_type,type,
% 0.30/0.46 exu: ( $i > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(exu,definition,
% 0.30/0.46 ( exu
% 0.30/0.46 = ( ^ [Xphi: $i > $o] :
% 0.30/0.46 ? [Xx: $i] :
% 0.30/0.46 ( ( Xphi @ Xx )
% 0.30/0.46 & ! [Xy: $i] :
% 0.30/0.46 ( ( Xphi @ Xy )
% 0.30/0.46 => ( Xx = Xy ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setextAx_type,type,
% 0.30/0.46 setextAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setextAx,definition,
% 0.30/0.46 ( setextAx
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 <=> ( in @ Xx @ B ) )
% 0.30/0.46 => ( A = B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptyset_type,type,
% 0.30/0.46 emptyset: $i ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetAx_type,type,
% 0.30/0.46 emptysetAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetAx,definition,
% 0.30/0.46 ( emptysetAx
% 0.30/0.46 = ( ! [Xx: $i] :
% 0.30/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoin_type,type,
% 0.30/0.46 setadjoin: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinAx_type,type,
% 0.30/0.46 setadjoinAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinAx,definition,
% 0.30/0.46 ( setadjoinAx
% 0.30/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.30/0.46 <=> ( ( Xy = Xx )
% 0.30/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(powerset_type,type,
% 0.30/0.46 powerset: $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(powersetAx_type,type,
% 0.30/0.46 powersetAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(powersetAx,definition,
% 0.30/0.46 ( powersetAx
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.30/0.46 <=> ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setunion_type,type,
% 0.30/0.46 setunion: $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(setunionAx_type,type,
% 0.30/0.46 setunionAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setunionAx,definition,
% 0.30/0.46 ( setunionAx
% 0.30/0.46 = ( ! [A: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.30/0.46 <=> ? [B: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 & ( in @ B @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(omega_type,type,
% 0.30/0.46 omega: $i ).
% 0.30/0.46
% 0.30/0.46 thf(omega0Ax_type,type,
% 0.30/0.46 omega0Ax: $o ).
% 0.30/0.46
% 0.30/0.46 thf(omega0Ax,definition,
% 0.30/0.46 ( omega0Ax
% 0.30/0.46 = ( in @ emptyset @ omega ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(omegaSAx_type,type,
% 0.30/0.46 omegaSAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(omegaSAx,definition,
% 0.30/0.46 ( omegaSAx
% 0.30/0.46 = ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ omega )
% 0.30/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(omegaIndAx_type,type,
% 0.30/0.46 omegaIndAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(omegaIndAx,definition,
% 0.30/0.46 ( omegaIndAx
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ( ( in @ emptyset @ A )
% 0.30/0.46 & ! [Xx: $i] :
% 0.30/0.46 ( ( ( in @ Xx @ omega )
% 0.30/0.46 & ( in @ Xx @ A ) )
% 0.30/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ omega )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(replAx_type,type,
% 0.30/0.46 replAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(replAx,definition,
% 0.30/0.46 ( replAx
% 0.30/0.46 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( exu
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.30/0.46 => ? [B: $i] :
% 0.30/0.46 ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 <=> ? [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ A )
% 0.30/0.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(foundationAx_type,type,
% 0.30/0.46 foundationAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(foundationAx,definition,
% 0.30/0.46 ( foundationAx
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.30/0.46 => ? [B: $i] :
% 0.30/0.46 ( ( in @ B @ A )
% 0.30/0.46 & ~ ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(wellorderingAx_type,type,
% 0.30/0.46 wellorderingAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(wellorderingAx,definition,
% 0.30/0.46 ( wellorderingAx
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ? [B: $i] :
% 0.30/0.46 ( ! [C: $i] :
% 0.30/0.46 ( ( in @ C @ B )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ C )
% 0.30/0.46 => ( in @ Xx @ A ) ) )
% 0.30/0.46 & ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( ( in @ Xx @ A )
% 0.30/0.46 & ( in @ Xy @ A ) )
% 0.30/0.46 => ( ! [C: $i] :
% 0.30/0.46 ( ( in @ C @ B )
% 0.30/0.46 => ( ( in @ Xx @ C )
% 0.30/0.46 <=> ( in @ Xy @ C ) ) )
% 0.30/0.46 => ( Xx = Xy ) ) )
% 0.30/0.46 & ! [C: $i,D: $i] :
% 0.30/0.46 ( ( ( in @ C @ B )
% 0.30/0.46 & ( in @ D @ B ) )
% 0.30/0.46 => ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ C )
% 0.30/0.46 => ( in @ Xx @ D ) )
% 0.30/0.46 | ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ D )
% 0.30/0.46 => ( in @ Xx @ C ) ) ) )
% 0.30/0.46 & ! [C: $i] :
% 0.30/0.46 ( ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ C )
% 0.30/0.46 => ( in @ Xx @ A ) )
% 0.30/0.46 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.30/0.46 => ? [D: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ D @ B )
% 0.30/0.46 & ( in @ Xx @ C )
% 0.30/0.46 & ~ ? [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ D )
% 0.30/0.46 & ( in @ Xy @ C ) )
% 0.30/0.46 & ! [E: $i] :
% 0.30/0.46 ( ( in @ E @ B )
% 0.30/0.46 => ( ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ E )
% 0.30/0.46 => ( in @ Xy @ D ) )
% 0.30/0.46 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(descr_type,type,
% 0.30/0.46 descr: ( $i > $o ) > $i ).
% 0.30/0.46
% 0.30/0.46 thf(descrp_type,type,
% 0.30/0.46 descrp: $o ).
% 0.30/0.46
% 0.30/0.46 thf(descrp,definition,
% 0.30/0.46 ( descrp
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 => ( Xphi
% 0.30/0.46 @ ( descr
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstr_type,type,
% 0.30/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrI_type,type,
% 0.30/0.46 dsetconstrI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrI,definition,
% 0.30/0.46 ( dsetconstrI
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ( Xphi @ Xx )
% 0.30/0.46 => ( in @ Xx
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrEL_type,type,
% 0.30/0.46 dsetconstrEL: $o ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrEL,definition,
% 0.30/0.46 ( dsetconstrEL
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrER_type,type,
% 0.30/0.46 dsetconstrER: $o ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrER,definition,
% 0.30/0.46 ( dsetconstrER
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exuE1_type,type,
% 0.30/0.46 exuE1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(exuE1,definition,
% 0.30/0.46 ( exuE1
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 => ? [Xx: $i] :
% 0.30/0.46 ( ( Xphi @ Xx )
% 0.30/0.46 & ! [Xy: $i] :
% 0.30/0.46 ( ( Xphi @ Xy )
% 0.30/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(prop2set_type,type,
% 0.30/0.46 prop2set: $o > $i ).
% 0.30/0.46
% 0.30/0.46 thf(prop2setE_type,type,
% 0.30/0.46 prop2setE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(prop2setE,definition,
% 0.30/0.46 ( prop2setE
% 0.30/0.46 = ( ! [Xphi: $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.30/0.46 => Xphi ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetE_type,type,
% 0.30/0.46 emptysetE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetE,definition,
% 0.30/0.46 ( emptysetE
% 0.30/0.46 = ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ emptyset )
% 0.30/0.46 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetimpfalse_type,type,
% 0.30/0.46 emptysetimpfalse: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetimpfalse,definition,
% 0.30/0.46 ( emptysetimpfalse
% 0.30/0.46 = ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ emptyset )
% 0.30/0.46 => $false ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(notinemptyset_type,type,
% 0.30/0.46 notinemptyset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(notinemptyset,definition,
% 0.30/0.46 ( notinemptyset
% 0.30/0.46 = ( ! [Xx: $i] :
% 0.30/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exuE3e_type,type,
% 0.30/0.46 exuE3e: $o ).
% 0.30/0.46
% 0.30/0.46 thf(exuE3e,definition,
% 0.30/0.46 ( exuE3e
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setext_type,type,
% 0.30/0.46 setext: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setext,definition,
% 0.30/0.46 ( setext
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ B ) )
% 0.30/0.46 => ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ A ) )
% 0.30/0.46 => ( A = B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptyI_type,type,
% 0.30/0.46 emptyI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptyI,definition,
% 0.30/0.46 ( emptyI
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ~ ( in @ Xx @ A )
% 0.30/0.46 => ( A = emptyset ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(noeltsimpempty_type,type,
% 0.30/0.46 noeltsimpempty: $o ).
% 0.30/0.46
% 0.30/0.46 thf(noeltsimpempty,definition,
% 0.30/0.46 ( noeltsimpempty
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ~ ( in @ Xx @ A )
% 0.30/0.46 => ( A = emptyset ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setbeta_type,type,
% 0.30/0.46 setbeta: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setbeta,definition,
% 0.30/0.46 ( setbeta
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ( in @ Xx
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/0.46 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(nonempty_type,type,
% 0.30/0.46 nonempty: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(nonempty,definition,
% 0.30/0.46 ( nonempty
% 0.30/0.46 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyE1_type,type,
% 0.30/0.46 nonemptyE1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyE1,definition,
% 0.30/0.46 ( nonemptyE1
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ( nonempty @ A )
% 0.30/0.46 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyI_type,type,
% 0.30/0.46 nonemptyI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyI,definition,
% 0.30/0.46 ( nonemptyI
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ( Xphi @ Xx )
% 0.30/0.46 => ( nonempty
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyI1_type,type,
% 0.30/0.46 nonemptyI1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyI1,definition,
% 0.30/0.46 ( nonemptyI1
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.30/0.46 => ( nonempty @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinIL_type,type,
% 0.30/0.46 setadjoinIL: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinIL,definition,
% 0.30/0.46 ( setadjoinIL
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptyinunitempty_type,type,
% 0.30/0.46 emptyinunitempty: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptyinunitempty,definition,
% 0.30/0.46 ( emptyinunitempty
% 0.30/0.46 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinIR_type,type,
% 0.30/0.46 setadjoinIR: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinIR,definition,
% 0.30/0.46 ( setadjoinIR
% 0.30/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ A )
% 0.30/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinE_type,type,
% 0.30/0.46 setadjoinE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinE,definition,
% 0.30/0.46 ( setadjoinE
% 0.30/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.30/0.46 => ! [Xphi: $o] :
% 0.30/0.46 ( ( ( Xy = Xx )
% 0.30/0.46 => Xphi )
% 0.30/0.46 => ( ( ( in @ Xy @ A )
% 0.30/0.46 => Xphi )
% 0.30/0.46 => Xphi ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinOr_type,type,
% 0.30/0.46 setadjoinOr: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinOr,definition,
% 0.30/0.46 ( setadjoinOr
% 0.30/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.30/0.46 => ( ( Xy = Xx )
% 0.30/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setoftrueEq_type,type,
% 0.30/0.46 setoftrueEq: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setoftrueEq,definition,
% 0.30/0.46 ( setoftrueEq
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xx: $i] : $true )
% 0.30/0.46 = A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(powersetI_type,type,
% 0.30/0.46 powersetI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(powersetI,definition,
% 0.30/0.46 ( powersetI
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ A ) )
% 0.30/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptyinPowerset_type,type,
% 0.30/0.46 emptyinPowerset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptyinPowerset,definition,
% 0.30/0.46 ( emptyinPowerset
% 0.30/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptyInPowerset_type,type,
% 0.30/0.46 emptyInPowerset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptyInPowerset,definition,
% 0.30/0.46 ( emptyInPowerset
% 0.30/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(powersetE_type,type,
% 0.30/0.46 powersetE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(powersetE,definition,
% 0.30/0.46 ( powersetE
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.30/0.46 => ( ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setunionI_type,type,
% 0.30/0.46 setunionI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setunionI,definition,
% 0.30/0.46 ( setunionI
% 0.30/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 => ( ( in @ B @ A )
% 0.30/0.46 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setunionE_type,type,
% 0.30/0.46 setunionE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setunionE,definition,
% 0.30/0.46 ( setunionE
% 0.30/0.46 = ( ! [A: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.30/0.46 => ! [Xphi: $o] :
% 0.30/0.46 ( ! [B: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 => ( ( in @ B @ A )
% 0.30/0.46 => Xphi ) )
% 0.30/0.46 => Xphi ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subPowSU_type,type,
% 0.30/0.46 subPowSU: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subPowSU,definition,
% 0.30/0.46 ( subPowSU
% 0.30/0.46 = ( ! [A: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exuE2_type,type,
% 0.30/0.46 exuE2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(exuE2,definition,
% 0.30/0.46 ( exuE2
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 => ? [Xx: $i] :
% 0.30/0.46 ! [Xy: $i] :
% 0.30/0.46 ( ( Xphi @ Xy )
% 0.30/0.46 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyImpWitness_type,type,
% 0.30/0.46 nonemptyImpWitness: $o ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyImpWitness,definition,
% 0.30/0.46 ( nonemptyImpWitness
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ( nonempty @ A )
% 0.30/0.46 => ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & $true ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(uniqinunit_type,type,
% 0.30/0.46 uniqinunit: $o ).
% 0.30/0.46
% 0.30/0.46 thf(uniqinunit,definition,
% 0.30/0.46 ( uniqinunit
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.30/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(notinsingleton_type,type,
% 0.30/0.46 notinsingleton: $o ).
% 0.30/0.46
% 0.30/0.46 thf(notinsingleton,definition,
% 0.30/0.46 ( notinsingleton
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xx != Xy )
% 0.30/0.46 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(eqinunit_type,type,
% 0.30/0.46 eqinunit: $o ).
% 0.30/0.46
% 0.30/0.46 thf(eqinunit,definition,
% 0.30/0.46 ( eqinunit
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xx = Xy )
% 0.30/0.46 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(singletonsswitch_type,type,
% 0.30/0.46 singletonsswitch: $o ).
% 0.30/0.46
% 0.30/0.46 thf(singletonsswitch,definition,
% 0.30/0.46 ( singletonsswitch
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.30/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(upairsetE_type,type,
% 0.30/0.46 upairsetE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(upairsetE,definition,
% 0.30/0.46 ( upairsetE
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.30/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.30/0.46 => ( ( Xz = Xx )
% 0.30/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(upairsetIL_type,type,
% 0.30/0.46 upairsetIL: $o ).
% 0.30/0.46
% 0.30/0.46 thf(upairsetIL,definition,
% 0.30/0.46 ( upairsetIL
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(upairsetIR_type,type,
% 0.30/0.46 upairsetIR: $o ).
% 0.30/0.46
% 0.30/0.46 thf(upairsetIR,definition,
% 0.30/0.46 ( upairsetIR
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptyE1_type,type,
% 0.30/0.46 emptyE1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptyE1,definition,
% 0.30/0.46 ( emptyE1
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ( Xphi @ Xx ) )
% 0.30/0.46 => ( ( ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 = emptyset )
% 0.30/0.46 => $false ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(vacuousDall_type,type,
% 0.30/0.46 vacuousDall: $o ).
% 0.30/0.46
% 0.30/0.46 thf(vacuousDall,definition,
% 0.30/0.46 ( vacuousDall
% 0.30/0.46 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ emptyset )
% 0.30/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(quantDeMorgan1_type,type,
% 0.30/0.46 quantDeMorgan1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(quantDeMorgan1,definition,
% 0.30/0.46 ( quantDeMorgan1
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ~ ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( Xphi @ Xx ) )
% 0.30/0.46 => ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(quantDeMorgan2_type,type,
% 0.30/0.46 quantDeMorgan2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(quantDeMorgan2,definition,
% 0.30/0.46 ( quantDeMorgan2
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ~ ( Xphi @ Xx ) )
% 0.30/0.46 => ~ ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(quantDeMorgan3_type,type,
% 0.30/0.46 quantDeMorgan3: $o ).
% 0.30/0.46
% 0.30/0.46 thf(quantDeMorgan3,definition,
% 0.30/0.46 ( quantDeMorgan3
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ~ ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ( Xphi @ Xx ) )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(quantDeMorgan4_type,type,
% 0.30/0.46 quantDeMorgan4: $o ).
% 0.30/0.46
% 0.30/0.46 thf(quantDeMorgan4,definition,
% 0.30/0.46 ( quantDeMorgan4
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ~ ( Xphi @ Xx ) )
% 0.30/0.46 => ~ ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(prop2setI_type,type,
% 0.30/0.46 prop2setI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(prop2setI,definition,
% 0.30/0.46 ( prop2setI
% 0.30/0.46 = ( ! [Xphi: $o] :
% 0.30/0.46 ( Xphi
% 0.30/0.46 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(set2prop_type,type,
% 0.30/0.46 set2prop: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(prop2set2propI_type,type,
% 0.30/0.46 prop2set2propI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(prop2set2propI,definition,
% 0.30/0.46 ( prop2set2propI
% 0.30/0.46 = ( ! [Xphi: $o] :
% 0.30/0.46 ( Xphi
% 0.30/0.46 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(notdexE_type,type,
% 0.30/0.46 notdexE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(notdexE,definition,
% 0.30/0.46 ( notdexE
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ~ ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ( Xphi @ Xx ) )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(notdallE_type,type,
% 0.30/0.46 notdallE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(notdallE,definition,
% 0.30/0.46 ( notdallE
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ~ ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( Xphi @ Xx ) )
% 0.30/0.46 => ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exuI1_type,type,
% 0.30/0.46 exuI1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(exuI1,definition,
% 0.30/0.46 ( exuI1
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ? [Xx: $i] :
% 0.30/0.46 ( ( Xphi @ Xx )
% 0.30/0.46 & ! [Xy: $i] :
% 0.30/0.46 ( ( Xphi @ Xy )
% 0.30/0.46 => ( Xx = Xy ) ) )
% 0.30/0.46 => ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exuI3_type,type,
% 0.30/0.46 exuI3: $o ).
% 0.30/0.46
% 0.30/0.46 thf(exuI3,definition,
% 0.30/0.46 ( exuI3
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.30/0.46 => ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xphi @ Xx )
% 0.30/0.46 => ( ( Xphi @ Xy )
% 0.30/0.46 => ( Xx = Xy ) ) )
% 0.30/0.46 => ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exuI2_type,type,
% 0.30/0.46 exuI2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(exuI2,definition,
% 0.30/0.46 ( exuI2
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ? [Xx: $i] :
% 0.30/0.46 ! [Xy: $i] :
% 0.30/0.46 ( ( Xphi @ Xy )
% 0.30/0.46 <=> ( Xy = Xx ) )
% 0.30/0.46 => ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(inCongP_type,type,
% 0.30/0.46 inCongP: $o ).
% 0.30/0.46
% 0.30/0.46 thf(inCongP,definition,
% 0.30/0.46 ( inCongP
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 => ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xx = Xy )
% 0.30/0.46 => ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(in__Cong_type,type,
% 0.30/0.46 in__Cong: $o ).
% 0.30/0.46
% 0.30/0.46 thf(in__Cong,definition,
% 0.30/0.46 ( in__Cong
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 => ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xx = Xy )
% 0.30/0.46 => ( ( in @ Xx @ A )
% 0.30/0.46 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exuE3u_type,type,
% 0.30/0.46 exuE3u: $o ).
% 0.30/0.46
% 0.30/0.46 thf(exuE3u,definition,
% 0.30/0.46 ( exuE3u
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 => ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xphi @ Xx )
% 0.30/0.46 => ( ( Xphi @ Xy )
% 0.30/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exu__Cong_type,type,
% 0.30/0.46 exu__Cong: $o ).
% 0.30/0.46
% 0.30/0.46 thf(exu__Cong,definition,
% 0.30/0.46 ( exu__Cong
% 0.30/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.30/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xx = Xy )
% 0.30/0.46 => ( ( Xphi @ Xx )
% 0.30/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.30/0.46 => ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 <=> ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptyset__Cong_type,type,
% 0.30/0.46 emptyset__Cong: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptyset__Cong,definition,
% 0.30/0.46 ( emptyset__Cong
% 0.30/0.46 = ( emptyset = emptyset ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoin__Cong_type,type,
% 0.30/0.46 setadjoin__Cong: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoin__Cong,definition,
% 0.30/0.46 ( setadjoin__Cong
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xx = Xy )
% 0.30/0.46 => ! [Xz: $i,Xu: $i] :
% 0.30/0.46 ( ( Xz = Xu )
% 0.30/0.46 => ( ( setadjoin @ Xx @ Xz )
% 0.30/0.46 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(powerset__Cong_type,type,
% 0.30/0.46 powerset__Cong: $o ).
% 0.30/0.46
% 0.30/0.46 thf(powerset__Cong,definition,
% 0.30/0.46 ( powerset__Cong
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 => ( ( powerset @ A )
% 0.30/0.46 = ( powerset @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setunion__Cong_type,type,
% 0.30/0.46 setunion__Cong: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setunion__Cong,definition,
% 0.30/0.46 ( setunion__Cong
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 => ( ( setunion @ A )
% 0.30/0.46 = ( setunion @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(omega__Cong_type,type,
% 0.30/0.46 omega__Cong: $o ).
% 0.30/0.46
% 0.30/0.46 thf(omega__Cong,definition,
% 0.30/0.46 ( omega__Cong
% 0.30/0.46 = ( omega = omega ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exuEu_type,type,
% 0.30/0.46 exuEu: $o ).
% 0.30/0.46
% 0.30/0.46 thf(exuEu,definition,
% 0.30/0.46 ( exuEu
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 => ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xphi @ Xx )
% 0.30/0.46 => ( ( Xphi @ Xy )
% 0.30/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(descr__Cong_type,type,
% 0.30/0.46 descr__Cong: $o ).
