%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU639^1 : 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 : n006.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 09:35:49 AM UTC 2026
% Result : Theorem 57.88s 9.52s
% Output : Refutation 57.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 17
% Syntax : Number of formulae : 108 ( 16 unt; 0 typ; 8 def)
% Number of atoms : 3567 ( 993 equ; 0 cnn)
% Maximal formula atoms : 161 ( 33 avg)
% Number of connectives : 2510 ( 241 ~; 255 |; 542 &; 796 @)
% ( 13 <=>; 663 =>; 0 <=; 0 <~>)
% Maximal formula depth : 167 ( 16 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 54 ( 54 >; 0 *; 0 +; 0 <<)
% Number of symbols : 301 ( 298 usr; 170 con; 0-4 aty)
% Number of variables : 259 ( 85 ^; 137 !; 37 ?; 259 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_153,type,
iskpair: $i > $o ).
thf(func_def_158,type,
kpair: $i > $i > $i ).
thf(func_def_160,type,
cartprod: $i > $i > $i ).
thf(func_def_177,type,
singleton: $i > $o ).
thf(func_def_179,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_193,type,
sP0: $o > $i > $i > $i > $o ).
thf(func_def_194,type,
sP1: $i > $i > $o ).
thf(func_def_195,type,
sP2: $i > $o ).
thf(func_def_196,type,
sP3: $i > $i > $o ).
thf(func_def_197,type,
sP4: $i > $i > $o ).
thf(func_def_207,type,
sK14: $i > $i ).
thf(func_def_211,type,
sK18: $i > $i > $i ).
thf(func_def_221,type,
sK28: $i > $i > $i ).
thf(func_def_228,type,
sK35: $i > $o ).
thf(func_def_236,type,
sK43: $i > $o ).
thf(func_def_239,type,
sK46: $i > ( $i > $o ) > $i ).
thf(func_def_251,type,
sK58: ( $i > $o ) > $i ).
thf(func_def_252,type,
sK59: ( $i > $o ) > $i ).
thf(func_def_253,type,
sK60: $i > $o ).
thf(func_def_264,type,
sK71: $i > ( $i > $o ) > $i ).
thf(func_def_265,type,
sK72: $i > $o ).
thf(func_def_273,type,
sK80: $i > $o ).
thf(func_def_274,type,
sK81: $i > $i ).
thf(func_def_275,type,
sK82: ( $i > $o ) > $i ).
thf(func_def_287,type,
sK94: $i > $o ).
thf(func_def_294,type,
sK101: $i > $i > $i ).
thf(func_def_295,type,
sK102: $i > $i > $i ).
thf(func_def_296,type,
sK103: $i > $i > $i ).
thf(func_def_297,type,
sK104: $i > $i > $i ).
thf(func_def_298,type,
sK105: $i > $i > $i ).
thf(func_def_299,type,
sK106: $i > $i > $i > $i ).
thf(func_def_300,type,
sK107: $i > $i ).
thf(func_def_301,type,
sK108: $i > $i ).
thf(func_def_302,type,
sK109: $i > $i ).
thf(func_def_303,type,
sK110: $i > $i ).
thf(func_def_304,type,
sK111: $i > $i > $i > $i ).
thf(func_def_305,type,
sK112: $i > $i > $i > $i ).
thf(func_def_306,type,
sK113: $i > $i > $i ).
thf(func_def_307,type,
sK114: $i > $i > $i ).
thf(func_def_308,type,
sK115: $i > $i > $i ).
thf(func_def_309,type,
sK116: $i > $i ).
thf(func_def_311,type,
sK118: $i > $i ).
thf(func_def_312,type,
sK119: $i > $i ).
thf(func_def_315,type,
sK122: ( $i > $o ) > $i ).
thf(func_def_316,type,
sK123: $i > $o ).
thf(func_def_317,type,
sK124: $i > $i ).
thf(func_def_321,type,
sK128: $i > $i > $i > $i ).
thf(func_def_322,type,
sK129: $i > $i > $i > $i ).
thf(func_def_333,type,
sK140: $i > $i ).
thf(func_def_334,type,
sK141: $i > $i > $i ).
thf(func_def_339,type,
sK146: $i > $i > $o ).
thf(func_def_340,type,
sK147: $i > $i ).
thf(func_def_341,type,
sK148: $i > $i ).
thf(func_def_342,type,
sK149: ( $i > $i > $o ) > $i > $i ).
thf(func_def_343,type,
sK150: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_344,type,
sK151: ( $i > $i > $o ) > $i > $i ).
thf(func_def_349,type,
sK156: ( $i > $o ) > $i > $i ).
thf(func_def_351,type,
sK158: $i > $o ).
thf(func_def_363,type,
sK170: $i > $i ).
thf(func_def_367,type,
sK174: $i > $i > $i ).
thf(func_def_369,type,
sK176: $i > $o ).
thf(func_def_370,type,
sK177: ( $i > $o ) > $i > $i ).
thf(func_def_375,type,
sK182: $i > $o ).
thf(func_def_376,type,
sK183: $o > $i > $i > $i ).
thf(func_def_382,type,
sK189: $i > $i ).
thf(func_def_383,type,
sK190: $i > $i ).
thf(func_def_391,type,
sK198: ( $i > $o ) > $i > $i ).
thf(func_def_393,type,
sK200: $i > $o ).
thf(func_def_395,type,
sK202: $i > $o ).
thf(func_def_398,type,
sK205: $i > ( $i > $o ) > $i ).
thf(func_def_399,type,
sK206: $i > ( $i > $o ) > $i ).
thf(func_def_402,type,
sK209: $i > $o ).
thf(func_def_422,type,
sK229: $i > $o ).
thf(func_def_423,type,
sK230: $i > $o ).
thf(func_def_424,type,
sK231: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_425,type,
sK232: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_426,type,
sK233: ( $i > $o ) > $i > $i ).
thf(func_def_428,type,
sK235: $i > $o ).
thf(func_def_434,type,
sK241: $i > $i > $i ).
thf(func_def_449,type,
sK256: $i > $i > $i ).
thf(func_def_460,type,
sK267: $i > $o ).
thf(func_def_461,type,
sK268: $i > $o ).
thf(func_def_462,type,
sK269: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_463,type,
sK270: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_466,type,
sK273: $i > $i ).
thf(func_def_482,type,
sK289: $i > $i ).
thf(func_def_498,type,
sK305: $i > $o ).
thf(func_def_500,type,
sK307: ( $i > $o ) > $i > $i ).
thf(func_def_503,type,
sK310: $i > $i > $i ).
thf(func_def_504,type,
sK311: $i > $i > $i ).
thf(func_def_505,type,
sK312: $i > $i > $i ).
thf(func_def_508,type,
sK315: $i > ( $i > $o ) > $i ).
thf(func_def_509,type,
sK316: $i > $o ).
thf(func_def_516,type,
sK323: $i > $o ).
thf(func_def_520,type,
sK327: $i > $o ).
thf(func_def_521,type,
sK328: $i > $o ).
thf(func_def_540,type,
sK347: $i > $o ).
thf(func_def_546,type,
sK353: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_547,type,
sK354: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_548,type,
sK355: $i > $o ).
thf(func_def_549,type,
sK356: $i > $o ).
thf(func_def_563,type,
sK370: $i > $o ).
thf(func_def_583,type,
sK390: $i > $o ).
thf(func_def_588,type,
sK395: $i > $i > $i ).
thf(func_def_601,type,
sK408: ( $i > $o ) > $i ).
thf(func_def_602,type,
sK409: $i > $o ).
thf(func_def_604,type,
sK411: $i > $o ).
thf(func_def_607,type,
sK414: $i > $o ).
thf(func_def_610,type,
sK417: $i > $o ).
thf(func_def_618,type,
sK425: $i > $o ).
thf(func_def_620,type,
sK427: $i > ( $i > $o ) > $i ).
thf(func_def_626,type,
ph433:
!>[X0: $tType] : X0 ).
thf(f5195,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f3001,f3046,f3050,f3058,f3073,f3091,f3209,f3756,f5194]) ).
thf(f5194,plain,
( ~ spl432_4
| ~ spl432_18
| ~ spl432_21
| ~ spl432_25
| ~ spl432_31 ),
inference(avatar_contradiction_clause,[status(thm)],[f5193]) ).
thf(f5193,plain,
( $false
| ~ spl432_4
| ~ spl432_18
| ~ spl432_21
| ~ spl432_25
| ~ spl432_31 ),
inference(subsumption_resolution,[status(thm)],[f5185,f1891]) ).
thf(f1891,plain,
( ( sK323 @ sK321 )
= $true ),
inference(cnf_transformation,[status(thm)],[f1213]) ).
thf(f1213,plain,
( ( dsetconstr__Cong = $true )
& ( powersetE = $true )
& ( setadjoinOr = $true )
& ( emptysetsubset = $true )
& ( setunionAx = $true )
& ( subsetemptysetimpeq = $true )
& ( setminusILneg = $true )
& ( binintersectER = $true )
& ( descr__Cong = $true )
& ( symdiffI1 = $true )
& ( wellorderingAx = $true )
& ( inPowerset = $true )
& ( setextsub = $true )
& ( notequalI1 = $true )
& ( notequalI2 = $true )
& ( notinsingleton = $true )
& ( setunion__Cong = $true )
& ( dsetconstrI = $true )
& ( setadjoinAx = $true )
& ( binintersectEL = $true )
& ( binunionIR = $true )
& ( subsetI2 = $true )
& ( setunionI = $true )
& ( binunionRsub = $true )
& ( ex1E1 = $true )
& ( setadjoinIR = $true )
& ( vacuousDall = $true )
& ( eqimpsubset2 = $true )
& ( exuE3e = $true )
& ( notsubsetI = $true )
& ( eqimpsubset1 = $true )
& ( setextAx = $true )
& ( emptysetimpfalse = $true )
& ( setadjoin__Cong = $true )
& ( prop2setI = $true )
& ( setext = $true )
& ( setadjoinSub = $true )
& ( upairset2E = $true )
& ( setunionsingleton = $true )
& ( binintersectSubset3 = $true )
& ( emptyinunitempty = $true )
& ( binintersectSubset5 = $true )
& ( emptysetAx = $true )
& ( setunionE = $true )
& ( binintersectSubset4 = $true )
& ( omegaSAx = $true )
& ( symdiffIneg2 = $true )
& ( notdallE = $true )
& ( emptyE1 = $true )
& ( cartprodpairin = $true )
& ( setminusLsub = $true )
& ( singletoninpowunion = $true )
& ( ubforcartprodlem2 = $true )
& ( bs114d = $true )
& ( sepSubset = $true )
& ( upairsubunion = $true )
& ( setukpairIL = $true )
& ( exuE3u = $true )
& ( powersetsubset = $true )
& ( setminusI = $true )
& ( exu__Cong = $true )
& ( setunionsingleton2 = $true )
& ( setadjoinSub2 = $true )
& ( subsetRefl = $true )
& ( dsetconstrER = $true )
& ( subsetE2 = $true )
& ( uniqinunit = $true )
& ( binintersectSubset2 = $true )
& ( setadjoinIL = $true )
& ( ubforcartprodlem1 = $true )
& ( setminusELneg = $true )
& ( kpairp = $true )
& ( binintersectSubset1 = $true )
& ( upairsetIR = $true )
& ( quantDeMorgan3 = $true )
& ( upairsetIL = $true )
& ( nonemptyI = $true )
& ( powersetAx = $true )
& ( subsetI1 = $true )
& ( inCongP = $true )
& ( upairinpowunion = $true )
& ( setminusERneg = $true )
& ( emptyInPowerset = $true )
& ( binunionIL = $true )
& ( emptysetE = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan4 = $true )
& ( powersetI = $true )
& ( binunionE = $true )
& ( powersetI1 = $true )
& ( exuI1 = $true )
& ( singletonsswitch = $true )
& ( ubforcartprodlem3 = $true )
& ( binunionLsub = $true )
& ( singletonsubset = $true )
& ( binunionEcases = $true )
& ( upairsetE = $true )
& ( cartprodmempair1 = $true )
& ( nonemptyI1 = $true )
& ( cartprodmempair = $true )
& ( setminusSubset2 = $true )
& ( omegaIndAx = $true )
& ( prop2setE = $true )
& ( upairset2IR = $true )
& ( subsetE = $true )
& ( exuE1 = $true )
& ( in__Cong = $true )
& ( replAx = $true )
& ( singletoninpowerset = $true )
& ( disjointsetsI1 = $true )
& ( emptyinPowerset = $true )
& ( secondinupair = $true )
& ( setunionE2 = $true )
& ( setminusSubset1 = $true )
& ( foundationAx = $true )
& ( kpairiskpair = $true )
& ( exuI3 = $true )
& ( setadjoinE = $true )
& ( binintersectLsub = $true )
& ( sepInPowerset = $true )
& ! [X3: $i] :
( ( $true
!= ( in @ X3 @ sK322 ) )
| ( sK321 = X3 )
| ( ( sK323 @ X3 )
!= $true ) )
& ( ( sK323 @ sK321 )
= $true )
& ( ( ex1 @ sK322
@ ^ [Y0: $i] : ( sK323 @ Y0 ) )
!= $true )
& ( ( in @ sK321 @ sK322 )
= $true )
& ( omega__Cong = $true )
& ( descrp = $true )
& ( nonemptyImpWitness = $true )
& ( notinemptyset = $true )
& ( setminusEL = $true )
& ( symdiffE = $true )
& ( binintersectRsub = $true )
& ( quantDeMorgan1 = $true )
& ( omega0Ax = $true )
& ( setbeta = $true )
& ( emptyI = $true )
& ( powerset__Cong = $true )
& ( exuEu = $true )
& ( prop2set2propI = $true )
& ( exuE2 = $true )
& ( setminusIRneg = $true )
& ( dsetconstrEL = $true )
& ( subset2powerset = $true )
& ( nonemptyE1 = $true )
& ( emptyset__Cong = $true )
& ( symdiffIneg1 = $true )
& ( exuI2 = $true )
& ( setukpairIR = $true )
& ( singletonprop = $true )
& ( powersetE1 = $true )
& ( subPowSU = $true )
& ( setunionsingleton1 = $true )
& ( binintersectI = $true )
& ( eqinunit = $true )
& ( subsetTrans = $true )
& ( notdexE = $true )
& ( setminusER = $true )
& ( setoftrueEq = $true )
& ( symdiffI2 = $true )
& ( noeltsimpempty = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK321,sK322,sK323])],[f649,f1212]) ).
thf(f1212,plain,
( ? [X0: $i,X1: $i,X2: $i > $o] :
( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( X0 = X3 )
| ( ( X2 @ X3 )
!= $true ) )
& ( ( X2 @ X0 )
= $true )
& ( $true
!= ( ex1 @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
& ( ( in @ X0 @ X1 )
= $true ) )
=> ( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ sK322 ) )
| ( sK321 = X3 )
| ( ( sK323 @ X3 )
!= $true ) )
& ( ( sK323 @ sK321 )
= $true )
& ( ( ex1 @ sK322
@ ^ [Y0: $i] : ( sK323 @ Y0 ) )
!= $true )
& ( ( in @ sK321 @ sK322 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f649,plain,
( ( dsetconstr__Cong = $true )
& ( powersetE = $true )
& ( setadjoinOr = $true )
& ( emptysetsubset = $true )
& ( setunionAx = $true )
& ( subsetemptysetimpeq = $true )
& ( setminusILneg = $true )
& ( binintersectER = $true )
& ( descr__Cong = $true )
& ( symdiffI1 = $true )
& ( wellorderingAx = $true )
& ( inPowerset = $true )
& ( setextsub = $true )
& ( notequalI1 = $true )
& ( notequalI2 = $true )
& ( notinsingleton = $true )
& ( setunion__Cong = $true )
& ( dsetconstrI = $true )
& ( setadjoinAx = $true )
& ( binintersectEL = $true )
& ( binunionIR = $true )
& ( subsetI2 = $true )
& ( setunionI = $true )
& ( binunionRsub = $true )
& ( ex1E1 = $true )
& ( setadjoinIR = $true )
& ( vacuousDall = $true )
& ( eqimpsubset2 = $true )
& ( exuE3e = $true )
& ( notsubsetI = $true )
& ( eqimpsubset1 = $true )
& ( setextAx = $true )
& ( emptysetimpfalse = $true )
& ( setadjoin__Cong = $true )
& ( prop2setI = $true )
& ( setext = $true )
& ( setadjoinSub = $true )
& ( upairset2E = $true )
& ( setunionsingleton = $true )
& ( binintersectSubset3 = $true )
& ( emptyinunitempty = $true )
& ( binintersectSubset5 = $true )
& ( emptysetAx = $true )
& ( setunionE = $true )
& ( binintersectSubset4 = $true )
& ( omegaSAx = $true )
& ( symdiffIneg2 = $true )
& ( notdallE = $true )
& ( emptyE1 = $true )
& ( cartprodpairin = $true )
& ( setminusLsub = $true )
& ( singletoninpowunion = $true )
& ( ubforcartprodlem2 = $true )
& ( bs114d = $true )
& ( sepSubset = $true )
& ( upairsubunion = $true )
& ( setukpairIL = $true )
& ( exuE3u = $true )
& ( powersetsubset = $true )
& ( setminusI = $true )
& ( exu__Cong = $true )
& ( setunionsingleton2 = $true )
& ( setadjoinSub2 = $true )
& ( subsetRefl = $true )
& ( dsetconstrER = $true )
& ( subsetE2 = $true )
& ( uniqinunit = $true )
& ( binintersectSubset2 = $true )
& ( setadjoinIL = $true )
& ( ubforcartprodlem1 = $true )
& ( setminusELneg = $true )
& ( kpairp = $true )
& ( binintersectSubset1 = $true )
& ( upairsetIR = $true )
& ( quantDeMorgan3 = $true )
& ( upairsetIL = $true )
& ( nonemptyI = $true )
& ( powersetAx = $true )
& ( subsetI1 = $true )
& ( inCongP = $true )
& ( upairinpowunion = $true )
& ( setminusERneg = $true )
& ( emptyInPowerset = $true )
& ( binunionIL = $true )
& ( emptysetE = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan4 = $true )
& ( powersetI = $true )
& ( binunionE = $true )
& ( powersetI1 = $true )
& ( exuI1 = $true )
& ( singletonsswitch = $true )
& ( ubforcartprodlem3 = $true )
& ( binunionLsub = $true )
& ( singletonsubset = $true )
& ( binunionEcases = $true )
& ( upairsetE = $true )
& ( cartprodmempair1 = $true )
& ( nonemptyI1 = $true )
& ( cartprodmempair = $true )
& ( setminusSubset2 = $true )
& ( omegaIndAx = $true )
& ( prop2setE = $true )
& ( upairset2IR = $true )
& ( subsetE = $true )
& ( exuE1 = $true )
& ( in__Cong = $true )
& ( replAx = $true )
& ( singletoninpowerset = $true )
& ( disjointsetsI1 = $true )
& ( emptyinPowerset = $true )
& ( secondinupair = $true )
& ( setunionE2 = $true )
& ( setminusSubset1 = $true )
& ( foundationAx = $true )
& ( kpairiskpair = $true )
& ( exuI3 = $true )
& ( setadjoinE = $true )
& ( binintersectLsub = $true )
& ( sepInPowerset = $true )
& ? [X0: $i,X1: $i,X2: $i > $o] :
( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
!= $true )
| ( X0 = X3 )
| ( ( X2 @ X3 )
!= $true ) )
& ( ( X2 @ X0 )
= $true )
& ( $true
!= ( ex1 @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
& ( ( in @ X0 @ X1 )
= $true ) )
& ( omega__Cong = $true )
& ( descrp = $true )
& ( nonemptyImpWitness = $true )
& ( notinemptyset = $true )
& ( setminusEL = $true )
& ( symdiffE = $true )
& ( binintersectRsub = $true )
& ( quantDeMorgan1 = $true )
& ( omega0Ax = $true )
& ( setbeta = $true )
& ( emptyI = $true )
& ( powerset__Cong = $true )
& ( exuEu = $true )
& ( prop2set2propI = $true )
& ( exuE2 = $true )
& ( setminusIRneg = $true )
& ( dsetconstrEL = $true )
& ( subset2powerset = $true )
& ( nonemptyE1 = $true )
& ( emptyset__Cong = $true )
& ( symdiffIneg1 = $true )
& ( exuI2 = $true )
& ( setukpairIR = $true )
& ( singletonprop = $true )
& ( powersetE1 = $true )
& ( subPowSU = $true )
& ( setunionsingleton1 = $true )
& ( binintersectI = $true )
& ( eqinunit = $true )
& ( subsetTrans = $true )
& ( notdexE = $true )
& ( setminusER = $true )
& ( setoftrueEq = $true )
& ( symdiffI2 = $true )
& ( noeltsimpempty = $true ) ),
inference(flattening,[status(thm)],[f648]) ).
thf(f648,plain,
( ? [X0: $i,X1: $i,X2: $i > $o] :
( ( $true
!= ( ex1 @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
& ! [X3: $i] :
( ( X0 = X3 )
| ( ( X2 @ X3 )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true ) )
& ( ( X2 @ X0 )
= $true )
& ( ( in @ X0 @ X1 )
= $true ) )
& ( ex1E1 = $true )
& ( singletonprop = $true )
& ( setunionsingleton = $true )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( setunionE2 = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( cartprodpairin = $true )
& ( ubforcartprodlem3 = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( upairsubunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f456]) ).
thf(f456,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X0 @ X1 )
= $true )
=> ( ( ( X2 @ X0 )
= $true )
=> ( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ( X2 @ X3 )
= $true )
=> ( X0 = X3 ) ) )
=> ( $true
= ( ex1 @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f455]) ).
thf(f455,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ! [X0: $i,X1: $i,X2: $i > $o] :
( ( in @ X0 @ X1 )
=> ( ( X2 @ X0 )
=> ( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X2 @ X3 )
=> ( X0 = X3 ) ) )
=> ( ex1 @ X1
@ ^ [X4: $i] : ( X2 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f163]) ).
thf(f163,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ! [X1: $i,X3: $i,X0: $i > $o] :
( ( in @ X1 @ X3 )
=> ( ( X0 @ X1 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X3 )
=> ( ( X0 @ X2 )
=> ( X1 = X2 ) ) )
=> ( ex1 @ X3
@ ^ [X2: $i] : ( X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f162]) ).
thf(f162,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ! [X1: $i,X3: $i,X0: $i > $o] :
( ( in @ X1 @ X3 )
=> ( ( X0 @ X1 )
=> ( ! [X2: $i] :
( ( in @ X2 @ X3 )
=> ( ( X0 @ X2 )
=> ( X1 = X2 ) ) )
=> ( ex1 @ X3
@ ^ [X2: $i] : ( X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0njZozgBRA/DTF2THF_1200.p',ex1I) ).
thf(f5185,plain,
( ( ( sK323 @ sK321 )
!= $true )
| ~ spl432_4
| ~ spl432_18
| ~ spl432_21
| ~ spl432_25
| ~ spl432_31 ),
inference(trivial_inequality_removal,[status(thm)],[f5171]) ).
thf(f5171,plain,
( ( ( sK323 @ sK321 )
!= $true )
| ( $true != $true )
| ~ spl432_4
| ~ spl432_18
| ~ spl432_21
| ~ spl432_25
| ~ spl432_31 ),
inference(superposition,[status(thm)],[f5118,f1889]) ).
thf(f1889,plain,
( ( in @ sK321 @ sK322 )
= $true ),
inference(cnf_transformation,[status(thm)],[f1213]) ).
thf(f5118,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sK322 )
!= $true )
| ( ( sK323 @ X0 )
!= $true ) )
| ~ spl432_4
| ~ spl432_18
| ~ spl432_21
| ~ spl432_25
| ~ spl432_31 ),
inference(subsumption_resolution,[status(thm)],[f4442,f4514]) ).
thf(f4514,plain,
( ( ( sK205 @ sK322 @ sK323 )
= sK321 )
| ~ spl432_25
| ~ spl432_31 ),
inference(subsumption_resolution,[status(thm)],[f4500,f3208]) ).
thf(f3208,plain,
( ( ( sK323 @ ( sK205 @ sK322 @ sK323 ) )
= $true )
| ~ spl432_31 ),
inference(avatar_component_clause,[status(thm)],[f3206]) ).
thf(f3206,definition,
( spl432_31
<=> ( ( sK323 @ ( sK205 @ sK322 @ sK323 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl432_31])],[avatar_definition]) ).
thf(f4500,plain,
( ( ( sK323 @ ( sK205 @ sK322 @ sK323 ) )
!= $true )
| ( ( sK205 @ sK322 @ sK323 )
= sK321 )
| ~ spl432_25 ),
inference(trivial_inequality_removal,[status(thm)],[f4478]) ).
thf(f4478,plain,
( ( ( sK205 @ sK322 @ sK323 )
= sK321 )
| ( ( sK323 @ ( sK205 @ sK322 @ sK323 ) )
!= $true )
| ( $true != $true )
| ~ spl432_25 ),
inference(superposition,[status(thm)],[f1892,f4359]) ).
thf(f4359,plain,
( ( $true
= ( in @ ( sK205 @ sK322 @ sK323 ) @ sK322 ) )
| ~ spl432_25 ),
inference(subsumption_resolution,[status(thm)],[f4335,f2813]) ).
thf(f2813,plain,
( $true
!= ( singleton @ ( dsetconstr @ sK322 @ sK323 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2553]) ).
thf(f2553,plain,
( $true
!= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) )
@ sK322
@ ^ [Y0: $i] : ( sK323 @ Y0 ) ) ),
inference(definition_unfolding,[status(thm)],[f1890,f1610]) ).
thf(f1610,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f408]) ).
thf(f408,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f407]) ).
thf(f407,plain,
( ex1
= ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f160]) ).
thf(f160,axiom,
( ex1
= ( ^ [X3: $i,X0: $i > $o] :
( singleton
@ ( dsetconstr @ X3
@ ^ [X1: $i] : ( X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.0njZozgBRA/DTF2THF_1200.p',ex1) ).
thf(f1890,plain,
( ( ex1 @ sK322
@ ^ [Y0: $i] : ( sK323 @ Y0 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f1213]) ).
thf(f4335,plain,
( ( $true
= ( in @ ( sK205 @ sK322 @ sK323 ) @ sK322 ) )
| ( $true
= ( singleton @ ( dsetconstr @ sK322 @ sK323 ) ) )
| ~ spl432_25 ),
inference(beta_eta_normalization,[status(thm)],[f4334]) ).
thf(f4334,plain,
( ( ( singleton
@ ( dsetconstr @ sK322
@ ^ [Y0: $i] :
( sK323
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) )
= $true )
| ( $true
= ( in
@ ( sK205 @ sK322
@ ^ [Y0: $i] :
( sK323
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) )
@ sK322 ) )
| ~ spl432_25 ),
inference(trivial_inequality_removal,[status(thm)],[f4267]) ).
thf(f4267,plain,
( ( $true != $true )
| ( $true
= ( in
@ ( sK205 @ sK322
@ ^ [Y0: $i] :
( sK323
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) )
@ sK322 ) )
| ( ( singleton
@ ( dsetconstr @ sK322
@ ^ [Y0: $i] :
( sK323
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) )
= $true )
| ~ spl432_25 ),
inference(superposition,[status(thm)],[f3432,f1891]) ).
thf(f3432,plain,
( ! [X0: $i > $o] :
( ( ( X0 @ sK321 )
!= $true )
| ( ( in @ ( sK205 @ sK322 @ X0 ) @ sK322 )
= $true )
| ( ( singleton @ ( dsetconstr @ sK322 @ X0 ) )
= $true ) )
| ~ spl432_25 ),
inference(trivial_inequality_removal,[status(thm)],[f3427]) ).
thf(f3427,plain,
( ! [X0: $i > $o] :
( ( ( X0 @ sK321 )
!= $true )
| ( $true != $true )
| ( ( singleton @ ( dsetconstr @ sK322 @ X0 ) )
= $true )
| ( ( in @ ( sK205 @ sK322 @ X0 ) @ sK322 )
= $true ) )
| ~ spl432_25 ),
inference(superposition,[status(thm)],[f3090,f1889]) ).
thf(f3090,plain,
( ! [X6: $i,X7: $i,X5: $i > $o] :
( ( ( in @ X7 @ X6 )
!= $true )
| ( $true
= ( singleton @ ( dsetconstr @ X6 @ X5 ) ) )
| ( ( in @ ( sK205 @ X6 @ X5 ) @ X6 )
= $true )
| ( ( X5 @ X7 )
!= $true ) )
| ~ spl432_25 ),
inference(avatar_component_clause,[status(thm)],[f3089]) ).
thf(f3089,definition,
( spl432_25
<=> ! [X6: $i,X5: $i > $o,X7: $i] :
( ( ( X5 @ X7 )
!= $true )
| ( ( in @ ( sK205 @ X6 @ X5 ) @ X6 )
= $true )
| ( $true
= ( singleton @ ( dsetconstr @ X6 @ X5 ) ) )
| ( ( in @ X7 @ X6 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl432_25])],[avatar_definition]) ).
thf(f1892,plain,
! [X3: $i] :
( ( $true
!= ( in @ X3 @ sK322 ) )
| ( ( sK323 @ X3 )
!= $true )
| ( sK321 = X3 ) ),
inference(cnf_transformation,[status(thm)],[f1213]) ).
thf(f4442,plain,
( ! [X0: $i] :
( ( ( sK323 @ X0 )
!= $true )
| ( ( sK205 @ sK322 @ sK323 )
!= sK321 )
| ( ( in @ X0 @ sK322 )
!= $true ) )
| ~ spl432_4
| ~ spl432_18
| ~ spl432_21 ),
inference(subsumption_resolution,[status(thm)],[f4441,f2813]) ).
thf(f4441,plain,
( ! [X0: $i] :
( ( $true
= ( singleton @ ( dsetconstr @ sK322 @ sK323 ) ) )
| ( ( sK205 @ sK322 @ sK323 )
!= sK321 )
| ( ( sK323 @ X0 )
!= $true )
| ( ( in @ X0 @ sK322 )
!= $true ) )
| ~ spl432_4
| ~ spl432_18
| ~ spl432_21 ),
inference(superposition,[status(thm)],[f3057,f4401]) ).
thf(f4401,plain,
( ( sK321
= ( sK206 @ sK322 @ sK323 ) )
| ~ spl432_4
| ~ spl432_21 ),
inference(subsumption_resolution,[status(thm)],[f4382,f3795]) ).
thf(f3795,plain,
( ( ( sK323 @ ( sK206 @ sK322 @ sK323 ) )
= $true )
| ~ spl432_21 ),
inference(subsumption_resolution,[status(thm)],[f3339,f2813]) ).
thf(f3339,plain,
( ( ( sK323 @ ( sK206 @ sK322 @ sK323 ) )
= $true )
| ( $true
= ( singleton @ ( dsetconstr @ sK322 @ sK323 ) ) )
| ~ spl432_21 ),
inference(beta_eta_normalization,[status(thm)],[f3338]) ).
thf(f3338,plain,
( ( ( ^ [Y0: $i] :
( sK323
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ ( sK206 @ sK322
@ ^ [Y0: $i] :
( sK323
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ sK322
@ ^ [Y0: $i] :
( sK323
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) )
= $true )
| ~ spl432_21 ),
inference(trivial_inequality_removal,[status(thm)],[f3328]) ).
thf(f3328,plain,
( ( $true != $true )
| ( ( ^ [Y0: $i] :
( sK323
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ ( sK206 @ sK322
@ ^ [Y0: $i] :
( sK323
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ sK322
@ ^ [Y0: $i] :
( sK323
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) )
= $true )
| ~ spl432_21 ),
inference(superposition,[status(thm)],[f3153,f1891]) ).
thf(f3153,plain,
( ! [X0: $i > $o] :
( ( ( X0 @ sK321 )
!= $true )
| ( ( X0 @ ( sK206 @ sK322 @ X0 ) )
= $true )
| ( ( singleton @ ( dsetconstr @ sK322 @ X0 ) )
= $true ) )
| ~ spl432_21 ),
inference(trivial_inequality_removal,[status(thm)],[f3150]) ).
thf(f3150,plain,
( ! [X0: $i > $o] :
( ( ( singleton @ ( dsetconstr @ sK322 @ X0 ) )
= $true )
| ( ( X0 @ ( sK206 @ sK322 @ X0 ) )
= $true )
| ( $true != $true )
| ( ( X0 @ sK321 )
!= $true ) )
| ~ spl432_21 ),
inference(superposition,[status(thm)],[f3072,f1889]) ).
thf(f3072,plain,
( ! [X6: $i,X7: $i,X5: $i > $o] :
( ( ( in @ X7 @ X6 )
!= $true )
| ( $true
= ( singleton @ ( dsetconstr @ X6 @ X5 ) ) )
| ( ( X5 @ X7 )
!= $true )
| ( ( X5 @ ( sK206 @ X6 @ X5 ) )
= $true ) )
| ~ spl432_21 ),
inference(avatar_component_clause,[status(thm)],[f3071]) ).
thf(f3071,definition,
( spl432_21
<=> ! [X6: $i,X5: $i > $o,X7: $i] :
( ( $true
= ( singleton @ ( dsetconstr @ X6 @ X5 ) ) )
| ( ( X5 @ X7 )
!= $true )
| ( ( in @ X7 @ X6 )
!= $true )
| ( ( X5 @ ( sK206 @ X6 @ X5 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl432_21])],[avatar_definition]) ).
thf(f4382,plain,
( ( sK321
= ( sK206 @ sK322 @ sK323 ) )
| ( ( sK323 @ ( sK206 @ sK322 @ sK323 ) )
!= $true )
| ~ spl432_4 ),
inference(trivial_inequality_removal,[status(thm)],[f4365]) ).
thf(f4365,plain,
( ( ( sK323 @ ( sK206 @ sK322 @ sK323 ) )
!= $true )
| ( $true != $true )
| ( sK321
= ( sK206 @ sK322 @ sK323 ) )
| ~ spl432_4 ),
inference(superposition,[status(thm)],[f1892,f4214]) ).
thf(f4214,plain,
( ( ( in @ ( sK206 @ sK322 @ sK323 ) @ sK322 )
= $true )
| ~ spl432_4 ),
inference(subsumption_resolution,[status(thm)],[f4149,f2813]) ).
thf(f4149,plain,
( ( $true
= ( singleton @ ( dsetconstr @ sK322 @ sK323 ) ) )
| ( ( in @ ( sK206 @ sK322 @ sK323 ) @ sK322 )
= $true )
| ~ spl432_4 ),
inference(beta_eta_normalization,[status(thm)],[f4148]) ).
thf(f4148,plain,
( ( ( in
@ ( sK206 @ sK322
@ ^ [Y0: $i] :
( sK323
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) )
@ sK322 )
= $true )
| ( ( singleton
@ ( dsetconstr @ sK322
@ ^ [Y0: $i] :
( sK323
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) )
= $true )
| ~ spl432_4 ),
inference(trivial_inequality_removal,[status(thm)],[f4122]) ).
thf(f4122,plain,
( ( $true != $true )
| ( ( singleton
@ ( dsetconstr @ sK322
@ ^ [Y0: $i] :
( sK323
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) )
= $true )
| ( ( in
@ ( sK206 @ sK322
@ ^ [Y0: $i] :
( sK323
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) )
@ sK322 )
= $true )
| ~ spl432_4 ),
inference(superposition,[status(thm)],[f3242,f1891]) ).
thf(f3242,plain,
( ! [X0: $i > $o] :
( ( ( X0 @ sK321 )
!= $true )
| ( ( in @ ( sK206 @ sK322 @ X0 ) @ sK322 )
= $true )
| ( ( singleton @ ( dsetconstr @ sK322 @ X0 ) )
= $true ) )
| ~ spl432_4 ),
inference(trivial_inequality_removal,[status(thm)],[f3237]) ).
thf(f3237,plain,
( ! [X0: $i > $o] :
( ( ( X0 @ sK321 )
!= $true )
| ( ( in @ ( sK206 @ sK322 @ X0 ) @ sK322 )
= $true )
| ( $true != $true )
| ( ( singleton @ ( dsetconstr @ sK322 @ X0 ) )
= $true ) )
| ~ spl432_4 ),
inference(superposition,[status(thm)],[f3000,f1889]) ).
thf(f3000,plain,
( ! [X6: $i,X7: $i,X5: $i > $o] :
( ( ( in @ X7 @ X6 )
!= $true )
| ( ( in @ ( sK206 @ X6 @ X5 ) @ X6 )
= $true )
| ( $true
= ( singleton @ ( dsetconstr @ X6 @ X5 ) ) )
| ( ( X5 @ X7 )
!= $true ) )
| ~ spl432_4 ),
inference(avatar_component_clause,[status(thm)],[f2999]) ).
thf(f2999,definition,
( spl432_4
<=> ! [X6: $i,X5: $i > $o,X7: $i] :
( ( $true
= ( singleton @ ( dsetconstr @ X6 @ X5 ) ) )
| ( ( in @ X7 @ X6 )
!= $true )
| ( ( in @ ( sK206 @ X6 @ X5 ) @ X6 )
= $true )
| ( ( X5 @ X7 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl432_4])],[avatar_definition]) ).
thf(f3057,plain,
( ! [X6: $i,X7: $i,X5: $i > $o] :
( ( ( sK205 @ X6 @ X5 )
!= ( sK206 @ X6 @ X5 ) )
| ( $true
= ( singleton @ ( dsetconstr @ X6 @ X5 ) ) )
| ( ( X5 @ X7 )
!= $true )
| ( ( in @ X7 @ X6 )
!= $true ) )
| ~ spl432_18 ),
inference(avatar_component_clause,[status(thm)],[f3056]) ).
thf(f3056,definition,
( spl432_18
<=> ! [X6: $i,X5: $i > $o,X7: $i] :
( ( $true
= ( singleton @ ( dsetconstr @ X6 @ X5 ) ) )
| ( ( X5 @ X7 )
!= $true )
| ( ( sK205 @ X6 @ X5 )
!= ( sK206 @ X6 @ X5 ) )
| ( ( in @ X7 @ X6 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl432_18])],[avatar_definition]) ).
thf(f3756,plain,
~ spl432_30,
inference(avatar_contradiction_clause,[status(thm)],[f3755]) ).
thf(f3755,plain,
( $false
| ~ spl432_30 ),
inference(subsumption_resolution,[status(thm)],[f2813,f3204]) ).
thf(f3204,plain,
( ( $true
= ( singleton @ ( dsetconstr @ sK322 @ sK323 ) ) )
| ~ spl432_30 ),
inference(avatar_component_clause,[status(thm)],[f3202]) ).
thf(f3202,definition,
( spl432_30
<=> ( $true
= ( singleton @ ( dsetconstr @ sK322 @ sK323 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl432_30])],[avatar_definition]) ).
thf(f3209,plain,
( spl432_30
| spl432_31
| ~ spl432_16 ),
inference(avatar_split_clause,[status(thm)],[f3173,f3048,f3206,f3202]) ).
thf(f3048,definition,
( spl432_16
<=> ! [X6: $i,X5: $i > $o,X7: $i] :
( ( $true
= ( singleton @ ( dsetconstr @ X6 @ X5 ) ) )
| ( ( X5 @ ( sK205 @ X6 @ X5 ) )
= $true )
| ( ( in @ X7 @ X6 )
!= $true )
| ( ( X5 @ X7 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl432_16])],[avatar_definition]) ).
thf(f3173,plain,
( ( ( sK323 @ ( sK205 @ sK322 @ sK323 ) )
= $true )
| ( $true
= ( singleton @ ( dsetconstr @ sK322 @ sK323 ) ) )
| ~ spl432_16 ),
inference(beta_eta_normalization,[status(thm)],[f3172]) ).
thf(f3172,plain,
( ( ( ^ [Y0: $i] :
( sK323
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ ( sK205 @ sK322
@ ^ [Y0: $i] :
( sK323
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ sK322
@ ^ [Y0: $i] :
( sK323
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) )
= $true )
| ~ spl432_16 ),
inference(trivial_inequality_removal,[status(thm)],[f3158]) ).
thf(f3158,plain,
( ( ( singleton
@ ( dsetconstr @ sK322
@ ^ [Y0: $i] :
( sK323
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( sK323
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ ( sK205 @ sK322
@ ^ [Y0: $i] :
( sK323
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) )
= $true )
| ( $true != $true )
| ~ spl432_16 ),
inference(superposition,[status(thm)],[f3101,f1891]) ).
thf(f3101,plain,
( ! [X0: $i > $o] :
( ( ( X0 @ sK321 )
!= $true )
| ( ( X0 @ ( sK205 @ sK322 @ X0 ) )
= $true )
| ( ( singleton @ ( dsetconstr @ sK322 @ X0 ) )
= $true ) )
| ~ spl432_16 ),
inference(trivial_inequality_removal,[status(thm)],[f3098]) ).
thf(f3098,plain,
( ! [X0: $i > $o] :
( ( ( X0 @ sK321 )
!= $true )
| ( ( singleton @ ( dsetconstr @ sK322 @ X0 ) )
= $true )
| ( ( X0 @ ( sK205 @ sK322 @ X0 ) )
= $true )
| ( $true != $true ) )
| ~ spl432_16 ),
inference(superposition,[status(thm)],[f3049,f1889]) ).
thf(f3049,plain,
( ! [X6: $i,X7: $i,X5: $i > $o] :
( ( ( in @ X7 @ X6 )
!= $true )
| ( ( X5 @ ( sK205 @ X6 @ X5 ) )
= $true )
| ( $true
= ( singleton @ ( dsetconstr @ X6 @ X5 ) ) )
| ( ( X5 @ X7 )
!= $true ) )
| ~ spl432_16 ),
inference(avatar_component_clause,[status(thm)],[f3048]) ).
thf(f3091,plain,
( ~ spl432_1
| spl432_25 ),
inference(avatar_split_clause,[status(thm)],[f2733,f3089,f2986]) ).
thf(f2986,definition,
( spl432_1
<=> ( $true = sP6 ) ),
introduced(definition,[new_symbols(naming,[spl432_1])],[avatar_definition]) ).
thf(f2733,plain,
! [X6: $i,X7: $i,X5: $i > $o] :
( ( ( X5 @ X7 )
!= $true )
| ( ( in @ X7 @ X6 )
!= $true )
| ( $true
= ( singleton @ ( dsetconstr @ X6 @ X5 ) ) )
| ( $true != sP6 )
| ( ( in @ ( sK205 @ X6 @ X5 ) @ X6 )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f1691]) ).
thf(f1691,plain,
! [X6: $i,X7: $i,X5: $i > $o] :
( ( $true
= ( singleton
@ ( dsetconstr @ X6
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) )
| ( ( in @ X7 @ X6 )
!= $true )
| ( ( X5 @ X7 )
!= $true )
| ( ( in @ ( sK205 @ X6 @ X5 ) @ X6 )
= $true )
| ( $true != sP6 ) ),
inference(cnf_transformation,[status(thm)],[f1030]) ).
thf(f1030,plain,
( ( ( $true = sP6 )
| ( ( ( sK202 @ sK204 )
= $true )
& ( $true
= ( in @ sK204 @ sK203 ) )
& ! [X3: $i] :
( ! [X4: $i] :
( ( ( sK202 @ X4 )
!= $true )
| ( ( sK202 @ X3 )
!= $true )
| ( $true
!= ( in @ X4 @ sK203 ) )
| ( X3 = X4 ) )
| ( ( in @ X3 @ sK203 )
!= $true ) )
& ( ( singleton
@ ( dsetconstr @ sK203
@ ^ [Y0: $i] : ( sK202 @ Y0 ) ) )
!= $true ) ) )
& ( ! [X5: $i > $o,X6: $i] :
( ! [X7: $i] :
( ( ( X5 @ X7 )
!= $true )
| ( ( in @ X7 @ X6 )
!= $true ) )
| ( ( ( X5 @ ( sK206 @ X6 @ X5 ) )
= $true )
& ( ( X5 @ ( sK205 @ X6 @ X5 ) )
= $true )
& ( ( in @ ( sK206 @ X6 @ X5 ) @ X6 )
= $true )
& ( ( sK205 @ X6 @ X5 )
!= ( sK206 @ X6 @ X5 ) )
& ( ( in @ ( sK205 @ X6 @ X5 ) @ X6 )
= $true ) )
| ( $true
= ( singleton
@ ( dsetconstr @ X6
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) ) )
| ( $true != sP6 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK202,sK203,sK204,sK205,sK206])],[f1025,f1029,f1028,f1027,f1026]) ).
thf(f1026,plain,
( ? [X0: $i > $o,X1: $i] :
( ? [X2: $i] :
( ( ( X0 @ X2 )
= $true )
& ( $true
= ( in @ X2 @ X1 ) ) )
& ! [X3: $i] :
( ! [X4: $i] :
( ( ( X0 @ X4 )
!= $true )
| ( ( X0 @ X3 )
!= $true )
| ( ( in @ X4 @ X1 )
!= $true )
| ( X3 = X4 ) )
| ( ( in @ X3 @ X1 )
!= $true ) )
& ( ( singleton
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true ) )
=> ( ? [X2: $i] :
( ( ( sK202 @ X2 )
= $true )
& ( ( in @ X2 @ sK203 )
= $true ) )
& ! [X3: $i] :
( ! [X4: $i] :
( ( ( sK202 @ X4 )
!= $true )
| ( ( sK202 @ X3 )
!= $true )
| ( $true
!= ( in @ X4 @ sK203 ) )
| ( X3 = X4 ) )
| ( ( in @ X3 @ sK203 )
!= $true ) )
& ( ( singleton
@ ( dsetconstr @ sK203
@ ^ [Y0: $i] : ( sK202 @ Y0 ) ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1027,plain,
( ? [X2: $i] :
( ( ( sK202 @ X2 )
= $true )
& ( ( in @ X2 @ sK203 )
= $true ) )
=> ( ( ( sK202 @ sK204 )
= $true )
& ( $true
= ( in @ sK204 @ sK203 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1028,plain,
! [X5: $i > $o,X6: $i] :
( ? [X8: $i] :
( ? [X9: $i] :
( ( ( X5 @ X9 )
= $true )
& ( ( X5 @ X8 )
= $true )
& ( ( in @ X9 @ X6 )
= $true )
& ( X8 != X9 ) )
& ( ( in @ X8 @ X6 )
= $true ) )
=> ( ? [X9: $i] :
( ( ( X5 @ X9 )
= $true )
& ( ( X5 @ ( sK205 @ X6 @ X5 ) )
= $true )
& ( ( in @ X9 @ X6 )
= $true )
& ( ( sK205 @ X6 @ X5 )
!= X9 ) )
& ( ( in @ ( sK205 @ X6 @ X5 ) @ X6 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1029,plain,
! [X5: $i > $o,X6: $i] :
( ? [X9: $i] :
( ( ( X5 @ X9 )
= $true )
& ( ( X5 @ ( sK205 @ X6 @ X5 ) )
= $true )
& ( ( in @ X9 @ X6 )
= $true )
& ( ( sK205 @ X6 @ X5 )
!= X9 ) )
=> ( ( ( X5 @ ( sK206 @ X6 @ X5 ) )
= $true )
& ( ( X5 @ ( sK205 @ X6 @ X5 ) )
= $true )
& ( ( in @ ( sK206 @ X6 @ X5 ) @ X6 )
= $true )
& ( ( sK205 @ X6 @ X5 )
!= ( sK206 @ X6 @ X5 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1025,plain,
( ( ( $true = sP6 )
| ? [X0: $i > $o,X1: $i] :
( ? [X2: $i] :
( ( ( X0 @ X2 )
= $true )
& ( $true
= ( in @ X2 @ X1 ) ) )
& ! [X3: $i] :
( ! [X4: $i] :
( ( ( X0 @ X4 )
!= $true )
| ( ( X0 @ X3 )
!= $true )
| ( ( in @ X4 @ X1 )
!= $true )
| ( X3 = X4 ) )
| ( ( in @ X3 @ X1 )
!= $true ) )
& ( ( singleton
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true ) ) )
& ( ! [X5: $i > $o,X6: $i] :
( ! [X7: $i] :
( ( ( X5 @ X7 )
!= $true )
| ( ( in @ X7 @ X6 )
!= $true ) )
| ? [X8: $i] :
( ? [X9: $i] :
( ( ( X5 @ X9 )
= $true )
& ( ( X5 @ X8 )
= $true )
& ( ( in @ X9 @ X6 )
= $true )
& ( X8 != X9 ) )
& ( ( in @ X8 @ X6 )
= $true ) )
| ( $true
= ( singleton
@ ( dsetconstr @ X6
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) ) )
| ( $true != sP6 ) ) ),
inference(rectify,[status(thm)],[f1024]) ).
thf(f1024,plain,
( ( ( $true = sP6 )
| ? [X0: $i > $o,X1: $i] :
( ? [X4: $i] :
( ( ( X0 @ X4 )
= $true )
& ( ( in @ X4 @ X1 )
= $true ) )
& ! [X2: $i] :
( ! [X3: $i] :
( ( ( X0 @ X3 )
!= $true )
| ( ( X0 @ X2 )
!= $true )
| ( ( in @ X3 @ X1 )
!= $true )
| ( X2 = X3 ) )
| ( $true
!= ( in @ X2 @ X1 ) ) )
& ( ( singleton
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
!= $true ) ) )
& ( ! [X0: $i > $o,X1: $i] :
( ! [X4: $i] :
( ( ( X0 @ X4 )
!= $true )
| ( ( in @ X4 @ X1 )
!= $true ) )
| ? [X2: $i] :
( ? [X3: $i] :
( ( ( X0 @ X3 )
= $true )
& ( ( X0 @ X2 )
= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( X2 != X3 ) )
& ( $true
= ( in @ X2 @ X1 ) ) )
| ( ( singleton
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= $true ) )
| ( $true != sP6 ) ) ),
inference(nnf_transformation,[status(thm)],[f687]) ).
