%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU610^1 : 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 : n031.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 09:35:35 AM UTC 2026
% Result : Theorem 50.23s 8.36s
% Output : Refutation 50.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 36
% Syntax : Number of formulae : 235 ( 49 unt; 0 typ; 5 def)
% Number of atoms : 4320 (1247 equ; 0 cnn)
% Maximal formula atoms : 128 ( 18 avg)
% Number of connectives : 3090 ( 417 ~; 325 |; 512 &;1220 @)
% ( 37 <=>; 579 =>; 0 <=; 0 <~>)
% Maximal formula depth : 133 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 282 ( 279 usr; 167 con; 0-4 aty)
% Number of variables : 471 ( 0 ^; 359 !; 112 ?; 471 :)
% 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_159,type,
sP1: $i > $i > $o ).
thf(func_def_160,type,
sP2: $i > $o ).
thf(func_def_161,type,
sP3: $i > $i > $o ).
thf(func_def_162,type,
sP4: $i > $i > $o ).
thf(func_def_171,type,
sK13: $i > $i ).
thf(func_def_175,type,
sK17: $i > $i > $i ).
thf(func_def_182,type,
sK24: $i > $o ).
thf(func_def_183,type,
sK25: ( $i > $o ) > $i ).
thf(func_def_184,type,
sK26: $i > $o ).
thf(func_def_185,type,
sK27: $i > $o ).
thf(func_def_186,type,
sK28: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_187,type,
sK29: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_203,type,
sK45: $i > $o ).
thf(func_def_205,type,
sK47: $i > ( $i > $o ) > $i ).
thf(func_def_206,type,
sK48: $i > $i > $o ).
thf(func_def_208,type,
sK50: $i > $i ).
thf(func_def_209,type,
sK51: $i > $i ).
thf(func_def_210,type,
sK52: $i > ( $i > $i > $o ) > $i ).
thf(func_def_211,type,
sK53: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_212,type,
sK54: $i > ( $i > $i > $o ) > $i ).
thf(func_def_216,type,
sK58: $i > $o ).
thf(func_def_228,type,
sK70: $i > $o ).
thf(func_def_235,type,
sK77: $i > $o ).
thf(func_def_241,type,
sK83: $i > $i ).
thf(func_def_246,type,
sK88: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_247,type,
sK89: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_248,type,
sK90: $i > $o ).
thf(func_def_249,type,
sK91: $i > $o ).
thf(func_def_268,type,
sK110: $i > $o ).
thf(func_def_269,type,
sK111: $i > $i ).
thf(func_def_270,type,
sK112: ( $i > $o ) > $i ).
thf(func_def_276,type,
sK118: $i > $i ).
thf(func_def_278,type,
sK120: $i > $i ).
thf(func_def_279,type,
sK121: $i > $o ).
thf(func_def_281,type,
sK123: ( $i > $o ) > $i ).
thf(func_def_282,type,
sK124: ( $i > $o ) > $i ).
thf(func_def_293,type,
sK135: $i > $i > $i ).
thf(func_def_301,type,
sK143: $i > ( $i > $o ) > $i ).
thf(func_def_302,type,
sK144: $i > $o ).
thf(func_def_306,type,
sK148: $i > $o ).
thf(func_def_309,type,
sK151: $i > $o ).
thf(func_def_312,type,
sK154: $i > $i > $i ).
thf(func_def_323,type,
sK165: $i > $i ).
thf(func_def_328,type,
sK170: $i > $i ).
thf(func_def_343,type,
sK185: $i > $o ).
thf(func_def_346,type,
sK188: $i > ( $i > $o ) > $i ).
thf(func_def_348,type,
sK190: $i > $o ).
thf(func_def_351,type,
sK193: $i > ( $i > $o ) > $i ).
thf(func_def_352,type,
sK194: $i > $o ).
thf(func_def_367,type,
sK209: $i > $o ).
thf(func_def_368,type,
sK210: $i > $i ).
thf(func_def_369,type,
sK211: ( $i > $o ) > $i ).
thf(func_def_370,type,
sK212: $i > $i > $i ).
thf(func_def_371,type,
sK213: $i > $i > $i ).
thf(func_def_372,type,
sK214: $i > $i > $i ).
thf(func_def_373,type,
sK215: $i > $i > $i ).
thf(func_def_374,type,
sK216: $i > $i > $i > $i ).
thf(func_def_375,type,
sK217: $i > $i ).
thf(func_def_376,type,
sK218: $i > $i ).
thf(func_def_377,type,
sK219: $i > $i ).
thf(func_def_378,type,
sK220: $i > $i ).
thf(func_def_379,type,
sK221: $i > $i > $i > $i ).
thf(func_def_380,type,
sK222: $i > $i > $i > $i ).
thf(func_def_381,type,
sK223: $i > $i > $i ).
thf(func_def_382,type,
sK224: $i > $i > $i ).
thf(func_def_383,type,
sK225: $i > $i > $i ).
thf(func_def_384,type,
sK226: $i > $i ).
thf(func_def_385,type,
sK227: $i > $i > $i ).
thf(func_def_387,type,
sK229: $i > $i ).
thf(func_def_388,type,
sK230: $i > $i ).
thf(func_def_389,type,
sK231: $i > $i > $i ).
thf(func_def_395,type,
sK237: $i > $o ).
thf(func_def_396,type,
sK238: $i > $o ).
thf(func_def_399,type,
sK241: $i > $o ).
thf(func_def_402,type,
sK244: $i > ( $i > $o ) > $i ).
thf(func_def_406,type,
sK248: $o > $i > $i > $i ).
thf(func_def_412,type,
sK254: $i > $o ).
thf(func_def_414,type,
sK256: ( $i > $o ) > $i > $i ).
thf(func_def_417,type,
sK259: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_418,type,
sK260: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_421,type,
sK263: $i > $o ).
thf(func_def_422,type,
sK264: $i > $o ).
thf(func_def_424,type,
sK266: $i > $o ).
thf(func_def_426,type,
sK268: ( $i > $o ) > $i > $i ).
thf(func_def_432,type,
sK274: ( $i > $o ) > $i > $i ).
thf(func_def_434,type,
sK276: $i > $o ).
thf(func_def_438,type,
sK280: $i > $i > $i ).
thf(func_def_456,type,
sK298: $i > $o ).
thf(func_def_460,type,
sK302: $i > $o ).
thf(func_def_463,type,
sK305: $i > $i ).
thf(func_def_469,type,
sK311: $i > $i > $i ).
thf(func_def_470,type,
sK312: $i > $i > $i ).
thf(func_def_476,type,
sK318: $i > $i > $i ).
thf(func_def_482,type,
sK324: $i > $i > $i ).
thf(func_def_486,type,
sK328: $i > $o ).
thf(func_def_497,type,
sK339: $i > $o ).
thf(func_def_505,type,
ph347:
!>[X0: $tType] : X0 ).
thf(f28469,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f6193,f16383,f17386,f26817,f28373,f28459]) ).
thf(f28459,plain,
( spl346_51
| ~ spl346_71 ),
inference(avatar_split_clause,[status(thm)],[f28458,f5891,f4972]) ).
thf(f4972,definition,
( spl346_51
<=> ( $true
= ( subset @ sK56 @ sK55 ) ) ),
introduced(definition,[new_symbols(naming,[spl346_51])],[avatar_definition]) ).
thf(f5891,definition,
( spl346_71
<=> ! [X0: $i] :
( ( $true
= ( subset @ X0 @ sK55 ) )
| ( $true
!= ( in @ ( sK280 @ X0 @ sK55 ) @ sK56 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl346_71])],[avatar_definition]) ).
thf(f28458,plain,
( ( $true
= ( subset @ sK56 @ sK55 ) )
| ~ spl346_71 ),
inference(trivial_inequality_removal,[status(thm)],[f28457]) ).
thf(f28457,plain,
( ( $true
= ( subset @ sK56 @ sK55 ) )
| ( $true != $true )
| ~ spl346_71 ),
inference(forward_demodulation,[status(thm)],[f28453,f1273]) ).
thf(f1273,plain,
subsetI2 = $true,
inference(cnf_transformation,[status(thm)],[f635]) ).
thf(f635,plain,
( ( setextsub = $true )
& ( powersetI = $true )
& ( emptysetAx = $true )
& ( setadjoinIL = $true )
& ( dsetconstrI = $true )
& ( setadjoinIR = $true )
& ( descrp = $true )
& ( exuEu = $true )
& ( replAx = $true )
& ( notsubsetI = $true )
& ( setadjoinSub = $true )
& ( binunionEcases = $true )
& ( exuI1 = $true )
& ( exuE1 = $true )
& ( noeltsimpempty = $true )
& ( setminusEL = $true )
& ( emptyE1 = $true )
& ( dsetconstrEL = $true )
& ( binintersectRsub = $true )
& ( singletonsswitch = $true )
& ( binunionE = $true )
& ( binunionLsub = $true )
& ( binunionIR = $true )
& ( setadjoinSub2 = $true )
& ( subPowSU = $true )
& ( bs114d = $true )
& ( exuE3u = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( binintersectSubset2 = $true )
& ( upairsetIR = $true )
& ( setext = $true )
& ( foundationAx = $true )
& ( uniqinunit = $true )
& ( setminusILneg = $true )
& ( omegaSAx = $true )
& ( emptyInPowerset = $true )
& ( quantDeMorgan2 = $true )
& ( eqimpsubset2 = $true )
& ( descr__Cong = $true )
& ( upairsetIL = $true )
& ( binintersectLsub = $true )
& ( nonemptyE1 = $true )
& ( nonemptyI = $true )
& ( subsetE = $true )
& ( emptyinunitempty = $true )
& ( powersetE1 = $true )
& ( setunion__Cong = $true )
& ( quantDeMorgan1 = $true )
& ( exuI3 = $true )
& ( eqimpsubset1 = $true )
& ( setminusLsub = $true )
& ( upairsetE = $true )
& ( subsetRefl = $true )
& ( nonemptyI1 = $true )
& ( upairset2IR = $true )
& ( omega__Cong = $true )
& ( vacuousDall = $true )
& ( subsetI2 = $true )
& ( notinemptyset = $true )
& ( powerset__Cong = $true )
& ( exu__Cong = $true )
& ( setadjoinOr = $true )
& ( setminusSubset2 = $true )
& ( emptyI = $true )
& ( binintersectSubset4 = $true )
& ( powersetAx = $true )
& ( disjointsetsI1 = $true )
& ( emptyset__Cong = $true )
& ( powersetsubset = $true )
& ( nonemptyImpWitness = $true )
& ( binintersectSubset1 = $true )
& ( setminusELneg = $true )
& ( setminusI = $true )
& ( emptyinPowerset = $true )
& ( setextAx = $true )
& ( quantDeMorgan4 = $true )
& ( setminusIRneg = $true )
& ( binintersectER = $true )
& ( dsetconstr__Cong = $true )
& ( setadjoinAx = $true )
& ( notequalI1 = $true )
& ( binintersectEL = $true )
& ( dsetconstrER = $true )
& ( prop2setI = $true )
& ( sepInPowerset = $true )
& ( setoftrueEq = $true )
& ( prop2set2propI = $true )
& ( subsetTrans = $true )
& ( binintersectSubset5 = $true )
& ( subsetI1 = $true )
& ( in__Cong = $true )
& ( wellorderingAx = $true )
& ( emptysetimpfalse = $true )
& ( powersetE = $true )
& ( binunionRsub = $true )
& ( exuI2 = $true )
& ( inPowerset = $true )
& ( subsetE2 = $true )
& ( eqinunit = $true )
& ( emptysetsubset = $true )
& ( setbeta = $true )
& ( notdallE = $true )
& ( prop2setE = $true )
& ( quantDeMorgan3 = $true )
& ( subsetemptysetimpeq = $true )
& ( exuE2 = $true )
& ( notequalI2 = $true )
& ( emptyset
= ( setminus @ sK56 @ sK55 ) )
& ( $true
!= ( subset @ sK56 @ sK55 ) )
& ( setminusER = $true )
& ( binunionIL = $true )
& ( subset2powerset = $true )
& ( notinsingleton = $true )
& ( notdexE = $true )
& ( setunionI = $true )
& ( binintersectSubset3 = $true )
& ( setadjoinE = $true )
& ( inCongP = $true )
& ( setminusERneg = $true )
& ( emptysetE = $true )
& ( omegaIndAx = $true )
& ( powersetI1 = $true )
& ( exuE3e = $true )
& ( setadjoin__Cong = $true )
& ( binintersectI = $true )
& ( setunionE = $true )
& ( sepSubset = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK55,sK56])],[f453,f634]) ).
thf(f634,plain,
( ? [X0: $i,X1: $i] :
( ( emptyset
= ( setminus @ X1 @ X0 ) )
& ( ( subset @ X1 @ X0 )
!= $true ) )
=> ( ( emptyset
= ( setminus @ sK56 @ sK55 ) )
& ( $true
!= ( subset @ sK56 @ sK55 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f453,plain,
( ( setextsub = $true )
& ( powersetI = $true )
& ( emptysetAx = $true )
& ( setadjoinIL = $true )
& ( dsetconstrI = $true )
& ( setadjoinIR = $true )
& ( descrp = $true )
& ( exuEu = $true )
& ( replAx = $true )
& ( notsubsetI = $true )
& ( setadjoinSub = $true )
& ( binunionEcases = $true )
& ( exuI1 = $true )
& ( exuE1 = $true )
& ( noeltsimpempty = $true )
& ( setminusEL = $true )
& ( emptyE1 = $true )
& ( dsetconstrEL = $true )
& ( binintersectRsub = $true )
& ( singletonsswitch = $true )
& ( binunionE = $true )
& ( binunionLsub = $true )
& ( binunionIR = $true )
& ( setadjoinSub2 = $true )
& ( subPowSU = $true )
& ( bs114d = $true )
& ( exuE3u = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( binintersectSubset2 = $true )
& ( upairsetIR = $true )
& ( setext = $true )
& ( foundationAx = $true )
& ( uniqinunit = $true )
& ( setminusILneg = $true )
& ( omegaSAx = $true )
& ( emptyInPowerset = $true )
& ( quantDeMorgan2 = $true )
& ( eqimpsubset2 = $true )
& ( descr__Cong = $true )
& ( upairsetIL = $true )
& ( binintersectLsub = $true )
& ( nonemptyE1 = $true )
& ( nonemptyI = $true )
& ( subsetE = $true )
& ( emptyinunitempty = $true )
& ( powersetE1 = $true )
& ( setunion__Cong = $true )
& ( quantDeMorgan1 = $true )
& ( exuI3 = $true )
& ( eqimpsubset1 = $true )
& ( setminusLsub = $true )
& ( upairsetE = $true )
& ( subsetRefl = $true )
& ( nonemptyI1 = $true )
& ( upairset2IR = $true )
& ( omega__Cong = $true )
& ( vacuousDall = $true )
& ( subsetI2 = $true )
& ( notinemptyset = $true )
& ( powerset__Cong = $true )
& ( exu__Cong = $true )
& ( setadjoinOr = $true )
& ( setminusSubset2 = $true )
& ( emptyI = $true )
& ( binintersectSubset4 = $true )
& ( powersetAx = $true )
& ( disjointsetsI1 = $true )
& ( emptyset__Cong = $true )
& ( powersetsubset = $true )
& ( nonemptyImpWitness = $true )
& ( binintersectSubset1 = $true )
& ( setminusELneg = $true )
& ( setminusI = $true )
& ( emptyinPowerset = $true )
& ( setextAx = $true )
& ( quantDeMorgan4 = $true )
& ( setminusIRneg = $true )
& ( binintersectER = $true )
& ( dsetconstr__Cong = $true )
& ( setadjoinAx = $true )
& ( notequalI1 = $true )
& ( binintersectEL = $true )
& ( dsetconstrER = $true )
& ( prop2setI = $true )
& ( sepInPowerset = $true )
& ( setoftrueEq = $true )
& ( prop2set2propI = $true )
& ( subsetTrans = $true )
& ( binintersectSubset5 = $true )
& ( subsetI1 = $true )
& ( in__Cong = $true )
& ( wellorderingAx = $true )
& ( emptysetimpfalse = $true )
& ( powersetE = $true )
& ( binunionRsub = $true )
& ( exuI2 = $true )
& ( inPowerset = $true )
& ( subsetE2 = $true )
& ( eqinunit = $true )
& ( emptysetsubset = $true )
& ( setbeta = $true )
& ( notdallE = $true )
& ( prop2setE = $true )
& ( quantDeMorgan3 = $true )
& ( subsetemptysetimpeq = $true )
& ( exuE2 = $true )
& ( notequalI2 = $true )
& ? [X0: $i,X1: $i] :
( ( emptyset
= ( setminus @ X1 @ X0 ) )
& ( ( subset @ X1 @ X0 )
!= $true ) )
& ( setminusER = $true )
& ( binunionIL = $true )
& ( subset2powerset = $true )
& ( notinsingleton = $true )
& ( notdexE = $true )
& ( setunionI = $true )
& ( binintersectSubset3 = $true )
& ( setadjoinE = $true )
& ( inCongP = $true )
& ( setminusERneg = $true )
& ( emptysetE = $true )
& ( omegaIndAx = $true )
& ( powersetI1 = $true )
& ( exuE3e = $true )
& ( setadjoin__Cong = $true )
& ( binintersectI = $true )
& ( setunionE = $true )
& ( sepSubset = $true ) ),
inference(flattening,[status(thm)],[f452]) ).