% 0.30/0.46
% 0.30/0.46 thf(descr__Cong,definition,
% 0.30/0.46 ( descr__Cong
% 0.30/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.30/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xx = Xy )
% 0.30/0.46 => ( ( Xphi @ Xx )
% 0.30/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.30/0.46 => ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 => ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.30/0.46 => ( ( descr
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 = ( descr
% 0.30/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstr__Cong_type,type,
% 0.30/0.46 dsetconstr__Cong: $o ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstr__Cong,definition,
% 0.30/0.46 ( dsetconstr__Cong
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ B )
% 0.30/0.46 => ( ( Xx = Xy )
% 0.30/0.46 => ( ( Xphi @ Xx )
% 0.30/0.46 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.30/0.46 => ( ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 = ( dsetconstr @ B
% 0.30/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subset_type,type,
% 0.30/0.46 subset: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(disjoint_type,type,
% 0.30/0.46 disjoint: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(setsmeet_type,type,
% 0.30/0.46 setsmeet: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetI1_type,type,
% 0.30/0.46 subsetI1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetI1,definition,
% 0.30/0.46 ( subsetI1
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ B ) )
% 0.30/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(eqimpsubset2_type,type,
% 0.30/0.46 eqimpsubset2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(eqimpsubset2,definition,
% 0.30/0.46 ( eqimpsubset2
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(eqimpsubset1_type,type,
% 0.30/0.46 eqimpsubset1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(eqimpsubset1,definition,
% 0.30/0.46 ( eqimpsubset1
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( A = B )
% 0.30/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subsetI2_type,type,
% 0.30/0.46 subsetI2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetI2,definition,
% 0.30/0.46 ( subsetI2
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ B ) )
% 0.30/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetsubset_type,type,
% 0.30/0.46 emptysetsubset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetsubset,definition,
% 0.30/0.46 ( emptysetsubset
% 0.30/0.46 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subsetE_type,type,
% 0.30/0.46 subsetE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetE,definition,
% 0.30/0.46 ( subsetE
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( subset @ A @ B )
% 0.30/0.46 => ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subsetE2_type,type,
% 0.30/0.46 subsetE2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetE2,definition,
% 0.30/0.46 ( subsetE2
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( subset @ A @ B )
% 0.30/0.46 => ( ~ ( in @ Xx @ B )
% 0.30/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(notsubsetI_type,type,
% 0.30/0.46 notsubsetI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(notsubsetI,definition,
% 0.30/0.46 ( notsubsetI
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ~ ( in @ Xx @ B )
% 0.30/0.46 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(notequalI1_type,type,
% 0.30/0.46 notequalI1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(notequalI1,definition,
% 0.30/0.46 ( notequalI1
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ~ ( subset @ A @ B )
% 0.30/0.46 => ( A != B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(notequalI2_type,type,
% 0.30/0.46 notequalI2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(notequalI2,definition,
% 0.30/0.46 ( notequalI2
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ~ ( in @ Xx @ B )
% 0.30/0.46 => ( A != B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subsetRefl_type,type,
% 0.30/0.46 subsetRefl: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetRefl,definition,
% 0.30/0.46 ( subsetRefl
% 0.30/0.46 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subsetTrans_type,type,
% 0.30/0.46 subsetTrans: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetTrans,definition,
% 0.30/0.46 ( subsetTrans
% 0.30/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.30/0.46 ( ( subset @ A @ B )
% 0.30/0.46 => ( ( subset @ B @ C )
% 0.30/0.46 => ( subset @ A @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinSub_type,type,
% 0.30/0.46 setadjoinSub: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinSub,definition,
% 0.30/0.46 ( setadjoinSub
% 0.30/0.46 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinSub2_type,type,
% 0.30/0.46 setadjoinSub2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinSub2,definition,
% 0.30/0.46 ( setadjoinSub2
% 0.30/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.30/0.46 ( ( subset @ A @ B )
% 0.30/0.46 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subset2powerset_type,type,
% 0.30/0.46 subset2powerset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subset2powerset,definition,
% 0.30/0.46 ( subset2powerset
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( subset @ A @ B )
% 0.30/0.46 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setextsub_type,type,
% 0.30/0.46 setextsub: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setextsub,definition,
% 0.30/0.46 ( setextsub
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( subset @ A @ B )
% 0.30/0.46 => ( ( subset @ B @ A )
% 0.30/0.46 => ( A = B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subsetemptysetimpeq_type,type,
% 0.30/0.46 subsetemptysetimpeq: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetemptysetimpeq,definition,
% 0.30/0.46 ( subsetemptysetimpeq
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ( subset @ A @ emptyset )
% 0.30/0.46 => ( A = emptyset ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(powersetI1_type,type,
% 0.30/0.46 powersetI1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(powersetI1,definition,
% 0.30/0.46 ( powersetI1
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( subset @ B @ A )
% 0.30/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(powersetE1_type,type,
% 0.30/0.46 powersetE1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(powersetE1,definition,
% 0.30/0.46 ( powersetE1
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.30/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(inPowerset_type,type,
% 0.30/0.46 inPowerset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(inPowerset,definition,
% 0.30/0.46 ( inPowerset
% 0.30/0.46 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(powersetsubset_type,type,
% 0.30/0.46 powersetsubset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(powersetsubset,definition,
% 0.30/0.46 ( powersetsubset
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( subset @ A @ B )
% 0.30/0.46 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sepInPowerset_type,type,
% 0.30/0.46 sepInPowerset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(sepInPowerset,definition,
% 0.30/0.46 ( sepInPowerset
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( in
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 @ ( powerset @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sepSubset_type,type,
% 0.30/0.46 sepSubset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(sepSubset,definition,
% 0.30/0.46 ( sepSubset
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( subset
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binunion_type,type,
% 0.30/0.46 binunion: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(binunionIL_type,type,
% 0.30/0.46 binunionIL: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binunionIL,definition,
% 0.30/0.46 ( binunionIL
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(upairset2IR_type,type,
% 0.30/0.46 upairset2IR: $o ).
% 0.30/0.46
% 0.30/0.46 thf(upairset2IR,definition,
% 0.30/0.46 ( upairset2IR
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binunionIR_type,type,
% 0.30/0.46 binunionIR: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binunionIR,definition,
% 0.30/0.46 ( binunionIR
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binunionEcases_type,type,
% 0.30/0.46 binunionEcases: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binunionEcases,definition,
% 0.30/0.46 ( binunionEcases
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.30/0.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.30/0.46 => ( ( ( in @ Xx @ A )
% 0.30/0.46 => Xphi )
% 0.30/0.46 => ( ( ( in @ Xx @ B )
% 0.30/0.46 => Xphi )
% 0.30/0.46 => Xphi ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binunionE_type,type,
% 0.30/0.46 binunionE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binunionE,definition,
% 0.30/0.46 ( binunionE
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.30/0.46 => ( ( in @ Xx @ A )
% 0.30/0.46 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binunionLsub_type,type,
% 0.30/0.46 binunionLsub: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binunionLsub,definition,
% 0.30/0.46 ( binunionLsub
% 0.30/0.46 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binunionRsub_type,type,
% 0.30/0.46 binunionRsub: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binunionRsub,definition,
% 0.30/0.46 ( binunionRsub
% 0.30/0.46 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersect_type,type,
% 0.30/0.46 binintersect: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectI_type,type,
% 0.30/0.46 binintersectI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectI,definition,
% 0.30/0.46 ( binintersectI
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectSubset5_type,type,
% 0.30/0.46 binintersectSubset5: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectSubset5,definition,
% 0.30/0.46 ( binintersectSubset5
% 0.30/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.30/0.46 ( ( subset @ C @ A )
% 0.30/0.46 => ( ( subset @ C @ B )
% 0.30/0.46 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectEL_type,type,
% 0.30/0.46 binintersectEL: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectEL,definition,
% 0.30/0.46 ( binintersectEL
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectLsub_type,type,
% 0.30/0.46 binintersectLsub: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectLsub,definition,
% 0.30/0.46 ( binintersectLsub
% 0.30/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectSubset2_type,type,
% 0.30/0.46 binintersectSubset2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectSubset2,definition,
% 0.30/0.46 ( binintersectSubset2
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( subset @ A @ B )
% 0.30/0.46 => ( ( binintersect @ A @ B )
% 0.30/0.46 = A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectSubset3_type,type,
% 0.30/0.46 binintersectSubset3: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectSubset3,definition,
% 0.30/0.46 ( binintersectSubset3
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( ( binintersect @ A @ B )
% 0.30/0.46 = B )
% 0.30/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectER_type,type,
% 0.30/0.46 binintersectER: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectER,definition,
% 0.30/0.46 ( binintersectER
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.30/0.46 => ( in @ Xx @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(disjointsetsI1_type,type,
% 0.30/0.46 disjointsetsI1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(disjointsetsI1,definition,
% 0.30/0.46 ( disjointsetsI1
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ~ ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ( in @ Xx @ B ) )
% 0.30/0.46 => ( ( binintersect @ A @ B )
% 0.30/0.46 = emptyset ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectRsub_type,type,
% 0.30/0.46 binintersectRsub: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectRsub,definition,
% 0.30/0.46 ( binintersectRsub
% 0.30/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectSubset4_type,type,
% 0.30/0.46 binintersectSubset4: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectSubset4,definition,
% 0.30/0.46 ( binintersectSubset4
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( subset @ B @ A )
% 0.30/0.46 => ( ( binintersect @ A @ B )
% 0.30/0.46 = B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectSubset1_type,type,
% 0.30/0.46 binintersectSubset1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(binintersectSubset1,definition,
% 0.30/0.46 ( binintersectSubset1
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( ( binintersect @ A @ B )
% 0.30/0.46 = A )
% 0.30/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(bs114d_type,type,
% 0.30/0.46 bs114d: $o ).
% 0.30/0.46
% 0.30/0.46 thf(bs114d,definition,
% 0.30/0.46 ( bs114d
% 0.30/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.30/0.46 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.30/0.46 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(regular_type,type,
% 0.30/0.46 regular: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminus_type,type,
% 0.30/0.46 setminus: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(setminusI_type,type,
% 0.30/0.46 setminusI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminusI,definition,
% 0.30/0.46 ( setminusI
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ~ ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setminusEL_type,type,
% 0.30/0.46 setminusEL: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminusEL,definition,
% 0.30/0.46 ( setminusEL
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setminusER_type,type,
% 0.30/0.46 setminusER: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminusER,definition,
% 0.30/0.46 ( setminusER
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.30/0.46 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setminusSubset2_type,type,
% 0.30/0.46 setminusSubset2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminusSubset2,definition,
% 0.30/0.46 ( setminusSubset2
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( subset @ A @ B )
% 0.30/0.46 => ( ( setminus @ A @ B )
% 0.30/0.46 = emptyset ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setminusERneg_type,type,
% 0.30/0.46 setminusERneg: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminusERneg,definition,
% 0.30/0.46 ( setminusERneg
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.30/0.46 => ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setminusELneg_type,type,
% 0.30/0.46 setminusELneg: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminusELneg,definition,
% 0.30/0.46 ( setminusELneg
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.30/0.46 => ( ~ ( in @ Xx @ B )
% 0.30/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setminusILneg_type,type,
% 0.30/0.46 setminusILneg: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminusILneg,definition,
% 0.30/0.46 ( setminusILneg
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ~ ( in @ Xx @ A )
% 0.30/0.46 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setminusIRneg_type,type,
% 0.30/0.46 setminusIRneg: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminusIRneg,definition,
% 0.30/0.46 ( setminusIRneg
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setminusLsub_type,type,
% 0.30/0.46 setminusLsub: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminusLsub,definition,
% 0.30/0.46 ( setminusLsub
% 0.30/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setminusSubset1_type,type,
% 0.30/0.46 setminusSubset1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminusSubset1,definition,
% 0.30/0.46 ( setminusSubset1
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( ( setminus @ A @ B )
% 0.30/0.46 = emptyset )
% 0.30/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(symdiff_type,type,
% 0.30/0.46 symdiff: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(symdiffE_type,type,
% 0.30/0.46 symdiffE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(symdiffE,definition,
% 0.30/0.46 ( symdiffE
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.30/0.46 => ! [Xphi: $o] :
% 0.30/0.46 ( ( ( in @ Xx @ A )
% 0.30/0.46 => ( ~ ( in @ Xx @ B )
% 0.30/0.46 => Xphi ) )
% 0.30/0.46 => ( ( ~ ( in @ Xx @ A )
% 0.30/0.46 => ( ( in @ Xx @ B )
% 0.30/0.46 => Xphi ) )
% 0.30/0.46 => Xphi ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(symdiffI1_type,type,
% 0.30/0.46 symdiffI1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(symdiffI1,definition,
% 0.30/0.46 ( symdiffI1
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ~ ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(symdiffI2_type,type,
% 0.30/0.46 symdiffI2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(symdiffI2,definition,
% 0.30/0.46 ( symdiffI2
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ~ ( in @ Xx @ A )
% 0.30/0.46 => ( ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(symdiffIneg1_type,type,
% 0.30/0.46 symdiffIneg1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(symdiffIneg1,definition,
% 0.30/0.46 ( symdiffIneg1
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ( in @ Xx @ B )
% 0.30/0.46 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(symdiffIneg2,conjecture,
% 0.30/0.46 ( setextAx
% 0.30/0.46 => ( emptysetAx
% 0.30/0.46 => ( setadjoinAx
% 0.30/0.46 => ( powersetAx
% 0.30/0.46 => ( setunionAx
% 0.30/0.46 => ( omega0Ax
% 0.30/0.46 => ( omegaSAx
% 0.30/0.46 => ( omegaIndAx
% 0.30/0.46 => ( replAx
% 0.30/0.46 => ( foundationAx
% 0.30/0.46 => ( wellorderingAx
% 0.30/0.46 => ( descrp
% 0.30/0.46 => ( dsetconstrI
% 0.30/0.46 => ( dsetconstrEL
% 0.30/0.46 => ( dsetconstrER
% 0.30/0.46 => ( exuE1
% 0.30/0.46 => ( prop2setE
% 0.30/0.46 => ( emptysetE
% 0.30/0.46 => ( emptysetimpfalse
% 0.30/0.46 => ( notinemptyset
% 0.30/0.46 => ( exuE3e
% 0.30/0.46 => ( setext
% 0.30/0.46 => ( emptyI
% 0.30/0.46 => ( noeltsimpempty
% 0.30/0.46 => ( setbeta
% 0.30/0.46 => ( nonemptyE1
% 0.30/0.46 => ( nonemptyI
% 0.30/0.46 => ( nonemptyI1
% 0.30/0.46 => ( setadjoinIL
% 0.30/0.46 => ( emptyinunitempty
% 0.30/0.46 => ( setadjoinIR
% 0.30/0.46 => ( setadjoinE
% 0.30/0.46 => ( setadjoinOr
% 0.30/0.46 => ( setoftrueEq
% 0.30/0.46 => ( powersetI
% 0.30/0.46 => ( emptyinPowerset
% 0.30/0.46 => ( emptyInPowerset
% 0.30/0.46 => ( powersetE
% 0.30/0.46 => ( setunionI
% 0.30/0.46 => ( setunionE
% 0.30/0.46 => ( subPowSU
% 0.30/0.46 => ( exuE2
% 0.30/0.46 => ( nonemptyImpWitness
% 0.30/0.46 => ( uniqinunit
% 0.30/0.46 => ( notinsingleton
% 0.30/0.46 => ( eqinunit
% 0.30/0.46 => ( singletonsswitch
% 0.30/0.46 => ( upairsetE
% 0.30/0.46 => ( upairsetIL
% 0.30/0.46 => ( upairsetIR
% 0.30/0.46 => ( emptyE1
% 0.30/0.46 => ( vacuousDall
% 0.30/0.46 => ( quantDeMorgan1
% 0.30/0.46 => ( quantDeMorgan2
% 0.30/0.46 => ( quantDeMorgan3
% 0.30/0.46 => ( quantDeMorgan4
% 0.30/0.46 => ( prop2setI
% 0.30/0.46 => ( prop2set2propI
% 0.30/0.46 => ( notdexE
% 0.30/0.46 => ( notdallE
% 0.30/0.46 => ( exuI1
% 0.30/0.46 => ( exuI3
% 0.30/0.46 => ( exuI2
% 0.30/0.46 => ( inCongP
% 0.30/0.46 => ( in__Cong
% 0.30/0.46 => ( exuE3u
% 0.30/0.46 => ( exu__Cong
% 0.30/0.46 => ( emptyset__Cong
% 0.30/0.46 => ( setadjoin__Cong
% 0.30/0.46 => ( powerset__Cong
% 0.30/0.46 => ( setunion__Cong
% 0.30/0.46 => ( omega__Cong
% 0.30/0.46 => ( exuEu
% 0.30/0.46 => ( descr__Cong
% 0.30/0.46 => ( dsetconstr__Cong
% 0.30/0.46 => ( subsetI1
% 0.30/0.46 => ( eqimpsubset2
% 0.30/0.46 => ( eqimpsubset1
% 0.30/0.46 => ( subsetI2
% 0.30/0.46 => ( emptysetsubset
% 0.30/0.46 => ( subsetE
% 0.30/0.46 => ( subsetE2
% 0.30/0.46 => ( notsubsetI
% 0.30/0.46 => ( notequalI1
% 0.30/0.46 => ( notequalI2
% 0.30/0.46 => ( subsetRefl
% 0.30/0.46 => ( subsetTrans
% 0.30/0.46 => ( setadjoinSub
% 0.30/0.46 => ( setadjoinSub2
% 0.30/0.46 => ( subset2powerset
% 0.30/0.46 => ( setextsub
% 0.30/0.46 => ( subsetemptysetimpeq
% 0.30/0.46 => ( powersetI1
% 0.30/0.46 => ( powersetE1
% 0.30/0.46 => ( inPowerset
% 0.30/0.46 => ( powersetsubset
% 0.30/0.46 => ( sepInPowerset
% 0.30/0.46 => ( sepSubset
% 0.30/0.46 => ( binunionIL
% 0.30/0.46 => ( upairset2IR
% 0.30/0.46 => ( binunionIR
% 0.30/0.46 => ( binunionEcases
% 0.30/0.46 => ( binunionE
% 0.30/0.46 => ( binunionLsub
% 0.30/0.46 => ( binunionRsub
% 0.30/0.46 => ( binintersectI
% 0.30/0.46 => ( binintersectSubset5
% 0.30/0.46 => ( binintersectEL
% 0.30/0.46 => ( binintersectLsub
% 0.30/0.46 => ( binintersectSubset2
% 0.30/0.46 => ( binintersectSubset3
% 0.30/0.46 => ( binintersectER
% 0.30/0.46 => ( disjointsetsI1
% 0.30/0.46 => ( binintersectRsub
% 0.30/0.46 => ( binintersectSubset4
% 0.30/0.46 => ( binintersectSubset1
% 0.30/0.46 => ( bs114d
% 0.30/0.46 => ( setminusI
% 0.30/0.46 => ( setminusEL
% 0.30/0.46 => ( setminusER
% 0.30/0.46 => ( setminusSubset2
% 0.30/0.46 => ( setminusERneg
% 0.30/0.46 => ( setminusELneg
% 0.30/0.46 => ( setminusILneg
% 0.30/0.46 => ( setminusIRneg
% 0.30/0.46 => ( setminusLsub
% 0.30/0.46 => ( setminusSubset1
% 0.30/0.46 => ( symdiffE
% 0.30/0.46 => ( symdiffI1
% 0.30/0.46 => ( symdiffI2
% 0.30/0.46 => ( symdiffIneg1
% 0.30/0.46 => ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ~ ( in @ Xx @ A )
% 0.30/0.46 => ( ~ ( in @ Xx @ B )
% 0.30/0.46 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 2.34/1.43 ---- Embedded in THF ---
% 2.34/1.43 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.34/1.43 %%% Generated on Tue Feb 24 12:29:10 EST 2026
% 2.34/1.43 %%% using '$$dhol' embedding, version 1.3.0.
% 2.34/1.43 %%% Logic specification used:
% 2.34/1.43 %%% thf(spec, logic, $$dhol).
% 2.34/1.43
% 2.34/1.43 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.75Z7m6xG9f/DTF2DTF28853.p
% See solution above
% 2.34/1.43 ------------------------
% 2.34/1.45 ---- Cleaned THF ---
% 2.34/1.45 thf(in_type,type,
% 2.34/1.45 in: $i > $i > $o ).
% 2.34/1.45
% 2.34/1.45 thf(exu_type,type,
% 2.34/1.45 exu: ( $i > $o ) > $o ).
% 2.34/1.45
% 2.34/1.45 thf(exu,definition,
% 2.34/1.45 ( exu
% 2.34/1.45 = ( ^ [Xphi: $i > $o] :
% 2.34/1.45 ? [Xx: $i] :
% 2.34/1.45 ( ( Xphi @ Xx )
% 2.34/1.45 & ! [Xy: $i] :
% 2.34/1.45 ( ( Xphi @ Xy )
% 2.34/1.45 => ( Xx = Xy ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setextAx_type,type,
% 2.34/1.45 setextAx: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setextAx,definition,
% 2.34/1.45 ( setextAx
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 <=> ( in @ Xx @ B ) )
% 2.34/1.45 => ( A = B ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(emptyset_type,type,
% 2.34/1.45 emptyset: $i ).
% 2.34/1.45
% 2.34/1.45 thf(emptysetAx_type,type,
% 2.34/1.45 emptysetAx: $o ).
% 2.34/1.45
% 2.34/1.45 thf(emptysetAx,definition,
% 2.34/1.45 ( emptysetAx
% 2.34/1.45 = ( ! [Xx: $i] :
% 2.34/1.45 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setadjoin_type,type,
% 2.34/1.45 setadjoin: $i > $i > $i ).
% 2.34/1.45
% 2.34/1.45 thf(setadjoinAx_type,type,
% 2.34/1.45 setadjoinAx: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setadjoinAx,definition,
% 2.34/1.45 ( setadjoinAx
% 2.34/1.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.34/1.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.34/1.45 <=> ( ( Xy = Xx )
% 2.34/1.45 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(powerset_type,type,
% 2.34/1.45 powerset: $i > $i ).
% 2.34/1.45
% 2.34/1.45 thf(powersetAx_type,type,
% 2.34/1.45 powersetAx: $o ).