thf(f687,plain,
( ( $true = sP6 )
<=> ! [X0: $i > $o,X1: $i] :
( ! [X4: $i] :
( ( ( X0 @ X4 )
!= $true )
| ( ( in @ X4 @ X1 )
!= $true ) )
| ? [X2: $i] :
( ? [X3: $i] :
( ( ( X0 @ X3 )
= $true )
& ( ( X0 @ X2 )
= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( X2 != X3 ) )
& ( $true
= ( in @ X2 @ X1 ) ) )
| ( ( singleton
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f3073,plain,
( spl432_21
| ~ spl432_1 ),
inference(avatar_split_clause,[status(thm)],[f2837,f2986,f3071]) ).
thf(f2837,plain,
! [X6: $i,X7: $i,X5: $i > $o] :
( ( $true != sP6 )
| ( $true
= ( singleton @ ( dsetconstr @ X6 @ X5 ) ) )
| ( ( X5 @ ( sK206 @ X6 @ X5 ) )
= $true )
| ( ( in @ X7 @ X6 )
!= $true )
| ( ( X5 @ X7 )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f1695]) ).
thf(f1695,plain,
! [X6: $i,X7: $i,X5: $i > $o] :
( ( ( in @ X7 @ X6 )
!= $true )
| ( $true
= ( singleton
@ ( dsetconstr @ X6
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) )
| ( ( X5 @ X7 )
!= $true )
| ( $true != sP6 )
| ( ( X5 @ ( sK206 @ X6 @ X5 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f1030]) ).
thf(f3058,plain,
( ~ spl432_1
| spl432_18 ),
inference(avatar_split_clause,[status(thm)],[f2854,f3056,f2986]) ).
thf(f2854,plain,
! [X6: $i,X7: $i,X5: $i > $o] :
( ( $true
= ( singleton @ ( dsetconstr @ X6 @ X5 ) ) )
| ( ( in @ X7 @ X6 )
!= $true )
| ( $true != sP6 )
| ( ( sK205 @ X6 @ X5 )
!= ( sK206 @ X6 @ X5 ) )
| ( ( X5 @ X7 )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f1692]) ).
thf(f1692,plain,
! [X6: $i,X7: $i,X5: $i > $o] :
( ( ( sK205 @ X6 @ X5 )
!= ( sK206 @ X6 @ X5 ) )
| ( ( X5 @ X7 )
!= $true )
| ( $true
= ( singleton
@ ( dsetconstr @ X6
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) )
| ( ( in @ X7 @ X6 )
!= $true )
| ( $true != sP6 ) ),
inference(cnf_transformation,[status(thm)],[f1030]) ).
thf(f3050,plain,
( ~ spl432_1
| spl432_16 ),
inference(avatar_split_clause,[status(thm)],[f2859,f3048,f2986]) ).
thf(f2859,plain,
! [X6: $i,X7: $i,X5: $i > $o] :
( ( $true
= ( singleton @ ( dsetconstr @ X6 @ X5 ) ) )
| ( ( X5 @ X7 )
!= $true )
| ( $true != sP6 )
| ( ( in @ X7 @ X6 )
!= $true )
| ( ( X5 @ ( sK205 @ X6 @ X5 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f1694]) ).
thf(f1694,plain,
! [X6: $i,X7: $i,X5: $i > $o] :
( ( ( X5 @ ( sK205 @ X6 @ X5 ) )
= $true )
| ( $true != sP6 )
| ( ( X5 @ X7 )
!= $true )
| ( ( in @ X7 @ X6 )
!= $true )
| ( $true
= ( singleton
@ ( dsetconstr @ X6
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f1030]) ).
thf(f3046,plain,
spl432_1,
inference(avatar_split_clause,[status(thm)],[f2868,f2986]) ).
thf(f2868,plain,
$true = sP6,
inference(trivial_inequality_removal,[status(thm)],[f2398]) ).
thf(f2398,plain,
( ( $true = sP6 )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f1701,f1865]) ).
thf(f1865,plain,
singletonprop = $true,
inference(cnf_transformation,[status(thm)],[f1213]) ).
thf(f1701,plain,
( ( $true = sP6 )
| ( singletonprop != $true ) ),
inference(cnf_transformation,[status(thm)],[f1031]) ).
thf(f1031,plain,
( ( ( $true = sP6 )
| ( singletonprop != $true ) )
& ( ( singletonprop = $true )
| ( $true != sP6 ) ) ),
inference(nnf_transformation,[status(thm)],[f688]) ).
thf(f688,plain,
( ( $true = sP6 )
<=> ( singletonprop = $true ) ),
inference(definition_folding,[status(thm)],[f637,f687]) ).
thf(f637,plain,
( ! [X0: $i > $o,X1: $i] :
( ! [X4: $i] :
( ( ( X0 @ X4 )
!= $true )
| ( ( in @ X4 @ X1 )
!= $true ) )
| ? [X2: $i] :
( ? [X3: $i] :
( ( ( X0 @ X3 )
= $true )
& ( ( X0 @ X2 )
= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( X2 != X3 ) )
& ( $true
= ( in @ X2 @ X1 ) ) )
| ( ( singleton
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= $true ) )
<=> ( singletonprop = $true ) ),
inference(flattening,[status(thm)],[f636]) ).
thf(f636,plain,
( ( singletonprop = $true )
<=> ! [X0: $i > $o,X1: $i] :
( ( ( singleton
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= $true )
| ! [X4: $i] :
( ( ( X0 @ X4 )
!= $true )
| ( ( in @ X4 @ X1 )
!= $true ) )
| ? [X2: $i] :
( ? [X3: $i] :
( ( X2 != X3 )
& ( ( X0 @ X3 )
= $true )
& ( ( X0 @ X2 )
= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( $true
= ( in @ X2 @ X1 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f480]) ).
thf(f480,plain,
( ( singletonprop = $true )
<=> ! [X0: $i > $o,X1: $i] :
( ! [X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ( X0 @ X2 )
= $true )
=> ( ( ( X0 @ X3 )
= $true )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X4: $i] :
( ( ( X0 @ X4 )
= $true )
& ( ( in @ X4 @ X1 )
= $true ) )
=> ( ( singleton
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f479]) ).
thf(f479,plain,
! [X0: $i > $o,X1: $i] :
( ( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( X0 @ X2 )
=> ( ( X0 @ X3 )
=> ( X2 = X3 ) ) ) ) )
=> ( ? [X4: $i] :
( ( X0 @ X4 )
& ( in @ X4 @ X1 ) )
=> ( singleton
@ ( dsetconstr @ X1
@ ^ [X5: $i] : ( X0 @ X5 ) ) ) ) )
= singletonprop ),
inference(rectify,[status(thm)],[f159]) ).
thf(f159,axiom,
! [X0: $i > $o,X3: $i] :
( ( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X3 )
=> ( ( X0 @ X1 )
=> ( ( X0 @ X2 )
=> ( X1 = X2 ) ) ) ) )
=> ( ? [X1: $i] :
( ( X0 @ X1 )
& ( in @ X1 @ X3 ) )
=> ( singleton
@ ( dsetconstr @ X3
@ ^ [X1: $i] : ( X0 @ X1 ) ) ) ) )
= singletonprop ),
file('/export/starexec/sandbox/tmp/tmp.0njZozgBRA/DTF2THF_1200.p',singletonprop) ).
thf(f3001,plain,
( spl432_4
| ~ spl432_1 ),
inference(avatar_split_clause,[status(thm)],[f2942,f2986,f2999]) ).
thf(f2942,plain,
! [X6: $i,X7: $i,X5: $i > $o] :
( ( $true
= ( singleton @ ( dsetconstr @ X6 @ X5 ) ) )
| ( ( X5 @ X7 )
!= $true )
| ( ( in @ ( sK206 @ X6 @ X5 ) @ X6 )
= $true )
| ( $true != sP6 )
| ( ( in @ X7 @ X6 )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f1693]) ).
thf(f1693,plain,
! [X6: $i,X7: $i,X5: $i > $o] :
( ( $true
= ( singleton
@ ( dsetconstr @ X6
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) ) )
| ( ( in @ X7 @ X6 )
!= $true )
| ( ( X5 @ X7 )
!= $true )
| ( ( in @ ( sK206 @ X6 @ X5 ) @ X6 )
= $true )
| ( $true != sP6 ) ),
inference(cnf_transformation,[status(thm)],[f1030]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU639^1 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n006.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:29:15 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.27/0.47 ---- Original DTF file ---
% 0.27/0.47 thf(spec,logic,$$dhol).
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 % File : SEU639^1 : TPTP v9.2.1. Released v3.7.0.
% 0.27/0.47 % Domain : Set Theory
% 0.27/0.47 % Problem : Ordered Pairs - Singletons
% 0.27/0.47 % Version : Especial.
% 0.27/0.47 % English : (! A:i.! phi:i>o.! x:i.in x A -> phi x -> (! y:i.in y A ->
% 0.27/0.47 % phi y -> y = x) -> ex1 A (^ y:i.phi y))
% 0.27/0.47
% 0.27/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.27/0.47 % Source : [Bro08]
% 0.27/0.47 % Names : ZFC141g [Bro08]
% 0.27/0.47
% 0.27/0.47 % Status : Theorem
% 0.27/0.47 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.50 v8.2.0, 0.69 v8.1.0, 0.64 v7.5.0, 0.57 v7.4.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.86 v6.4.0, 0.83 v6.3.0, 1.00 v6.2.0, 0.86 v5.5.0, 1.00 v3.7.0
% 0.27/0.47 % Syntax : Number of formulae : 342 ( 161 unt; 180 typ; 161 def)
% 0.27/0.47 % Number of atoms : 853 ( 226 equ; 0 cnn)
% 0.27/0.47 % Maximal formula atoms : 159 ( 5 avg)
% 0.27/0.47 % Number of connectives : 1472 ( 47 ~; 7 |; 36 &; 992 @)
% 0.27/0.47 % ( 14 <=>; 376 =>; 0 <=; 0 <~>)
% 0.27/0.47 % Maximal formula depth : 166 ( 2 avg)
% 0.27/0.47 % Number of types : 2 ( 0 usr)
% 0.27/0.47 % Number of type conns : 77 ( 77 >; 0 *; 0 +; 0 <<)
% 0.27/0.47 % Number of symbols : 183 ( 180 usr; 159 con; 0-2 aty)
% 0.27/0.47 % Number of variables : 469 ( 40 ^; 392 !; 37 ?; 469 :)
% 0.27/0.47 % SPC : TH0_THM_EQU_NAR
% 0.27/0.47
% 0.27/0.47 % Comments : http://mathgate.info/detsetitem.php?id=196
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 thf(in_type,type,
% 0.27/0.47 in: $i > $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(exu_type,type,
% 0.27/0.47 exu: ( $i > $o ) > $o ).
% 0.27/0.47
% 0.27/0.47 thf(exu,definition,
% 0.27/0.47 ( exu
% 0.27/0.47 = ( ^ [Xphi: $i > $o] :
% 0.27/0.47 ? [Xx: $i] :
% 0.27/0.47 ( ( Xphi @ Xx )
% 0.27/0.47 & ! [Xy: $i] :
% 0.27/0.47 ( ( Xphi @ Xy )
% 0.27/0.47 => ( Xx = Xy ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setextAx_type,type,
% 0.27/0.47 setextAx: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setextAx,definition,
% 0.27/0.47 ( setextAx
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 <=> ( in @ Xx @ B ) )
% 0.27/0.47 => ( A = B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(emptyset_type,type,
% 0.27/0.47 emptyset: $i ).
% 0.27/0.47
% 0.27/0.47 thf(emptysetAx_type,type,
% 0.27/0.47 emptysetAx: $o ).
% 0.27/0.47
% 0.27/0.47 thf(emptysetAx,definition,
% 0.27/0.47 ( emptysetAx
% 0.27/0.47 = ( ! [Xx: $i] :
% 0.27/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setadjoin_type,type,
% 0.27/0.47 setadjoin: $i > $i > $i ).
% 0.27/0.47
% 0.27/0.47 thf(setadjoinAx_type,type,
% 0.27/0.47 setadjoinAx: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setadjoinAx,definition,
% 0.27/0.47 ( setadjoinAx
% 0.27/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.27/0.47 <=> ( ( Xy = Xx )
% 0.27/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(powerset_type,type,
% 0.27/0.47 powerset: $i > $i ).
% 0.27/0.47
% 0.27/0.47 thf(powersetAx_type,type,
% 0.27/0.47 powersetAx: $o ).
% 0.27/0.47
% 0.27/0.47 thf(powersetAx,definition,
% 0.27/0.47 ( powersetAx
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.27/0.47 <=> ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ B )
% 0.27/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setunion_type,type,
% 0.27/0.47 setunion: $i > $i ).
% 0.27/0.47
% 0.27/0.47 thf(setunionAx_type,type,
% 0.27/0.47 setunionAx: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setunionAx,definition,
% 0.27/0.47 ( setunionAx
% 0.27/0.47 = ( ! [A: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.27/0.47 <=> ? [B: $i] :
% 0.27/0.47 ( ( in @ Xx @ B )
% 0.27/0.47 & ( in @ B @ A ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(omega_type,type,
% 0.27/0.47 omega: $i ).
% 0.27/0.47
% 0.27/0.47 thf(omega0Ax_type,type,
% 0.27/0.47 omega0Ax: $o ).
% 0.27/0.47
% 0.27/0.47 thf(omega0Ax,definition,
% 0.27/0.47 ( omega0Ax
% 0.27/0.47 = ( in @ emptyset @ omega ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(omegaSAx_type,type,
% 0.27/0.47 omegaSAx: $o ).
% 0.27/0.47
% 0.27/0.47 thf(omegaSAx,definition,
% 0.27/0.47 ( omegaSAx
% 0.27/0.47 = ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ omega )
% 0.27/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(omegaIndAx_type,type,
% 0.27/0.47 omegaIndAx: $o ).
% 0.27/0.47
% 0.27/0.47 thf(omegaIndAx,definition,
% 0.27/0.47 ( omegaIndAx
% 0.27/0.47 = ( ! [A: $i] :
% 0.27/0.47 ( ( ( in @ emptyset @ A )
% 0.27/0.47 & ! [Xx: $i] :
% 0.27/0.47 ( ( ( in @ Xx @ omega )
% 0.27/0.47 & ( in @ Xx @ A ) )
% 0.27/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ omega )
% 0.27/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(replAx_type,type,
% 0.27/0.47 replAx: $o ).
% 0.27/0.47
% 0.27/0.47 thf(replAx,definition,
% 0.27/0.47 ( replAx
% 0.27/0.47 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.27/0.47 ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( exu
% 0.27/0.47 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.27/0.47 => ? [B: $i] :
% 0.27/0.47 ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ B )
% 0.27/0.47 <=> ? [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ A )
% 0.27/0.47 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(foundationAx_type,type,
% 0.27/0.47 foundationAx: $o ).
% 0.27/0.47
% 0.27/0.47 thf(foundationAx,definition,
% 0.27/0.47 ( foundationAx
% 0.27/0.47 = ( ! [A: $i] :
% 0.27/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.27/0.47 => ? [B: $i] :
% 0.27/0.47 ( ( in @ B @ A )
% 0.27/0.47 & ~ ? [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ B )
% 0.27/0.47 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(wellorderingAx_type,type,
% 0.27/0.47 wellorderingAx: $o ).
% 0.27/0.47
% 0.27/0.47 thf(wellorderingAx,definition,
% 0.27/0.47 ( wellorderingAx
% 0.27/0.47 = ( ! [A: $i] :
% 0.27/0.47 ? [B: $i] :
% 0.27/0.47 ( ! [C: $i] :
% 0.27/0.47 ( ( in @ C @ B )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ C )
% 0.27/0.47 => ( in @ Xx @ A ) ) )
% 0.27/0.47 & ! [Xx: $i,Xy: $i] :
% 0.27/0.47 ( ( ( in @ Xx @ A )
% 0.27/0.47 & ( in @ Xy @ A ) )
% 0.27/0.47 => ( ! [C: $i] :
% 0.27/0.47 ( ( in @ C @ B )
% 0.27/0.47 => ( ( in @ Xx @ C )
% 0.27/0.47 <=> ( in @ Xy @ C ) ) )
% 0.27/0.47 => ( Xx = Xy ) ) )
% 0.27/0.47 & ! [C: $i,D: $i] :
% 0.27/0.47 ( ( ( in @ C @ B )
% 0.27/0.47 & ( in @ D @ B ) )
% 0.27/0.47 => ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ C )
% 0.27/0.47 => ( in @ Xx @ D ) )
% 0.27/0.47 | ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ D )
% 0.27/0.47 => ( in @ Xx @ C ) ) ) )
% 0.27/0.47 & ! [C: $i] :
% 0.27/0.47 ( ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ C )
% 0.27/0.47 => ( in @ Xx @ A ) )
% 0.27/0.47 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.27/0.47 => ? [D: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ D @ B )
% 0.27/0.47 & ( in @ Xx @ C )
% 0.27/0.47 & ~ ? [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ D )
% 0.27/0.47 & ( in @ Xy @ C ) )
% 0.27/0.47 & ! [E: $i] :
% 0.27/0.47 ( ( in @ E @ B )
% 0.27/0.47 => ( ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ E )
% 0.27/0.47 => ( in @ Xy @ D ) )
% 0.27/0.47 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(descr_type,type,
% 0.27/0.47 descr: ( $i > $o ) > $i ).
% 0.27/0.47
% 0.27/0.47 thf(descrp_type,type,
% 0.27/0.47 descrp: $o ).
% 0.27/0.47
% 0.27/0.47 thf(descrp,definition,
% 0.27/0.47 ( descrp
% 0.27/0.47 = ( ! [Xphi: $i > $o] :
% 0.27/0.47 ( ( exu
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.47 => ( Xphi
% 0.27/0.47 @ ( descr
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(dsetconstr_type,type,
% 0.27/0.47 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.27/0.47
% 0.27/0.47 thf(dsetconstrI_type,type,
% 0.27/0.47 dsetconstrI: $o ).
% 0.27/0.47
% 0.27/0.47 thf(dsetconstrI,definition,
% 0.27/0.47 ( dsetconstrI
% 0.27/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( Xphi @ Xx )
% 0.27/0.47 => ( in @ Xx
% 0.27/0.47 @ ( dsetconstr @ A
% 0.27/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(dsetconstrEL_type,type,
% 0.27/0.47 dsetconstrEL: $o ).
% 0.27/0.47
% 0.27/0.47 thf(dsetconstrEL,definition,
% 0.27/0.47 ( dsetconstrEL
% 0.27/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx
% 0.27/0.47 @ ( dsetconstr @ A
% 0.27/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.27/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(dsetconstrER_type,type,
% 0.27/0.47 dsetconstrER: $o ).
% 0.27/0.47
% 0.27/0.47 thf(dsetconstrER,definition,
% 0.27/0.47 ( dsetconstrER
% 0.27/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx
% 0.27/0.47 @ ( dsetconstr @ A
% 0.27/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.27/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(exuE1_type,type,
% 0.27/0.47 exuE1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(exuE1,definition,
% 0.27/0.47 ( exuE1
% 0.27/0.47 = ( ! [Xphi: $i > $o] :
% 0.27/0.47 ( ( exu
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.47 => ? [Xx: $i] :
% 0.27/0.47 ( ( Xphi @ Xx )
% 0.27/0.47 & ! [Xy: $i] :
% 0.27/0.47 ( ( Xphi @ Xy )
% 0.27/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(prop2set_type,type,
% 0.27/0.47 prop2set: $o > $i ).
% 0.27/0.47
% 0.27/0.47 thf(prop2setE_type,type,
% 0.27/0.47 prop2setE: $o ).
% 0.27/0.47
% 0.27/0.47 thf(prop2setE,definition,
% 0.27/0.47 ( prop2setE
% 0.27/0.47 = ( ! [Xphi: $o,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.27/0.47 => Xphi ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(emptysetE_type,type,
% 0.27/0.47 emptysetE: $o ).
% 0.27/0.47
% 0.27/0.47 thf(emptysetE,definition,
% 0.27/0.47 ( emptysetE
% 0.27/0.47 = ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ emptyset )
% 0.27/0.47 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(emptysetimpfalse_type,type,
% 0.27/0.47 emptysetimpfalse: $o ).
% 0.27/0.47
% 0.27/0.47 thf(emptysetimpfalse,definition,
% 0.27/0.47 ( emptysetimpfalse
% 0.27/0.47 = ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ emptyset )
% 0.27/0.47 => $false ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(notinemptyset_type,type,
% 0.27/0.47 notinemptyset: $o ).
% 0.27/0.47
% 0.27/0.47 thf(notinemptyset,definition,
% 0.27/0.47 ( notinemptyset
% 0.27/0.47 = ( ! [Xx: $i] :
% 0.27/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(exuE3e_type,type,
% 0.27/0.47 exuE3e: $o ).
% 0.27/0.47
% 0.27/0.47 thf(exuE3e,definition,
% 0.27/0.47 ( exuE3e
% 0.27/0.47 = ( ! [Xphi: $i > $o] :
% 0.27/0.47 ( ( exu
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.47 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setext_type,type,
% 0.27/0.47 setext: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setext,definition,
% 0.27/0.47 ( setext
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( in @ Xx @ B ) )
% 0.27/0.47 => ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ B )
% 0.27/0.47 => ( in @ Xx @ A ) )
% 0.27/0.47 => ( A = B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(emptyI_type,type,
% 0.27/0.47 emptyI: $o ).
% 0.27/0.47
% 0.27/0.47 thf(emptyI,definition,
% 0.27/0.47 ( emptyI
% 0.27/0.47 = ( ! [A: $i] :
% 0.27/0.47 ( ! [Xx: $i] :
% 0.27/0.47 ~ ( in @ Xx @ A )
% 0.27/0.47 => ( A = emptyset ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(noeltsimpempty_type,type,
% 0.27/0.47 noeltsimpempty: $o ).
% 0.27/0.47
% 0.27/0.47 thf(noeltsimpempty,definition,
% 0.27/0.47 ( noeltsimpempty
% 0.27/0.47 = ( ! [A: $i] :
% 0.27/0.47 ( ! [Xx: $i] :
% 0.27/0.47 ~ ( in @ Xx @ A )
% 0.27/0.47 => ( A = emptyset ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setbeta_type,type,
% 0.27/0.47 setbeta: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setbeta,definition,
% 0.27/0.47 ( setbeta
% 0.27/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ Xx
% 0.27/0.47 @ ( dsetconstr @ A
% 0.27/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.27/0.47 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(nonempty_type,type,
% 0.27/0.47 nonempty: $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(nonempty,definition,
% 0.27/0.47 ( nonempty
% 0.27/0.47 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(nonemptyE1_type,type,
% 0.27/0.47 nonemptyE1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(nonemptyE1,definition,
% 0.27/0.47 ( nonemptyE1
% 0.27/0.47 = ( ! [A: $i] :
% 0.27/0.47 ( ( nonempty @ A )
% 0.27/0.47 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(nonemptyI_type,type,
% 0.27/0.47 nonemptyI: $o ).
% 0.27/0.47
% 0.27/0.47 thf(nonemptyI,definition,
% 0.27/0.47 ( nonemptyI
% 0.27/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( Xphi @ Xx )
% 0.27/0.47 => ( nonempty
% 0.27/0.47 @ ( dsetconstr @ A
% 0.27/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(nonemptyI1_type,type,
% 0.27/0.47 nonemptyI1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(nonemptyI1,definition,
% 0.27/0.47 ( nonemptyI1
% 0.27/0.47 = ( ! [A: $i] :
% 0.27/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.27/0.47 => ( nonempty @ A ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setadjoinIL_type,type,
% 0.27/0.47 setadjoinIL: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setadjoinIL,definition,
% 0.27/0.47 ( setadjoinIL
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(emptyinunitempty_type,type,
% 0.27/0.47 emptyinunitempty: $o ).
% 0.27/0.47
% 0.27/0.47 thf(emptyinunitempty,definition,
% 0.27/0.47 ( emptyinunitempty
% 0.27/0.47 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setadjoinIR_type,type,
% 0.27/0.47 setadjoinIR: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setadjoinIR,definition,
% 0.27/0.47 ( setadjoinIR
% 0.27/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ A )
% 0.27/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setadjoinE_type,type,
% 0.27/0.47 setadjoinE: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setadjoinE,definition,
% 0.27/0.47 ( setadjoinE
% 0.27/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.27/0.47 => ! [Xphi: $o] :
% 0.27/0.47 ( ( ( Xy = Xx )
% 0.27/0.47 => Xphi )
% 0.27/0.47 => ( ( ( in @ Xy @ A )
% 0.27/0.47 => Xphi )
% 0.27/0.47 => Xphi ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setadjoinOr_type,type,
% 0.27/0.47 setadjoinOr: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setadjoinOr,definition,
% 0.27/0.47 ( setadjoinOr
% 0.27/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.27/0.47 => ( ( Xy = Xx )
% 0.27/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setoftrueEq_type,type,
% 0.27/0.47 setoftrueEq: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setoftrueEq,definition,
% 0.27/0.47 ( setoftrueEq
% 0.27/0.47 = ( ! [A: $i] :
% 0.27/0.47 ( ( dsetconstr @ A
% 0.27/0.47 @ ^ [Xx: $i] : $true )
% 0.27/0.47 = A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(powersetI_type,type,
% 0.27/0.47 powersetI: $o ).
% 0.27/0.47
% 0.27/0.47 thf(powersetI,definition,
% 0.27/0.47 ( powersetI
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ B )
% 0.27/0.47 => ( in @ Xx @ A ) )
% 0.27/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(emptyinPowerset_type,type,
% 0.27/0.47 emptyinPowerset: $o ).
% 0.27/0.47
% 0.27/0.47 thf(emptyinPowerset,definition,
% 0.27/0.47 ( emptyinPowerset
% 0.27/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(emptyInPowerset_type,type,
% 0.27/0.47 emptyInPowerset: $o ).
% 0.27/0.47
% 0.27/0.47 thf(emptyInPowerset,definition,
% 0.27/0.47 ( emptyInPowerset
% 0.27/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(powersetE_type,type,
% 0.27/0.47 powersetE: $o ).
% 0.27/0.47
% 0.27/0.47 thf(powersetE,definition,
% 0.27/0.47 ( powersetE
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.27/0.47 => ( ( in @ Xx @ B )
% 0.27/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setunionI_type,type,
% 0.27/0.47 setunionI: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setunionI,definition,
% 0.27/0.47 ( setunionI
% 0.27/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.27/0.47 ( ( in @ Xx @ B )
% 0.27/0.47 => ( ( in @ B @ A )
% 0.27/0.47 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setunionE_type,type,
% 0.27/0.47 setunionE: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setunionE,definition,
% 0.27/0.47 ( setunionE
% 0.27/0.47 = ( ! [A: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.27/0.47 => ! [Xphi: $o] :
% 0.27/0.47 ( ! [B: $i] :
% 0.27/0.47 ( ( in @ Xx @ B )
% 0.27/0.47 => ( ( in @ B @ A )
% 0.27/0.47 => Xphi ) )
% 0.27/0.47 => Xphi ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(subPowSU_type,type,
% 0.27/0.47 subPowSU: $o ).
% 0.27/0.47
% 0.27/0.47 thf(subPowSU,definition,
% 0.27/0.47 ( subPowSU
% 0.27/0.47 = ( ! [A: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(exuE2_type,type,
% 0.27/0.47 exuE2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(exuE2,definition,
% 0.27/0.47 ( exuE2
% 0.27/0.47 = ( ! [Xphi: $i > $o] :
% 0.27/0.47 ( ( exu
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.47 => ? [Xx: $i] :
% 0.27/0.47 ! [Xy: $i] :
% 0.27/0.47 ( ( Xphi @ Xy )
% 0.27/0.47 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(nonemptyImpWitness_type,type,
% 0.27/0.47 nonemptyImpWitness: $o ).
% 0.27/0.47
% 0.27/0.47 thf(nonemptyImpWitness,definition,
% 0.27/0.47 ( nonemptyImpWitness
% 0.27/0.47 = ( ! [A: $i] :
% 0.27/0.47 ( ( nonempty @ A )
% 0.27/0.47 => ? [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 & $true ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(uniqinunit_type,type,
% 0.27/0.47 uniqinunit: $o ).
% 0.27/0.47
% 0.27/0.47 thf(uniqinunit,definition,
% 0.27/0.47 ( uniqinunit
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.27/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.27/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(notinsingleton_type,type,
% 0.27/0.47 notinsingleton: $o ).
% 0.27/0.47
% 0.27/0.47 thf(notinsingleton,definition,
% 0.27/0.47 ( notinsingleton
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.27/0.47 ( ( Xx != Xy )
% 0.27/0.47 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(eqinunit_type,type,
% 0.27/0.47 eqinunit: $o ).
% 0.27/0.47
% 0.27/0.47 thf(eqinunit,definition,
% 0.27/0.47 ( eqinunit
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.27/0.47 ( ( Xx = Xy )
% 0.27/0.47 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(singletonsswitch_type,type,
% 0.27/0.47 singletonsswitch: $o ).
% 0.27/0.47
% 0.27/0.47 thf(singletonsswitch,definition,
% 0.27/0.47 ( singletonsswitch
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.27/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.27/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(upairsetE_type,type,
% 0.27/0.47 upairsetE: $o ).
% 0.27/0.47
% 0.27/0.47 thf(upairsetE,definition,
% 0.27/0.47 ( upairsetE
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.27/0.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.27/0.47 => ( ( Xz = Xx )
% 0.27/0.47 | ( Xz = Xy ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(upairsetIL_type,type,
% 0.27/0.47 upairsetIL: $o ).
% 0.27/0.47
% 0.27/0.47 thf(upairsetIL,definition,
% 0.27/0.47 ( upairsetIL
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(upairsetIR_type,type,
% 0.27/0.47 upairsetIR: $o ).
% 0.27/0.47
% 0.27/0.47 thf(upairsetIR,definition,
% 0.27/0.47 ( upairsetIR
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(emptyE1_type,type,
% 0.27/0.47 emptyE1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(emptyE1,definition,
% 0.27/0.47 ( emptyE1
% 0.27/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.47 ( ? [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 & ( Xphi @ Xx ) )
% 0.27/0.47 => ( ( ( dsetconstr @ A
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.47 = emptyset )
% 0.27/0.47 => $false ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(vacuousDall_type,type,
% 0.27/0.47 vacuousDall: $o ).
% 0.27/0.47
% 0.27/0.47 thf(vacuousDall,definition,
% 0.27/0.47 ( vacuousDall
% 0.27/0.47 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ emptyset )
% 0.27/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(quantDeMorgan1_type,type,
% 0.27/0.47 quantDeMorgan1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(quantDeMorgan1,definition,
% 0.27/0.47 ( quantDeMorgan1
% 0.27/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.47 ( ~ ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( Xphi @ Xx ) )
% 0.27/0.47 => ? [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(quantDeMorgan2_type,type,
% 0.27/0.47 quantDeMorgan2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(quantDeMorgan2,definition,
% 0.27/0.47 ( quantDeMorgan2
% 0.27/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.47 ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ~ ( Xphi @ Xx ) )
% 0.27/0.47 => ~ ? [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(quantDeMorgan3_type,type,
% 0.27/0.47 quantDeMorgan3: $o ).
% 0.27/0.47
% 0.27/0.47 thf(quantDeMorgan3,definition,
% 0.27/0.47 ( quantDeMorgan3
% 0.27/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.47 ( ~ ? [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 & ( Xphi @ Xx ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(quantDeMorgan4_type,type,
% 0.27/0.47 quantDeMorgan4: $o ).
% 0.27/0.47
% 0.27/0.47 thf(quantDeMorgan4,definition,
% 0.27/0.47 ( quantDeMorgan4
% 0.27/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.47 ( ? [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 & ~ ( Xphi @ Xx ) )
% 0.27/0.47 => ~ ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(prop2setI_type,type,
% 0.27/0.47 prop2setI: $o ).
% 0.27/0.47
% 0.27/0.47 thf(prop2setI,definition,
% 0.27/0.47 ( prop2setI
% 0.27/0.47 = ( ! [Xphi: $o] :
% 0.27/0.47 ( Xphi
% 0.27/0.47 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(set2prop_type,type,
% 0.27/0.47 set2prop: $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(prop2set2propI_type,type,
% 0.27/0.47 prop2set2propI: $o ).
% 0.27/0.47
% 0.27/0.47 thf(prop2set2propI,definition,
% 0.27/0.47 ( prop2set2propI
% 0.27/0.47 = ( ! [Xphi: $o] :
% 0.27/0.47 ( Xphi
% 0.27/0.47 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(notdexE_type,type,
% 0.27/0.47 notdexE: $o ).
% 0.27/0.47
% 0.27/0.47 thf(notdexE,definition,
% 0.27/0.47 ( notdexE
% 0.27/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.47 ( ~ ? [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 & ( Xphi @ Xx ) )
% 0.27/0.47 => ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(notdallE_type,type,
% 0.27/0.47 notdallE: $o ).
% 0.27/0.47
% 0.27/0.47 thf(notdallE,definition,
% 0.27/0.47 ( notdallE
% 0.27/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.47 ( ~ ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( Xphi @ Xx ) )
% 0.27/0.47 => ? [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(exuI1_type,type,
% 0.27/0.47 exuI1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(exuI1,definition,
% 0.27/0.47 ( exuI1
% 0.27/0.47 = ( ! [Xphi: $i > $o] :
% 0.27/0.47 ( ? [Xx: $i] :
% 0.27/0.47 ( ( Xphi @ Xx )
% 0.27/0.47 & ! [Xy: $i] :
% 0.27/0.47 ( ( Xphi @ Xy )
% 0.27/0.47 => ( Xx = Xy ) ) )
% 0.27/0.47 => ( exu
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(exuI3_type,type,
% 0.27/0.47 exuI3: $o ).
% 0.27/0.47
% 0.27/0.47 thf(exuI3,definition,
% 0.27/0.47 ( exuI3
% 0.27/0.47 = ( ! [Xphi: $i > $o] :
% 0.27/0.47 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.27/0.47 => ( ! [Xx: $i,Xy: $i] :
% 0.27/0.47 ( ( Xphi @ Xx )
% 0.27/0.47 => ( ( Xphi @ Xy )
% 0.27/0.47 => ( Xx = Xy ) ) )
% 0.27/0.47 => ( exu
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(exuI2_type,type,
% 0.27/0.47 exuI2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(exuI2,definition,
% 0.27/0.47 ( exuI2
% 0.27/0.47 = ( ! [Xphi: $i > $o] :
% 0.27/0.47 ( ? [Xx: $i] :
% 0.27/0.47 ! [Xy: $i] :
% 0.27/0.47 ( ( Xphi @ Xy )
% 0.27/0.47 <=> ( Xy = Xx ) )
% 0.27/0.47 => ( exu
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(inCongP_type,type,
% 0.27/0.47 inCongP: $o ).
% 0.27/0.47
% 0.27/0.47 thf(inCongP,definition,
% 0.27/0.47 ( inCongP
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( A = B )
% 0.27/0.47 => ! [Xx: $i,Xy: $i] :
% 0.27/0.47 ( ( Xx = Xy )
% 0.27/0.47 => ( ( in @ Xx @ A )
% 0.27/0.47 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(in__Cong_type,type,
% 0.27/0.47 in__Cong: $o ).
% 0.27/0.47
% 0.27/0.47 thf(in__Cong,definition,
% 0.27/0.47 ( in__Cong
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( A = B )
% 0.27/0.47 => ! [Xx: $i,Xy: $i] :
% 0.27/0.47 ( ( Xx = Xy )
% 0.27/0.47 => ( ( in @ Xx @ A )
% 0.27/0.47 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(exuE3u_type,type,
% 0.27/0.47 exuE3u: $o ).
% 0.27/0.47
% 0.27/0.47 thf(exuE3u,definition,
% 0.27/0.47 ( exuE3u
% 0.27/0.47 = ( ! [Xphi: $i > $o] :
% 0.27/0.47 ( ( exu
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.47 => ! [Xx: $i,Xy: $i] :
% 0.27/0.47 ( ( Xphi @ Xx )
% 0.27/0.47 => ( ( Xphi @ Xy )
% 0.27/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(exu__Cong_type,type,
% 0.27/0.47 exu__Cong: $o ).
% 0.27/0.47
% 0.27/0.47 thf(exu__Cong,definition,
% 0.27/0.47 ( exu__Cong
% 0.27/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.27/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.27/0.47 ( ( Xx = Xy )
% 0.27/0.47 => ( ( Xphi @ Xx )
% 0.27/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.27/0.47 => ( ( exu
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.47 <=> ( exu
% 0.27/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(emptyset__Cong_type,type,
% 0.27/0.47 emptyset__Cong: $o ).
% 0.27/0.47
% 0.27/0.47 thf(emptyset__Cong,definition,
% 0.27/0.47 ( emptyset__Cong
% 0.27/0.47 = ( emptyset = emptyset ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setadjoin__Cong_type,type,
% 0.27/0.47 setadjoin__Cong: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setadjoin__Cong,definition,
% 0.27/0.47 ( setadjoin__Cong
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.27/0.47 ( ( Xx = Xy )
% 0.27/0.47 => ! [Xz: $i,Xu: $i] :
% 0.27/0.47 ( ( Xz = Xu )
% 0.27/0.47 => ( ( setadjoin @ Xx @ Xz )
% 0.27/0.47 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(powerset__Cong_type,type,
% 0.27/0.47 powerset__Cong: $o ).
% 0.27/0.47
% 0.27/0.47 thf(powerset__Cong,definition,
% 0.27/0.47 ( powerset__Cong
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( A = B )
% 0.27/0.47 => ( ( powerset @ A )
% 0.27/0.47 = ( powerset @ B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setunion__Cong_type,type,
% 0.27/0.47 setunion__Cong: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setunion__Cong,definition,
% 0.27/0.47 ( setunion__Cong
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( A = B )
% 0.27/0.47 => ( ( setunion @ A )
% 0.27/0.47 = ( setunion @ B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(omega__Cong_type,type,
% 0.27/0.47 omega__Cong: $o ).
% 0.27/0.47
% 0.27/0.47 thf(omega__Cong,definition,
% 0.27/0.47 ( omega__Cong
% 0.27/0.47 = ( omega = omega ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(exuEu_type,type,
% 0.27/0.47 exuEu: $o ).
% 0.27/0.47
% 0.27/0.47 thf(exuEu,definition,
% 0.27/0.47 ( exuEu
% 0.27/0.47 = ( ! [Xphi: $i > $o] :
% 0.27/0.47 ( ( exu
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.47 => ! [Xx: $i,Xy: $i] :
% 0.27/0.47 ( ( Xphi @ Xx )
% 0.27/0.47 => ( ( Xphi @ Xy )
% 0.27/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(descr__Cong_type,type,
% 0.27/0.47 descr__Cong: $o ).
% 0.27/0.47
% 0.27/0.47 thf(descr__Cong,definition,
% 0.27/0.47 ( descr__Cong
% 0.27/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.27/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.27/0.47 ( ( Xx = Xy )
% 0.27/0.47 => ( ( Xphi @ Xx )
% 0.27/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.27/0.47 => ( ( exu
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.47 => ( ( exu
% 0.27/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.27/0.47 => ( ( descr
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.47 = ( descr
% 0.27/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(dsetconstr__Cong_type,type,
% 0.27/0.47 dsetconstr__Cong: $o ).
% 0.27/0.47
% 0.27/0.47 thf(dsetconstr__Cong,definition,
% 0.27/0.47 ( dsetconstr__Cong
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( A = B )
% 0.27/0.47 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.27/0.47 ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ B )
% 0.27/0.47 => ( ( Xx = Xy )
% 0.27/0.47 => ( ( Xphi @ Xx )
% 0.27/0.47 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.27/0.47 => ( ( dsetconstr @ A
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.47 = ( dsetconstr @ B
% 0.27/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(subset_type,type,
% 0.27/0.47 subset: $i > $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(disjoint_type,type,
% 0.27/0.47 disjoint: $i > $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(setsmeet_type,type,
% 0.27/0.47 setsmeet: $i > $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(subsetI1_type,type,
% 0.27/0.47 subsetI1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(subsetI1,definition,
% 0.27/0.47 ( subsetI1
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( in @ Xx @ B ) )
% 0.27/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(eqimpsubset2_type,type,
% 0.27/0.47 eqimpsubset2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(eqimpsubset2,definition,
% 0.27/0.47 ( eqimpsubset2
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( A = B )
% 0.27/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(eqimpsubset1_type,type,
% 0.27/0.47 eqimpsubset1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(eqimpsubset1,definition,
% 0.27/0.47 ( eqimpsubset1
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( A = B )
% 0.27/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(subsetI2_type,type,
% 0.27/0.47 subsetI2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(subsetI2,definition,
% 0.27/0.47 ( subsetI2
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( in @ Xx @ B ) )
% 0.27/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(emptysetsubset_type,type,
% 0.27/0.47 emptysetsubset: $o ).
% 0.27/0.47
% 0.27/0.47 thf(emptysetsubset,definition,
% 0.27/0.47 ( emptysetsubset
% 0.27/0.47 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(subsetE_type,type,
% 0.27/0.47 subsetE: $o ).
% 0.27/0.47
% 0.27/0.47 thf(subsetE,definition,
% 0.27/0.47 ( subsetE
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( subset @ A @ B )
% 0.27/0.47 => ( ( in @ Xx @ A )
% 0.27/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(subsetE2_type,type,
% 0.27/0.47 subsetE2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(subsetE2,definition,
% 0.27/0.47 ( subsetE2
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( subset @ A @ B )
% 0.27/0.47 => ( ~ ( in @ Xx @ B )
% 0.27/0.47 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(notsubsetI_type,type,
% 0.27/0.47 notsubsetI: $o ).
% 0.27/0.47
% 0.27/0.47 thf(notsubsetI,definition,
% 0.27/0.47 ( notsubsetI
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ~ ( in @ Xx @ B )
% 0.27/0.47 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(notequalI1_type,type,
% 0.27/0.47 notequalI1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(notequalI1,definition,
% 0.27/0.47 ( notequalI1
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ~ ( subset @ A @ B )
% 0.27/0.47 => ( A != B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(notequalI2_type,type,
% 0.27/0.47 notequalI2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(notequalI2,definition,
% 0.27/0.47 ( notequalI2
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ~ ( in @ Xx @ B )
% 0.27/0.47 => ( A != B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(subsetRefl_type,type,
% 0.27/0.47 subsetRefl: $o ).
% 0.27/0.47
% 0.27/0.47 thf(subsetRefl,definition,
% 0.27/0.47 ( subsetRefl
% 0.27/0.47 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(subsetTrans_type,type,
% 0.27/0.47 subsetTrans: $o ).
% 0.27/0.47
% 0.27/0.47 thf(subsetTrans,definition,
% 0.27/0.47 ( subsetTrans
% 0.27/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.27/0.47 ( ( subset @ A @ B )
% 0.27/0.47 => ( ( subset @ B @ C )
% 0.27/0.47 => ( subset @ A @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setadjoinSub_type,type,
% 0.27/0.47 setadjoinSub: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setadjoinSub,definition,
% 0.27/0.47 ( setadjoinSub
% 0.27/0.47 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setadjoinSub2_type,type,
% 0.27/0.47 setadjoinSub2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setadjoinSub2,definition,
% 0.27/0.47 ( setadjoinSub2
% 0.27/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.27/0.47 ( ( subset @ A @ B )
% 0.27/0.47 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(subset2powerset_type,type,
% 0.27/0.47 subset2powerset: $o ).
% 0.27/0.47
% 0.27/0.47 thf(subset2powerset,definition,
% 0.27/0.47 ( subset2powerset
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( subset @ A @ B )
% 0.27/0.47 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setextsub_type,type,
% 0.27/0.47 setextsub: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setextsub,definition,
% 0.27/0.47 ( setextsub
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( subset @ A @ B )
% 0.27/0.47 => ( ( subset @ B @ A )
% 0.27/0.47 => ( A = B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(subsetemptysetimpeq_type,type,
% 0.27/0.47 subsetemptysetimpeq: $o ).
% 0.27/0.47
% 0.27/0.47 thf(subsetemptysetimpeq,definition,
% 0.27/0.47 ( subsetemptysetimpeq
% 0.27/0.47 = ( ! [A: $i] :
% 0.27/0.47 ( ( subset @ A @ emptyset )
% 0.27/0.47 => ( A = emptyset ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(powersetI1_type,type,
% 0.27/0.47 powersetI1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(powersetI1,definition,
% 0.27/0.47 ( powersetI1
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( subset @ B @ A )
% 0.27/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(powersetE1_type,type,
% 0.27/0.47 powersetE1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(powersetE1,definition,
% 0.27/0.47 ( powersetE1
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.27/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(inPowerset_type,type,
% 0.27/0.47 inPowerset: $o ).
% 0.27/0.47
% 0.27/0.47 thf(inPowerset,definition,
% 0.27/0.47 ( inPowerset
% 0.27/0.47 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(powersetsubset_type,type,
% 0.27/0.47 powersetsubset: $o ).
% 0.27/0.47
% 0.27/0.47 thf(powersetsubset,definition,
% 0.27/0.47 ( powersetsubset
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( subset @ A @ B )
% 0.27/0.47 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(sepInPowerset_type,type,
% 0.27/0.47 sepInPowerset: $o ).
% 0.27/0.47
% 0.27/0.47 thf(sepInPowerset,definition,
% 0.27/0.47 ( sepInPowerset
% 0.27/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.47 ( in
% 0.27/0.47 @ ( dsetconstr @ A
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.47 @ ( powerset @ A ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(sepSubset_type,type,
% 0.27/0.47 sepSubset: $o ).
% 0.27/0.47
% 0.27/0.47 thf(sepSubset,definition,
% 0.27/0.47 ( sepSubset
% 0.27/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.47 ( subset
% 0.27/0.47 @ ( dsetconstr @ A
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.47 @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binunion_type,type,
% 0.27/0.47 binunion: $i > $i > $i ).
% 0.27/0.47
% 0.27/0.47 thf(binunionIL_type,type,
% 0.27/0.47 binunionIL: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binunionIL,definition,
% 0.27/0.47 ( binunionIL
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(upairset2IR_type,type,
% 0.27/0.47 upairset2IR: $o ).
% 0.27/0.47
% 0.27/0.47 thf(upairset2IR,definition,
% 0.27/0.47 ( upairset2IR
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binunionIR_type,type,
% 0.27/0.47 binunionIR: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binunionIR,definition,
% 0.27/0.47 ( binunionIR
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ B )
% 0.27/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binunionEcases_type,type,
% 0.27/0.47 binunionEcases: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binunionEcases,definition,
% 0.27/0.47 ( binunionEcases
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.27/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.27/0.47 => ( ( ( in @ Xx @ A )
% 0.27/0.47 => Xphi )
% 0.27/0.47 => ( ( ( in @ Xx @ B )
% 0.27/0.47 => Xphi )
% 0.27/0.47 => Xphi ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binunionE_type,type,
% 0.27/0.47 binunionE: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binunionE,definition,
% 0.27/0.47 ( binunionE
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.27/0.47 => ( ( in @ Xx @ A )
% 0.27/0.47 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binunionLsub_type,type,
% 0.27/0.47 binunionLsub: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binunionLsub,definition,
% 0.27/0.47 ( binunionLsub
% 0.27/0.47 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binunionRsub_type,type,
% 0.27/0.47 binunionRsub: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binunionRsub,definition,
% 0.27/0.47 ( binunionRsub
% 0.27/0.47 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binintersect_type,type,
% 0.27/0.47 binintersect: $i > $i > $i ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectI_type,type,
% 0.27/0.47 binintersectI: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectI,definition,
% 0.27/0.47 ( binintersectI
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ Xx @ B )
% 0.27/0.47 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectSubset5_type,type,
% 0.27/0.47 binintersectSubset5: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectSubset5,definition,
% 0.27/0.47 ( binintersectSubset5
% 0.27/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.27/0.47 ( ( subset @ C @ A )
% 0.27/0.47 => ( ( subset @ C @ B )
% 0.27/0.47 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectEL_type,type,
% 0.27/0.47 binintersectEL: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectEL,definition,
% 0.27/0.47 ( binintersectEL
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.27/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectLsub_type,type,
% 0.27/0.47 binintersectLsub: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectLsub,definition,
% 0.27/0.47 ( binintersectLsub
% 0.27/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectSubset2_type,type,
% 0.27/0.47 binintersectSubset2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectSubset2,definition,
% 0.27/0.47 ( binintersectSubset2
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( subset @ A @ B )
% 0.27/0.47 => ( ( binintersect @ A @ B )
% 0.27/0.47 = A ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectSubset3_type,type,
% 0.27/0.47 binintersectSubset3: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectSubset3,definition,
% 0.27/0.47 ( binintersectSubset3
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( ( binintersect @ A @ B )
% 0.27/0.47 = B )
% 0.27/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectER_type,type,
% 0.27/0.47 binintersectER: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectER,definition,
% 0.27/0.47 ( binintersectER
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.27/0.47 => ( in @ Xx @ B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(disjointsetsI1_type,type,
% 0.27/0.47 disjointsetsI1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(disjointsetsI1,definition,
% 0.27/0.47 ( disjointsetsI1
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ~ ? [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 & ( in @ Xx @ B ) )
% 0.27/0.47 => ( ( binintersect @ A @ B )
% 0.27/0.47 = emptyset ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectRsub_type,type,
% 0.27/0.47 binintersectRsub: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectRsub,definition,
% 0.27/0.47 ( binintersectRsub
% 0.27/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectSubset4_type,type,
% 0.27/0.47 binintersectSubset4: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectSubset4,definition,
% 0.27/0.47 ( binintersectSubset4
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( subset @ B @ A )
% 0.27/0.47 => ( ( binintersect @ A @ B )
% 0.27/0.47 = B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectSubset1_type,type,
% 0.27/0.47 binintersectSubset1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(binintersectSubset1,definition,
% 0.27/0.47 ( binintersectSubset1
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( ( binintersect @ A @ B )
% 0.27/0.47 = A )
% 0.27/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(bs114d_type,type,
% 0.27/0.47 bs114d: $o ).
% 0.27/0.47
% 0.27/0.47 thf(bs114d,definition,
% 0.27/0.47 ( bs114d
% 0.27/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.27/0.47 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.27/0.47 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(regular_type,type,
% 0.27/0.47 regular: $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(setminus_type,type,
% 0.27/0.47 setminus: $i > $i > $i ).