thf(f452,plain,
( ? [X0: $i,X1: $i] :
( ( emptyset
= ( setminus @ X1 @ X0 ) )
& ( ( subset @ X1 @ X0 )
!= $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)],[f369]) ).
thf(f369,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 )
=> ! [X0: $i,X1: $i] :
( ( emptyset
= ( setminus @ X1 @ X0 ) )
=> ( ( subset @ X1 @ X0 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f368]) ).
thf(f368,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
=> ! [X0: $i,X1: $i] :
( ( emptyset
= ( setminus @ X1 @ X0 ) )
=> ( subset @ X1 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f130]) ).
thf(f130,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
=> ! [X4: $i,X3: $i] :
( ( emptyset
= ( setminus @ X3 @ X4 ) )
=> ( subset @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f129]) ).
thf(f129,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
=> ! [X4: $i,X3: $i] :
( ( emptyset
= ( setminus @ X3 @ X4 ) )
=> ( subset @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mU0PE1mI9q/DTF2THF_13954.p',setminusSubset1) ).
thf(f28453,plain,
( ( subsetI2 != $true )
| ( $true
= ( subset @ sK56 @ sK55 ) )
| ~ spl346_71 ),
inference(trivial_inequality_removal,[status(thm)],[f28452]) ).
thf(f28452,plain,
( ( subsetI2 != $true )
| ( $true
= ( subset @ sK56 @ sK55 ) )
| ( $true != $true )
| ~ spl346_71 ),
inference(duplicate_literal_removal,[status(thm)],[f28434]) ).
thf(f28434,plain,
( ( subsetI2 != $true )
| ( $true != $true )
| ( $true
= ( subset @ sK56 @ sK55 ) )
| ( $true
= ( subset @ sK56 @ sK55 ) )
| ~ spl346_71 ),
inference(superposition,[status(thm)],[f5892,f1662]) ).
thf(f1662,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK280 @ X1 @ X0 ) @ X1 ) )
| ( subsetI2 != $true )
| ( ( subset @ X1 @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f1020]) ).
thf(f1020,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( $true
= ( in @ ( sK280 @ X1 @ X0 ) @ X1 ) )
& ( ( in @ ( sK280 @ X1 @ X0 ) @ X0 )
!= $true ) )
| ( ( subset @ X1 @ X0 )
= $true ) )
| ( subsetI2 != $true ) )
& ( ( subsetI2 = $true )
| ( ! [X5: $i] :
( ( ( in @ X5 @ sK282 )
!= $true )
| ( $true
= ( in @ X5 @ sK281 ) ) )
& ( $true
!= ( subset @ sK282 @ sK281 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK280,sK281,sK282])],[f1017,f1019,f1018]) ).
thf(f1018,plain,
! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
& ( $true
!= ( in @ X2 @ X0 ) ) )
=> ( ( $true
= ( in @ ( sK280 @ X1 @ X0 ) @ X1 ) )
& ( ( in @ ( sK280 @ X1 @ X0 ) @ X0 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1019,plain,
( ? [X3: $i,X4: $i] :
( ! [X5: $i] :
( ( ( in @ X5 @ X4 )
!= $true )
| ( $true
= ( in @ X5 @ X3 ) ) )
& ( ( subset @ X4 @ X3 )
!= $true ) )
=> ( ! [X5: $i] :
( ( ( in @ X5 @ sK282 )
!= $true )
| ( $true
= ( in @ X5 @ sK281 ) ) )
& ( $true
!= ( subset @ sK282 @ sK281 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1017,plain,
( ( ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
& ( $true
!= ( in @ X2 @ X0 ) ) )
| ( ( subset @ X1 @ X0 )
= $true ) )
| ( subsetI2 != $true ) )
& ( ( subsetI2 = $true )
| ? [X3: $i,X4: $i] :
( ! [X5: $i] :
( ( ( in @ X5 @ X4 )
!= $true )
| ( $true
= ( in @ X5 @ X3 ) ) )
& ( ( subset @ X4 @ X3 )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f1016]) ).
thf(f1016,plain,
( ( ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
& ( $true
!= ( in @ X2 @ X0 ) ) )
| ( ( subset @ X1 @ X0 )
= $true ) )
| ( subsetI2 != $true ) )
& ( ( subsetI2 = $true )
| ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ X1 ) )
| ( $true
= ( in @ X2 @ X0 ) ) )
& ( ( subset @ X1 @ X0 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f445]) ).
thf(f445,plain,
( ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
& ( $true
!= ( in @ X2 @ X0 ) ) )
| ( ( subset @ X1 @ X0 )
= $true ) )
<=> ( subsetI2 = $true ) ),
inference(ennf_transformation,[status(thm)],[f200]) ).
thf(f200,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
=> ( $true
= ( in @ X2 @ X0 ) ) )
=> ( ( subset @ X1 @ X0 )
= $true ) )
<=> ( subsetI2 = $true ) ),
inference(fool_elimination,[status(thm)],[f199]) ).
thf(f199,plain,
( subsetI2
= ( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) )
=> ( subset @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f81]) ).
thf(f81,axiom,
( subsetI2
= ( ! [X4: $i,X3: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( in @ X1 @ X4 ) )
=> ( subset @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mU0PE1mI9q/DTF2THF_13954.p',subsetI2) ).
thf(f5892,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ ( sK280 @ X0 @ sK55 ) @ sK56 ) )
| ( $true
= ( subset @ X0 @ sK55 ) ) )
| ~ spl346_71 ),
inference(avatar_component_clause,[status(thm)],[f5891]) ).
thf(f28373,plain,
spl346_36,
inference(avatar_split_clause,[status(thm)],[f28263,f2341]) ).
thf(f2341,definition,
( spl346_36
<=> ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl346_36])],[avatar_definition]) ).
thf(f28263,plain,
! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true ),
inference(duplicate_literal_removal,[status(thm)],[f28194]) ).
thf(f28194,plain,
! [X0: $i] :
( ( ( in @ X0 @ emptyset )
!= $true )
| ( ( in @ X0 @ emptyset )
!= $true ) ),
inference(superposition,[status(thm)],[f4566,f3898]) ).
thf(f3898,plain,
( emptyset
= ( binintersect @ sK55 @ emptyset ) ),
inference(trivial_inequality_removal,[status(thm)],[f3897]) ).
thf(f3897,plain,
( ( emptyset
= ( binintersect @ sK55 @ emptyset ) )
| ( $true != $true ) ),
inference(forward_demodulation,[status(thm)],[f3885,f1264]) ).
thf(f1264,plain,
disjointsetsI1 = $true,
inference(cnf_transformation,[status(thm)],[f635]) ).
thf(f3885,plain,
( ( disjointsetsI1 != $true )
| ( emptyset
= ( binintersect @ sK55 @ emptyset ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f3884]) ).
thf(f3884,plain,
( ( emptyset
= ( binintersect @ sK55 @ emptyset ) )
| ( disjointsetsI1 != $true )
| ( $true != $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f3878]) ).
thf(f3878,plain,
( ( disjointsetsI1 != $true )
| ( emptyset
= ( binintersect @ sK55 @ emptyset ) )
| ( emptyset
= ( binintersect @ sK55 @ emptyset ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f2526,f1479]) ).
thf(f1479,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK154 @ X1 @ X0 ) @ X0 )
= $true )
| ( disjointsetsI1 != $true )
| ( emptyset
= ( binintersect @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f813]) ).
thf(f813,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( ( in @ ( sK154 @ X1 @ X0 ) @ X0 )
= $true )
& ( $true
= ( in @ ( sK154 @ X1 @ X0 ) @ X1 ) ) )
| ( emptyset
= ( binintersect @ X1 @ X0 ) ) )
| ( disjointsetsI1 != $true ) )
& ( ( disjointsetsI1 = $true )
| ( ! [X5: $i] :
( ( $true
!= ( in @ X5 @ sK155 ) )
| ( $true
!= ( in @ X5 @ sK156 ) ) )
& ( emptyset
!= ( binintersect @ sK156 @ sK155 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK154,sK155,sK156])],[f810,f812,f811]) ).
thf(f811,plain,
! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ X0 ) )
& ( $true
= ( in @ X2 @ X1 ) ) )
=> ( ( ( in @ ( sK154 @ X1 @ X0 ) @ X0 )
= $true )
& ( $true
= ( in @ ( sK154 @ X1 @ X0 ) @ X1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f812,plain,
( ? [X3: $i,X4: $i] :
( ! [X5: $i] :
( ( $true
!= ( in @ X5 @ X3 ) )
| ( ( in @ X5 @ X4 )
!= $true ) )
& ( emptyset
!= ( binintersect @ X4 @ X3 ) ) )
=> ( ! [X5: $i] :
( ( $true
!= ( in @ X5 @ sK155 ) )
| ( $true
!= ( in @ X5 @ sK156 ) ) )
& ( emptyset
!= ( binintersect @ sK156 @ sK155 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f810,plain,
( ( ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ X0 ) )
& ( $true
= ( in @ X2 @ X1 ) ) )
| ( emptyset
= ( binintersect @ X1 @ X0 ) ) )
| ( disjointsetsI1 != $true ) )
& ( ( disjointsetsI1 = $true )
| ? [X3: $i,X4: $i] :
( ! [X5: $i] :
( ( $true
!= ( in @ X5 @ X3 ) )
| ( ( in @ X5 @ X4 )
!= $true ) )
& ( emptyset
!= ( binintersect @ X4 @ X3 ) ) ) ) ),
inference(rectify,[status(thm)],[f809]) ).
thf(f809,plain,
( ( ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ X0 ) )
& ( $true
= ( in @ X2 @ X1 ) ) )
| ( emptyset
= ( binintersect @ X1 @ X0 ) ) )
| ( disjointsetsI1 != $true ) )
& ( ( disjointsetsI1 = $true )
| ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
!= ( in @ X2 @ X0 ) )
| ( $true
!= ( in @ X2 @ X1 ) ) )
& ( emptyset
!= ( binintersect @ X1 @ X0 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f446]) ).
thf(f446,plain,
( ! [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( $true
= ( in @ X2 @ X0 ) )
& ( $true
= ( in @ X2 @ X1 ) ) )
| ( emptyset
= ( binintersect @ X1 @ X0 ) ) )
<=> ( disjointsetsI1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f268]) ).
thf(f268,plain,
( ! [X0: $i,X1: $i] :
( ~ ? [X2: $i] :
( ( $true
= ( in @ X2 @ X0 ) )
& ( $true
= ( in @ X2 @ X1 ) ) )
=> ( emptyset
= ( binintersect @ X1 @ X0 ) ) )
<=> ( disjointsetsI1 = $true ) ),
inference(fool_elimination,[status(thm)],[f267]) ).
thf(f267,plain,
( disjointsetsI1
= ( ! [X0: $i,X1: $i] :
( ~ ? [X2: $i] :
( ( in @ X2 @ X0 )
& ( in @ X2 @ X1 ) )
=> ( emptyset
= ( binintersect @ X1 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f115]) ).
thf(f115,axiom,
( disjointsetsI1
= ( ! [X4: $i,X3: $i] :
( ~ ? [X1: $i] :
( ( in @ X1 @ X4 )
& ( in @ X1 @ X3 ) )
=> ( emptyset
= ( binintersect @ X3 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mU0PE1mI9q/DTF2THF_13954.p',disjointsetsI1) ).
thf(f2526,plain,
! [X0: $i] :
( ( $true
!= ( in @ ( sK154 @ sK55 @ X0 ) @ emptyset ) )
| ( emptyset
= ( binintersect @ sK55 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f2525]) ).
thf(f2525,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( in @ ( sK154 @ sK55 @ X0 ) @ emptyset ) )
| ( emptyset
= ( binintersect @ sK55 @ X0 ) ) ),
inference(forward_demodulation,[status(thm)],[f2505,f1264]) ).
thf(f2505,plain,
! [X0: $i] :
( ( disjointsetsI1 != $true )
| ( emptyset
= ( binintersect @ sK55 @ X0 ) )
| ( $true
!= ( in @ ( sK154 @ sK55 @ X0 ) @ emptyset ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f2431]) ).
thf(f2431,plain,
! [X0: $i] :
( ( $true
!= ( in @ ( sK154 @ sK55 @ X0 ) @ emptyset ) )
| ( emptyset
= ( binintersect @ sK55 @ X0 ) )
| ( disjointsetsI1 != $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1880,f1478]) ).
thf(f1478,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( sK154 @ X1 @ X0 ) @ X1 ) )
| ( disjointsetsI1 != $true )
| ( emptyset
= ( binintersect @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f813]) ).
thf(f1880,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK55 )
!= $true )
| ( ( in @ X0 @ emptyset )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f1879]) ).