% 2.34/1.45
% 2.34/1.45 thf(powersetAx,definition,
% 2.34/1.45 ( powersetAx
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ( in @ B @ ( powerset @ A ) )
% 2.34/1.45 <=> ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ B )
% 2.34/1.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setunion_type,type,
% 2.34/1.45 setunion: $i > $i ).
% 2.34/1.45
% 2.34/1.45 thf(setunionAx_type,type,
% 2.34/1.45 setunionAx: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setunionAx,definition,
% 2.34/1.45 ( setunionAx
% 2.34/1.45 = ( ! [A: $i,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ ( setunion @ A ) )
% 2.34/1.45 <=> ? [B: $i] :
% 2.34/1.45 ( ( in @ Xx @ B )
% 2.34/1.45 & ( in @ B @ A ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(omega_type,type,
% 2.34/1.45 omega: $i ).
% 2.34/1.45
% 2.34/1.45 thf(omega0Ax_type,type,
% 2.34/1.45 omega0Ax: $o ).
% 2.34/1.45
% 2.34/1.45 thf(omega0Ax,definition,
% 2.34/1.45 ( omega0Ax
% 2.34/1.45 = ( in @ emptyset @ omega ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(omegaSAx_type,type,
% 2.34/1.45 omegaSAx: $o ).
% 2.34/1.45
% 2.34/1.45 thf(omegaSAx,definition,
% 2.34/1.45 ( omegaSAx
% 2.34/1.45 = ( ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ omega )
% 2.34/1.45 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(omegaIndAx_type,type,
% 2.34/1.45 omegaIndAx: $o ).
% 2.34/1.45
% 2.34/1.45 thf(omegaIndAx,definition,
% 2.34/1.45 ( omegaIndAx
% 2.34/1.45 = ( ! [A: $i] :
% 2.34/1.45 ( ( ( in @ emptyset @ A )
% 2.34/1.45 & ! [Xx: $i] :
% 2.34/1.45 ( ( ( in @ Xx @ omega )
% 2.34/1.45 & ( in @ Xx @ A ) )
% 2.34/1.45 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.34/1.45 => ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ omega )
% 2.34/1.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(replAx_type,type,
% 2.34/1.45 replAx: $o ).
% 2.34/1.45
% 2.34/1.45 thf(replAx,definition,
% 2.34/1.45 ( replAx
% 2.34/1.45 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.34/1.45 ( ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ( exu
% 2.34/1.45 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.34/1.45 => ? [B: $i] :
% 2.34/1.45 ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ B )
% 2.34/1.45 <=> ? [Xy: $i] :
% 2.34/1.45 ( ( in @ Xy @ A )
% 2.34/1.45 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(foundationAx_type,type,
% 2.34/1.45 foundationAx: $o ).
% 2.34/1.45
% 2.34/1.45 thf(foundationAx,definition,
% 2.34/1.45 ( foundationAx
% 2.34/1.45 = ( ! [A: $i] :
% 2.34/1.45 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.34/1.45 => ? [B: $i] :
% 2.34/1.45 ( ( in @ B @ A )
% 2.34/1.45 & ~ ? [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ B )
% 2.34/1.45 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(wellorderingAx_type,type,
% 2.34/1.45 wellorderingAx: $o ).
% 2.34/1.45
% 2.34/1.45 thf(wellorderingAx,definition,
% 2.34/1.45 ( wellorderingAx
% 2.34/1.45 = ( ! [A: $i] :
% 2.34/1.45 ? [B: $i] :
% 2.34/1.45 ( ! [C: $i] :
% 2.34/1.45 ( ( in @ C @ B )
% 2.34/1.45 => ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ C )
% 2.34/1.45 => ( in @ Xx @ A ) ) )
% 2.34/1.45 & ! [Xx: $i,Xy: $i] :
% 2.34/1.45 ( ( ( in @ Xx @ A )
% 2.34/1.45 & ( in @ Xy @ A ) )
% 2.34/1.45 => ( ! [C: $i] :
% 2.34/1.45 ( ( in @ C @ B )
% 2.34/1.45 => ( ( in @ Xx @ C )
% 2.34/1.45 <=> ( in @ Xy @ C ) ) )
% 2.34/1.45 => ( Xx = Xy ) ) )
% 2.34/1.45 & ! [C: $i,D: $i] :
% 2.34/1.45 ( ( ( in @ C @ B )
% 2.34/1.45 & ( in @ D @ B ) )
% 2.34/1.45 => ( ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ C )
% 2.34/1.45 => ( in @ Xx @ D ) )
% 2.34/1.45 | ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ D )
% 2.34/1.45 => ( in @ Xx @ C ) ) ) )
% 2.34/1.45 & ! [C: $i] :
% 2.34/1.45 ( ( ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ C )
% 2.34/1.45 => ( in @ Xx @ A ) )
% 2.34/1.45 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.34/1.45 => ? [D: $i,Xx: $i] :
% 2.34/1.45 ( ( in @ D @ B )
% 2.34/1.45 & ( in @ Xx @ C )
% 2.34/1.45 & ~ ? [Xy: $i] :
% 2.34/1.45 ( ( in @ Xy @ D )
% 2.34/1.45 & ( in @ Xy @ C ) )
% 2.34/1.45 & ! [E: $i] :
% 2.34/1.45 ( ( in @ E @ B )
% 2.34/1.45 => ( ! [Xy: $i] :
% 2.34/1.45 ( ( in @ Xy @ E )
% 2.34/1.45 => ( in @ Xy @ D ) )
% 2.34/1.45 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(descr_type,type,
% 2.34/1.45 descr: ( $i > $o ) > $i ).
% 2.34/1.45
% 2.34/1.45 thf(descrp_type,type,
% 2.34/1.45 descrp: $o ).
% 2.34/1.45
% 2.34/1.45 thf(descrp,definition,
% 2.34/1.45 ( descrp
% 2.34/1.45 = ( ! [Xphi: $i > $o] :
% 2.34/1.45 ( ( exu
% 2.34/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.34/1.45 => ( Xphi
% 2.34/1.45 @ ( descr
% 2.34/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(dsetconstr_type,type,
% 2.34/1.45 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.34/1.45
% 2.34/1.45 thf(dsetconstrI_type,type,
% 2.34/1.45 dsetconstrI: $o ).
% 2.34/1.45
% 2.34/1.45 thf(dsetconstrI,definition,
% 2.34/1.45 ( dsetconstrI
% 2.34/1.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ( ( Xphi @ Xx )
% 2.34/1.45 => ( in @ Xx
% 2.34/1.45 @ ( dsetconstr @ A
% 2.34/1.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(dsetconstrEL_type,type,
% 2.34/1.45 dsetconstrEL: $o ).
% 2.34/1.45
% 2.34/1.45 thf(dsetconstrEL,definition,
% 2.34/1.45 ( dsetconstrEL
% 2.34/1.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx
% 2.34/1.45 @ ( dsetconstr @ A
% 2.34/1.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.34/1.45 => ( in @ Xx @ A ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(dsetconstrER_type,type,
% 2.34/1.45 dsetconstrER: $o ).
% 2.34/1.45
% 2.34/1.45 thf(dsetconstrER,definition,
% 2.34/1.45 ( dsetconstrER
% 2.34/1.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx
% 2.34/1.45 @ ( dsetconstr @ A
% 2.34/1.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.34/1.45 => ( Xphi @ Xx ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(exuE1_type,type,
% 2.34/1.45 exuE1: $o ).
% 2.34/1.45
% 2.34/1.45 thf(exuE1,definition,
% 2.34/1.45 ( exuE1
% 2.34/1.45 = ( ! [Xphi: $i > $o] :
% 2.34/1.45 ( ( exu
% 2.34/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.34/1.45 => ? [Xx: $i] :
% 2.34/1.45 ( ( Xphi @ Xx )
% 2.34/1.45 & ! [Xy: $i] :
% 2.34/1.45 ( ( Xphi @ Xy )
% 2.34/1.45 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(prop2set_type,type,
% 2.34/1.45 prop2set: $o > $i ).
% 2.34/1.45
% 2.34/1.45 thf(prop2setE_type,type,
% 2.34/1.45 prop2setE: $o ).
% 2.34/1.45
% 2.34/1.45 thf(prop2setE,definition,
% 2.34/1.45 ( prop2setE
% 2.34/1.45 = ( ! [Xphi: $o,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.34/1.45 => Xphi ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(emptysetE_type,type,
% 2.34/1.45 emptysetE: $o ).
% 2.34/1.45
% 2.34/1.45 thf(emptysetE,definition,
% 2.34/1.45 ( emptysetE
% 2.34/1.45 = ( ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ emptyset )
% 2.34/1.45 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(emptysetimpfalse_type,type,
% 2.34/1.45 emptysetimpfalse: $o ).
% 2.34/1.45
% 2.34/1.45 thf(emptysetimpfalse,definition,
% 2.34/1.45 ( emptysetimpfalse
% 2.34/1.45 = ( ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ emptyset )
% 2.34/1.45 => $false ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(notinemptyset_type,type,
% 2.34/1.45 notinemptyset: $o ).
% 2.34/1.45
% 2.34/1.45 thf(notinemptyset,definition,
% 2.34/1.45 ( notinemptyset
% 2.34/1.45 = ( ! [Xx: $i] :
% 2.34/1.45 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(exuE3e_type,type,
% 2.34/1.45 exuE3e: $o ).
% 2.34/1.45
% 2.34/1.45 thf(exuE3e,definition,
% 2.34/1.45 ( exuE3e
% 2.34/1.45 = ( ! [Xphi: $i > $o] :
% 2.34/1.45 ( ( exu
% 2.34/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.34/1.45 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setext_type,type,
% 2.34/1.45 setext: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setext,definition,
% 2.34/1.45 ( setext
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ( in @ Xx @ B ) )
% 2.34/1.45 => ( ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ B )
% 2.34/1.45 => ( in @ Xx @ A ) )
% 2.34/1.45 => ( A = B ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(emptyI_type,type,
% 2.34/1.45 emptyI: $o ).
% 2.34/1.45
% 2.34/1.45 thf(emptyI,definition,
% 2.34/1.45 ( emptyI
% 2.34/1.45 = ( ! [A: $i] :
% 2.34/1.45 ( ! [Xx: $i] :
% 2.34/1.45 ~ ( in @ Xx @ A )
% 2.34/1.45 => ( A = emptyset ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(noeltsimpempty_type,type,
% 2.34/1.45 noeltsimpempty: $o ).
% 2.34/1.45
% 2.34/1.45 thf(noeltsimpempty,definition,
% 2.34/1.45 ( noeltsimpempty
% 2.34/1.45 = ( ! [A: $i] :
% 2.34/1.45 ( ! [Xx: $i] :
% 2.34/1.45 ~ ( in @ Xx @ A )
% 2.34/1.45 => ( A = emptyset ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setbeta_type,type,
% 2.34/1.45 setbeta: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setbeta,definition,
% 2.34/1.45 ( setbeta
% 2.34/1.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ( ( in @ Xx
% 2.34/1.45 @ ( dsetconstr @ A
% 2.34/1.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.34/1.45 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(nonempty_type,type,
% 2.34/1.45 nonempty: $i > $o ).
% 2.34/1.45
% 2.34/1.45 thf(nonempty,definition,
% 2.34/1.45 ( nonempty
% 2.34/1.45 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(nonemptyE1_type,type,
% 2.34/1.45 nonemptyE1: $o ).
% 2.34/1.45
% 2.34/1.45 thf(nonemptyE1,definition,
% 2.34/1.45 ( nonemptyE1
% 2.34/1.45 = ( ! [A: $i] :
% 2.34/1.45 ( ( nonempty @ A )
% 2.34/1.45 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(nonemptyI_type,type,
% 2.34/1.45 nonemptyI: $o ).
% 2.34/1.45
% 2.34/1.45 thf(nonemptyI,definition,
% 2.34/1.45 ( nonemptyI
% 2.34/1.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ( ( Xphi @ Xx )
% 2.34/1.45 => ( nonempty
% 2.34/1.45 @ ( dsetconstr @ A
% 2.34/1.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(nonemptyI1_type,type,
% 2.34/1.45 nonemptyI1: $o ).
% 2.34/1.45
% 2.34/1.45 thf(nonemptyI1,definition,
% 2.34/1.45 ( nonemptyI1
% 2.34/1.45 = ( ! [A: $i] :
% 2.34/1.45 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.34/1.45 => ( nonempty @ A ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setadjoinIL_type,type,
% 2.34/1.45 setadjoinIL: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setadjoinIL,definition,
% 2.34/1.45 ( setadjoinIL
% 2.34/1.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(emptyinunitempty_type,type,
% 2.34/1.45 emptyinunitempty: $o ).
% 2.34/1.45
% 2.34/1.45 thf(emptyinunitempty,definition,
% 2.34/1.45 ( emptyinunitempty
% 2.34/1.45 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setadjoinIR_type,type,
% 2.34/1.45 setadjoinIR: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setadjoinIR,definition,
% 2.34/1.45 ( setadjoinIR
% 2.34/1.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.34/1.45 ( ( in @ Xy @ A )
% 2.34/1.45 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setadjoinE_type,type,
% 2.34/1.45 setadjoinE: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setadjoinE,definition,
% 2.34/1.45 ( setadjoinE
% 2.34/1.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.34/1.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.34/1.45 => ! [Xphi: $o] :
% 2.34/1.45 ( ( ( Xy = Xx )
% 2.34/1.45 => Xphi )
% 2.34/1.45 => ( ( ( in @ Xy @ A )
% 2.34/1.45 => Xphi )
% 2.34/1.45 => Xphi ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setadjoinOr_type,type,
% 2.34/1.45 setadjoinOr: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setadjoinOr,definition,
% 2.34/1.45 ( setadjoinOr
% 2.34/1.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.34/1.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.34/1.45 => ( ( Xy = Xx )
% 2.34/1.45 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setoftrueEq_type,type,
% 2.34/1.45 setoftrueEq: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setoftrueEq,definition,
% 2.34/1.45 ( setoftrueEq
% 2.34/1.45 = ( ! [A: $i] :
% 2.34/1.45 ( ( dsetconstr @ A
% 2.34/1.45 @ ^ [Xx: $i] : $true )
% 2.34/1.45 = A ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(powersetI_type,type,
% 2.34/1.45 powersetI: $o ).
% 2.34/1.45
% 2.34/1.45 thf(powersetI,definition,
% 2.34/1.45 ( powersetI
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ B )
% 2.34/1.45 => ( in @ Xx @ A ) )
% 2.34/1.45 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(emptyinPowerset_type,type,
% 2.34/1.45 emptyinPowerset: $o ).
% 2.34/1.45
% 2.34/1.45 thf(emptyinPowerset,definition,
% 2.34/1.45 ( emptyinPowerset
% 2.34/1.45 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(emptyInPowerset_type,type,
% 2.34/1.45 emptyInPowerset: $o ).
% 2.34/1.45
% 2.34/1.45 thf(emptyInPowerset,definition,
% 2.34/1.45 ( emptyInPowerset
% 2.34/1.45 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(powersetE_type,type,
% 2.34/1.45 powersetE: $o ).
% 2.34/1.45
% 2.34/1.45 thf(powersetE,definition,
% 2.34/1.45 ( powersetE
% 2.34/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.34/1.45 ( ( in @ B @ ( powerset @ A ) )
% 2.34/1.45 => ( ( in @ Xx @ B )
% 2.34/1.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setunionI_type,type,
% 2.34/1.45 setunionI: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setunionI,definition,
% 2.34/1.45 ( setunionI
% 2.34/1.45 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.34/1.45 ( ( in @ Xx @ B )
% 2.34/1.45 => ( ( in @ B @ A )
% 2.34/1.45 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setunionE_type,type,
% 2.34/1.45 setunionE: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setunionE,definition,
% 2.34/1.45 ( setunionE
% 2.34/1.45 = ( ! [A: $i,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ ( setunion @ A ) )
% 2.34/1.45 => ! [Xphi: $o] :
% 2.34/1.45 ( ! [B: $i] :
% 2.34/1.45 ( ( in @ Xx @ B )
% 2.34/1.45 => ( ( in @ B @ A )
% 2.34/1.45 => Xphi ) )
% 2.34/1.45 => Xphi ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(subPowSU_type,type,
% 2.34/1.45 subPowSU: $o ).
% 2.34/1.45
% 2.34/1.45 thf(subPowSU,definition,
% 2.34/1.45 ( subPowSU
% 2.34/1.45 = ( ! [A: $i,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(exuE2_type,type,
% 2.34/1.45 exuE2: $o ).
% 2.34/1.45
% 2.34/1.45 thf(exuE2,definition,
% 2.34/1.45 ( exuE2
% 2.34/1.45 = ( ! [Xphi: $i > $o] :
% 2.34/1.45 ( ( exu
% 2.34/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.34/1.45 => ? [Xx: $i] :
% 2.34/1.45 ! [Xy: $i] :
% 2.34/1.45 ( ( Xphi @ Xy )
% 2.34/1.45 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(nonemptyImpWitness_type,type,
% 2.34/1.45 nonemptyImpWitness: $o ).
% 2.34/1.45
% 2.34/1.45 thf(nonemptyImpWitness,definition,
% 2.34/1.45 ( nonemptyImpWitness
% 2.34/1.45 = ( ! [A: $i] :
% 2.34/1.45 ( ( nonempty @ A )
% 2.34/1.45 => ? [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 & $true ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(uniqinunit_type,type,
% 2.34/1.45 uniqinunit: $o ).
% 2.34/1.45
% 2.34/1.45 thf(uniqinunit,definition,
% 2.34/1.45 ( uniqinunit
% 2.34/1.45 = ( ! [Xx: $i,Xy: $i] :
% 2.34/1.45 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.34/1.45 => ( Xx = Xy ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(notinsingleton_type,type,
% 2.34/1.45 notinsingleton: $o ).
% 2.34/1.45
% 2.34/1.45 thf(notinsingleton,definition,
% 2.34/1.45 ( notinsingleton
% 2.34/1.45 = ( ! [Xx: $i,Xy: $i] :
% 2.34/1.45 ( ( Xx != Xy )
% 2.34/1.45 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(eqinunit_type,type,
% 2.34/1.45 eqinunit: $o ).
% 2.34/1.45
% 2.34/1.45 thf(eqinunit,definition,
% 2.34/1.45 ( eqinunit
% 2.34/1.45 = ( ! [Xx: $i,Xy: $i] :
% 2.34/1.45 ( ( Xx = Xy )
% 2.34/1.45 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(singletonsswitch_type,type,
% 2.34/1.45 singletonsswitch: $o ).
% 2.34/1.45
% 2.34/1.45 thf(singletonsswitch,definition,
% 2.34/1.45 ( singletonsswitch
% 2.34/1.45 = ( ! [Xx: $i,Xy: $i] :
% 2.34/1.45 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.34/1.45 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(upairsetE_type,type,
% 2.34/1.45 upairsetE: $o ).
% 2.34/1.45
% 2.34/1.45 thf(upairsetE,definition,
% 2.34/1.45 ( upairsetE
% 2.34/1.45 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.34/1.45 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.34/1.45 => ( ( Xz = Xx )
% 2.34/1.45 | ( Xz = Xy ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(upairsetIL_type,type,
% 2.34/1.45 upairsetIL: $o ).
% 2.34/1.45
% 2.34/1.45 thf(upairsetIL,definition,
% 2.34/1.45 ( upairsetIL
% 2.34/1.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(upairsetIR_type,type,
% 2.34/1.45 upairsetIR: $o ).
% 2.34/1.45
% 2.34/1.45 thf(upairsetIR,definition,
% 2.34/1.45 ( upairsetIR
% 2.34/1.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(emptyE1_type,type,
% 2.34/1.45 emptyE1: $o ).
% 2.34/1.45
% 2.34/1.45 thf(emptyE1,definition,
% 2.34/1.45 ( emptyE1
% 2.34/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.34/1.45 ( ? [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 & ( Xphi @ Xx ) )
% 2.34/1.45 => ( ( ( dsetconstr @ A
% 2.34/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.34/1.45 = emptyset )
% 2.34/1.45 => $false ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(vacuousDall_type,type,
% 2.34/1.45 vacuousDall: $o ).
% 2.34/1.45
% 2.34/1.45 thf(vacuousDall,definition,
% 2.34/1.45 ( vacuousDall
% 2.34/1.45 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ emptyset )
% 2.34/1.45 => ( Xphi @ Xx ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(quantDeMorgan1_type,type,
% 2.34/1.45 quantDeMorgan1: $o ).
% 2.34/1.45
% 2.34/1.45 thf(quantDeMorgan1,definition,
% 2.34/1.45 ( quantDeMorgan1
% 2.34/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.34/1.45 ( ~ ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ( Xphi @ Xx ) )
% 2.34/1.45 => ? [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(quantDeMorgan2_type,type,
% 2.34/1.45 quantDeMorgan2: $o ).
% 2.34/1.45
% 2.34/1.45 thf(quantDeMorgan2,definition,
% 2.34/1.45 ( quantDeMorgan2
% 2.34/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.34/1.45 ( ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ~ ( Xphi @ Xx ) )
% 2.34/1.45 => ~ ? [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(quantDeMorgan3_type,type,
% 2.34/1.45 quantDeMorgan3: $o ).
% 2.34/1.45
% 2.34/1.45 thf(quantDeMorgan3,definition,
% 2.34/1.45 ( quantDeMorgan3
% 2.34/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.34/1.45 ( ~ ? [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 & ( Xphi @ Xx ) )
% 2.34/1.45 => ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(quantDeMorgan4_type,type,
% 2.34/1.45 quantDeMorgan4: $o ).
% 2.34/1.45
% 2.34/1.45 thf(quantDeMorgan4,definition,
% 2.34/1.45 ( quantDeMorgan4
% 2.34/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.34/1.45 ( ? [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 & ~ ( Xphi @ Xx ) )
% 2.34/1.45 => ~ ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(prop2setI_type,type,
% 2.34/1.45 prop2setI: $o ).