% 0.27/0.47
% 0.27/0.47 thf(setminusI_type,type,
% 0.27/0.47 setminusI: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setminusI,definition,
% 0.27/0.47 ( setminusI
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ~ ( in @ Xx @ B )
% 0.27/0.47 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setminusEL_type,type,
% 0.27/0.47 setminusEL: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setminusEL,definition,
% 0.27/0.47 ( setminusEL
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.27/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setminusER_type,type,
% 0.27/0.47 setminusER: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setminusER,definition,
% 0.27/0.47 ( setminusER
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.27/0.47 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setminusSubset2_type,type,
% 0.27/0.47 setminusSubset2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setminusSubset2,definition,
% 0.27/0.47 ( setminusSubset2
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( subset @ A @ B )
% 0.27/0.47 => ( ( setminus @ A @ B )
% 0.27/0.47 = emptyset ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setminusERneg_type,type,
% 0.27/0.47 setminusERneg: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setminusERneg,definition,
% 0.27/0.47 ( setminusERneg
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.27/0.47 => ( ( in @ Xx @ A )
% 0.27/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setminusELneg_type,type,
% 0.27/0.47 setminusELneg: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setminusELneg,definition,
% 0.27/0.47 ( setminusELneg
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.27/0.47 => ( ~ ( in @ Xx @ B )
% 0.27/0.47 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setminusILneg_type,type,
% 0.27/0.47 setminusILneg: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setminusILneg,definition,
% 0.27/0.47 ( setminusILneg
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ~ ( in @ Xx @ A )
% 0.27/0.47 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setminusIRneg_type,type,
% 0.27/0.47 setminusIRneg: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setminusIRneg,definition,
% 0.27/0.47 ( setminusIRneg
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ B )
% 0.27/0.47 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setminusLsub_type,type,
% 0.27/0.47 setminusLsub: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setminusLsub,definition,
% 0.27/0.47 ( setminusLsub
% 0.27/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setminusSubset1_type,type,
% 0.27/0.47 setminusSubset1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setminusSubset1,definition,
% 0.27/0.47 ( setminusSubset1
% 0.27/0.47 = ( ! [A: $i,B: $i] :
% 0.27/0.47 ( ( ( setminus @ A @ B )
% 0.27/0.47 = emptyset )
% 0.27/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(symdiff_type,type,
% 0.27/0.47 symdiff: $i > $i > $i ).
% 0.27/0.47
% 0.27/0.47 thf(symdiffE_type,type,
% 0.27/0.47 symdiffE: $o ).
% 0.27/0.47
% 0.27/0.47 thf(symdiffE,definition,
% 0.27/0.47 ( symdiffE
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.27/0.47 => ! [Xphi: $o] :
% 0.27/0.47 ( ( ( in @ Xx @ A )
% 0.27/0.47 => ( ~ ( in @ Xx @ B )
% 0.27/0.47 => Xphi ) )
% 0.27/0.47 => ( ( ~ ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ Xx @ B )
% 0.27/0.47 => Xphi ) )
% 0.27/0.47 => Xphi ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(symdiffI1_type,type,
% 0.27/0.47 symdiffI1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(symdiffI1,definition,
% 0.27/0.47 ( symdiffI1
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ~ ( in @ Xx @ B )
% 0.27/0.47 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(symdiffI2_type,type,
% 0.27/0.47 symdiffI2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(symdiffI2,definition,
% 0.27/0.47 ( symdiffI2
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ~ ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ Xx @ B )
% 0.27/0.47 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(symdiffIneg1_type,type,
% 0.27/0.47 symdiffIneg1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(symdiffIneg1,definition,
% 0.27/0.47 ( symdiffIneg1
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( in @ Xx @ B )
% 0.27/0.47 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(symdiffIneg2_type,type,
% 0.27/0.47 symdiffIneg2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(symdiffIneg2,definition,
% 0.27/0.47 ( symdiffIneg2
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ~ ( in @ Xx @ A )
% 0.27/0.47 => ( ~ ( in @ Xx @ B )
% 0.27/0.47 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(iskpair_type,type,
% 0.27/0.47 iskpair: $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(iskpair,definition,
% 0.27/0.47 ( iskpair
% 0.27/0.47 = ( ^ [A: $i] :
% 0.27/0.47 ? [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.27/0.47 & ? [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ ( setunion @ A ) )
% 0.27/0.47 & ( A
% 0.27/0.47 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(secondinupair_type,type,
% 0.27/0.47 secondinupair: $o ).
% 0.27/0.47
% 0.27/0.47 thf(secondinupair,definition,
% 0.27/0.47 ( secondinupair
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setukpairIL_type,type,
% 0.27/0.47 setukpairIL: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setukpairIL,definition,
% 0.27/0.47 ( setukpairIL
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setukpairIR_type,type,
% 0.27/0.47 setukpairIR: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setukpairIR,definition,
% 0.27/0.47 ( setukpairIR
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(kpairiskpair_type,type,
% 0.27/0.47 kpairiskpair: $o ).
% 0.27/0.47
% 0.27/0.47 thf(kpairiskpair,definition,
% 0.27/0.47 ( kpairiskpair
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(kpair_type,type,
% 0.27/0.47 kpair: $i > $i > $i ).
% 0.27/0.47
% 0.27/0.47 thf(kpair,definition,
% 0.27/0.47 ( kpair
% 0.27/0.47 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(kpairp_type,type,
% 0.27/0.47 kpairp: $o ).
% 0.27/0.47
% 0.27/0.47 thf(kpairp,definition,
% 0.27/0.47 ( kpairp
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(cartprod_type,type,
% 0.27/0.47 cartprod: $i > $i > $i ).
% 0.27/0.47
% 0.27/0.47 thf(singletonsubset_type,type,
% 0.27/0.47 singletonsubset: $o ).
% 0.27/0.47
% 0.27/0.47 thf(singletonsubset,definition,
% 0.27/0.47 ( singletonsubset
% 0.27/0.47 = ( ! [A: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(singletoninpowerset_type,type,
% 0.27/0.47 singletoninpowerset: $o ).
% 0.27/0.47
% 0.27/0.47 thf(singletoninpowerset,definition,
% 0.27/0.47 ( singletoninpowerset
% 0.27/0.47 = ( ! [A: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(singletoninpowunion_type,type,
% 0.27/0.47 singletoninpowunion: $o ).
% 0.27/0.47
% 0.27/0.47 thf(singletoninpowunion,definition,
% 0.27/0.47 ( singletoninpowunion
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(upairset2E_type,type,
% 0.27/0.47 upairset2E: $o ).
% 0.27/0.47
% 0.27/0.47 thf(upairset2E,definition,
% 0.27/0.47 ( upairset2E
% 0.27/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.27/0.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.27/0.47 => ( ( Xz = Xx )
% 0.27/0.47 | ( Xz = Xy ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(upairsubunion_type,type,
% 0.27/0.47 upairsubunion: $o ).
% 0.27/0.47
% 0.27/0.47 thf(upairsubunion,definition,
% 0.27/0.47 ( upairsubunion
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ B )
% 0.27/0.47 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(upairinpowunion_type,type,
% 0.27/0.47 upairinpowunion: $o ).
% 0.27/0.47
% 0.27/0.47 thf(upairinpowunion,definition,
% 0.27/0.47 ( upairinpowunion
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ B )
% 0.27/0.47 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(ubforcartprodlem1_type,type,
% 0.27/0.47 ubforcartprodlem1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(ubforcartprodlem1,definition,
% 0.27/0.47 ( ubforcartprodlem1
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ B )
% 0.27/0.47 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(ubforcartprodlem2_type,type,
% 0.27/0.47 ubforcartprodlem2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(ubforcartprodlem2,definition,
% 0.27/0.47 ( ubforcartprodlem2
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ B )
% 0.27/0.47 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(ubforcartprodlem3_type,type,
% 0.27/0.47 ubforcartprodlem3: $o ).
% 0.27/0.47
% 0.27/0.47 thf(ubforcartprodlem3,definition,
% 0.27/0.47 ( ubforcartprodlem3
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ B )
% 0.27/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(cartprodpairin_type,type,
% 0.27/0.47 cartprodpairin: $o ).
% 0.27/0.47
% 0.27/0.47 thf(cartprodpairin,definition,
% 0.27/0.47 ( cartprodpairin
% 0.27/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ B )
% 0.27/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(cartprodmempair1_type,type,
% 0.27/0.47 cartprodmempair1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(cartprodmempair1,definition,
% 0.27/0.47 ( cartprodmempair1
% 0.27/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.27/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.27/0.47 => ? [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 & ? [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ B )
% 0.27/0.47 & ( Xu
% 0.27/0.47 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(cartprodmempair_type,type,
% 0.27/0.47 cartprodmempair: $o ).
% 0.27/0.47
% 0.27/0.47 thf(cartprodmempair,definition,
% 0.27/0.47 ( cartprodmempair
% 0.27/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.27/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.27/0.47 => ( iskpair @ Xu ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setunionE2_type,type,
% 0.27/0.47 setunionE2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setunionE2,definition,
% 0.27/0.47 ( setunionE2
% 0.27/0.47 = ( ! [A: $i,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.27/0.47 => ? [X: $i] :
% 0.27/0.47 ( ( in @ X @ A )
% 0.27/0.47 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setunionsingleton1_type,type,
% 0.27/0.47 setunionsingleton1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setunionsingleton1,definition,
% 0.27/0.47 ( setunionsingleton1
% 0.27/0.47 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setunionsingleton2_type,type,
% 0.27/0.47 setunionsingleton2: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setunionsingleton2,definition,
% 0.27/0.47 ( setunionsingleton2
% 0.27/0.47 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(setunionsingleton_type,type,
% 0.27/0.47 setunionsingleton: $o ).
% 0.27/0.47
% 0.27/0.47 thf(setunionsingleton,definition,
% 0.27/0.47 ( setunionsingleton
% 0.27/0.47 = ( ! [Xx: $i] :
% 0.27/0.47 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.27/0.47 = Xx ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(singleton_type,type,
% 0.27/0.47 singleton: $i > $o ).
% 0.27/0.47
% 0.27/0.47 thf(singleton,definition,
% 0.27/0.47 ( singleton
% 0.27/0.47 = ( ^ [A: $i] :
% 0.27/0.47 ? [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 & ( A
% 0.27/0.47 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(singletonprop_type,type,
% 0.27/0.47 singletonprop: $o ).
% 0.27/0.47
% 0.27/0.47 thf(singletonprop,definition,
% 0.27/0.47 ( singletonprop
% 0.27/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.47 ( ! [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ A )
% 0.27/0.47 => ( ( Xphi @ Xx )
% 0.27/0.47 => ( ( Xphi @ Xy )
% 0.27/0.47 => ( Xx = Xy ) ) ) ) )
% 0.27/0.47 => ( ? [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 & ( Xphi @ Xx ) )
% 0.27/0.47 => ( singleton
% 0.27/0.47 @ ( dsetconstr @ A
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(ex1_type,type,
% 0.27/0.47 ex1: $i > ( $i > $o ) > $o ).
% 0.27/0.47
% 0.27/0.47 thf(ex1,definition,
% 0.27/0.47 ( ex1
% 0.27/0.47 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.27/0.47 ( singleton
% 0.27/0.47 @ ( dsetconstr @ A
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(ex1E1_type,type,
% 0.27/0.47 ex1E1: $o ).
% 0.27/0.47
% 0.27/0.47 thf(ex1E1,definition,
% 0.27/0.47 ( ex1E1
% 0.27/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.47 ( ( ex1 @ A
% 0.27/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.47 => ? [Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(ex1I,conjecture,
% 0.27/0.47 ( setextAx
% 0.27/0.47 => ( emptysetAx
% 0.27/0.47 => ( setadjoinAx
% 0.27/0.47 => ( powersetAx
% 0.27/0.47 => ( setunionAx
% 0.27/0.47 => ( omega0Ax
% 0.27/0.47 => ( omegaSAx
% 0.27/0.47 => ( omegaIndAx
% 0.27/0.47 => ( replAx
% 0.27/0.47 => ( foundationAx
% 0.27/0.47 => ( wellorderingAx
% 0.27/0.47 => ( descrp
% 0.27/0.47 => ( dsetconstrI
% 0.27/0.47 => ( dsetconstrEL
% 0.27/0.47 => ( dsetconstrER
% 0.27/0.47 => ( exuE1
% 0.27/0.47 => ( prop2setE
% 0.27/0.47 => ( emptysetE
% 0.27/0.47 => ( emptysetimpfalse
% 0.27/0.47 => ( notinemptyset
% 0.27/0.47 => ( exuE3e
% 0.27/0.47 => ( setext
% 0.27/0.47 => ( emptyI
% 0.27/0.47 => ( noeltsimpempty
% 0.27/0.47 => ( setbeta
% 0.27/0.47 => ( nonemptyE1
% 0.27/0.47 => ( nonemptyI
% 0.27/0.47 => ( nonemptyI1
% 0.27/0.47 => ( setadjoinIL
% 0.27/0.47 => ( emptyinunitempty
% 0.27/0.47 => ( setadjoinIR
% 0.27/0.47 => ( setadjoinE
% 0.27/0.47 => ( setadjoinOr
% 0.27/0.47 => ( setoftrueEq
% 0.27/0.47 => ( powersetI
% 0.27/0.47 => ( emptyinPowerset
% 0.27/0.47 => ( emptyInPowerset
% 0.27/0.47 => ( powersetE
% 0.27/0.47 => ( setunionI
% 0.27/0.47 => ( setunionE
% 0.27/0.47 => ( subPowSU
% 0.27/0.47 => ( exuE2
% 0.27/0.47 => ( nonemptyImpWitness
% 0.27/0.47 => ( uniqinunit
% 0.27/0.47 => ( notinsingleton
% 0.27/0.47 => ( eqinunit
% 0.27/0.47 => ( singletonsswitch
% 0.27/0.47 => ( upairsetE
% 0.27/0.47 => ( upairsetIL
% 0.27/0.47 => ( upairsetIR
% 0.27/0.47 => ( emptyE1
% 0.27/0.47 => ( vacuousDall
% 0.27/0.47 => ( quantDeMorgan1
% 0.27/0.47 => ( quantDeMorgan2
% 0.27/0.47 => ( quantDeMorgan3
% 0.27/0.47 => ( quantDeMorgan4
% 0.27/0.47 => ( prop2setI
% 0.27/0.47 => ( prop2set2propI
% 0.27/0.47 => ( notdexE
% 0.27/0.47 => ( notdallE
% 0.27/0.47 => ( exuI1
% 0.27/0.47 => ( exuI3
% 0.27/0.47 => ( exuI2
% 0.27/0.47 => ( inCongP
% 0.27/0.47 => ( in__Cong
% 0.27/0.47 => ( exuE3u
% 0.27/0.47 => ( exu__Cong
% 0.27/0.47 => ( emptyset__Cong
% 0.27/0.47 => ( setadjoin__Cong
% 0.27/0.47 => ( powerset__Cong
% 0.27/0.47 => ( setunion__Cong
% 0.27/0.47 => ( omega__Cong
% 0.27/0.47 => ( exuEu
% 0.27/0.47 => ( descr__Cong
% 0.27/0.47 => ( dsetconstr__Cong
% 0.27/0.47 => ( subsetI1
% 0.27/0.47 => ( eqimpsubset2
% 0.27/0.47 => ( eqimpsubset1
% 0.27/0.47 => ( subsetI2
% 0.27/0.47 => ( emptysetsubset
% 0.27/0.47 => ( subsetE
% 0.27/0.47 => ( subsetE2
% 0.27/0.47 => ( notsubsetI
% 0.27/0.47 => ( notequalI1
% 0.27/0.47 => ( notequalI2
% 0.27/0.47 => ( subsetRefl
% 0.27/0.47 => ( subsetTrans
% 0.27/0.47 => ( setadjoinSub
% 0.27/0.47 => ( setadjoinSub2
% 0.27/0.47 => ( subset2powerset
% 0.27/0.47 => ( setextsub
% 0.27/0.47 => ( subsetemptysetimpeq
% 0.27/0.47 => ( powersetI1
% 0.27/0.47 => ( powersetE1
% 0.27/0.47 => ( inPowerset
% 0.27/0.47 => ( powersetsubset
% 0.27/0.47 => ( sepInPowerset
% 0.27/0.47 => ( sepSubset
% 0.27/0.47 => ( binunionIL
% 0.27/0.47 => ( upairset2IR
% 0.27/0.47 => ( binunionIR
% 0.27/0.47 => ( binunionEcases
% 0.27/0.47 => ( binunionE
% 0.27/0.47 => ( binunionLsub
% 0.27/0.47 => ( binunionRsub
% 0.27/0.47 => ( binintersectI
% 0.27/0.47 => ( binintersectSubset5
% 0.27/0.47 => ( binintersectEL
% 0.27/0.47 => ( binintersectLsub
% 0.27/0.47 => ( binintersectSubset2
% 0.27/0.47 => ( binintersectSubset3
% 0.27/0.47 => ( binintersectER
% 0.27/0.47 => ( disjointsetsI1
% 0.27/0.47 => ( binintersectRsub
% 0.27/0.47 => ( binintersectSubset4
% 0.27/0.47 => ( binintersectSubset1
% 0.27/0.47 => ( bs114d
% 0.27/0.47 => ( setminusI
% 0.27/0.47 => ( setminusEL
% 0.27/0.47 => ( setminusER
% 0.27/0.47 => ( setminusSubset2
% 0.27/0.47 => ( setminusERneg
% 0.27/0.47 => ( setminusELneg
% 0.27/0.47 => ( setminusILneg
% 0.27/0.47 => ( setminusIRneg
% 0.27/0.47 => ( setminusLsub
% 0.27/0.47 => ( setminusSubset1
% 0.27/0.47 => ( symdiffE
% 0.27/0.47 => ( symdiffI1
% 0.27/0.47 => ( symdiffI2
% 0.27/0.47 => ( symdiffIneg1
% 0.27/0.47 => ( symdiffIneg2
% 0.27/0.47 => ( secondinupair
% 0.27/0.47 => ( setukpairIL
% 0.27/0.47 => ( setukpairIR
% 0.27/0.47 => ( kpairiskpair
% 0.27/0.47 => ( kpairp
% 0.27/0.47 => ( singletonsubset
% 0.27/0.47 => ( singletoninpowerset
% 0.27/0.47 => ( singletoninpowunion
% 0.27/0.47 => ( upairset2E
% 0.27/0.47 => ( upairsubunion
% 0.27/0.47 => ( upairinpowunion
% 0.27/0.47 => ( ubforcartprodlem1
% 0.27/0.47 => ( ubforcartprodlem2
% 0.27/0.47 => ( ubforcartprodlem3
% 0.27/0.47 => ( cartprodpairin
% 0.27/0.47 => ( cartprodmempair1
% 0.27/0.47 => ( cartprodmempair
% 0.27/0.47 => ( setunionE2
% 0.27/0.47 => ( setunionsingleton1
% 0.27/0.47 => ( setunionsingleton2
% 0.27/0.47 => ( setunionsingleton
% 0.27/0.47 => ( singletonprop
% 0.27/0.47 => ( ex1E1
% 0.27/0.47 => ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.47 ( ( in @ Xx @ A )
% 0.27/0.47 => ( ( Xphi @ Xx )
% 0.27/0.47 => ( ! [Xy: $i] :
% 0.27/0.47 ( ( in @ Xy @ A )
% 0.27/0.47 => ( ( Xphi @ Xy )
% 0.27/0.47 => ( Xy = Xx ) ) )
% 0.27/0.47 => ( ex1 @ A
% 0.27/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 ------------------------
% 2.41/1.42 ---- Embedded in THF ---
% 2.41/1.43 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.41/1.43 %%% Generated on Tue Feb 24 12:29:16 EST 2026
% 2.41/1.43 %%% using '$$dhol' embedding, version 1.3.0.
% 2.41/1.43 %%% Logic specification used:
% 2.41/1.43 %%% thf(spec, logic, $$dhol).
% 2.41/1.43
% 2.41/1.43 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.0njZozgBRA/DTF2DTF1200.p
% See solution above
% 2.41/1.43 ------------------------
% 2.41/1.45 ---- Cleaned THF ---
% 2.41/1.45 thf(in_type,type,
% 2.41/1.45 in: $i > $i > $o ).
% 2.41/1.45
% 2.41/1.45 thf(exu_type,type,
% 2.41/1.45 exu: ( $i > $o ) > $o ).
% 2.41/1.45
% 2.41/1.45 thf(exu,definition,
% 2.41/1.45 ( exu
% 2.41/1.45 = ( ^ [Xphi: $i > $o] :
% 2.41/1.45 ? [Xx: $i] :
% 2.41/1.45 ( ( Xphi @ Xx )
% 2.41/1.45 & ! [Xy: $i] :
% 2.41/1.45 ( ( Xphi @ Xy )
% 2.41/1.45 => ( Xx = Xy ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setextAx_type,type,
% 2.41/1.45 setextAx: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setextAx,definition,
% 2.41/1.45 ( setextAx
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ! [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 <=> ( in @ Xx @ B ) )
% 2.41/1.45 => ( A = B ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(emptyset_type,type,
% 2.41/1.45 emptyset: $i ).
% 2.41/1.45
% 2.41/1.45 thf(emptysetAx_type,type,
% 2.41/1.45 emptysetAx: $o ).
% 2.41/1.45
% 2.41/1.45 thf(emptysetAx,definition,
% 2.41/1.45 ( emptysetAx
% 2.41/1.45 = ( ! [Xx: $i] :
% 2.41/1.45 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setadjoin_type,type,
% 2.41/1.45 setadjoin: $i > $i > $i ).
% 2.41/1.45
% 2.41/1.45 thf(setadjoinAx_type,type,
% 2.41/1.45 setadjoinAx: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setadjoinAx,definition,
% 2.41/1.45 ( setadjoinAx
% 2.41/1.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.41/1.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.41/1.45 <=> ( ( Xy = Xx )
% 2.41/1.45 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(powerset_type,type,
% 2.41/1.45 powerset: $i > $i ).
% 2.41/1.45
% 2.41/1.45 thf(powersetAx_type,type,
% 2.41/1.45 powersetAx: $o ).
% 2.41/1.45
% 2.41/1.45 thf(powersetAx,definition,
% 2.41/1.45 ( powersetAx
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( in @ B @ ( powerset @ A ) )
% 2.41/1.45 <=> ! [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ B )
% 2.41/1.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setunion_type,type,
% 2.41/1.45 setunion: $i > $i ).
% 2.41/1.45
% 2.41/1.45 thf(setunionAx_type,type,
% 2.41/1.45 setunionAx: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setunionAx,definition,
% 2.41/1.45 ( setunionAx
% 2.41/1.45 = ( ! [A: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ ( setunion @ A ) )
% 2.41/1.45 <=> ? [B: $i] :
% 2.41/1.45 ( ( in @ Xx @ B )
% 2.41/1.45 & ( in @ B @ A ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(omega_type,type,
% 2.41/1.45 omega: $i ).
% 2.41/1.45
% 2.41/1.45 thf(omega0Ax_type,type,
% 2.41/1.45 omega0Ax: $o ).
% 2.41/1.45
% 2.41/1.45 thf(omega0Ax,definition,
% 2.41/1.45 ( omega0Ax
% 2.41/1.45 = ( in @ emptyset @ omega ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(omegaSAx_type,type,
% 2.41/1.45 omegaSAx: $o ).
% 2.41/1.45
% 2.41/1.45 thf(omegaSAx,definition,
% 2.41/1.45 ( omegaSAx
% 2.41/1.45 = ( ! [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ omega )
% 2.41/1.45 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(omegaIndAx_type,type,
% 2.41/1.45 omegaIndAx: $o ).
% 2.41/1.45
% 2.41/1.45 thf(omegaIndAx,definition,
% 2.41/1.45 ( omegaIndAx
% 2.41/1.45 = ( ! [A: $i] :
% 2.41/1.45 ( ( ( in @ emptyset @ A )
% 2.41/1.45 & ! [Xx: $i] :
% 2.41/1.45 ( ( ( in @ Xx @ omega )
% 2.41/1.45 & ( in @ Xx @ A ) )
% 2.41/1.45 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.41/1.45 => ! [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ omega )
% 2.41/1.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(replAx_type,type,
% 2.41/1.45 replAx: $o ).
% 2.41/1.45
% 2.41/1.45 thf(replAx,definition,
% 2.41/1.45 ( replAx
% 2.41/1.45 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.41/1.45 ( ! [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ( exu
% 2.41/1.45 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.41/1.45 => ? [B: $i] :
% 2.41/1.45 ! [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ B )
% 2.41/1.45 <=> ? [Xy: $i] :
% 2.41/1.45 ( ( in @ Xy @ A )
% 2.41/1.45 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(foundationAx_type,type,
% 2.41/1.45 foundationAx: $o ).
% 2.41/1.45
% 2.41/1.45 thf(foundationAx,definition,
% 2.41/1.45 ( foundationAx
% 2.41/1.45 = ( ! [A: $i] :
% 2.41/1.45 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.41/1.45 => ? [B: $i] :
% 2.41/1.45 ( ( in @ B @ A )
% 2.41/1.45 & ~ ? [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ B )
% 2.41/1.45 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(wellorderingAx_type,type,
% 2.41/1.45 wellorderingAx: $o ).
% 2.41/1.45
% 2.41/1.45 thf(wellorderingAx,definition,
% 2.41/1.45 ( wellorderingAx
% 2.41/1.45 = ( ! [A: $i] :
% 2.41/1.45 ? [B: $i] :
% 2.41/1.45 ( ! [C: $i] :
% 2.41/1.45 ( ( in @ C @ B )
% 2.41/1.45 => ! [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ C )
% 2.41/1.45 => ( in @ Xx @ A ) ) )
% 2.41/1.45 & ! [Xx: $i,Xy: $i] :
% 2.41/1.45 ( ( ( in @ Xx @ A )
% 2.41/1.45 & ( in @ Xy @ A ) )
% 2.41/1.45 => ( ! [C: $i] :
% 2.41/1.45 ( ( in @ C @ B )
% 2.41/1.45 => ( ( in @ Xx @ C )
% 2.41/1.45 <=> ( in @ Xy @ C ) ) )
% 2.41/1.45 => ( Xx = Xy ) ) )
% 2.41/1.45 & ! [C: $i,D: $i] :
% 2.41/1.45 ( ( ( in @ C @ B )
% 2.41/1.45 & ( in @ D @ B ) )
% 2.41/1.45 => ( ! [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ C )
% 2.41/1.45 => ( in @ Xx @ D ) )
% 2.41/1.45 | ! [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ D )
% 2.41/1.45 => ( in @ Xx @ C ) ) ) )
% 2.41/1.45 & ! [C: $i] :
% 2.41/1.45 ( ( ! [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ C )
% 2.41/1.45 => ( in @ Xx @ A ) )
% 2.41/1.45 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.41/1.45 => ? [D: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ D @ B )
% 2.41/1.45 & ( in @ Xx @ C )
% 2.41/1.45 & ~ ? [Xy: $i] :
% 2.41/1.45 ( ( in @ Xy @ D )
% 2.41/1.45 & ( in @ Xy @ C ) )
% 2.41/1.45 & ! [E: $i] :
% 2.41/1.45 ( ( in @ E @ B )
% 2.41/1.45 => ( ! [Xy: $i] :
% 2.41/1.45 ( ( in @ Xy @ E )
% 2.41/1.45 => ( in @ Xy @ D ) )
% 2.41/1.45 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(descr_type,type,
% 2.41/1.45 descr: ( $i > $o ) > $i ).
% 2.41/1.45
% 2.41/1.45 thf(descrp_type,type,
% 2.41/1.45 descrp: $o ).
% 2.41/1.45
% 2.41/1.45 thf(descrp,definition,
% 2.41/1.45 ( descrp
% 2.41/1.45 = ( ! [Xphi: $i > $o] :
% 2.41/1.45 ( ( exu
% 2.41/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.41/1.45 => ( Xphi
% 2.41/1.45 @ ( descr
% 2.41/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(dsetconstr_type,type,
% 2.41/1.45 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.41/1.45
% 2.41/1.45 thf(dsetconstrI_type,type,
% 2.41/1.45 dsetconstrI: $o ).
% 2.41/1.45
% 2.41/1.45 thf(dsetconstrI,definition,
% 2.41/1.45 ( dsetconstrI
% 2.41/1.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ( ( Xphi @ Xx )
% 2.41/1.45 => ( in @ Xx
% 2.41/1.45 @ ( dsetconstr @ A
% 2.41/1.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(dsetconstrEL_type,type,
% 2.41/1.45 dsetconstrEL: $o ).
% 2.41/1.45
% 2.41/1.45 thf(dsetconstrEL,definition,
% 2.41/1.45 ( dsetconstrEL
% 2.41/1.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx
% 2.41/1.45 @ ( dsetconstr @ A
% 2.41/1.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.41/1.45 => ( in @ Xx @ A ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(dsetconstrER_type,type,
% 2.41/1.45 dsetconstrER: $o ).
% 2.41/1.45
% 2.41/1.45 thf(dsetconstrER,definition,
% 2.41/1.45 ( dsetconstrER
% 2.41/1.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx
% 2.41/1.45 @ ( dsetconstr @ A
% 2.41/1.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.41/1.45 => ( Xphi @ Xx ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(exuE1_type,type,
% 2.41/1.45 exuE1: $o ).
% 2.41/1.45
% 2.41/1.45 thf(exuE1,definition,
% 2.41/1.45 ( exuE1
% 2.41/1.45 = ( ! [Xphi: $i > $o] :
% 2.41/1.45 ( ( exu
% 2.41/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.41/1.45 => ? [Xx: $i] :
% 2.41/1.45 ( ( Xphi @ Xx )
% 2.41/1.45 & ! [Xy: $i] :
% 2.41/1.45 ( ( Xphi @ Xy )
% 2.41/1.45 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(prop2set_type,type,
% 2.41/1.45 prop2set: $o > $i ).
% 2.41/1.45
% 2.41/1.45 thf(prop2setE_type,type,
% 2.41/1.45 prop2setE: $o ).
% 2.41/1.45
% 2.41/1.45 thf(prop2setE,definition,
% 2.41/1.45 ( prop2setE
% 2.41/1.45 = ( ! [Xphi: $o,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.41/1.45 => Xphi ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(emptysetE_type,type,
% 2.41/1.45 emptysetE: $o ).
% 2.41/1.45
% 2.41/1.45 thf(emptysetE,definition,
% 2.41/1.45 ( emptysetE
% 2.41/1.45 = ( ! [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ emptyset )
% 2.41/1.45 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(emptysetimpfalse_type,type,
% 2.41/1.45 emptysetimpfalse: $o ).
% 2.41/1.45
% 2.41/1.45 thf(emptysetimpfalse,definition,
% 2.41/1.45 ( emptysetimpfalse
% 2.41/1.45 = ( ! [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ emptyset )
% 2.41/1.45 => $false ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(notinemptyset_type,type,
% 2.41/1.45 notinemptyset: $o ).
% 2.41/1.45
% 2.41/1.45 thf(notinemptyset,definition,
% 2.41/1.45 ( notinemptyset
% 2.41/1.45 = ( ! [Xx: $i] :
% 2.41/1.45 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(exuE3e_type,type,
% 2.41/1.45 exuE3e: $o ).
% 2.41/1.45
% 2.41/1.45 thf(exuE3e,definition,
% 2.41/1.45 ( exuE3e
% 2.41/1.45 = ( ! [Xphi: $i > $o] :
% 2.41/1.45 ( ( exu
% 2.41/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.41/1.45 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setext_type,type,
% 2.41/1.45 setext: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setext,definition,
% 2.41/1.45 ( setext
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ! [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ( in @ Xx @ B ) )
% 2.41/1.45 => ( ! [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ B )
% 2.41/1.45 => ( in @ Xx @ A ) )
% 2.41/1.45 => ( A = B ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(emptyI_type,type,
% 2.41/1.45 emptyI: $o ).
% 2.41/1.45
% 2.41/1.45 thf(emptyI,definition,
% 2.41/1.45 ( emptyI
% 2.41/1.45 = ( ! [A: $i] :
% 2.41/1.45 ( ! [Xx: $i] :
% 2.41/1.45 ~ ( in @ Xx @ A )
% 2.41/1.45 => ( A = emptyset ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(noeltsimpempty_type,type,
% 2.41/1.45 noeltsimpempty: $o ).
% 2.41/1.45
% 2.41/1.45 thf(noeltsimpempty,definition,
% 2.41/1.45 ( noeltsimpempty
% 2.41/1.45 = ( ! [A: $i] :
% 2.41/1.45 ( ! [Xx: $i] :
% 2.41/1.45 ~ ( in @ Xx @ A )
% 2.41/1.45 => ( A = emptyset ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setbeta_type,type,
% 2.41/1.45 setbeta: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setbeta,definition,
% 2.41/1.45 ( setbeta
% 2.41/1.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ( ( in @ Xx
% 2.41/1.45 @ ( dsetconstr @ A
% 2.41/1.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.41/1.45 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(nonempty_type,type,
% 2.41/1.45 nonempty: $i > $o ).
% 2.41/1.45
% 2.41/1.45 thf(nonempty,definition,
% 2.41/1.45 ( nonempty
% 2.41/1.45 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(nonemptyE1_type,type,
% 2.41/1.45 nonemptyE1: $o ).
% 2.41/1.45
% 2.41/1.45 thf(nonemptyE1,definition,
% 2.41/1.45 ( nonemptyE1
% 2.41/1.45 = ( ! [A: $i] :
% 2.41/1.45 ( ( nonempty @ A )
% 2.41/1.45 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(nonemptyI_type,type,
% 2.41/1.45 nonemptyI: $o ).
% 2.41/1.45
% 2.41/1.45 thf(nonemptyI,definition,
% 2.41/1.45 ( nonemptyI
% 2.41/1.45 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ( ( Xphi @ Xx )
% 2.41/1.45 => ( nonempty
% 2.41/1.45 @ ( dsetconstr @ A
% 2.41/1.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(nonemptyI1_type,type,
% 2.41/1.45 nonemptyI1: $o ).
% 2.41/1.45
% 2.41/1.45 thf(nonemptyI1,definition,
% 2.41/1.45 ( nonemptyI1
% 2.41/1.45 = ( ! [A: $i] :
% 2.41/1.45 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.41/1.45 => ( nonempty @ A ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setadjoinIL_type,type,
% 2.41/1.45 setadjoinIL: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setadjoinIL,definition,
% 2.41/1.45 ( setadjoinIL
% 2.41/1.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(emptyinunitempty_type,type,
% 2.41/1.45 emptyinunitempty: $o ).
% 2.41/1.45
% 2.41/1.45 thf(emptyinunitempty,definition,
% 2.41/1.45 ( emptyinunitempty
% 2.41/1.45 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setadjoinIR_type,type,
% 2.41/1.45 setadjoinIR: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setadjoinIR,definition,
% 2.41/1.45 ( setadjoinIR
% 2.41/1.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.41/1.45 ( ( in @ Xy @ A )
% 2.41/1.45 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setadjoinE_type,type,
% 2.41/1.45 setadjoinE: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setadjoinE,definition,
% 2.41/1.45 ( setadjoinE
% 2.41/1.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.41/1.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.41/1.45 => ! [Xphi: $o] :
% 2.41/1.45 ( ( ( Xy = Xx )
% 2.41/1.45 => Xphi )
% 2.41/1.45 => ( ( ( in @ Xy @ A )
% 2.41/1.45 => Xphi )
% 2.41/1.45 => Xphi ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setadjoinOr_type,type,
% 2.41/1.45 setadjoinOr: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setadjoinOr,definition,
% 2.41/1.45 ( setadjoinOr
% 2.41/1.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.41/1.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.41/1.45 => ( ( Xy = Xx )
% 2.41/1.45 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setoftrueEq_type,type,
% 2.41/1.45 setoftrueEq: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setoftrueEq,definition,
% 2.41/1.45 ( setoftrueEq
% 2.41/1.45 = ( ! [A: $i] :
% 2.41/1.45 ( ( dsetconstr @ A
% 2.41/1.45 @ ^ [Xx: $i] : $true )
% 2.41/1.45 = A ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(powersetI_type,type,
% 2.41/1.45 powersetI: $o ).
% 2.41/1.45
% 2.41/1.45 thf(powersetI,definition,
% 2.41/1.45 ( powersetI
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ! [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ B )
% 2.41/1.45 => ( in @ Xx @ A ) )
% 2.41/1.45 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(emptyinPowerset_type,type,
% 2.41/1.45 emptyinPowerset: $o ).
% 2.41/1.45
% 2.41/1.45 thf(emptyinPowerset,definition,
% 2.41/1.45 ( emptyinPowerset
% 2.41/1.45 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(emptyInPowerset_type,type,
% 2.41/1.45 emptyInPowerset: $o ).
% 2.41/1.45
% 2.41/1.45 thf(emptyInPowerset,definition,
% 2.41/1.45 ( emptyInPowerset
% 2.41/1.45 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(powersetE_type,type,
% 2.41/1.45 powersetE: $o ).
% 2.41/1.45
% 2.41/1.45 thf(powersetE,definition,
% 2.41/1.45 ( powersetE
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ B @ ( powerset @ A ) )
% 2.41/1.45 => ( ( in @ Xx @ B )
% 2.41/1.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setunionI_type,type,
% 2.41/1.45 setunionI: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setunionI,definition,
% 2.41/1.45 ( setunionI
% 2.41/1.45 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.41/1.45 ( ( in @ Xx @ B )
% 2.41/1.45 => ( ( in @ B @ A )
% 2.41/1.45 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setunionE_type,type,
% 2.41/1.45 setunionE: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setunionE,definition,
% 2.41/1.45 ( setunionE
% 2.41/1.45 = ( ! [A: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ ( setunion @ A ) )
% 2.41/1.45 => ! [Xphi: $o] :
% 2.41/1.45 ( ! [B: $i] :
% 2.41/1.45 ( ( in @ Xx @ B )
% 2.41/1.45 => ( ( in @ B @ A )
% 2.41/1.45 => Xphi ) )
% 2.41/1.45 => Xphi ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(subPowSU_type,type,
% 2.41/1.45 subPowSU: $o ).
% 2.41/1.45
% 2.41/1.45 thf(subPowSU,definition,
% 2.41/1.45 ( subPowSU
% 2.41/1.45 = ( ! [A: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(exuE2_type,type,
% 2.41/1.45 exuE2: $o ).
% 2.41/1.45
% 2.41/1.45 thf(exuE2,definition,
% 2.41/1.45 ( exuE2
% 2.41/1.45 = ( ! [Xphi: $i > $o] :
% 2.41/1.45 ( ( exu
% 2.41/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.41/1.45 => ? [Xx: $i] :
% 2.41/1.45 ! [Xy: $i] :
% 2.41/1.45 ( ( Xphi @ Xy )
% 2.41/1.45 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(nonemptyImpWitness_type,type,
% 2.41/1.45 nonemptyImpWitness: $o ).
% 2.41/1.45
% 2.41/1.45 thf(nonemptyImpWitness,definition,
% 2.41/1.45 ( nonemptyImpWitness
% 2.41/1.45 = ( ! [A: $i] :
% 2.41/1.45 ( ( nonempty @ A )
% 2.41/1.45 => ? [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 & $true ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(uniqinunit_type,type,
% 2.41/1.45 uniqinunit: $o ).
% 2.41/1.45
% 2.41/1.45 thf(uniqinunit,definition,
% 2.41/1.45 ( uniqinunit
% 2.41/1.45 = ( ! [Xx: $i,Xy: $i] :
% 2.41/1.45 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.41/1.45 => ( Xx = Xy ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(notinsingleton_type,type,
% 2.41/1.45 notinsingleton: $o ).
% 2.41/1.45
% 2.41/1.45 thf(notinsingleton,definition,
% 2.41/1.45 ( notinsingleton
% 2.41/1.45 = ( ! [Xx: $i,Xy: $i] :
% 2.41/1.45 ( ( Xx != Xy )
% 2.41/1.45 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(eqinunit_type,type,
% 2.41/1.45 eqinunit: $o ).
% 2.41/1.45
% 2.41/1.45 thf(eqinunit,definition,
% 2.41/1.45 ( eqinunit
% 2.41/1.45 = ( ! [Xx: $i,Xy: $i] :
% 2.41/1.45 ( ( Xx = Xy )
% 2.41/1.45 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(singletonsswitch_type,type,
% 2.41/1.45 singletonsswitch: $o ).
% 2.41/1.45
% 2.41/1.45 thf(singletonsswitch,definition,
% 2.41/1.45 ( singletonsswitch
% 2.41/1.45 = ( ! [Xx: $i,Xy: $i] :
% 2.41/1.45 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.41/1.45 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(upairsetE_type,type,
% 2.41/1.45 upairsetE: $o ).
% 2.41/1.45
% 2.41/1.45 thf(upairsetE,definition,
% 2.41/1.45 ( upairsetE
% 2.41/1.45 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.41/1.45 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.41/1.45 => ( ( Xz = Xx )
% 2.41/1.45 | ( Xz = Xy ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(upairsetIL_type,type,
% 2.41/1.45 upairsetIL: $o ).
% 2.41/1.45
% 2.41/1.45 thf(upairsetIL,definition,
% 2.41/1.45 ( upairsetIL
% 2.41/1.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(upairsetIR_type,type,
% 2.41/1.45 upairsetIR: $o ).
% 2.41/1.45
% 2.41/1.45 thf(upairsetIR,definition,
% 2.41/1.45 ( upairsetIR
% 2.41/1.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(emptyE1_type,type,
% 2.41/1.45 emptyE1: $o ).
% 2.41/1.45
% 2.41/1.45 thf(emptyE1,definition,
% 2.41/1.45 ( emptyE1
% 2.41/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.41/1.45 ( ? [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 & ( Xphi @ Xx ) )
% 2.41/1.45 => ( ( ( dsetconstr @ A
% 2.41/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.41/1.45 = emptyset )
% 2.41/1.45 => $false ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(vacuousDall_type,type,
% 2.41/1.45 vacuousDall: $o ).
% 2.41/1.45
% 2.41/1.45 thf(vacuousDall,definition,
% 2.41/1.45 ( vacuousDall
% 2.41/1.45 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ emptyset )
% 2.41/1.45 => ( Xphi @ Xx ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(quantDeMorgan1_type,type,
% 2.41/1.45 quantDeMorgan1: $o ).
% 2.41/1.45
% 2.41/1.45 thf(quantDeMorgan1,definition,
% 2.41/1.45 ( quantDeMorgan1
% 2.41/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.41/1.45 ( ~ ! [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ( Xphi @ Xx ) )
% 2.41/1.45 => ? [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(quantDeMorgan2_type,type,
% 2.41/1.45 quantDeMorgan2: $o ).
% 2.41/1.45
% 2.41/1.45 thf(quantDeMorgan2,definition,
% 2.41/1.45 ( quantDeMorgan2
% 2.41/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.41/1.45 ( ! [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ~ ( Xphi @ Xx ) )
% 2.41/1.45 => ~ ? [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(quantDeMorgan3_type,type,
% 2.41/1.45 quantDeMorgan3: $o ).
% 2.41/1.45
% 2.41/1.45 thf(quantDeMorgan3,definition,
% 2.41/1.45 ( quantDeMorgan3
% 2.41/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.41/1.45 ( ~ ? [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 & ( Xphi @ Xx ) )
% 2.41/1.45 => ! [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(quantDeMorgan4_type,type,
% 2.41/1.45 quantDeMorgan4: $o ).
% 2.41/1.45
% 2.41/1.45 thf(quantDeMorgan4,definition,
% 2.41/1.45 ( quantDeMorgan4
% 2.41/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.41/1.45 ( ? [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 & ~ ( Xphi @ Xx ) )
% 2.41/1.45 => ~ ! [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(prop2setI_type,type,
% 2.41/1.45 prop2setI: $o ).
% 2.41/1.45
% 2.41/1.45 thf(prop2setI,definition,
% 2.41/1.45 ( prop2setI
% 2.41/1.45 = ( ! [Xphi: $o] :
% 2.41/1.45 ( Xphi
% 2.41/1.45 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(set2prop_type,type,
% 2.41/1.45 set2prop: $i > $o ).
% 2.41/1.45
% 2.41/1.45 thf(prop2set2propI_type,type,
% 2.41/1.45 prop2set2propI: $o ).
% 2.41/1.45
% 2.41/1.45 thf(prop2set2propI,definition,
% 2.41/1.45 ( prop2set2propI
% 2.41/1.45 = ( ! [Xphi: $o] :
% 2.41/1.45 ( Xphi
% 2.41/1.45 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(notdexE_type,type,
% 2.41/1.45 notdexE: $o ).
% 2.41/1.45
% 2.41/1.45 thf(notdexE,definition,
% 2.41/1.45 ( notdexE
% 2.41/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.41/1.45 ( ~ ? [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 & ( Xphi @ Xx ) )
% 2.41/1.45 => ! [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(notdallE_type,type,
% 2.41/1.45 notdallE: $o ).
% 2.41/1.45
% 2.41/1.45 thf(notdallE,definition,
% 2.41/1.45 ( notdallE
% 2.41/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.41/1.45 ( ~ ! [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ( Xphi @ Xx ) )
% 2.41/1.45 => ? [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(exuI1_type,type,
% 2.41/1.45 exuI1: $o ).
% 2.41/1.45
% 2.41/1.45 thf(exuI1,definition,
% 2.41/1.45 ( exuI1
% 2.41/1.45 = ( ! [Xphi: $i > $o] :
% 2.41/1.45 ( ? [Xx: $i] :
% 2.41/1.45 ( ( Xphi @ Xx )
% 2.41/1.45 & ! [Xy: $i] :
% 2.41/1.45 ( ( Xphi @ Xy )
% 2.41/1.45 => ( Xx = Xy ) ) )
% 2.41/1.45 => ( exu
% 2.41/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(exuI3_type,type,
% 2.41/1.45 exuI3: $o ).
% 2.41/1.45
% 2.41/1.45 thf(exuI3,definition,
% 2.41/1.45 ( exuI3
% 2.41/1.45 = ( ! [Xphi: $i > $o] :
% 2.41/1.45 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.41/1.45 => ( ! [Xx: $i,Xy: $i] :
% 2.41/1.45 ( ( Xphi @ Xx )
% 2.41/1.45 => ( ( Xphi @ Xy )
% 2.41/1.45 => ( Xx = Xy ) ) )
% 2.41/1.45 => ( exu
% 2.41/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(exuI2_type,type,
% 2.41/1.45 exuI2: $o ).
% 2.41/1.45
% 2.41/1.45 thf(exuI2,definition,
% 2.41/1.45 ( exuI2
% 2.41/1.45 = ( ! [Xphi: $i > $o] :
% 2.41/1.45 ( ? [Xx: $i] :
% 2.41/1.45 ! [Xy: $i] :
% 2.41/1.45 ( ( Xphi @ Xy )
% 2.41/1.45 <=> ( Xy = Xx ) )
% 2.41/1.45 => ( exu
% 2.41/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(inCongP_type,type,
% 2.41/1.45 inCongP: $o ).
% 2.41/1.45
% 2.41/1.45 thf(inCongP,definition,
% 2.41/1.45 ( inCongP
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( A = B )
% 2.41/1.45 => ! [Xx: $i,Xy: $i] :
% 2.41/1.45 ( ( Xx = Xy )
% 2.41/1.45 => ( ( in @ Xx @ A )
% 2.41/1.45 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(in__Cong_type,type,
% 2.41/1.45 in__Cong: $o ).
% 2.41/1.45
% 2.41/1.45 thf(in__Cong,definition,
% 2.41/1.45 ( in__Cong
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( A = B )
% 2.41/1.45 => ! [Xx: $i,Xy: $i] :
% 2.41/1.45 ( ( Xx = Xy )
% 2.41/1.45 => ( ( in @ Xx @ A )
% 2.41/1.45 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(exuE3u_type,type,
% 2.41/1.45 exuE3u: $o ).
% 2.41/1.45
% 2.41/1.45 thf(exuE3u,definition,
% 2.41/1.45 ( exuE3u
% 2.41/1.45 = ( ! [Xphi: $i > $o] :
% 2.41/1.45 ( ( exu
% 2.41/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.41/1.45 => ! [Xx: $i,Xy: $i] :
% 2.41/1.45 ( ( Xphi @ Xx )
% 2.41/1.45 => ( ( Xphi @ Xy )
% 2.41/1.45 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(exu__Cong_type,type,
% 2.41/1.45 exu__Cong: $o ).
% 2.41/1.45
% 2.41/1.45 thf(exu__Cong,definition,
% 2.41/1.45 ( exu__Cong
% 2.41/1.45 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.41/1.45 ( ! [Xx: $i,Xy: $i] :
% 2.41/1.45 ( ( Xx = Xy )
% 2.41/1.45 => ( ( Xphi @ Xx )
% 2.41/1.45 <=> ( Xpsi @ Xy ) ) )
% 2.41/1.45 => ( ( exu
% 2.41/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.41/1.45 <=> ( exu
% 2.41/1.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(emptyset__Cong_type,type,
% 2.41/1.45 emptyset__Cong: $o ).
% 2.41/1.45
% 2.41/1.45 thf(emptyset__Cong,definition,
% 2.41/1.45 ( emptyset__Cong
% 2.41/1.45 = ( emptyset = emptyset ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setadjoin__Cong_type,type,
% 2.41/1.45 setadjoin__Cong: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setadjoin__Cong,definition,
% 2.41/1.45 ( setadjoin__Cong
% 2.41/1.45 = ( ! [Xx: $i,Xy: $i] :
% 2.41/1.45 ( ( Xx = Xy )
% 2.41/1.45 => ! [Xz: $i,Xu: $i] :
% 2.41/1.45 ( ( Xz = Xu )
% 2.41/1.45 => ( ( setadjoin @ Xx @ Xz )
% 2.41/1.45 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(powerset__Cong_type,type,
% 2.41/1.45 powerset__Cong: $o ).