thf(f1879,plain,
! [X0: $i] :
( ( ( in @ X0 @ emptyset )
!= $true )
| ( ( in @ X0 @ sK55 )
!= $true )
| ( $true != $true ) ),
inference(forward_demodulation,[status(thm)],[f1866,f1221]) ).
thf(f1221,plain,
setminusER = $true,
inference(cnf_transformation,[status(thm)],[f635]) ).
thf(f1866,plain,
! [X0: $i] :
( ( setminusER != $true )
| ( ( in @ X0 @ sK55 )
!= $true )
| ( ( in @ X0 @ emptyset )
!= $true ) ),
inference(superposition,[status(thm)],[f1682,f1223]) ).
thf(f1223,plain,
( emptyset
= ( setminus @ sK56 @ sK55 ) ),
inference(cnf_transformation,[status(thm)],[f635]) ).
thf(f1682,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( setminus @ X0 @ X2 ) ) )
| ( setminusER != $true )
| ( $true
!= ( in @ X1 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f1045]) ).
thf(f1045,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( setminus @ X0 @ X2 ) ) )
| ( $true
!= ( in @ X1 @ X2 ) ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ( ( $true
= ( in @ sK293 @ ( setminus @ sK292 @ sK294 ) ) )
& ( $true
= ( in @ sK293 @ sK294 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK292,sK293,sK294])],[f1043,f1044]) ).
thf(f1044,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setminus @ X3 @ X5 ) )
= $true )
& ( $true
= ( in @ X4 @ X5 ) ) )
=> ( ( $true
= ( in @ sK293 @ ( setminus @ sK292 @ sK294 ) ) )
& ( $true
= ( in @ sK293 @ sK294 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1043,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( setminus @ X0 @ X2 ) ) )
| ( $true
!= ( in @ X1 @ X2 ) ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setminus @ X3 @ X5 ) )
= $true )
& ( $true
= ( in @ X4 @ X5 ) ) ) ) ),
inference(rectify,[status(thm)],[f1042]) ).
thf(f1042,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( setminus @ X0 @ X2 ) ) )
| ( $true
!= ( in @ X1 @ X2 ) ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( setminus @ X0 @ X2 ) ) )
& ( $true
= ( in @ X1 @ X2 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f481]) ).
thf(f481,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( setminus @ X0 @ X2 ) ) )
| ( $true
!= ( in @ X1 @ X2 ) ) )
<=> ( setminusER = $true ) ),
inference(ennf_transformation,[status(thm)],[f402]) ).
thf(f402,plain,
( ( setminusER = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( setminus @ X0 @ X2 ) ) )
=> ( $true
!= ( in @ X1 @ X2 ) ) ) ),
inference(flattening,[status(thm)],[f272]) ).
thf(f272,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( setminus @ X0 @ X2 ) ) )
=> ( $true
!= ( in @ X1 @ X2 ) ) )
<=> ( setminusER = $true ) ),
inference(fool_elimination,[status(thm)],[f271]) ).
thf(f271,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setminus @ X0 @ X2 ) )
=> ~ ( in @ X1 @ X2 ) )
= setminusER ),
inference(rectify,[status(thm)],[f122]) ).
thf(f122,axiom,
! [X3: $i,X1: $i,X4: $i] :
( ( ( in @ X1 @ ( setminus @ X3 @ X4 ) )
=> ~ ( in @ X1 @ X4 ) )
= setminusER ),
file('/export/starexec/sandbox/tmp/tmp.mU0PE1mI9q/DTF2THF_13954.p',setminusER) ).
thf(f4566,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ ( binintersect @ sK55 @ X0 ) ) )
| ( ( in @ X1 @ emptyset )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f4565]) ).
thf(f4565,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( $true
!= ( in @ X1 @ ( binintersect @ sK55 @ X0 ) ) )
| ( ( in @ X1 @ emptyset )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f4523,f1290]) ).
thf(f1290,plain,
binintersectLsub = $true,
inference(cnf_transformation,[status(thm)],[f635]) ).
thf(f4523,plain,
! [X0: $i,X1: $i] :
( ( binintersectLsub != $true )
| ( ( in @ X1 @ emptyset )
!= $true )
| ( $true
!= ( in @ X1 @ ( binintersect @ sK55 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f4518]) ).
thf(f4518,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X1 @ emptyset )
!= $true )
| ( $true != $true )
| ( binintersectLsub != $true )
| ( $true
!= ( in @ X1 @ ( binintersect @ sK55 @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f2577,f1357]) ).
thf(f1357,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ ( binintersect @ X1 @ X0 ) @ X1 )
= $true )
| ( binintersectLsub != $true ) ),
inference(cnf_transformation,[status(thm)],[f668]) ).
thf(f668,plain,
( ( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X1 )
= $true )
| ( binintersectLsub != $true ) )
& ( ( binintersectLsub = $true )
| ( $true
!= ( subset @ ( binintersect @ sK73 @ sK72 ) @ sK73 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK72,sK73])],[f666,f667]) ).
thf(f667,plain,
( ? [X2: $i,X3: $i] :
( $true
!= ( subset @ ( binintersect @ X3 @ X2 ) @ X3 ) )
=> ( $true
!= ( subset @ ( binintersect @ sK73 @ sK72 ) @ sK73 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f666,plain,
( ( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X1 )
= $true )
| ( binintersectLsub != $true ) )
& ( ( binintersectLsub = $true )
| ? [X2: $i,X3: $i] :
( $true
!= ( subset @ ( binintersect @ X3 @ X2 ) @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f665]) ).
thf(f665,plain,
( ( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X1 )
= $true )
| ( binintersectLsub != $true ) )
& ( ( binintersectLsub = $true )
| ? [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X1 )
!= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f141]) ).
thf(f141,plain,
( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X1 )
= $true )
<=> ( binintersectLsub = $true ) ),
inference(fool_elimination,[status(thm)],[f140]) ).
thf(f140,plain,
( binintersectLsub
= ( ! [X0: $i,X1: $i] : ( subset @ ( binintersect @ X1 @ X0 ) @ X1 ) ) ),
inference(rectify,[status(thm)],[f111]) ).
thf(f111,axiom,
( binintersectLsub
= ( ! [X4: $i,X3: $i] : ( subset @ ( binintersect @ X3 @ X4 ) @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mU0PE1mI9q/DTF2THF_13954.p',binintersectLsub) ).
thf(f2577,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X1 @ sK55 ) )
| ( ( in @ X0 @ emptyset )
!= $true )
| ( $true
!= ( in @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f2576]) ).
thf(f2576,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X1 @ sK55 ) )
| ( ( in @ X0 @ emptyset )
!= $true )
| ( $true != $true )
| ( $true
!= ( in @ X0 @ X1 ) ) ),
inference(forward_demodulation,[status(thm)],[f2475,f1322]) ).
thf(f1322,plain,
notsubsetI = $true,
inference(cnf_transformation,[status(thm)],[f635]) ).
thf(f2475,plain,
! [X0: $i,X1: $i] :
( ( notsubsetI != $true )
| ( ( in @ X0 @ emptyset )
!= $true )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( $true
!= ( subset @ X1 @ sK55 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f2418]) ).
thf(f2418,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X1 @ sK55 ) )
| ( $true
!= ( in @ X0 @ X1 ) )
| ( ( in @ X0 @ emptyset )
!= $true )
| ( notsubsetI != $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1880,f1394]) ).
thf(f1394,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X2 @ X0 ) )
| ( notsubsetI != $true )
| ( ( subset @ X1 @ X0 )
!= $true )
| ( $true
!= ( in @ X2 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f711]) ).
thf(f711,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( $true
= ( in @ X2 @ X0 ) )
| ( $true
!= ( in @ X2 @ X1 ) ) )
| ( notsubsetI != $true ) )
& ( ( notsubsetI = $true )
| ( ( $true
= ( subset @ sK100 @ sK99 ) )
& ( ( in @ sK101 @ sK99 )
!= $true )
& ( $true
= ( in @ sK101 @ sK100 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK99,sK100,sK101])],[f709,f710]) ).
thf(f710,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X4 @ X3 )
= $true )
& ( $true
!= ( in @ X5 @ X3 ) )
& ( ( in @ X5 @ X4 )
= $true ) )
=> ( ( $true
= ( subset @ sK100 @ sK99 ) )
& ( ( in @ sK101 @ sK99 )
!= $true )
& ( $true
= ( in @ sK101 @ sK100 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f709,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( $true
= ( in @ X2 @ X0 ) )
| ( $true
!= ( in @ X2 @ X1 ) ) )
| ( notsubsetI != $true ) )
& ( ( notsubsetI = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X4 @ X3 )
= $true )
& ( $true
!= ( in @ X5 @ X3 ) )
& ( ( in @ X5 @ X4 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f708]) ).
thf(f708,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( $true
= ( in @ X2 @ X0 ) )
| ( $true
!= ( in @ X2 @ X1 ) ) )
| ( notsubsetI != $true ) )
& ( ( notsubsetI = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
& ( $true
!= ( in @ X2 @ X0 ) )
& ( $true
= ( in @ X2 @ X1 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f538]) ).
thf(f538,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( $true
= ( in @ X2 @ X0 ) )
| ( $true
!= ( in @ X2 @ X1 ) ) )
<=> ( notsubsetI = $true ) ),
inference(flattening,[status(thm)],[f537]) ).
thf(f537,plain,
( ( notsubsetI = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( $true
= ( in @ X2 @ X0 ) )
| ( $true
!= ( in @ X2 @ X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f392]) ).
thf(f392,plain,
( ( notsubsetI = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
=> ( ( $true
!= ( in @ X2 @ X0 ) )
=> ( ( subset @ X1 @ X0 )
!= $true ) ) ) ),
inference(flattening,[status(thm)],[f188]) ).
thf(f188,plain,
( ( notsubsetI = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
=> ( ( $true
!= ( in @ X2 @ X0 ) )
=> ( ( subset @ X1 @ X0 )
!= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f187]) ).
thf(f187,plain,
( notsubsetI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ( ~ ( in @ X2 @ X0 )
=> ~ ( subset @ X1 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f85]) ).
thf(f85,axiom,
( notsubsetI
= ( ! [X4: $i,X3: $i,X1: $i] :
( ( in @ X1 @ X3 )
=> ( ~ ( in @ X1 @ X4 )
=> ~ ( subset @ X3 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mU0PE1mI9q/DTF2THF_13954.p',notsubsetI) ).
thf(f26817,plain,
~ spl346_51,
inference(avatar_split_clause,[status(thm)],[f3903,f4972]) ).
thf(f3903,plain,
( $true
!= ( subset @ sK56 @ sK55 ) ),
inference(trivial_inequality_removal,[status(thm)],[f3902]) ).
thf(f3902,plain,
( ( $true != $true )
| ( $true
!= ( subset @ sK56 @ sK55 ) ) ),
inference(forward_demodulation,[status(thm)],[f3901,f1266]) ).
thf(f1266,plain,
binintersectSubset4 = $true,
inference(cnf_transformation,[status(thm)],[f635]) ).
thf(f3901,plain,
( ( $true
!= ( subset @ sK56 @ sK55 ) )
| ( binintersectSubset4 != $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f3900]) ).
thf(f3900,plain,
( ( $true
!= ( subset @ sK56 @ sK55 ) )
| ( binintersectSubset4 != $true )
| ( sK56 != sK56 ) ),
inference(superposition,[status(thm)],[f2808,f1702]) ).
thf(f1702,plain,
! [X2: $i,X3: $i] :
( ( ( binintersect @ X2 @ X3 )
= X3 )
| ( binintersectSubset4 != $true )
| ( $true
!= ( subset @ X3 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f1071]) ).
thf(f1071,plain,
( ( ( binintersectSubset4 = $true )
| ( ( ( binintersect @ sK308 @ sK309 )
!= sK309 )
& ( $true
= ( subset @ sK309 @ sK308 ) ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( binintersect @ X2 @ X3 )
= X3 )
| ( $true
!= ( subset @ X3 @ X2 ) ) )
| ( binintersectSubset4 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK308,sK309])],[f1069,f1070]) ).
thf(f1070,plain,
( ? [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
!= X1 )
& ( ( subset @ X1 @ X0 )
= $true ) )
=> ( ( ( binintersect @ sK308 @ sK309 )
!= sK309 )
& ( $true
= ( subset @ sK309 @ sK308 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1069,plain,
( ( ( binintersectSubset4 = $true )
| ? [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
!= X1 )
& ( ( subset @ X1 @ X0 )
= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( binintersect @ X2 @ X3 )
= X3 )
| ( $true
!= ( subset @ X3 @ X2 ) ) )
| ( binintersectSubset4 != $true ) ) ),
inference(rectify,[status(thm)],[f1068]) ).
thf(f1068,plain,
( ( ( binintersectSubset4 = $true )
| ? [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
!= X1 )
& ( ( subset @ X1 @ X0 )
= $true ) ) )
& ( ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X1 )
| ( ( subset @ X1 @ X0 )
!= $true ) )
| ( binintersectSubset4 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f497]) ).
thf(f497,plain,
( ( binintersectSubset4 = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X1 )
| ( ( subset @ X1 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f171]) ).
thf(f171,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
=> ( ( binintersect @ X0 @ X1 )
= X1 ) )
<=> ( binintersectSubset4 = $true ) ),
inference(fool_elimination,[status(thm)],[f170]) ).
thf(f170,plain,
( binintersectSubset4
= ( ! [X0: $i,X1: $i] :
( ( subset @ X1 @ X0 )
=> ( ( binintersect @ X0 @ X1 )
= X1 ) ) ) ),
inference(rectify,[status(thm)],[f117]) ).
thf(f117,axiom,
( binintersectSubset4
= ( ! [X3: $i,X4: $i] :
( ( subset @ X4 @ X3 )
=> ( ( binintersect @ X3 @ X4 )
= X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mU0PE1mI9q/DTF2THF_13954.p',binintersectSubset4) ).
thf(f2808,plain,
( ( binintersect @ sK55 @ sK56 )
!= sK56 ),
inference(trivial_inequality_removal,[status(thm)],[f2807]) ).
thf(f2807,plain,
( ( ( binintersect @ sK55 @ sK56 )
!= sK56 )
| ( $true != $true ) ),
inference(forward_demodulation,[status(thm)],[f2806,f1215]) ).
thf(f1215,plain,
binintersectSubset3 = $true,
inference(cnf_transformation,[status(thm)],[f635]) ).
thf(f2806,plain,
( ( binintersectSubset3 != $true )
| ( ( binintersect @ sK55 @ sK56 )
!= sK56 ) ),
inference(trivial_inequality_removal,[status(thm)],[f2802]) ).
thf(f2802,plain,
( ( ( binintersect @ sK55 @ sK56 )
!= sK56 )
| ( $true != $true )
| ( binintersectSubset3 != $true ) ),
inference(superposition,[status(thm)],[f1994,f1629]) ).
thf(f1629,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
| ( binintersectSubset3 != $true )
| ( ( binintersect @ X0 @ X1 )
!= X1 ) ),
inference(cnf_transformation,[status(thm)],[f980]) ).