% 2.34/1.45
% 2.34/1.45 thf(prop2setI,definition,
% 2.34/1.45 ( prop2setI
% 2.34/1.45 = ( ! [Xphi: $o] :
% 2.34/1.45 ( Xphi
% 2.34/1.45 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(set2prop_type,type,
% 2.34/1.45 set2prop: $i > $o ).
% 2.34/1.45
% 2.34/1.45 thf(prop2set2propI_type,type,
% 2.34/1.45 prop2set2propI: $o ).
% 2.34/1.45
% 2.34/1.45 thf(prop2set2propI,definition,
% 2.34/1.45 ( prop2set2propI
% 2.34/1.45 = ( ! [Xphi: $o] :
% 2.34/1.45 ( Xphi
% 2.34/1.45 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(notdexE_type,type,
% 2.34/1.45 notdexE: $o ).
% 2.34/1.45
% 2.34/1.45 thf(notdexE,definition,
% 2.34/1.45 ( notdexE
% 2.34/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.34/1.45 ( ~ ? [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 & ( Xphi @ Xx ) )
% 2.34/1.45 => ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(notdallE_type,type,
% 2.34/1.45 notdallE: $o ).
% 2.34/1.45
% 2.34/1.45 thf(notdallE,definition,
% 2.34/1.45 ( notdallE
% 2.34/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.34/1.45 ( ~ ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ( Xphi @ Xx ) )
% 2.34/1.45 => ? [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(exuI1_type,type,
% 2.34/1.45 exuI1: $o ).
% 2.34/1.45
% 2.34/1.45 thf(exuI1,definition,
% 2.34/1.45 ( exuI1
% 2.34/1.45 = ( ! [Xphi: $i > $o] :
% 2.34/1.45 ( ? [Xx: $i] :
% 2.34/1.45 ( ( Xphi @ Xx )
% 2.34/1.45 & ! [Xy: $i] :
% 2.34/1.45 ( ( Xphi @ Xy )
% 2.34/1.45 => ( Xx = Xy ) ) )
% 2.34/1.45 => ( exu
% 2.34/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(exuI3_type,type,
% 2.34/1.45 exuI3: $o ).
% 2.34/1.45
% 2.34/1.45 thf(exuI3,definition,
% 2.34/1.45 ( exuI3
% 2.34/1.45 = ( ! [Xphi: $i > $o] :
% 2.34/1.45 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.34/1.45 => ( ! [Xx: $i,Xy: $i] :
% 2.34/1.45 ( ( Xphi @ Xx )
% 2.34/1.45 => ( ( Xphi @ Xy )
% 2.34/1.45 => ( Xx = Xy ) ) )
% 2.34/1.45 => ( exu
% 2.34/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(exuI2_type,type,
% 2.34/1.45 exuI2: $o ).
% 2.34/1.45
% 2.34/1.45 thf(exuI2,definition,
% 2.34/1.45 ( exuI2
% 2.34/1.45 = ( ! [Xphi: $i > $o] :
% 2.34/1.45 ( ? [Xx: $i] :
% 2.34/1.45 ! [Xy: $i] :
% 2.34/1.45 ( ( Xphi @ Xy )
% 2.34/1.45 <=> ( Xy = Xx ) )
% 2.34/1.45 => ( exu
% 2.34/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(inCongP_type,type,
% 2.34/1.45 inCongP: $o ).
% 2.34/1.45
% 2.34/1.45 thf(inCongP,definition,
% 2.34/1.45 ( inCongP
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ( A = B )
% 2.34/1.45 => ! [Xx: $i,Xy: $i] :
% 2.34/1.45 ( ( Xx = Xy )
% 2.34/1.45 => ( ( in @ Xx @ A )
% 2.34/1.45 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(in__Cong_type,type,
% 2.34/1.45 in__Cong: $o ).
% 2.34/1.45
% 2.34/1.45 thf(in__Cong,definition,
% 2.34/1.45 ( in__Cong
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ( A = B )
% 2.34/1.45 => ! [Xx: $i,Xy: $i] :
% 2.34/1.45 ( ( Xx = Xy )
% 2.34/1.45 => ( ( in @ Xx @ A )
% 2.34/1.45 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(exuE3u_type,type,
% 2.34/1.45 exuE3u: $o ).
% 2.34/1.45
% 2.34/1.45 thf(exuE3u,definition,
% 2.34/1.45 ( exuE3u
% 2.34/1.45 = ( ! [Xphi: $i > $o] :
% 2.34/1.45 ( ( exu
% 2.34/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.34/1.45 => ! [Xx: $i,Xy: $i] :
% 2.34/1.45 ( ( Xphi @ Xx )
% 2.34/1.45 => ( ( Xphi @ Xy )
% 2.34/1.45 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(exu__Cong_type,type,
% 2.34/1.45 exu__Cong: $o ).
% 2.34/1.45
% 2.34/1.45 thf(exu__Cong,definition,
% 2.34/1.45 ( exu__Cong
% 2.34/1.45 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.34/1.45 ( ! [Xx: $i,Xy: $i] :
% 2.34/1.45 ( ( Xx = Xy )
% 2.34/1.45 => ( ( Xphi @ Xx )
% 2.34/1.45 <=> ( Xpsi @ Xy ) ) )
% 2.34/1.45 => ( ( exu
% 2.34/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.34/1.45 <=> ( exu
% 2.34/1.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(emptyset__Cong_type,type,
% 2.34/1.45 emptyset__Cong: $o ).
% 2.34/1.45
% 2.34/1.45 thf(emptyset__Cong,definition,
% 2.34/1.45 ( emptyset__Cong
% 2.34/1.45 = ( emptyset = emptyset ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setadjoin__Cong_type,type,
% 2.34/1.45 setadjoin__Cong: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setadjoin__Cong,definition,
% 2.34/1.45 ( setadjoin__Cong
% 2.34/1.45 = ( ! [Xx: $i,Xy: $i] :
% 2.34/1.45 ( ( Xx = Xy )
% 2.34/1.45 => ! [Xz: $i,Xu: $i] :
% 2.34/1.45 ( ( Xz = Xu )
% 2.34/1.45 => ( ( setadjoin @ Xx @ Xz )
% 2.34/1.45 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(powerset__Cong_type,type,
% 2.34/1.45 powerset__Cong: $o ).
% 2.34/1.45
% 2.34/1.45 thf(powerset__Cong,definition,
% 2.34/1.45 ( powerset__Cong
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ( A = B )
% 2.34/1.45 => ( ( powerset @ A )
% 2.34/1.45 = ( powerset @ B ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setunion__Cong_type,type,
% 2.34/1.45 setunion__Cong: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setunion__Cong,definition,
% 2.34/1.45 ( setunion__Cong
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ( A = B )
% 2.34/1.45 => ( ( setunion @ A )
% 2.34/1.45 = ( setunion @ B ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(omega__Cong_type,type,
% 2.34/1.45 omega__Cong: $o ).
% 2.34/1.45
% 2.34/1.45 thf(omega__Cong,definition,
% 2.34/1.45 ( omega__Cong
% 2.34/1.45 = ( omega = omega ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(exuEu_type,type,
% 2.34/1.45 exuEu: $o ).
% 2.34/1.45
% 2.34/1.45 thf(exuEu,definition,
% 2.34/1.45 ( exuEu
% 2.34/1.45 = ( ! [Xphi: $i > $o] :
% 2.34/1.45 ( ( exu
% 2.34/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.34/1.45 => ! [Xx: $i,Xy: $i] :
% 2.34/1.45 ( ( Xphi @ Xx )
% 2.34/1.45 => ( ( Xphi @ Xy )
% 2.34/1.45 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(descr__Cong_type,type,
% 2.34/1.45 descr__Cong: $o ).
% 2.34/1.45
% 2.34/1.45 thf(descr__Cong,definition,
% 2.34/1.45 ( descr__Cong
% 2.34/1.45 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.34/1.45 ( ! [Xx: $i,Xy: $i] :
% 2.34/1.45 ( ( Xx = Xy )
% 2.34/1.45 => ( ( Xphi @ Xx )
% 2.34/1.45 <=> ( Xpsi @ Xy ) ) )
% 2.34/1.45 => ( ( exu
% 2.34/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.34/1.45 => ( ( exu
% 2.34/1.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.34/1.45 => ( ( descr
% 2.34/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.34/1.45 = ( descr
% 2.34/1.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(dsetconstr__Cong_type,type,
% 2.34/1.45 dsetconstr__Cong: $o ).
% 2.34/1.45
% 2.34/1.45 thf(dsetconstr__Cong,definition,
% 2.34/1.45 ( dsetconstr__Cong
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ( A = B )
% 2.34/1.45 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.34/1.45 ( ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ! [Xy: $i] :
% 2.34/1.45 ( ( in @ Xy @ B )
% 2.34/1.45 => ( ( Xx = Xy )
% 2.34/1.45 => ( ( Xphi @ Xx )
% 2.34/1.45 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.34/1.45 => ( ( dsetconstr @ A
% 2.34/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.34/1.45 = ( dsetconstr @ B
% 2.34/1.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(subset_type,type,
% 2.34/1.45 subset: $i > $i > $o ).
% 2.34/1.45
% 2.34/1.45 thf(disjoint_type,type,
% 2.34/1.45 disjoint: $i > $i > $o ).
% 2.34/1.45
% 2.34/1.45 thf(setsmeet_type,type,
% 2.34/1.45 setsmeet: $i > $i > $o ).
% 2.34/1.45
% 2.34/1.45 thf(subsetI1_type,type,
% 2.34/1.45 subsetI1: $o ).
% 2.34/1.45
% 2.34/1.45 thf(subsetI1,definition,
% 2.34/1.45 ( subsetI1
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ( in @ Xx @ B ) )
% 2.34/1.45 => ( subset @ A @ B ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(eqimpsubset2_type,type,
% 2.34/1.45 eqimpsubset2: $o ).
% 2.34/1.45
% 2.34/1.45 thf(eqimpsubset2,definition,
% 2.34/1.45 ( eqimpsubset2
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ( A = B )
% 2.34/1.45 => ( subset @ B @ A ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(eqimpsubset1_type,type,
% 2.34/1.45 eqimpsubset1: $o ).
% 2.34/1.45
% 2.34/1.45 thf(eqimpsubset1,definition,
% 2.34/1.45 ( eqimpsubset1
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ( A = B )
% 2.34/1.45 => ( subset @ A @ B ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(subsetI2_type,type,
% 2.34/1.45 subsetI2: $o ).
% 2.34/1.45
% 2.34/1.45 thf(subsetI2,definition,
% 2.34/1.45 ( subsetI2
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ! [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ( in @ Xx @ B ) )
% 2.34/1.45 => ( subset @ A @ B ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(emptysetsubset_type,type,
% 2.34/1.45 emptysetsubset: $o ).
% 2.34/1.45
% 2.34/1.45 thf(emptysetsubset,definition,
% 2.34/1.45 ( emptysetsubset
% 2.34/1.45 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(subsetE_type,type,
% 2.34/1.45 subsetE: $o ).
% 2.34/1.45
% 2.34/1.45 thf(subsetE,definition,
% 2.34/1.45 ( subsetE
% 2.34/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.34/1.45 ( ( subset @ A @ B )
% 2.34/1.45 => ( ( in @ Xx @ A )
% 2.34/1.45 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(subsetE2_type,type,
% 2.34/1.45 subsetE2: $o ).
% 2.34/1.45
% 2.34/1.45 thf(subsetE2,definition,
% 2.34/1.45 ( subsetE2
% 2.34/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.34/1.45 ( ( subset @ A @ B )
% 2.34/1.45 => ( ~ ( in @ Xx @ B )
% 2.34/1.45 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(notsubsetI_type,type,
% 2.34/1.45 notsubsetI: $o ).
% 2.34/1.45
% 2.34/1.45 thf(notsubsetI,definition,
% 2.34/1.45 ( notsubsetI
% 2.34/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ( ~ ( in @ Xx @ B )
% 2.34/1.45 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(notequalI1_type,type,
% 2.34/1.45 notequalI1: $o ).
% 2.34/1.45
% 2.34/1.45 thf(notequalI1,definition,
% 2.34/1.45 ( notequalI1
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ~ ( subset @ A @ B )
% 2.34/1.45 => ( A != B ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(notequalI2_type,type,
% 2.34/1.45 notequalI2: $o ).
% 2.34/1.45
% 2.34/1.45 thf(notequalI2,definition,
% 2.34/1.45 ( notequalI2
% 2.34/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ( ~ ( in @ Xx @ B )
% 2.34/1.45 => ( A != B ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(subsetRefl_type,type,
% 2.34/1.45 subsetRefl: $o ).
% 2.34/1.45
% 2.34/1.45 thf(subsetRefl,definition,
% 2.34/1.45 ( subsetRefl
% 2.34/1.45 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(subsetTrans_type,type,
% 2.34/1.45 subsetTrans: $o ).
% 2.34/1.45
% 2.34/1.45 thf(subsetTrans,definition,
% 2.34/1.45 ( subsetTrans
% 2.34/1.45 = ( ! [A: $i,B: $i,C: $i] :
% 2.34/1.45 ( ( subset @ A @ B )
% 2.34/1.45 => ( ( subset @ B @ C )
% 2.34/1.45 => ( subset @ A @ C ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setadjoinSub_type,type,
% 2.34/1.45 setadjoinSub: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setadjoinSub,definition,
% 2.34/1.45 ( setadjoinSub
% 2.34/1.45 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setadjoinSub2_type,type,
% 2.34/1.45 setadjoinSub2: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setadjoinSub2,definition,
% 2.34/1.45 ( setadjoinSub2
% 2.34/1.45 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.34/1.45 ( ( subset @ A @ B )
% 2.34/1.45 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(subset2powerset_type,type,
% 2.34/1.45 subset2powerset: $o ).
% 2.34/1.45
% 2.34/1.45 thf(subset2powerset,definition,
% 2.34/1.45 ( subset2powerset
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ( subset @ A @ B )
% 2.34/1.45 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setextsub_type,type,
% 2.34/1.45 setextsub: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setextsub,definition,
% 2.34/1.45 ( setextsub
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ( subset @ A @ B )
% 2.34/1.45 => ( ( subset @ B @ A )
% 2.34/1.45 => ( A = B ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(subsetemptysetimpeq_type,type,
% 2.34/1.45 subsetemptysetimpeq: $o ).
% 2.34/1.45
% 2.34/1.45 thf(subsetemptysetimpeq,definition,
% 2.34/1.45 ( subsetemptysetimpeq
% 2.34/1.45 = ( ! [A: $i] :
% 2.34/1.45 ( ( subset @ A @ emptyset )
% 2.34/1.45 => ( A = emptyset ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(powersetI1_type,type,
% 2.34/1.45 powersetI1: $o ).
% 2.34/1.45
% 2.34/1.45 thf(powersetI1,definition,
% 2.34/1.45 ( powersetI1
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ( subset @ B @ A )
% 2.34/1.45 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(powersetE1_type,type,
% 2.34/1.45 powersetE1: $o ).
% 2.34/1.45
% 2.34/1.45 thf(powersetE1,definition,
% 2.34/1.45 ( powersetE1
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ( in @ B @ ( powerset @ A ) )
% 2.34/1.45 => ( subset @ B @ A ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(inPowerset_type,type,
% 2.34/1.45 inPowerset: $o ).
% 2.34/1.45
% 2.34/1.45 thf(inPowerset,definition,
% 2.34/1.45 ( inPowerset
% 2.34/1.45 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(powersetsubset_type,type,
% 2.34/1.45 powersetsubset: $o ).
% 2.34/1.45
% 2.34/1.45 thf(powersetsubset,definition,
% 2.34/1.45 ( powersetsubset
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ( subset @ A @ B )
% 2.34/1.45 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(sepInPowerset_type,type,
% 2.34/1.45 sepInPowerset: $o ).
% 2.34/1.45
% 2.34/1.45 thf(sepInPowerset,definition,
% 2.34/1.45 ( sepInPowerset
% 2.34/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.34/1.45 ( in
% 2.34/1.45 @ ( dsetconstr @ A
% 2.34/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.34/1.45 @ ( powerset @ A ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(sepSubset_type,type,
% 2.34/1.45 sepSubset: $o ).
% 2.34/1.45
% 2.34/1.45 thf(sepSubset,definition,
% 2.34/1.45 ( sepSubset
% 2.34/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.34/1.45 ( subset
% 2.34/1.45 @ ( dsetconstr @ A
% 2.34/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.34/1.45 @ A ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(binunion_type,type,
% 2.34/1.45 binunion: $i > $i > $i ).
% 2.34/1.45
% 2.34/1.45 thf(binunionIL_type,type,
% 2.34/1.45 binunionIL: $o ).
% 2.34/1.45
% 2.34/1.45 thf(binunionIL,definition,
% 2.34/1.45 ( binunionIL
% 2.34/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(upairset2IR_type,type,
% 2.34/1.45 upairset2IR: $o ).
% 2.34/1.45
% 2.34/1.45 thf(upairset2IR,definition,
% 2.34/1.45 ( upairset2IR
% 2.34/1.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(binunionIR_type,type,
% 2.34/1.45 binunionIR: $o ).
% 2.34/1.45
% 2.34/1.45 thf(binunionIR,definition,
% 2.34/1.45 ( binunionIR
% 2.34/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ B )
% 2.34/1.45 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(binunionEcases_type,type,
% 2.34/1.45 binunionEcases: $o ).
% 2.34/1.45
% 2.34/1.45 thf(binunionEcases,definition,
% 2.34/1.45 ( binunionEcases
% 2.34/1.45 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.34/1.45 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.34/1.45 => ( ( ( in @ Xx @ A )
% 2.34/1.45 => Xphi )
% 2.34/1.45 => ( ( ( in @ Xx @ B )
% 2.34/1.45 => Xphi )
% 2.34/1.45 => Xphi ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(binunionE_type,type,
% 2.34/1.45 binunionE: $o ).
% 2.34/1.45
% 2.34/1.45 thf(binunionE,definition,
% 2.34/1.45 ( binunionE
% 2.34/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.34/1.45 => ( ( in @ Xx @ A )
% 2.34/1.45 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(binunionLsub_type,type,
% 2.34/1.45 binunionLsub: $o ).
% 2.34/1.45
% 2.34/1.45 thf(binunionLsub,definition,
% 2.34/1.45 ( binunionLsub
% 2.34/1.45 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(binunionRsub_type,type,
% 2.34/1.45 binunionRsub: $o ).
% 2.34/1.45
% 2.34/1.45 thf(binunionRsub,definition,
% 2.34/1.45 ( binunionRsub
% 2.34/1.45 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(binintersect_type,type,
% 2.34/1.45 binintersect: $i > $i > $i ).
% 2.34/1.45
% 2.34/1.45 thf(binintersectI_type,type,
% 2.34/1.45 binintersectI: $o ).
% 2.34/1.45
% 2.34/1.45 thf(binintersectI,definition,
% 2.34/1.45 ( binintersectI
% 2.34/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ( ( in @ Xx @ B )
% 2.34/1.45 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(binintersectSubset5_type,type,
% 2.34/1.45 binintersectSubset5: $o ).
% 2.34/1.45
% 2.34/1.45 thf(binintersectSubset5,definition,
% 2.34/1.45 ( binintersectSubset5
% 2.34/1.45 = ( ! [A: $i,B: $i,C: $i] :
% 2.34/1.45 ( ( subset @ C @ A )
% 2.34/1.45 => ( ( subset @ C @ B )
% 2.34/1.45 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(binintersectEL_type,type,
% 2.34/1.45 binintersectEL: $o ).
% 2.34/1.45
% 2.34/1.45 thf(binintersectEL,definition,
% 2.34/1.45 ( binintersectEL
% 2.34/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.34/1.45 => ( in @ Xx @ A ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(binintersectLsub_type,type,
% 2.34/1.45 binintersectLsub: $o ).
% 2.34/1.45
% 2.34/1.45 thf(binintersectLsub,definition,
% 2.34/1.45 ( binintersectLsub
% 2.34/1.45 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(binintersectSubset2_type,type,
% 2.34/1.45 binintersectSubset2: $o ).
% 2.34/1.45
% 2.34/1.45 thf(binintersectSubset2,definition,
% 2.34/1.45 ( binintersectSubset2
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ( subset @ A @ B )
% 2.34/1.45 => ( ( binintersect @ A @ B )
% 2.34/1.45 = A ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(binintersectSubset3_type,type,
% 2.34/1.45 binintersectSubset3: $o ).
% 2.34/1.45
% 2.34/1.45 thf(binintersectSubset3,definition,
% 2.34/1.45 ( binintersectSubset3
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ( ( binintersect @ A @ B )
% 2.34/1.45 = B )
% 2.34/1.45 => ( subset @ B @ A ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(binintersectER_type,type,
% 2.34/1.45 binintersectER: $o ).
% 2.34/1.45
% 2.34/1.45 thf(binintersectER,definition,
% 2.34/1.45 ( binintersectER
% 2.34/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.34/1.45 => ( in @ Xx @ B ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(disjointsetsI1_type,type,
% 2.34/1.45 disjointsetsI1: $o ).
% 2.34/1.45
% 2.34/1.45 thf(disjointsetsI1,definition,
% 2.34/1.45 ( disjointsetsI1
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ~ ? [Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 & ( in @ Xx @ B ) )
% 2.34/1.45 => ( ( binintersect @ A @ B )
% 2.34/1.45 = emptyset ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(binintersectRsub_type,type,
% 2.34/1.45 binintersectRsub: $o ).
% 2.34/1.45
% 2.34/1.45 thf(binintersectRsub,definition,
% 2.34/1.45 ( binintersectRsub
% 2.34/1.45 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(binintersectSubset4_type,type,
% 2.34/1.45 binintersectSubset4: $o ).