% 2.41/1.45
% 2.41/1.45 thf(powerset__Cong,definition,
% 2.41/1.45 ( powerset__Cong
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( A = B )
% 2.41/1.45 => ( ( powerset @ A )
% 2.41/1.45 = ( powerset @ B ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setunion__Cong_type,type,
% 2.41/1.45 setunion__Cong: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setunion__Cong,definition,
% 2.41/1.45 ( setunion__Cong
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( A = B )
% 2.41/1.45 => ( ( setunion @ A )
% 2.41/1.45 = ( setunion @ B ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(omega__Cong_type,type,
% 2.41/1.45 omega__Cong: $o ).
% 2.41/1.45
% 2.41/1.45 thf(omega__Cong,definition,
% 2.41/1.45 ( omega__Cong
% 2.41/1.45 = ( omega = omega ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(exuEu_type,type,
% 2.41/1.45 exuEu: $o ).
% 2.41/1.45
% 2.41/1.45 thf(exuEu,definition,
% 2.41/1.45 ( exuEu
% 2.41/1.45 = ( ! [Xphi: $i > $o] :
% 2.41/1.45 ( ( exu
% 2.41/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.41/1.45 => ! [Xx: $i,Xy: $i] :
% 2.41/1.45 ( ( Xphi @ Xx )
% 2.41/1.45 => ( ( Xphi @ Xy )
% 2.41/1.45 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(descr__Cong_type,type,
% 2.41/1.45 descr__Cong: $o ).
% 2.41/1.45
% 2.41/1.45 thf(descr__Cong,definition,
% 2.41/1.45 ( descr__Cong
% 2.41/1.45 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.41/1.45 ( ! [Xx: $i,Xy: $i] :
% 2.41/1.45 ( ( Xx = Xy )
% 2.41/1.45 => ( ( Xphi @ Xx )
% 2.41/1.45 <=> ( Xpsi @ Xy ) ) )
% 2.41/1.45 => ( ( exu
% 2.41/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.41/1.45 => ( ( exu
% 2.41/1.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.41/1.45 => ( ( descr
% 2.41/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.41/1.45 = ( descr
% 2.41/1.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(dsetconstr__Cong_type,type,
% 2.41/1.45 dsetconstr__Cong: $o ).
% 2.41/1.45
% 2.41/1.45 thf(dsetconstr__Cong,definition,
% 2.41/1.45 ( dsetconstr__Cong
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( A = B )
% 2.41/1.45 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.41/1.45 ( ! [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ! [Xy: $i] :
% 2.41/1.45 ( ( in @ Xy @ B )
% 2.41/1.45 => ( ( Xx = Xy )
% 2.41/1.45 => ( ( Xphi @ Xx )
% 2.41/1.45 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.41/1.45 => ( ( dsetconstr @ A
% 2.41/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.41/1.45 = ( dsetconstr @ B
% 2.41/1.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(subset_type,type,
% 2.41/1.45 subset: $i > $i > $o ).
% 2.41/1.45
% 2.41/1.45 thf(disjoint_type,type,
% 2.41/1.45 disjoint: $i > $i > $o ).
% 2.41/1.45
% 2.41/1.45 thf(setsmeet_type,type,
% 2.41/1.45 setsmeet: $i > $i > $o ).
% 2.41/1.45
% 2.41/1.45 thf(subsetI1_type,type,
% 2.41/1.45 subsetI1: $o ).
% 2.41/1.45
% 2.41/1.45 thf(subsetI1,definition,
% 2.41/1.45 ( subsetI1
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ! [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ( in @ Xx @ B ) )
% 2.41/1.45 => ( subset @ A @ B ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(eqimpsubset2_type,type,
% 2.41/1.45 eqimpsubset2: $o ).
% 2.41/1.45
% 2.41/1.45 thf(eqimpsubset2,definition,
% 2.41/1.45 ( eqimpsubset2
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( A = B )
% 2.41/1.45 => ( subset @ B @ A ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(eqimpsubset1_type,type,
% 2.41/1.45 eqimpsubset1: $o ).
% 2.41/1.45
% 2.41/1.45 thf(eqimpsubset1,definition,
% 2.41/1.45 ( eqimpsubset1
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( A = B )
% 2.41/1.45 => ( subset @ A @ B ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(subsetI2_type,type,
% 2.41/1.45 subsetI2: $o ).
% 2.41/1.45
% 2.41/1.45 thf(subsetI2,definition,
% 2.41/1.45 ( subsetI2
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ! [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ( in @ Xx @ B ) )
% 2.41/1.45 => ( subset @ A @ B ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(emptysetsubset_type,type,
% 2.41/1.45 emptysetsubset: $o ).
% 2.41/1.45
% 2.41/1.45 thf(emptysetsubset,definition,
% 2.41/1.45 ( emptysetsubset
% 2.41/1.45 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(subsetE_type,type,
% 2.41/1.45 subsetE: $o ).
% 2.41/1.45
% 2.41/1.45 thf(subsetE,definition,
% 2.41/1.45 ( subsetE
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( subset @ A @ B )
% 2.41/1.45 => ( ( in @ Xx @ A )
% 2.41/1.45 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(subsetE2_type,type,
% 2.41/1.45 subsetE2: $o ).
% 2.41/1.45
% 2.41/1.45 thf(subsetE2,definition,
% 2.41/1.45 ( subsetE2
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( subset @ A @ B )
% 2.41/1.45 => ( ~ ( in @ Xx @ B )
% 2.41/1.45 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(notsubsetI_type,type,
% 2.41/1.45 notsubsetI: $o ).
% 2.41/1.45
% 2.41/1.45 thf(notsubsetI,definition,
% 2.41/1.45 ( notsubsetI
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ( ~ ( in @ Xx @ B )
% 2.41/1.45 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(notequalI1_type,type,
% 2.41/1.45 notequalI1: $o ).
% 2.41/1.45
% 2.41/1.45 thf(notequalI1,definition,
% 2.41/1.45 ( notequalI1
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ~ ( subset @ A @ B )
% 2.41/1.45 => ( A != B ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(notequalI2_type,type,
% 2.41/1.45 notequalI2: $o ).
% 2.41/1.45
% 2.41/1.45 thf(notequalI2,definition,
% 2.41/1.45 ( notequalI2
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ( ~ ( in @ Xx @ B )
% 2.41/1.45 => ( A != B ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(subsetRefl_type,type,
% 2.41/1.45 subsetRefl: $o ).
% 2.41/1.45
% 2.41/1.45 thf(subsetRefl,definition,
% 2.41/1.45 ( subsetRefl
% 2.41/1.45 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(subsetTrans_type,type,
% 2.41/1.45 subsetTrans: $o ).
% 2.41/1.45
% 2.41/1.45 thf(subsetTrans,definition,
% 2.41/1.45 ( subsetTrans
% 2.41/1.45 = ( ! [A: $i,B: $i,C: $i] :
% 2.41/1.45 ( ( subset @ A @ B )
% 2.41/1.45 => ( ( subset @ B @ C )
% 2.41/1.45 => ( subset @ A @ C ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setadjoinSub_type,type,
% 2.41/1.45 setadjoinSub: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setadjoinSub,definition,
% 2.41/1.45 ( setadjoinSub
% 2.41/1.45 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setadjoinSub2_type,type,
% 2.41/1.45 setadjoinSub2: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setadjoinSub2,definition,
% 2.41/1.45 ( setadjoinSub2
% 2.41/1.45 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.41/1.45 ( ( subset @ A @ B )
% 2.41/1.45 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(subset2powerset_type,type,
% 2.41/1.45 subset2powerset: $o ).
% 2.41/1.45
% 2.41/1.45 thf(subset2powerset,definition,
% 2.41/1.45 ( subset2powerset
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( subset @ A @ B )
% 2.41/1.45 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setextsub_type,type,
% 2.41/1.45 setextsub: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setextsub,definition,
% 2.41/1.45 ( setextsub
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( subset @ A @ B )
% 2.41/1.45 => ( ( subset @ B @ A )
% 2.41/1.45 => ( A = B ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(subsetemptysetimpeq_type,type,
% 2.41/1.45 subsetemptysetimpeq: $o ).
% 2.41/1.45
% 2.41/1.45 thf(subsetemptysetimpeq,definition,
% 2.41/1.45 ( subsetemptysetimpeq
% 2.41/1.45 = ( ! [A: $i] :
% 2.41/1.45 ( ( subset @ A @ emptyset )
% 2.41/1.45 => ( A = emptyset ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(powersetI1_type,type,
% 2.41/1.45 powersetI1: $o ).
% 2.41/1.45
% 2.41/1.45 thf(powersetI1,definition,
% 2.41/1.45 ( powersetI1
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( subset @ B @ A )
% 2.41/1.45 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(powersetE1_type,type,
% 2.41/1.45 powersetE1: $o ).
% 2.41/1.45
% 2.41/1.45 thf(powersetE1,definition,
% 2.41/1.45 ( powersetE1
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( in @ B @ ( powerset @ A ) )
% 2.41/1.45 => ( subset @ B @ A ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(inPowerset_type,type,
% 2.41/1.45 inPowerset: $o ).
% 2.41/1.45
% 2.41/1.45 thf(inPowerset,definition,
% 2.41/1.45 ( inPowerset
% 2.41/1.45 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(powersetsubset_type,type,
% 2.41/1.45 powersetsubset: $o ).
% 2.41/1.45
% 2.41/1.45 thf(powersetsubset,definition,
% 2.41/1.45 ( powersetsubset
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( subset @ A @ B )
% 2.41/1.45 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(sepInPowerset_type,type,
% 2.41/1.45 sepInPowerset: $o ).
% 2.41/1.45
% 2.41/1.45 thf(sepInPowerset,definition,
% 2.41/1.45 ( sepInPowerset
% 2.41/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.41/1.45 ( in
% 2.41/1.45 @ ( dsetconstr @ A
% 2.41/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.41/1.45 @ ( powerset @ A ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(sepSubset_type,type,
% 2.41/1.45 sepSubset: $o ).
% 2.41/1.45
% 2.41/1.45 thf(sepSubset,definition,
% 2.41/1.45 ( sepSubset
% 2.41/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.41/1.45 ( subset
% 2.41/1.45 @ ( dsetconstr @ A
% 2.41/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.41/1.45 @ A ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(binunion_type,type,
% 2.41/1.45 binunion: $i > $i > $i ).
% 2.41/1.45
% 2.41/1.45 thf(binunionIL_type,type,
% 2.41/1.45 binunionIL: $o ).
% 2.41/1.45
% 2.41/1.45 thf(binunionIL,definition,
% 2.41/1.45 ( binunionIL
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(upairset2IR_type,type,
% 2.41/1.45 upairset2IR: $o ).
% 2.41/1.45
% 2.41/1.45 thf(upairset2IR,definition,
% 2.41/1.45 ( upairset2IR
% 2.41/1.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(binunionIR_type,type,
% 2.41/1.45 binunionIR: $o ).
% 2.41/1.45
% 2.41/1.45 thf(binunionIR,definition,
% 2.41/1.45 ( binunionIR
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ B )
% 2.41/1.45 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(binunionEcases_type,type,
% 2.41/1.45 binunionEcases: $o ).
% 2.41/1.45
% 2.41/1.45 thf(binunionEcases,definition,
% 2.41/1.45 ( binunionEcases
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.41/1.45 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.41/1.45 => ( ( ( in @ Xx @ A )
% 2.41/1.45 => Xphi )
% 2.41/1.45 => ( ( ( in @ Xx @ B )
% 2.41/1.45 => Xphi )
% 2.41/1.45 => Xphi ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(binunionE_type,type,
% 2.41/1.45 binunionE: $o ).
% 2.41/1.45
% 2.41/1.45 thf(binunionE,definition,
% 2.41/1.45 ( binunionE
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.41/1.45 => ( ( in @ Xx @ A )
% 2.41/1.45 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(binunionLsub_type,type,
% 2.41/1.45 binunionLsub: $o ).
% 2.41/1.45
% 2.41/1.45 thf(binunionLsub,definition,
% 2.41/1.45 ( binunionLsub
% 2.41/1.45 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(binunionRsub_type,type,
% 2.41/1.45 binunionRsub: $o ).
% 2.41/1.45
% 2.41/1.45 thf(binunionRsub,definition,
% 2.41/1.45 ( binunionRsub
% 2.41/1.45 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(binintersect_type,type,
% 2.41/1.45 binintersect: $i > $i > $i ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectI_type,type,
% 2.41/1.45 binintersectI: $o ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectI,definition,
% 2.41/1.45 ( binintersectI
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ( ( in @ Xx @ B )
% 2.41/1.45 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectSubset5_type,type,
% 2.41/1.45 binintersectSubset5: $o ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectSubset5,definition,
% 2.41/1.45 ( binintersectSubset5
% 2.41/1.45 = ( ! [A: $i,B: $i,C: $i] :
% 2.41/1.45 ( ( subset @ C @ A )
% 2.41/1.45 => ( ( subset @ C @ B )
% 2.41/1.45 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectEL_type,type,
% 2.41/1.45 binintersectEL: $o ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectEL,definition,
% 2.41/1.45 ( binintersectEL
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.41/1.45 => ( in @ Xx @ A ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectLsub_type,type,
% 2.41/1.45 binintersectLsub: $o ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectLsub,definition,
% 2.41/1.45 ( binintersectLsub
% 2.41/1.45 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectSubset2_type,type,
% 2.41/1.45 binintersectSubset2: $o ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectSubset2,definition,
% 2.41/1.45 ( binintersectSubset2
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( subset @ A @ B )
% 2.41/1.45 => ( ( binintersect @ A @ B )
% 2.41/1.45 = A ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectSubset3_type,type,
% 2.41/1.45 binintersectSubset3: $o ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectSubset3,definition,
% 2.41/1.45 ( binintersectSubset3
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( ( binintersect @ A @ B )
% 2.41/1.45 = B )
% 2.41/1.45 => ( subset @ B @ A ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectER_type,type,
% 2.41/1.45 binintersectER: $o ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectER,definition,
% 2.41/1.45 ( binintersectER
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.41/1.45 => ( in @ Xx @ B ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(disjointsetsI1_type,type,
% 2.41/1.45 disjointsetsI1: $o ).
% 2.41/1.45
% 2.41/1.45 thf(disjointsetsI1,definition,
% 2.41/1.45 ( disjointsetsI1
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ~ ? [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 & ( in @ Xx @ B ) )
% 2.41/1.45 => ( ( binintersect @ A @ B )
% 2.41/1.45 = emptyset ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectRsub_type,type,
% 2.41/1.45 binintersectRsub: $o ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectRsub,definition,
% 2.41/1.45 ( binintersectRsub
% 2.41/1.45 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectSubset4_type,type,
% 2.41/1.45 binintersectSubset4: $o ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectSubset4,definition,
% 2.41/1.45 ( binintersectSubset4
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( subset @ B @ A )
% 2.41/1.45 => ( ( binintersect @ A @ B )
% 2.41/1.45 = B ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectSubset1_type,type,
% 2.41/1.45 binintersectSubset1: $o ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectSubset1,definition,
% 2.41/1.45 ( binintersectSubset1
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( ( binintersect @ A @ B )
% 2.41/1.45 = A )
% 2.41/1.45 => ( subset @ A @ B ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(bs114d_type,type,
% 2.41/1.45 bs114d: $o ).
% 2.41/1.45
% 2.41/1.45 thf(bs114d,definition,
% 2.41/1.45 ( bs114d
% 2.41/1.45 = ( ! [A: $i,B: $i,C: $i] :
% 2.41/1.45 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.41/1.45 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(regular_type,type,
% 2.41/1.45 regular: $i > $o ).
% 2.41/1.45
% 2.41/1.45 thf(setminus_type,type,
% 2.41/1.45 setminus: $i > $i > $i ).
% 2.41/1.45
% 2.41/1.45 thf(setminusI_type,type,
% 2.41/1.45 setminusI: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setminusI,definition,
% 2.41/1.45 ( setminusI
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ( ~ ( in @ Xx @ B )
% 2.41/1.45 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setminusEL_type,type,
% 2.41/1.45 setminusEL: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setminusEL,definition,
% 2.41/1.45 ( setminusEL
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.41/1.45 => ( in @ Xx @ A ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setminusER_type,type,
% 2.41/1.45 setminusER: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setminusER,definition,
% 2.41/1.45 ( setminusER
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.41/1.45 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setminusSubset2_type,type,
% 2.41/1.45 setminusSubset2: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setminusSubset2,definition,
% 2.41/1.45 ( setminusSubset2
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( subset @ A @ B )
% 2.41/1.45 => ( ( setminus @ A @ B )
% 2.41/1.45 = emptyset ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setminusERneg_type,type,
% 2.41/1.45 setminusERneg: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setminusERneg,definition,
% 2.41/1.45 ( setminusERneg
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.41/1.45 => ( ( in @ Xx @ A )
% 2.41/1.45 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setminusELneg_type,type,
% 2.41/1.45 setminusELneg: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setminusELneg,definition,
% 2.41/1.45 ( setminusELneg
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.41/1.45 => ( ~ ( in @ Xx @ B )
% 2.41/1.45 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setminusILneg_type,type,
% 2.41/1.45 setminusILneg: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setminusILneg,definition,
% 2.41/1.45 ( setminusILneg
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ~ ( in @ Xx @ A )
% 2.41/1.45 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setminusIRneg_type,type,
% 2.41/1.45 setminusIRneg: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setminusIRneg,definition,
% 2.41/1.45 ( setminusIRneg
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ B )
% 2.41/1.45 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setminusLsub_type,type,
% 2.41/1.45 setminusLsub: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setminusLsub,definition,
% 2.41/1.45 ( setminusLsub
% 2.41/1.45 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setminusSubset1_type,type,
% 2.41/1.45 setminusSubset1: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setminusSubset1,definition,
% 2.41/1.45 ( setminusSubset1
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( ( setminus @ A @ B )
% 2.41/1.45 = emptyset )
% 2.41/1.45 => ( subset @ A @ B ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(symdiff_type,type,
% 2.41/1.45 symdiff: $i > $i > $i ).
% 2.41/1.45
% 2.41/1.45 thf(symdiffE_type,type,
% 2.41/1.45 symdiffE: $o ).
% 2.41/1.45
% 2.41/1.45 thf(symdiffE,definition,
% 2.41/1.45 ( symdiffE
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.41/1.45 => ! [Xphi: $o] :
% 2.41/1.45 ( ( ( in @ Xx @ A )
% 2.41/1.45 => ( ~ ( in @ Xx @ B )
% 2.41/1.45 => Xphi ) )
% 2.41/1.45 => ( ( ~ ( in @ Xx @ A )
% 2.41/1.45 => ( ( in @ Xx @ B )
% 2.41/1.45 => Xphi ) )
% 2.41/1.45 => Xphi ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(symdiffI1_type,type,
% 2.41/1.45 symdiffI1: $o ).
% 2.41/1.45
% 2.41/1.45 thf(symdiffI1,definition,
% 2.41/1.45 ( symdiffI1
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ( ~ ( in @ Xx @ B )
% 2.41/1.45 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(symdiffI2_type,type,
% 2.41/1.45 symdiffI2: $o ).
% 2.41/1.45
% 2.41/1.45 thf(symdiffI2,definition,
% 2.41/1.45 ( symdiffI2
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ~ ( in @ Xx @ A )
% 2.41/1.45 => ( ( in @ Xx @ B )
% 2.41/1.45 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(symdiffIneg1_type,type,
% 2.41/1.45 symdiffIneg1: $o ).
% 2.41/1.45
% 2.41/1.45 thf(symdiffIneg1,definition,
% 2.41/1.45 ( symdiffIneg1
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ( ( in @ Xx @ B )
% 2.41/1.45 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(symdiffIneg2_type,type,
% 2.41/1.45 symdiffIneg2: $o ).
% 2.41/1.45
% 2.41/1.45 thf(symdiffIneg2,definition,
% 2.41/1.45 ( symdiffIneg2
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ~ ( in @ Xx @ A )
% 2.41/1.45 => ( ~ ( in @ Xx @ B )
% 2.41/1.45 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(iskpair_type,type,
% 2.41/1.45 iskpair: $i > $o ).
% 2.41/1.45
% 2.41/1.45 thf(iskpair,definition,
% 2.41/1.45 ( iskpair
% 2.41/1.45 = ( ^ [A: $i] :
% 2.41/1.45 ? [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ ( setunion @ A ) )
% 2.41/1.45 & ? [Xy: $i] :
% 2.41/1.45 ( ( in @ Xy @ ( setunion @ A ) )
% 2.41/1.45 & ( A
% 2.41/1.45 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(secondinupair_type,type,
% 2.41/1.45 secondinupair: $o ).
% 2.41/1.45
% 2.41/1.45 thf(secondinupair,definition,
% 2.41/1.45 ( secondinupair
% 2.41/1.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setukpairIL_type,type,
% 2.41/1.45 setukpairIL: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setukpairIL,definition,
% 2.41/1.45 ( setukpairIL
% 2.41/1.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setukpairIR_type,type,
% 2.41/1.45 setukpairIR: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setukpairIR,definition,
% 2.41/1.45 ( setukpairIR
% 2.41/1.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(kpairiskpair_type,type,
% 2.41/1.45 kpairiskpair: $o ).
% 2.41/1.45
% 2.41/1.45 thf(kpairiskpair,definition,
% 2.41/1.45 ( kpairiskpair
% 2.41/1.45 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(kpair_type,type,
% 2.41/1.45 kpair: $i > $i > $i ).
% 2.41/1.45
% 2.41/1.45 thf(kpair,definition,
% 2.41/1.45 ( kpair
% 2.41/1.45 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(kpairp_type,type,
% 2.41/1.45 kpairp: $o ).
% 2.41/1.45
% 2.41/1.45 thf(kpairp,definition,
% 2.41/1.45 ( kpairp
% 2.41/1.45 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(cartprod_type,type,
% 2.41/1.45 cartprod: $i > $i > $i ).
% 2.41/1.45
% 2.41/1.45 thf(singletonsubset_type,type,
% 2.41/1.45 singletonsubset: $o ).
% 2.41/1.45
% 2.41/1.45 thf(singletonsubset,definition,
% 2.41/1.45 ( singletonsubset
% 2.41/1.45 = ( ! [A: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(singletoninpowerset_type,type,
% 2.41/1.45 singletoninpowerset: $o ).
% 2.41/1.45
% 2.41/1.45 thf(singletoninpowerset,definition,
% 2.41/1.45 ( singletoninpowerset
% 2.41/1.45 = ( ! [A: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(singletoninpowunion_type,type,
% 2.41/1.45 singletoninpowunion: $o ).
% 2.41/1.45
% 2.41/1.45 thf(singletoninpowunion,definition,
% 2.41/1.45 ( singletoninpowunion
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(upairset2E_type,type,
% 2.41/1.45 upairset2E: $o ).
% 2.41/1.45
% 2.41/1.45 thf(upairset2E,definition,
% 2.41/1.45 ( upairset2E
% 2.41/1.45 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.41/1.45 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.41/1.45 => ( ( Xz = Xx )
% 2.41/1.45 | ( Xz = Xy ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(upairsubunion_type,type,
% 2.41/1.45 upairsubunion: $o ).
% 2.41/1.45
% 2.41/1.45 thf(upairsubunion,definition,
% 2.41/1.45 ( upairsubunion
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ! [Xy: $i] :
% 2.41/1.45 ( ( in @ Xy @ B )
% 2.41/1.45 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(upairinpowunion_type,type,
% 2.41/1.45 upairinpowunion: $o ).
% 2.41/1.45
% 2.41/1.45 thf(upairinpowunion,definition,
% 2.41/1.45 ( upairinpowunion
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ! [Xy: $i] :
% 2.41/1.45 ( ( in @ Xy @ B )
% 2.41/1.45 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(ubforcartprodlem1_type,type,
% 2.41/1.45 ubforcartprodlem1: $o ).
% 2.41/1.45
% 2.41/1.45 thf(ubforcartprodlem1,definition,
% 2.41/1.45 ( ubforcartprodlem1
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ! [Xy: $i] :
% 2.41/1.45 ( ( in @ Xy @ B )
% 2.41/1.45 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(ubforcartprodlem2_type,type,
% 2.41/1.45 ubforcartprodlem2: $o ).
% 2.41/1.45
% 2.41/1.45 thf(ubforcartprodlem2,definition,
% 2.41/1.45 ( ubforcartprodlem2
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ! [Xy: $i] :
% 2.41/1.45 ( ( in @ Xy @ B )
% 2.41/1.45 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(ubforcartprodlem3_type,type,
% 2.41/1.45 ubforcartprodlem3: $o ).
% 2.41/1.45
% 2.41/1.45 thf(ubforcartprodlem3,definition,
% 2.41/1.45 ( ubforcartprodlem3
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ! [Xy: $i] :
% 2.41/1.45 ( ( in @ Xy @ B )
% 2.41/1.45 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(cartprodpairin_type,type,
% 2.41/1.45 cartprodpairin: $o ).
% 2.41/1.45
% 2.41/1.45 thf(cartprodpairin,definition,
% 2.41/1.45 ( cartprodpairin
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ! [Xy: $i] :
% 2.41/1.45 ( ( in @ Xy @ B )
% 2.41/1.45 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(cartprodmempair1_type,type,
% 2.41/1.45 cartprodmempair1: $o ).
% 2.41/1.45
% 2.41/1.45 thf(cartprodmempair1,definition,
% 2.41/1.45 ( cartprodmempair1
% 2.41/1.45 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.41/1.45 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.41/1.45 => ? [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 & ? [Xy: $i] :
% 2.41/1.45 ( ( in @ Xy @ B )
% 2.41/1.45 & ( Xu
% 2.41/1.45 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(cartprodmempair_type,type,
% 2.41/1.45 cartprodmempair: $o ).
% 2.41/1.45
% 2.41/1.45 thf(cartprodmempair,definition,
% 2.41/1.45 ( cartprodmempair
% 2.41/1.45 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.41/1.45 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.41/1.45 => ( iskpair @ Xu ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setunionE2_type,type,
% 2.41/1.45 setunionE2: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setunionE2,definition,
% 2.41/1.45 ( setunionE2
% 2.41/1.45 = ( ! [A: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ ( setunion @ A ) )
% 2.41/1.45 => ? [X: $i] :
% 2.41/1.45 ( ( in @ X @ A )
% 2.41/1.45 & ( in @ Xx @ X ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setunionsingleton1_type,type,
% 2.41/1.45 setunionsingleton1: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setunionsingleton1,definition,
% 2.41/1.45 ( setunionsingleton1
% 2.41/1.45 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setunionsingleton2_type,type,
% 2.41/1.45 setunionsingleton2: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setunionsingleton2,definition,
% 2.41/1.45 ( setunionsingleton2
% 2.41/1.45 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setunionsingleton_type,type,
% 2.41/1.45 setunionsingleton: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setunionsingleton,definition,
% 2.41/1.45 ( setunionsingleton
% 2.41/1.45 = ( ! [Xx: $i] :
% 2.41/1.45 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 2.41/1.45 = Xx ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(singleton_type,type,
% 2.41/1.45 singleton: $i > $o ).
% 2.41/1.45
% 2.41/1.45 thf(singleton,definition,
% 2.41/1.45 ( singleton
% 2.41/1.45 = ( ^ [A: $i] :
% 2.41/1.45 ? [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 & ( A
% 2.41/1.45 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(singletonprop_type,type,
% 2.41/1.45 singletonprop: $o ).
% 2.41/1.45
% 2.41/1.45 thf(singletonprop,definition,
% 2.41/1.45 ( singletonprop
% 2.41/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.41/1.45 ( ! [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ! [Xy: $i] :
% 2.41/1.45 ( ( in @ Xy @ A )
% 2.41/1.45 => ( ( Xphi @ Xx )
% 2.41/1.45 => ( ( Xphi @ Xy )
% 2.41/1.45 => ( Xx = Xy ) ) ) ) )
% 2.41/1.45 => ( ? [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 & ( Xphi @ Xx ) )
% 2.41/1.45 => ( singleton
% 2.41/1.45 @ ( dsetconstr @ A
% 2.41/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(ex1_type,type,
% 2.41/1.45 ex1: $i > ( $i > $o ) > $o ).
% 2.41/1.45
% 2.41/1.45 thf(ex1,definition,
% 2.41/1.45 ( ex1
% 2.41/1.45 = ( ^ [A: $i,Xphi: $i > $o] :
% 2.41/1.45 ( singleton
% 2.41/1.45 @ ( dsetconstr @ A
% 2.41/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(ex1E1_type,type,
% 2.41/1.45 ex1E1: $o ).
% 2.41/1.45
% 2.41/1.45 thf(ex1E1,definition,
% 2.41/1.45 ( ex1E1
% 2.41/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.41/1.45 ( ( ex1 @ A
% 2.41/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.41/1.45 => ? [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(ex1I,conjecture,
% 2.41/1.45 ( setextAx
% 2.41/1.45 => ( emptysetAx
% 2.41/1.45 => ( setadjoinAx
% 2.41/1.45 => ( powersetAx
% 2.41/1.45 => ( setunionAx
% 2.41/1.45 => ( omega0Ax
% 2.41/1.45 => ( omegaSAx
% 2.41/1.45 => ( omegaIndAx
% 2.41/1.45 => ( replAx
% 2.41/1.45 => ( foundationAx
% 2.41/1.45 => ( wellorderingAx
% 2.41/1.45 => ( descrp
% 2.41/1.45 => ( dsetconstrI
% 2.41/1.45 => ( dsetconstrEL
% 2.41/1.45 => ( dsetconstrER
% 2.41/1.45 => ( exuE1
% 2.41/1.45 => ( prop2setE
% 2.41/1.45 => ( emptysetE
% 2.41/1.45 => ( emptysetimpfalse
% 2.41/1.45 => ( notinemptyset
% 2.41/1.45 => ( exuE3e
% 2.41/1.45 => ( setext
% 2.41/1.45 => ( emptyI
% 2.41/1.45 => ( noeltsimpempty
% 2.41/1.45 => ( setbeta
% 2.41/1.45 => ( nonemptyE1
% 2.41/1.45 => ( nonemptyI
% 2.41/1.45 => ( nonemptyI1
% 2.41/1.45 => ( setadjoinIL
% 2.41/1.45 => ( emptyinunitempty
% 2.41/1.45 => ( setadjoinIR
% 2.41/1.45 => ( setadjoinE
% 2.41/1.45 => ( setadjoinOr
% 2.41/1.45 => ( setoftrueEq
% 2.41/1.45 => ( powersetI
% 2.41/1.45 => ( emptyinPowerset
% 2.41/1.45 => ( emptyInPowerset
% 2.41/1.45 => ( powersetE
% 2.41/1.45 => ( setunionI
% 2.41/1.45 => ( setunionE
% 2.41/1.45 => ( subPowSU
% 2.41/1.45 => ( exuE2
% 2.41/1.45 => ( nonemptyImpWitness
% 2.41/1.45 => ( uniqinunit
% 2.41/1.45 => ( notinsingleton
% 2.41/1.45 => ( eqinunit
% 2.41/1.45 => ( singletonsswitch
% 2.41/1.45 => ( upairsetE
% 2.41/1.45 => ( upairsetIL
% 2.41/1.45 => ( upairsetIR
% 2.41/1.45 => ( emptyE1
% 2.41/1.45 => ( vacuousDall
% 2.41/1.45 => ( quantDeMorgan1
% 2.41/1.45 => ( quantDeMorgan2
% 2.41/1.45 => ( quantDeMorgan3
% 2.41/1.45 => ( quantDeMorgan4
% 2.41/1.45 => ( prop2setI
% 2.41/1.45 => ( prop2set2propI
% 2.41/1.45 => ( notdexE
% 2.41/1.45 => ( notdallE
% 2.41/1.45 => ( exuI1
% 2.41/1.45 => ( exuI3
% 2.41/1.45 => ( exuI2
% 2.41/1.45 => ( inCongP
% 2.41/1.45 => ( in__Cong
% 2.41/1.45 => ( exuE3u
% 2.41/1.45 => ( exu__Cong
% 2.41/1.45 => ( emptyset__Cong
% 2.41/1.45 => ( setadjoin__Cong
% 2.41/1.45 => ( powerset__Cong
% 2.41/1.45 => ( setunion__Cong
% 2.41/1.45 => ( omega__Cong
% 2.41/1.45 => ( exuEu
% 2.41/1.45 => ( descr__Cong
% 2.41/1.45 => ( dsetconstr__Cong
% 2.41/1.45 => ( subsetI1
% 2.41/1.45 => ( eqimpsubset2
% 2.41/1.45 => ( eqimpsubset1
% 2.41/1.45 => ( subsetI2
% 2.41/1.45 => ( emptysetsubset
% 2.41/1.45 => ( subsetE
% 2.41/1.45 => ( subsetE2
% 2.41/1.45 => ( notsubsetI
% 2.41/1.45 => ( notequalI1
% 2.41/1.45 => ( notequalI2
% 2.41/1.45 => ( subsetRefl
% 2.41/1.45 => ( subsetTrans
% 2.41/1.45 => ( setadjoinSub
% 2.41/1.45 => ( setadjoinSub2
% 2.41/1.45 => ( subset2powerset
% 2.41/1.45 => ( setextsub
% 2.41/1.45 => ( subsetemptysetimpeq
% 2.41/1.45 => ( powersetI1
% 2.41/1.45 => ( powersetE1
% 2.41/1.45 => ( inPowerset
% 2.41/1.45 => ( powersetsubset
% 2.41/1.45 => ( sepInPowerset
% 2.41/1.45 => ( sepSubset
% 2.41/1.45 => ( binunionIL
% 2.41/1.45 => ( upairset2IR
% 2.41/1.45 => ( binunionIR
% 2.41/1.45 => ( binunionEcases
% 2.41/1.45 => ( binunionE
% 2.41/1.45 => ( binunionLsub
% 2.41/1.45 => ( binunionRsub
% 2.41/1.45 => ( binintersectI
% 2.41/1.45 => ( binintersectSubset5
% 2.41/1.45 => ( binintersectEL
% 2.41/1.45 => ( binintersectLsub
% 2.41/1.45 => ( binintersectSubset2
% 2.41/1.45 => ( binintersectSubset3
% 2.41/1.45 => ( binintersectER
% 2.41/1.45 => ( disjointsetsI1
% 2.41/1.45 => ( binintersectRsub
% 2.41/1.45 => ( binintersectSubset4
% 2.41/1.45 => ( binintersectSubset1
% 2.41/1.45 => ( bs114d
% 2.41/1.45 => ( setminusI
% 2.41/1.45 => ( setminusEL
% 2.41/1.45 => ( setminusER
% 2.41/1.45 => ( setminusSubset2
% 2.41/1.45 => ( setminusERneg
% 2.41/1.45 => ( setminusELneg
% 2.41/1.45 => ( setminusILneg
% 2.41/1.45 => ( setminusIRneg
% 2.41/1.45 => ( setminusLsub
% 2.41/1.45 => ( setminusSubset1
% 2.41/1.45 => ( symdiffE
% 2.41/1.45 => ( symdiffI1
% 2.41/1.45 => ( symdiffI2
% 2.41/1.45 => ( symdiffIneg1
% 2.41/1.45 => ( symdiffIneg2
% 2.41/1.45 => ( secondinupair
% 2.41/1.45 => ( setukpairIL
% 2.41/1.45 => ( setukpairIR
% 2.41/1.45 => ( kpairiskpair
% 2.41/1.45 => ( kpairp
% 2.41/1.45 => ( singletonsubset
% 2.41/1.45 => ( singletoninpowerset
% 2.41/1.45 => ( singletoninpowunion
% 2.41/1.45 => ( upairset2E
% 2.41/1.45 => ( upairsubunion
% 2.41/1.45 => ( upairinpowunion
% 2.41/1.45 => ( ubforcartprodlem1
% 2.41/1.45 => ( ubforcartprodlem2
% 2.41/1.45 => ( ubforcartprodlem3
% 2.41/1.45 => ( cartprodpairin
% 2.41/1.45 => ( cartprodmempair1
% 2.41/1.45 => ( cartprodmempair
% 2.41/1.45 => ( setunionE2
% 2.41/1.45 => ( setunionsingleton1
% 2.41/1.45 => ( setunionsingleton2
% 2.41/1.45 => ( setunionsingleton
% 2.41/1.45 => ( singletonprop
% 2.41/1.45 => ( ex1E1
% 2.41/1.45 => ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ( ( Xphi @ Xx )
% 2.41/1.45 => ( ! [Xy: $i] :
% 2.41/1.45 ( ( in @ Xy @ A )
% 2.41/1.45 => ( ( Xphi @ Xy )
% 2.41/1.45 => ( Xy = Xx ) ) )
% 2.41/1.45 => ( ex1 @ A
% 2.41/1.45 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.41/1.45 ------------------------
% 2.41/1.47 % (1486)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_1200 for (2999ds/2Mi)
% 2.41/1.47 % (1486)Instruction limit reached!
% 2.41/1.47 % (1486)------------------------------
% 2.41/1.47 % (1486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.47 % (1486)Termination reason: Unknown
% 2.41/1.47 % (1486)Termination phase: shuffling
% 2.41/1.47
% 2.41/1.47 % (1486)Memory used [KB]: 1279
% 2.41/1.47 % (1486)Time elapsed: 0.002 s
% 2.41/1.47 % (1486)Instructions burned: 2 (million)
% 2.41/1.47 % (1486)------------------------------
% 2.41/1.47 % (1486)------------------------------
% 2.41/1.47 % (1483)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_1200 for (2999ds/4Mi)
% 2.41/1.47 % (1482)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1200 for (2999ds/183Mi)
% 2.41/1.48 % (1483)Instruction limit reached!
% 2.41/1.48 % (1483)------------------------------
% 2.41/1.48 % (1483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.48 % (1483)Termination reason: Unknown
% 2.41/1.48 % (1483)Termination phase: shuffling
% 2.41/1.48
% 2.41/1.48 % (1483)Memory used [KB]: 1279
% 2.41/1.48 % (1483)Time elapsed: 0.003 s
% 2.41/1.48 % (1483)Instructions burned: 6 (million)
% 2.41/1.48 % (1483)------------------------------
% 2.41/1.48 % (1483)------------------------------
% 2.41/1.48 % (1484)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_1200 for (2999ds/27Mi)
% 2.41/1.48 % (1485)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1200 for (2999ds/2Mi)
% 2.41/1.48 % (1487)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_1200 for (2999ds/275Mi)
% 2.41/1.48 % (1488)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1200 for (2999ds/18Mi)
% 2.41/1.48 % (1485)Instruction limit reached!
% 2.41/1.48 % (1485)------------------------------
% 2.41/1.48 % (1485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.48 % (1485)Termination reason: Unknown
% 2.41/1.48 % (1485)Termination phase: shuffling
% 2.41/1.48
% 2.41/1.48 % (1485)Memory used [KB]: 1279
% 2.41/1.48 % (1485)Time elapsed: 0.003 s
% 2.41/1.48 % (1485)Instructions burned: 3 (million)
% 2.41/1.48 % (1485)------------------------------
% 2.41/1.48 % (1485)------------------------------
% 2.41/1.48 % (1489)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_1200 for (2999ds/3Mi)
% 2.41/1.49 % (1489)Instruction limit reached!
% 2.41/1.49 % (1489)------------------------------
% 2.41/1.49 % (1489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.49 % (1489)Termination reason: Unknown
% 2.41/1.49 % (1489)Termination phase: shuffling
% 2.41/1.49
% 2.41/1.49 % (1489)Memory used [KB]: 1279
% 2.41/1.49 % (1489)Time elapsed: 0.002 s
% 2.41/1.49 % (1489)Instructions burned: 3 (million)
% 2.41/1.49 % (1489)------------------------------
% 2.41/1.49 % (1489)------------------------------
% 2.41/1.49 % (1490)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_1200 for (2999ds/37Mi)
% 2.41/1.49 % (1488)Instruction limit reached!
% 2.41/1.49 % (1488)------------------------------
% 2.41/1.49 % (1488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.49 % (1488)Termination reason: Unknown
% 2.41/1.49 % (1488)Termination phase: Property scanning
% 2.41/1.49
% 2.41/1.49 % (1488)Memory used [KB]: 1535
% 2.41/1.49 % (1488)Time elapsed: 0.013 s
% 2.41/1.49 % (1488)Instructions burned: 18 (million)
% 2.41/1.49 % (1488)------------------------------
% 2.41/1.49 % (1488)------------------------------
% 2.41/1.50 % (1492)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_1200 for (2999ds/3Mi)
% 2.52/1.50 % (1492)Instruction limit reached!
% 2.52/1.50 % (1492)------------------------------
% 2.52/1.50 % (1492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.50 % (1492)Termination reason: Unknown
% 2.52/1.50 % (1492)Termination phase: shuffling
% 2.52/1.50
% 2.52/1.50 % (1492)Memory used [KB]: 1279
% 2.52/1.50 % (1492)Time elapsed: 0.003 s
% 2.52/1.50 % (1492)Instructions burned: 6 (million)
% 2.52/1.50 % (1492)------------------------------
% 2.52/1.50 % (1492)------------------------------
% 2.52/1.50 % (1484)Instruction limit reached!
% 2.52/1.50 % (1484)------------------------------
% 2.52/1.50 % (1484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.50 % (1484)Termination reason: Unknown
% 2.52/1.50 % (1484)Termination phase: Property scanning
% 2.52/1.50
% 2.52/1.50 % (1484)Memory used [KB]: 1663
% 2.52/1.50 % (1484)Time elapsed: 0.017 s
% 2.52/1.50 % (1484)Instructions burned: 29 (million)
% 2.52/1.50 % (1484)------------------------------
% 2.52/1.50 % (1484)------------------------------
% 2.52/1.50 % (1490)Instruction limit reached!
% 2.52/1.50 % (1490)------------------------------
% 2.52/1.50 % (1490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.50 % (1490)Termination reason: Unknown
% 2.52/1.50 % (1490)Termination phase: Property scanning
% 2.52/1.50
% 2.52/1.50 % (1490)Memory used [KB]: 1791
% 2.52/1.50 % (1490)Time elapsed: 0.012 s
% 2.52/1.50 % (1490)Instructions burned: 39 (million)
% 2.52/1.50 % (1490)------------------------------
% 2.52/1.50 % (1490)------------------------------
% 2.52/1.50 % (1491)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_1200 for (2999ds/15Mi)
% 2.52/1.51 % (1494)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_1200 for (2999ds/7Mi)
% 2.52/1.51 % (1495)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_1200 for (2999ds/16Mi)
% 2.52/1.51 % (1494)Instruction limit reached!
% 2.52/1.51 % (1494)------------------------------
% 2.52/1.51 % (1494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.51 % (1494)Termination reason: Unknown
% 2.52/1.51 % (1494)Termination phase: shuffling
% 2.52/1.51
% 2.52/1.51 % (1494)Memory used [KB]: 1407
% 2.52/1.51 % (1494)Time elapsed: 0.003 s
% 2.52/1.51 % (1494)Instructions burned: 8 (million)
% 2.52/1.51 % (1494)------------------------------
% 2.52/1.51 % (1494)------------------------------
% 2.52/1.51 % (1491)Instruction limit reached!
% 2.52/1.51 % (1491)------------------------------
% 2.52/1.51 % (1491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.51 % (1491)Termination reason: Unknown
% 2.52/1.51 % (1491)Termination phase: Property scanning
% 2.52/1.51
% 2.52/1.51 % (1491)Memory used [KB]: 1535
% 2.52/1.51 % (1491)Time elapsed: 0.011 s
% 2.52/1.51 % (1491)Instructions burned: 15 (million)
% 2.52/1.51 % (1491)------------------------------
% 2.52/1.51 % (1491)------------------------------
% 2.52/1.51 % (1495)Instruction limit reached!
% 2.52/1.51 % (1495)------------------------------
% 2.52/1.51 % (1495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.51 % (1495)Termination reason: Unknown
% 2.52/1.51 % (1495)Termination phase: shuffling
% 2.52/1.51
% 2.52/1.51 % (1495)Memory used [KB]: 1663
% 2.52/1.51 % (1495)Time elapsed: 0.006 s
% 2.52/1.51 % (1495)Instructions burned: 19 (million)
% 2.52/1.51 % (1495)------------------------------
% 2.52/1.51 % (1495)------------------------------
% 2.52/1.51 % (1493)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_1200 for (2999ds/1041Mi)
% 2.52/1.51 % (1496)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_1200 for (2999ds/3Mi)
% 2.52/1.52 % (1496)Instruction limit reached!
% 2.52/1.52 % (1496)------------------------------
% 2.52/1.52 % (1496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.52 % (1496)Termination reason: Unknown
% 2.52/1.52 % (1496)Termination phase: shuffling
% 2.52/1.52
% 2.52/1.52 % (1496)Memory used [KB]: 1279
% 2.52/1.52 % (1496)Time elapsed: 0.004 s
% 2.52/1.52 % (1496)Instructions burned: 4 (million)
% 2.52/1.52 % (1496)------------------------------
% 2.52/1.52 % (1496)------------------------------
% 2.52/1.52 % (1497)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_1200 for (2999ds/3Mi)
% 2.52/1.52 % (1497)Instruction limit reached!
% 2.52/1.52 % (1497)------------------------------
% 2.52/1.52 % (1497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.52 % (1497)Termination reason: Unknown
% 2.52/1.52 % (1497)Termination phase: shuffling
% 2.52/1.52
% 2.52/1.52 % (1497)Memory used [KB]: 1279
% 2.52/1.52 % (1497)Time elapsed: 0.002 s
% 2.52/1.52 % (1497)Instructions burned: 3 (million)
% 2.52/1.52 % (1497)------------------------------
% 2.52/1.52 % (1497)------------------------------
% 2.52/1.52 % (1499)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_1200 for (2999ds/3Mi)
% 2.52/1.52 % (1499)Instruction limit reached!
% 2.52/1.52 % (1499)------------------------------
% 2.52/1.52 % (1499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.52 % (1499)Termination reason: Unknown
% 2.52/1.52 % (1499)Termination phase: shuffling
% 2.52/1.52
% 2.52/1.52 % (1499)Memory used [KB]: 1279
% 2.52/1.52 % (1499)Time elapsed: 0.002 s
% 2.52/1.52 % (1499)Instructions burned: 4 (million)
% 2.52/1.52 % (1499)------------------------------
% 2.52/1.52 % (1499)------------------------------
% 2.52/1.53 % (1501)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_1200 for (2999ds/18Mi)
% 2.52/1.53 % (1498)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_1200 for (2999ds/7Mi)
% 2.52/1.53 % (1482)Instruction limit reached!
% 2.52/1.53 % (1482)------------------------------
% 2.52/1.53 % (1482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.53 % (1482)Termination reason: Unknown
% 2.52/1.53 % (1482)Termination phase: Saturation
% 2.52/1.53
% 2.52/1.53 % (1482)Memory used [KB]: 7419
% 2.52/1.53 % (1482)Time elapsed: 0.056 s
% 2.52/1.53 % (1482)Instructions burned: 185 (million)
% 2.52/1.53 % (1482)------------------------------
% 2.52/1.53 % (1482)------------------------------
% 2.52/1.53 % (1502)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_1200 for (2999ds/710Mi)
% 2.52/1.53 % (1498)Instruction limit reached!
% 2.52/1.53 % (1498)------------------------------
% 2.52/1.53 % (1498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.53 % (1498)Termination reason: Unknown
% 2.52/1.53 % (1498)Termination phase: shuffling
% 2.52/1.53
% 2.52/1.53 % (1498)Memory used [KB]: 1407
% 2.52/1.53 % (1498)Time elapsed: 0.006 s
% 2.52/1.53 % (1498)Instructions burned: 8 (million)
% 2.52/1.53 % (1498)------------------------------
% 2.52/1.53 % (1498)------------------------------
% 2.52/1.53 % (1500)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_1200 for (2999ds/4Mi)
% 2.52/1.53 % (1501)Instruction limit reached!
% 2.52/1.53 % (1501)------------------------------
% 2.52/1.53 % (1501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.53 % (1501)Termination reason: Unknown
% 2.52/1.53 % (1501)Termination phase: shuffling
% 2.52/1.53
% 2.52/1.53 % (1501)Memory used [KB]: 1663
% 2.52/1.53 % (1501)Time elapsed: 0.007 s
% 2.52/1.53 % (1501)Instructions burned: 21 (million)
% 2.52/1.53 % (1501)------------------------------
% 2.52/1.53 % (1501)------------------------------
% 2.52/1.54 % (1500)Instruction limit reached!
% 2.52/1.54 % (1500)------------------------------
% 2.52/1.54 % (1500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.54 % (1500)Termination reason: Unknown
% 2.52/1.54 % (1500)Termination phase: shuffling
% 2.52/1.54
% 2.52/1.54 % (1500)Memory used [KB]: 1279
% 2.52/1.54 % (1500)Time elapsed: 0.004 s
% 2.52/1.54 % (1500)Instructions burned: 6 (million)
% 2.52/1.54 % (1500)------------------------------
% 2.52/1.54 % (1500)------------------------------
% 2.52/1.54 % (1503)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_1200 for (2999ds/6Mi)
% 2.52/1.54 % (1503)Instruction limit reached!
% 2.52/1.54 % (1503)------------------------------
% 2.52/1.54 % (1503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.54 % (1503)Termination reason: Unknown
% 2.52/1.54 % (1503)Termination phase: shuffling
% 2.52/1.54
% 2.52/1.54 % (1503)Memory used [KB]: 1407
% 2.52/1.54 % (1503)Time elapsed: 0.004 s
% 2.52/1.54 % (1503)Instructions burned: 7 (million)
% 2.52/1.54 % (1503)------------------------------
% 2.52/1.54 % (1503)------------------------------
% 2.52/1.54 % (1505)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_1200 for (2999ds/21Mi)
% 2.52/1.55 % (1506)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_1200 for (2999ds/5Mi)
% 2.52/1.55 % (1506)Instruction limit reached!