thf(f980,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
!= X1 )
| ( ( subset @ X1 @ X0 )
= $true ) )
| ( binintersectSubset3 != $true ) )
& ( ( binintersectSubset3 = $true )
| ( ( sK258
= ( binintersect @ sK257 @ sK258 ) )
& ( $true
!= ( subset @ sK258 @ sK257 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK257,sK258])],[f978,f979]) ).
thf(f979,plain,
( ? [X2: $i,X3: $i] :
( ( ( binintersect @ X2 @ X3 )
= X3 )
& ( $true
!= ( subset @ X3 @ X2 ) ) )
=> ( ( sK258
= ( binintersect @ sK257 @ sK258 ) )
& ( $true
!= ( subset @ sK258 @ sK257 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f978,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
!= X1 )
| ( ( subset @ X1 @ X0 )
= $true ) )
| ( binintersectSubset3 != $true ) )
& ( ( binintersectSubset3 = $true )
| ? [X2: $i,X3: $i] :
( ( ( binintersect @ X2 @ X3 )
= X3 )
& ( $true
!= ( subset @ X3 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f977]) ).
thf(f977,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
!= X1 )
| ( ( subset @ X1 @ X0 )
= $true ) )
| ( binintersectSubset3 != $true ) )
& ( ( binintersectSubset3 = $true )
| ? [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X1 )
& ( ( subset @ X1 @ X0 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f484]) ).
thf(f484,plain,
( ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
!= X1 )
| ( ( subset @ X1 @ X0 )
= $true ) )
<=> ( binintersectSubset3 = $true ) ),
inference(ennf_transformation,[status(thm)],[f260]) ).
thf(f260,plain,
( ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X1 )
=> ( ( subset @ X1 @ X0 )
= $true ) )
<=> ( binintersectSubset3 = $true ) ),
inference(fool_elimination,[status(thm)],[f259]) ).
thf(f259,plain,
! [X0: $i,X1: $i] :
( ( ( ( binintersect @ X0 @ X1 )
= X1 )
=> ( subset @ X1 @ X0 ) )
= binintersectSubset3 ),
inference(rectify,[status(thm)],[f113]) ).
thf(f113,axiom,
! [X3: $i,X4: $i] :
( ( ( ( binintersect @ X3 @ X4 )
= X4 )
=> ( subset @ X4 @ X3 ) )
= binintersectSubset3 ),
file('/export/starexec/sandbox/tmp/tmp.mU0PE1mI9q/DTF2THF_13954.p',binintersectSubset3) ).
thf(f1994,plain,
( $true
!= ( subset @ sK56 @ sK55 ) ),
inference(trivial_inequality_removal,[status(thm)],[f1993]) ).
thf(f1993,plain,
( ( $true != $true )
| ( $true
!= ( subset @ sK56 @ sK55 ) ) ),
inference(forward_demodulation,[status(thm)],[f1960,f1281]) ).
thf(f1281,plain,
eqimpsubset1 = $true,
inference(cnf_transformation,[status(thm)],[f635]) ).
thf(f1960,plain,
( ( $true
!= ( subset @ sK56 @ sK55 ) )
| ( eqimpsubset1 != $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f1925]) ).
thf(f1925,plain,
( ( eqimpsubset1 != $true )
| ( $true
!= ( subset @ sK56 @ sK55 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1856,f1763]) ).
thf(f1763,plain,
! [X3: $i] :
( ( ( subset @ X3 @ X3 )
= $true )
| ( eqimpsubset1 != $true ) ),
inference(equality_resolution,[status(thm)],[f1443]) ).
thf(f1443,plain,
! [X2: $i,X3: $i] :
( ( $true
= ( subset @ X3 @ X2 ) )
| ( X2 != X3 )
| ( eqimpsubset1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f772]) ).
thf(f772,plain,
( ( ( eqimpsubset1 = $true )
| ( ( ( subset @ sK134 @ sK133 )
!= $true )
& ( sK134 = sK133 ) ) )
& ( ! [X2: $i,X3: $i] :
( ( $true
= ( subset @ X3 @ X2 ) )
| ( X2 != X3 ) )
| ( eqimpsubset1 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK133,sK134])],[f770,f771]) ).
thf(f771,plain,
( ? [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
& ( X0 = X1 ) )
=> ( ( ( subset @ sK134 @ sK133 )
!= $true )
& ( sK134 = sK133 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f770,plain,
( ( ( eqimpsubset1 = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
& ( X0 = X1 ) ) )
& ( ! [X2: $i,X3: $i] :
( ( $true
= ( subset @ X3 @ X2 ) )
| ( X2 != X3 ) )
| ( eqimpsubset1 != $true ) ) ),
inference(rectify,[status(thm)],[f769]) ).
thf(f769,plain,
( ( ( eqimpsubset1 = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
& ( X0 = X1 ) ) )
& ( ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
| ( X0 != X1 ) )
| ( eqimpsubset1 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f423]) ).
thf(f423,plain,
( ( eqimpsubset1 = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
| ( X0 != X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f143]) ).
thf(f143,plain,
( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( ( subset @ X1 @ X0 )
= $true ) )
<=> ( eqimpsubset1 = $true ) ),
inference(fool_elimination,[status(thm)],[f142]) ).
thf(f142,plain,
! [X0: $i,X1: $i] :
( ( ( X0 = X1 )
=> ( subset @ X1 @ X0 ) )
= eqimpsubset1 ),
inference(rectify,[status(thm)],[f80]) ).
thf(f80,axiom,
! [X4: $i,X3: $i] :
( ( ( X3 = X4 )
=> ( subset @ X3 @ X4 ) )
= eqimpsubset1 ),
file('/export/starexec/sandbox/tmp/tmp.mU0PE1mI9q/DTF2THF_13954.p',eqimpsubset1) ).
thf(f1856,plain,
! [X0: $i] :
( ( $true
!= ( subset @ sK56 @ X0 ) )
| ( $true
!= ( subset @ X0 @ sK55 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f1855]) ).
thf(f1855,plain,
! [X0: $i] :
( ( $true
!= ( subset @ sK56 @ X0 ) )
| ( $true
!= ( subset @ X0 @ sK55 ) )
| ( $true != $true ) ),
inference(forward_demodulation,[status(thm)],[f1851,f1243]) ).
thf(f1243,plain,
subsetTrans = $true,
inference(cnf_transformation,[status(thm)],[f635]) ).
thf(f1851,plain,
! [X0: $i] :
( ( $true
!= ( subset @ X0 @ sK55 ) )
| ( subsetTrans != $true )
| ( $true
!= ( subset @ sK56 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f1849]) ).
thf(f1849,plain,
! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( subset @ X0 @ sK55 ) )
| ( $true
!= ( subset @ sK56 @ X0 ) )
| ( subsetTrans != $true ) ),
inference(superposition,[status(thm)],[f1222,f1735]) ).
thf(f1735,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X4 @ X5 )
= $true )
| ( subsetTrans != $true )
| ( ( subset @ X4 @ X3 )
!= $true )
| ( ( subset @ X3 @ X5 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1116]) ).
thf(f1116,plain,
( ( ( subsetTrans = $true )
| ( ( $true
= ( subset @ sK330 @ sK329 ) )
& ( $true
!= ( subset @ sK330 @ sK331 ) )
& ( $true
= ( subset @ sK329 @ sK331 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X4 @ X3 )
!= $true )
| ( ( subset @ X4 @ X5 )
= $true )
| ( ( subset @ X3 @ X5 )
!= $true ) )
| ( subsetTrans != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK329,sK330,sK331])],[f1114,f1115]) ).
thf(f1115,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
& ( $true
!= ( subset @ X1 @ X2 ) )
& ( $true
= ( subset @ X0 @ X2 ) ) )
=> ( ( $true
= ( subset @ sK330 @ sK329 ) )
& ( $true
!= ( subset @ sK330 @ sK331 ) )
& ( $true
= ( subset @ sK329 @ sK331 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1114,plain,
( ( ( subsetTrans = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
& ( $true
!= ( subset @ X1 @ X2 ) )
& ( $true
= ( subset @ X0 @ X2 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X4 @ X3 )
!= $true )
| ( ( subset @ X4 @ X5 )
= $true )
| ( ( subset @ X3 @ X5 )
!= $true ) )
| ( subsetTrans != $true ) ) ),
inference(rectify,[status(thm)],[f1113]) ).
thf(f1113,plain,
( ( ( subsetTrans = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
& ( $true
!= ( subset @ X1 @ X2 ) )
& ( $true
= ( subset @ X0 @ X2 ) ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( $true
= ( subset @ X1 @ X2 ) )
| ( $true
!= ( subset @ X0 @ X2 ) ) )
| ( subsetTrans != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f522]) ).
thf(f522,plain,
( ( subsetTrans = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( $true
= ( subset @ X1 @ X2 ) )
| ( $true
!= ( subset @ X0 @ X2 ) ) ) ),
inference(flattening,[status(thm)],[f521]) ).
thf(f521,plain,
( ( subsetTrans = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( subset @ X1 @ X2 ) )
| ( $true
!= ( subset @ X0 @ X2 ) )
| ( ( subset @ X1 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f256]) ).
thf(f256,plain,
( ( subsetTrans = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
=> ( ( $true
= ( subset @ X0 @ X2 ) )
=> ( $true
= ( subset @ X1 @ X2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f255]) ).
thf(f255,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X0 )
=> ( ( subset @ X0 @ X2 )
=> ( subset @ X1 @ X2 ) ) )
= subsetTrans ),
inference(rectify,[status(thm)],[f89]) ).
thf(f89,axiom,
! [X4: $i,X3: $i,X5: $i] :
( ( ( subset @ X3 @ X4 )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ X3 @ X5 ) ) )
= subsetTrans ),
file('/export/starexec/sandbox/tmp/tmp.mU0PE1mI9q/DTF2THF_13954.p',subsetTrans) ).
thf(f1222,plain,
( $true
!= ( subset @ sK56 @ sK55 ) ),
inference(cnf_transformation,[status(thm)],[f635]) ).
thf(f17386,plain,
~ spl346_5,
inference(avatar_contradiction_clause,[status(thm)],[f17385]) ).
thf(f17385,plain,
( $false
| ~ spl346_5 ),
inference(trivial_inequality_removal,[status(thm)],[f17384]) ).
thf(f17384,plain,
( ( $true != $true )
| ~ spl346_5 ),
inference(superposition,[status(thm)],[f17245,f1250]) ).
thf(f1250,plain,
notequalI1 = $true,
inference(cnf_transformation,[status(thm)],[f635]) ).
thf(f17245,plain,
( ( notequalI1 != $true )
| ~ spl346_5 ),
inference(trivial_inequality_removal,[status(thm)],[f17229]) ).
thf(f17229,plain,
( ( $true != $true )
| ( notequalI1 != $true )
| ~ spl346_5 ),
inference(superposition,[status(thm)],[f1970,f1771]) ).
thf(f1771,plain,
! [X1: $i] :
( ( $true
= ( subset @ X1 @ X1 ) )
| ( notequalI1 != $true ) ),
inference(equality_resolution,[status(thm)],[f1543]) ).
thf(f1543,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X0 @ X1 ) )
| ( X0 != X1 )
| ( notequalI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f898]) ).
thf(f898,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X0 @ X1 ) )
| ( X0 != X1 ) )
| ( notequalI1 != $true ) )
& ( ( notequalI1 = $true )
| ( ( ( subset @ sK205 @ sK206 )
!= $true )
& ( sK205 = sK206 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK205,sK206])],[f896,f897]) ).
thf(f897,plain,
( ? [X2: $i,X3: $i] :
( ( $true
!= ( subset @ X2 @ X3 ) )
& ( X2 = X3 ) )
=> ( ( ( subset @ sK205 @ sK206 )
!= $true )
& ( sK205 = sK206 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f896,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X0 @ X1 ) )
| ( X0 != X1 ) )
| ( notequalI1 != $true ) )
& ( ( notequalI1 = $true )
| ? [X2: $i,X3: $i] :
( ( $true
!= ( subset @ X2 @ X3 ) )
& ( X2 = X3 ) ) ) ),
inference(rectify,[status(thm)],[f895]) ).
thf(f895,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X0 @ X1 ) )
| ( X0 != X1 ) )
| ( notequalI1 != $true ) )
& ( ( notequalI1 = $true )
| ? [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X0 @ X1 ) )
& ( X0 = X1 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f416]) ).
thf(f416,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X0 @ X1 ) )
| ( X0 != X1 ) )
<=> ( notequalI1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f399]) ).
thf(f399,plain,
( ( notequalI1 = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X0 @ X1 ) )
=> ( X0 != X1 ) ) ),
inference(flattening,[status(thm)],[f242]) ).
thf(f242,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X0 @ X1 ) )
=> ( X0 != X1 ) )
<=> ( notequalI1 = $true ) ),
inference(fool_elimination,[status(thm)],[f241]) ).
thf(f241,plain,
! [X0: $i,X1: $i] :
( ( ~ ( subset @ X0 @ X1 )
=> ( X0 != X1 ) )
= notequalI1 ),
inference(rectify,[status(thm)],[f86]) ).
thf(f86,axiom,
! [X3: $i,X4: $i] :
( ( ~ ( subset @ X3 @ X4 )
=> ( X3 != X4 ) )
= notequalI1 ),
file('/export/starexec/sandbox/tmp/tmp.mU0PE1mI9q/DTF2THF_13954.p',notequalI1) ).
thf(f1970,plain,
( ! [X0: $i] :
( $true
!= ( subset @ sK56 @ X0 ) )
| ~ spl346_5 ),
inference(avatar_component_clause,[status(thm)],[f1969]) ).
thf(f1969,definition,
( spl346_5
<=> ! [X0: $i] :
( $true
!= ( subset @ sK56 @ X0 ) ) ),
introduced(definition,[new_symbols(naming,[spl346_5])],[avatar_definition]) ).
thf(f16383,plain,
( spl346_5
| ~ spl346_45 ),
inference(avatar_split_clause,[status(thm)],[f15852,f2980,f1969]) ).
thf(f2980,definition,
( spl346_45
<=> ! [X0: $o] : ( $true = X0 ) ),
introduced(definition,[new_symbols(naming,[spl346_45])],[avatar_definition]) ).
thf(f15852,plain,
( ! [X1: $i] :
( $true
!= ( subset @ sK56 @ X1 ) )
| ~ spl346_45 ),
inference(trivial_inequality_removal,[status(thm)],[f15721]) ).
thf(f15721,plain,
( ! [X1: $i] :
( ( $true != $true )
| ( $true
!= ( subset @ sK56 @ X1 ) ) )
| ~ spl346_45 ),
inference(superposition,[status(thm)],[f2029,f2981]) ).
thf(f2981,plain,
( ! [X0: $o] : ( $true = X0 )
| ~ spl346_45 ),
inference(avatar_component_clause,[status(thm)],[f2980]) ).
thf(f2029,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( subset @ ( setadjoin @ X0 @ X1 ) @ sK55 ) )
| ( $true
!= ( subset @ sK56 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f2028]) ).
thf(f2028,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( subset @ ( setadjoin @ X0 @ X1 ) @ sK55 ) )
| ( $true
!= ( subset @ sK56 @ X1 ) )
| ( $true != $true ) ),
inference(forward_demodulation,[status(thm)],[f1952,f1308]) ).