% 2.34/1.45
% 2.34/1.45 thf(binintersectSubset4,definition,
% 2.34/1.45 ( binintersectSubset4
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ( subset @ B @ A )
% 2.34/1.45 => ( ( binintersect @ A @ B )
% 2.34/1.45 = B ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(binintersectSubset1_type,type,
% 2.34/1.45 binintersectSubset1: $o ).
% 2.34/1.45
% 2.34/1.45 thf(binintersectSubset1,definition,
% 2.34/1.45 ( binintersectSubset1
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ( ( binintersect @ A @ B )
% 2.34/1.45 = A )
% 2.34/1.45 => ( subset @ A @ B ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(bs114d_type,type,
% 2.34/1.45 bs114d: $o ).
% 2.34/1.45
% 2.34/1.45 thf(bs114d,definition,
% 2.34/1.45 ( bs114d
% 2.34/1.45 = ( ! [A: $i,B: $i,C: $i] :
% 2.34/1.45 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.34/1.45 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(regular_type,type,
% 2.34/1.45 regular: $i > $o ).
% 2.34/1.45
% 2.34/1.45 thf(setminus_type,type,
% 2.34/1.45 setminus: $i > $i > $i ).
% 2.34/1.45
% 2.34/1.45 thf(setminusI_type,type,
% 2.34/1.45 setminusI: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setminusI,definition,
% 2.34/1.45 ( setminusI
% 2.34/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ( ~ ( in @ Xx @ B )
% 2.34/1.45 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setminusEL_type,type,
% 2.34/1.45 setminusEL: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setminusEL,definition,
% 2.34/1.45 ( setminusEL
% 2.34/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.34/1.45 => ( in @ Xx @ A ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setminusER_type,type,
% 2.34/1.45 setminusER: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setminusER,definition,
% 2.34/1.45 ( setminusER
% 2.34/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.34/1.45 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setminusSubset2_type,type,
% 2.34/1.45 setminusSubset2: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setminusSubset2,definition,
% 2.34/1.45 ( setminusSubset2
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ( subset @ A @ B )
% 2.34/1.45 => ( ( setminus @ A @ B )
% 2.34/1.45 = emptyset ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setminusERneg_type,type,
% 2.34/1.45 setminusERneg: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setminusERneg,definition,
% 2.34/1.45 ( setminusERneg
% 2.34/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.34/1.45 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.34/1.45 => ( ( in @ Xx @ A )
% 2.34/1.45 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setminusELneg_type,type,
% 2.34/1.45 setminusELneg: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setminusELneg,definition,
% 2.34/1.45 ( setminusELneg
% 2.34/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.34/1.45 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.34/1.45 => ( ~ ( in @ Xx @ B )
% 2.34/1.45 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setminusILneg_type,type,
% 2.34/1.45 setminusILneg: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setminusILneg,definition,
% 2.34/1.45 ( setminusILneg
% 2.34/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.34/1.45 ( ~ ( in @ Xx @ A )
% 2.34/1.45 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setminusIRneg_type,type,
% 2.34/1.45 setminusIRneg: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setminusIRneg,definition,
% 2.34/1.45 ( setminusIRneg
% 2.34/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ B )
% 2.34/1.45 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setminusLsub_type,type,
% 2.34/1.45 setminusLsub: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setminusLsub,definition,
% 2.34/1.45 ( setminusLsub
% 2.34/1.45 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(setminusSubset1_type,type,
% 2.34/1.45 setminusSubset1: $o ).
% 2.34/1.45
% 2.34/1.45 thf(setminusSubset1,definition,
% 2.34/1.45 ( setminusSubset1
% 2.34/1.45 = ( ! [A: $i,B: $i] :
% 2.34/1.45 ( ( ( setminus @ A @ B )
% 2.34/1.45 = emptyset )
% 2.34/1.45 => ( subset @ A @ B ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(symdiff_type,type,
% 2.34/1.45 symdiff: $i > $i > $i ).
% 2.34/1.45
% 2.34/1.45 thf(symdiffE_type,type,
% 2.34/1.45 symdiffE: $o ).
% 2.34/1.45
% 2.34/1.45 thf(symdiffE,definition,
% 2.34/1.45 ( symdiffE
% 2.34/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.34/1.45 => ! [Xphi: $o] :
% 2.34/1.45 ( ( ( in @ Xx @ A )
% 2.34/1.45 => ( ~ ( in @ Xx @ B )
% 2.34/1.45 => Xphi ) )
% 2.34/1.45 => ( ( ~ ( in @ Xx @ A )
% 2.34/1.45 => ( ( in @ Xx @ B )
% 2.34/1.45 => Xphi ) )
% 2.34/1.45 => Xphi ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(symdiffI1_type,type,
% 2.34/1.45 symdiffI1: $o ).
% 2.34/1.45
% 2.34/1.45 thf(symdiffI1,definition,
% 2.34/1.45 ( symdiffI1
% 2.34/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ( ~ ( in @ Xx @ B )
% 2.34/1.45 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(symdiffI2_type,type,
% 2.34/1.45 symdiffI2: $o ).
% 2.34/1.45
% 2.34/1.45 thf(symdiffI2,definition,
% 2.34/1.45 ( symdiffI2
% 2.34/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.34/1.45 ( ~ ( in @ Xx @ A )
% 2.34/1.45 => ( ( in @ Xx @ B )
% 2.34/1.45 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(symdiffIneg1_type,type,
% 2.34/1.45 symdiffIneg1: $o ).
% 2.34/1.45
% 2.34/1.45 thf(symdiffIneg1,definition,
% 2.34/1.45 ( symdiffIneg1
% 2.34/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.34/1.45 ( ( in @ Xx @ A )
% 2.34/1.45 => ( ( in @ Xx @ B )
% 2.34/1.45 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.34/1.45
% 2.34/1.45 thf(symdiffIneg2,conjecture,
% 2.34/1.45 ( setextAx
% 2.34/1.45 => ( emptysetAx
% 2.34/1.45 => ( setadjoinAx
% 2.34/1.45 => ( powersetAx
% 2.34/1.45 => ( setunionAx
% 2.34/1.45 => ( omega0Ax
% 2.34/1.45 => ( omegaSAx
% 2.34/1.45 => ( omegaIndAx
% 2.34/1.45 => ( replAx
% 2.34/1.45 => ( foundationAx
% 2.34/1.45 => ( wellorderingAx
% 2.34/1.45 => ( descrp
% 2.34/1.45 => ( dsetconstrI
% 2.34/1.45 => ( dsetconstrEL
% 2.34/1.45 => ( dsetconstrER
% 2.34/1.45 => ( exuE1
% 2.34/1.45 => ( prop2setE
% 2.34/1.45 => ( emptysetE
% 2.34/1.45 => ( emptysetimpfalse
% 2.34/1.45 => ( notinemptyset
% 2.34/1.45 => ( exuE3e
% 2.34/1.45 => ( setext
% 2.34/1.45 => ( emptyI
% 2.34/1.45 => ( noeltsimpempty
% 2.34/1.45 => ( setbeta
% 2.34/1.45 => ( nonemptyE1
% 2.34/1.45 => ( nonemptyI
% 2.34/1.45 => ( nonemptyI1
% 2.34/1.45 => ( setadjoinIL
% 2.34/1.45 => ( emptyinunitempty
% 2.34/1.45 => ( setadjoinIR
% 2.34/1.45 => ( setadjoinE
% 2.34/1.45 => ( setadjoinOr
% 2.34/1.45 => ( setoftrueEq
% 2.34/1.45 => ( powersetI
% 2.34/1.45 => ( emptyinPowerset
% 2.34/1.45 => ( emptyInPowerset
% 2.34/1.45 => ( powersetE
% 2.34/1.45 => ( setunionI
% 2.34/1.45 => ( setunionE
% 2.34/1.45 => ( subPowSU
% 2.34/1.45 => ( exuE2
% 2.34/1.45 => ( nonemptyImpWitness
% 2.34/1.45 => ( uniqinunit
% 2.34/1.45 => ( notinsingleton
% 2.34/1.45 => ( eqinunit
% 2.34/1.45 => ( singletonsswitch
% 2.34/1.45 => ( upairsetE
% 2.34/1.45 => ( upairsetIL
% 2.34/1.45 => ( upairsetIR
% 2.34/1.45 => ( emptyE1
% 2.34/1.45 => ( vacuousDall
% 2.34/1.45 => ( quantDeMorgan1
% 2.34/1.45 => ( quantDeMorgan2
% 2.34/1.45 => ( quantDeMorgan3
% 2.34/1.45 => ( quantDeMorgan4
% 2.34/1.45 => ( prop2setI
% 2.34/1.45 => ( prop2set2propI
% 2.34/1.45 => ( notdexE
% 2.34/1.45 => ( notdallE
% 2.34/1.45 => ( exuI1
% 2.34/1.45 => ( exuI3
% 2.34/1.45 => ( exuI2
% 2.34/1.45 => ( inCongP
% 2.34/1.45 => ( in__Cong
% 2.34/1.45 => ( exuE3u
% 2.34/1.45 => ( exu__Cong
% 2.34/1.45 => ( emptyset__Cong
% 2.34/1.45 => ( setadjoin__Cong
% 2.34/1.45 => ( powerset__Cong
% 2.34/1.45 => ( setunion__Cong
% 2.34/1.45 => ( omega__Cong
% 2.34/1.45 => ( exuEu
% 2.34/1.45 => ( descr__Cong
% 2.34/1.45 => ( dsetconstr__Cong
% 2.34/1.45 => ( subsetI1
% 2.34/1.45 => ( eqimpsubset2
% 2.34/1.45 => ( eqimpsubset1
% 2.34/1.45 => ( subsetI2
% 2.34/1.45 => ( emptysetsubset
% 2.34/1.45 => ( subsetE
% 2.34/1.45 => ( subsetE2
% 2.34/1.45 => ( notsubsetI
% 2.34/1.45 => ( notequalI1
% 2.34/1.45 => ( notequalI2
% 2.34/1.45 => ( subsetRefl
% 2.34/1.45 => ( subsetTrans
% 2.34/1.45 => ( setadjoinSub
% 2.34/1.45 => ( setadjoinSub2
% 2.34/1.45 => ( subset2powerset
% 2.34/1.45 => ( setextsub
% 2.34/1.45 => ( subsetemptysetimpeq
% 2.34/1.45 => ( powersetI1
% 2.34/1.45 => ( powersetE1
% 2.34/1.45 => ( inPowerset
% 2.34/1.45 => ( powersetsubset
% 2.34/1.45 => ( sepInPowerset
% 2.34/1.45 => ( sepSubset
% 2.34/1.45 => ( binunionIL
% 2.34/1.45 => ( upairset2IR
% 2.34/1.45 => ( binunionIR
% 2.34/1.45 => ( binunionEcases
% 2.34/1.45 => ( binunionE
% 2.34/1.45 => ( binunionLsub
% 2.34/1.45 => ( binunionRsub
% 2.34/1.45 => ( binintersectI
% 2.34/1.45 => ( binintersectSubset5
% 2.34/1.45 => ( binintersectEL
% 2.34/1.45 => ( binintersectLsub
% 2.34/1.45 => ( binintersectSubset2
% 2.34/1.45 => ( binintersectSubset3
% 2.34/1.45 => ( binintersectER
% 2.34/1.45 => ( disjointsetsI1
% 2.34/1.45 => ( binintersectRsub
% 2.34/1.45 => ( binintersectSubset4
% 2.34/1.45 => ( binintersectSubset1
% 2.34/1.45 => ( bs114d
% 2.34/1.45 => ( setminusI
% 2.34/1.45 => ( setminusEL
% 2.34/1.45 => ( setminusER
% 2.34/1.45 => ( setminusSubset2
% 2.34/1.45 => ( setminusERneg
% 2.34/1.45 => ( setminusELneg
% 2.34/1.45 => ( setminusILneg
% 2.34/1.45 => ( setminusIRneg
% 2.34/1.45 => ( setminusLsub
% 2.34/1.45 => ( setminusSubset1
% 2.34/1.45 => ( symdiffE
% 2.34/1.45 => ( symdiffI1
% 2.34/1.45 => ( symdiffI2
% 2.34/1.45 => ( symdiffIneg1
% 2.34/1.45 => ! [A: $i,B: $i,Xx: $i] :
% 2.34/1.45 ( ~ ( in @ Xx @ A )
% 2.34/1.45 => ( ~ ( in @ Xx @ B )
% 2.34/1.45 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.34/1.45 ------------------------
% 2.34/1.47 % (29133)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_28853 for (2999ds/4Mi)
% 2.34/1.47 % (29132)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28853 for (2999ds/183Mi)
% 2.34/1.47 % (29134)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_28853 for (2999ds/27Mi)
% 2.34/1.47 % (29133)Instruction limit reached!
% 2.34/1.47 % (29133)------------------------------
% 2.34/1.47 % (29133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.34/1.47 % (29133)Termination reason: Unknown
% 2.34/1.47 % (29133)Termination phase: shuffling
% 2.34/1.47
% 2.34/1.47 % (29133)Memory used [KB]: 1279
% 2.34/1.47 % (29133)Time elapsed: 0.003 s
% 2.34/1.47 % (29133)Instructions burned: 6 (million)
% 2.34/1.47 % (29133)------------------------------
% 2.34/1.47 % (29133)------------------------------
% 2.34/1.48 % (29135)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_28853 for (2999ds/2Mi)
% 2.34/1.48 % (29136)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_28853 for (2999ds/2Mi)
% 2.34/1.48 % (29137)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_28853 for (2999ds/275Mi)
% 2.34/1.48 % (29138)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_28853 for (2999ds/18Mi)
% 2.34/1.48 % (29134)Instruction limit reached!
% 2.34/1.48 % (29134)------------------------------
% 2.34/1.48 % (29134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.34/1.48 % (29134)Termination reason: Unknown
% 2.34/1.48 % (29134)Termination phase: Property scanning
% 2.34/1.48
% 2.34/1.48 % (29134)Memory used [KB]: 1663
% 2.34/1.48 % (29134)Time elapsed: 0.009 s
% 2.34/1.48 % (29134)Instructions burned: 27 (million)
% 2.34/1.48 % (29134)------------------------------
% 2.34/1.48 % (29134)------------------------------
% 2.34/1.48 % (29135)Instruction limit reached!
% 2.34/1.48 % (29135)------------------------------
% 2.34/1.48 % (29135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.34/1.48 % (29135)Termination reason: Unknown
% 2.34/1.48 % (29135)Termination phase: shuffling
% 2.34/1.48
% 2.34/1.48 % (29135)Memory used [KB]: 1151
% 2.34/1.48 % (29135)Time elapsed: 0.004 s
% 2.34/1.48 % (29135)Instructions burned: 3 (million)
% 2.34/1.48 % (29135)------------------------------
% 2.34/1.48 % (29135)------------------------------
% 2.34/1.48 % (29136)Instruction limit reached!
% 2.34/1.48 % (29136)------------------------------
% 2.34/1.48 % (29136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.34/1.48 % (29136)Termination reason: Unknown
% 2.34/1.48 % (29136)Termination phase: shuffling
% 2.34/1.48
% 2.34/1.48 % (29136)Memory used [KB]: 1279
% 2.34/1.48 % (29136)Time elapsed: 0.004 s
% 2.34/1.48 % (29136)Instructions burned: 3 (million)
% 2.34/1.48 % (29136)------------------------------
% 2.34/1.48 % (29136)------------------------------
% 2.34/1.48 % (29139)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_28853 for (2999ds/3Mi)
% 2.34/1.48 % (29139)Instruction limit reached!
% 2.34/1.48 % (29139)------------------------------
% 2.34/1.48 % (29139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.34/1.48 % (29139)Termination reason: Unknown
% 2.34/1.48 % (29139)Termination phase: shuffling
% 2.34/1.48
% 2.34/1.48 % (29139)Memory used [KB]: 1279
% 2.34/1.48 % (29139)Time elapsed: 0.002 s
% 2.34/1.48 % (29139)Instructions burned: 4 (million)
% 2.34/1.48 % (29139)------------------------------
% 2.34/1.48 % (29139)------------------------------
% 2.34/1.49 % (29140)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_28853 for (2999ds/37Mi)
% 2.34/1.49 % (29138)Instruction limit reached!
% 2.34/1.49 % (29138)------------------------------
% 2.34/1.49 % (29138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.34/1.49 % (29138)Termination reason: Unknown
% 2.34/1.49 % (29138)Termination phase: Naming
% 2.34/1.49
% 2.34/1.49 % (29138)Memory used [KB]: 1535
% 2.34/1.49 % (29138)Time elapsed: 0.013 s
% 2.34/1.49 % (29138)Instructions burned: 19 (million)
% 2.34/1.49 % (29138)------------------------------
% 2.34/1.49 % (29138)------------------------------
% 2.34/1.49 % (29143)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_28853 for (2999ds/1041Mi)
% 2.42/1.50 % (29141)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_28853 for (2999ds/15Mi)
% 2.42/1.50 % (29142)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_28853 for (2999ds/3Mi)
% 2.42/1.50 % (29142)Instruction limit reached!
% 2.42/1.50 % (29142)------------------------------
% 2.42/1.50 % (29142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.50 % (29142)Termination reason: Unknown
% 2.42/1.50 % (29142)Termination phase: shuffling
% 2.42/1.50
% 2.42/1.50 % (29142)Memory used [KB]: 1279
% 2.42/1.50 % (29142)Time elapsed: 0.004 s
% 2.42/1.50 % (29142)Instructions burned: 4 (million)
% 2.42/1.50 % (29142)------------------------------
% 2.42/1.50 % (29142)------------------------------
% 2.42/1.50 % (29140)Instruction limit reached!
% 2.42/1.50 % (29140)------------------------------
% 2.42/1.50 % (29140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.50 % (29140)Termination reason: Unknown
% 2.42/1.50 % (29140)Termination phase: Property scanning
% 2.42/1.50
% 2.42/1.50 % (29140)Memory used [KB]: 1663
% 2.42/1.50 % (29140)Time elapsed: 0.013 s
% 2.42/1.50 % (29140)Instructions burned: 39 (million)
% 2.42/1.50 % (29140)------------------------------
% 2.42/1.50 % (29140)------------------------------
% 2.42/1.51 % (29141)Instruction limit reached!
% 2.42/1.51 % (29141)------------------------------
% 2.42/1.51 % (29141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.51 % (29141)Termination reason: Unknown
% 2.42/1.51 % (29141)Termination phase: Property scanning
% 2.42/1.51
% 2.42/1.51 % (29141)Memory used [KB]: 1407
% 2.42/1.51 % (29141)Time elapsed: 0.011 s
% 2.42/1.51 % (29141)Instructions burned: 16 (million)
% 2.42/1.51 % (29141)------------------------------
% 2.42/1.51 % (29141)------------------------------
% 2.42/1.51 % (29144)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_28853 for (2999ds/7Mi)
% 2.42/1.51 % (29146)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_28853 for (2999ds/3Mi)
% 2.42/1.51 % (29144)Instruction limit reached!
% 2.42/1.51 % (29144)------------------------------
% 2.42/1.51 % (29144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.51 % (29144)Termination reason: Unknown
% 2.42/1.51 % (29144)Termination phase: shuffling
% 2.42/1.51
% 2.42/1.51 % (29144)Memory used [KB]: 1279
% 2.42/1.51 % (29144)Time elapsed: 0.006 s
% 2.42/1.51 % (29144)Instructions burned: 8 (million)
% 2.42/1.51 % (29144)------------------------------
% 2.42/1.51 % (29144)------------------------------
% 2.42/1.51 % (29146)Instruction limit reached!
% 2.42/1.51 % (29146)------------------------------
% 2.42/1.51 % (29146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.51 % (29146)Termination reason: Unknown
% 2.42/1.51 % (29146)Termination phase: shuffling
% 2.42/1.51
% 2.42/1.51 % (29146)Memory used [KB]: 1279
% 2.42/1.51 % (29146)Time elapsed: 0.003 s
% 2.42/1.51 % (29146)Instructions burned: 4 (million)
% 2.42/1.51 % (29146)------------------------------
% 2.42/1.51 % (29146)------------------------------
% 2.42/1.52 % (29145)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_28853 for (2999ds/16Mi)
% 2.42/1.52 % (29147)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_28853 for (2999ds/3Mi)
% 2.42/1.52 % (29132)Instruction limit reached!
% 2.42/1.52 % (29132)------------------------------
% 2.42/1.52 % (29132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.52 % (29132)Termination reason: Unknown
% 2.42/1.52 % (29132)Termination phase: Saturation
% 2.42/1.52
% 2.42/1.52 % (29132)Memory used [KB]: 7036
% 2.42/1.52 % (29132)Time elapsed: 0.052 s
% 2.42/1.52 % (29132)Instructions burned: 183 (million)
% 2.42/1.52 % (29132)------------------------------
% 2.42/1.52 % (29132)------------------------------
% 2.42/1.52 % (29149)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_28853 for (2999ds/3Mi)
% 2.42/1.52 % (29147)Instruction limit reached!
% 2.42/1.52 % (29147)------------------------------
% 2.42/1.52 % (29147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.52 % (29147)Termination reason: Unknown
% 2.42/1.52 % (29147)Termination phase: shuffling
% 2.42/1.52
% 2.42/1.52 % (29147)Memory used [KB]: 1279
% 2.42/1.52 % (29147)Time elapsed: 0.003 s
% 2.42/1.52 % (29147)Instructions burned: 5 (million)
% 2.42/1.52 % (29147)------------------------------
% 2.42/1.52 % (29147)------------------------------
% 2.42/1.52 % (29149)Instruction limit reached!
% 2.42/1.52 % (29149)------------------------------
% 2.42/1.52 % (29149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.52 % (29149)Termination reason: Unknown
% 2.42/1.52 % (29149)Termination phase: shuffling
% 2.42/1.52
% 2.42/1.52 % (29149)Memory used [KB]: 1279
% 2.42/1.52 % (29149)Time elapsed: 0.003 s
% 2.42/1.52 % (29149)Instructions burned: 4 (million)
% 2.42/1.52 % (29149)------------------------------
% 2.42/1.52 % (29149)------------------------------
% 2.42/1.53 % (29145)Instruction limit reached!