% 2.52/1.55 % (1506)------------------------------
% 2.52/1.55 % (1506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.55 % (1506)Termination reason: Unknown
% 2.52/1.55 % (1506)Termination phase: shuffling
% 2.52/1.55
% 2.52/1.55 % (1506)Memory used [KB]: 1407
% 2.52/1.55 % (1506)Time elapsed: 0.004 s
% 2.52/1.55 % (1506)Instructions burned: 8 (million)
% 2.52/1.55 % (1506)------------------------------
% 2.52/1.55 % (1506)------------------------------
% 2.52/1.55 % (1504)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_1200 for (2999ds/902Mi)
% 2.52/1.55 % (1505)Instruction limit reached!
% 2.52/1.55 % (1505)------------------------------
% 2.52/1.55 % (1505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.55 % (1505)Termination reason: Unknown
% 2.52/1.55 % (1505)Termination phase: shuffling
% 2.52/1.55
% 2.52/1.55 % (1505)Memory used [KB]: 1663
% 2.52/1.55 % (1505)Time elapsed: 0.007 s
% 2.52/1.55 % (1505)Instructions burned: 22 (million)
% 2.52/1.55 % (1505)------------------------------
% 2.52/1.55 % (1505)------------------------------
% 2.52/1.55 % (1507)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_1200 for (2999ds/6Mi)
% 2.52/1.55 % (1507)Instruction limit reached!
% 2.52/1.55 % (1507)------------------------------
% 2.52/1.55 % (1507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.55 % (1507)Termination reason: Unknown
% 2.52/1.55 % (1507)Termination phase: shuffling
% 2.52/1.55
% 2.52/1.55 % (1507)Memory used [KB]: 1407
% 2.52/1.55 % (1507)Time elapsed: 0.004 s
% 2.52/1.55 % (1507)Instructions burned: 8 (million)
% 2.52/1.55 % (1507)------------------------------
% 2.52/1.55 % (1507)------------------------------
% 2.52/1.56 % (1508)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_1200 for (2999ds/377Mi)
% 2.52/1.56 % (1509)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_1200 for (2999ds/779Mi)
% 2.52/1.56 % (1510)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_1200 for (2999ds/19Mi)
% 2.52/1.57 % (1510)Instruction limit reached!
% 2.52/1.57 % (1510)------------------------------
% 2.52/1.57 % (1510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.57 % (1510)Termination reason: Unknown
% 2.52/1.57 % (1510)Termination phase: shuffling
% 2.52/1.57
% 2.52/1.57 % (1510)Memory used [KB]: 1663
% 2.52/1.57 % (1510)Time elapsed: 0.007 s
% 2.52/1.57 % (1510)Instructions burned: 20 (million)
% 2.52/1.57 % (1510)------------------------------
% 2.52/1.57 % (1510)------------------------------
% 2.52/1.58 % (1511)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_1200 for (2998ds/879Mi)
% 2.52/1.62 % (1487)Instruction limit reached!
% 2.52/1.62 % (1487)------------------------------
% 2.52/1.62 % (1487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.62 % (1487)Termination reason: Unknown
% 2.52/1.62 % (1487)Termination phase: Saturation
% 2.52/1.62
% 2.52/1.62 % (1487)Memory used [KB]: 8187
% 2.52/1.62 % (1487)Time elapsed: 0.137 s
% 2.52/1.62 % (1487)Instructions burned: 277 (million)
% 2.52/1.62 % (1487)------------------------------
% 2.52/1.62 % (1487)------------------------------
% 2.52/1.63 % (1512)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_1200 for (2998ds/17Mi)
% 2.52/1.63 % (1512)Instruction limit reached!
% 2.52/1.63 % (1512)------------------------------
% 2.52/1.63 % (1512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.63 % (1512)Termination reason: Unknown
% 2.52/1.63 % (1512)Termination phase: shuffling
% 2.52/1.63
% 2.52/1.63 % (1512)Memory used [KB]: 1535
% 2.52/1.63 % (1512)Time elapsed: 0.006 s
% 2.52/1.63 % (1512)Instructions burned: 17 (million)
% 2.52/1.63 % (1512)------------------------------
% 2.52/1.63 % (1512)------------------------------
% 2.52/1.64 % (1513)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_1200 for (2998ds/3Mi)
% 2.52/1.64 % (1513)Instruction limit reached!
% 2.52/1.64 % (1513)------------------------------
% 2.52/1.64 % (1513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.64 % (1513)Termination reason: Unknown
% 2.52/1.64 % (1513)Termination phase: shuffling
% 2.52/1.64
% 2.52/1.64 % (1513)Memory used [KB]: 1279
% 2.52/1.64 % (1513)Time elapsed: 0.002 s
% 2.52/1.64 % (1513)Instructions burned: 4 (million)
% 2.52/1.64 % (1513)------------------------------
% 2.52/1.64 % (1513)------------------------------
% 2.52/1.65 % (1514)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_1200 for (2998ds/30Mi)
% 2.52/1.66 % (1514)Instruction limit reached!
% 2.52/1.66 % (1514)------------------------------
% 2.52/1.66 % (1514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.66 % (1514)Termination reason: Unknown
% 2.52/1.66 % (1514)Termination phase: Property scanning
% 2.52/1.66
% 2.52/1.66 % (1514)Memory used [KB]: 1791
% 2.52/1.66 % (1514)Time elapsed: 0.011 s
% 2.52/1.66 % (1514)Instructions burned: 32 (million)
% 2.52/1.66 % (1514)------------------------------
% 2.52/1.66 % (1514)------------------------------
% 2.52/1.67 % (1515)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_1200 for (2998ds/127Mi)
% 2.52/1.68 % (1508)Instruction limit reached!
% 2.52/1.68 % (1508)------------------------------
% 2.52/1.68 % (1508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.68 % (1508)Termination reason: Unknown
% 2.52/1.68 % (1508)Termination phase: Saturation
% 2.52/1.68
% 2.52/1.68 % (1508)Memory used [KB]: 7803
% 2.52/1.68 % (1508)Time elapsed: 0.122 s
% 2.52/1.68 % (1508)Instructions burned: 377 (million)
% 2.52/1.68 % (1508)------------------------------
% 2.52/1.68 % (1508)------------------------------
% 2.52/1.69 % (1516)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_1200 for (2997ds/100Mi)
% 2.52/1.71 % (1515)Instruction limit reached!
% 2.52/1.71 % (1515)------------------------------
% 2.52/1.71 % (1515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.71 % (1515)Termination reason: Unknown
% 2.52/1.71 % (1515)Termination phase: Saturation
% 2.52/1.71
% 2.52/1.71 % (1515)Memory used [KB]: 6908
% 2.52/1.71 % (1515)Time elapsed: 0.038 s
% 2.52/1.71 % (1515)Instructions burned: 128 (million)
% 2.52/1.71 % (1515)------------------------------
% 2.52/1.71 % (1515)------------------------------
% 2.52/1.72 % (1516)Instruction limit reached!
% 2.52/1.72 % (1516)------------------------------
% 2.52/1.72 % (1516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.72 % (1516)Termination reason: Unknown
% 2.52/1.72 % (1516)Termination phase: Saturation
% 2.52/1.72
% 2.52/1.72 % (1516)Memory used [KB]: 6652
% 2.52/1.72 % (1516)Time elapsed: 0.030 s
% 2.52/1.72 % (1516)Instructions burned: 102 (million)
% 2.52/1.72 % (1516)------------------------------
% 2.52/1.72 % (1516)------------------------------
% 2.52/1.72 % (1517)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_1200 for (2997ds/3Mi)
% 2.52/1.72 % (1517)Instruction limit reached!
% 2.52/1.72 % (1517)------------------------------
% 2.52/1.72 % (1517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.72 % (1517)Termination reason: Unknown
% 2.52/1.72 % (1517)Termination phase: shuffling
% 2.52/1.72
% 2.52/1.72 % (1517)Memory used [KB]: 1279
% 2.52/1.72 % (1517)Time elapsed: 0.002 s
% 2.52/1.72 % (1517)Instructions burned: 4 (million)
% 2.52/1.72 % (1517)------------------------------
% 2.52/1.72 % (1517)------------------------------
% 2.52/1.73 % (1518)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_1200 for (2997ds/20Mi)
% 2.52/1.73 % (1519)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_1200 for (2997ds/86Mi)
% 2.52/1.74 % (1518)Instruction limit reached!
% 2.52/1.74 % (1518)------------------------------
% 2.52/1.74 % (1518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.74 % (1518)Termination reason: Unknown
% 2.52/1.74 % (1518)Termination phase: SInE selection
% 2.52/1.74
% 2.52/1.74 % (1518)Memory used [KB]: 1535
% 2.52/1.74 % (1518)Time elapsed: 0.008 s
% 2.52/1.74 % (1518)Instructions burned: 23 (million)
% 2.52/1.74 % (1518)------------------------------
% 2.52/1.74 % (1518)------------------------------
% 2.52/1.74 % (1509)Instruction limit reached!
% 2.52/1.74 % (1509)------------------------------
% 2.52/1.74 % (1509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.74 % (1509)Termination reason: Unknown
% 2.52/1.74 % (1509)Termination phase: Saturation
% 2.52/1.74
% 2.52/1.74 % (1509)Memory used [KB]: 6652
% 2.52/1.74 % (1509)Time elapsed: 0.183 s
% 2.52/1.74 % (1509)Instructions burned: 782 (million)
% 2.52/1.74 % (1509)------------------------------
% 2.52/1.74 % (1509)------------------------------
% 2.52/1.75 % (1520)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_1200 for (2997ds/107Mi)
% 2.52/1.75 % (1521)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_1200 for (2997ds/39Mi)
% 2.52/1.76 % (1519)Instruction limit reached!
% 2.52/1.76 % (1519)------------------------------
% 2.52/1.76 % (1519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.76 % (1519)Termination reason: Unknown
% 2.52/1.76 % (1519)Termination phase: Saturation
% 2.52/1.76
% 2.52/1.76 % (1519)Memory used [KB]: 6524
% 2.52/1.76 % (1519)Time elapsed: 0.026 s
% 2.52/1.76 % (1519)Instructions burned: 87 (million)
% 2.52/1.76 % (1519)------------------------------
% 2.52/1.76 % (1519)------------------------------
% 2.52/1.76 % (1502)Instruction limit reached!
% 2.52/1.76 % (1502)------------------------------
% 2.52/1.76 % (1502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.76 % (1502)Termination reason: Unknown
% 2.52/1.76 % (1502)Termination phase: Saturation
% 2.52/1.76
% 2.52/1.76 % (1502)Memory used [KB]: 9466
% 2.52/1.76 % (1502)Time elapsed: 0.226 s
% 2.52/1.76 % (1502)Instructions burned: 711 (million)
% 2.52/1.76 % (1502)------------------------------
% 2.52/1.76 % (1502)------------------------------
% 2.52/1.76 % (1521)Instruction limit reached!
% 2.52/1.76 % (1521)------------------------------
% 2.52/1.76 % (1521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.76 % (1521)Termination reason: Unknown
% 2.52/1.76 % (1521)Termination phase: Property scanning
% 2.52/1.76
% 2.52/1.76 % (1521)Memory used [KB]: 1791
% 2.52/1.76 % (1521)Time elapsed: 0.012 s
% 2.52/1.76 % (1521)Instructions burned: 40 (million)
% 2.52/1.76 % (1521)------------------------------
% 2.52/1.76 % (1521)------------------------------
% 2.52/1.77 % (1523)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_1200 for (2997ds/46Mi)
% 2.52/1.77 % (1522)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_1200 for (2997ds/448Mi)
% 2.52/1.77 % (1524)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_1200 for (2997ds/98Mi)
% 2.52/1.78 % (1520)Instruction limit reached!
% 2.52/1.78 % (1520)------------------------------
% 2.52/1.78 % (1520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.78 % (1520)Termination reason: Unknown
% 2.52/1.78 % (1520)Termination phase: Saturation
% 2.52/1.78
% 2.52/1.78 % (1520)Memory used [KB]: 6652
% 2.52/1.78 % (1520)Time elapsed: 0.032 s
% 2.52/1.78 % (1520)Instructions burned: 107 (million)
% 2.52/1.78 % (1520)------------------------------
% 2.52/1.78 % (1520)------------------------------
% 2.52/1.78 % (1523)Instruction limit reached!
% 2.52/1.78 % (1523)------------------------------
% 2.52/1.78 % (1523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.78 % (1523)Termination reason: Unknown
% 2.52/1.78 % (1523)Termination phase: SInE selection
% 2.52/1.78
% 2.52/1.78 % (1523)Memory used [KB]: 1791
% 2.52/1.78 % (1523)Time elapsed: 0.013 s
% 2.52/1.78 % (1523)Instructions burned: 46 (million)
% 2.52/1.78 % (1523)------------------------------
% 2.52/1.78 % (1523)------------------------------
% 2.52/1.79 % (1525)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_1200 for (2996ds/507Mi)
% 2.52/1.79 % (1526)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_1200 for (2996ds/149Mi)
% 2.52/1.80 % (1524)Instruction limit reached!
% 2.52/1.80 % (1524)------------------------------
% 2.52/1.80 % (1524)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.80 % (1524)Termination reason: Unknown
% 2.52/1.80 % (1524)Termination phase: Saturation
% 2.52/1.80
% 2.52/1.80 % (1524)Memory used [KB]: 2046
% 2.52/1.80 % (1524)Time elapsed: 0.026 s
% 2.52/1.80 % (1524)Instructions burned: 100 (million)
% 2.52/1.80 % (1524)------------------------------
% 2.52/1.80 % (1524)------------------------------
% 2.52/1.80 % (1493)Instruction limit reached!
% 2.52/1.80 % (1493)------------------------------
% 2.52/1.80 % (1493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.80 % (1493)Termination reason: Unknown
% 2.52/1.80 % (1493)Termination phase: Saturation
% 2.52/1.80
% 2.52/1.80 % (1493)Memory used [KB]: 9466
% 2.52/1.80 % (1493)Time elapsed: 0.295 s
% 2.52/1.80 % (1493)Instructions burned: 1043 (million)
% 2.52/1.80 % (1493)------------------------------
% 2.52/1.80 % (1493)------------------------------
% 2.52/1.80 % (1527)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_1200 for (2996ds/39Mi)
% 2.52/1.82 % (1528)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_1200 for (2996ds/6Mi)
% 2.52/1.82 % (1527)Instruction limit reached!
% 2.52/1.82 % (1527)------------------------------
% 2.52/1.82 % (1527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.82 % (1527)Termination reason: Unknown
% 2.52/1.82 % (1527)Termination phase: Property scanning
% 2.52/1.82
% 2.52/1.82 % (1527)Memory used [KB]: 1918
% 2.52/1.82 % (1527)Time elapsed: 0.012 s
% 2.52/1.82 % (1527)Instructions burned: 42 (million)
% 2.52/1.82 % (1527)------------------------------
% 2.52/1.82 % (1527)------------------------------
% 2.52/1.82 % (1528)Instruction limit reached!
% 2.52/1.82 % (1528)------------------------------
% 2.52/1.82 % (1528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.82 % (1528)Termination reason: Unknown
% 2.52/1.82 % (1528)Termination phase: shuffling
% 2.52/1.82
% 2.52/1.82 % (1528)Memory used [KB]: 1407
% 2.52/1.82 % (1528)Time elapsed: 0.003 s
% 2.52/1.82 % (1528)Instructions burned: 7 (million)
% 2.52/1.82 % (1528)------------------------------
% 2.52/1.82 % (1528)------------------------------
% 2.52/1.83 % (1529)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_1200 for (2996ds/1087Mi)
% 2.52/1.83 % (1530)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_1200 for (2996ds/47Mi)
% 2.52/1.83 % (1526)Instruction limit reached!
% 2.52/1.83 % (1526)------------------------------
% 2.52/1.83 % (1526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.83 % (1526)Termination reason: Unknown
% 2.52/1.83 % (1526)Termination phase: Saturation
% 2.52/1.83
% 2.52/1.83 % (1526)Memory used [KB]: 7036
% 2.52/1.83 % (1526)Time elapsed: 0.066 s
% 2.52/1.83 % (1526)Instructions burned: 151 (million)
% 2.52/1.83 % (1526)------------------------------
% 2.52/1.83 % (1526)------------------------------
% 2.52/1.84 % (1531)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_1200 for (2996ds/44Mi)
% 2.52/1.84 % (1530)Instruction limit reached!
% 2.52/1.84 % (1530)------------------------------
% 2.52/1.84 % (1530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.84 % (1530)Termination reason: Unknown
% 2.52/1.84 % (1530)Termination phase: Property scanning
% 2.52/1.84
% 2.52/1.84 % (1530)Memory used [KB]: 1918
% 2.52/1.84 % (1530)Time elapsed: 0.015 s
% 2.52/1.84 % (1530)Instructions burned: 47 (million)
% 2.52/1.84 % (1530)------------------------------
% 2.52/1.84 % (1530)------------------------------
% 2.52/1.84 % (1504)Instruction limit reached!
% 2.52/1.84 % (1504)------------------------------
% 2.52/1.84 % (1504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.84 % (1504)Termination reason: Unknown
% 2.52/1.84 % (1504)Termination phase: Saturation
% 2.52/1.84
% 2.52/1.84 % (1504)Memory used [KB]: 10234
% 2.52/1.84 % (1504)Time elapsed: 0.295 s
% 2.52/1.84 % (1504)Instructions burned: 903 (million)
% 2.52/1.84 % (1504)------------------------------
% 2.52/1.84 % (1504)------------------------------
% 2.52/1.85 % (1532)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_1200 for (2996ds/432Mi)
% 2.52/1.85 % (1511)Instruction limit reached!
% 2.52/1.85 % (1511)------------------------------
% 2.52/1.85 % (1511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.85 % (1511)Termination reason: Unknown
% 2.52/1.85 % (1511)Termination phase: Saturation
% 2.52/1.85
% 2.52/1.85 % (1511)Memory used [KB]: 8315
% 2.52/1.85 % (1511)Time elapsed: 0.273 s
% 2.52/1.85 % (1511)Instructions burned: 880 (million)
% 2.52/1.85 % (1511)------------------------------
% 2.52/1.85 % (1511)------------------------------
% 2.52/1.85 % (1531)Instruction limit reached!
% 2.52/1.85 % (1531)------------------------------
% 2.52/1.85 % (1531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.85 % (1531)Termination reason: Unknown
% 2.52/1.85 % (1531)Termination phase: SInE selection
% 2.52/1.85
% 2.52/1.85 % (1531)Memory used [KB]: 1791
% 2.52/1.85 % (1531)Time elapsed: 0.013 s
% 2.52/1.85 % (1531)Instructions burned: 47 (million)
% 2.52/1.85 % (1531)------------------------------
% 2.52/1.85 % (1531)------------------------------
% 2.52/1.85 % (1533)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_1200 for (2996ds/62Mi)
% 2.52/1.86 % (1534)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_1200 for (2996ds/31Mi)
% 2.52/1.86 % (1535)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_1200 for (2996ds/96Mi)
% 2.52/1.87 % (1533)Instruction limit reached!
% 2.52/1.87 % (1533)------------------------------
% 2.52/1.87 % (1533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.87 % (1533)Termination reason: Unknown
% 2.52/1.87 % (1533)Termination phase: Property scanning
% 2.52/1.87
% 2.52/1.87 % (1533)Memory used [KB]: 1791
% 2.52/1.87 % (1533)Time elapsed: 0.018 s
% 2.52/1.87 % (1533)Instructions burned: 63 (million)
% 2.52/1.87 % (1533)------------------------------
% 2.52/1.87 % (1533)------------------------------
% 2.52/1.87 % (1534)Instruction limit reached!
% 2.52/1.87 % (1534)------------------------------
% 2.52/1.87 % (1534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.87 % (1534)Termination reason: Unknown
% 2.52/1.87 % (1534)Termination phase: Property scanning
% 2.52/1.87
% 2.52/1.87 % (1534)Memory used [KB]: 1791
% 2.52/1.87 % (1534)Time elapsed: 0.010 s
% 2.52/1.87 % (1534)Instructions burned: 31 (million)
% 2.52/1.87 % (1534)------------------------------
% 2.52/1.87 % (1534)------------------------------
% 2.52/1.88 % (1537)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_1200 for (2995ds/71Mi)
% 2.52/1.88 % (1536)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_1200 for (2995ds/453Mi)
% 2.52/1.88 % (1522)Instruction limit reached!
% 2.52/1.88 % (1522)------------------------------
% 2.52/1.88 % (1522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.88 % (1522)Termination reason: Unknown
% 2.52/1.88 % (1522)Termination phase: Saturation
% 2.52/1.88
% 2.52/1.88 % (1522)Memory used [KB]: 6652
% 2.52/1.88 % (1522)Time elapsed: 0.115 s
% 2.52/1.88 % (1522)Instructions burned: 449 (million)
% 2.52/1.88 % (1522)------------------------------
% 2.52/1.88 % (1522)------------------------------
% 2.52/1.89 % (1535)Instruction limit reached!
% 2.52/1.89 % (1535)------------------------------
% 2.52/1.89 % (1535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.89 % (1535)Termination reason: Unknown
% 2.52/1.89 % (1535)Termination phase: Saturation
% 2.52/1.89
% 2.52/1.89 % (1535)Memory used [KB]: 6780
% 2.52/1.89 % (1535)Time elapsed: 0.027 s
% 2.52/1.89 % (1535)Instructions burned: 98 (million)
% 2.52/1.89 % (1535)------------------------------
% 2.52/1.89 % (1535)------------------------------
% 2.52/1.89 % (1538)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_1200 for (2995ds/83Mi)
% 2.52/1.90 % (1539)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_1200 for (2995ds/11Mi)
% 2.52/1.90 % (1537)Instruction limit reached!
% 2.52/1.90 % (1537)------------------------------
% 2.52/1.90 % (1537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.90 % (1537)Termination reason: Unknown
% 2.52/1.90 % (1537)Termination phase: Property scanning
% 2.52/1.90
% 2.52/1.90 % (1537)Memory used [KB]: 1918
% 2.52/1.90 % (1537)Time elapsed: 0.019 s
% 2.52/1.90 % (1537)Instructions burned: 71 (million)
% 2.52/1.90 % (1537)------------------------------
% 2.52/1.90 % (1537)------------------------------
% 2.52/1.90 % (1539)Instruction limit reached!
% 2.52/1.90 % (1539)------------------------------
% 2.52/1.90 % (1539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.90 % (1539)Termination reason: Unknown
% 2.52/1.90 % (1539)Termination phase: shuffling
% 2.52/1.90
% 2.52/1.90 % (1539)Memory used [KB]: 1407
% 2.52/1.90 % (1539)Time elapsed: 0.004 s
% 2.52/1.90 % (1539)Instructions burned: 12 (million)
% 2.52/1.90 % (1539)------------------------------
% 2.52/1.90 % (1539)------------------------------
% 2.52/1.91 % (1540)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_1200 for (2995ds/41Mi)
% 2.52/1.91 % (1541)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_1200 for (2995ds/6Mi)
% 2.52/1.91 % (1541)Instruction limit reached!
% 2.52/1.91 % (1541)------------------------------
% 2.52/1.91 % (1541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.91 % (1541)Termination reason: Unknown
% 2.52/1.91 % (1541)Termination phase: shuffling
% 2.52/1.91
% 2.52/1.91 % (1541)Memory used [KB]: 1407
% 2.52/1.91 % (1541)Time elapsed: 0.003 s
% 2.52/1.91 % (1541)Instructions burned: 7 (million)
% 2.52/1.91 % (1541)------------------------------
% 2.52/1.91 % (1541)------------------------------
% 2.52/1.91 % (1538)Instruction limit reached!
% 2.52/1.91 % (1538)------------------------------
% 2.52/1.91 % (1538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.91 % (1538)Termination reason: Unknown
% 2.52/1.91 % (1538)Termination phase: Property scanning
% 2.52/1.91
% 2.52/1.91 % (1538)Memory used [KB]: 1918
% 2.52/1.91 % (1538)Time elapsed: 0.025 s
% 2.52/1.91 % (1538)Instructions burned: 85 (million)
% 2.52/1.91 % (1538)------------------------------
% 2.52/1.91 % (1538)------------------------------
% 2.52/1.92 % (1540)Instruction limit reached!
% 2.52/1.92 % (1540)------------------------------
% 2.52/1.92 % (1540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.92 % (1540)Termination reason: Unknown
% 2.52/1.92 % (1540)Termination phase: Property scanning
% 2.52/1.92
% 2.52/1.92 % (1540)Memory used [KB]: 1791
% 2.52/1.92 % (1540)Time elapsed: 0.012 s
% 2.52/1.92 % (1540)Instructions burned: 42 (million)
% 2.52/1.92 % (1540)------------------------------
% 2.52/1.92 % (1540)------------------------------
% 2.52/1.92 % (1542)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_1200 for (2995ds/150Mi)
% 2.52/1.92 % (1543)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_1200 for (2995ds/343Mi)
% 2.52/1.93 % (1544)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_1200 for (2995ds/109Mi)
% 2.52/1.94 % (1525)Instruction limit reached!
% 2.52/1.94 % (1525)------------------------------
% 2.52/1.94 % (1525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.94 % (1525)Termination reason: Unknown
% 2.52/1.94 % (1525)Termination phase: Saturation
% 2.52/1.94
% 2.52/1.94 % (1525)Memory used [KB]: 7291
% 2.52/1.94 % (1525)Time elapsed: 0.181 s
% 2.52/1.94 % (1525)Instructions burned: 509 (million)
% 2.52/1.94 % (1525)------------------------------
% 2.52/1.94 % (1525)------------------------------
% 2.52/1.95 % (1545)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_1200 for (2995ds/253Mi)
% 2.52/1.96 % (1544)Instruction limit reached!
% 2.52/1.96 % (1544)------------------------------
% 2.52/1.96 % (1544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.96 % (1544)Termination reason: Unknown
% 2.52/1.96 % (1544)Termination phase: Saturation
% 2.52/1.96
% 2.52/1.96 % (1544)Memory used [KB]: 6652
% 2.52/1.96 % (1544)Time elapsed: 0.031 s
% 2.52/1.96 % (1544)Instructions burned: 112 (million)
% 2.52/1.96 % (1544)------------------------------
% 2.52/1.96 % (1544)------------------------------
% 2.52/1.96 % (1532)Instruction limit reached!
% 2.52/1.96 % (1532)------------------------------
% 2.52/1.96 % (1532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.96 % (1532)Termination reason: Unknown
% 2.52/1.96 % (1532)Termination phase: Saturation
% 2.52/1.96
% 2.52/1.96 % (1532)Memory used [KB]: 3070
% 2.52/1.96 % (1532)Time elapsed: 0.114 s
% 2.52/1.96 % (1532)Instructions burned: 434 (million)
% 2.52/1.96 % (1532)------------------------------
% 2.52/1.96 % (1532)------------------------------
% 2.52/1.96 % (1542)Instruction limit reached!
% 2.52/1.96 % (1542)------------------------------
% 2.52/1.96 % (1542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.96 % (1542)Termination reason: Unknown
% 2.52/1.96 % (1542)Termination phase: Saturation
% 2.52/1.96
% 2.52/1.96 % (1542)Memory used [KB]: 7803
% 2.52/1.96 % (1542)Time elapsed: 0.046 s
% 2.52/1.96 % (1542)Instructions burned: 150 (million)
% 2.52/1.96 % (1542)------------------------------
% 2.52/1.96 % (1542)------------------------------
% 2.52/1.97 % (1546)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_1200 for (2995ds/140Mi)
% 2.52/1.97 % (1547)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_1200 for (2994ds/614Mi)
% 2.52/1.97 % (1548)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_1200 for (2994ds/202Mi)
% 2.52/1.99 % (1536)Instruction limit reached!
% 2.52/1.99 % (1536)------------------------------
% 2.52/1.99 % (1536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/1.99 % (1536)Termination reason: Unknown
% 2.52/1.99 % (1536)Termination phase: Saturation
% 2.52/1.99
% 2.52/1.99 % (1536)Memory used [KB]: 6652
% 2.52/1.99 % (1536)Time elapsed: 0.112 s
% 2.52/1.99 % (1536)Instructions burned: 453 (million)
% 2.52/1.99 % (1536)------------------------------
% 2.52/1.99 % (1536)------------------------------
% 2.52/2.00 % (1549)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_1200 for (2994ds/339Mi)
% 2.52/2.00 % (1546)Instruction limit reached!
% 2.52/2.00 % (1546)------------------------------
% 2.52/2.00 % (1546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.52/2.00 % (1546)Termination reason: Unknown
% 2.52/2.00 % (1546)Termination phase: Saturation
% 2.52/2.00
% 2.52/2.00 % (1546)Memory used [KB]: 6524
% 2.52/2.00 % (1546)Time elapsed: 0.039 s
% 2.52/2.00 % (1546)Instructions burned: 142 (million)
% 2.52/2.00 % (1546)------------------------------
% 2.52/2.00 % (1546)------------------------------
% 6.28/2.01 % (1550)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_1200 for (2994ds/283Mi)
% 6.28/2.02 % (1543)Instruction limit reached!
% 6.28/2.02 % (1543)------------------------------
% 6.28/2.02 % (1543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.02 % (1543)Termination reason: Unknown
% 6.28/2.02 % (1543)Termination phase: Saturation
% 6.28/2.02
% 6.28/2.02 % (1543)Memory used [KB]: 7931
% 6.28/2.02 % (1543)Time elapsed: 0.102 s
% 6.28/2.02 % (1543)Instructions burned: 343 (million)
% 6.28/2.02 % (1543)------------------------------
% 6.28/2.02 % (1543)------------------------------
% 6.28/2.03 % (1545)Instruction limit reached!
% 6.28/2.03 % (1545)------------------------------
% 6.28/2.03 % (1545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.03 % (1545)Termination reason: Unknown
% 6.28/2.03 % (1545)Termination phase: Saturation
% 6.28/2.03
% 6.28/2.03 % (1545)Memory used [KB]: 8187
% 6.28/2.03 % (1545)Time elapsed: 0.077 s
% 6.28/2.03 % (1545)Instructions burned: 255 (million)
% 6.28/2.03 % (1545)------------------------------
% 6.28/2.03 % (1545)------------------------------
% 6.28/2.03 % (1551)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_1200 for (2994ds/134Mi)
% 6.28/2.04 % (1548)Instruction limit reached!
% 6.28/2.04 % (1548)------------------------------
% 6.28/2.04 % (1548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.04 % (1548)Termination reason: Unknown
% 6.28/2.04 % (1548)Termination phase: Saturation
% 6.28/2.04
% 6.28/2.04 % (1548)Memory used [KB]: 8571
% 6.28/2.04 % (1548)Time elapsed: 0.062 s
% 6.28/2.04 % (1548)Instructions burned: 204 (million)
% 6.28/2.04 % (1548)------------------------------
% 6.28/2.04 % (1548)------------------------------
% 6.28/2.04 % (1552)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_1200 for (2994ds/298Mi)
% 6.28/2.05 % (1553)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_1200 for (2994ds/192Mi)
% 6.28/2.07 % (1551)Instruction limit reached!
% 6.28/2.07 % (1551)------------------------------
% 6.28/2.07 % (1551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.07 % (1551)Termination reason: Unknown
% 6.28/2.07 % (1551)Termination phase: Saturation
% 6.28/2.07
% 6.28/2.07 % (1551)Memory used [KB]: 6908
% 6.28/2.07 % (1551)Time elapsed: 0.037 s
% 6.28/2.07 % (1551)Instructions burned: 136 (million)
% 6.28/2.07 % (1551)------------------------------
% 6.28/2.07 % (1551)------------------------------
% 6.28/2.08 % (1554)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_1200 for (2993ds/258Mi)
% 6.28/2.08 % (1550)Instruction limit reached!
% 6.28/2.08 % (1550)------------------------------
% 6.28/2.08 % (1550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.08 % (1550)Termination reason: Unknown
% 6.28/2.08 % (1550)Termination phase: Saturation
% 6.28/2.08
% 6.28/2.08 % (1550)Memory used [KB]: 9083
% 6.28/2.08 % (1550)Time elapsed: 0.072 s
% 6.28/2.08 % (1550)Instructions burned: 286 (million)
% 6.28/2.08 % (1550)------------------------------
% 6.28/2.08 % (1550)------------------------------
% 6.28/2.09 % (1555)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_1200 for (2993ds/90Mi)
% 6.28/2.10 % (1553)Instruction limit reached!
% 6.28/2.10 % (1553)------------------------------
% 6.28/2.10 % (1553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.10 % (1553)Termination reason: Unknown
% 6.28/2.10 % (1553)Termination phase: Saturation
% 6.28/2.10
% 6.28/2.10 % (1553)Memory used [KB]: 7419
% 6.28/2.10 % (1553)Time elapsed: 0.054 s
% 6.28/2.10 % (1553)Instructions burned: 192 (million)
% 6.28/2.10 % (1553)------------------------------
% 6.28/2.10 % (1553)------------------------------
% 6.28/2.10 % (1549)Instruction limit reached!
% 6.28/2.10 % (1549)------------------------------
% 6.28/2.10 % (1549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.10 % (1549)Termination reason: Unknown
% 6.28/2.10 % (1549)Termination phase: Saturation
% 6.28/2.10
% 6.28/2.10 % (1549)Memory used [KB]: 7803
% 6.28/2.10 % (1549)Time elapsed: 0.101 s
% 6.28/2.10 % (1549)Instructions burned: 339 (million)
% 6.28/2.10 % (1549)------------------------------
% 6.28/2.10 % (1549)------------------------------
% 6.28/2.11 % (1556)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_1200 for (2993ds/231Mi)
% 6.28/2.11 % (1557)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_1200 for (2993ds/458Mi)
% 6.88/2.11 % (1552)Instruction limit reached!
% 6.88/2.11 % (1552)------------------------------
% 6.88/2.11 % (1552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.88/2.11 % (1552)Termination reason: Unknown
% 6.88/2.11 % (1552)Termination phase: Saturation
% 6.88/2.11
% 6.88/2.11 % (1552)Memory used [KB]: 6524
% 6.88/2.11 % (1552)Time elapsed: 0.076 s
% 6.88/2.11 % (1552)Instructions burned: 299 (million)
% 6.88/2.11 % (1552)------------------------------
% 6.88/2.11 % (1552)------------------------------
% 6.88/2.12 % (1555)Instruction limit reached!
% 6.88/2.12 % (1555)------------------------------
% 6.88/2.12 % (1555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.88/2.12 % (1555)Termination reason: Unknown
% 6.88/2.12 % (1555)Termination phase: Saturation
% 6.88/2.12
% 6.88/2.12 % (1555)Memory used [KB]: 6908
% 6.88/2.12 % (1555)Time elapsed: 0.025 s
% 6.88/2.12 % (1555)Instructions burned: 91 (million)
% 6.88/2.12 % (1555)------------------------------
% 6.88/2.12 % (1555)------------------------------
% 6.88/2.12 % (1558)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_1200 for (2993ds/31Mi)
% 6.88/2.13 % (1559)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_1200 for (2993ds/297Mi)
% 6.88/2.13 % (1558)Instruction limit reached!
% 6.88/2.13 % (1558)------------------------------
% 6.88/2.13 % (1558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.88/2.13 % (1558)Termination reason: Unknown
% 6.88/2.13 % (1558)Termination phase: Property scanning
% 6.88/2.13
% 6.88/2.13 % (1558)Memory used [KB]: 1791
% 6.88/2.13 % (1558)Time elapsed: 0.010 s
% 6.88/2.13 % (1558)Instructions burned: 31 (million)
% 6.88/2.13 % (1558)------------------------------
% 6.88/2.13 % (1558)------------------------------
% 6.88/2.14 % (1560)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_1200 for (2993ds/987Mi)
% 6.88/2.15 % (1554)Instruction limit reached!
% 6.88/2.15 % (1554)------------------------------
% 6.88/2.15 % (1554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.88/2.15 % (1554)Termination reason: Unknown
% 6.88/2.15 % (1554)Termination phase: Saturation
% 6.88/2.15
% 6.88/2.15 % (1554)Memory used [KB]: 7547
% 6.88/2.15 % (1554)Time elapsed: 0.075 s
% 6.88/2.15 % (1554)Instructions burned: 259 (million)
% 6.88/2.15 % (1554)------------------------------
% 6.88/2.15 % (1554)------------------------------
% 6.88/2.16 % (1561)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_1200 for (2993ds/182Mi)
% 6.88/2.17 % (1529)Instruction limit reached!
% 6.88/2.17 % (1529)------------------------------
% 6.88/2.17 % (1529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.88/2.17 % (1529)Termination reason: Unknown
% 6.88/2.17 % (1529)Termination phase: Saturation
% 6.88/2.17
% 6.88/2.17 % (1529)Memory used [KB]: 10106
% 6.88/2.17 % (1529)Time elapsed: 0.373 s
% 6.88/2.17 % (1529)Instructions burned: 1088 (million)
% 6.88/2.17 % (1529)------------------------------
% 6.88/2.17 % (1529)------------------------------
% 6.88/2.17 % (1556)Instruction limit reached!
% 6.88/2.17 % (1556)------------------------------
% 6.88/2.17 % (1556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.88/2.17 % (1556)Termination reason: Unknown
% 6.88/2.17 % (1556)Termination phase: Saturation
% 6.88/2.17
% 6.88/2.17 % (1556)Memory used [KB]: 10746
% 6.88/2.17 % (1556)Time elapsed: 0.067 s
% 6.88/2.17 % (1556)Instructions burned: 234 (million)
% 6.88/2.17 % (1556)------------------------------
% 6.88/2.17 % (1556)------------------------------
% 6.88/2.18 % (1562)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_1200 for (2992ds/182Mi)
% 6.88/2.18 % (1563)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_1200 for (2992ds/154Mi)
% 7.31/2.20 % (1559)Instruction limit reached!
% 7.31/2.20 % (1559)------------------------------
% 7.31/2.20 % (1559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.20 % (1559)Termination reason: Unknown
% 7.31/2.20 % (1559)Termination phase: Saturation
% 7.31/2.20
% 7.31/2.20 % (1559)Memory used [KB]: 7931
% 7.31/2.20 % (1559)Time elapsed: 0.075 s
% 7.31/2.20 % (1559)Instructions burned: 300 (million)
% 7.31/2.20 % (1559)------------------------------
% 7.31/2.20 % (1559)------------------------------
% 7.31/2.21 % (1564)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_1200 for (2992ds/79Mi)
% 7.31/2.21 % (1561)Instruction limit reached!
% 7.31/2.21 % (1561)------------------------------
% 7.31/2.21 % (1561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.21 % (1561)Termination reason: Unknown
% 7.31/2.21 % (1561)Termination phase: Saturation
% 7.31/2.21
% 7.31/2.21 % (1561)Memory used [KB]: 7419
% 7.31/2.21 % (1561)Time elapsed: 0.051 s
% 7.31/2.21 % (1561)Instructions burned: 184 (million)
% 7.31/2.21 % (1561)------------------------------
% 7.31/2.21 % (1561)------------------------------
% 7.31/2.22 % (1547)Instruction limit reached!
% 7.31/2.22 % (1547)------------------------------
% 7.31/2.22 % (1547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.22 % (1547)Termination reason: Unknown
% 7.31/2.22 % (1547)Termination phase: Saturation
% 7.31/2.22
% 7.31/2.22 % (1547)Memory used [KB]: 8315
% 7.31/2.22 % (1547)Time elapsed: 0.245 s
% 7.31/2.22 % (1547)Instructions burned: 615 (million)
% 7.31/2.22 % (1547)------------------------------
% 7.31/2.22 % (1547)------------------------------
% 7.31/2.22 % (1565)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_1200 for (2992ds/216Mi)
% 7.31/2.22 % (1563)Instruction limit reached!
% 7.31/2.22 % (1563)------------------------------
% 7.31/2.22 % (1563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.22 % (1563)Termination reason: Unknown
% 7.31/2.22 % (1563)Termination phase: Saturation
% 7.31/2.22
% 7.31/2.22 % (1563)Memory used [KB]: 6524
% 7.31/2.22 % (1563)Time elapsed: 0.040 s
% 7.31/2.22 % (1563)Instructions burned: 156 (million)
% 7.31/2.22 % (1563)------------------------------
% 7.31/2.22 % (1563)------------------------------
% 7.31/2.23 % (1566)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_1200 for (2992ds/114Mi)
% 7.31/2.23 % (1567)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_1200 for (2992ds/922Mi)
% 7.31/2.23 % (1564)Instruction limit reached!
% 7.31/2.23 % (1564)------------------------------
% 7.31/2.23 % (1564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.23 % (1564)Termination reason: Unknown
% 7.31/2.23 % (1564)Termination phase: Saturation
% 7.31/2.23
% 7.31/2.23 % (1564)Memory used [KB]: 6396
% 7.31/2.23 % (1564)Time elapsed: 0.022 s
% 7.31/2.23 % (1564)Instructions burned: 80 (million)
% 7.31/2.23 % (1564)------------------------------
% 7.31/2.23 % (1564)------------------------------
% 7.31/2.24 % (1562)Instruction limit reached!
% 7.31/2.24 % (1562)------------------------------
% 7.31/2.24 % (1562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.24 % (1562)Termination reason: Unknown
% 7.31/2.24 % (1562)Termination phase: Saturation
% 7.31/2.24
% 7.31/2.24 % (1562)Memory used [KB]: 9466
% 7.31/2.24 % (1562)Time elapsed: 0.077 s
% 7.31/2.24 % (1562)Instructions burned: 183 (million)
% 7.31/2.24 % (1562)------------------------------
% 7.31/2.24 % (1562)------------------------------
% 7.31/2.24 % (1568)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_1200 for (2992ds/182Mi)
% 7.31/2.24 % (1557)Instruction limit reached!
% 7.31/2.24 % (1557)------------------------------
% 7.31/2.24 % (1557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.24 % (1557)Termination reason: Unknown
% 7.31/2.24 % (1557)Termination phase: Saturation
% 7.31/2.24
% 7.31/2.24 % (1557)Memory used [KB]: 7803
% 7.31/2.24 % (1557)Time elapsed: 0.137 s
% 7.31/2.24 % (1557)Instructions burned: 460 (million)
% 7.31/2.24 % (1557)------------------------------
% 7.31/2.24 % (1557)------------------------------
% 7.31/2.25 % (1569)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_1200 for (2992ds/164Mi)
% 7.31/2.25 % (1570)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_1200 for (2992ds/50Mi)
% 7.31/2.26 % (1566)Instruction limit reached!
% 7.31/2.26 % (1566)------------------------------
% 7.31/2.26 % (1566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.26 % (1566)Termination reason: Unknown
% 7.31/2.26 % (1566)Termination phase: Saturation
% 7.31/2.26
% 7.31/2.26 % (1566)Memory used [KB]: 6780
% 7.31/2.26 % (1566)Time elapsed: 0.034 s
% 7.31/2.26 % (1566)Instructions burned: 117 (million)
% 7.31/2.26 % (1566)------------------------------
% 7.31/2.26 % (1566)------------------------------
% 7.31/2.27 % (1570)Instruction limit reached!
% 7.31/2.27 % (1570)------------------------------
% 7.31/2.27 % (1570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.27 % (1570)Termination reason: Unknown
% 7.31/2.27 % (1570)Termination phase: Property scanning
% 7.31/2.27
% 7.31/2.27 % (1570)Memory used [KB]: 1791
% 7.31/2.27 % (1570)Time elapsed: 0.014 s
% 7.31/2.27 % (1570)Instructions burned: 50 (million)
% 7.31/2.27 % (1570)------------------------------
% 7.31/2.27 % (1570)------------------------------
% 7.31/2.27 % (1571)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_1200 for (2991ds/368Mi)
% 7.31/2.28 % (1565)Instruction limit reached!
% 7.31/2.28 % (1565)------------------------------
% 7.31/2.28 % (1565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.28 % (1565)Termination reason: Unknown
% 7.31/2.28 % (1565)Termination phase: Saturation
% 7.31/2.28
% 7.31/2.28 % (1565)Memory used [KB]: 6524
% 7.31/2.28 % (1565)Time elapsed: 0.055 s
% 7.31/2.28 % (1565)Instructions burned: 217 (million)
% 7.31/2.28 % (1565)------------------------------
% 7.31/2.28 % (1565)------------------------------
% 7.31/2.28 % (1572)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_1200 for (2991ds/1021Mi)
% 7.31/2.29 % (1573)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_1200 for (2991ds/267Mi)
% 7.31/2.29 % (1568)Instruction limit reached!
% 7.31/2.29 % (1568)------------------------------
% 7.31/2.29 % (1568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.29 % (1568)Termination reason: Unknown
% 7.31/2.29 % (1568)Termination phase: Saturation
% 7.31/2.29
% 7.31/2.29 % (1568)Memory used [KB]: 6524
% 7.31/2.29 % (1568)Time elapsed: 0.047 s
% 7.31/2.29 % (1568)Instructions burned: 185 (million)
% 7.31/2.29 % (1568)------------------------------
% 7.31/2.29 % (1568)------------------------------
% 7.31/2.29 % (1569)Instruction limit reached!
% 7.31/2.29 % (1569)------------------------------
% 7.31/2.29 % (1569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.31/2.29 % (1569)Termination reason: Unknown
% 7.31/2.29 % (1569)Termination phase: Saturation
% 7.31/2.29
% 7.31/2.29 % (1569)Memory used [KB]: 2302
% 7.31/2.29 % (1569)Time elapsed: 0.046 s
% 7.31/2.29 % (1569)Instructions burned: 164 (million)
% 7.31/2.29 % (1569)------------------------------
% 7.31/2.29 % (1569)------------------------------
% 8.02/2.30 % (1574)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_1200 for (2991ds/204Mi)
% 8.02/2.30 % (1575)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_1200 for (2991ds/26Mi)
% 8.02/2.31 % (1575)Instruction limit reached!
% 8.02/2.31 % (1575)------------------------------
% 8.02/2.31 % (1575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.31 % (1575)Termination reason: Unknown
% 8.02/2.31 % (1575)Termination phase: Property scanning
% 8.02/2.31
% 8.02/2.31 % (1575)Memory used [KB]: 1663
% 8.02/2.31 % (1575)Time elapsed: 0.009 s
% 8.02/2.31 % (1575)Instructions burned: 28 (million)
% 8.02/2.31 % (1575)------------------------------
% 8.02/2.31 % (1575)------------------------------
% 8.02/2.32 % (1576)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_1200 for (2991ds/53Mi)
% 8.02/2.33 % (1576)Instruction limit reached!
% 8.02/2.33 % (1576)------------------------------
% 8.02/2.33 % (1576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.33 % (1576)Termination reason: Unknown
% 8.02/2.33 % (1576)Termination phase: Function definition elimination
% 8.02/2.33
% 8.02/2.33 % (1576)Memory used [KB]: 1791
% 8.02/2.33 % (1576)Time elapsed: 0.015 s
% 8.02/2.33 % (1576)Instructions burned: 56 (million)
% 8.02/2.33 % (1576)------------------------------
% 8.02/2.33 % (1576)------------------------------
% 8.02/2.34 % (1577)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_1200 for (2991ds/4436Mi)
% 8.02/2.35 % (1573)Instruction limit reached!
% 8.02/2.35 % (1573)------------------------------
% 8.02/2.35 % (1573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.35 % (1573)Termination reason: Unknown
% 8.02/2.35 % (1573)Termination phase: Saturation
% 8.02/2.35
% 8.02/2.35 % (1573)Memory used [KB]: 8827
% 8.02/2.35 % (1573)Time elapsed: 0.068 s
% 8.02/2.35 % (1573)Instructions burned: 268 (million)
% 8.02/2.35 % (1573)------------------------------
% 8.02/2.35 % (1573)------------------------------
% 8.02/2.35 % (1574)Instruction limit reached!
% 8.02/2.35 % (1574)------------------------------
% 8.02/2.35 % (1574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.35 % (1574)Termination reason: Unknown
% 8.02/2.35 % (1574)Termination phase: Saturation
% 8.02/2.35
% 8.02/2.35 % (1574)Memory used [KB]: 7419
% 8.02/2.35 % (1574)Time elapsed: 0.058 s
% 8.02/2.35 % (1574)Instructions burned: 206 (million)
% 8.02/2.35 % (1574)------------------------------
% 8.02/2.35 % (1574)------------------------------
% 8.02/2.36 % (1578)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_1200 for (2991ds/1539Mi)
% 8.02/2.36 % (1579)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_1200 for (2991ds/408Mi)
% 8.02/2.38 % (1560)Instruction limit reached!
% 8.02/2.38 % (1560)------------------------------
% 8.02/2.38 % (1560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.38 % (1560)Termination reason: Unknown
% 8.02/2.38 % (1560)Termination phase: Saturation
% 8.02/2.38
% 8.02/2.38 % (1560)Memory used [KB]: 9594
% 8.02/2.38 % (1560)Time elapsed: 0.263 s
% 8.02/2.38 % (1560)Instructions burned: 991 (million)
% 8.02/2.38 % (1560)------------------------------
% 8.02/2.38 % (1560)------------------------------
% 8.02/2.39 % (1571)Instruction limit reached!
% 8.02/2.39 % (1571)------------------------------
% 8.02/2.39 % (1571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.39 % (1571)Termination reason: Unknown
% 8.02/2.39 % (1571)Termination phase: Saturation
% 8.02/2.39
% 8.02/2.39 % (1571)Memory used [KB]: 7931
% 8.02/2.39 % (1571)Time elapsed: 0.120 s
% 8.02/2.39 % (1571)Instructions burned: 370 (million)
% 8.02/2.39 % (1571)------------------------------
% 8.02/2.39 % (1571)------------------------------
% 8.02/2.39 % (1580)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_1200 for (2990ds/5205Mi)
% 8.58/2.40 % (1581)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_1200 for (2990ds/1913Mi)
% 8.58/2.49 % (1579)Instruction limit reached!
% 8.58/2.49 % (1579)------------------------------
% 8.58/2.49 % (1579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.58/2.49 % (1579)Termination reason: Unknown
% 8.58/2.49 % (1579)Termination phase: Saturation
% 8.58/2.49
% 8.58/2.49 % (1579)Memory used [KB]: 9083
% 8.58/2.49 % (1579)Time elapsed: 0.130 s
% 8.58/2.49 % (1579)Instructions burned: 408 (million)
% 8.58/2.49 % (1579)------------------------------
% 8.58/2.49 % (1579)------------------------------
% 8.73/2.50 % (1582)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_1200 for (2989ds/4350Mi)
% 8.73/2.52 % (1567)Instruction limit reached!