thf(f1308,plain,
setadjoinSub2 = $true,
inference(cnf_transformation,[status(thm)],[f635]) ).
thf(f1952,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( subset @ sK56 @ X1 ) )
| ( $true
!= ( subset @ ( setadjoin @ X0 @ X1 ) @ sK55 ) )
| ( setadjoinSub2 != $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f1922]) ).
thf(f1922,plain,
! [X0: $i,X1: $i] :
( ( setadjoinSub2 != $true )
| ( $true
!= ( subset @ sK56 @ X1 ) )
| ( $true != $true )
| ( $true
!= ( subset @ ( setadjoin @ X0 @ X1 ) @ sK55 ) ) ),
inference(superposition,[status(thm)],[f1856,f1175]) ).
thf(f1175,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( subset @ X5 @ ( setadjoin @ X3 @ X4 ) ) )
| ( ( subset @ X5 @ X4 )
!= $true )
| ( setadjoinSub2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f605]) ).
thf(f605,plain,
( ( ( setadjoinSub2 = $true )
| ( ( ( subset @ sK37 @ ( setadjoin @ sK35 @ sK36 ) )
!= $true )
& ( $true
= ( subset @ sK37 @ sK36 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( subset @ X5 @ ( setadjoin @ X3 @ X4 ) ) )
| ( ( subset @ X5 @ X4 )
!= $true ) )
| ( setadjoinSub2 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK35,sK36,sK37])],[f603,f604]) ).
thf(f604,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( subset @ X2 @ ( setadjoin @ X0 @ X1 ) ) )
& ( ( subset @ X2 @ X1 )
= $true ) )
=> ( ( ( subset @ sK37 @ ( setadjoin @ sK35 @ sK36 ) )
!= $true )
& ( $true
= ( subset @ sK37 @ sK36 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f603,plain,
( ( ( setadjoinSub2 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( subset @ X2 @ ( setadjoin @ X0 @ X1 ) ) )
& ( ( subset @ X2 @ X1 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( subset @ X5 @ ( setadjoin @ X3 @ X4 ) ) )
| ( ( subset @ X5 @ X4 )
!= $true ) )
| ( setadjoinSub2 != $true ) ) ),
inference(rectify,[status(thm)],[f602]) ).
thf(f602,plain,
( ( ( setadjoinSub2 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( subset @ X2 @ ( setadjoin @ X0 @ X1 ) ) )
& ( ( subset @ X2 @ X1 )
= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( subset @ X2 @ ( setadjoin @ X0 @ X1 ) ) )
| ( ( subset @ X2 @ X1 )
!= $true ) )
| ( setadjoinSub2 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f516]) ).
thf(f516,plain,
( ( setadjoinSub2 = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( subset @ X2 @ ( setadjoin @ X0 @ X1 ) ) )
| ( ( subset @ X2 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f240]) ).
thf(f240,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X2 @ X1 )
= $true )
=> ( $true
= ( subset @ X2 @ ( setadjoin @ X0 @ X1 ) ) ) )
<=> ( setadjoinSub2 = $true ) ),
inference(fool_elimination,[status(thm)],[f239]) ).
thf(f239,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X2 @ X1 )
=> ( subset @ X2 @ ( setadjoin @ X0 @ X1 ) ) )
= setadjoinSub2 ),
inference(rectify,[status(thm)],[f91]) ).
thf(f91,axiom,
! [X1: $i,X4: $i,X3: $i] :
( ( ( subset @ X3 @ X4 )
=> ( subset @ X3 @ ( setadjoin @ X1 @ X4 ) ) )
= setadjoinSub2 ),
file('/export/starexec/sandbox/tmp/tmp.mU0PE1mI9q/DTF2THF_13954.p',setadjoinSub2) ).
thf(f6193,plain,
( spl346_71
| spl346_45
| ~ spl346_36 ),
inference(avatar_split_clause,[status(thm)],[f6192,f2341,f2980,f5891]) ).
thf(f6192,plain,
( ! [X0: $i,X1: $o] :
( ( $true
= ( subset @ X0 @ sK55 ) )
| ( $true
!= ( in @ ( sK280 @ X0 @ sK55 ) @ sK56 ) )
| ( $true = X1 ) )
| ~ spl346_36 ),
inference(trivial_inequality_removal,[status(thm)],[f6191]) ).
thf(f6191,plain,
( ! [X0: $i,X1: $o] :
( ( $true
= ( subset @ X0 @ sK55 ) )
| ( $true
!= ( in @ ( sK280 @ X0 @ sK55 ) @ sK56 ) )
| ( $true != $true )
| ( $true = X1 ) )
| ~ spl346_36 ),
inference(forward_demodulation,[status(thm)],[f6166,f4166]) ).
thf(f4166,plain,
( ( emptysetE = $true )
| ~ spl346_36 ),
inference(trivial_inequality_removal,[status(thm)],[f4153]) ).
thf(f4153,plain,
( ( emptysetE = $true )
| ( $true != $true )
| ~ spl346_36 ),
inference(superposition,[status(thm)],[f2342,f1404]) ).
thf(f1404,plain,
( ( $true
= ( in @ sK106 @ emptyset ) )
| ( emptysetE = $true ) ),
inference(cnf_transformation,[status(thm)],[f724]) ).
thf(f724,plain,
( ( ( emptysetE = $true )
| ( ( $true
= ( in @ sK106 @ emptyset ) )
& ( $true != sK107 ) ) )
& ( ! [X2: $i] :
( ( ( in @ X2 @ emptyset )
!= $true )
| ! [X3: $o] : ( $true = X3 ) )
| ( emptysetE != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK106,sK107])],[f721,f723,f722]) ).
thf(f722,plain,
( ? [X0: $i] :
( ( ( in @ X0 @ emptyset )
= $true )
& ? [X1: $o] : ( $true != X1 ) )
=> ( ( $true
= ( in @ sK106 @ emptyset ) )
& ? [X1: $o] : ( $true != X1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f723,plain,
( ? [X1: $o] : ( $true != X1 )
=> ( $true != sK107 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f721,plain,
( ( ( emptysetE = $true )
| ? [X0: $i] :
( ( ( in @ X0 @ emptyset )
= $true )
& ? [X1: $o] : ( $true != X1 ) ) )
& ( ! [X2: $i] :
( ( ( in @ X2 @ emptyset )
!= $true )
| ! [X3: $o] : ( $true = X3 ) )
| ( emptysetE != $true ) ) ),
inference(rectify,[status(thm)],[f720]) ).
thf(f720,plain,
( ( ( emptysetE = $true )
| ? [X0: $i] :
( ( ( in @ X0 @ emptyset )
= $true )
& ? [X1: $o] : ( $true != X1 ) ) )
& ( ! [X0: $i] :
( ( ( in @ X0 @ emptyset )
!= $true )
| ! [X1: $o] : ( $true = X1 ) )
| ( emptysetE != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f424]) ).
thf(f424,plain,
( ( emptysetE = $true )
<=> ! [X0: $i] :
( ( ( in @ X0 @ emptyset )
!= $true )
| ! [X1: $o] : ( $true = X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f274]) ).
thf(f274,plain,
( ( emptysetE = $true )
<=> ! [X0: $i] :
( ( ( in @ X0 @ emptyset )
= $true )
=> ! [X1: $o] : ( $true = X1 ) ) ),
inference(fool_elimination,[status(thm)],[f273]) ).
thf(f273,plain,
( emptysetE
= ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
=> ! [X1: $o] : X1 ) ) ),
inference(rectify,[status(thm)],[f19]) ).
thf(f19,axiom,
( emptysetE
= ( ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> ! [X0: $o] : X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mU0PE1mI9q/DTF2THF_13954.p',emptysetE) ).
thf(f2342,plain,
( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
| ~ spl346_36 ),
inference(avatar_component_clause,[status(thm)],[f2341]) ).
thf(f6166,plain,
! [X0: $i,X1: $o] :
( ( $true
!= ( in @ ( sK280 @ X0 @ sK55 ) @ sK56 ) )
| ( $true
= ( subset @ X0 @ sK55 ) )
| ( $true = X1 )
| ( emptysetE != $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f6159]) ).
thf(f6159,plain,
! [X0: $i,X1: $o] :
( ( $true
= ( subset @ X0 @ sK55 ) )
| ( $true
!= ( in @ ( sK280 @ X0 @ sK55 ) @ sK56 ) )
| ( $true = X1 )
| ( $true != $true )
| ( emptysetE != $true ) ),
inference(superposition,[status(thm)],[f1402,f2733]) ).
thf(f2733,plain,
! [X0: $i] :
( ( ( in @ ( sK280 @ X0 @ sK55 ) @ emptyset )
= $true )
| ( $true
= ( subset @ X0 @ sK55 ) )
| ( $true
!= ( in @ ( sK280 @ X0 @ sK55 ) @ sK56 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f2732]) ).
thf(f2732,plain,
! [X0: $i] :
( ( $true
!= ( in @ ( sK280 @ X0 @ sK55 ) @ sK56 ) )
| ( ( in @ ( sK280 @ X0 @ sK55 ) @ emptyset )
= $true )
| ( $true
= ( subset @ X0 @ sK55 ) )
| ( $true != $true ) ),
inference(forward_demodulation,[status(thm)],[f2722,f1273]) ).
thf(f2722,plain,
! [X0: $i] :
( ( subsetI2 != $true )
| ( ( in @ ( sK280 @ X0 @ sK55 ) @ emptyset )
= $true )
| ( $true
= ( subset @ X0 @ sK55 ) )
| ( $true
!= ( in @ ( sK280 @ X0 @ sK55 ) @ sK56 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f2710]) ).
thf(f2710,plain,
! [X0: $i] :
( ( $true
= ( subset @ X0 @ sK55 ) )
| ( subsetI2 != $true )
| ( $true
!= ( in @ ( sK280 @ X0 @ sK55 ) @ sK56 ) )
| ( ( in @ ( sK280 @ X0 @ sK55 ) @ emptyset )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1661,f1882]) ).
thf(f1882,plain,
! [X0: $i] :
( ( ( in @ X0 @ sK55 )
= $true )
| ( $true
!= ( in @ X0 @ sK56 ) )
| ( ( in @ X0 @ emptyset )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f1881]) ).
thf(f1881,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( in @ X0 @ emptyset )
= $true )
| ( ( in @ X0 @ sK55 )
= $true )
| ( $true
!= ( in @ X0 @ sK56 ) ) ),
inference(forward_demodulation,[status(thm)],[f1865,f1258]) ).
thf(f1258,plain,
setminusI = $true,
inference(cnf_transformation,[status(thm)],[f635]) ).
thf(f1865,plain,
! [X0: $i] :
( ( setminusI != $true )
| ( $true
!= ( in @ X0 @ sK56 ) )
| ( ( in @ X0 @ sK55 )
= $true )
| ( ( in @ X0 @ emptyset )
= $true ) ),
inference(superposition,[status(thm)],[f1647,f1223]) ).
thf(f1647,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setminus @ X3 @ X5 ) )
= $true )
| ( $true
= ( in @ X4 @ X5 ) )
| ( ( in @ X4 @ X3 )
!= $true )
| ( setminusI != $true ) ),
inference(cnf_transformation,[status(thm)],[f1005]) ).
thf(f1005,plain,
( ( ( setminusI = $true )
| ( ( $true
= ( in @ sK272 @ sK271 ) )
& ( $true
!= ( in @ sK272 @ sK273 ) )
& ( $true
!= ( in @ sK272 @ ( setminus @ sK271 @ sK273 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X3 )
!= $true )
| ( $true
= ( in @ X4 @ X5 ) )
| ( ( in @ X4 @ ( setminus @ X3 @ X5 ) )
= $true ) )
| ( setminusI != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK271,sK272,sK273])],[f1003,f1004]) ).
thf(f1004,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
& ( $true
!= ( in @ X1 @ X2 ) )
& ( $true
!= ( in @ X1 @ ( setminus @ X0 @ X2 ) ) ) )
=> ( ( $true
= ( in @ sK272 @ sK271 ) )
& ( $true
!= ( in @ sK272 @ sK273 ) )
& ( $true
!= ( in @ sK272 @ ( setminus @ sK271 @ sK273 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1003,plain,
( ( ( setminusI = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
& ( $true
!= ( in @ X1 @ X2 ) )
& ( $true
!= ( in @ X1 @ ( setminus @ X0 @ X2 ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X3 )
!= $true )
| ( $true
= ( in @ X4 @ X5 ) )
| ( ( in @ X4 @ ( setminus @ X3 @ X5 ) )
= $true ) )
| ( setminusI != $true ) ) ),
inference(rectify,[status(thm)],[f1002]) ).
thf(f1002,plain,
( ( ( setminusI = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
& ( $true
!= ( in @ X1 @ X2 ) )
& ( $true
!= ( in @ X1 @ ( setminus @ X0 @ X2 ) ) ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ X0 ) )
| ( $true
= ( in @ X1 @ X2 ) )
| ( $true
= ( in @ X1 @ ( setminus @ X0 @ X2 ) ) ) )
| ( setminusI != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f419]) ).
thf(f419,plain,
( ( setminusI = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ X0 ) )
| ( $true
= ( in @ X1 @ X2 ) )
| ( $true
= ( in @ X1 @ ( setminus @ X0 @ X2 ) ) ) ) ),
inference(flattening,[status(thm)],[f418]) ).
thf(f418,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( setminus @ X0 @ X2 ) ) )
| ( $true
= ( in @ X1 @ X2 ) )
| ( $true
!= ( in @ X1 @ X0 ) ) )
<=> ( setminusI = $true ) ),
inference(ennf_transformation,[status(thm)],[f397]) ).
thf(f397,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
=> ( ( $true
!= ( in @ X1 @ X2 ) )
=> ( $true
= ( in @ X1 @ ( setminus @ X0 @ X2 ) ) ) ) )
<=> ( setminusI = $true ) ),
inference(flattening,[status(thm)],[f232]) ).
thf(f232,plain,
( ( setminusI = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
=> ( ( $true
!= ( in @ X1 @ X2 ) )
=> ( $true
= ( in @ X1 @ ( setminus @ X0 @ X2 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f231]) ).
thf(f231,plain,
( setminusI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X0 )
=> ( ~ ( in @ X1 @ X2 )
=> ( in @ X1 @ ( setminus @ X0 @ X2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f120]) ).
thf(f120,axiom,
( setminusI
= ( ! [X3: $i,X1: $i,X4: $i] :
( ( in @ X1 @ X3 )
=> ( ~ ( in @ X1 @ X4 )
=> ( in @ X1 @ ( setminus @ X3 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.mU0PE1mI9q/DTF2THF_13954.p',setminusI) ).
thf(f1661,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK280 @ X1 @ X0 ) @ X0 )
!= $true )
| ( ( subset @ X1 @ X0 )
= $true )
| ( subsetI2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f1020]) ).
thf(f1402,plain,
! [X2: $i,X3: $o] :
( ( ( in @ X2 @ emptyset )
!= $true )
| ( emptysetE != $true )
| ( $true = X3 ) ),
inference(cnf_transformation,[status(thm)],[f724]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU610^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n031.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 12:29:48 EST 2026
% 0.17/0.35 % CPUTime :
% 0.17/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.27/0.48 ---- Original DTF file ---
% 0.27/0.48 thf(spec,logic,$$dhol).