% 2.42/1.53 % (29145)------------------------------
% 2.42/1.53 % (29145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.53 % (29145)Termination reason: Unknown
% 2.42/1.53 % (29145)Termination phase: shuffling
% 2.42/1.53
% 2.42/1.53 % (29145)Memory used [KB]: 1407
% 2.42/1.53 % (29145)Time elapsed: 0.010 s
% 2.42/1.53 % (29145)Instructions burned: 16 (million)
% 2.42/1.53 % (29145)------------------------------
% 2.42/1.53 % (29145)------------------------------
% 2.42/1.53 % (29148)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_28853 for (2999ds/7Mi)
% 2.42/1.53 % (29150)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_28853 for (2999ds/4Mi)
% 2.42/1.53 % (29150)Instruction limit reached!
% 2.42/1.53 % (29150)------------------------------
% 2.42/1.53 % (29150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.53 % (29150)Termination reason: Unknown
% 2.42/1.53 % (29150)Termination phase: shuffling
% 2.42/1.53
% 2.42/1.53 % (29150)Memory used [KB]: 1279
% 2.42/1.53 % (29150)Time elapsed: 0.002 s
% 2.42/1.53 % (29150)Instructions burned: 4 (million)
% 2.42/1.53 % (29150)------------------------------
% 2.42/1.53 % (29150)------------------------------
% 2.42/1.53 % (29148)Instruction limit reached!
% 2.42/1.53 % (29148)------------------------------
% 2.42/1.53 % (29148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.53 % (29148)Termination reason: Unknown
% 2.42/1.53 % (29148)Termination phase: shuffling
% 2.42/1.53
% 2.42/1.53 % (29148)Memory used [KB]: 1279
% 2.42/1.53 % (29148)Time elapsed: 0.006 s
% 2.42/1.53 % (29148)Instructions burned: 8 (million)
% 2.42/1.53 % (29148)------------------------------
% 2.42/1.53 % (29148)------------------------------
% 2.42/1.53 % (29151)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_28853 for (2999ds/18Mi)
% 2.42/1.53 % (29152)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_28853 for (2999ds/710Mi)
% 2.42/1.54 % (29151)Instruction limit reached!
% 2.42/1.54 % (29151)------------------------------
% 2.42/1.54 % (29151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.54 % (29151)Termination reason: Unknown
% 2.42/1.54 % (29151)Termination phase: shuffling
% 2.42/1.54
% 2.42/1.54 % (29151)Memory used [KB]: 1535
% 2.42/1.54 % (29151)Time elapsed: 0.007 s
% 2.42/1.54 % (29151)Instructions burned: 18 (million)
% 2.42/1.54 % (29151)------------------------------
% 2.42/1.54 % (29151)------------------------------
% 2.42/1.54 % (29154)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_28853 for (2999ds/902Mi)
% 2.42/1.54 % (29153)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_28853 for (2999ds/6Mi)
% 2.42/1.55 % (29153)Instruction limit reached!
% 2.42/1.55 % (29153)------------------------------
% 2.42/1.55 % (29153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.55 % (29153)Termination reason: Unknown
% 2.42/1.55 % (29153)Termination phase: shuffling
% 2.42/1.55
% 2.42/1.55 % (29153)Memory used [KB]: 1279
% 2.42/1.55 % (29153)Time elapsed: 0.005 s
% 2.42/1.55 % (29153)Instructions burned: 6 (million)
% 2.42/1.55 % (29153)------------------------------
% 2.42/1.55 % (29153)------------------------------
% 2.42/1.55 % (29156)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_28853 for (2999ds/5Mi)
% 2.42/1.55 % (29155)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_28853 for (2999ds/21Mi)
% 2.42/1.55 % (29156)Instruction limit reached!
% 2.42/1.55 % (29156)------------------------------
% 2.42/1.55 % (29156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.55 % (29156)Termination reason: Unknown
% 2.42/1.55 % (29156)Termination phase: shuffling
% 2.42/1.55
% 2.42/1.55 % (29156)Memory used [KB]: 1279
% 2.42/1.55 % (29156)Time elapsed: 0.004 s
% 2.42/1.55 % (29156)Instructions burned: 8 (million)
% 2.42/1.55 % (29156)------------------------------
% 2.42/1.55 % (29156)------------------------------
% 2.42/1.56 % (29155)Instruction limit reached!
% 2.42/1.56 % (29155)------------------------------
% 2.42/1.56 % (29155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.56 % (29155)Termination reason: Unknown
% 2.42/1.56 % (29155)Termination phase: Property scanning
% 2.42/1.56
% 2.42/1.56 % (29155)Memory used [KB]: 1663
% 2.42/1.56 % (29155)Time elapsed: 0.013 s
% 2.42/1.56 % (29155)Instructions burned: 21 (million)
% 2.42/1.56 % (29155)------------------------------
% 2.42/1.56 % (29155)------------------------------
% 2.42/1.56 % (29158)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_28853 for (2999ds/377Mi)
% 2.42/1.56 % (29157)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_28853 for (2999ds/6Mi)
% 2.42/1.57 % (29157)Instruction limit reached!
% 2.42/1.57 % (29157)------------------------------
% 2.42/1.57 % (29157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.57 % (29157)Termination reason: Unknown
% 2.42/1.57 % (29157)Termination phase: shuffling
% 2.42/1.57
% 2.42/1.57 % (29157)Memory used [KB]: 1279
% 2.42/1.57 % (29157)Time elapsed: 0.004 s
% 2.42/1.57 % (29157)Instructions burned: 6 (million)
% 2.42/1.57 % (29157)------------------------------
% 2.42/1.57 % (29157)------------------------------
% 2.42/1.58 % (29160)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_28853 for (2998ds/19Mi)
% 2.42/1.58 % (29159)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_28853 for (2999ds/779Mi)
% 2.42/1.58 % (29160)Instruction limit reached!
% 2.42/1.58 % (29160)------------------------------
% 2.42/1.58 % (29160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.58 % (29160)Termination reason: Unknown
% 2.42/1.58 % (29160)Termination phase: shuffling
% 2.42/1.58
% 2.42/1.58 % (29160)Memory used [KB]: 1535
% 2.42/1.58 % (29160)Time elapsed: 0.007 s
% 2.42/1.58 % (29160)Instructions burned: 19 (million)
% 2.42/1.58 % (29160)------------------------------
% 2.42/1.58 % (29160)------------------------------
% 2.42/1.59 % (29161)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_28853 for (2998ds/879Mi)
% 2.42/1.61 % (29137)Instruction limit reached!
% 2.42/1.61 % (29137)------------------------------
% 2.42/1.61 % (29137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.61 % (29137)Termination reason: Unknown
% 2.42/1.61 % (29137)Termination phase: Saturation
% 2.42/1.61
% 2.42/1.61 % (29137)Memory used [KB]: 7803
% 2.42/1.61 % (29137)Time elapsed: 0.135 s
% 2.42/1.61 % (29137)Instructions burned: 275 (million)
% 2.42/1.61 % (29137)------------------------------
% 2.42/1.61 % (29137)------------------------------
% 2.42/1.62 % (29162)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_28853 for (2998ds/17Mi)
% 2.42/1.63 % (29162)Instruction limit reached!
% 2.42/1.63 % (29162)------------------------------
% 2.42/1.63 % (29162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.63 % (29162)Termination reason: Unknown
% 2.42/1.63 % (29162)Termination phase: shuffling
% 2.42/1.63
% 2.42/1.63 % (29162)Memory used [KB]: 1535
% 2.42/1.63 % (29162)Time elapsed: 0.007 s
% 2.42/1.63 % (29162)Instructions burned: 17 (million)
% 2.42/1.63 % (29162)------------------------------
% 2.42/1.63 % (29162)------------------------------
% 2.42/1.64 % (29163)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_28853 for (2998ds/3Mi)
% 2.42/1.64 % (29163)Instruction limit reached!
% 2.42/1.64 % (29163)------------------------------
% 2.42/1.64 % (29163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.64 % (29163)Termination reason: Unknown
% 2.42/1.64 % (29163)Termination phase: shuffling
% 2.42/1.64
% 2.42/1.64 % (29163)Memory used [KB]: 1279
% 2.42/1.64 % (29163)Time elapsed: 0.003 s
% 2.42/1.64 % (29163)Instructions burned: 5 (million)
% 2.42/1.64 % (29163)------------------------------
% 2.42/1.64 % (29163)------------------------------
% 2.42/1.65 % (29164)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_28853 for (2998ds/30Mi)
% 2.42/1.66 % (29164)Instruction limit reached!
% 2.42/1.66 % (29164)------------------------------
% 2.42/1.66 % (29164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.66 % (29164)Termination reason: Unknown
% 2.42/1.66 % (29164)Termination phase: Preprocessing 3
% 2.42/1.66
% 2.42/1.66 % (29164)Memory used [KB]: 1791
% 2.42/1.66 % (29164)Time elapsed: 0.011 s
% 2.42/1.66 % (29164)Instructions burned: 32 (million)
% 2.42/1.66 % (29164)------------------------------
% 2.42/1.66 % (29164)------------------------------
% 2.42/1.67 % (29165)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_28853 for (2998ds/127Mi)
% 2.42/1.68 % (29158)Instruction limit reached!
% 2.42/1.68 % (29158)------------------------------
% 2.42/1.68 % (29158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.68 % (29158)Termination reason: Unknown
% 2.42/1.68 % (29158)Termination phase: Saturation
% 2.42/1.68
% 2.42/1.68 % (29158)Memory used [KB]: 7419
% 2.42/1.68 % (29158)Time elapsed: 0.124 s
% 2.42/1.68 % (29158)Instructions burned: 379 (million)
% 2.42/1.68 % (29158)------------------------------
% 2.42/1.68 % (29158)------------------------------
% 2.42/1.69 % (29166)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_28853 for (2997ds/100Mi)
% 2.42/1.70 % (29165)Instruction limit reached!
% 2.42/1.70 % (29165)------------------------------
% 2.42/1.70 % (29165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.70 % (29165)Termination reason: Unknown
% 2.42/1.70 % (29165)Termination phase: Saturation
% 2.42/1.70
% 2.42/1.71 % (29165)Memory used [KB]: 6780
% 2.42/1.71 % (29165)Time elapsed: 0.038 s
% 2.42/1.71 % (29165)Instructions burned: 127 (million)
% 2.42/1.71 % (29165)------------------------------
% 2.42/1.71 % (29165)------------------------------
% 2.42/1.72 % (29167)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_28853 for (2997ds/3Mi)
% 2.42/1.72 % (29167)Instruction limit reached!
% 2.42/1.72 % (29167)------------------------------
% 2.42/1.72 % (29167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.72 % (29167)Termination reason: Unknown
% 2.42/1.72 % (29167)Termination phase: shuffling
% 2.42/1.72
% 2.42/1.72 % (29167)Memory used [KB]: 1279
% 2.42/1.72 % (29167)Time elapsed: 0.003 s
% 2.42/1.72 % (29167)Instructions burned: 4 (million)
% 2.42/1.72 % (29167)------------------------------
% 2.42/1.72 % (29167)------------------------------
% 2.42/1.72 % (29166)Instruction limit reached!
% 2.42/1.72 % (29166)------------------------------
% 2.42/1.72 % (29166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.72 % (29166)Termination reason: Unknown
% 2.42/1.72 % (29166)Termination phase: Saturation
% 2.42/1.72
% 2.42/1.72 % (29166)Memory used [KB]: 6396
% 2.42/1.72 % (29166)Time elapsed: 0.031 s
% 2.42/1.72 % (29166)Instructions burned: 101 (million)
% 2.42/1.72 % (29166)------------------------------
% 2.42/1.72 % (29166)------------------------------
% 2.42/1.73 % (29168)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_28853 for (2997ds/20Mi)
% 2.42/1.73 % (29168)Instruction limit reached!
% 2.42/1.73 % (29168)------------------------------
% 2.42/1.73 % (29168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.73 % (29168)Termination reason: Unknown
% 2.42/1.73 % (29168)Termination phase: SInE selection
% 2.42/1.73
% 2.42/1.73 % (29168)Memory used [KB]: 1407
% 2.42/1.73 % (29168)Time elapsed: 0.008 s
% 2.42/1.73 % (29168)Instructions burned: 20 (million)
% 2.42/1.73 % (29168)------------------------------
% 2.42/1.73 % (29168)------------------------------
% 2.42/1.73 % (29169)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_28853 for (2997ds/86Mi)
% 2.42/1.74 % (29143)Instruction limit reached!
% 2.42/1.74 % (29143)------------------------------
% 2.42/1.74 % (29143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.74 % (29143)Termination reason: Unknown
% 2.42/1.74 % (29143)Termination phase: Saturation
% 2.42/1.74
% 2.42/1.74 % (29143)Memory used [KB]: 8827
% 2.42/1.74 % (29143)Time elapsed: 0.251 s
% 2.42/1.74 % (29143)Instructions burned: 1042 (million)
% 2.42/1.74 % (29143)------------------------------
% 2.42/1.74 % (29143)------------------------------
% 2.42/1.74 % (29170)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_28853 for (2997ds/107Mi)
% 2.42/1.75 % (29171)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_28853 for (2997ds/39Mi)
% 2.42/1.76 % (29169)Instruction limit reached!
% 2.42/1.76 % (29169)------------------------------
% 2.42/1.76 % (29169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.76 % (29169)Termination reason: Unknown
% 2.42/1.76 % (29169)Termination phase: Saturation
% 2.42/1.76
% 2.42/1.76 % (29169)Memory used [KB]: 6524
% 2.42/1.76 % (29169)Time elapsed: 0.026 s
% 2.42/1.76 % (29169)Instructions burned: 86 (million)
% 2.42/1.76 % (29169)------------------------------
% 2.42/1.76 % (29169)------------------------------
% 2.42/1.76 % (29171)Instruction limit reached!
% 2.42/1.76 % (29171)------------------------------
% 2.42/1.76 % (29171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.76 % (29171)Termination reason: Unknown
% 2.42/1.76 % (29171)Termination phase: Property scanning
% 2.42/1.76
% 2.42/1.76 % (29171)Memory used [KB]: 1663
% 2.42/1.76 % (29171)Time elapsed: 0.011 s
% 2.42/1.76 % (29171)Instructions burned: 40 (million)
% 2.42/1.76 % (29171)------------------------------
% 2.42/1.76 % (29171)------------------------------
% 2.42/1.76 % (29152)Instruction limit reached!
% 2.42/1.76 % (29152)------------------------------
% 2.42/1.76 % (29152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.76 % (29152)Termination reason: Unknown
% 2.42/1.76 % (29152)Termination phase: Saturation
% 2.42/1.76
% 2.42/1.76 % (29152)Memory used [KB]: 9338
% 2.42/1.76 % (29152)Time elapsed: 0.231 s
% 2.42/1.76 % (29152)Instructions burned: 712 (million)
% 2.42/1.76 % (29152)------------------------------
% 2.42/1.76 % (29152)------------------------------
% 2.42/1.77 % (29172)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_28853 for (2996ds/448Mi)
% 2.42/1.77 % (29173)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_28853 for (2996ds/46Mi)
% 2.42/1.77 % (29170)Instruction limit reached!
% 2.42/1.77 % (29170)------------------------------
% 2.42/1.77 % (29170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.77 % (29170)Termination reason: Unknown
% 2.42/1.77 % (29170)Termination phase: Saturation
% 2.42/1.77
% 2.42/1.77 % (29170)Memory used [KB]: 6652
% 2.42/1.77 % (29170)Time elapsed: 0.032 s
% 2.42/1.77 % (29170)Instructions burned: 107 (million)
% 2.42/1.77 % (29170)------------------------------
% 2.42/1.77 % (29170)------------------------------
% 2.42/1.77 % (29174)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_28853 for (2996ds/98Mi)
% 2.42/1.78 % (29159)Instruction limit reached!
% 2.42/1.78 % (29159)------------------------------
% 2.42/1.78 % (29159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.78 % (29159)Termination reason: Unknown
% 2.42/1.78 % (29159)Termination phase: Saturation
% 2.42/1.78
% 2.42/1.78 % (29159)Memory used [KB]: 6524
% 2.42/1.78 % (29159)Time elapsed: 0.200 s
% 2.42/1.78 % (29159)Instructions burned: 783 (million)
% 2.42/1.78 % (29159)------------------------------
% 2.42/1.78 % (29159)------------------------------
% 2.42/1.78 % (29175)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_28853 for (2996ds/507Mi)
% 2.42/1.78 % (29173)Instruction limit reached!
% 2.42/1.78 % (29173)------------------------------
% 2.42/1.78 % (29173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.78 % (29173)Termination reason: Unknown
% 2.42/1.78 % (29173)Termination phase: Property scanning
% 2.42/1.78
% 2.42/1.78 % (29173)Memory used [KB]: 1663
% 2.42/1.78 % (29173)Time elapsed: 0.013 s
% 2.42/1.78 % (29173)Instructions burned: 46 (million)
% 2.42/1.78 % (29173)------------------------------
% 2.42/1.78 % (29173)------------------------------
% 2.42/1.79 % (29176)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_28853 for (2996ds/149Mi)
% 2.42/1.79 % (29177)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_28853 for (2996ds/39Mi)
% 2.42/1.80 % (29174)Instruction limit reached!
% 2.42/1.80 % (29174)------------------------------
% 2.42/1.80 % (29174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.80 % (29174)Termination reason: Unknown
% 2.42/1.80 % (29174)Termination phase: Saturation
% 2.42/1.80
% 2.42/1.80 % (29174)Memory used [KB]: 1791
% 2.42/1.80 % (29174)Time elapsed: 0.027 s
% 2.42/1.80 % (29174)Instructions burned: 101 (million)
% 2.42/1.80 % (29174)------------------------------
% 2.42/1.80 % (29174)------------------------------
% 2.42/1.80 % (29177)Instruction limit reached!
% 2.42/1.80 % (29177)------------------------------
% 2.42/1.80 % (29177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.80 % (29177)Termination reason: Unknown
% 2.42/1.80 % (29177)Termination phase: Property scanning
% 2.42/1.80
% 2.42/1.80 % (29177)Memory used [KB]: 1663
% 2.42/1.80 % (29177)Time elapsed: 0.012 s
% 2.42/1.80 % (29177)Instructions burned: 42 (million)
% 2.42/1.80 % (29177)------------------------------
% 2.42/1.80 % (29177)------------------------------
% 2.42/1.81 % (29178)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_28853 for (2996ds/6Mi)
% 2.42/1.81 % (29178)Instruction limit reached!
% 2.42/1.81 % (29178)------------------------------
% 2.42/1.81 % (29178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.81 % (29178)Termination reason: Unknown
% 2.42/1.81 % (29178)Termination phase: shuffling
% 2.42/1.81
% 2.42/1.81 % (29178)Memory used [KB]: 1279
% 2.42/1.81 % (29178)Time elapsed: 0.003 s
% 2.42/1.81 % (29178)Instructions burned: 8 (million)
% 2.42/1.81 % (29178)------------------------------
% 2.42/1.81 % (29178)------------------------------
% 2.42/1.81 % (29179)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_28853 for (2996ds/1087Mi)
% 2.42/1.82 % (29154)Instruction limit reached!
% 2.42/1.82 % (29154)------------------------------
% 2.42/1.82 % (29154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.82 % (29154)Termination reason: Unknown
% 2.42/1.82 % (29154)Termination phase: Saturation
% 2.42/1.82
% 2.42/1.82 % (29154)Memory used [KB]: 11001
% 2.42/1.82 % (29154)Time elapsed: 0.276 s
% 2.42/1.82 % (29154)Instructions burned: 902 (million)
% 2.42/1.82 % (29154)------------------------------
% 2.42/1.82 % (29154)------------------------------
% 2.42/1.82 % (29180)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_28853 for (2996ds/47Mi)
% 2.42/1.83 % (29181)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_28853 for (2996ds/44Mi)
% 2.42/1.83 % (29180)Instruction limit reached!
% 2.42/1.83 % (29180)------------------------------
% 2.42/1.83 % (29180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.83 % (29180)Termination reason: Unknown
% 2.42/1.83 % (29180)Termination phase: Property scanning
% 2.42/1.83
% 2.42/1.83 % (29180)Memory used [KB]: 1791
% 2.42/1.83 % (29180)Time elapsed: 0.014 s
% 2.42/1.83 % (29180)Instructions burned: 49 (million)
% 2.42/1.83 % (29180)------------------------------
% 2.42/1.83 % (29180)------------------------------
% 2.42/1.83 % (29176)Instruction limit reached!
% 2.42/1.83 % (29176)------------------------------
% 2.42/1.83 % (29176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.83 % (29176)Termination reason: Unknown
% 2.42/1.83 % (29176)Termination phase: Saturation
% 2.42/1.83
% 2.42/1.83 % (29176)Memory used [KB]: 6908
% 2.42/1.83 % (29176)Time elapsed: 0.049 s
% 2.42/1.83 % (29176)Instructions burned: 150 (million)
% 2.42/1.83 % (29176)------------------------------
% 2.42/1.83 % (29176)------------------------------
% 2.42/1.84 % (29181)Instruction limit reached!
% 2.42/1.84 % (29181)------------------------------
% 2.42/1.84 % (29181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.84 % (29181)Termination reason: Unknown
% 2.42/1.84 % (29181)Termination phase: Property scanning
% 2.42/1.84
% 2.42/1.84 % (29181)Memory used [KB]: 1663
% 2.42/1.84 % (29181)Time elapsed: 0.013 s
% 2.42/1.84 % (29181)Instructions burned: 47 (million)
% 2.42/1.84 % (29181)------------------------------
% 2.42/1.84 % (29181)------------------------------
% 2.42/1.84 % (29182)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_28853 for (2996ds/432Mi)
% 2.42/1.84 % (29183)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_28853 for (2996ds/62Mi)
% 2.42/1.85 % (29184)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_28853 for (2996ds/31Mi)
% 2.42/1.86 % (29184)Instruction limit reached!