% 8.73/2.52 % (1567)------------------------------
% 8.73/2.52 % (1567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.73/2.52 % (1567)Termination reason: Unknown
% 8.73/2.52 % (1567)Termination phase: Saturation
% 8.73/2.52
% 8.73/2.52 % (1567)Memory used [KB]: 9594
% 8.73/2.52 % (1567)Time elapsed: 0.292 s
% 8.73/2.52 % (1567)Instructions burned: 922 (million)
% 8.73/2.52 % (1567)------------------------------
% 8.73/2.52 % (1567)------------------------------
% 8.73/2.53 % (1583)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_1200 for (2989ds/68Mi)
% 8.73/2.55 % (1583)Instruction limit reached!
% 8.73/2.55 % (1583)------------------------------
% 8.73/2.55 % (1583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.73/2.55 % (1583)Termination reason: Unknown
% 8.73/2.55 % (1583)Termination phase: Property scanning
% 8.73/2.55
% 8.73/2.55 % (1583)Memory used [KB]: 1918
% 8.73/2.55 % (1583)Time elapsed: 0.019 s
% 8.73/2.55 % (1583)Instructions burned: 70 (million)
% 8.73/2.55 % (1583)------------------------------
% 8.73/2.55 % (1583)------------------------------
% 8.73/2.56 % (1584)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_1200 for (2989ds/358Mi)
% 9.06/2.60 % (1572)Instruction limit reached!
% 9.06/2.60 % (1572)------------------------------
% 9.06/2.60 % (1572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.06/2.60 % (1572)Termination reason: Unknown
% 9.06/2.60 % (1572)Termination phase: Saturation
% 9.06/2.60
% 9.06/2.60 % (1572)Memory used [KB]: 9978
% 9.06/2.60 % (1572)Time elapsed: 0.321 s
% 9.06/2.60 % (1572)Instructions burned: 1023 (million)
% 9.06/2.60 % (1572)------------------------------
% 9.06/2.60 % (1572)------------------------------
% 9.06/2.61 % (1585)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_1200 for (2988ds/31Mi)
% 9.06/2.62 % (1585)Instruction limit reached!
% 9.06/2.62 % (1585)------------------------------
% 9.06/2.62 % (1585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.06/2.62 % (1585)Termination reason: Unknown
% 9.06/2.62 % (1585)Termination phase: Property scanning
% 9.06/2.62
% 9.06/2.62 % (1585)Memory used [KB]: 1663
% 9.06/2.62 % (1585)Time elapsed: 0.010 s
% 9.06/2.62 % (1585)Instructions burned: 34 (million)
% 9.06/2.62 % (1585)------------------------------
% 9.06/2.62 % (1585)------------------------------
% 9.06/2.62 % (1586)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_1200 for (2988ds/279Mi)
% 9.06/2.67 % (1584)Instruction limit reached!
% 9.06/2.67 % (1584)------------------------------
% 9.06/2.67 % (1584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.06/2.67 % (1584)Termination reason: Unknown
% 9.06/2.67 % (1584)Termination phase: Saturation
% 9.06/2.67
% 9.06/2.67 % (1584)Memory used [KB]: 7675
% 9.06/2.67 % (1584)Time elapsed: 0.106 s
% 9.06/2.67 % (1584)Instructions burned: 360 (million)
% 9.06/2.67 % (1584)------------------------------
% 9.06/2.67 % (1584)------------------------------
% 9.06/2.67 % (1587)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_1200 for (2987ds/258Mi)
% 9.06/2.69 % (1586)Instruction limit reached!
% 9.06/2.69 % (1586)------------------------------
% 9.06/2.69 % (1586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.06/2.69 % (1586)Termination reason: Unknown
% 9.06/2.69 % (1586)Termination phase: Saturation
% 9.06/2.69
% 9.06/2.69 % (1586)Memory used [KB]: 6652
% 9.06/2.69 % (1586)Time elapsed: 0.069 s
% 9.06/2.69 % (1586)Instructions burned: 282 (million)
% 9.06/2.69 % (1586)------------------------------
% 9.06/2.69 % (1586)------------------------------
% 9.60/2.70 % (1588)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_1200 for (2987ds/26Mi)
% 9.60/2.71 % (1588)Instruction limit reached!
% 9.60/2.71 % (1588)------------------------------
% 9.60/2.71 % (1588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.60/2.71 % (1588)Termination reason: Unknown
% 9.60/2.71 % (1588)Termination phase: Property scanning
% 9.60/2.71
% 9.60/2.71 % (1588)Memory used [KB]: 1663
% 9.60/2.71 % (1588)Time elapsed: 0.008 s
% 9.60/2.71 % (1588)Instructions burned: 26 (million)
% 9.60/2.71 % (1588)------------------------------
% 9.60/2.71 % (1588)------------------------------
% 9.60/2.72 % (1589)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_1200 for (2987ds/995Mi)
% 9.60/2.74 % (1587)Instruction limit reached!
% 9.60/2.74 % (1587)------------------------------
% 9.60/2.74 % (1587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.60/2.74 % (1587)Termination reason: Unknown
% 9.60/2.74 % (1587)Termination phase: Saturation
% 9.60/2.74
% 9.60/2.74 % (1587)Memory used [KB]: 7931
% 9.60/2.74 % (1587)Time elapsed: 0.071 s
% 9.60/2.74 % (1587)Instructions burned: 260 (million)
% 9.60/2.74 % (1587)------------------------------
% 9.60/2.74 % (1587)------------------------------
% 9.60/2.75 % (1590)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_1200 for (2987ds/373Mi)
% 9.60/2.78 % (1578)Instruction limit reached!
% 9.60/2.78 % (1578)------------------------------
% 9.60/2.78 % (1578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.60/2.78 % (1578)Termination reason: Unknown
% 9.60/2.78 % (1578)Termination phase: Saturation
% 9.60/2.78
% 9.60/2.78 % (1578)Memory used [KB]: 8443
% 9.60/2.78 % (1578)Time elapsed: 0.416 s
% 9.60/2.78 % (1578)Instructions burned: 1540 (million)
% 9.60/2.78 % (1578)------------------------------
% 9.60/2.78 % (1578)------------------------------
% 9.60/2.79 % (1591)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_1200 for (2986ds/253Mi)
% 10.12/2.85 % (1591)Instruction limit reached!
% 10.12/2.85 % (1591)------------------------------
% 10.12/2.85 % (1591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.12/2.85 % (1591)Termination reason: Unknown
% 10.12/2.85 % (1591)Termination phase: Saturation
% 10.12/2.85
% 10.12/2.85 % (1591)Memory used [KB]: 6780
% 10.12/2.85 % (1591)Time elapsed: 0.065 s
% 10.12/2.85 % (1591)Instructions burned: 253 (million)
% 10.12/2.85 % (1591)------------------------------
% 10.12/2.85 % (1591)------------------------------
% 10.12/2.86 % (1592)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_1200 for (2986ds/832Mi)
% 10.12/2.87 % (1590)Instruction limit reached!
% 10.12/2.87 % (1590)------------------------------
% 10.12/2.87 % (1590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.12/2.87 % (1590)Termination reason: Unknown
% 10.12/2.87 % (1590)Termination phase: Saturation
% 10.12/2.87
% 10.12/2.87 % (1590)Memory used [KB]: 7675
% 10.12/2.87 % (1590)Time elapsed: 0.115 s
% 10.12/2.87 % (1590)Instructions burned: 373 (million)
% 10.12/2.87 % (1590)------------------------------
% 10.12/2.87 % (1590)------------------------------
% 10.12/2.88 % (1593)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_1200 for (2985ds/668Mi)
% 10.33/2.96 % (1589)Instruction limit reached!
% 10.33/2.96 % (1589)------------------------------
% 10.33/2.96 % (1589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.33/2.96 % (1589)Termination reason: Unknown
% 10.33/2.96 % (1589)Termination phase: Saturation
% 10.33/2.96
% 10.33/2.96 % (1589)Memory used [KB]: 9338
% 10.33/2.96 % (1589)Time elapsed: 0.243 s
% 10.33/2.96 % (1589)Instructions burned: 997 (million)
% 10.33/2.96 % (1589)------------------------------
% 10.33/2.96 % (1589)------------------------------
% 10.33/2.97 % (1594)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_1200 for (2985ds/40Mi)
% 10.33/2.98 % (1594)Instruction limit reached!
% 10.33/2.98 % (1594)------------------------------
% 10.33/2.98 % (1594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.33/2.98 % (1594)Termination reason: Unknown
% 10.33/2.98 % (1594)Termination phase: Property scanning
% 10.33/2.98
% 10.33/2.98 % (1594)Memory used [KB]: 1791
% 10.33/2.98 % (1594)Time elapsed: 0.012 s
% 10.33/2.98 % (1594)Instructions burned: 42 (million)
% 10.33/2.98 % (1594)------------------------------
% 10.33/2.98 % (1594)------------------------------
% 10.33/2.99 % (1595)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_1200 for (2984ds/294Mi)
% 10.33/3.00 % (1581)Instruction limit reached!
% 10.33/3.00 % (1581)------------------------------
% 10.33/3.00 % (1581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.33/3.00 % (1581)Termination reason: Unknown
% 10.33/3.00 % (1581)Termination phase: Saturation
% 10.33/3.00
% 10.33/3.00 % (1581)Memory used [KB]: 4349
% 10.33/3.00 % (1581)Time elapsed: 0.597 s
% 10.33/3.00 % (1581)Instructions burned: 1913 (million)
% 10.33/3.00 % (1581)------------------------------
% 10.33/3.00 % (1581)------------------------------
% 10.33/3.01 % (1597)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_1200 for (2984ds/187Mi)
% 13.33/3.04 % (1593)Instruction limit reached!
% 13.33/3.04 % (1593)------------------------------
% 13.33/3.04 % (1593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.33/3.04 % (1593)Termination reason: Unknown
% 13.33/3.04 % (1593)Termination phase: Saturation
% 13.33/3.04
% 13.33/3.04 % (1593)Memory used [KB]: 13944
% 13.33/3.04 % (1593)Time elapsed: 0.163 s
% 13.33/3.04 % (1593)Instructions burned: 670 (million)
% 13.33/3.04 % (1593)------------------------------
% 13.33/3.04 % (1593)------------------------------
% 13.33/3.05 % (1598)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_1200 for (2984ds/371Mi)
% 13.33/3.06 % (1597)Instruction limit reached!
% 13.33/3.06 % (1597)------------------------------
% 13.33/3.06 % (1597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.33/3.06 % (1597)Termination reason: Unknown
% 13.33/3.06 % (1597)Termination phase: Saturation
% 13.33/3.06
% 13.33/3.06 % (1597)Memory used [KB]: 7547
% 13.33/3.06 % (1597)Time elapsed: 0.052 s
% 13.33/3.06 % (1597)Instructions burned: 187 (million)
% 13.33/3.06 % (1597)------------------------------
% 13.33/3.06 % (1597)------------------------------
% 13.33/3.06 % (1595)Instruction limit reached!
% 13.33/3.06 % (1595)------------------------------
% 13.33/3.06 % (1595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.33/3.06 % (1595)Termination reason: Unknown
% 13.33/3.06 % (1595)Termination phase: Saturation
% 13.33/3.06
% 13.33/3.06 % (1595)Memory used [KB]: 6524
% 13.33/3.06 % (1595)Time elapsed: 0.074 s
% 13.33/3.06 % (1595)Instructions burned: 294 (million)
% 13.33/3.06 % (1595)------------------------------
% 13.33/3.06 % (1595)------------------------------
% 13.33/3.07 % (1599)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_1200 for (2984ds/1827Mi)
% 13.33/3.07 % (1600)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_1200 for (2984ds/70Mi)
% 13.33/3.09 % (1600)Instruction limit reached!
% 13.33/3.09 % (1600)------------------------------
% 13.33/3.09 % (1600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.33/3.09 % (1600)Termination reason: Unknown
% 13.33/3.09 % (1600)Termination phase: Property scanning
% 13.33/3.09
% 13.33/3.09 % (1600)Memory used [KB]: 1791
% 13.33/3.09 % (1600)Time elapsed: 0.019 s
% 13.33/3.09 % (1600)Instructions burned: 72 (million)
% 13.33/3.09 % (1600)------------------------------
% 13.33/3.09 % (1600)------------------------------
% 13.33/3.10 % (1601)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_1200 for (2983ds/316Mi)
% 13.33/3.12 % (1592)Instruction limit reached!
% 13.33/3.12 % (1592)------------------------------
% 13.33/3.12 % (1592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.33/3.12 % (1592)Termination reason: Unknown
% 13.33/3.12 % (1592)Termination phase: Saturation
% 13.33/3.12
% 13.33/3.12 % (1592)Memory used [KB]: 9594
% 13.33/3.12 % (1592)Time elapsed: 0.257 s
% 13.33/3.12 % (1592)Instructions burned: 832 (million)
% 13.33/3.12 % (1592)------------------------------
% 13.33/3.12 % (1592)------------------------------
% 13.94/3.13 % (1602)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_1200 for (2983ds/932Mi)
% 13.94/3.16 % (1598)Instruction limit reached!
% 13.94/3.16 % (1598)------------------------------
% 13.94/3.16 % (1598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.94/3.16 % (1598)Termination reason: Unknown
% 13.94/3.16 % (1598)Termination phase: Saturation
% 13.94/3.16
% 13.94/3.16 % (1598)Memory used [KB]: 7803
% 13.94/3.16 % (1598)Time elapsed: 0.109 s
% 13.94/3.16 % (1598)Instructions burned: 373 (million)
% 13.94/3.16 % (1598)------------------------------
% 13.94/3.16 % (1598)------------------------------
% 13.94/3.17 % (1603)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_1200 for (2983ds/4714Mi)
% 13.94/3.18 % (1601)Instruction limit reached!
% 13.94/3.18 % (1601)------------------------------
% 13.94/3.18 % (1601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.94/3.18 % (1601)Termination reason: Unknown
% 13.94/3.18 % (1601)Termination phase: Saturation
% 13.94/3.18
% 13.94/3.18 % (1601)Memory used [KB]: 7547
% 13.94/3.18 % (1601)Time elapsed: 0.080 s
% 13.94/3.18 % (1601)Instructions burned: 318 (million)
% 13.94/3.18 % (1601)------------------------------
% 13.94/3.18 % (1601)------------------------------
% 13.94/3.19 % (1604)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_1200 for (2982ds/8250Mi)
% 14.67/3.36 % (1602)Instruction limit reached!
% 14.67/3.36 % (1602)------------------------------
% 14.67/3.36 % (1602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.67/3.36 % (1602)Termination reason: Unknown
% 14.67/3.36 % (1602)Termination phase: Saturation
% 14.67/3.36
% 14.67/3.36 % (1602)Memory used [KB]: 10490
% 14.67/3.36 % (1602)Time elapsed: 0.258 s
% 14.67/3.36 % (1602)Instructions burned: 933 (million)
% 14.67/3.36 % (1602)------------------------------
% 14.67/3.36 % (1602)------------------------------
% 14.67/3.37 % (1605)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_1200 for (2980ds/770Mi)
% 15.52/3.59 % (1605)Instruction limit reached!
% 15.52/3.59 % (1605)------------------------------
% 15.52/3.59 % (1605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.52/3.59 % (1605)Termination reason: Unknown
% 15.52/3.59 % (1605)Termination phase: Saturation
% 15.52/3.59
% 15.52/3.59 % (1605)Memory used [KB]: 6908
% 15.52/3.59 % (1605)Time elapsed: 0.214 s
% 15.52/3.59 % (1605)Instructions burned: 773 (million)
% 15.52/3.59 % (1605)------------------------------
% 15.52/3.59 % (1605)------------------------------
% 15.52/3.59 % (1606)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_1200 for (2978ds/794Mi)
% 16.05/3.61 % (1599)Instruction limit reached!
% 16.05/3.61 % (1599)------------------------------
% 16.05/3.61 % (1599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.05/3.61 % (1599)Termination reason: Unknown
% 16.05/3.61 % (1599)Termination phase: Saturation
% 16.05/3.61
% 16.05/3.61 % (1599)Memory used [KB]: 15991
% 16.05/3.61 % (1599)Time elapsed: 0.542 s
% 16.05/3.61 % (1599)Instructions burned: 1829 (million)
% 16.05/3.61 % (1599)------------------------------
% 16.05/3.61 % (1599)------------------------------
% 16.05/3.62 % (1607)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_1200 for (2978ds/464Mi)
% 16.05/3.63 % (1580)Instruction limit reached!
% 16.05/3.63 % (1580)------------------------------
% 16.05/3.63 % (1580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.05/3.63 % (1580)Termination reason: Unknown
% 16.05/3.63 % (1580)Termination phase: Saturation
% 16.05/3.63
% 16.05/3.63 % (1580)Memory used [KB]: 9978
% 16.05/3.63 % (1580)Time elapsed: 1.234 s
% 16.05/3.63 % (1580)Instructions burned: 5208 (million)
% 16.05/3.63 % (1580)------------------------------
% 16.05/3.63 % (1580)------------------------------
% 16.05/3.64 % (1608)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_1200 for (2978ds/1376Mi)
% 16.85/3.75 % (1577)Instruction limit reached!
% 16.85/3.75 % (1577)------------------------------
% 16.85/3.75 % (1577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.85/3.75 % (1577)Termination reason: Unknown
% 16.85/3.75 % (1577)Termination phase: Saturation
% 16.85/3.75
% 16.85/3.75 % (1577)Memory used [KB]: 16630
% 16.85/3.75 % (1577)Time elapsed: 1.409 s
% 16.85/3.75 % (1577)Instructions burned: 4438 (million)
% 16.85/3.75 % (1577)------------------------------
% 16.85/3.75 % (1577)------------------------------
% 16.85/3.76 % (1609)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_1200 for (2977ds/906Mi)
% 16.85/3.76 % (1607)Instruction limit reached!
% 16.85/3.76 % (1607)------------------------------
% 16.85/3.76 % (1607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.85/3.76 % (1607)Termination reason: Unknown
% 16.85/3.76 % (1607)Termination phase: Saturation
% 16.85/3.76
% 16.85/3.76 % (1607)Memory used [KB]: 8059
% 16.85/3.76 % (1607)Time elapsed: 0.145 s
% 16.85/3.76 % (1607)Instructions burned: 464 (million)
% 16.85/3.76 % (1607)------------------------------
% 16.85/3.76 % (1607)------------------------------
% 16.85/3.77 % (1610)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_1200 for (2976ds/434Mi)
% 17.16/3.83 % (1582)Instruction limit reached!
% 17.16/3.83 % (1582)------------------------------
% 17.16/3.83 % (1582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.16/3.83 % (1582)Termination reason: Unknown
% 17.16/3.83 % (1582)Termination phase: Saturation
% 17.16/3.83
% 17.16/3.83 % (1582)Memory used [KB]: 10874
% 17.16/3.83 % (1582)Time elapsed: 1.327 s
% 17.16/3.83 % (1582)Instructions burned: 4350 (million)
% 17.16/3.83 % (1582)------------------------------
% 17.16/3.83 % (1582)------------------------------
% 17.16/3.84 % (1611)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_1200 for (2976ds/865Mi)
% 17.16/3.84 % (1606)Instruction limit reached!
% 17.16/3.84 % (1606)------------------------------
% 17.16/3.84 % (1606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.16/3.84 % (1606)Termination reason: Unknown
% 17.16/3.84 % (1606)Termination phase: Saturation
% 17.16/3.84
% 17.16/3.84 % (1606)Memory used [KB]: 4093
% 17.16/3.84 % (1606)Time elapsed: 0.250 s
% 17.16/3.84 % (1606)Instructions burned: 795 (million)
% 17.16/3.84 % (1606)------------------------------
% 17.16/3.84 % (1606)------------------------------
% 17.16/3.85 % (1612)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_1200 for (2976ds/593Mi)
% 17.46/3.90 % (1610)Instruction limit reached!
% 17.46/3.90 % (1610)------------------------------
% 17.46/3.90 % (1610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.46/3.90 % (1610)Termination reason: Unknown
% 17.46/3.90 % (1610)Termination phase: Saturation
% 17.46/3.90
% 17.46/3.90 % (1610)Memory used [KB]: 8955
% 17.46/3.90 % (1610)Time elapsed: 0.128 s
% 17.46/3.90 % (1610)Instructions burned: 434 (million)
% 17.46/3.90 % (1610)------------------------------
% 17.46/3.90 % (1610)------------------------------
% 17.46/3.91 % (1613)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_1200 for (2975ds/443Mi)
% 17.46/3.98 % (1608)Instruction limit reached!
% 17.46/3.98 % (1608)------------------------------
% 17.46/3.98 % (1608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.46/3.98 % (1608)Termination reason: Unknown
% 17.46/3.98 % (1608)Termination phase: Saturation
% 17.46/3.98
% 17.46/3.98 % (1608)Memory used [KB]: 8315
% 17.46/3.98 % (1608)Time elapsed: 0.346 s
% 17.46/3.98 % (1608)Instructions burned: 1379 (million)
% 17.46/3.98 % (1608)------------------------------
% 17.46/3.98 % (1608)------------------------------
% 17.46/3.99 % (1612)Instruction limit reached!
% 17.46/3.99 % (1612)------------------------------
% 17.46/3.99 % (1612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.46/3.99 % (1612)Termination reason: Unknown
% 17.46/3.99 % (1612)Termination phase: Saturation
% 17.46/3.99
% 17.46/3.99 % (1612)Memory used [KB]: 6652
% 17.46/3.99 % (1612)Time elapsed: 0.138 s
% 17.46/3.99 % (1612)Instructions burned: 593 (million)
% 17.46/3.99 % (1612)------------------------------
% 17.46/3.99 % (1612)------------------------------
% 17.46/3.99 % (1614)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_1200 for (2974ds/594Mi)
% 17.46/4.03 % (1615)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_1200 for (2974ds/327Mi)
% 20.41/4.04 % (1609)Instruction limit reached!
% 20.41/4.04 % (1609)------------------------------
% 20.41/4.04 % (1609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.41/4.04 % (1609)Termination reason: Unknown
% 20.41/4.04 % (1609)Termination phase: Saturation
% 20.41/4.04
% 20.41/4.04 % (1609)Memory used [KB]: 9083
% 20.41/4.04 % (1609)Time elapsed: 0.278 s
% 20.41/4.04 % (1609)Instructions burned: 908 (million)
% 20.41/4.04 % (1609)------------------------------
% 20.41/4.04 % (1609)------------------------------
% 20.41/4.04 % (1613)Instruction limit reached!
% 20.41/4.04 % (1613)------------------------------
% 20.41/4.04 % (1613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.41/4.04 % (1613)Termination reason: Unknown
% 20.41/4.04 % (1613)Termination phase: Saturation
% 20.41/4.04
% 20.41/4.04 % (1613)Memory used [KB]: 8059
% 20.41/4.04 % (1613)Time elapsed: 0.134 s
% 20.41/4.04 % (1613)Instructions burned: 444 (million)
% 20.41/4.04 % (1613)------------------------------
% 20.41/4.04 % (1613)------------------------------
% 20.41/4.05 % (1616)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_1200 for (2974ds/5411Mi)
% 20.41/4.05 % (1617)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_1200 for (2974ds/1762Mi)
% 20.41/4.10 % (1611)Instruction limit reached!
% 20.41/4.10 % (1611)------------------------------
% 20.41/4.10 % (1611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.41/4.10 % (1611)Termination reason: Unknown
% 20.41/4.10 % (1611)Termination phase: Saturation
% 20.41/4.10
% 20.41/4.10 % (1611)Memory used [KB]: 8443
% 20.41/4.10 % (1611)Time elapsed: 0.265 s
% 20.41/4.10 % (1611)Instructions burned: 865 (million)
% 20.41/4.10 % (1611)------------------------------
% 20.41/4.10 % (1611)------------------------------
% 20.41/4.11 % (1618)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_1200 for (2973ds/96Mi)
% 20.98/4.13 % (1615)Instruction limit reached!
% 20.98/4.13 % (1615)------------------------------
% 20.98/4.13 % (1615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.98/4.13 % (1615)Termination reason: Unknown
% 20.98/4.13 % (1615)Termination phase: Saturation
% 20.98/4.13
% 20.98/4.13 % (1615)Memory used [KB]: 9338
% 20.98/4.13 % (1615)Time elapsed: 0.129 s
% 20.98/4.13 % (1615)Instructions burned: 327 (million)
% 20.98/4.13 % (1615)------------------------------
% 20.98/4.13 % (1615)------------------------------
% 20.98/4.14 % (1618)Instruction limit reached!
% 20.98/4.14 % (1618)------------------------------
% 20.98/4.14 % (1618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.98/4.14 % (1618)Termination reason: Unknown
% 20.98/4.14 % (1618)Termination phase: Saturation
% 20.98/4.14
% 20.98/4.14 % (1618)Memory used [KB]: 6524
% 20.98/4.14 % (1618)Time elapsed: 0.025 s
% 20.98/4.14 % (1618)Instructions burned: 96 (million)
% 20.98/4.14 % (1618)------------------------------
% 20.98/4.14 % (1618)------------------------------
% 20.98/4.14 % (1619)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_1200 for (2973ds/503Mi)
% 20.98/4.15 % (1620)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_1200 for (2973ds/90Mi)
% 20.98/4.17 % (1620)Instruction limit reached!
% 20.98/4.17 % (1620)------------------------------
% 20.98/4.17 % (1620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.98/4.17 % (1620)Termination reason: Unknown
% 20.98/4.17 % (1620)Termination phase: Saturation
% 20.98/4.17
% 20.98/4.17 % (1620)Memory used [KB]: 6908
% 20.98/4.17 % (1620)Time elapsed: 0.025 s
% 20.98/4.17 % (1620)Instructions burned: 91 (million)
% 20.98/4.17 % (1620)------------------------------
% 20.98/4.17 % (1620)------------------------------
% 20.98/4.17 % (1614)Instruction limit reached!
% 20.98/4.17 % (1614)------------------------------
% 20.98/4.17 % (1614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.98/4.17 % (1614)Termination reason: Unknown
% 20.98/4.17 % (1614)Termination phase: Saturation
% 20.98/4.17
% 20.98/4.17 % (1614)Memory used [KB]: 8059
% 20.98/4.17 % (1614)Time elapsed: 0.184 s
% 20.98/4.17 % (1614)Instructions burned: 597 (million)
% 20.98/4.17 % (1614)------------------------------
% 20.98/4.17 % (1614)------------------------------
% 20.98/4.18 % (1621)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_1200 for (2972ds/593Mi)
% 20.98/4.18 % (1622)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_1200 for (2972ds/1512Mi)
% 21.24/4.23 % (1603)Instruction limit reached!
% 21.24/4.23 % (1603)------------------------------
% 21.24/4.23 % (1603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.24/4.23 % (1603)Termination reason: Unknown
% 21.24/4.23 % (1603)Termination phase: Saturation
% 21.24/4.23
% 21.24/4.23 % (1603)Memory used [KB]: 7036
% 21.24/4.23 % (1603)Time elapsed: 1.090 s
% 21.24/4.23 % (1603)Instructions burned: 4719 (million)
% 21.24/4.23 % (1603)------------------------------
% 21.24/4.23 % (1603)------------------------------
% 21.24/4.24 % (1623)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_1200 for (2972ds/569Mi)
% 21.24/4.29 % (1619)Instruction limit reached!
% 21.24/4.29 % (1619)------------------------------
% 21.24/4.29 % (1619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.24/4.29 % (1619)Termination reason: Unknown
% 21.24/4.29 % (1619)Termination phase: Saturation
% 21.24/4.29
% 21.24/4.29 % (1619)Memory used [KB]: 8187
% 21.24/4.29 % (1619)Time elapsed: 0.152 s
% 21.24/4.29 % (1619)Instructions burned: 505 (million)
% 21.24/4.29 % (1619)------------------------------
% 21.24/4.29 % (1619)------------------------------
% 21.54/4.30 % (1624)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_1200 for (2971ds/501Mi)
% 21.54/4.36 % (1621)Instruction limit reached!
% 21.54/4.36 % (1621)------------------------------
% 21.54/4.36 % (1621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.54/4.36 % (1621)Termination reason: Unknown
% 21.54/4.36 % (1621)Termination phase: Saturation
% 21.54/4.36
% 21.54/4.36 % (1621)Memory used [KB]: 8059
% 21.54/4.36 % (1621)Time elapsed: 0.182 s
% 21.54/4.36 % (1621)Instructions burned: 594 (million)
% 21.54/4.36 % (1621)------------------------------
% 21.54/4.36 % (1621)------------------------------
% 21.54/4.37 % (1625)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_1200 for (2971ds/562Mi)
% 21.54/4.38 % (1623)Instruction limit reached!
% 21.54/4.38 % (1623)------------------------------
% 21.54/4.38 % (1623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.54/4.38 % (1623)Termination reason: Unknown
% 21.54/4.38 % (1623)Termination phase: Saturation
% 21.54/4.38
% 21.54/4.38 % (1623)Memory used [KB]: 8955
% 21.54/4.38 % (1623)Time elapsed: 0.141 s
% 21.54/4.38 % (1623)Instructions burned: 570 (million)
% 21.54/4.38 % (1623)------------------------------
% 21.54/4.38 % (1623)------------------------------
% 21.54/4.39 % (1626)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_1200 for (2970ds/406Mi)
% 21.98/4.46 % (1624)Instruction limit reached!
% 21.98/4.46 % (1624)------------------------------
% 21.98/4.46 % (1624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.98/4.46 % (1624)Termination reason: Unknown
% 21.98/4.46 % (1624)Termination phase: Saturation
% 21.98/4.46
% 21.98/4.46 % (1624)Memory used [KB]: 8955
% 21.98/4.46 % (1624)Time elapsed: 0.154 s
% 21.98/4.46 % (1624)Instructions burned: 503 (million)
% 21.98/4.46 % (1624)------------------------------
% 21.98/4.46 % (1624)------------------------------
% 21.98/4.47 % (1627)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_1200 for (2970ds/582Mi)
% 21.98/4.49 % (1617)Instruction limit reached!
% 21.98/4.49 % (1617)------------------------------
% 21.98/4.49 % (1617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.98/4.49 % (1617)Termination reason: Unknown
% 21.98/4.49 % (1617)Termination phase: Saturation
% 21.98/4.49
% 21.98/4.49 % (1617)Memory used [KB]: 12537
% 21.98/4.49 % (1617)Time elapsed: 0.444 s
% 21.98/4.49 % (1617)Instructions burned: 1762 (million)
% 21.98/4.49 % (1617)------------------------------
% 21.98/4.49 % (1617)------------------------------
% 22.70/4.50 % (1628)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_1200 for (2969ds/456Mi)
% 22.70/4.51 % (1626)Instruction limit reached!
% 22.70/4.51 % (1626)------------------------------
% 22.70/4.51 % (1626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.70/4.51 % (1626)Termination reason: Unknown
% 22.70/4.51 % (1626)Termination phase: Saturation
% 22.70/4.51
% 22.70/4.51 % (1626)Memory used [KB]: 6908
% 22.70/4.51 % (1626)Time elapsed: 0.113 s
% 22.70/4.51 % (1626)Instructions burned: 408 (million)
% 22.70/4.51 % (1626)------------------------------
% 22.70/4.51 % (1626)------------------------------
% 22.70/4.52 % (1629)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_1200 for (2969ds/393Mi)
% 22.70/4.53 % (1625)Instruction limit reached!
% 22.70/4.53 % (1625)------------------------------
% 22.70/4.53 % (1625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.70/4.53 % (1625)Termination reason: Unknown
% 22.70/4.53 % (1625)Termination phase: Saturation
% 22.70/4.53
% 22.70/4.53 % (1625)Memory used [KB]: 7803
% 22.70/4.53 % (1625)Time elapsed: 0.165 s
% 22.70/4.53 % (1625)Instructions burned: 562 (million)
% 22.70/4.53 % (1625)------------------------------
% 22.70/4.53 % (1625)------------------------------
% 22.70/4.54 % (1630)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_1200 for (2969ds/1335Mi)
% 23.10/4.62 % (1629)Instruction limit reached!
% 23.10/4.62 % (1629)------------------------------
% 23.10/4.62 % (1629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.10/4.62 % (1629)Termination reason: Unknown
% 23.10/4.62 % (1629)Termination phase: Saturation
% 23.10/4.62
% 23.10/4.62 % (1629)Memory used [KB]: 8315
% 23.10/4.62 % (1629)Time elapsed: 0.106 s
% 23.10/4.62 % (1629)Instructions burned: 394 (million)
% 23.10/4.62 % (1629)------------------------------
% 23.10/4.62 % (1629)------------------------------
% 23.10/4.63 % (1631)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_1200 for (2968ds/3373Mi)
% 23.10/4.64 % (1628)Instruction limit reached!
% 23.10/4.64 % (1628)------------------------------
% 23.10/4.64 % (1628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.10/4.64 % (1628)Termination reason: Unknown
% 23.10/4.64 % (1628)Termination phase: Saturation
% 23.10/4.64
% 23.10/4.64 % (1628)Memory used [KB]: 8059
% 23.10/4.64 % (1628)Time elapsed: 0.136 s
% 23.10/4.64 % (1628)Instructions burned: 456 (million)
% 23.10/4.64 % (1628)------------------------------
% 23.10/4.64 % (1628)------------------------------
% 23.10/4.65 % (1627)Instruction limit reached!
% 23.10/4.65 % (1627)------------------------------
% 23.10/4.65 % (1627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.10/4.65 % (1627)Termination reason: Unknown
% 23.10/4.65 % (1627)Termination phase: Saturation
% 23.10/4.65
% 23.10/4.65 % (1627)Memory used [KB]: 9083
% 23.10/4.65 % (1627)Time elapsed: 0.183 s
% 23.10/4.65 % (1627)Instructions burned: 582 (million)
% 23.10/4.65 % (1627)------------------------------
% 23.10/4.65 % (1627)------------------------------
% 23.10/4.65 % (1632)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_1200 for (2968ds/474Mi)
% 23.10/4.65 % (1622)Instruction limit reached!
% 23.10/4.65 % (1622)------------------------------
% 23.10/4.65 % (1622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.10/4.65 % (1622)Termination reason: Unknown
% 23.10/4.65 % (1622)Termination phase: Saturation
% 23.10/4.65
% 23.10/4.65 % (1622)Memory used [KB]: 10234
% 23.10/4.65 % (1622)Time elapsed: 0.472 s
% 23.10/4.65 % (1622)Instructions burned: 1513 (million)
% 23.10/4.65 % (1622)------------------------------
% 23.10/4.65 % (1622)------------------------------
% 23.10/4.66 % (1633)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_1200 for (2968ds/157Mi)
% 23.10/4.66 % (1634)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_1200 for (2968ds/590Mi)
% 24.13/4.70 % (1633)Instruction limit reached!
% 24.13/4.70 % (1633)------------------------------
% 24.13/4.70 % (1633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.13/4.70 % (1633)Termination reason: Unknown
% 24.13/4.70 % (1633)Termination phase: Saturation
% 24.13/4.70
% 24.13/4.70 % (1633)Memory used [KB]: 6524
% 24.13/4.70 % (1633)Time elapsed: 0.042 s
% 24.13/4.70 % (1633)Instructions burned: 157 (million)
% 24.13/4.70 % (1633)------------------------------
% 24.13/4.70 % (1633)------------------------------
% 24.13/4.71 % (1635)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_1200 for (2967ds/104Mi)
% 24.13/4.74 % (1635)Instruction limit reached!
% 24.13/4.74 % (1635)------------------------------
% 24.13/4.74 % (1635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.13/4.74 % (1635)Termination reason: Unknown
% 24.13/4.74 % (1635)Termination phase: Saturation
% 24.13/4.74
% 24.13/4.74 % (1635)Memory used [KB]: 6780
% 24.13/4.74 % (1635)Time elapsed: 0.029 s
% 24.13/4.74 % (1635)Instructions burned: 107 (million)
% 24.13/4.74 % (1635)------------------------------
% 24.13/4.74 % (1635)------------------------------
% 24.13/4.74 % (1636)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_1200 for (2967ds/414Mi)
% 24.13/4.77 % (1632)Instruction limit reached!
% 24.13/4.77 % (1632)------------------------------
% 24.13/4.77 % (1632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.13/4.77 % (1632)Termination reason: Unknown
% 24.13/4.77 % (1632)Termination phase: Saturation
% 24.13/4.77
% 24.13/4.77 % (1632)Memory used [KB]: 9466
% 24.13/4.77 % (1632)Time elapsed: 0.119 s
% 24.13/4.77 % (1632)Instructions burned: 476 (million)
% 24.13/4.77 % (1632)------------------------------
% 24.13/4.77 % (1632)------------------------------
% 24.13/4.78 % (1637)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_1200 for (2967ds/715Mi)
% 24.44/4.84 % (1634)Instruction limit reached!
% 24.44/4.84 % (1634)------------------------------
% 24.44/4.84 % (1634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.44/4.84 % (1634)Termination reason: Unknown
% 24.44/4.84 % (1634)Termination phase: Saturation
% 24.44/4.84
% 24.44/4.84 % (1634)Memory used [KB]: 9210
% 24.44/4.84 % (1634)Time elapsed: 0.178 s
% 24.44/4.84 % (1634)Instructions burned: 590 (million)
% 24.44/4.84 % (1634)------------------------------
% 24.44/4.84 % (1634)------------------------------
% 24.44/4.84 % (1636)Instruction limit reached!
% 24.44/4.84 % (1636)------------------------------
% 24.44/4.84 % (1636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.44/4.84 % (1636)Termination reason: Unknown
% 24.44/4.84 % (1636)Termination phase: Saturation
% 24.44/4.84
% 24.44/4.84 % (1636)Memory used [KB]: 6652
% 24.44/4.84 % (1636)Time elapsed: 0.099 s
% 24.44/4.84 % (1636)Instructions burned: 414 (million)
% 24.44/4.84 % (1636)------------------------------
% 24.44/4.84 % (1636)------------------------------
% 24.44/4.85 % (1638)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_1200 for (2966ds/961Mi)
% 24.44/4.85 % (1639)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_1200 for (2966ds/1213Mi)
% 24.85/4.96 % (1630)Instruction limit reached!
% 24.85/4.96 % (1630)------------------------------
% 24.85/4.96 % (1630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.85/4.96 % (1630)Termination reason: Unknown
% 24.85/4.96 % (1630)Termination phase: Saturation
% 24.85/4.96
% 24.85/4.96 % (1630)Memory used [KB]: 8443
% 24.85/4.96 % (1630)Time elapsed: 0.414 s
% 24.85/4.96 % (1630)Instructions burned: 1337 (million)
% 24.85/4.96 % (1630)------------------------------
% 24.85/4.96 % (1630)------------------------------
% 24.85/4.97 % (1640)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_1200 for (2965ds/1979Mi)
% 24.85/5.00 % (1637)Instruction limit reached!
% 24.85/5.00 % (1637)------------------------------
% 24.85/5.00 % (1637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.85/5.00 % (1637)Termination reason: Unknown
% 24.85/5.00 % (1637)Termination phase: Saturation
% 24.85/5.00
% 24.85/5.00 % (1637)Memory used [KB]: 3709
% 24.85/5.00 % (1637)Time elapsed: 0.241 s
% 24.85/5.00 % (1637)Instructions burned: 716 (million)
% 24.85/5.00 % (1637)------------------------------
% 24.85/5.00 % (1637)------------------------------
% 24.85/5.01 % (1641)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_1200 for (2964ds/481Mi)
% 27.38/5.12 % (1641)Instruction limit reached!
% 27.38/5.12 % (1641)------------------------------
% 27.38/5.12 % (1641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.38/5.12 % (1641)Termination reason: Unknown
% 27.38/5.12 % (1641)Termination phase: Saturation
% 27.38/5.12
% 27.38/5.12 % (1641)Memory used [KB]: 9466
% 27.38/5.12 % (1641)Time elapsed: 0.119 s
% 27.38/5.12 % (1641)Instructions burned: 483 (million)
% 27.38/5.12 % (1641)------------------------------
% 27.38/5.12 % (1641)------------------------------
% 28.00/5.13 % (1642)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_1200 for (2963ds/783Mi)
% 28.00/5.15 % (1638)Instruction limit reached!
% 28.00/5.15 % (1638)------------------------------
% 28.00/5.15 % (1638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.00/5.15 % (1638)Termination reason: Unknown
% 28.00/5.15 % (1638)Termination phase: Saturation
% 28.00/5.15
% 28.00/5.15 % (1638)Memory used [KB]: 8571
% 28.00/5.15 % (1638)Time elapsed: 0.323 s
% 28.00/5.15 % (1638)Instructions burned: 963 (million)
% 28.00/5.15 % (1638)------------------------------
% 28.00/5.15 % (1638)------------------------------
% 28.00/5.16 % (1643)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_1200 for (2963ds/432Mi)
% 28.55/5.23 % (1639)Instruction limit reached!
% 28.55/5.23 % (1639)------------------------------
% 28.55/5.23 % (1639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.55/5.23 % (1639)Termination reason: Unknown
% 28.55/5.23 % (1639)Termination phase: Saturation
% 28.55/5.23
% 28.55/5.23 % (1639)Memory used [KB]: 11385
% 28.55/5.23 % (1639)Time elapsed: 0.399 s
% 28.55/5.23 % (1639)Instructions burned: 1213 (million)
% 28.55/5.23 % (1639)------------------------------
% 28.55/5.23 % (1639)------------------------------
% 28.55/5.24 % (1644)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_1200 for (2962ds/1670Mi)
% 28.55/5.29 % (1643)Instruction limit reached!
% 28.55/5.29 % (1643)------------------------------
% 28.55/5.29 % (1643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.55/5.29 % (1643)Termination reason: Unknown
% 28.55/5.29 % (1643)Termination phase: Saturation
% 28.55/5.29
% 28.55/5.29 % (1643)Memory used [KB]: 7675
% 28.55/5.29 % (1643)Time elapsed: 0.133 s
% 28.55/5.29 % (1643)Instructions burned: 433 (million)
% 28.55/5.29 % (1643)------------------------------
% 28.55/5.29 % (1643)------------------------------
% 29.13/5.30 % (1645)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_1200 for (2961ds/90Mi)
% 29.13/5.33 % (1645)Instruction limit reached!
% 29.13/5.33 % (1645)------------------------------
% 29.13/5.33 % (1645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.13/5.33 % (1645)Termination reason: Unknown
% 29.13/5.33 % (1645)Termination phase: Saturation
% 29.13/5.33
% 29.13/5.33 % (1645)Memory used [KB]: 6524
% 29.13/5.33 % (1645)Time elapsed: 0.026 s
% 29.13/5.33 % (1645)Instructions burned: 91 (million)
% 29.13/5.33 % (1645)------------------------------
% 29.13/5.33 % (1645)------------------------------
% 29.13/5.34 % (1646)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_1200 for (2961ds/346Mi)
% 29.13/5.38 % (1642)Instruction limit reached!
% 29.13/5.38 % (1642)------------------------------
% 29.13/5.38 % (1642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.13/5.38 % (1642)Termination reason: Unknown
% 29.13/5.38 % (1642)Termination phase: Saturation
% 29.13/5.38
% 29.13/5.38 % (1642)Memory used [KB]: 10106
% 29.13/5.38 % (1642)Time elapsed: 0.250 s
% 29.13/5.38 % (1642)Instructions burned: 786 (million)
% 29.13/5.38 % (1642)------------------------------
% 29.13/5.38 % (1642)------------------------------
% 29.13/5.39 % (1647)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_1200 for (2960ds/401Mi)
% 29.82/5.42 % (1646)Instruction limit reached!
% 29.82/5.42 % (1646)------------------------------
% 29.82/5.42 % (1646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.82/5.42 % (1646)Termination reason: Unknown
% 29.82/5.42 % (1646)Termination phase: Saturation
% 29.82/5.42
% 29.82/5.42 % (1646)Memory used [KB]: 9083
% 29.82/5.42 % (1646)Time elapsed: 0.086 s
% 29.82/5.42 % (1646)Instructions burned: 349 (million)
% 29.82/5.42 % (1646)------------------------------
% 29.82/5.42 % (1646)------------------------------
% 29.82/5.43 % (1648)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_1200 for (2960ds/6454Mi)
% 29.82/5.49 % (1647)Instruction limit reached!
% 29.82/5.49 % (1647)------------------------------
% 29.82/5.49 % (1647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.82/5.49 % (1647)Termination reason: Unknown
% 29.82/5.49 % (1647)Termination phase: Saturation
% 29.82/5.49
% 29.82/5.49 % (1647)Memory used [KB]: 6652
% 29.82/5.49 % (1647)Time elapsed: 0.099 s
% 29.82/5.49 % (1647)Instructions burned: 402 (million)
% 29.82/5.49 % (1647)------------------------------
% 29.82/5.49 % (1647)------------------------------
% 30.42/5.50 % (1649)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_1200 for (2959ds/283Mi)
% 30.42/5.58 % (1649)Instruction limit reached!
% 30.42/5.58 % (1649)------------------------------
% 30.42/5.58 % (1649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.42/5.58 % (1649)Termination reason: Unknown
% 30.42/5.58 % (1649)Termination phase: Saturation
% 30.42/5.58
% 30.42/5.58 % (1649)Memory used [KB]: 7675
% 30.42/5.58 % (1649)Time elapsed: 0.083 s
% 30.42/5.58 % (1649)Instructions burned: 283 (million)
% 30.42/5.58 % (1649)------------------------------
% 30.42/5.58 % (1649)------------------------------
% 30.42/5.58 % (1640)Instruction limit reached!
% 30.42/5.58 % (1640)------------------------------
% 30.42/5.58 % (1640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.42/5.58 % (1640)Termination reason: Unknown
% 30.42/5.58 % (1640)Termination phase: Saturation
% 30.42/5.58
% 30.42/5.58 % (1640)Memory used [KB]: 8827
% 30.42/5.58 % (1640)Time elapsed: 0.637 s
% 30.42/5.58 % (1640)Instructions burned: 1979 (million)
% 30.42/5.58 % (1640)------------------------------
% 30.42/5.58 % (1640)------------------------------
% 30.42/5.59 % (1650)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_1200 for (2958ds/865Mi)
% 30.42/5.59 % (1651)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_1200 for (2958ds/4528Mi)
% 30.91/5.65 % (1644)Instruction limit reached!
% 30.91/5.65 % (1644)------------------------------
% 30.91/5.65 % (1644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.91/5.65 % (1644)Termination reason: Unknown
% 30.91/5.65 % (1644)Termination phase: Saturation
% 30.91/5.65
% 30.91/5.65 % (1644)Memory used [KB]: 10234
% 30.91/5.65 % (1644)Time elapsed: 0.416 s
% 30.91/5.65 % (1644)Instructions burned: 1673 (million)
% 30.91/5.65 % (1644)------------------------------
% 30.91/5.65 % (1644)------------------------------
% 30.91/5.66 % (1651)Refutation not found, incomplete strategy
% 30.91/5.66 % (1651)------------------------------
% 30.91/5.66 % (1651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.91/5.66 % (1651)Termination reason: Refutation not found, incomplete strategy
% 30.91/5.66
% 30.91/5.66
% 30.91/5.66 % (1651)Memory used [KB]: 2046
% 30.91/5.66 % (1651)Time elapsed: 0.066 s
% 30.91/5.66 % (1651)Instructions burned: 235 (million)
% 30.91/5.66 % (1651)------------------------------
% 30.91/5.66 % (1651)------------------------------
% 30.91/5.66 % (1652)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_1200 for (2958ds/1001Mi)
% 30.91/5.67 % (1653)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_1200 for (2958ds/102Mi)
% 30.91/5.67 % (1631)Instruction limit reached!
% 30.91/5.67 % (1631)------------------------------
% 30.91/5.67 % (1631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.91/5.67 % (1631)Termination reason: Unknown
% 30.91/5.67 % (1631)Termination phase: Saturation
% 30.91/5.67
% 30.91/5.67 % (1631)Memory used [KB]: 12153
% 30.91/5.67 % (1631)Time elapsed: 1.039 s
% 30.91/5.67 % (1631)Instructions burned: 3375 (million)
% 30.91/5.67 % (1631)------------------------------
% 30.91/5.67 % (1631)------------------------------
% 30.91/5.68 % (1654)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_1200 for (2957ds/952Mi)
% 30.91/5.69 % (1653)Instruction limit reached!
% 30.91/5.69 % (1653)------------------------------
% 30.91/5.69 % (1653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.91/5.69 % (1653)Termination reason: Unknown
% 30.91/5.69 % (1653)Termination phase: Saturation
% 30.91/5.69
% 30.91/5.69 % (1653)Memory used [KB]: 6652
% 30.91/5.69 % (1653)Time elapsed: 0.028 s
% 30.91/5.69 % (1653)Instructions burned: 102 (million)
% 30.91/5.69 % (1653)------------------------------
% 30.91/5.69 % (1653)------------------------------
% 31.73/5.70 % (1655)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_1200 for (2957ds/578Mi)
% 31.73/5.77 % (1616)Instruction limit reached!
% 31.73/5.77 % (1616)------------------------------
% 31.73/5.77 % (1616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.73/5.77 % (1616)Termination reason: Unknown
% 31.73/5.77 % (1616)Termination phase: Saturation
% 31.73/5.77
% 31.73/5.77 % (1616)Memory used [KB]: 14328
% 31.73/5.77 % (1616)Time elapsed: 1.727 s
% 31.73/5.77 % (1616)Instructions burned: 5412 (million)
% 31.73/5.77 % (1616)------------------------------
% 31.73/5.77 % (1616)------------------------------
% 31.73/5.78 % (1656)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_1200 for (2956ds/643Mi)
% 31.92/5.84 % (1650)Instruction limit reached!