% 0.27/0.48 %------------------------------------------------------------------------------
% 0.27/0.48 % File : SEU610^1 : TPTP v9.2.1. Released v3.7.0.
% 0.27/0.48 % Domain : Set Theory
% 0.27/0.48 % Problem : Preliminary Notions - Operations on Sets - Set Difference
% 0.27/0.48 % Version : Especial.
% 0.27/0.48 % English : (! A:i.! B:i.setminus A B = emptyset -> subset A B)
% 0.27/0.48
% 0.27/0.48 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.27/0.48 % Source : [Bro08]
% 0.27/0.48 % Names : ZFC112g [Bro08]
% 0.27/0.48
% 0.27/0.48 % Status : Theorem
% 0.27/0.48 % Rating : 0.44 v9.1.0, 0.38 v9.0.0, 0.40 v8.2.0, 0.38 v8.1.0, 0.27 v7.5.0, 0.29 v7.4.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.43 v6.1.0, 0.71 v6.0.0, 0.57 v5.5.0, 0.83 v5.4.0, 0.80 v4.1.0, 1.00 v3.7.0
% 0.27/0.48 % Syntax : Number of formulae : 274 ( 128 unt; 145 typ; 128 def)
% 0.27/0.48 % Number of atoms : 681 ( 185 equ; 0 cnn)
% 0.27/0.48 % Maximal formula atoms : 128 ( 5 avg)
% 0.27/0.48 % Number of connectives : 1079 ( 39 ~; 6 |; 28 &; 691 @)
% 0.27/0.48 % ( 14 <=>; 301 =>; 0 <=; 0 <~>)
% 0.27/0.48 % Maximal formula depth : 132 ( 2 avg)
% 0.27/0.48 % Number of types : 2 ( 0 usr)
% 0.27/0.48 % Number of type conns : 62 ( 62 >; 0 *; 0 +; 0 <<)
% 0.27/0.48 % Number of symbols : 148 ( 145 usr; 130 con; 0-2 aty)
% 0.27/0.48 % Number of variables : 370 ( 30 ^; 311 !; 29 ?; 370 :)
% 0.27/0.48 % SPC : TH0_THM_EQU_NAR
% 0.27/0.48
% 0.27/0.48 % Comments : http://mathgate.info/detsetitem.php?id=465
% 0.27/0.48 %------------------------------------------------------------------------------
% 0.27/0.48 thf(in_type,type,
% 0.27/0.48 in: $i > $i > $o ).
% 0.27/0.48
% 0.27/0.48 thf(exu_type,type,
% 0.27/0.48 exu: ( $i > $o ) > $o ).
% 0.27/0.48
% 0.27/0.48 thf(exu,definition,
% 0.27/0.48 ( exu
% 0.27/0.48 = ( ^ [Xphi: $i > $o] :
% 0.27/0.48 ? [Xx: $i] :
% 0.27/0.48 ( ( Xphi @ Xx )
% 0.27/0.48 & ! [Xy: $i] :
% 0.27/0.48 ( ( Xphi @ Xy )
% 0.27/0.48 => ( Xx = Xy ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(setextAx_type,type,
% 0.27/0.48 setextAx: $o ).
% 0.27/0.48
% 0.27/0.48 thf(setextAx,definition,
% 0.27/0.48 ( setextAx
% 0.27/0.48 = ( ! [A: $i,B: $i] :
% 0.27/0.48 ( ! [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ A )
% 0.27/0.48 <=> ( in @ Xx @ B ) )
% 0.27/0.48 => ( A = B ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(emptyset_type,type,
% 0.27/0.48 emptyset: $i ).
% 0.27/0.48
% 0.27/0.48 thf(emptysetAx_type,type,
% 0.27/0.48 emptysetAx: $o ).
% 0.27/0.48
% 0.27/0.48 thf(emptysetAx,definition,
% 0.27/0.48 ( emptysetAx
% 0.27/0.48 = ( ! [Xx: $i] :
% 0.27/0.48 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(setadjoin_type,type,
% 0.27/0.48 setadjoin: $i > $i > $i ).
% 0.27/0.48
% 0.27/0.48 thf(setadjoinAx_type,type,
% 0.27/0.48 setadjoinAx: $o ).
% 0.27/0.48
% 0.27/0.48 thf(setadjoinAx,definition,
% 0.27/0.48 ( setadjoinAx
% 0.27/0.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.27/0.48 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.27/0.48 <=> ( ( Xy = Xx )
% 0.27/0.48 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(powerset_type,type,
% 0.27/0.48 powerset: $i > $i ).
% 0.27/0.48
% 0.27/0.48 thf(powersetAx_type,type,
% 0.27/0.48 powersetAx: $o ).
% 0.27/0.48
% 0.27/0.48 thf(powersetAx,definition,
% 0.27/0.48 ( powersetAx
% 0.27/0.48 = ( ! [A: $i,B: $i] :
% 0.27/0.48 ( ( in @ B @ ( powerset @ A ) )
% 0.27/0.48 <=> ! [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ B )
% 0.27/0.48 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(setunion_type,type,
% 0.27/0.48 setunion: $i > $i ).
% 0.27/0.48
% 0.27/0.48 thf(setunionAx_type,type,
% 0.27/0.48 setunionAx: $o ).
% 0.27/0.48
% 0.27/0.48 thf(setunionAx,definition,
% 0.27/0.48 ( setunionAx
% 0.27/0.48 = ( ! [A: $i,Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ ( setunion @ A ) )
% 0.27/0.48 <=> ? [B: $i] :
% 0.27/0.48 ( ( in @ Xx @ B )
% 0.27/0.48 & ( in @ B @ A ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(omega_type,type,
% 0.27/0.48 omega: $i ).
% 0.27/0.48
% 0.27/0.48 thf(omega0Ax_type,type,
% 0.27/0.48 omega0Ax: $o ).
% 0.27/0.48
% 0.27/0.48 thf(omega0Ax,definition,
% 0.27/0.48 ( omega0Ax
% 0.27/0.48 = ( in @ emptyset @ omega ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(omegaSAx_type,type,
% 0.27/0.48 omegaSAx: $o ).
% 0.27/0.48
% 0.27/0.48 thf(omegaSAx,definition,
% 0.27/0.48 ( omegaSAx
% 0.27/0.48 = ( ! [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ omega )
% 0.27/0.48 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(omegaIndAx_type,type,
% 0.27/0.48 omegaIndAx: $o ).
% 0.27/0.48
% 0.27/0.48 thf(omegaIndAx,definition,
% 0.27/0.48 ( omegaIndAx
% 0.27/0.48 = ( ! [A: $i] :
% 0.27/0.48 ( ( ( in @ emptyset @ A )
% 0.27/0.48 & ! [Xx: $i] :
% 0.27/0.48 ( ( ( in @ Xx @ omega )
% 0.27/0.48 & ( in @ Xx @ A ) )
% 0.27/0.48 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.27/0.48 => ! [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ omega )
% 0.27/0.48 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(replAx_type,type,
% 0.27/0.48 replAx: $o ).
% 0.27/0.48
% 0.27/0.48 thf(replAx,definition,
% 0.27/0.48 ( replAx
% 0.27/0.48 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.27/0.48 ( ! [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ A )
% 0.27/0.48 => ( exu
% 0.27/0.48 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.27/0.48 => ? [B: $i] :
% 0.27/0.48 ! [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ B )
% 0.27/0.48 <=> ? [Xy: $i] :
% 0.27/0.48 ( ( in @ Xy @ A )
% 0.27/0.48 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(foundationAx_type,type,
% 0.27/0.48 foundationAx: $o ).
% 0.27/0.48
% 0.27/0.48 thf(foundationAx,definition,
% 0.27/0.48 ( foundationAx
% 0.27/0.48 = ( ! [A: $i] :
% 0.27/0.48 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.27/0.48 => ? [B: $i] :
% 0.27/0.48 ( ( in @ B @ A )
% 0.27/0.48 & ~ ? [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ B )
% 0.27/0.48 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(wellorderingAx_type,type,
% 0.27/0.48 wellorderingAx: $o ).
% 0.27/0.48
% 0.27/0.48 thf(wellorderingAx,definition,
% 0.27/0.48 ( wellorderingAx
% 0.27/0.48 = ( ! [A: $i] :
% 0.27/0.48 ? [B: $i] :
% 0.27/0.48 ( ! [C: $i] :
% 0.27/0.48 ( ( in @ C @ B )
% 0.27/0.48 => ! [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ C )
% 0.27/0.48 => ( in @ Xx @ A ) ) )
% 0.27/0.48 & ! [Xx: $i,Xy: $i] :
% 0.27/0.48 ( ( ( in @ Xx @ A )
% 0.27/0.48 & ( in @ Xy @ A ) )
% 0.27/0.48 => ( ! [C: $i] :
% 0.27/0.48 ( ( in @ C @ B )
% 0.27/0.48 => ( ( in @ Xx @ C )
% 0.27/0.48 <=> ( in @ Xy @ C ) ) )
% 0.27/0.48 => ( Xx = Xy ) ) )
% 0.27/0.48 & ! [C: $i,D: $i] :
% 0.27/0.48 ( ( ( in @ C @ B )
% 0.27/0.48 & ( in @ D @ B ) )
% 0.27/0.48 => ( ! [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ C )
% 0.27/0.48 => ( in @ Xx @ D ) )
% 0.27/0.48 | ! [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ D )
% 0.27/0.48 => ( in @ Xx @ C ) ) ) )
% 0.27/0.48 & ! [C: $i] :
% 0.27/0.48 ( ( ! [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ C )
% 0.27/0.48 => ( in @ Xx @ A ) )
% 0.27/0.48 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.27/0.48 => ? [D: $i,Xx: $i] :
% 0.27/0.48 ( ( in @ D @ B )
% 0.27/0.48 & ( in @ Xx @ C )
% 0.27/0.48 & ~ ? [Xy: $i] :
% 0.27/0.48 ( ( in @ Xy @ D )
% 0.27/0.48 & ( in @ Xy @ C ) )
% 0.27/0.48 & ! [E: $i] :
% 0.27/0.48 ( ( in @ E @ B )
% 0.27/0.48 => ( ! [Xy: $i] :
% 0.27/0.48 ( ( in @ Xy @ E )
% 0.27/0.48 => ( in @ Xy @ D ) )
% 0.27/0.48 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(descr_type,type,
% 0.27/0.48 descr: ( $i > $o ) > $i ).
% 0.27/0.48
% 0.27/0.48 thf(descrp_type,type,
% 0.27/0.48 descrp: $o ).
% 0.27/0.48
% 0.27/0.48 thf(descrp,definition,
% 0.27/0.48 ( descrp
% 0.27/0.48 = ( ! [Xphi: $i > $o] :
% 0.27/0.48 ( ( exu
% 0.27/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.48 => ( Xphi
% 0.27/0.48 @ ( descr
% 0.27/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(dsetconstr_type,type,
% 0.27/0.48 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.27/0.48
% 0.27/0.48 thf(dsetconstrI_type,type,
% 0.27/0.48 dsetconstrI: $o ).
% 0.27/0.48
% 0.27/0.48 thf(dsetconstrI,definition,
% 0.27/0.48 ( dsetconstrI
% 0.27/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ A )
% 0.27/0.48 => ( ( Xphi @ Xx )
% 0.27/0.48 => ( in @ Xx
% 0.27/0.48 @ ( dsetconstr @ A
% 0.27/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(dsetconstrEL_type,type,
% 0.27/0.48 dsetconstrEL: $o ).
% 0.27/0.48
% 0.27/0.48 thf(dsetconstrEL,definition,
% 0.27/0.48 ( dsetconstrEL
% 0.27/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.48 ( ( in @ Xx
% 0.27/0.48 @ ( dsetconstr @ A
% 0.27/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.27/0.48 => ( in @ Xx @ A ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(dsetconstrER_type,type,
% 0.27/0.48 dsetconstrER: $o ).
% 0.27/0.48
% 0.27/0.48 thf(dsetconstrER,definition,
% 0.27/0.48 ( dsetconstrER
% 0.27/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.48 ( ( in @ Xx
% 0.27/0.48 @ ( dsetconstr @ A
% 0.27/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.27/0.48 => ( Xphi @ Xx ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(exuE1_type,type,
% 0.27/0.48 exuE1: $o ).
% 0.27/0.48
% 0.27/0.48 thf(exuE1,definition,
% 0.27/0.48 ( exuE1
% 0.27/0.48 = ( ! [Xphi: $i > $o] :
% 0.27/0.48 ( ( exu
% 0.27/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.48 => ? [Xx: $i] :
% 0.27/0.48 ( ( Xphi @ Xx )
% 0.27/0.48 & ! [Xy: $i] :
% 0.27/0.48 ( ( Xphi @ Xy )
% 0.27/0.48 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(prop2set_type,type,
% 0.27/0.48 prop2set: $o > $i ).
% 0.27/0.48
% 0.27/0.48 thf(prop2setE_type,type,
% 0.27/0.48 prop2setE: $o ).
% 0.27/0.48
% 0.27/0.48 thf(prop2setE,definition,
% 0.27/0.48 ( prop2setE
% 0.27/0.48 = ( ! [Xphi: $o,Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.27/0.48 => Xphi ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(emptysetE_type,type,
% 0.27/0.48 emptysetE: $o ).
% 0.27/0.48
% 0.27/0.48 thf(emptysetE,definition,
% 0.27/0.48 ( emptysetE
% 0.27/0.48 = ( ! [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ emptyset )
% 0.27/0.48 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(emptysetimpfalse_type,type,
% 0.27/0.48 emptysetimpfalse: $o ).
% 0.27/0.48
% 0.27/0.48 thf(emptysetimpfalse,definition,
% 0.27/0.48 ( emptysetimpfalse
% 0.27/0.48 = ( ! [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ emptyset )
% 0.27/0.48 => $false ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(notinemptyset_type,type,
% 0.27/0.48 notinemptyset: $o ).
% 0.27/0.48
% 0.27/0.48 thf(notinemptyset,definition,
% 0.27/0.48 ( notinemptyset
% 0.27/0.48 = ( ! [Xx: $i] :
% 0.27/0.48 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(exuE3e_type,type,
% 0.27/0.48 exuE3e: $o ).
% 0.27/0.48
% 0.27/0.48 thf(exuE3e,definition,
% 0.27/0.48 ( exuE3e
% 0.27/0.48 = ( ! [Xphi: $i > $o] :
% 0.27/0.48 ( ( exu
% 0.27/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.48 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(setext_type,type,
% 0.27/0.48 setext: $o ).
% 0.27/0.48
% 0.27/0.48 thf(setext,definition,
% 0.27/0.48 ( setext
% 0.27/0.48 = ( ! [A: $i,B: $i] :
% 0.27/0.48 ( ! [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ A )
% 0.27/0.48 => ( in @ Xx @ B ) )
% 0.27/0.48 => ( ! [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ B )
% 0.27/0.48 => ( in @ Xx @ A ) )
% 0.27/0.48 => ( A = B ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(emptyI_type,type,
% 0.27/0.48 emptyI: $o ).