% 2.42/1.86 % (29184)------------------------------
% 2.42/1.86 % (29184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.86 % (29184)Termination reason: Unknown
% 2.42/1.86 % (29184)Termination phase: Preprocessing 3
% 2.42/1.86
% 2.42/1.86 % (29184)Memory used [KB]: 1663
% 2.42/1.86 % (29184)Time elapsed: 0.010 s
% 2.42/1.86 % (29184)Instructions burned: 32 (million)
% 2.42/1.86 % (29184)------------------------------
% 2.42/1.86 % (29184)------------------------------
% 2.42/1.86 % (29183)Instruction limit reached!
% 2.42/1.86 % (29183)------------------------------
% 2.42/1.86 % (29183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.86 % (29183)Termination reason: Unknown
% 2.42/1.86 % (29183)Termination phase: Saturation
% 2.42/1.86
% 2.42/1.86 % (29183)Memory used [KB]: 6268
% 2.42/1.86 % (29183)Time elapsed: 0.019 s
% 2.42/1.86 % (29183)Instructions burned: 64 (million)
% 2.42/1.86 % (29183)------------------------------
% 2.42/1.86 % (29183)------------------------------
% 2.42/1.87 % (29185)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_28853 for (2995ds/96Mi)
% 2.42/1.87 % (29186)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_28853 for (2995ds/453Mi)
% 2.42/1.88 % (29172)Instruction limit reached!
% 2.42/1.88 % (29172)------------------------------
% 2.42/1.88 % (29172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.88 % (29172)Termination reason: Unknown
% 2.42/1.88 % (29172)Termination phase: Saturation
% 2.42/1.88
% 2.42/1.88 % (29172)Memory used [KB]: 6524
% 2.42/1.88 % (29172)Time elapsed: 0.116 s
% 2.42/1.88 % (29172)Instructions burned: 449 (million)
% 2.42/1.88 % (29172)------------------------------
% 2.42/1.88 % (29172)------------------------------
% 2.42/1.89 % (29161)Instruction limit reached!
% 2.42/1.89 % (29161)------------------------------
% 2.42/1.89 % (29161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.89 % (29161)Termination reason: Unknown
% 2.42/1.89 % (29161)Termination phase: Saturation
% 2.42/1.89
% 2.42/1.89 % (29161)Memory used [KB]: 8059
% 2.42/1.89 % (29161)Time elapsed: 0.296 s
% 2.42/1.89 % (29161)Instructions burned: 881 (million)
% 2.42/1.89 % (29161)------------------------------
% 2.42/1.89 % (29161)------------------------------
% 2.42/1.89 % (29185)Instruction limit reached!
% 2.42/1.89 % (29185)------------------------------
% 2.42/1.89 % (29185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.89 % (29185)Termination reason: Unknown
% 2.42/1.89 % (29185)Termination phase: Saturation
% 2.42/1.89
% 2.42/1.89 % (29185)Memory used [KB]: 6652
% 2.42/1.89 % (29185)Time elapsed: 0.027 s
% 2.42/1.89 % (29185)Instructions burned: 96 (million)
% 2.42/1.89 % (29185)------------------------------
% 2.42/1.89 % (29185)------------------------------
% 2.42/1.89 % (29187)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_28853 for (2995ds/71Mi)
% 2.42/1.90 % (29188)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_28853 for (2995ds/83Mi)
% 2.42/1.90 % (29189)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_28853 for (2995ds/11Mi)
% 2.42/1.91 % (29189)Instruction limit reached!
% 2.42/1.91 % (29189)------------------------------
% 2.42/1.91 % (29189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.91 % (29189)Termination reason: Unknown
% 2.42/1.91 % (29189)Termination phase: shuffling
% 2.42/1.91
% 2.42/1.91 % (29189)Memory used [KB]: 1407
% 2.42/1.91 % (29189)Time elapsed: 0.004 s
% 2.42/1.91 % (29189)Instructions burned: 11 (million)
% 2.42/1.91 % (29189)------------------------------
% 2.42/1.91 % (29189)------------------------------
% 2.42/1.91 % (29187)Instruction limit reached!
% 2.42/1.91 % (29187)------------------------------
% 2.42/1.91 % (29187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.91 % (29187)Termination reason: Unknown
% 2.42/1.91 % (29187)Termination phase: Saturation
% 2.42/1.91
% 2.42/1.91 % (29187)Memory used [KB]: 6268
% 2.42/1.91 % (29187)Time elapsed: 0.021 s
% 2.42/1.91 % (29187)Instructions burned: 71 (million)
% 2.42/1.91 % (29187)------------------------------
% 2.42/1.91 % (29187)------------------------------
% 2.42/1.92 % (29190)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_28853 for (2995ds/41Mi)
% 2.42/1.92 % (29188)Instruction limit reached!
% 2.42/1.92 % (29188)------------------------------
% 2.42/1.92 % (29188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.92 % (29188)Termination reason: Unknown
% 2.42/1.92 % (29188)Termination phase: Saturation
% 2.42/1.92
% 2.42/1.92 % (29188)Memory used [KB]: 6268
% 2.42/1.92 % (29188)Time elapsed: 0.025 s
% 2.42/1.92 % (29188)Instructions burned: 84 (million)
% 2.42/1.92 % (29188)------------------------------
% 2.42/1.92 % (29188)------------------------------
% 2.42/1.92 % (29191)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_28853 for (2995ds/6Mi)
% 2.42/1.92 % (29191)Instruction limit reached!
% 2.42/1.92 % (29191)------------------------------
% 2.42/1.92 % (29191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.92 % (29191)Termination reason: Unknown
% 2.42/1.92 % (29191)Termination phase: shuffling
% 2.42/1.92
% 2.42/1.92 % (29191)Memory used [KB]: 1279
% 2.42/1.92 % (29191)Time elapsed: 0.003 s
% 2.42/1.92 % (29191)Instructions burned: 7 (million)
% 2.42/1.92 % (29191)------------------------------
% 2.42/1.92 % (29191)------------------------------
% 2.42/1.93 % (29190)Instruction limit reached!
% 2.42/1.93 % (29190)------------------------------
% 2.42/1.93 % (29190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.93 % (29190)Termination reason: Unknown
% 2.42/1.93 % (29190)Termination phase: Property scanning
% 2.42/1.93
% 2.42/1.93 % (29190)Memory used [KB]: 1663
% 2.42/1.93 % (29190)Time elapsed: 0.012 s
% 2.42/1.93 % (29190)Instructions burned: 42 (million)
% 2.42/1.93 % (29190)------------------------------
% 2.42/1.93 % (29190)------------------------------
% 2.42/1.93 % (29192)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_28853 for (2995ds/150Mi)
% 2.42/1.93 % (29193)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_28853 for (2995ds/343Mi)
% 2.42/1.94 % (29194)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_28853 for (2995ds/109Mi)
% 2.42/1.95 % (29175)Instruction limit reached!
% 2.42/1.95 % (29175)------------------------------
% 2.42/1.95 % (29175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.95 % (29175)Termination reason: Unknown
% 2.42/1.95 % (29175)Termination phase: Saturation
% 2.42/1.95
% 2.42/1.95 % (29175)Memory used [KB]: 7164
% 2.42/1.95 % (29175)Time elapsed: 0.164 s
% 2.42/1.95 % (29175)Instructions burned: 510 (million)
% 2.42/1.95 % (29175)------------------------------
% 2.42/1.95 % (29175)------------------------------
% 2.42/1.95 % (29182)Instruction limit reached!
% 2.42/1.95 % (29182)------------------------------
% 2.42/1.95 % (29182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.95 % (29182)Termination reason: Unknown
% 2.42/1.95 % (29182)Termination phase: Saturation
% 2.42/1.95
% 2.42/1.95 % (29182)Memory used [KB]: 2814
% 2.42/1.95 % (29182)Time elapsed: 0.111 s
% 2.42/1.95 % (29182)Instructions burned: 435 (million)
% 2.42/1.95 % (29182)------------------------------
% 2.42/1.95 % (29182)------------------------------
% 2.42/1.96 % (29195)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_28853 for (2995ds/253Mi)
% 2.42/1.96 % (29196)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_28853 for (2995ds/140Mi)
% 2.42/1.96 % (29192)First to succeed.
% 2.42/1.96 % (29194)Instruction limit reached!
% 2.42/1.96 % (29194)------------------------------
% 2.42/1.96 % (29194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.96 % (29194)Termination reason: Unknown
% 2.42/1.96 % (29194)Termination phase: Saturation
% 2.42/1.96
% 2.42/1.96 % (29194)Memory used [KB]: 6652
% 2.42/1.96 % (29194)Time elapsed: 0.030 s
% 2.42/1.96 % (29194)Instructions burned: 110 (million)
% 2.42/1.96 % (29194)------------------------------
% 2.42/1.96 % (29194)------------------------------
% 2.42/1.97 % (29192)Refutation found. Thanks to Tanya!
% 2.42/1.97 % SZS status Theorem for DTF2THF_28853
% 2.42/1.97 % SZS output start Proof for DTF2THF_28853
% 2.42/1.97 thf(func_def_0, type, in: $i > $i > $o).
% 2.42/1.97 thf(func_def_1, type, exu: ($i > $o) > $o).
% 2.42/1.97 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 2.42/1.97 thf(func_def_8, type, powerset: $i > $i).
% 2.42/1.97 thf(func_def_10, type, setunion: $i > $i).
% 2.42/1.97 thf(func_def_19, type, descr: ($i > $o) > $i).
% 2.42/1.97 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 2.42/1.97 thf(func_def_26, type, prop2set: $o > $i).
% 2.42/1.97 thf(func_def_36, type, nonempty: $i > $o).
% 2.42/1.97 thf(func_def_69, type, set2prop: $i > $o).
% 2.42/1.97 thf(func_def_88, type, subset: $i > $i > $o).
% 2.42/1.97 thf(func_def_89, type, disjoint: $i > $i > $o).
% 2.42/1.97 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 2.42/1.97 thf(func_def_114, type, binunion: $i > $i > $i).
% 2.42/1.97 thf(func_def_122, type, binintersect: $i > $i > $i).
% 2.42/1.97 thf(func_def_135, type, regular: $i > $o).
% 2.42/1.97 thf(func_def_136, type, setminus: $i > $i > $i).
% 2.42/1.97 thf(func_def_147, type, symdiff: $i > $i > $i).
% 2.42/1.97 thf(func_def_164, type, sP0: $i > $i > $o).
% 2.42/1.97 thf(func_def_165, type, sP1: $i > $o).
% 2.42/1.97 thf(func_def_167, type, sK3: $i > $i).
% 2.42/1.97 thf(func_def_169, type, sK5: $i > $i).
% 2.42/1.97 thf(func_def_180, type, sK16: $i > $o).
% 2.42/1.97 thf(func_def_182, type, sK18: $i > ($i > $o) > $i).
% 2.42/1.97 thf(func_def_200, type, sK36: $i > $i > $i).
% 2.42/1.97 thf(func_def_217, type, sK53: $i > $o).
% 2.42/1.97 thf(func_def_221, type, sK57: $i > $o).
% 2.42/1.97 thf(func_def_226, type, sK62: $i > $i).
% 2.42/1.97 thf(func_def_235, type, sK71: $i > $i > $i).
% 2.42/1.97 thf(func_def_237, type, sK73: $i > $i).
% 2.42/1.97 thf(func_def_238, type, sK74: $i > $i > $i).
% 2.42/1.97 thf(func_def_243, type, sK79: $i > $i > $i).
% 2.42/1.97 thf(func_def_244, type, sK80: $i > ($i > $o) > $i).
% 2.42/1.97 thf(func_def_245, type, sK81: $i > $o).
% 2.42/1.97 thf(func_def_248, type, sK84: $i > $o).
% 2.42/1.97 thf(func_def_253, type, sK89: $i > ($i > $o) > $i).
% 2.42/1.97 thf(func_def_254, type, sK90: $i > $o).
% 2.42/1.97 thf(func_def_259, type, sK95: $i > $i > $i).
% 2.42/1.97 thf(func_def_260, type, sK96: $i > $i > $i).
% 2.42/1.97 thf(func_def_266, type, sK102: $i > ($i > $i > $o) > $i).
% 2.42/1.97 thf(func_def_267, type, sK103: $i > ($i > $i > $o) > $i).
% 2.42/1.97 thf(func_def_268, type, sK104: $i > $i > ($i > $i > $o) > $i).
% 2.42/1.97 thf(func_def_269, type, sK105: $i > $i > $o).
% 2.42/1.97 thf(func_def_271, type, sK107: $i > $i).
% 2.42/1.97 thf(func_def_272, type, sK108: $i > $i).
% 2.42/1.97 thf(func_def_273, type, sK109: $i > $o).
% 2.42/1.97 thf(func_def_274, type, sK110: $i > $i).
% 2.42/1.97 thf(func_def_275, type, sK111: ($i > $o) > $i).
% 2.42/1.97 thf(func_def_278, type, sK114: $i > $i).
% 2.42/1.97 thf(func_def_303, type, sK139: $i > $o).
% 2.42/1.97 thf(func_def_307, type, sK143: $i > $o).
% 2.42/1.97 thf(func_def_311, type, sK147: $i > $o).
% 2.42/1.97 thf(func_def_314, type, sK150: $i > $o).
% 2.42/1.97 thf(func_def_316, type, sK152: ($i > $o) > $i).
% 2.42/1.97 thf(func_def_317, type, sK153: ($i > $o) > $i).
% 2.42/1.97 thf(func_def_321, type, sK157: $i > $o).
% 2.42/1.97 thf(func_def_334, type, sK170: $i > $o).
% 2.42/1.97 thf(func_def_351, type, sK187: $i > $i > $i).
% 2.42/1.97 thf(func_def_368, type, sK204: $o > $i > $i > $i).
% 2.42/1.97 thf(func_def_377, type, sK213: $i > $o).
% 2.42/1.97 thf(func_def_378, type, sK214: $i > $i).
% 2.42/1.97 thf(func_def_379, type, sK215: ($i > $o) > $i).
% 2.42/1.97 thf(func_def_380, type, sK216: $i > $i > $i).
% 2.42/1.97 thf(func_def_387, type, sK223: $i > $o).
% 2.42/1.97 thf(func_def_389, type, sK225: ($i > $o) > $i > $i).
% 2.42/1.97 thf(func_def_391, type, sK227: $i > $o).
% 2.42/1.97 thf(func_def_393, type, sK229: $i > $o).
% 2.42/1.97 thf(func_def_394, type, sK230: $i > $o).
% 2.42/1.97 thf(func_def_395, type, sK231: ($i > $o) > ($i > $o) > $i).
% 2.42/1.97 thf(func_def_396, type, sK232: ($i > $o) > ($i > $o) > $i).
% 2.42/1.97 thf(func_def_402, type, sK238: $i > ($i > $o) > $i).
% 2.42/1.97 thf(func_def_403, type, sK239: $i > $o).
% 2.42/1.97 thf(func_def_419, type, sK255: $i > $i > $i).
% 2.42/1.97 thf(func_def_423, type, sK259: $i > ($i > $o) > $i).
% 2.42/1.97 thf(func_def_424, type, sK260: $i > $o).
% 2.42/1.97 thf(func_def_427, type, sK263: $i > $i).
% 2.42/1.97 thf(func_def_436, type, sK272: ($i > $o) > ($i > $o) > $i > $i > $i).
% 2.42/1.97 thf(func_def_437, type, sK273: ($i > $o) > ($i > $o) > $i > $i > $i).
% 2.42/1.97 thf(func_def_440, type, sK276: $i > $o).
% 2.42/1.97 thf(func_def_441, type, sK277: $i > $o).
% 2.42/1.97 thf(func_def_444, type, sK280: $i > $o).
% 2.42/1.97 thf(func_def_451, type, sK287: $i > $i).
% 2.42/1.97 thf(func_def_452, type, sK288: $i > $i).
% 2.42/1.97 thf(func_def_453, type, sK289: $i > $i).
% 2.42/1.97 thf(func_def_454, type, sK290: $i > $i).
% 2.42/1.97 thf(func_def_455, type, sK291: $i > $i > $i).
% 2.42/1.97 thf(func_def_456, type, sK292: $i > $i > $i).
% 2.42/1.97 thf(func_def_457, type, sK293: $i > $i > $i > $i).
% 2.42/1.97 thf(func_def_458, type, sK294: $i > $i > $i > $i).
% 2.42/1.97 thf(func_def_459, type, sK295: $i > $i > $i > $i).
% 2.42/1.97 thf(func_def_460, type, sK296: $i > $i > $i).
% 2.42/1.97 thf(func_def_461, type, sK297: $i > $i > $i).
% 2.42/1.97 thf(func_def_462, type, sK298: $i > $i > $i).
% 2.42/1.97 thf(func_def_463, type, sK299: $i > $i).
% 2.42/1.97 thf(func_def_464, type, sK300: $i > $i > $i > $i).
% 2.42/1.97 thf(func_def_466, type, sK302: $i > $i).
% 2.42/1.97 thf(func_def_467, type, sK303: $i > $i).
% 2.42/1.97 thf(func_def_468, type, sK304: $i > $i).
% 2.42/1.97 thf(func_def_469, type, sK305: $i > $i).
% 2.42/1.97 thf(func_def_470, type, sK306: ($i > $o) > $i > $i).
% 2.42/1.97 thf(func_def_472, type, sK308: $i > $o).
% 2.42/1.97 thf(func_def_475, type, sK311: $i > $i).
% 2.42/1.97 thf(func_def_484, type, sK320: $i > $o).
% 2.42/1.97 thf(func_def_486, type, sK322: $i > $o).
% 2.42/1.97 thf(func_def_491, type, sK327: ($i > $o) > ($i > $o) > $i).
% 2.42/1.97 thf(func_def_492, type, sK328: ($i > $o) > ($i > $o) > $i).
% 2.42/1.97 thf(func_def_493, type, sK329: $i > $o).
% 2.42/1.97 thf(func_def_494, type, sK330: $i > $o).
% 2.42/1.97 thf(func_def_501, type, sK337: $i > $o).
% 2.42/1.97 thf(func_def_502, type, sK338: ($i > $o) > $i).
% 2.42/1.97 thf(func_def_519, type, sK355: $i > $o).
% 2.42/1.97 thf(func_def_522, type, sK358: $i > ($i > $o) > $i).
% 2.42/1.97 thf(func_def_524, type, ph360: !>[X0: $tType]:(X0)).
% 2.42/1.97 thf(f2684,plain,(
% 2.42/1.97 $false),
% 2.42/1.97 inference(avatar_sat_refutation,[status(thm)],[f2590,f2661,f2680])).
% 2.42/1.97 thf(f2680,plain,(
% 2.42/1.97 ~spl359_2),
% 2.42/1.97 inference(avatar_contradiction_clause,[status(thm)],[f2679])).
% 2.42/1.97 thf(f2679,plain,(
% 2.42/1.97 $false | ~spl359_2),
% 2.42/1.97 inference(trivial_inequality_removal,[status(thm)],[f2669])).
% 2.42/1.97 thf(f2669,plain,(
% 2.42/1.97 ($true != $true) | ~spl359_2),
% 2.42/1.97 inference(superposition,[status(thm)],[f1282,f2581])).
% 2.42/1.97 thf(f2581,plain,(
% 2.42/1.97 ( ! [X3 : $o] : (($true = X3)) ) | ~spl359_2),
% 2.42/1.97 inference(avatar_component_clause,[status(thm)],[f2580])).
% 2.42/1.97 thf(f2580,definition,(
% 2.42/1.97 spl359_2 <=> ! [X3 : $o] : ($true = X3)),
% 2.42/1.97 introduced(definition,[new_symbols(naming,[spl359_2])],[avatar_definition])).
% 2.42/1.97 thf(f1282,plain,(
% 2.42/1.97 ($true != (in @ sK51 @ sK50))),
% 2.42/1.97 inference(cnf_transformation,[status(thm)],[f672])).