% 31.92/5.84 % (1650)------------------------------
% 31.92/5.84 % (1650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.92/5.84 % (1650)Termination reason: Unknown
% 31.92/5.84 % (1650)Termination phase: Saturation
% 31.92/5.84
% 31.92/5.84 % (1650)Memory used [KB]: 7675
% 31.92/5.84 % (1650)Time elapsed: 0.250 s
% 31.92/5.84 % (1650)Instructions burned: 866 (million)
% 31.92/5.84 % (1650)------------------------------
% 31.92/5.84 % (1650)------------------------------
% 31.92/5.84 % (1655)Instruction limit reached!
% 31.92/5.84 % (1655)------------------------------
% 31.92/5.84 % (1655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.92/5.84 % (1655)Termination reason: Unknown
% 31.92/5.84 % (1655)Termination phase: Saturation
% 31.92/5.84
% 31.92/5.84 % (1655)Memory used [KB]: 7675
% 31.92/5.84 % (1655)Time elapsed: 0.141 s
% 31.92/5.84 % (1655)Instructions burned: 579 (million)
% 31.92/5.84 % (1655)------------------------------
% 31.92/5.84 % (1655)------------------------------
% 31.92/5.85 % (1657)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_1200 for (2956ds/865Mi)
% 31.92/5.85 % (1658)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_1200 for (2956ds/1174Mi)
% 31.92/5.86 % (1604)Instruction limit reached!
% 31.92/5.86 % (1604)------------------------------
% 31.92/5.86 % (1604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.92/5.86 % (1604)Termination reason: Unknown
% 31.92/5.86 % (1604)Termination phase: Saturation
% 31.92/5.86
% 31.92/5.86 % (1604)Memory used [KB]: 22899
% 31.92/5.86 % (1604)Time elapsed: 2.688 s
% 31.92/5.86 % (1604)Instructions burned: 8252 (million)
% 31.92/5.86 % (1604)------------------------------
% 31.92/5.86 % (1604)------------------------------
% 31.92/5.87 % (1659)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_1200 for (2956ds/644Mi)
% 32.40/5.94 % (1652)Instruction limit reached!
% 32.40/5.94 % (1652)------------------------------
% 32.40/5.94 % (1652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.40/5.94 % (1652)Termination reason: Unknown
% 32.40/5.94 % (1652)Termination phase: Saturation
% 32.40/5.94
% 32.40/5.94 % (1652)Memory used [KB]: 9083
% 32.40/5.94 % (1652)Time elapsed: 0.278 s
% 32.40/5.94 % (1652)Instructions burned: 1005 (million)
% 32.40/5.94 % (1652)------------------------------
% 32.40/5.94 % (1652)------------------------------
% 32.40/5.94 % (1656)Instruction limit reached!
% 32.40/5.94 % (1656)------------------------------
% 32.40/5.94 % (1656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.40/5.94 % (1656)Termination reason: Unknown
% 32.40/5.94 % (1656)Termination phase: Saturation
% 32.40/5.94
% 32.40/5.94 % (1656)Memory used [KB]: 9210
% 32.40/5.94 % (1656)Time elapsed: 0.159 s
% 32.40/5.94 % (1656)Instructions burned: 644 (million)
% 32.40/5.94 % (1656)------------------------------
% 32.40/5.94 % (1656)------------------------------
% 32.40/5.95 % (1660)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_1200 for (2955ds/1201Mi)
% 32.40/5.95 % (1661)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_1200 for (2955ds/1046Mi)
% 32.40/5.98 % (1654)Instruction limit reached!
% 32.40/5.98 % (1654)------------------------------
% 32.40/5.98 % (1654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.40/5.98 % (1654)Termination reason: Unknown
% 32.40/5.98 % (1654)Termination phase: Saturation
% 32.40/5.98
% 32.40/5.98 % (1654)Memory used [KB]: 8443
% 32.40/5.98 % (1654)Time elapsed: 0.303 s
% 32.40/5.98 % (1654)Instructions burned: 954 (million)
% 32.40/5.98 % (1654)------------------------------
% 32.40/5.98 % (1654)------------------------------
% 32.40/5.99 % (1662)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_1200 for (2954ds/222Mi)
% 34.41/6.04 % (1662)Instruction limit reached!
% 34.41/6.04 % (1662)------------------------------
% 34.41/6.04 % (1662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.41/6.04 % (1662)Termination reason: Unknown
% 34.41/6.04 % (1662)Termination phase: Saturation
% 34.41/6.04
% 34.41/6.04 % (1662)Memory used [KB]: 6524
% 34.41/6.04 % (1662)Time elapsed: 0.056 s
% 34.41/6.04 % (1662)Instructions burned: 226 (million)
% 34.41/6.04 % (1662)------------------------------
% 34.41/6.04 % (1662)------------------------------
% 34.41/6.05 % (1663)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_1200 for (2954ds/68Mi)
% 34.41/6.06 % (1659)Instruction limit reached!
% 34.41/6.06 % (1659)------------------------------
% 34.41/6.06 % (1659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.41/6.06 % (1659)Termination reason: Unknown
% 34.41/6.06 % (1659)Termination phase: Saturation
% 34.41/6.06
% 34.41/6.06 % (1659)Memory used [KB]: 7291
% 34.41/6.06 % (1659)Time elapsed: 0.198 s
% 34.41/6.06 % (1659)Instructions burned: 644 (million)
% 34.41/6.06 % (1659)------------------------------
% 34.41/6.06 % (1659)------------------------------
% 34.41/6.07 % (1663)Instruction limit reached!
% 34.41/6.07 % (1663)------------------------------
% 34.41/6.07 % (1663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.41/6.07 % (1663)Termination reason: Unknown
% 34.41/6.07 % (1663)Termination phase: Property scanning
% 34.41/6.07
% 34.41/6.07 % (1663)Memory used [KB]: 1918
% 34.41/6.07 % (1663)Time elapsed: 0.019 s
% 34.41/6.07 % (1663)Instructions burned: 70 (million)
% 34.41/6.07 % (1663)------------------------------
% 34.41/6.07 % (1663)------------------------------
% 34.41/6.07 % (1664)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_1200 for (2953ds/454Mi)
% 34.41/6.08 % (1665)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_1200 for (2953ds/360Mi)
% 34.41/6.09 % (1657)Instruction limit reached!
% 34.41/6.09 % (1657)------------------------------
% 34.41/6.09 % (1657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.41/6.09 % (1657)Termination reason: Unknown
% 34.41/6.09 % (1657)Termination phase: Saturation
% 34.41/6.09
% 34.41/6.09 % (1657)Memory used [KB]: 6780
% 34.41/6.09 % (1657)Time elapsed: 0.242 s
% 34.41/6.09 % (1657)Instructions burned: 865 (million)
% 34.41/6.09 % (1657)------------------------------
% 34.41/6.09 % (1657)------------------------------
% 34.41/6.10 % (1666)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_1200 for (2953ds/157Mi)
% 35.04/6.14 % (1666)Instruction limit reached!
% 35.04/6.14 % (1666)------------------------------
% 35.04/6.14 % (1666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.04/6.14 % (1666)Termination reason: Unknown
% 35.04/6.14 % (1666)Termination phase: Saturation
% 35.04/6.14
% 35.04/6.14 % (1666)Memory used [KB]: 6524
% 35.04/6.14 % (1666)Time elapsed: 0.043 s
% 35.04/6.14 % (1666)Instructions burned: 159 (million)
% 35.04/6.14 % (1666)------------------------------
% 35.04/6.14 % (1666)------------------------------
% 35.04/6.15 % (1667)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_1200 for (2953ds/5061Mi)
% 35.04/6.17 % (1665)Instruction limit reached!
% 35.04/6.17 % (1665)------------------------------
% 35.04/6.17 % (1665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.04/6.17 % (1665)Termination reason: Unknown
% 35.04/6.17 % (1665)Termination phase: Saturation
% 35.04/6.17
% 35.04/6.17 % (1665)Memory used [KB]: 6652
% 35.04/6.17 % (1665)Time elapsed: 0.089 s
% 35.04/6.17 % (1665)Instructions burned: 361 (million)
% 35.04/6.17 % (1665)------------------------------
% 35.04/6.17 % (1665)------------------------------
% 35.04/6.18 % (1668)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_1200 for (2952ds/2401Mi)
% 35.04/6.19 % (1664)Instruction limit reached!
% 35.04/6.19 % (1664)------------------------------
% 35.04/6.19 % (1664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.04/6.19 % (1664)Termination reason: Unknown
% 35.04/6.19 % (1664)Termination phase: Saturation
% 35.04/6.19
% 35.04/6.19 % (1664)Memory used [KB]: 13816
% 35.04/6.19 % (1664)Time elapsed: 0.115 s
% 35.04/6.19 % (1664)Instructions burned: 454 (million)
% 35.04/6.19 % (1664)------------------------------
% 35.04/6.19 % (1664)------------------------------
% 35.04/6.20 % (1669)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_1200 for (2952ds/5798Mi)
% 35.60/6.20 % (1661)Instruction limit reached!
% 35.60/6.20 % (1661)------------------------------
% 35.60/6.20 % (1661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.60/6.20 % (1661)Termination reason: Unknown
% 35.60/6.20 % (1661)Termination phase: Saturation
% 35.60/6.20
% 35.60/6.20 % (1661)Memory used [KB]: 6780
% 35.60/6.20 % (1661)Time elapsed: 0.248 s
% 35.60/6.20 % (1661)Instructions burned: 1049 (million)
% 35.60/6.20 % (1661)------------------------------
% 35.60/6.20 % (1661)------------------------------
% 35.60/6.21 % (1670)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_1200 for (2952ds/346Mi)
% 35.60/6.22 % (1658)Instruction limit reached!
% 35.60/6.22 % (1658)------------------------------
% 35.60/6.22 % (1658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.60/6.22 % (1658)Termination reason: Unknown
% 35.60/6.22 % (1658)Termination phase: Saturation
% 35.60/6.22
% 35.60/6.22 % (1658)Memory used [KB]: 8315
% 35.60/6.22 % (1658)Time elapsed: 0.371 s
% 35.60/6.22 % (1658)Instructions burned: 1176 (million)
% 35.60/6.22 % (1658)------------------------------
% 35.60/6.22 % (1658)------------------------------
% 35.60/6.23 % (1671)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_1200 for (2952ds/1321Mi)
% 35.60/6.29 % (1660)Instruction limit reached!
% 35.60/6.29 % (1660)------------------------------
% 35.60/6.29 % (1660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.60/6.29 % (1660)Termination reason: Unknown
% 35.60/6.29 % (1660)Termination phase: Saturation
% 35.60/6.29
% 35.60/6.29 % (1660)Memory used [KB]: 9466
% 35.60/6.29 % (1660)Time elapsed: 0.340 s
% 35.60/6.29 % (1660)Instructions burned: 1203 (million)
% 35.60/6.29 % (1660)------------------------------
% 35.60/6.29 % (1660)------------------------------
% 35.60/6.29 % (1670)Instruction limit reached!
% 35.60/6.29 % (1670)------------------------------
% 35.60/6.29 % (1670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.60/6.29 % (1670)Termination reason: Unknown
% 35.60/6.29 % (1670)Termination phase: Saturation
% 35.60/6.29
% 35.60/6.29 % (1670)Memory used [KB]: 9083
% 35.60/6.29 % (1670)Time elapsed: 0.087 s
% 35.60/6.29 % (1670)Instructions burned: 350 (million)
% 35.60/6.29 % (1670)------------------------------
% 35.60/6.29 % (1670)------------------------------
% 35.93/6.30 % (1672)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_1200 for (2951ds/1312Mi)
% 35.93/6.30 % (1673)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_1200 for (2951ds/672Mi)
% 36.14/6.51 % (1673)Instruction limit reached!
% 36.14/6.51 % (1673)------------------------------
% 36.14/6.51 % (1673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.14/6.51 % (1673)Termination reason: Unknown
% 36.14/6.51 % (1673)Termination phase: Saturation
% 36.14/6.51
% 36.14/6.51 % (1673)Memory used [KB]: 9338
% 36.14/6.51 % (1673)Time elapsed: 0.205 s
% 36.14/6.51 % (1673)Instructions burned: 674 (million)
% 36.14/6.51 % (1673)------------------------------
% 36.14/6.51 % (1673)------------------------------
% 36.14/6.52 % (1674)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_1200 for (2949ds/1897Mi)
% 36.45/6.64 % (1671)Instruction limit reached!
% 36.45/6.64 % (1671)------------------------------
% 36.45/6.64 % (1671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.45/6.64 % (1671)Termination reason: Unknown
% 36.45/6.64 % (1671)Termination phase: Saturation
% 36.45/6.64
% 36.45/6.64 % (1671)Memory used [KB]: 6140
% 36.45/6.64 % (1671)Time elapsed: 0.404 s
% 36.45/6.64 % (1671)Instructions burned: 1322 (million)
% 36.45/6.64 % (1671)------------------------------
% 36.45/6.64 % (1671)------------------------------
% 36.45/6.64 % (1672)Instruction limit reached!
% 36.45/6.64 % (1672)------------------------------
% 36.45/6.64 % (1672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.45/6.64 % (1672)Termination reason: Unknown
% 36.45/6.64 % (1672)Termination phase: Saturation
% 36.45/6.64
% 36.45/6.64 % (1672)Memory used [KB]: 9978
% 36.45/6.64 % (1672)Time elapsed: 0.342 s
% 36.45/6.64 % (1672)Instructions burned: 1314 (million)
% 36.45/6.64 % (1672)------------------------------
% 36.45/6.64 % (1672)------------------------------
% 36.45/6.65 % (1675)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_1200 for (2948ds/1202Mi)
% 36.45/6.65 % (1676)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_1200 for (2948ds/1493Mi)
% 37.53/6.90 % (1668)Instruction limit reached!
% 37.53/6.90 % (1668)------------------------------
% 37.53/6.90 % (1668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.53/6.90 % (1668)Termination reason: Unknown
% 37.53/6.90 % (1668)Termination phase: Saturation
% 37.53/6.90
% 37.53/6.90 % (1668)Memory used [KB]: 7547
% 37.53/6.90 % (1668)Time elapsed: 0.725 s
% 37.53/6.90 % (1668)Instructions burned: 2401 (million)
% 37.53/6.90 % (1668)------------------------------
% 37.53/6.90 % (1668)------------------------------
% 37.53/6.91 % (1677)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_1200 for (2945ds/7679Mi)
% 37.53/6.99 % (1676)Instruction limit reached!
% 37.53/6.99 % (1676)------------------------------
% 37.53/6.99 % (1676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.53/6.99 % (1676)Termination reason: Unknown
% 37.53/6.99 % (1676)Termination phase: Saturation
% 37.53/6.99
% 37.53/6.99 % (1676)Memory used [KB]: 6780
% 37.53/6.99 % (1676)Time elapsed: 0.338 s
% 37.53/6.99 % (1676)Instructions burned: 1495 (million)
% 37.53/6.99 % (1676)------------------------------
% 37.53/6.99 % (1676)------------------------------
% 37.53/6.99 % (1675)Instruction limit reached!
% 37.53/6.99 % (1675)------------------------------
% 37.53/6.99 % (1675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.53/6.99 % (1675)Termination reason: Unknown
% 37.53/6.99 % (1675)Termination phase: Saturation
% 37.53/6.99
% 37.53/6.99 % (1675)Memory used [KB]: 6524
% 37.53/6.99 % (1675)Time elapsed: 0.347 s
% 37.53/6.99 % (1675)Instructions burned: 1203 (million)
% 37.53/6.99 % (1675)------------------------------
% 37.53/6.99 % (1675)------------------------------
% 37.53/7.00 % (1678)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_1200 for (2944ds/340Mi)
% 37.53/7.00 % (1679)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_1200 for (2944ds/3672Mi)
% 41.42/7.10 % (1678)Instruction limit reached!
% 41.42/7.10 % (1678)------------------------------
% 41.42/7.10 % (1678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.42/7.10 % (1678)Termination reason: Unknown
% 41.42/7.10 % (1678)Termination phase: Saturation
% 41.42/7.10
% 41.42/7.10 % (1678)Memory used [KB]: 8955
% 41.42/7.10 % (1678)Time elapsed: 0.109 s
% 41.42/7.10 % (1678)Instructions burned: 342 (million)
% 41.42/7.10 % (1678)------------------------------
% 41.42/7.10 % (1678)------------------------------
% 41.42/7.11 % (1674)Instruction limit reached!
% 41.42/7.11 % (1674)------------------------------
% 41.42/7.11 % (1674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.42/7.11 % (1674)Termination reason: Unknown
% 41.42/7.11 % (1674)Termination phase: Saturation
% 41.42/7.11
% 41.42/7.11 % (1674)Memory used [KB]: 11769
% 41.42/7.11 % (1674)Time elapsed: 0.597 s
% 41.42/7.11 % (1674)Instructions burned: 1898 (million)
% 41.42/7.11 % (1674)------------------------------
% 41.42/7.11 % (1674)------------------------------
% 41.42/7.11 % (1680)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_1200 for (2943ds/1535Mi)
% 41.42/7.12 % (1681)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on DTF2THF_1200 for (2943ds/4637Mi)
% 43.53/7.48 % (1648)Refutation not found, non-redundant clauses discarded% (1648)------------------------------
% 43.53/7.48 % (1648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.53/7.48 % (1648)Termination reason: Refutation not found, non-redundant clauses discarded
% 43.53/7.48
% 43.53/7.48 % (1648)Memory used [KB]: 13048
% 43.53/7.48 % (1648)Time elapsed: 2.048 s
% 43.53/7.48 % (1648)Instructions burned: 6441 (million)
% 43.53/7.48 % (1648)------------------------------
% 43.53/7.48 % (1648)------------------------------
% 43.53/7.49 % (1682)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_1200 for (2939ds/3174Mi)
% 44.02/7.50 % (1680)Instruction limit reached!
% 44.02/7.50 % (1680)------------------------------
% 44.02/7.50 % (1680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.02/7.50 % (1680)Termination reason: Unknown
% 44.02/7.50 % (1680)Termination phase: Saturation
% 44.02/7.50
% 44.02/7.50 % (1680)Memory used [KB]: 11513
% 44.02/7.50 % (1680)Time elapsed: 0.387 s
% 44.02/7.50 % (1680)Instructions burned: 1535 (million)
% 44.02/7.50 % (1680)------------------------------
% 44.02/7.50 % (1680)------------------------------
% 44.02/7.51 % (1683)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_1200 for (2939ds/307Mi)
% 44.02/7.56 % (1667)Instruction limit reached!
% 44.02/7.56 % (1667)------------------------------
% 44.02/7.56 % (1667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.02/7.56 % (1667)Termination reason: Unknown
% 44.02/7.56 % (1667)Termination phase: Saturation
% 44.02/7.56
% 44.02/7.56 % (1667)Memory used [KB]: 9210
% 44.02/7.56 % (1667)Time elapsed: 1.410 s
% 44.02/7.56 % (1667)Instructions burned: 5063 (million)
% 44.02/7.56 % (1667)------------------------------
% 44.02/7.56 % (1667)------------------------------
% 44.02/7.57 % (1684)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on DTF2THF_1200 for (2938ds/3619Mi)
% 44.02/7.58 % (1683)Instruction limit reached!
% 44.02/7.58 % (1683)------------------------------
% 44.02/7.58 % (1683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.02/7.58 % (1683)Termination reason: Unknown
% 44.02/7.58 % (1683)Termination phase: Saturation
% 44.02/7.58
% 44.02/7.58 % (1683)Memory used [KB]: 6524
% 44.02/7.58 % (1683)Time elapsed: 0.075 s
% 44.02/7.58 % (1683)Instructions burned: 310 (million)
% 44.02/7.58 % (1683)------------------------------
% 44.02/7.58 % (1683)------------------------------
% 44.02/7.59 % (1685)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_1200 for (2938ds/2325Mi)
% 45.79/8.02 % (1669)Instruction limit reached!
% 45.79/8.02 % (1669)------------------------------
% 45.79/8.02 % (1669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.79/8.02 % (1669)Termination reason: Unknown
% 45.79/8.02 % (1669)Termination phase: Saturation
% 45.79/8.02
% 45.79/8.02 % (1669)Memory used [KB]: 12409
% 45.79/8.02 % (1669)Time elapsed: 1.827 s
% 45.79/8.02 % (1669)Instructions burned: 5798 (million)
% 45.79/8.02 % (1669)------------------------------
% 45.79/8.02 % (1669)------------------------------
% 48.44/8.03 % (1686)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on DTF2THF_1200 for (2934ds/2341Mi)
% 49.09/8.17 % (1679)Instruction limit reached!
% 49.09/8.17 % (1679)------------------------------
% 49.09/8.17 % (1679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.09/8.17 % (1679)Termination reason: Unknown
% 49.09/8.17 % (1679)Termination phase: Saturation
% 49.09/8.17
% 49.09/8.17 % (1679)Memory used [KB]: 11641
% 49.09/8.17 % (1679)Time elapsed: 1.174 s
% 49.09/8.17 % (1679)Instructions burned: 3672 (million)
% 49.09/8.17 % (1679)------------------------------
% 49.09/8.17 % (1679)------------------------------
% 49.09/8.18 % (1687)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on DTF2THF_1200 for (2932ds/7257Mi)
% 50.02/8.34 % (1685)Instruction limit reached!
% 50.02/8.34 % (1685)------------------------------
% 50.02/8.34 % (1685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.02/8.34 % (1685)Termination reason: Unknown
% 50.02/8.34 % (1685)Termination phase: Saturation
% 50.02/8.34
% 50.02/8.34 % (1685)Memory used [KB]: 13304
% 50.02/8.34 % (1685)Time elapsed: 0.749 s
% 50.02/8.34 % (1685)Instructions burned: 2327 (million)
% 50.02/8.34 % (1685)------------------------------
% 50.02/8.34 % (1685)------------------------------
% 50.02/8.35 % (1688)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on DTF2THF_1200 for (2931ds/3710Mi)
% 50.46/8.48 % (1682)Instruction limit reached!
% 50.46/8.48 % (1682)------------------------------
% 50.46/8.48 % (1682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.46/8.48 % (1682)Termination reason: Unknown
% 50.46/8.48 % (1682)Termination phase: Saturation
% 50.46/8.48
% 50.46/8.48 % (1682)Memory used [KB]: 15991
% 50.46/8.48 % (1682)Time elapsed: 0.995 s
% 50.46/8.48 % (1682)Instructions burned: 3177 (million)
% 50.46/8.48 % (1682)------------------------------
% 50.46/8.48 % (1682)------------------------------
% 50.46/8.49 % (1689)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on DTF2THF_1200 for (2929ds/326Mi)
% 50.87/8.59 % (1689)Instruction limit reached!
% 50.87/8.59 % (1689)------------------------------
% 50.87/8.59 % (1689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.87/8.59 % (1689)Termination reason: Unknown
% 50.87/8.59 % (1689)Termination phase: Saturation
% 50.87/8.59
% 50.87/8.59 % (1689)Memory used [KB]: 7419
% 50.87/8.59 % (1689)Time elapsed: 0.096 s
% 50.87/8.59 % (1689)Instructions burned: 326 (million)
% 50.87/8.59 % (1689)------------------------------
% 50.87/8.59 % (1689)------------------------------
% 51.29/8.60 % (1690)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on DTF2THF_1200 for (2928ds/1100Mi)
% 51.29/8.62 % (1681)Instruction limit reached!
% 51.29/8.62 % (1681)------------------------------
% 51.29/8.62 % (1681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.29/8.62 % (1681)Termination reason: Unknown
% 51.29/8.62 % (1681)Termination phase: Saturation
% 51.29/8.62
% 51.29/8.62 % (1681)Memory used [KB]: 11129
% 51.29/8.62 % (1681)Time elapsed: 1.502 s
% 51.29/8.62 % (1681)Instructions burned: 4637 (million)
% 51.29/8.62 % (1681)------------------------------
% 51.29/8.62 % (1681)------------------------------
% 51.29/8.63 % (1691)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_1200 for (2928ds/406Mi)
% 51.29/8.68 % (1684)Instruction limit reached!
% 51.29/8.68 % (1684)------------------------------
% 51.29/8.68 % (1684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.29/8.68 % (1684)Termination reason: Unknown
% 51.29/8.68 % (1684)Termination phase: Saturation
% 51.29/8.68
% 51.29/8.68 % (1684)Memory used [KB]: 17398
% 51.29/8.68 % (1684)Time elapsed: 1.106 s
% 51.29/8.68 % (1684)Instructions burned: 3619 (million)
% 51.29/8.68 % (1684)------------------------------
% 51.29/8.68 % (1684)------------------------------
% 51.29/8.69 % (1692)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1871:si=on:rtra=on_0 on DTF2THF_1200 for (2927ds/1871Mi)
% 51.51/8.75 % (1691)Instruction limit reached!
% 51.51/8.75 % (1691)------------------------------
% 51.51/8.75 % (1691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.51/8.75 % (1691)Termination reason: Unknown
% 51.51/8.75 % (1691)Termination phase: Saturation
% 51.51/8.75
% 51.51/8.75 % (1691)Memory used [KB]: 6908
% 51.51/8.75 % (1691)Time elapsed: 0.136 s
% 51.51/8.75 % (1691)Instructions burned: 408 (million)
% 51.51/8.75 % (1691)------------------------------
% 51.51/8.75 % (1691)------------------------------
% 51.51/8.76 % (1693)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1194:si=on:rtra=on_0 on DTF2THF_1200 for (2927ds/1194Mi)
% 51.51/8.77 % (1686)Instruction limit reached!
% 51.51/8.77 % (1686)------------------------------
% 51.51/8.77 % (1686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.51/8.77 % (1686)Termination reason: Unknown
% 51.51/8.77 % (1686)Termination phase: Saturation
% 51.51/8.77
% 51.51/8.77 % (1686)Memory used [KB]: 9594
% 51.51/8.77 % (1686)Time elapsed: 0.743 s
% 51.51/8.77 % (1686)Instructions burned: 2343 (million)
% 51.51/8.77 % (1686)------------------------------
% 51.51/8.77 % (1686)------------------------------
% 51.51/8.78 % (1694)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_1200 for (2926ds/474Mi)
% 52.59/8.90 % (1694)Instruction limit reached!
% 52.59/8.90 % (1694)------------------------------
% 52.59/8.90 % (1694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.59/8.90 % (1694)Termination reason: Unknown
% 52.59/8.90 % (1694)Termination phase: Saturation
% 52.59/8.90
% 52.59/8.90 % (1694)Memory used [KB]: 9466
% 52.59/8.90 % (1694)Time elapsed: 0.138 s
% 52.59/8.90 % (1694)Instructions burned: 474 (million)
% 52.59/8.90 % (1694)------------------------------
% 52.59/8.90 % (1694)------------------------------
% 52.59/8.91 % (1695)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3115:si=on:rtra=on_0 on DTF2THF_1200 for (2925ds/3115Mi)
% 52.59/8.95 % (1690)Instruction limit reached!
% 52.59/8.95 % (1690)------------------------------
% 52.59/8.95 % (1690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.59/8.95 % (1690)Termination reason: Unknown
% 52.59/8.95 % (1690)Termination phase: Saturation
% 52.59/8.95
% 52.59/8.95 % (1690)Memory used [KB]: 11513
% 52.59/8.95 % (1690)Time elapsed: 0.371 s
% 52.59/8.95 % (1690)Instructions burned: 1102 (million)
% 52.59/8.95 % (1690)------------------------------
% 52.59/8.95 % (1690)------------------------------
% 52.59/8.96 % (1696)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_1200 for (2925ds/831Mi)
% 56.23/9.13 % (1693)Instruction limit reached!
% 56.23/9.13 % (1693)------------------------------
% 56.23/9.13 % (1693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.23/9.13 % (1693)Termination reason: Unknown
% 56.23/9.13 % (1693)Termination phase: Saturation
% 56.23/9.13
% 56.23/9.13 % (1693)Memory used [KB]: 10234
% 56.23/9.13 % (1693)Time elapsed: 0.397 s
% 56.23/9.13 % (1693)Instructions burned: 1194 (million)
% 56.23/9.13 % (1693)------------------------------
% 56.23/9.13 % (1693)------------------------------
% 56.23/9.14 % (1697)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_1200 for (2923ds/1188Mi)
% 56.67/9.22 % (1696)Instruction limit reached!
% 56.67/9.22 % (1696)------------------------------
% 56.67/9.22 % (1696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.67/9.22 % (1696)Termination reason: Unknown
% 56.67/9.22 % (1696)Termination phase: Saturation
% 56.67/9.22
% 56.67/9.22 % (1696)Memory used [KB]: 8443
% 56.67/9.22 % (1696)Time elapsed: 0.261 s
% 56.67/9.22 % (1696)Instructions burned: 833 (million)
% 56.67/9.22 % (1696)------------------------------
% 56.67/9.22 % (1696)------------------------------
% 56.67/9.23 % (1698)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=2868:si=on:rtra=on_0 on DTF2THF_1200 for (2922ds/2868Mi)
% 56.67/9.27 % (1692)Instruction limit reached!
% 56.67/9.27 % (1692)------------------------------
% 56.67/9.27 % (1692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.67/9.27 % (1692)Termination reason: Unknown
% 56.67/9.27 % (1692)Termination phase: Saturation
% 56.67/9.27
% 56.67/9.27 % (1692)Memory used [KB]: 15095
% 56.67/9.27 % (1692)Time elapsed: 0.606 s
% 56.67/9.27 % (1692)Instructions burned: 1872 (million)
% 56.67/9.27 % (1692)------------------------------
% 56.67/9.27 % (1692)------------------------------
% 56.67/9.28 % (1677)Instruction limit reached!
% 56.67/9.28 % (1677)------------------------------
% 56.67/9.28 % (1677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.67/9.28 % (1677)Termination reason: Unknown
% 56.67/9.28 % (1677)Termination phase: Saturation
% 56.67/9.28
% 56.67/9.28 % (1677)Memory used [KB]: 15351
% 56.67/9.28 % (1677)Time elapsed: 2.365 s
% 56.67/9.28 % (1677)Instructions burned: 7680 (million)
% 56.67/9.28 % (1677)------------------------------
% 56.67/9.28 % (1677)------------------------------
% 56.67/9.28 % (1688)Instruction limit reached!
% 56.67/9.28 % (1688)------------------------------
% 56.67/9.28 % (1688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.67/9.28 % (1688)Termination reason: Unknown
% 56.67/9.28 % (1688)Termination phase: Saturation
% 56.67/9.28
% 56.67/9.28 % (1688)Memory used [KB]: 10746
% 56.67/9.28 % (1688)Time elapsed: 0.927 s
% 56.67/9.28 % (1688)Instructions burned: 3712 (million)
% 56.67/9.28 % (1688)------------------------------
% 56.67/9.28 % (1688)------------------------------
% 56.67/9.28 % (1699)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on DTF2THF_1200 for (2921ds/1516Mi)
% 56.67/9.29 % (1700)lrs+1002_1:20_afp=1000:au=on:bsd=on:cnfonf=lazy_not_gen_be_off:sos=all:sp=const_max:i=2321:si=on:rtra=on_0 on DTF2THF_1200 for (2921ds/2321Mi)
% 56.67/9.29 % (1701)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_1200 for (2921ds/2812Mi)
% 57.36/9.44 % (1697)Instruction limit reached!
% 57.36/9.44 % (1697)------------------------------
% 57.36/9.44 % (1697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.36/9.44 % (1697)Termination reason: Unknown
% 57.36/9.44 % (1697)Termination phase: Saturation
% 57.36/9.44
% 57.36/9.44 % (1697)Memory used [KB]: 10362
% 57.36/9.44 % (1697)Time elapsed: 0.303 s
% 57.36/9.44 % (1697)Instructions burned: 1191 (million)
% 57.36/9.44 % (1697)------------------------------
% 57.36/9.44 % (1697)------------------------------
% 57.36/9.45 % (1703)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_1200 for (2920ds/4604Mi)
% 57.88/9.51 % (1699)First to succeed.
% 57.88/9.52 % (1699)Refutation found. Thanks to Tanya!
% 57.88/9.52 % SZS status Theorem for DTF2THF_1200
% 57.88/9.52 % SZS output start Proof for DTF2THF_1200
% 57.88/9.52 thf(func_def_0, type, in: $i > $i > $o).
% 57.88/9.52 thf(func_def_1, type, exu: ($i > $o) > $o).
% 57.88/9.52 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 57.88/9.52 thf(func_def_8, type, powerset: $i > $i).
% 57.88/9.52 thf(func_def_10, type, setunion: $i > $i).
% 57.88/9.52 thf(func_def_19, type, descr: ($i > $o) > $i).
% 57.88/9.52 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 57.88/9.52 thf(func_def_26, type, prop2set: $o > $i).
% 57.88/9.52 thf(func_def_36, type, nonempty: $i > $o).
% 57.88/9.52 thf(func_def_69, type, set2prop: $i > $o).
% 57.88/9.52 thf(func_def_88, type, subset: $i > $i > $o).
% 57.88/9.52 thf(func_def_89, type, disjoint: $i > $i > $o).
% 57.88/9.52 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 57.88/9.52 thf(func_def_114, type, binunion: $i > $i > $i).
% 57.88/9.52 thf(func_def_122, type, binintersect: $i > $i > $i).
% 57.88/9.52 thf(func_def_135, type, regular: $i > $o).
% 57.88/9.52 thf(func_def_136, type, setminus: $i > $i > $i).
% 57.88/9.52 thf(func_def_147, type, symdiff: $i > $i > $i).
% 57.88/9.52 thf(func_def_153, type, iskpair: $i > $o).
% 57.88/9.52 thf(func_def_158, type, kpair: $i > $i > $i).
% 57.88/9.52 thf(func_def_160, type, cartprod: $i > $i > $i).
% 57.88/9.52 thf(func_def_177, type, singleton: $i > $o).
% 57.88/9.52 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 57.88/9.52 thf(func_def_193, type, sP0: $o > $i > $i > $i > $o).
% 57.88/9.52 thf(func_def_194, type, sP1: $i > $i > $o).
% 57.88/9.52 thf(func_def_195, type, sP2: $i > $o).
% 57.88/9.52 thf(func_def_196, type, sP3: $i > $i > $o).
% 57.88/9.52 thf(func_def_197, type, sP4: $i > $i > $o).
% 57.88/9.52 thf(func_def_207, type, sK14: $i > $i).
% 57.88/9.52 thf(func_def_211, type, sK18: $i > $i > $i).
% 57.88/9.52 thf(func_def_221, type, sK28: $i > $i > $i).
% 57.88/9.52 thf(func_def_228, type, sK35: $i > $o).
% 57.88/9.52 thf(func_def_236, type, sK43: $i > $o).
% 57.88/9.52 thf(func_def_239, type, sK46: $i > ($i > $o) > $i).
% 57.88/9.52 thf(func_def_251, type, sK58: ($i > $o) > $i).
% 57.88/9.52 thf(func_def_252, type, sK59: ($i > $o) > $i).
% 57.88/9.52 thf(func_def_253, type, sK60: $i > $o).
% 57.88/9.52 thf(func_def_264, type, sK71: $i > ($i > $o) > $i).
% 57.88/9.52 thf(func_def_265, type, sK72: $i > $o).
% 57.88/9.52 thf(func_def_273, type, sK80: $i > $o).
% 57.88/9.52 thf(func_def_274, type, sK81: $i > $i).
% 57.88/9.52 thf(func_def_275, type, sK82: ($i > $o) > $i).
% 57.88/9.52 thf(func_def_287, type, sK94: $i > $o).
% 57.88/9.52 thf(func_def_294, type, sK101: $i > $i > $i).
% 57.88/9.52 thf(func_def_295, type, sK102: $i > $i > $i).
% 57.88/9.52 thf(func_def_296, type, sK103: $i > $i > $i).
% 57.88/9.52 thf(func_def_297, type, sK104: $i > $i > $i).
% 57.88/9.52 thf(func_def_298, type, sK105: $i > $i > $i).
% 57.88/9.52 thf(func_def_299, type, sK106: $i > $i > $i > $i).
% 57.88/9.52 thf(func_def_300, type, sK107: $i > $i).
% 57.88/9.52 thf(func_def_301, type, sK108: $i > $i).
% 57.88/9.52 thf(func_def_302, type, sK109: $i > $i).
% 57.88/9.52 thf(func_def_303, type, sK110: $i > $i).
% 57.88/9.52 thf(func_def_304, type, sK111: $i > $i > $i > $i).
% 57.88/9.52 thf(func_def_305, type, sK112: $i > $i > $i > $i).
% 57.88/9.52 thf(func_def_306, type, sK113: $i > $i > $i).
% 57.88/9.52 thf(func_def_307, type, sK114: $i > $i > $i).
% 57.88/9.52 thf(func_def_308, type, sK115: $i > $i > $i).
% 57.88/9.52 thf(func_def_309, type, sK116: $i > $i).
% 57.88/9.52 thf(func_def_311, type, sK118: $i > $i).
% 57.88/9.52 thf(func_def_312, type, sK119: $i > $i).
% 57.88/9.52 thf(func_def_315, type, sK122: ($i > $o) > $i).
% 57.88/9.52 thf(func_def_316, type, sK123: $i > $o).
% 57.88/9.52 thf(func_def_317, type, sK124: $i > $i).
% 57.88/9.52 thf(func_def_321, type, sK128: $i > $i > $i > $i).
% 57.88/9.52 thf(func_def_322, type, sK129: $i > $i > $i > $i).
% 57.88/9.52 thf(func_def_333, type, sK140: $i > $i).
% 57.88/9.52 thf(func_def_334, type, sK141: $i > $i > $i).
% 57.88/9.52 thf(func_def_339, type, sK146: $i > $i > $o).
% 57.88/9.52 thf(func_def_340, type, sK147: $i > $i).
% 57.88/9.52 thf(func_def_341, type, sK148: $i > $i).
% 57.88/9.52 thf(func_def_342, type, sK149: ($i > $i > $o) > $i > $i).
% 57.88/9.52 thf(func_def_343, type, sK150: $i > ($i > $i > $o) > $i > $i).
% 57.88/9.52 thf(func_def_344, type, sK151: ($i > $i > $o) > $i > $i).
% 57.88/9.52 thf(func_def_349, type, sK156: ($i > $o) > $i > $i).
% 57.88/9.52 thf(func_def_351, type, sK158: $i > $o).
% 57.88/9.52 thf(func_def_363, type, sK170: $i > $i).
% 57.88/9.52 thf(func_def_367, type, sK174: $i > $i > $i).
% 57.88/9.52 thf(func_def_369, type, sK176: $i > $o).
% 57.88/9.52 thf(func_def_370, type, sK177: ($i > $o) > $i > $i).
% 57.88/9.52 thf(func_def_375, type, sK182: $i > $o).
% 57.88/9.52 thf(func_def_376, type, sK183: $o > $i > $i > $i).
% 57.88/9.52 thf(func_def_382, type, sK189: $i > $i).
% 57.88/9.52 thf(func_def_383, type, sK190: $i > $i).
% 57.88/9.52 thf(func_def_391, type, sK198: ($i > $o) > $i > $i).
% 57.88/9.52 thf(func_def_393, type, sK200: $i > $o).
% 57.88/9.52 thf(func_def_395, type, sK202: $i > $o).
% 57.88/9.52 thf(func_def_398, type, sK205: $i > ($i > $o) > $i).
% 57.88/9.52 thf(func_def_399, type, sK206: $i > ($i > $o) > $i).
% 57.88/9.52 thf(func_def_402, type, sK209: $i > $o).
% 57.88/9.52 thf(func_def_422, type, sK229: $i > $o).
% 57.88/9.52 thf(func_def_423, type, sK230: $i > $o).
% 57.88/9.52 thf(func_def_424, type, sK231: ($i > $o) > ($i > $o) > $i).
% 57.88/9.52 thf(func_def_425, type, sK232: ($i > $o) > ($i > $o) > $i).
% 57.88/9.52 thf(func_def_426, type, sK233: ($i > $o) > $i > $i).
% 57.88/9.52 thf(func_def_428, type, sK235: $i > $o).
% 57.88/9.52 thf(func_def_434, type, sK241: $i > $i > $i).
% 57.88/9.52 thf(func_def_449, type, sK256: $i > $i > $i).
% 57.88/9.52 thf(func_def_460, type, sK267: $i > $o).
% 57.88/9.52 thf(func_def_461, type, sK268: $i > $o).
% 57.88/9.52 thf(func_def_462, type, sK269: ($i > $o) > ($i > $o) > $i > $i > $i).
% 57.88/9.52 thf(func_def_463, type, sK270: ($i > $o) > ($i > $o) > $i > $i > $i).
% 57.88/9.52 thf(func_def_466, type, sK273: $i > $i).
% 57.88/9.52 thf(func_def_482, type, sK289: $i > $i).
% 57.88/9.52 thf(func_def_498, type, sK305: $i > $o).
% 57.88/9.52 thf(func_def_500, type, sK307: ($i > $o) > $i > $i).
% 57.88/9.52 thf(func_def_503, type, sK310: $i > $i > $i).
% 57.88/9.52 thf(func_def_504, type, sK311: $i > $i > $i).
% 57.88/9.52 thf(func_def_505, type, sK312: $i > $i > $i).
% 57.88/9.52 thf(func_def_508, type, sK315: $i > ($i > $o) > $i).
% 57.88/9.52 thf(func_def_509, type, sK316: $i > $o).
% 57.88/9.52 thf(func_def_516, type, sK323: $i > $o).
% 57.88/9.52 thf(func_def_520, type, sK327: $i > $o).
% 57.88/9.52 thf(func_def_521, type, sK328: $i > $o).
% 57.88/9.52 thf(func_def_540, type, sK347: $i > $o).
% 57.88/9.52 thf(func_def_546, type, sK353: ($i > $o) > ($i > $o) > $i).
% 57.88/9.52 thf(func_def_547, type, sK354: ($i > $o) > ($i > $o) > $i).
% 57.88/9.52 thf(func_def_548, type, sK355: $i > $o).
% 57.88/9.52 thf(func_def_549, type, sK356: $i > $o).
% 57.88/9.52 thf(func_def_563, type, sK370: $i > $o).
% 57.88/9.52 thf(func_def_583, type, sK390: $i > $o).
% 57.88/9.52 thf(func_def_588, type, sK395: $i > $i > $i).
% 57.88/9.52 thf(func_def_601, type, sK408: ($i > $o) > $i).
% 57.88/9.52 thf(func_def_602, type, sK409: $i > $o).
% 57.88/9.52 thf(func_def_604, type, sK411: $i > $o).
% 57.88/9.52 thf(func_def_607, type, sK414: $i > $o).
% 57.88/9.52 thf(func_def_610, type, sK417: $i > $o).
% 57.88/9.52 thf(func_def_618, type, sK425: $i > $o).
% 57.88/9.52 thf(func_def_620, type, sK427: $i > ($i > $o) > $i).
% 57.88/9.52 thf(func_def_626, type, ph433: !>[X0: $tType]:(X0)).
% 57.88/9.52 thf(f5195,plain,(
% 57.88/9.52 $false),
% 57.88/9.52 inference(avatar_sat_refutation,[status(thm)],[f3001,f3046,f3050,f3058,f3073,f3091,f3209,f3756,f5194])).
% 57.88/9.52 thf(f5194,plain,(
% 57.88/9.52 ~spl432_4 | ~spl432_18 | ~spl432_21 | ~spl432_25 | ~spl432_31),
% 57.88/9.52 inference(avatar_contradiction_clause,[status(thm)],[f5193])).
% 57.88/9.52 thf(f5193,plain,(
% 57.88/9.52 $false | (~spl432_4 | ~spl432_18 | ~spl432_21 | ~spl432_25 | ~spl432_31)),
% 57.88/9.52 inference(subsumption_resolution,[status(thm)],[f5185,f1891])).
% 57.88/9.52 thf(f1891,plain,(
% 57.88/9.52 ((sK323 @ sK321) = $true)),
% 57.88/9.52 inference(cnf_transformation,[status(thm)],[f1213])).
% 57.88/9.52 thf(f1213,plain,(
% 57.88/9.52 (dsetconstr__Cong = $true) & (powersetE = $true) & (setadjoinOr = $true) & (emptysetsubset = $true) & (setunionAx = $true) & (subsetemptysetimpeq = $true) & (setminusILneg = $true) & (binintersectER = $true) & (descr__Cong = $true) & (symdiffI1 = $true) & (wellorderingAx = $true) & (inPowerset = $true) & (setextsub = $true) & (notequalI1 = $true) & (notequalI2 = $true) & (notinsingleton = $true) & (setunion__Cong = $true) & (dsetconstrI = $true) & (setadjoinAx = $true) & (binintersectEL = $true) & (binunionIR = $true) & (subsetI2 = $true) & (setunionI = $true) & (binunionRsub = $true) & (ex1E1 = $true) & (setadjoinIR = $true) & (vacuousDall = $true) & (eqimpsubset2 = $true) & (exuE3e = $true) & (notsubsetI = $true) & (eqimpsubset1 = $true) & (setextAx = $true) & (emptysetimpfalse = $true) & (setadjoin__Cong = $true) & (prop2setI = $true) & (setext = $true) & (setadjoinSub = $true) & (upairset2E = $true) & (setunionsingleton = $true) & (binintersectSubset3 = $true) & (emptyinunitempty = $true) & (binintersectSubset5 = $true) & (emptysetAx = $true) & (setunionE = $true) & (binintersectSubset4 = $true) & (omegaSAx = $true) & (symdiffIneg2 = $true) & (notdallE = $true) & (emptyE1 = $true) & (cartprodpairin = $true) & (setminusLsub = $true) & (singletoninpowunion = $true) & (ubforcartprodlem2 = $true) & (bs114d = $true) & (sepSubset = $true) & (upairsubunion = $true) & (setukpairIL = $true) & (exuE3u = $true) & (powersetsubset = $true) & (setminusI = $true) & (exu__Cong = $true) & (setunionsingleton2 = $true) & (setadjoinSub2 = $true) & (subsetRefl = $true) & (dsetconstrER = $true) & (subsetE2 = $true) & (uniqinunit = $true) & (binintersectSubset2 = $true) & (setadjoinIL = $true) & (ubforcartprodlem1 = $true) & (setminusELneg = $true) & (kpairp = $true) & (binintersectSubset1 = $true) & (upairsetIR = $true) & (quantDeMorgan3 = $true) & (upairsetIL = $true) & (nonemptyI = $true) & (powersetAx = $true) & (subsetI1 = $true) & (inCongP = $true) & (upairinpowunion = $true) & (setminusERneg = $true) & (emptyInPowerset = $true) & (binunionIL = $true) & (emptysetE = $true) & (quantDeMorgan2 = $true) & (quantDeMorgan4 = $true) & (powersetI = $true) & (binunionE = $true) & (powersetI1 = $true) & (exuI1 = $true) & (singletonsswitch = $true) & (ubforcartprodlem3 = $true) & (binunionLsub = $true) & (singletonsubset = $true) & (binunionEcases = $true) & (upairsetE = $true) & (cartprodmempair1 = $true) & (nonemptyI1 = $true) & (cartprodmempair = $true) & (setminusSubset2 = $true) & (omegaIndAx = $true) & (prop2setE = $true) & (upairset2IR = $true) & (subsetE = $true) & (exuE1 = $true) & (in__Cong = $true) & (replAx = $true) & (singletoninpowerset = $true) & (disjointsetsI1 = $true) & (emptyinPowerset = $true) & (secondinupair = $true) & (setunionE2 = $true) & (setminusSubset1 = $true) & (foundationAx = $true) & (kpairiskpair = $true) & (exuI3 = $true) & (setadjoinE = $true) & (binintersectLsub = $true) & (sepInPowerset = $true) & (! [X3 : $i] : (($true != (in @ X3 @ sK322)) | (sK321 = X3) | ((sK323 @ X3) != $true)) & ((sK323 @ sK321) = $true) & ((ex1 @ sK322 @ (^[Y0 : $i]: (sK323 @ Y0))) != $true) & ((in @ sK321 @ sK322) = $true)) & (omega__Cong = $true) & (descrp = $true) & (nonemptyImpWitness = $true) & (notinemptyset = $true) & (setminusEL = $true) & (symdiffE = $true) & (binintersectRsub = $true) & (quantDeMorgan1 = $true) & (omega0Ax = $true) & (setbeta = $true) & (emptyI = $true) & (powerset__Cong = $true) & (exuEu = $true) & (prop2set2propI = $true) & (exuE2 = $true) & (setminusIRneg = $true) & (dsetconstrEL = $true) & (subset2powerset = $true) & (nonemptyE1 = $true) & (emptyset__Cong = $true) & (symdiffIneg1 = $true) & (exuI2 = $true) & (setukpairIR = $true) & (singletonprop = $true) & (powersetE1 = $true) & (subPowSU = $true) & (setunionsingleton1 = $true) & (binintersectI = $true) & (eqinunit = $true) & (subsetTrans = $true) & (notdexE = $true) & (setminusER = $true) & (setoftrueEq = $true) & (symdiffI2 = $true) & (noeltsimpempty = $true)),
% 57.88/9.52 inference(skolemisation,[status(esa),new_symbols(skolem,[sK321,sK322,sK323])],[f649,f1212])).
% 57.88/9.52 thf(f1212,plain,(
% 57.88/9.52 ? [X0 : $i,X1 : $i,X2 : $i > $o] : (! [X3 : $i] : (((in @ X3 @ X1) != $true) | (X0 = X3) | ((X2 @ X3) != $true)) & ((X2 @ X0) = $true) & ($true != (ex1 @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) & ((in @ X0 @ X1) = $true)) => (! [X3 : $i] : (($true != (in @ X3 @ sK322)) | (sK321 = X3) | ((sK323 @ X3) != $true)) & ((sK323 @ sK321) = $true) & ((ex1 @ sK322 @ (^[Y0 : $i]: (sK323 @ Y0))) != $true) & ((in @ sK321 @ sK322) = $true))),
% 57.88/9.52 introduced(definition,[],[choice_axiom])).