% 0.27/0.48
% 0.27/0.48 thf(emptyI,definition,
% 0.27/0.48 ( emptyI
% 0.27/0.48 = ( ! [A: $i] :
% 0.27/0.48 ( ! [Xx: $i] :
% 0.27/0.48 ~ ( in @ Xx @ A )
% 0.27/0.48 => ( A = emptyset ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(noeltsimpempty_type,type,
% 0.27/0.48 noeltsimpempty: $o ).
% 0.27/0.48
% 0.27/0.48 thf(noeltsimpempty,definition,
% 0.27/0.48 ( noeltsimpempty
% 0.27/0.48 = ( ! [A: $i] :
% 0.27/0.48 ( ! [Xx: $i] :
% 0.27/0.48 ~ ( in @ Xx @ A )
% 0.27/0.48 => ( A = emptyset ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(setbeta_type,type,
% 0.27/0.48 setbeta: $o ).
% 0.27/0.48
% 0.27/0.48 thf(setbeta,definition,
% 0.27/0.48 ( setbeta
% 0.27/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ A )
% 0.27/0.48 => ( ( in @ Xx
% 0.27/0.48 @ ( dsetconstr @ A
% 0.27/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.27/0.48 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(nonempty_type,type,
% 0.27/0.48 nonempty: $i > $o ).
% 0.27/0.48
% 0.27/0.48 thf(nonempty,definition,
% 0.27/0.48 ( nonempty
% 0.27/0.48 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(nonemptyE1_type,type,
% 0.27/0.48 nonemptyE1: $o ).
% 0.27/0.48
% 0.27/0.48 thf(nonemptyE1,definition,
% 0.27/0.48 ( nonemptyE1
% 0.27/0.48 = ( ! [A: $i] :
% 0.27/0.48 ( ( nonempty @ A )
% 0.27/0.48 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(nonemptyI_type,type,
% 0.27/0.48 nonemptyI: $o ).
% 0.27/0.48
% 0.27/0.48 thf(nonemptyI,definition,
% 0.27/0.48 ( nonemptyI
% 0.27/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ A )
% 0.27/0.48 => ( ( Xphi @ Xx )
% 0.27/0.48 => ( nonempty
% 0.27/0.48 @ ( dsetconstr @ A
% 0.27/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(nonemptyI1_type,type,
% 0.27/0.48 nonemptyI1: $o ).
% 0.27/0.48
% 0.27/0.48 thf(nonemptyI1,definition,
% 0.27/0.48 ( nonemptyI1
% 0.27/0.48 = ( ! [A: $i] :
% 0.27/0.48 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.27/0.48 => ( nonempty @ A ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(setadjoinIL_type,type,
% 0.27/0.48 setadjoinIL: $o ).
% 0.27/0.48
% 0.27/0.48 thf(setadjoinIL,definition,
% 0.27/0.48 ( setadjoinIL
% 0.27/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(emptyinunitempty_type,type,
% 0.27/0.48 emptyinunitempty: $o ).
% 0.27/0.48
% 0.27/0.48 thf(emptyinunitempty,definition,
% 0.27/0.48 ( emptyinunitempty
% 0.27/0.48 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(setadjoinIR_type,type,
% 0.27/0.48 setadjoinIR: $o ).
% 0.27/0.48
% 0.27/0.48 thf(setadjoinIR,definition,
% 0.27/0.48 ( setadjoinIR
% 0.27/0.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.27/0.48 ( ( in @ Xy @ A )
% 0.27/0.48 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(setadjoinE_type,type,
% 0.27/0.48 setadjoinE: $o ).
% 0.27/0.48
% 0.27/0.48 thf(setadjoinE,definition,
% 0.27/0.48 ( setadjoinE
% 0.27/0.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.27/0.48 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.27/0.48 => ! [Xphi: $o] :
% 0.27/0.48 ( ( ( Xy = Xx )
% 0.27/0.48 => Xphi )
% 0.27/0.48 => ( ( ( in @ Xy @ A )
% 0.27/0.48 => Xphi )
% 0.27/0.48 => Xphi ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(setadjoinOr_type,type,
% 0.27/0.48 setadjoinOr: $o ).
% 0.27/0.48
% 0.27/0.48 thf(setadjoinOr,definition,
% 0.27/0.48 ( setadjoinOr
% 0.27/0.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.27/0.48 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.27/0.48 => ( ( Xy = Xx )
% 0.27/0.48 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(setoftrueEq_type,type,
% 0.27/0.48 setoftrueEq: $o ).
% 0.27/0.48
% 0.27/0.48 thf(setoftrueEq,definition,
% 0.27/0.48 ( setoftrueEq
% 0.27/0.48 = ( ! [A: $i] :
% 0.27/0.48 ( ( dsetconstr @ A
% 0.27/0.48 @ ^ [Xx: $i] : $true )
% 0.27/0.48 = A ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(powersetI_type,type,
% 0.27/0.48 powersetI: $o ).
% 0.27/0.48
% 0.27/0.48 thf(powersetI,definition,
% 0.27/0.48 ( powersetI
% 0.27/0.48 = ( ! [A: $i,B: $i] :
% 0.27/0.48 ( ! [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ B )
% 0.27/0.48 => ( in @ Xx @ A ) )
% 0.27/0.48 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(emptyinPowerset_type,type,
% 0.27/0.48 emptyinPowerset: $o ).
% 0.27/0.48
% 0.27/0.48 thf(emptyinPowerset,definition,
% 0.27/0.48 ( emptyinPowerset
% 0.27/0.48 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(emptyInPowerset_type,type,
% 0.27/0.48 emptyInPowerset: $o ).
% 0.27/0.48
% 0.27/0.48 thf(emptyInPowerset,definition,
% 0.27/0.48 ( emptyInPowerset
% 0.27/0.48 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(powersetE_type,type,
% 0.27/0.48 powersetE: $o ).
% 0.27/0.48
% 0.27/0.48 thf(powersetE,definition,
% 0.27/0.48 ( powersetE
% 0.27/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.48 ( ( in @ B @ ( powerset @ A ) )
% 0.27/0.48 => ( ( in @ Xx @ B )
% 0.27/0.48 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(setunionI_type,type,
% 0.27/0.48 setunionI: $o ).
% 0.27/0.48
% 0.27/0.48 thf(setunionI,definition,
% 0.27/0.48 ( setunionI
% 0.27/0.48 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.27/0.48 ( ( in @ Xx @ B )
% 0.27/0.48 => ( ( in @ B @ A )
% 0.27/0.48 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(setunionE_type,type,
% 0.27/0.48 setunionE: $o ).
% 0.27/0.48
% 0.27/0.48 thf(setunionE,definition,
% 0.27/0.48 ( setunionE
% 0.27/0.48 = ( ! [A: $i,Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ ( setunion @ A ) )
% 0.27/0.48 => ! [Xphi: $o] :
% 0.27/0.48 ( ! [B: $i] :
% 0.27/0.48 ( ( in @ Xx @ B )
% 0.27/0.48 => ( ( in @ B @ A )
% 0.27/0.48 => Xphi ) )
% 0.27/0.48 => Xphi ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(subPowSU_type,type,
% 0.27/0.48 subPowSU: $o ).
% 0.27/0.48
% 0.27/0.48 thf(subPowSU,definition,
% 0.27/0.48 ( subPowSU
% 0.27/0.48 = ( ! [A: $i,Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ A )
% 0.27/0.48 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(exuE2_type,type,
% 0.27/0.48 exuE2: $o ).
% 0.27/0.48
% 0.27/0.48 thf(exuE2,definition,
% 0.27/0.48 ( exuE2
% 0.27/0.48 = ( ! [Xphi: $i > $o] :
% 0.27/0.48 ( ( exu
% 0.27/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.48 => ? [Xx: $i] :
% 0.27/0.48 ! [Xy: $i] :
% 0.27/0.48 ( ( Xphi @ Xy )
% 0.27/0.48 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(nonemptyImpWitness_type,type,
% 0.27/0.48 nonemptyImpWitness: $o ).
% 0.27/0.48
% 0.27/0.48 thf(nonemptyImpWitness,definition,
% 0.27/0.48 ( nonemptyImpWitness
% 0.27/0.48 = ( ! [A: $i] :
% 0.27/0.48 ( ( nonempty @ A )
% 0.27/0.48 => ? [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ A )
% 0.27/0.48 & $true ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(uniqinunit_type,type,
% 0.27/0.48 uniqinunit: $o ).
% 0.27/0.48
% 0.27/0.48 thf(uniqinunit,definition,
% 0.27/0.48 ( uniqinunit
% 0.27/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.27/0.48 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.27/0.48 => ( Xx = Xy ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(notinsingleton_type,type,
% 0.27/0.48 notinsingleton: $o ).
% 0.27/0.48
% 0.27/0.48 thf(notinsingleton,definition,
% 0.27/0.48 ( notinsingleton
% 0.27/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.27/0.48 ( ( Xx != Xy )
% 0.27/0.48 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(eqinunit_type,type,
% 0.27/0.48 eqinunit: $o ).
% 0.27/0.48
% 0.27/0.48 thf(eqinunit,definition,
% 0.27/0.48 ( eqinunit
% 0.27/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.27/0.48 ( ( Xx = Xy )
% 0.27/0.48 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(singletonsswitch_type,type,
% 0.27/0.48 singletonsswitch: $o ).
% 0.27/0.48
% 0.27/0.48 thf(singletonsswitch,definition,
% 0.27/0.48 ( singletonsswitch
% 0.27/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.27/0.48 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.27/0.48 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(upairsetE_type,type,
% 0.27/0.48 upairsetE: $o ).
% 0.27/0.48
% 0.27/0.48 thf(upairsetE,definition,
% 0.27/0.48 ( upairsetE
% 0.27/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.27/0.48 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.27/0.48 => ( ( Xz = Xx )
% 0.27/0.48 | ( Xz = Xy ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(upairsetIL_type,type,
% 0.27/0.48 upairsetIL: $o ).
% 0.27/0.48
% 0.27/0.48 thf(upairsetIL,definition,
% 0.27/0.48 ( upairsetIL
% 0.27/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(upairsetIR_type,type,
% 0.27/0.48 upairsetIR: $o ).
% 0.27/0.48
% 0.27/0.48 thf(upairsetIR,definition,
% 0.27/0.48 ( upairsetIR
% 0.27/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(emptyE1_type,type,
% 0.27/0.48 emptyE1: $o ).
% 0.27/0.48
% 0.27/0.48 thf(emptyE1,definition,
% 0.27/0.48 ( emptyE1
% 0.27/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.48 ( ? [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ A )
% 0.27/0.48 & ( Xphi @ Xx ) )
% 0.27/0.48 => ( ( ( dsetconstr @ A
% 0.27/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.48 = emptyset )
% 0.27/0.48 => $false ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(vacuousDall_type,type,
% 0.27/0.48 vacuousDall: $o ).
% 0.27/0.48
% 0.27/0.48 thf(vacuousDall,definition,
% 0.27/0.48 ( vacuousDall
% 0.27/0.48 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ emptyset )
% 0.27/0.48 => ( Xphi @ Xx ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(quantDeMorgan1_type,type,
% 0.27/0.48 quantDeMorgan1: $o ).
% 0.27/0.48
% 0.27/0.48 thf(quantDeMorgan1,definition,
% 0.27/0.48 ( quantDeMorgan1
% 0.27/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.48 ( ~ ! [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ A )
% 0.27/0.48 => ( Xphi @ Xx ) )
% 0.27/0.48 => ? [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ A )
% 0.27/0.48 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(quantDeMorgan2_type,type,
% 0.27/0.48 quantDeMorgan2: $o ).
% 0.27/0.48
% 0.27/0.48 thf(quantDeMorgan2,definition,
% 0.27/0.48 ( quantDeMorgan2
% 0.27/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.48 ( ! [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ A )
% 0.27/0.48 => ~ ( Xphi @ Xx ) )
% 0.27/0.48 => ~ ? [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ A )
% 0.27/0.48 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(quantDeMorgan3_type,type,
% 0.27/0.48 quantDeMorgan3: $o ).
% 0.27/0.48
% 0.27/0.48 thf(quantDeMorgan3,definition,
% 0.27/0.48 ( quantDeMorgan3
% 0.27/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.48 ( ~ ? [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ A )
% 0.27/0.48 & ( Xphi @ Xx ) )
% 0.27/0.48 => ! [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ A )
% 0.27/0.48 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(quantDeMorgan4_type,type,
% 0.27/0.48 quantDeMorgan4: $o ).
% 0.27/0.48
% 0.27/0.48 thf(quantDeMorgan4,definition,
% 0.27/0.48 ( quantDeMorgan4
% 0.27/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.48 ( ? [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ A )
% 0.27/0.48 & ~ ( Xphi @ Xx ) )
% 0.27/0.48 => ~ ! [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ A )
% 0.27/0.48 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(prop2setI_type,type,
% 0.27/0.48 prop2setI: $o ).
% 0.27/0.48
% 0.27/0.48 thf(prop2setI,definition,
% 0.27/0.48 ( prop2setI
% 0.27/0.48 = ( ! [Xphi: $o] :
% 0.27/0.48 ( Xphi
% 0.27/0.48 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(set2prop_type,type,
% 0.27/0.48 set2prop: $i > $o ).
% 0.27/0.48
% 0.27/0.48 thf(prop2set2propI_type,type,
% 0.27/0.48 prop2set2propI: $o ).
% 0.27/0.48
% 0.27/0.48 thf(prop2set2propI,definition,
% 0.27/0.48 ( prop2set2propI
% 0.27/0.48 = ( ! [Xphi: $o] :
% 0.27/0.48 ( Xphi
% 0.27/0.48 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(notdexE_type,type,
% 0.27/0.48 notdexE: $o ).
% 0.27/0.48
% 0.27/0.48 thf(notdexE,definition,
% 0.27/0.48 ( notdexE
% 0.27/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.48 ( ~ ? [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ A )
% 0.27/0.48 & ( Xphi @ Xx ) )
% 0.27/0.48 => ! [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ A )
% 0.27/0.48 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(notdallE_type,type,
% 0.27/0.48 notdallE: $o ).
% 0.27/0.48
% 0.27/0.48 thf(notdallE,definition,
% 0.27/0.48 ( notdallE
% 0.27/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.48 ( ~ ! [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ A )
% 0.27/0.48 => ( Xphi @ Xx ) )
% 0.27/0.48 => ? [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ A )
% 0.27/0.48 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(exuI1_type,type,
% 0.27/0.48 exuI1: $o ).
% 0.27/0.48
% 0.27/0.48 thf(exuI1,definition,
% 0.27/0.48 ( exuI1
% 0.27/0.48 = ( ! [Xphi: $i > $o] :
% 0.27/0.48 ( ? [Xx: $i] :
% 0.27/0.48 ( ( Xphi @ Xx )
% 0.27/0.48 & ! [Xy: $i] :
% 0.27/0.48 ( ( Xphi @ Xy )
% 0.27/0.48 => ( Xx = Xy ) ) )
% 0.27/0.48 => ( exu
% 0.27/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(exuI3_type,type,
% 0.27/0.48 exuI3: $o ).