% 2.42/1.97 thf(f672,plain,(
% 2.42/1.97 (noeltsimpempty = $true) & (setunionI = $true) & (emptyinunitempty = $true) & (setextAx = $true) & (dsetconstrER = $true) & (emptyinPowerset = $true) & (prop2setE = $true) & (omegaSAx = $true) & (subsetE = $true) & (sepInPowerset = $true) & (subsetE2 = $true) & (omegaIndAx = $true) & (setadjoinIL = $true) & (prop2set2propI = $true) & (symdiffI1 = $true) & (binintersectER = $true) & (notequalI2 = $true) & (setminusEL = $true) & (exu__Cong = $true) & (binunionLsub = $true) & (setadjoinE = $true) & (binunionRsub = $true) & (symdiffIneg1 = $true) & (quantDeMorgan1 = $true) & (emptysetsubset = $true) & (setbeta = $true) & (powersetE1 = $true) & (nonemptyImpWitness = $true) & (binunionE = $true) & (binintersectSubset5 = $true) & (binintersectSubset4 = $true) & (exuE3u = $true) & (binintersectRsub = $true) & (binintersectEL = $true) & (setminusSubset2 = $true) & (setadjoinSub2 = $true) & (eqinunit = $true) & (upairsetIR = $true) & (setadjoinOr = $true) & (notdallE = $true) & (eqimpsubset2 = $true) & (omega__Cong = $true) & (exuI2 = $true) & (setminusILneg = $true) & (binunionEcases = $true) & (in__Cong = $true) & (quantDeMorgan2 = $true) & (emptysetimpfalse = $true) & (emptyInPowerset = $true) & (emptyI = $true) & (powersetsubset = $true) & (binunionIL = $true) & (prop2setI = $true) & (exuE3e = $true) & (setoftrueEq = $true) & (setunionAx = $true) & (notinemptyset = $true) & (inCongP = $true) & (powersetI1 = $true) & (setminusELneg = $true) & (setadjoin__Cong = $true) & (notdexE = $true) & (setminusIRneg = $true) & (setadjoinAx = $true) & (notinsingleton = $true) & (setunionE = $true) & (exuE2 = $true) & (quantDeMorgan4 = $true) & (quantDeMorgan3 = $true) & (powersetI = $true) & (emptysetE = $true) & (powersetE = $true) & (setextsub = $true) & (descr__Cong = $true) & (sepSubset = $true) & (upairsetE = $true) & (subsetTrans = $true) & (binunionIR = $true) & (exuEu = $true) & (nonemptyI = $true) & (subPowSU = $true) & (setminusERneg = $true) & (eqimpsubset1 = $true) & (symdiffI2 = $true) & (notsubsetI = $true) & (setadjoinSub = $true) & (setminusER = $true) & (binintersectI = $true) & (emptyE1 = $true) & (dsetconstr__Cong = $true) & (bs114d = $true) & (setunion__Cong = $true) & (exuI1 = $true) & (setminusSubset1 = $true) & (subsetI1 = $true) & (binintersectSubset1 = $true) & (disjointsetsI1 = $true) & (nonemptyE1 = $true) & (powerset__Cong = $true) & (exuE1 = $true) & (vacuousDall = $true) & (($true != (in @ sK51 @ sK52)) & ((in @ sK51 @ (symdiff @ sK52 @ sK50)) = $true) & ($true != (in @ sK51 @ sK50))) & (nonemptyI1 = $true) & (symdiffE = $true) & (binintersectLsub = $true) & (setminusI = $true) & (dsetconstrEL = $true) & (subsetRefl = $true) & (binintersectSubset3 = $true) & (notequalI1 = $true) & (emptysetAx = $true) & (replAx = $true) & (powersetAx = $true) & (omega0Ax = $true) & (subsetemptysetimpeq = $true) & (descrp = $true) & (emptyset__Cong = $true) & (setadjoinIR = $true) & (inPowerset = $true) & (setext = $true) & (upairsetIL = $true) & (subsetI2 = $true) & (upairset2IR = $true) & (setminusLsub = $true) & (binintersectSubset2 = $true) & (foundationAx = $true) & (singletonsswitch = $true) & (dsetconstrI = $true) & (subset2powerset = $true) & (uniqinunit = $true) & (exuI3 = $true) & (wellorderingAx = $true)),
% 2.42/1.97 inference(skolemisation,[status(esa),new_symbols(skolem,[sK50,sK51,sK52])],[f482,f671])).
% 2.42/1.97 thf(f671,plain,(
% 2.42/1.97 ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ X2)) & ((in @ X1 @ (symdiff @ X2 @ X0)) = $true) & ((in @ X1 @ X0) != $true)) => (($true != (in @ sK51 @ sK52)) & ((in @ sK51 @ (symdiff @ sK52 @ sK50)) = $true) & ($true != (in @ sK51 @ sK50)))),
% 2.42/1.97 introduced(definition,[],[choice_axiom])).
% 2.42/1.97 thf(f482,plain,(
% 2.42/1.97 (noeltsimpempty = $true) & (setunionI = $true) & (emptyinunitempty = $true) & (setextAx = $true) & (dsetconstrER = $true) & (emptyinPowerset = $true) & (prop2setE = $true) & (omegaSAx = $true) & (subsetE = $true) & (sepInPowerset = $true) & (subsetE2 = $true) & (omegaIndAx = $true) & (setadjoinIL = $true) & (prop2set2propI = $true) & (symdiffI1 = $true) & (binintersectER = $true) & (notequalI2 = $true) & (setminusEL = $true) & (exu__Cong = $true) & (binunionLsub = $true) & (setadjoinE = $true) & (binunionRsub = $true) & (symdiffIneg1 = $true) & (quantDeMorgan1 = $true) & (emptysetsubset = $true) & (setbeta = $true) & (powersetE1 = $true) & (nonemptyImpWitness = $true) & (binunionE = $true) & (binintersectSubset5 = $true) & (binintersectSubset4 = $true) & (exuE3u = $true) & (binintersectRsub = $true) & (binintersectEL = $true) & (setminusSubset2 = $true) & (setadjoinSub2 = $true) & (eqinunit = $true) & (upairsetIR = $true) & (setadjoinOr = $true) & (notdallE = $true) & (eqimpsubset2 = $true) & (omega__Cong = $true) & (exuI2 = $true) & (setminusILneg = $true) & (binunionEcases = $true) & (in__Cong = $true) & (quantDeMorgan2 = $true) & (emptysetimpfalse = $true) & (emptyInPowerset = $true) & (emptyI = $true) & (powersetsubset = $true) & (binunionIL = $true) & (prop2setI = $true) & (exuE3e = $true) & (setoftrueEq = $true) & (setunionAx = $true) & (notinemptyset = $true) & (inCongP = $true) & (powersetI1 = $true) & (setminusELneg = $true) & (setadjoin__Cong = $true) & (notdexE = $true) & (setminusIRneg = $true) & (setadjoinAx = $true) & (notinsingleton = $true) & (setunionE = $true) & (exuE2 = $true) & (quantDeMorgan4 = $true) & (quantDeMorgan3 = $true) & (powersetI = $true) & (emptysetE = $true) & (powersetE = $true) & (setextsub = $true) & (descr__Cong = $true) & (sepSubset = $true) & (upairsetE = $true) & (subsetTrans = $true) & (binunionIR = $true) & (exuEu = $true) & (nonemptyI = $true) & (subPowSU = $true) & (setminusERneg = $true) & (eqimpsubset1 = $true) & (symdiffI2 = $true) & (notsubsetI = $true) & (setadjoinSub = $true) & (setminusER = $true) & (binintersectI = $true) & (emptyE1 = $true) & (dsetconstr__Cong = $true) & (bs114d = $true) & (setunion__Cong = $true) & (exuI1 = $true) & (setminusSubset1 = $true) & (subsetI1 = $true) & (binintersectSubset1 = $true) & (disjointsetsI1 = $true) & (nonemptyE1 = $true) & (powerset__Cong = $true) & (exuE1 = $true) & (vacuousDall = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ X2)) & ((in @ X1 @ (symdiff @ X2 @ X0)) = $true) & ((in @ X1 @ X0) != $true)) & (nonemptyI1 = $true) & (symdiffE = $true) & (binintersectLsub = $true) & (setminusI = $true) & (dsetconstrEL = $true) & (subsetRefl = $true) & (binintersectSubset3 = $true) & (notequalI1 = $true) & (emptysetAx = $true) & (replAx = $true) & (powersetAx = $true) & (omega0Ax = $true) & (subsetemptysetimpeq = $true) & (descrp = $true) & (emptyset__Cong = $true) & (setadjoinIR = $true) & (inPowerset = $true) & (setext = $true) & (upairsetIL = $true) & (subsetI2 = $true) & (upairset2IR = $true) & (setminusLsub = $true) & (binintersectSubset2 = $true) & (foundationAx = $true) & (singletonsswitch = $true) & (dsetconstrI = $true) & (subset2powerset = $true) & (uniqinunit = $true) & (exuI3 = $true) & (wellorderingAx = $true)),
% 2.42/1.97 inference(flattening,[status(thm)],[f481])).
% 2.42/1.97 thf(f481,plain,(
% 2.42/1.97 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ (symdiff @ X2 @ X0)) = $true) & ((in @ X1 @ X0) != $true)) & ($true != (in @ X1 @ X2))) & (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)),
% 2.42/1.97 inference(ennf_transformation,[status(thm)],[f426])).
% 2.42/1.97 thf(f426,plain,(
% 2.42/1.97 ~((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) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ X2)) => (((in @ X1 @ X0) != $true) => ((in @ X1 @ (symdiff @ X2 @ X0)) != $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.42/1.97 inference(flattening,[status(thm)],[f307])).
% 2.42/1.97 thf(f307,plain,(
% 2.42/1.97 ~((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) => ! [X0 : $i,X1 : $i,X2 : $i] : (~($true = (in @ X1 @ X2)) => (~((in @ X1 @ X0) = $true) => ~((in @ X1 @ (symdiff @ X2 @ X0)) = $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.42/1.97 inference(fool_elimination,[status(thm)],[f306])).
% 2.42/1.97 thf(f306,plain,(
% 2.42/1.97 ~(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 => ! [X0 : $i,X1 : $i,X2 : $i] : (~(in @ X1 @ X2) => (~(in @ X1 @ X0) => ~(in @ X1 @ (symdiff @ X2 @ X0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.42/1.97 inference(rectify,[status(thm)],[f135])).
% 2.42/1.97 thf(f135,negated_conjecture,(
% 2.42/1.97 ~(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 => ! [X4 : $i,X1 : $i,X3 : $i] : (~(in @ X1 @ X3) => (~(in @ X1 @ X4) => ~(in @ X1 @ (symdiff @ X3 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.42/1.97 inference(negated_conjecture,[status(cth)],[f134])).
% 2.42/1.97 thf(f134,conjecture,(
% 2.42/1.97 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 => ! [X4 : $i,X1 : $i,X3 : $i] : (~(in @ X1 @ X3) => (~(in @ X1 @ X4) => ~(in @ X1 @ (symdiff @ X3 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.42/1.97 file('/export/starexec/sandbox/tmp/tmp.75Z7m6xG9f/DTF2THF_28853.p',symdiffIneg2)).
% 2.42/1.97 thf(f2661,plain,(
% 2.42/1.97 ~spl359_4),
% 2.42/1.97 inference(avatar_contradiction_clause,[status(thm)],[f2660])).
% 2.42/1.97 thf(f2660,plain,(
% 2.42/1.97 $false | ~spl359_4),
% 2.42/1.97 inference(subsumption_resolution,[status(thm)],[f2659,f1282])).
% 2.42/1.97 thf(f2659,plain,(
% 2.42/1.97 ($true = (in @ sK51 @ sK50)) | ~spl359_4),
% 2.42/1.97 inference(subsumption_resolution,[status(thm)],[f2657,f1284])).
% 2.42/1.97 thf(f1284,plain,(
% 2.42/1.97 ($true != (in @ sK51 @ sK52))),
% 2.42/1.97 inference(cnf_transformation,[status(thm)],[f672])).
% 2.42/1.97 thf(f2657,plain,(
% 2.42/1.97 ($true = (in @ sK51 @ sK52)) | ($true = (in @ sK51 @ sK50)) | ~spl359_4),
% 2.42/1.97 inference(trivial_inequality_removal,[status(thm)],[f2655])).
% 2.42/1.97 thf(f2655,plain,(
% 2.42/1.97 ($true = (in @ sK51 @ sK52)) | ($true = (in @ sK51 @ sK50)) | ($true != $true) | ~spl359_4),
% 2.42/1.97 inference(superposition,[status(thm)],[f2589,f1283])).
% 2.42/1.97 thf(f1283,plain,(
% 2.42/1.97 ((in @ sK51 @ (symdiff @ sK52 @ sK50)) = $true)),
% 2.42/1.97 inference(cnf_transformation,[status(thm)],[f672])).
% 2.42/1.97 thf(f2589,plain,(
% 2.42/1.97 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ (symdiff @ X1 @ X2)) != $true) | ((in @ X0 @ X1) = $true) | ((in @ X0 @ X2) = $true)) ) | ~spl359_4),
% 2.42/1.97 inference(avatar_component_clause,[status(thm)],[f2588])).
% 2.42/1.97 thf(f2588,definition,(
% 2.42/1.97 spl359_4 <=> ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ X1) = $true) | ((in @ X0 @ X2) = $true) | ((in @ X0 @ (symdiff @ X1 @ X2)) != $true))),
% 2.42/1.97 introduced(definition,[new_symbols(naming,[spl359_4])],[avatar_definition])).
% 2.42/1.97 thf(f2590,plain,(
% 2.42/1.97 spl359_2 | spl359_4),
% 2.42/1.97 inference(avatar_split_clause,[status(thm)],[f2426,f2588,f2580])).
% 2.42/1.97 thf(f2426,plain,(
% 2.42/1.97 ( ! [X2 : $i,X3 : $o,X0 : $i,X1 : $i] : (((in @ X0 @ X1) = $true) | ((in @ X0 @ (symdiff @ X1 @ X2)) != $true) | ($true = X3) | ((in @ X0 @ X2) = $true)) )),
% 2.42/1.97 inference(trivial_inequality_removal,[status(thm)],[f2006])).
% 2.42/1.97 thf(f2006,plain,(
% 2.42/1.97 ( ! [X2 : $i,X3 : $o,X0 : $i,X1 : $i] : (((in @ X0 @ (symdiff @ X1 @ X2)) != $true) | ((in @ X0 @ X1) = $true) | ((in @ X0 @ X2) = $true) | ($true != $true) | ($true = X3)) )),
% 2.42/1.97 inference(definition_unfolding,[status(thm)],[f1487,f1280])).
% 2.42/1.97 thf(f1280,plain,(
% 2.42/1.97 (symdiffE = $true)),
% 2.42/1.97 inference(cnf_transformation,[status(thm)],[f672])).
% 2.42/1.97 thf(f1487,plain,(
% 2.42/1.97 ( ! [X2 : $i,X3 : $o,X0 : $i,X1 : $i] : (((in @ X0 @ X1) = $true) | ((in @ X0 @ X2) = $true) | ($true = X3) | ((in @ X0 @ (symdiff @ X1 @ X2)) != $true) | (symdiffE != $true)) )),
% 2.42/1.97 inference(cnf_transformation,[status(thm)],[f788])).
% 2.42/1.97 thf(f788,plain,(
% 2.42/1.97 (! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $o] : ((((in @ X0 @ X2) != $true) & ((in @ X0 @ X1) = $true) & ($true != X3)) | (((in @ X0 @ X1) != $true) & ($true != X3) & ((in @ X0 @ X2) = $true)) | ($true = X3)) | ((in @ X0 @ (symdiff @ X1 @ X2)) != $true)) | (symdiffE != $true)) & ((symdiffE = $true) | (((($true = (in @ sK118 @ sK120)) | ((in @ sK118 @ sK119) != $true) | (sK121 = $true)) & (((in @ sK118 @ sK119) = $true) | (sK121 = $true) | ($true != (in @ sK118 @ sK120))) & (sK121 != $true)) & ($true = (in @ sK118 @ (symdiff @ sK119 @ sK120)))))),
% 2.42/1.97 inference(skolemisation,[status(esa),new_symbols(skolem,[sK118,sK119,sK120,sK121])],[f785,f787,f786])).
% 2.42/1.97 thf(f786,plain,(
% 2.42/1.97 ? [X4 : $i,X5 : $i,X6 : $i] : (? [X7 : $o] : ((((in @ X4 @ X6) = $true) | ($true != (in @ X4 @ X5)) | ($true = X7)) & (($true = (in @ X4 @ X5)) | ($true = X7) | ((in @ X4 @ X6) != $true)) & ($true != X7)) & ($true = (in @ X4 @ (symdiff @ X5 @ X6)))) => (? [X7 : $o] : ((($true = (in @ sK118 @ sK120)) | ((in @ sK118 @ sK119) != $true) | ($true = X7)) & (((in @ sK118 @ sK119) = $true) | ($true = X7) | ($true != (in @ sK118 @ sK120))) & ($true != X7)) & ($true = (in @ sK118 @ (symdiff @ sK119 @ sK120))))),
% 2.42/1.97 introduced(definition,[],[choice_axiom])).
% 2.42/1.97 thf(f787,plain,(
% 2.42/1.97 ? [X7 : $o] : ((($true = (in @ sK118 @ sK120)) | ((in @ sK118 @ sK119) != $true) | ($true = X7)) & (((in @ sK118 @ sK119) = $true) | ($true = X7) | ($true != (in @ sK118 @ sK120))) & ($true != X7)) => ((($true = (in @ sK118 @ sK120)) | ((in @ sK118 @ sK119) != $true) | (sK121 = $true)) & (((in @ sK118 @ sK119) = $true) | (sK121 = $true) | ($true != (in @ sK118 @ sK120))) & (sK121 != $true))),
% 2.42/1.97 introduced(definition,[],[choice_axiom])).
% 2.42/1.97 thf(f785,plain,(
% 2.42/1.97 (! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $o] : ((((in @ X0 @ X2) != $true) & ((in @ X0 @ X1) = $true) & ($true != X3)) | (((in @ X0 @ X1) != $true) & ($true != X3) & ((in @ X0 @ X2) = $true)) | ($true = X3)) | ((in @ X0 @ (symdiff @ X1 @ X2)) != $true)) | (symdiffE != $true)) & ((symdiffE = $true) | ? [X4 : $i,X5 : $i,X6 : $i] : (? [X7 : $o] : ((((in @ X4 @ X6) = $true) | ($true != (in @ X4 @ X5)) | ($true = X7)) & (($true = (in @ X4 @ X5)) | ($true = X7) | ((in @ X4 @ X6) != $true)) & ($true != X7)) & ($true = (in @ X4 @ (symdiff @ X5 @ X6)))))),
% 2.42/1.97 inference(rectify,[status(thm)],[f784])).
% 2.42/1.97 thf(f784,plain,(
% 2.42/1.97 (! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $o] : ((((in @ X0 @ X2) != $true) & ((in @ X0 @ X1) = $true) & ($true != X3)) | (((in @ X0 @ X1) != $true) & ($true != X3) & ((in @ X0 @ X2) = $true)) | ($true = X3)) | ((in @ X0 @ (symdiff @ X1 @ X2)) != $true)) | (symdiffE != $true)) & ((symdiffE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $o] : ((((in @ X0 @ X2) = $true) | ((in @ X0 @ X1) != $true) | ($true = X3)) & (((in @ X0 @ X1) = $true) | ($true = X3) | ((in @ X0 @ X2) != $true)) & ($true != X3)) & ((in @ X0 @ (symdiff @ X1 @ X2)) = $true)))),
% 2.42/1.97 inference(nnf_transformation,[status(thm)],[f447])).
% 2.42/1.97 thf(f447,plain,(
% 2.42/1.97 ! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $o] : ((((in @ X0 @ X2) != $true) & ((in @ X0 @ X1) = $true) & ($true != X3)) | (((in @ X0 @ X1) != $true) & ($true != X3) & ((in @ X0 @ X2) = $true)) | ($true = X3)) | ((in @ X0 @ (symdiff @ X1 @ X2)) != $true)) <=> (symdiffE = $true)),
% 2.42/1.97 inference(flattening,[status(thm)],[f446])).
% 2.42/1.97 thf(f446,plain,(
% 2.42/1.97 ! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $o] : ((($true = X3) | ((($true != X3) & ((in @ X0 @ X2) = $true)) & ((in @ X0 @ X1) != $true))) | ((($true != X3) & ((in @ X0 @ X2) != $true)) & ((in @ X0 @ X1) = $true))) | ((in @ X0 @ (symdiff @ X1 @ X2)) != $true)) <=> (symdiffE = $true)),
% 2.42/1.97 inference(ennf_transformation,[status(thm)],[f430])).
% 2.42/1.97 thf(f430,plain,(
% 2.42/1.97 ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (symdiff @ X1 @ X2)) = $true) => ! [X3 : $o] : ((((in @ X0 @ X1) = $true) => (((in @ X0 @ X2) != $true) => ($true = X3))) => ((((in @ X0 @ X1) != $true) => (((in @ X0 @ X2) = $true) => ($true = X3))) => ($true = X3)))) <=> (symdiffE = $true)),
% 2.42/1.97 inference(flattening,[status(thm)],[f323])).
% 2.42/1.97 thf(f323,plain,(
% 2.42/1.97 (symdiffE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (symdiff @ X1 @ X2)) = $true) => ! [X3 : $o] : ((((in @ X0 @ X1) = $true) => (~((in @ X0 @ X2) = $true) => ($true = X3))) => ((~((in @ X0 @ X1) = $true) => (((in @ X0 @ X2) = $true) => ($true = X3))) => ($true = X3))))),
% 2.42/1.97 inference(fool_elimination,[status(thm)],[f322])).
% 2.42/1.97 thf(f322,plain,(
% 2.42/1.97 (symdiffE = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (symdiff @ X1 @ X2)) => ! [X3 : $o] : (((in @ X0 @ X1) => (~(in @ X0 @ X2) => X3)) => ((~(in @ X0 @ X1) => ((in @ X0 @ X2) => X3)) => X3))))),
% 2.42/1.97 inference(rectify,[status(thm)],[f130])).
% 2.42/1.97 thf(f130,axiom,(
% 2.42/1.97 (symdiffE = ! [X1 : $i,X3 : $i,X4 : $i] : ((in @ X1 @ (symdiff @ X3 @ X4)) => ! [X0 : $o] : (((in @ X1 @ X3) => (~(in @ X1 @ X4) => X0)) => ((~(in @ X1 @ X3) => ((in @ X1 @ X4) => X0)) => X0))))),
% 2.42/1.97 file('/export/starexec/sandbox/tmp/tmp.75Z7m6xG9f/DTF2THF_28853.p',symdiffE)).
% 2.42/1.97 % SZS output end Proof for DTF2THF_28853
% 2.42/1.97 % (29192)------------------------------
% 2.42/1.97 % (29192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.42/1.97 % (29192)Termination reason: Refutation
% 2.42/1.97
% 2.42/1.97 % (29192)Memory used [KB]: 7547
% 2.42/1.97 % (29192)Time elapsed: 0.037 s
% 2.42/1.97 % (29192)Instructions burned: 113 (million)
% 2.42/1.97 % (29192)------------------------------
% 2.42/1.97 % (29192)------------------------------
% 2.42/1.97 % (29131)Success in time 0.502 s
%------------------------------------------------------------------------------