% 57.88/9.52 thf(f649,plain,(
% 57.88/9.52 (dsetconstr__Cong = $true) & (powersetE = $true) & (setadjoinOr = $true) & (emptysetsubset = $true) & (setunionAx = $true) & (subsetemptysetimpeq = $true) & (setminusILneg = $true) & (binintersectER = $true) & (descr__Cong = $true) & (symdiffI1 = $true) & (wellorderingAx = $true) & (inPowerset = $true) & (setextsub = $true) & (notequalI1 = $true) & (notequalI2 = $true) & (notinsingleton = $true) & (setunion__Cong = $true) & (dsetconstrI = $true) & (setadjoinAx = $true) & (binintersectEL = $true) & (binunionIR = $true) & (subsetI2 = $true) & (setunionI = $true) & (binunionRsub = $true) & (ex1E1 = $true) & (setadjoinIR = $true) & (vacuousDall = $true) & (eqimpsubset2 = $true) & (exuE3e = $true) & (notsubsetI = $true) & (eqimpsubset1 = $true) & (setextAx = $true) & (emptysetimpfalse = $true) & (setadjoin__Cong = $true) & (prop2setI = $true) & (setext = $true) & (setadjoinSub = $true) & (upairset2E = $true) & (setunionsingleton = $true) & (binintersectSubset3 = $true) & (emptyinunitempty = $true) & (binintersectSubset5 = $true) & (emptysetAx = $true) & (setunionE = $true) & (binintersectSubset4 = $true) & (omegaSAx = $true) & (symdiffIneg2 = $true) & (notdallE = $true) & (emptyE1 = $true) & (cartprodpairin = $true) & (setminusLsub = $true) & (singletoninpowunion = $true) & (ubforcartprodlem2 = $true) & (bs114d = $true) & (sepSubset = $true) & (upairsubunion = $true) & (setukpairIL = $true) & (exuE3u = $true) & (powersetsubset = $true) & (setminusI = $true) & (exu__Cong = $true) & (setunionsingleton2 = $true) & (setadjoinSub2 = $true) & (subsetRefl = $true) & (dsetconstrER = $true) & (subsetE2 = $true) & (uniqinunit = $true) & (binintersectSubset2 = $true) & (setadjoinIL = $true) & (ubforcartprodlem1 = $true) & (setminusELneg = $true) & (kpairp = $true) & (binintersectSubset1 = $true) & (upairsetIR = $true) & (quantDeMorgan3 = $true) & (upairsetIL = $true) & (nonemptyI = $true) & (powersetAx = $true) & (subsetI1 = $true) & (inCongP = $true) & (upairinpowunion = $true) & (setminusERneg = $true) & (emptyInPowerset = $true) & (binunionIL = $true) & (emptysetE = $true) & (quantDeMorgan2 = $true) & (quantDeMorgan4 = $true) & (powersetI = $true) & (binunionE = $true) & (powersetI1 = $true) & (exuI1 = $true) & (singletonsswitch = $true) & (ubforcartprodlem3 = $true) & (binunionLsub = $true) & (singletonsubset = $true) & (binunionEcases = $true) & (upairsetE = $true) & (cartprodmempair1 = $true) & (nonemptyI1 = $true) & (cartprodmempair = $true) & (setminusSubset2 = $true) & (omegaIndAx = $true) & (prop2setE = $true) & (upairset2IR = $true) & (subsetE = $true) & (exuE1 = $true) & (in__Cong = $true) & (replAx = $true) & (singletoninpowerset = $true) & (disjointsetsI1 = $true) & (emptyinPowerset = $true) & (secondinupair = $true) & (setunionE2 = $true) & (setminusSubset1 = $true) & (foundationAx = $true) & (kpairiskpair = $true) & (exuI3 = $true) & (setadjoinE = $true) & (binintersectLsub = $true) & (sepInPowerset = $true) & ? [X0 : $i,X1 : $i,X2 : $i > $o] : (! [X3 : $i] : (((in @ X3 @ X1) != $true) | (X0 = X3) | ((X2 @ X3) != $true)) & ((X2 @ X0) = $true) & ($true != (ex1 @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) & ((in @ X0 @ X1) = $true)) & (omega__Cong = $true) & (descrp = $true) & (nonemptyImpWitness = $true) & (notinemptyset = $true) & (setminusEL = $true) & (symdiffE = $true) & (binintersectRsub = $true) & (quantDeMorgan1 = $true) & (omega0Ax = $true) & (setbeta = $true) & (emptyI = $true) & (powerset__Cong = $true) & (exuEu = $true) & (prop2set2propI = $true) & (exuE2 = $true) & (setminusIRneg = $true) & (dsetconstrEL = $true) & (subset2powerset = $true) & (nonemptyE1 = $true) & (emptyset__Cong = $true) & (symdiffIneg1 = $true) & (exuI2 = $true) & (setukpairIR = $true) & (singletonprop = $true) & (powersetE1 = $true) & (subPowSU = $true) & (setunionsingleton1 = $true) & (binintersectI = $true) & (eqinunit = $true) & (subsetTrans = $true) & (notdexE = $true) & (setminusER = $true) & (setoftrueEq = $true) & (symdiffI2 = $true) & (noeltsimpempty = $true)),
% 57.88/9.52 inference(flattening,[status(thm)],[f648])).
% 57.88/9.52 thf(f648,plain,(
% 57.88/9.52 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i > $o] : (((($true != (ex1 @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) & ! [X3 : $i] : (((X0 = X3) | ((X2 @ X3) != $true)) | ((in @ X3 @ X1) != $true))) & ((X2 @ X0) = $true)) & ((in @ X0 @ X1) = $true)) & (ex1E1 = $true)) & (singletonprop = $true)) & (setunionsingleton = $true)) & (setunionsingleton2 = $true)) & (setunionsingleton1 = $true)) & (setunionE2 = $true)) & (cartprodmempair = $true)) & (cartprodmempair1 = $true)) & (cartprodpairin = $true)) & (ubforcartprodlem3 = $true)) & (ubforcartprodlem2 = $true)) & (ubforcartprodlem1 = $true)) & (upairinpowunion = $true)) & (upairsubunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (singletoninpowerset = $true)) & (singletonsubset = $true)) & (kpairp = $true)) & (kpairiskpair = $true)) & (setukpairIR = $true)) & (setukpairIL = $true)) & (secondinupair = $true)) & (symdiffIneg2 = $true)) & (symdiffIneg1 = $true)) & (symdiffI2 = $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 57.88/9.52 inference(ennf_transformation,[status(thm)],[f456])).
% 57.88/9.52 thf(f456,plain,(
% 57.88/9.52 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ((ubforcartprodlem1 = $true) => ((ubforcartprodlem2 = $true) => ((ubforcartprodlem3 = $true) => ((cartprodpairin = $true) => ((cartprodmempair1 = $true) => ((cartprodmempair = $true) => ((setunionE2 = $true) => ((setunionsingleton1 = $true) => ((setunionsingleton2 = $true) => ((setunionsingleton = $true) => ((singletonprop = $true) => ((ex1E1 = $true) => ! [X0 : $i,X1 : $i,X2 : $i > $o] : (((in @ X0 @ X1) = $true) => (((X2 @ X0) = $true) => (! [X3 : $i] : (((in @ X3 @ X1) = $true) => (((X2 @ X3) = $true) => (X0 = X3))) => ($true = (ex1 @ X1 @ (^[Y0 : $i]: (X2 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 57.88/9.52 inference(fool_elimination,[status(thm)],[f455])).
% 57.88/9.52 thf(f455,plain,(
% 57.88/9.52 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => ! [X0 : $i,X1 : $i,X2 : $i > $o] : ((in @ X0 @ X1) => ((X2 @ X0) => (! [X3 : $i] : ((in @ X3 @ X1) => ((X2 @ X3) => (X0 = X3))) => (ex1 @ X1 @ (^[X4 : $i] : (X2 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 57.88/9.52 inference(rectify,[status(thm)],[f163])).
% 57.88/9.52 thf(f163,negated_conjecture,(
% 57.88/9.52 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => ! [X1 : $i,X3 : $i,X0 : $i > $o] : ((in @ X1 @ X3) => ((X0 @ X1) => (! [X2 : $i] : ((in @ X2 @ X3) => ((X0 @ X2) => (X1 = X2))) => (ex1 @ X3 @ (^[X2 : $i] : (X0 @ X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 57.88/9.52 inference(negated_conjecture,[status(cth)],[f162])).
% 57.88/9.52 thf(f162,conjecture,(
% 57.88/9.52 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => ! [X1 : $i,X3 : $i,X0 : $i > $o] : ((in @ X1 @ X3) => ((X0 @ X1) => (! [X2 : $i] : ((in @ X2 @ X3) => ((X0 @ X2) => (X1 = X2))) => (ex1 @ X3 @ (^[X2 : $i] : (X0 @ X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 57.88/9.52 file('/export/starexec/sandbox/tmp/tmp.0njZozgBRA/DTF2THF_1200.p',ex1I)).
% 57.88/9.52 thf(f5185,plain,(
% 57.88/9.52 ((sK323 @ sK321) != $true) | (~spl432_4 | ~spl432_18 | ~spl432_21 | ~spl432_25 | ~spl432_31)),
% 57.88/9.52 inference(trivial_inequality_removal,[status(thm)],[f5171])).
% 57.88/9.52 thf(f5171,plain,(
% 57.88/9.52 ((sK323 @ sK321) != $true) | ($true != $true) | (~spl432_4 | ~spl432_18 | ~spl432_21 | ~spl432_25 | ~spl432_31)),
% 57.88/9.52 inference(superposition,[status(thm)],[f5118,f1889])).
% 57.88/9.52 thf(f1889,plain,(
% 57.88/9.52 ((in @ sK321 @ sK322) = $true)),
% 57.88/9.52 inference(cnf_transformation,[status(thm)],[f1213])).
% 57.88/9.52 thf(f5118,plain,(
% 57.88/9.52 ( ! [X0 : $i] : (((in @ X0 @ sK322) != $true) | ((sK323 @ X0) != $true)) ) | (~spl432_4 | ~spl432_18 | ~spl432_21 | ~spl432_25 | ~spl432_31)),
% 57.88/9.52 inference(subsumption_resolution,[status(thm)],[f4442,f4514])).
% 57.88/9.52 thf(f4514,plain,(
% 57.88/9.52 ((sK205 @ sK322 @ sK323) = sK321) | (~spl432_25 | ~spl432_31)),
% 57.88/9.52 inference(subsumption_resolution,[status(thm)],[f4500,f3208])).
% 57.88/9.52 thf(f3208,plain,(
% 57.88/9.52 ((sK323 @ (sK205 @ sK322 @ sK323)) = $true) | ~spl432_31),
% 57.88/9.52 inference(avatar_component_clause,[status(thm)],[f3206])).
% 57.88/9.52 thf(f3206,definition,(
% 57.88/9.52 spl432_31 <=> ((sK323 @ (sK205 @ sK322 @ sK323)) = $true)),
% 57.88/9.52 introduced(definition,[new_symbols(naming,[spl432_31])],[avatar_definition])).
% 57.88/9.52 thf(f4500,plain,(
% 57.88/9.52 ((sK323 @ (sK205 @ sK322 @ sK323)) != $true) | ((sK205 @ sK322 @ sK323) = sK321) | ~spl432_25),
% 57.88/9.52 inference(trivial_inequality_removal,[status(thm)],[f4478])).
% 57.88/9.52 thf(f4478,plain,(
% 57.88/9.52 ((sK205 @ sK322 @ sK323) = sK321) | ((sK323 @ (sK205 @ sK322 @ sK323)) != $true) | ($true != $true) | ~spl432_25),
% 57.88/9.52 inference(superposition,[status(thm)],[f1892,f4359])).
% 57.88/9.52 thf(f4359,plain,(
% 57.88/9.52 ($true = (in @ (sK205 @ sK322 @ sK323) @ sK322)) | ~spl432_25),
% 57.88/9.52 inference(subsumption_resolution,[status(thm)],[f4335,f2813])).
% 57.88/9.52 thf(f2813,plain,(
% 57.88/9.52 ($true != (singleton @ (dsetconstr @ sK322 @ sK323)))),
% 57.88/9.52 inference(beta_eta_normalization,[status(thm)],[f2553])).
% 57.88/9.52 thf(f2553,plain,(
% 57.88/9.52 ($true != ((^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))) @ sK322 @ (^[Y0 : $i]: (sK323 @ Y0))))),
% 57.88/9.52 inference(definition_unfolding,[status(thm)],[f1890,f1610])).
% 57.88/9.52 thf(f1610,plain,(
% 57.88/9.52 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 57.88/9.52 inference(cnf_transformation,[status(thm)],[f408])).
% 57.88/9.52 thf(f408,plain,(
% 57.88/9.52 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 57.88/9.52 inference(fool_elimination,[status(thm)],[f407])).
% 57.88/9.52 thf(f407,plain,(
% 57.88/9.52 (ex1 = (^[X0 : $i, X1 : $i > $o] : (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))))))),
% 57.88/9.52 inference(rectify,[status(thm)],[f160])).
% 57.88/9.52 thf(f160,axiom,(
% 57.88/9.52 (ex1 = (^[X3 : $i, X0 : $i > $o] : (singleton @ (dsetconstr @ X3 @ (^[X1 : $i] : (X0 @ X1))))))),
% 57.88/9.52 file('/export/starexec/sandbox/tmp/tmp.0njZozgBRA/DTF2THF_1200.p',ex1)).
% 57.88/9.52 thf(f1890,plain,(
% 57.88/9.52 ((ex1 @ sK322 @ (^[Y0 : $i]: (sK323 @ Y0))) != $true)),
% 57.88/9.52 inference(cnf_transformation,[status(thm)],[f1213])).
% 57.88/9.52 thf(f4335,plain,(
% 57.88/9.52 ($true = (in @ (sK205 @ sK322 @ sK323) @ sK322)) | ($true = (singleton @ (dsetconstr @ sK322 @ sK323))) | ~spl432_25),
% 57.88/9.52 inference(beta_eta_normalization,[status(thm)],[f4334])).
% 57.88/9.52 thf(f4334,plain,(
% 57.88/9.52 ((singleton @ (dsetconstr @ sK322 @ (^[Y0 : $i]: (sK323 @ ((^[Y1 : $i]: (Y1)) @ Y0))))) = $true) | ($true = (in @ (sK205 @ sK322 @ (^[Y0 : $i]: (sK323 @ ((^[Y1 : $i]: (Y1)) @ Y0)))) @ sK322)) | ~spl432_25),
% 57.88/9.52 inference(trivial_inequality_removal,[status(thm)],[f4267])).
% 57.88/9.52 thf(f4267,plain,(
% 57.88/9.52 ($true != $true) | ($true = (in @ (sK205 @ sK322 @ (^[Y0 : $i]: (sK323 @ ((^[Y1 : $i]: (Y1)) @ Y0)))) @ sK322)) | ((singleton @ (dsetconstr @ sK322 @ (^[Y0 : $i]: (sK323 @ ((^[Y1 : $i]: (Y1)) @ Y0))))) = $true) | ~spl432_25),
% 57.88/9.52 inference(superposition,[status(thm)],[f3432,f1891])).
% 57.88/9.52 thf(f3432,plain,(
% 57.88/9.52 ( ! [X0 : $i > $o] : (((X0 @ sK321) != $true) | ((in @ (sK205 @ sK322 @ X0) @ sK322) = $true) | ((singleton @ (dsetconstr @ sK322 @ X0)) = $true)) ) | ~spl432_25),
% 57.88/9.52 inference(trivial_inequality_removal,[status(thm)],[f3427])).
% 57.88/9.52 thf(f3427,plain,(
% 57.88/9.52 ( ! [X0 : $i > $o] : (((X0 @ sK321) != $true) | ($true != $true) | ((singleton @ (dsetconstr @ sK322 @ X0)) = $true) | ((in @ (sK205 @ sK322 @ X0) @ sK322) = $true)) ) | ~spl432_25),
% 57.88/9.52 inference(superposition,[status(thm)],[f3090,f1889])).
% 57.88/9.52 thf(f3090,plain,(
% 57.88/9.52 ( ! [X6 : $i,X7 : $i,X5 : $i > $o] : (((in @ X7 @ X6) != $true) | ($true = (singleton @ (dsetconstr @ X6 @ X5))) | ((in @ (sK205 @ X6 @ X5) @ X6) = $true) | ((X5 @ X7) != $true)) ) | ~spl432_25),
% 57.88/9.52 inference(avatar_component_clause,[status(thm)],[f3089])).
% 57.88/9.52 thf(f3089,definition,(
% 57.88/9.52 spl432_25 <=> ! [X6 : $i,X5 : $i > $o,X7 : $i] : (((X5 @ X7) != $true) | ((in @ (sK205 @ X6 @ X5) @ X6) = $true) | ($true = (singleton @ (dsetconstr @ X6 @ X5))) | ((in @ X7 @ X6) != $true))),
% 57.88/9.52 introduced(definition,[new_symbols(naming,[spl432_25])],[avatar_definition])).
% 57.88/9.52 thf(f1892,plain,(
% 57.88/9.52 ( ! [X3 : $i] : (($true != (in @ X3 @ sK322)) | ((sK323 @ X3) != $true) | (sK321 = X3)) )),
% 57.88/9.52 inference(cnf_transformation,[status(thm)],[f1213])).
% 57.88/9.52 thf(f4442,plain,(
% 57.88/9.52 ( ! [X0 : $i] : (((sK323 @ X0) != $true) | ((sK205 @ sK322 @ sK323) != sK321) | ((in @ X0 @ sK322) != $true)) ) | (~spl432_4 | ~spl432_18 | ~spl432_21)),
% 57.88/9.52 inference(subsumption_resolution,[status(thm)],[f4441,f2813])).
% 57.88/9.52 thf(f4441,plain,(
% 57.88/9.52 ( ! [X0 : $i] : (($true = (singleton @ (dsetconstr @ sK322 @ sK323))) | ((sK205 @ sK322 @ sK323) != sK321) | ((sK323 @ X0) != $true) | ((in @ X0 @ sK322) != $true)) ) | (~spl432_4 | ~spl432_18 | ~spl432_21)),
% 57.88/9.52 inference(superposition,[status(thm)],[f3057,f4401])).
% 57.88/9.52 thf(f4401,plain,(
% 57.88/9.52 (sK321 = (sK206 @ sK322 @ sK323)) | (~spl432_4 | ~spl432_21)),
% 57.88/9.52 inference(subsumption_resolution,[status(thm)],[f4382,f3795])).
% 57.88/9.52 thf(f3795,plain,(
% 57.88/9.52 ((sK323 @ (sK206 @ sK322 @ sK323)) = $true) | ~spl432_21),
% 57.88/9.52 inference(subsumption_resolution,[status(thm)],[f3339,f2813])).
% 57.88/9.52 thf(f3339,plain,(
% 57.88/9.52 ((sK323 @ (sK206 @ sK322 @ sK323)) = $true) | ($true = (singleton @ (dsetconstr @ sK322 @ sK323))) | ~spl432_21),
% 57.88/9.52 inference(beta_eta_normalization,[status(thm)],[f3338])).
% 57.88/9.52 thf(f3338,plain,(
% 57.88/9.52 (((^[Y0 : $i]: (sK323 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sK206 @ sK322 @ (^[Y0 : $i]: (sK323 @ ((^[Y1 : $i]: (Y1)) @ Y0))))) = $true) | ((singleton @ (dsetconstr @ sK322 @ (^[Y0 : $i]: (sK323 @ ((^[Y1 : $i]: (Y1)) @ Y0))))) = $true) | ~spl432_21),
% 57.88/9.52 inference(trivial_inequality_removal,[status(thm)],[f3328])).
% 57.88/9.52 thf(f3328,plain,(
% 57.88/9.52 ($true != $true) | (((^[Y0 : $i]: (sK323 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sK206 @ sK322 @ (^[Y0 : $i]: (sK323 @ ((^[Y1 : $i]: (Y1)) @ Y0))))) = $true) | ((singleton @ (dsetconstr @ sK322 @ (^[Y0 : $i]: (sK323 @ ((^[Y1 : $i]: (Y1)) @ Y0))))) = $true) | ~spl432_21),
% 57.88/9.52 inference(superposition,[status(thm)],[f3153,f1891])).
% 57.88/9.52 thf(f3153,plain,(
% 57.88/9.52 ( ! [X0 : $i > $o] : (((X0 @ sK321) != $true) | ((X0 @ (sK206 @ sK322 @ X0)) = $true) | ((singleton @ (dsetconstr @ sK322 @ X0)) = $true)) ) | ~spl432_21),
% 57.88/9.52 inference(trivial_inequality_removal,[status(thm)],[f3150])).
% 57.88/9.52 thf(f3150,plain,(
% 57.88/9.52 ( ! [X0 : $i > $o] : (((singleton @ (dsetconstr @ sK322 @ X0)) = $true) | ((X0 @ (sK206 @ sK322 @ X0)) = $true) | ($true != $true) | ((X0 @ sK321) != $true)) ) | ~spl432_21),
% 57.88/9.52 inference(superposition,[status(thm)],[f3072,f1889])).
% 57.88/9.52 thf(f3072,plain,(
% 57.88/9.52 ( ! [X6 : $i,X7 : $i,X5 : $i > $o] : (((in @ X7 @ X6) != $true) | ($true = (singleton @ (dsetconstr @ X6 @ X5))) | ((X5 @ X7) != $true) | ((X5 @ (sK206 @ X6 @ X5)) = $true)) ) | ~spl432_21),
% 57.88/9.52 inference(avatar_component_clause,[status(thm)],[f3071])).
% 57.88/9.52 thf(f3071,definition,(
% 57.88/9.52 spl432_21 <=> ! [X6 : $i,X5 : $i > $o,X7 : $i] : (($true = (singleton @ (dsetconstr @ X6 @ X5))) | ((X5 @ X7) != $true) | ((in @ X7 @ X6) != $true) | ((X5 @ (sK206 @ X6 @ X5)) = $true))),
% 57.88/9.52 introduced(definition,[new_symbols(naming,[spl432_21])],[avatar_definition])).
% 57.88/9.52 thf(f4382,plain,(
% 57.88/9.52 (sK321 = (sK206 @ sK322 @ sK323)) | ((sK323 @ (sK206 @ sK322 @ sK323)) != $true) | ~spl432_4),
% 57.88/9.52 inference(trivial_inequality_removal,[status(thm)],[f4365])).
% 57.88/9.52 thf(f4365,plain,(
% 57.88/9.52 ((sK323 @ (sK206 @ sK322 @ sK323)) != $true) | ($true != $true) | (sK321 = (sK206 @ sK322 @ sK323)) | ~spl432_4),
% 57.88/9.52 inference(superposition,[status(thm)],[f1892,f4214])).
% 57.88/9.52 thf(f4214,plain,(
% 57.88/9.52 ((in @ (sK206 @ sK322 @ sK323) @ sK322) = $true) | ~spl432_4),
% 57.88/9.52 inference(subsumption_resolution,[status(thm)],[f4149,f2813])).
% 57.88/9.52 thf(f4149,plain,(
% 57.88/9.52 ($true = (singleton @ (dsetconstr @ sK322 @ sK323))) | ((in @ (sK206 @ sK322 @ sK323) @ sK322) = $true) | ~spl432_4),
% 57.88/9.52 inference(beta_eta_normalization,[status(thm)],[f4148])).
% 57.88/9.52 thf(f4148,plain,(
% 57.88/9.52 ((in @ (sK206 @ sK322 @ (^[Y0 : $i]: (sK323 @ ((^[Y1 : $i]: (Y1)) @ Y0)))) @ sK322) = $true) | ((singleton @ (dsetconstr @ sK322 @ (^[Y0 : $i]: (sK323 @ ((^[Y1 : $i]: (Y1)) @ Y0))))) = $true) | ~spl432_4),
% 57.88/9.52 inference(trivial_inequality_removal,[status(thm)],[f4122])).
% 57.88/9.52 thf(f4122,plain,(
% 57.88/9.52 ($true != $true) | ((singleton @ (dsetconstr @ sK322 @ (^[Y0 : $i]: (sK323 @ ((^[Y1 : $i]: (Y1)) @ Y0))))) = $true) | ((in @ (sK206 @ sK322 @ (^[Y0 : $i]: (sK323 @ ((^[Y1 : $i]: (Y1)) @ Y0)))) @ sK322) = $true) | ~spl432_4),
% 57.88/9.52 inference(superposition,[status(thm)],[f3242,f1891])).
% 57.88/9.52 thf(f3242,plain,(
% 57.88/9.52 ( ! [X0 : $i > $o] : (((X0 @ sK321) != $true) | ((in @ (sK206 @ sK322 @ X0) @ sK322) = $true) | ((singleton @ (dsetconstr @ sK322 @ X0)) = $true)) ) | ~spl432_4),
% 57.88/9.52 inference(trivial_inequality_removal,[status(thm)],[f3237])).
% 57.88/9.52 thf(f3237,plain,(
% 57.88/9.52 ( ! [X0 : $i > $o] : (((X0 @ sK321) != $true) | ((in @ (sK206 @ sK322 @ X0) @ sK322) = $true) | ($true != $true) | ((singleton @ (dsetconstr @ sK322 @ X0)) = $true)) ) | ~spl432_4),
% 57.88/9.52 inference(superposition,[status(thm)],[f3000,f1889])).
% 57.88/9.52 thf(f3000,plain,(
% 57.88/9.52 ( ! [X6 : $i,X7 : $i,X5 : $i > $o] : (((in @ X7 @ X6) != $true) | ((in @ (sK206 @ X6 @ X5) @ X6) = $true) | ($true = (singleton @ (dsetconstr @ X6 @ X5))) | ((X5 @ X7) != $true)) ) | ~spl432_4),
% 57.88/9.52 inference(avatar_component_clause,[status(thm)],[f2999])).
% 57.88/9.52 thf(f2999,definition,(
% 57.88/9.52 spl432_4 <=> ! [X6 : $i,X5 : $i > $o,X7 : $i] : (($true = (singleton @ (dsetconstr @ X6 @ X5))) | ((in @ X7 @ X6) != $true) | ((in @ (sK206 @ X6 @ X5) @ X6) = $true) | ((X5 @ X7) != $true))),
% 57.88/9.52 introduced(definition,[new_symbols(naming,[spl432_4])],[avatar_definition])).
% 57.88/9.52 thf(f3057,plain,(
% 57.88/9.52 ( ! [X6 : $i,X7 : $i,X5 : $i > $o] : (((sK205 @ X6 @ X5) != (sK206 @ X6 @ X5)) | ($true = (singleton @ (dsetconstr @ X6 @ X5))) | ((X5 @ X7) != $true) | ((in @ X7 @ X6) != $true)) ) | ~spl432_18),
% 57.88/9.52 inference(avatar_component_clause,[status(thm)],[f3056])).
% 57.88/9.52 thf(f3056,definition,(
% 57.88/9.52 spl432_18 <=> ! [X6 : $i,X5 : $i > $o,X7 : $i] : (($true = (singleton @ (dsetconstr @ X6 @ X5))) | ((X5 @ X7) != $true) | ((sK205 @ X6 @ X5) != (sK206 @ X6 @ X5)) | ((in @ X7 @ X6) != $true))),
% 57.88/9.52 introduced(definition,[new_symbols(naming,[spl432_18])],[avatar_definition])).
% 57.88/9.52 thf(f3756,plain,(
% 57.88/9.52 ~spl432_30),
% 57.88/9.52 inference(avatar_contradiction_clause,[status(thm)],[f3755])).
% 57.88/9.52 thf(f3755,plain,(
% 57.88/9.52 $false | ~spl432_30),
% 57.88/9.52 inference(subsumption_resolution,[status(thm)],[f2813,f3204])).
% 57.88/9.52 thf(f3204,plain,(
% 57.88/9.52 ($true = (singleton @ (dsetconstr @ sK322 @ sK323))) | ~spl432_30),
% 57.88/9.52 inference(avatar_component_clause,[status(thm)],[f3202])).
% 57.88/9.52 thf(f3202,definition,(
% 57.88/9.52 spl432_30 <=> ($true = (singleton @ (dsetconstr @ sK322 @ sK323)))),
% 57.88/9.52 introduced(definition,[new_symbols(naming,[spl432_30])],[avatar_definition])).
% 57.88/9.52 thf(f3209,plain,(
% 57.88/9.52 spl432_30 | spl432_31 | ~spl432_16),
% 57.88/9.52 inference(avatar_split_clause,[status(thm)],[f3173,f3048,f3206,f3202])).
% 57.88/9.52 thf(f3048,definition,(
% 57.88/9.52 spl432_16 <=> ! [X6 : $i,X5 : $i > $o,X7 : $i] : (($true = (singleton @ (dsetconstr @ X6 @ X5))) | ((X5 @ (sK205 @ X6 @ X5)) = $true) | ((in @ X7 @ X6) != $true) | ((X5 @ X7) != $true))),
% 57.88/9.52 introduced(definition,[new_symbols(naming,[spl432_16])],[avatar_definition])).
% 57.88/9.52 thf(f3173,plain,(
% 57.88/9.52 ((sK323 @ (sK205 @ sK322 @ sK323)) = $true) | ($true = (singleton @ (dsetconstr @ sK322 @ sK323))) | ~spl432_16),
% 57.88/9.52 inference(beta_eta_normalization,[status(thm)],[f3172])).
% 57.88/9.52 thf(f3172,plain,(
% 57.88/9.52 (((^[Y0 : $i]: (sK323 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sK205 @ sK322 @ (^[Y0 : $i]: (sK323 @ ((^[Y1 : $i]: (Y1)) @ Y0))))) = $true) | ((singleton @ (dsetconstr @ sK322 @ (^[Y0 : $i]: (sK323 @ ((^[Y1 : $i]: (Y1)) @ Y0))))) = $true) | ~spl432_16),
% 57.88/9.52 inference(trivial_inequality_removal,[status(thm)],[f3158])).
% 57.88/9.52 thf(f3158,plain,(
% 57.88/9.52 ((singleton @ (dsetconstr @ sK322 @ (^[Y0 : $i]: (sK323 @ ((^[Y1 : $i]: (Y1)) @ Y0))))) = $true) | (((^[Y0 : $i]: (sK323 @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sK205 @ sK322 @ (^[Y0 : $i]: (sK323 @ ((^[Y1 : $i]: (Y1)) @ Y0))))) = $true) | ($true != $true) | ~spl432_16),
% 57.88/9.52 inference(superposition,[status(thm)],[f3101,f1891])).
% 57.88/9.52 thf(f3101,plain,(
% 57.88/9.52 ( ! [X0 : $i > $o] : (((X0 @ sK321) != $true) | ((X0 @ (sK205 @ sK322 @ X0)) = $true) | ((singleton @ (dsetconstr @ sK322 @ X0)) = $true)) ) | ~spl432_16),
% 57.88/9.52 inference(trivial_inequality_removal,[status(thm)],[f3098])).
% 57.88/9.52 thf(f3098,plain,(
% 57.88/9.52 ( ! [X0 : $i > $o] : (((X0 @ sK321) != $true) | ((singleton @ (dsetconstr @ sK322 @ X0)) = $true) | ((X0 @ (sK205 @ sK322 @ X0)) = $true) | ($true != $true)) ) | ~spl432_16),
% 57.88/9.52 inference(superposition,[status(thm)],[f3049,f1889])).
% 57.88/9.52 thf(f3049,plain,(
% 57.88/9.52 ( ! [X6 : $i,X7 : $i,X5 : $i > $o] : (((in @ X7 @ X6) != $true) | ((X5 @ (sK205 @ X6 @ X5)) = $true) | ($true = (singleton @ (dsetconstr @ X6 @ X5))) | ((X5 @ X7) != $true)) ) | ~spl432_16),
% 57.88/9.52 inference(avatar_component_clause,[status(thm)],[f3048])).
% 57.88/9.52 thf(f3091,plain,(
% 57.88/9.52 ~spl432_1 | spl432_25),
% 57.88/9.52 inference(avatar_split_clause,[status(thm)],[f2733,f3089,f2986])).
% 57.88/9.52 thf(f2986,definition,(
% 57.88/9.52 spl432_1 <=> ($true = sP6)),
% 57.88/9.52 introduced(definition,[new_symbols(naming,[spl432_1])],[avatar_definition])).
% 57.88/9.52 thf(f2733,plain,(
% 57.88/9.52 ( ! [X6 : $i,X7 : $i,X5 : $i > $o] : (((X5 @ X7) != $true) | ((in @ X7 @ X6) != $true) | ($true = (singleton @ (dsetconstr @ X6 @ X5))) | ($true != sP6) | ((in @ (sK205 @ X6 @ X5) @ X6) = $true)) )),
% 57.88/9.52 inference(beta_eta_normalization,[status(thm)],[f1691])).
% 57.88/9.52 thf(f1691,plain,(
% 57.88/9.52 ( ! [X6 : $i,X7 : $i,X5 : $i > $o] : (($true = (singleton @ (dsetconstr @ X6 @ (^[Y0 : $i]: (X5 @ Y0))))) | ((in @ X7 @ X6) != $true) | ((X5 @ X7) != $true) | ((in @ (sK205 @ X6 @ X5) @ X6) = $true) | ($true != sP6)) )),
% 57.88/9.52 inference(cnf_transformation,[status(thm)],[f1030])).
% 57.88/9.52 thf(f1030,plain,(
% 57.88/9.52 (($true = sP6) | ((((sK202 @ sK204) = $true) & ($true = (in @ sK204 @ sK203))) & ! [X3 : $i] : (! [X4 : $i] : (((sK202 @ X4) != $true) | ((sK202 @ X3) != $true) | ($true != (in @ X4 @ sK203)) | (X3 = X4)) | ((in @ X3 @ sK203) != $true)) & ((singleton @ (dsetconstr @ sK203 @ (^[Y0 : $i]: (sK202 @ Y0)))) != $true))) & (! [X5 : $i > $o,X6 : $i] : (! [X7 : $i] : (((X5 @ X7) != $true) | ((in @ X7 @ X6) != $true)) | ((((X5 @ (sK206 @ X6 @ X5)) = $true) & ((X5 @ (sK205 @ X6 @ X5)) = $true) & ((in @ (sK206 @ X6 @ X5) @ X6) = $true) & ((sK205 @ X6 @ X5) != (sK206 @ X6 @ X5))) & ((in @ (sK205 @ X6 @ X5) @ X6) = $true)) | ($true = (singleton @ (dsetconstr @ X6 @ (^[Y0 : $i]: (X5 @ Y0)))))) | ($true != sP6))),
% 57.88/9.52 inference(skolemisation,[status(esa),new_symbols(skolem,[sK202,sK203,sK204,sK205,sK206])],[f1025,f1029,f1028,f1027,f1026])).
% 57.88/9.52 thf(f1026,plain,(
% 57.88/9.52 ? [X0 : $i > $o,X1 : $i] : (? [X2 : $i] : (((X0 @ X2) = $true) & ($true = (in @ X2 @ X1))) & ! [X3 : $i] : (! [X4 : $i] : (((X0 @ X4) != $true) | ((X0 @ X3) != $true) | ((in @ X4 @ X1) != $true) | (X3 = X4)) | ((in @ X3 @ X1) != $true)) & ((singleton @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true)) => (? [X2 : $i] : (((sK202 @ X2) = $true) & ((in @ X2 @ sK203) = $true)) & ! [X3 : $i] : (! [X4 : $i] : (((sK202 @ X4) != $true) | ((sK202 @ X3) != $true) | ($true != (in @ X4 @ sK203)) | (X3 = X4)) | ((in @ X3 @ sK203) != $true)) & ((singleton @ (dsetconstr @ sK203 @ (^[Y0 : $i]: (sK202 @ Y0)))) != $true))),
% 57.88/9.52 introduced(definition,[],[choice_axiom])).
% 57.88/9.52 thf(f1027,plain,(
% 57.88/9.52 ? [X2 : $i] : (((sK202 @ X2) = $true) & ((in @ X2 @ sK203) = $true)) => (((sK202 @ sK204) = $true) & ($true = (in @ sK204 @ sK203)))),
% 57.88/9.52 introduced(definition,[],[choice_axiom])).
% 57.88/9.52 thf(f1028,plain,(
% 57.88/9.52 ! [X5 : $i > $o,X6 : $i] : (? [X8 : $i] : (? [X9 : $i] : (((X5 @ X9) = $true) & ((X5 @ X8) = $true) & ((in @ X9 @ X6) = $true) & (X8 != X9)) & ((in @ X8 @ X6) = $true)) => (? [X9 : $i] : (((X5 @ X9) = $true) & ((X5 @ (sK205 @ X6 @ X5)) = $true) & ((in @ X9 @ X6) = $true) & ((sK205 @ X6 @ X5) != X9)) & ((in @ (sK205 @ X6 @ X5) @ X6) = $true)))),
% 57.88/9.52 introduced(definition,[],[choice_axiom])).
% 57.88/9.52 thf(f1029,plain,(
% 57.88/9.52 ! [X5 : $i > $o,X6 : $i] : (? [X9 : $i] : (((X5 @ X9) = $true) & ((X5 @ (sK205 @ X6 @ X5)) = $true) & ((in @ X9 @ X6) = $true) & ((sK205 @ X6 @ X5) != X9)) => (((X5 @ (sK206 @ X6 @ X5)) = $true) & ((X5 @ (sK205 @ X6 @ X5)) = $true) & ((in @ (sK206 @ X6 @ X5) @ X6) = $true) & ((sK205 @ X6 @ X5) != (sK206 @ X6 @ X5))))),
% 57.88/9.52 introduced(definition,[],[choice_axiom])).
% 57.88/9.52 thf(f1025,plain,(
% 57.88/9.52 (($true = sP6) | ? [X0 : $i > $o,X1 : $i] : (? [X2 : $i] : (((X0 @ X2) = $true) & ($true = (in @ X2 @ X1))) & ! [X3 : $i] : (! [X4 : $i] : (((X0 @ X4) != $true) | ((X0 @ X3) != $true) | ((in @ X4 @ X1) != $true) | (X3 = X4)) | ((in @ X3 @ X1) != $true)) & ((singleton @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true))) & (! [X5 : $i > $o,X6 : $i] : (! [X7 : $i] : (((X5 @ X7) != $true) | ((in @ X7 @ X6) != $true)) | ? [X8 : $i] : (? [X9 : $i] : (((X5 @ X9) = $true) & ((X5 @ X8) = $true) & ((in @ X9 @ X6) = $true) & (X8 != X9)) & ((in @ X8 @ X6) = $true)) | ($true = (singleton @ (dsetconstr @ X6 @ (^[Y0 : $i]: (X5 @ Y0)))))) | ($true != sP6))),
% 57.88/9.52 inference(rectify,[status(thm)],[f1024])).
% 57.88/9.52 thf(f1024,plain,(
% 57.88/9.52 (($true = sP6) | ? [X0 : $i > $o,X1 : $i] : (? [X4 : $i] : (((X0 @ X4) = $true) & ((in @ X4 @ X1) = $true)) & ! [X2 : $i] : (! [X3 : $i] : (((X0 @ X3) != $true) | ((X0 @ X2) != $true) | ((in @ X3 @ X1) != $true) | (X2 = X3)) | ($true != (in @ X2 @ X1))) & ((singleton @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true))) & (! [X0 : $i > $o,X1 : $i] : (! [X4 : $i] : (((X0 @ X4) != $true) | ((in @ X4 @ X1) != $true)) | ? [X2 : $i] : (? [X3 : $i] : (((X0 @ X3) = $true) & ((X0 @ X2) = $true) & ((in @ X3 @ X1) = $true) & (X2 != X3)) & ($true = (in @ X2 @ X1))) | ((singleton @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true)) | ($true != sP6))),
% 57.88/9.52 inference(nnf_transformation,[status(thm)],[f687])).
% 57.88/9.52 thf(f687,plain,(
% 57.88/9.52 ($true = sP6) <=> ! [X0 : $i > $o,X1 : $i] : (! [X4 : $i] : (((X0 @ X4) != $true) | ((in @ X4 @ X1) != $true)) | ? [X2 : $i] : (? [X3 : $i] : (((X0 @ X3) = $true) & ((X0 @ X2) = $true) & ((in @ X3 @ X1) = $true) & (X2 != X3)) & ($true = (in @ X2 @ X1))) | ((singleton @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true))),
% 57.88/9.52 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 57.88/9.52 thf(f3073,plain,(
% 57.88/9.52 spl432_21 | ~spl432_1),
% 57.88/9.52 inference(avatar_split_clause,[status(thm)],[f2837,f2986,f3071])).
% 57.88/9.52 thf(f2837,plain,(
% 57.88/9.52 ( ! [X6 : $i,X7 : $i,X5 : $i > $o] : (($true != sP6) | ($true = (singleton @ (dsetconstr @ X6 @ X5))) | ((X5 @ (sK206 @ X6 @ X5)) = $true) | ((in @ X7 @ X6) != $true) | ((X5 @ X7) != $true)) )),
% 57.88/9.52 inference(beta_eta_normalization,[status(thm)],[f1695])).
% 57.88/9.52 thf(f1695,plain,(
% 57.88/9.52 ( ! [X6 : $i,X7 : $i,X5 : $i > $o] : (((in @ X7 @ X6) != $true) | ($true = (singleton @ (dsetconstr @ X6 @ (^[Y0 : $i]: (X5 @ Y0))))) | ((X5 @ X7) != $true) | ($true != sP6) | ((X5 @ (sK206 @ X6 @ X5)) = $true)) )),
% 57.88/9.52 inference(cnf_transformation,[status(thm)],[f1030])).
% 57.88/9.52 thf(f3058,plain,(
% 57.88/9.52 ~spl432_1 | spl432_18),
% 57.88/9.52 inference(avatar_split_clause,[status(thm)],[f2854,f3056,f2986])).
% 57.88/9.52 thf(f2854,plain,(
% 57.88/9.52 ( ! [X6 : $i,X7 : $i,X5 : $i > $o] : (($true = (singleton @ (dsetconstr @ X6 @ X5))) | ((in @ X7 @ X6) != $true) | ($true != sP6) | ((sK205 @ X6 @ X5) != (sK206 @ X6 @ X5)) | ((X5 @ X7) != $true)) )),
% 57.88/9.52 inference(beta_eta_normalization,[status(thm)],[f1692])).
% 57.88/9.52 thf(f1692,plain,(
% 57.88/9.52 ( ! [X6 : $i,X7 : $i,X5 : $i > $o] : (((sK205 @ X6 @ X5) != (sK206 @ X6 @ X5)) | ((X5 @ X7) != $true) | ($true = (singleton @ (dsetconstr @ X6 @ (^[Y0 : $i]: (X5 @ Y0))))) | ((in @ X7 @ X6) != $true) | ($true != sP6)) )),
% 57.88/9.52 inference(cnf_transformation,[status(thm)],[f1030])).
% 57.88/9.52 thf(f3050,plain,(
% 57.88/9.52 ~spl432_1 | spl432_16),
% 57.88/9.52 inference(avatar_split_clause,[status(thm)],[f2859,f3048,f2986])).
% 57.88/9.52 thf(f2859,plain,(
% 57.88/9.52 ( ! [X6 : $i,X7 : $i,X5 : $i > $o] : (($true = (singleton @ (dsetconstr @ X6 @ X5))) | ((X5 @ X7) != $true) | ($true != sP6) | ((in @ X7 @ X6) != $true) | ((X5 @ (sK205 @ X6 @ X5)) = $true)) )),
% 57.88/9.52 inference(beta_eta_normalization,[status(thm)],[f1694])).
% 57.88/9.52 thf(f1694,plain,(
% 57.88/9.52 ( ! [X6 : $i,X7 : $i,X5 : $i > $o] : (((X5 @ (sK205 @ X6 @ X5)) = $true) | ($true != sP6) | ((X5 @ X7) != $true) | ((in @ X7 @ X6) != $true) | ($true = (singleton @ (dsetconstr @ X6 @ (^[Y0 : $i]: (X5 @ Y0)))))) )),
% 57.88/9.52 inference(cnf_transformation,[status(thm)],[f1030])).
% 57.88/9.52 thf(f3046,plain,(
% 57.88/9.52 spl432_1),
% 57.88/9.52 inference(avatar_split_clause,[status(thm)],[f2868,f2986])).
% 57.88/9.52 thf(f2868,plain,(
% 57.88/9.52 ($true = sP6)),
% 57.88/9.52 inference(trivial_inequality_removal,[status(thm)],[f2398])).
% 57.88/9.52 thf(f2398,plain,(
% 57.88/9.52 ($true = sP6) | ($true != $true)),
% 57.88/9.52 inference(definition_unfolding,[status(thm)],[f1701,f1865])).
% 57.88/9.52 thf(f1865,plain,(
% 57.88/9.52 (singletonprop = $true)),
% 57.88/9.52 inference(cnf_transformation,[status(thm)],[f1213])).
% 57.88/9.52 thf(f1701,plain,(
% 57.88/9.52 ($true = sP6) | (singletonprop != $true)),
% 57.88/9.52 inference(cnf_transformation,[status(thm)],[f1031])).
% 57.88/9.52 thf(f1031,plain,(
% 57.88/9.52 (($true = sP6) | (singletonprop != $true)) & ((singletonprop = $true) | ($true != sP6))),
% 57.88/9.52 inference(nnf_transformation,[status(thm)],[f688])).
% 57.88/9.52 thf(f688,plain,(
% 57.88/9.52 ($true = sP6) <=> (singletonprop = $true)),
% 57.88/9.52 inference(definition_folding,[status(thm)],[f637,f687])).
% 57.88/9.52 thf(f637,plain,(
% 57.88/9.52 ! [X0 : $i > $o,X1 : $i] : (! [X4 : $i] : (((X0 @ X4) != $true) | ((in @ X4 @ X1) != $true)) | ? [X2 : $i] : (? [X3 : $i] : (((X0 @ X3) = $true) & ((X0 @ X2) = $true) & ((in @ X3 @ X1) = $true) & (X2 != X3)) & ($true = (in @ X2 @ X1))) | ((singleton @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true)) <=> (singletonprop = $true)),
% 57.88/9.52 inference(flattening,[status(thm)],[f636])).
% 57.88/9.52 thf(f636,plain,(
% 57.88/9.52 (singletonprop = $true) <=> ! [X0 : $i > $o,X1 : $i] : ((((singleton @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true) | ! [X4 : $i] : (((X0 @ X4) != $true) | ((in @ X4 @ X1) != $true))) | ? [X2 : $i] : (? [X3 : $i] : ((((X2 != X3) & ((X0 @ X3) = $true)) & ((X0 @ X2) = $true)) & ((in @ X3 @ X1) = $true)) & ($true = (in @ X2 @ X1))))),
% 57.88/9.52 inference(ennf_transformation,[status(thm)],[f480])).
% 57.88/9.52 thf(f480,plain,(
% 57.88/9.52 (singletonprop = $true) <=> ! [X0 : $i > $o,X1 : $i] : (! [X2 : $i] : (($true = (in @ X2 @ X1)) => ! [X3 : $i] : (((in @ X3 @ X1) = $true) => (((X0 @ X2) = $true) => (((X0 @ X3) = $true) => (X2 = X3))))) => (? [X4 : $i] : (((X0 @ X4) = $true) & ((in @ X4 @ X1) = $true)) => ((singleton @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true)))),
% 57.88/9.52 inference(fool_elimination,[status(thm)],[f479])).
% 57.88/9.52 thf(f479,plain,(
% 57.88/9.52 (! [X0 : $i > $o,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => ! [X3 : $i] : ((in @ X3 @ X1) => ((X0 @ X2) => ((X0 @ X3) => (X2 = X3))))) => (? [X4 : $i] : ((X0 @ X4) & (in @ X4 @ X1)) => (singleton @ (dsetconstr @ X1 @ (^[X5 : $i] : (X0 @ X5)))))) = singletonprop)),
% 57.88/9.52 inference(rectify,[status(thm)],[f159])).
% 57.88/9.52 thf(f159,axiom,(
% 57.88/9.52 (! [X0 : $i > $o,X3 : $i] : (! [X1 : $i] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X3) => ((X0 @ X1) => ((X0 @ X2) => (X1 = X2))))) => (? [X1 : $i] : ((X0 @ X1) & (in @ X1 @ X3)) => (singleton @ (dsetconstr @ X3 @ (^[X1 : $i] : (X0 @ X1)))))) = singletonprop)),
% 57.88/9.52 file('/export/starexec/sandbox/tmp/tmp.0njZozgBRA/DTF2THF_1200.p',singletonprop)).
% 57.88/9.52 thf(f3001,plain,(
% 57.88/9.52 spl432_4 | ~spl432_1),
% 57.88/9.52 inference(avatar_split_clause,[status(thm)],[f2942,f2986,f2999])).
% 57.88/9.52 thf(f2942,plain,(
% 57.88/9.52 ( ! [X6 : $i,X7 : $i,X5 : $i > $o] : (($true = (singleton @ (dsetconstr @ X6 @ X5))) | ((X5 @ X7) != $true) | ((in @ (sK206 @ X6 @ X5) @ X6) = $true) | ($true != sP6) | ((in @ X7 @ X6) != $true)) )),
% 57.88/9.52 inference(beta_eta_normalization,[status(thm)],[f1693])).
% 57.88/9.52 thf(f1693,plain,(
% 57.88/9.52 ( ! [X6 : $i,X7 : $i,X5 : $i > $o] : (($true = (singleton @ (dsetconstr @ X6 @ (^[Y0 : $i]: (X5 @ Y0))))) | ((in @ X7 @ X6) != $true) | ((X5 @ X7) != $true) | ((in @ (sK206 @ X6 @ X5) @ X6) = $true) | ($true != sP6)) )),
% 57.88/9.52 inference(cnf_transformation,[status(thm)],[f1030])).
% 57.88/9.52 % SZS output end Proof for DTF2THF_1200
% 57.88/9.52 % (1699)------------------------------
% 57.88/9.52 % (1699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.88/9.52 % (1699)Termination reason: Refutation
% 57.88/9.52
% 57.88/9.52 % (1699)Memory used [KB]: 9466
% 57.88/9.52 % (1699)Time elapsed: 0.241 s
% 57.88/9.52 % (1699)Instructions burned: 755 (million)
% 57.88/9.52 % (1699)------------------------------
% 57.88/9.52 % (1699)------------------------------
% 57.88/9.52 % (1481)Success in time 8.053 s
%------------------------------------------------------------------------------