% 0.27/0.48
% 0.27/0.48 thf(exuI3,definition,
% 0.27/0.48 ( exuI3
% 0.27/0.48 = ( ! [Xphi: $i > $o] :
% 0.27/0.48 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.27/0.48 => ( ! [Xx: $i,Xy: $i] :
% 0.27/0.48 ( ( Xphi @ Xx )
% 0.27/0.48 => ( ( Xphi @ Xy )
% 0.27/0.48 => ( Xx = Xy ) ) )
% 0.27/0.48 => ( exu
% 0.27/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(exuI2_type,type,
% 0.27/0.48 exuI2: $o ).
% 0.27/0.48
% 0.27/0.48 thf(exuI2,definition,
% 0.27/0.48 ( exuI2
% 0.27/0.48 = ( ! [Xphi: $i > $o] :
% 0.27/0.48 ( ? [Xx: $i] :
% 0.27/0.48 ! [Xy: $i] :
% 0.27/0.48 ( ( Xphi @ Xy )
% 0.27/0.48 <=> ( Xy = Xx ) )
% 0.27/0.48 => ( exu
% 0.27/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(inCongP_type,type,
% 0.27/0.48 inCongP: $o ).
% 0.27/0.48
% 0.27/0.48 thf(inCongP,definition,
% 0.27/0.48 ( inCongP
% 0.27/0.48 = ( ! [A: $i,B: $i] :
% 0.27/0.48 ( ( A = B )
% 0.27/0.48 => ! [Xx: $i,Xy: $i] :
% 0.27/0.48 ( ( Xx = Xy )
% 0.27/0.48 => ( ( in @ Xx @ A )
% 0.27/0.48 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(in__Cong_type,type,
% 0.27/0.48 in__Cong: $o ).
% 0.27/0.48
% 0.27/0.48 thf(in__Cong,definition,
% 0.27/0.48 ( in__Cong
% 0.27/0.48 = ( ! [A: $i,B: $i] :
% 0.27/0.48 ( ( A = B )
% 0.27/0.48 => ! [Xx: $i,Xy: $i] :
% 0.27/0.48 ( ( Xx = Xy )
% 0.27/0.48 => ( ( in @ Xx @ A )
% 0.27/0.48 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(exuE3u_type,type,
% 0.27/0.48 exuE3u: $o ).
% 0.27/0.48
% 0.27/0.48 thf(exuE3u,definition,
% 0.27/0.48 ( exuE3u
% 0.27/0.48 = ( ! [Xphi: $i > $o] :
% 0.27/0.48 ( ( exu
% 0.27/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.48 => ! [Xx: $i,Xy: $i] :
% 0.27/0.48 ( ( Xphi @ Xx )
% 0.27/0.48 => ( ( Xphi @ Xy )
% 0.27/0.48 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(exu__Cong_type,type,
% 0.27/0.48 exu__Cong: $o ).
% 0.27/0.48
% 0.27/0.48 thf(exu__Cong,definition,
% 0.27/0.48 ( exu__Cong
% 0.27/0.48 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.27/0.48 ( ! [Xx: $i,Xy: $i] :
% 0.27/0.48 ( ( Xx = Xy )
% 0.27/0.48 => ( ( Xphi @ Xx )
% 0.27/0.48 <=> ( Xpsi @ Xy ) ) )
% 0.27/0.48 => ( ( exu
% 0.27/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.48 <=> ( exu
% 0.27/0.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(emptyset__Cong_type,type,
% 0.27/0.48 emptyset__Cong: $o ).
% 0.27/0.48
% 0.27/0.48 thf(emptyset__Cong,definition,
% 0.27/0.48 ( emptyset__Cong
% 0.27/0.48 = ( emptyset = emptyset ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(setadjoin__Cong_type,type,
% 0.27/0.48 setadjoin__Cong: $o ).
% 0.27/0.48
% 0.27/0.48 thf(setadjoin__Cong,definition,
% 0.27/0.48 ( setadjoin__Cong
% 0.27/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.27/0.48 ( ( Xx = Xy )
% 0.27/0.48 => ! [Xz: $i,Xu: $i] :
% 0.27/0.48 ( ( Xz = Xu )
% 0.27/0.48 => ( ( setadjoin @ Xx @ Xz )
% 0.27/0.48 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(powerset__Cong_type,type,
% 0.27/0.48 powerset__Cong: $o ).
% 0.27/0.48
% 0.27/0.48 thf(powerset__Cong,definition,
% 0.27/0.48 ( powerset__Cong
% 0.27/0.48 = ( ! [A: $i,B: $i] :
% 0.27/0.48 ( ( A = B )
% 0.27/0.48 => ( ( powerset @ A )
% 0.27/0.48 = ( powerset @ B ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(setunion__Cong_type,type,
% 0.27/0.48 setunion__Cong: $o ).
% 0.27/0.48
% 0.27/0.48 thf(setunion__Cong,definition,
% 0.27/0.48 ( setunion__Cong
% 0.27/0.48 = ( ! [A: $i,B: $i] :
% 0.27/0.48 ( ( A = B )
% 0.27/0.48 => ( ( setunion @ A )
% 0.27/0.48 = ( setunion @ B ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(omega__Cong_type,type,
% 0.27/0.48 omega__Cong: $o ).
% 0.27/0.48
% 0.27/0.48 thf(omega__Cong,definition,
% 0.27/0.48 ( omega__Cong
% 0.27/0.48 = ( omega = omega ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(exuEu_type,type,
% 0.27/0.48 exuEu: $o ).
% 0.27/0.48
% 0.27/0.48 thf(exuEu,definition,
% 0.27/0.48 ( exuEu
% 0.27/0.48 = ( ! [Xphi: $i > $o] :
% 0.27/0.48 ( ( exu
% 0.27/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.48 => ! [Xx: $i,Xy: $i] :
% 0.27/0.48 ( ( Xphi @ Xx )
% 0.27/0.48 => ( ( Xphi @ Xy )
% 0.27/0.48 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(descr__Cong_type,type,
% 0.27/0.48 descr__Cong: $o ).
% 0.27/0.48
% 0.27/0.48 thf(descr__Cong,definition,
% 0.27/0.48 ( descr__Cong
% 0.27/0.48 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.27/0.48 ( ! [Xx: $i,Xy: $i] :
% 0.27/0.48 ( ( Xx = Xy )
% 0.27/0.48 => ( ( Xphi @ Xx )
% 0.27/0.48 <=> ( Xpsi @ Xy ) ) )
% 0.27/0.48 => ( ( exu
% 0.27/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.48 => ( ( exu
% 0.27/0.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.27/0.48 => ( ( descr
% 0.27/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.48 = ( descr
% 0.27/0.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(dsetconstr__Cong_type,type,
% 0.27/0.48 dsetconstr__Cong: $o ).
% 0.27/0.48
% 0.27/0.48 thf(dsetconstr__Cong,definition,
% 0.27/0.48 ( dsetconstr__Cong
% 0.27/0.48 = ( ! [A: $i,B: $i] :
% 0.27/0.48 ( ( A = B )
% 0.27/0.48 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.27/0.48 ( ! [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ A )
% 0.27/0.48 => ! [Xy: $i] :
% 0.27/0.48 ( ( in @ Xy @ B )
% 0.27/0.48 => ( ( Xx = Xy )
% 0.27/0.48 => ( ( Xphi @ Xx )
% 0.27/0.48 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.27/0.48 => ( ( dsetconstr @ A
% 0.27/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.48 = ( dsetconstr @ B
% 0.27/0.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(subset_type,type,
% 0.27/0.48 subset: $i > $i > $o ).
% 0.27/0.48
% 0.27/0.48 thf(disjoint_type,type,
% 0.27/0.48 disjoint: $i > $i > $o ).
% 0.27/0.48
% 0.27/0.48 thf(setsmeet_type,type,
% 0.27/0.48 setsmeet: $i > $i > $o ).
% 0.27/0.48
% 0.27/0.48 thf(subsetI1_type,type,
% 0.27/0.48 subsetI1: $o ).
% 0.27/0.48
% 0.27/0.48 thf(subsetI1,definition,
% 0.27/0.48 ( subsetI1
% 0.27/0.48 = ( ! [A: $i,B: $i] :
% 0.27/0.48 ( ! [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ A )
% 0.27/0.48 => ( in @ Xx @ B ) )
% 0.27/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(eqimpsubset2_type,type,
% 0.27/0.48 eqimpsubset2: $o ).
% 0.27/0.48
% 0.27/0.48 thf(eqimpsubset2,definition,
% 0.27/0.48 ( eqimpsubset2
% 0.27/0.48 = ( ! [A: $i,B: $i] :
% 0.27/0.48 ( ( A = B )
% 0.27/0.48 => ( subset @ B @ A ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(eqimpsubset1_type,type,
% 0.27/0.48 eqimpsubset1: $o ).
% 0.27/0.48
% 0.27/0.48 thf(eqimpsubset1,definition,
% 0.27/0.48 ( eqimpsubset1
% 0.27/0.48 = ( ! [A: $i,B: $i] :
% 0.27/0.48 ( ( A = B )
% 0.27/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(subsetI2_type,type,
% 0.27/0.48 subsetI2: $o ).
% 0.27/0.48
% 0.27/0.48 thf(subsetI2,definition,
% 0.27/0.48 ( subsetI2
% 0.27/0.48 = ( ! [A: $i,B: $i] :
% 0.27/0.48 ( ! [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ A )
% 0.27/0.48 => ( in @ Xx @ B ) )
% 0.27/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(emptysetsubset_type,type,
% 0.27/0.48 emptysetsubset: $o ).
% 0.27/0.48
% 0.27/0.48 thf(emptysetsubset,definition,
% 0.27/0.48 ( emptysetsubset
% 0.27/0.48 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(subsetE_type,type,
% 0.27/0.48 subsetE: $o ).
% 0.27/0.48
% 0.27/0.48 thf(subsetE,definition,
% 0.27/0.48 ( subsetE
% 0.27/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.48 ( ( subset @ A @ B )
% 0.27/0.48 => ( ( in @ Xx @ A )
% 0.27/0.48 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(subsetE2_type,type,
% 0.27/0.48 subsetE2: $o ).
% 0.27/0.48
% 0.27/0.48 thf(subsetE2,definition,
% 0.27/0.48 ( subsetE2
% 0.27/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.48 ( ( subset @ A @ B )
% 0.27/0.48 => ( ~ ( in @ Xx @ B )
% 0.27/0.48 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(notsubsetI_type,type,
% 0.27/0.48 notsubsetI: $o ).
% 0.27/0.48
% 0.27/0.48 thf(notsubsetI,definition,
% 0.27/0.48 ( notsubsetI
% 0.27/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ A )
% 0.27/0.48 => ( ~ ( in @ Xx @ B )
% 0.27/0.48 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(notequalI1_type,type,
% 0.27/0.48 notequalI1: $o ).
% 0.27/0.48
% 0.27/0.48 thf(notequalI1,definition,
% 0.27/0.48 ( notequalI1
% 0.27/0.48 = ( ! [A: $i,B: $i] :
% 0.27/0.48 ( ~ ( subset @ A @ B )
% 0.27/0.48 => ( A != B ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(notequalI2_type,type,
% 0.27/0.48 notequalI2: $o ).
% 0.27/0.48
% 0.27/0.48 thf(notequalI2,definition,
% 0.27/0.48 ( notequalI2
% 0.27/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ A )
% 0.27/0.48 => ( ~ ( in @ Xx @ B )
% 0.27/0.48 => ( A != B ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(subsetRefl_type,type,
% 0.27/0.48 subsetRefl: $o ).
% 0.27/0.48
% 0.27/0.48 thf(subsetRefl,definition,
% 0.27/0.48 ( subsetRefl
% 0.27/0.48 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(subsetTrans_type,type,
% 0.27/0.48 subsetTrans: $o ).
% 0.27/0.48
% 0.27/0.48 thf(subsetTrans,definition,
% 0.27/0.48 ( subsetTrans
% 0.27/0.48 = ( ! [A: $i,B: $i,C: $i] :
% 0.27/0.48 ( ( subset @ A @ B )
% 0.27/0.48 => ( ( subset @ B @ C )
% 0.27/0.48 => ( subset @ A @ C ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(setadjoinSub_type,type,
% 0.27/0.48 setadjoinSub: $o ).
% 0.27/0.48
% 0.27/0.48 thf(setadjoinSub,definition,
% 0.27/0.48 ( setadjoinSub
% 0.27/0.48 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(setadjoinSub2_type,type,
% 0.27/0.48 setadjoinSub2: $o ).
% 0.27/0.48
% 0.27/0.48 thf(setadjoinSub2,definition,
% 0.27/0.48 ( setadjoinSub2
% 0.27/0.48 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.27/0.48 ( ( subset @ A @ B )
% 0.27/0.48 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(subset2powerset_type,type,
% 0.27/0.48 subset2powerset: $o ).
% 0.27/0.48
% 0.27/0.48 thf(subset2powerset,definition,
% 0.27/0.48 ( subset2powerset
% 0.27/0.48 = ( ! [A: $i,B: $i] :
% 0.27/0.48 ( ( subset @ A @ B )
% 0.27/0.48 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(setextsub_type,type,
% 0.27/0.48 setextsub: $o ).
% 0.27/0.48
% 0.27/0.48 thf(setextsub,definition,
% 0.27/0.48 ( setextsub
% 0.27/0.48 = ( ! [A: $i,B: $i] :
% 0.27/0.48 ( ( subset @ A @ B )
% 0.27/0.48 => ( ( subset @ B @ A )
% 0.27/0.48 => ( A = B ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(subsetemptysetimpeq_type,type,
% 0.27/0.48 subsetemptysetimpeq: $o ).
% 0.27/0.48
% 0.27/0.48 thf(subsetemptysetimpeq,definition,
% 0.27/0.48 ( subsetemptysetimpeq
% 0.27/0.48 = ( ! [A: $i] :
% 0.27/0.48 ( ( subset @ A @ emptyset )
% 0.27/0.48 => ( A = emptyset ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(powersetI1_type,type,
% 0.27/0.48 powersetI1: $o ).
% 0.27/0.48
% 0.27/0.48 thf(powersetI1,definition,
% 0.27/0.48 ( powersetI1
% 0.27/0.48 = ( ! [A: $i,B: $i] :
% 0.27/0.48 ( ( subset @ B @ A )
% 0.27/0.48 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(powersetE1_type,type,
% 0.27/0.48 powersetE1: $o ).
% 0.27/0.48
% 0.27/0.48 thf(powersetE1,definition,
% 0.27/0.48 ( powersetE1
% 0.27/0.48 = ( ! [A: $i,B: $i] :
% 0.27/0.48 ( ( in @ B @ ( powerset @ A ) )
% 0.27/0.48 => ( subset @ B @ A ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(inPowerset_type,type,
% 0.27/0.48 inPowerset: $o ).
% 0.27/0.48
% 0.27/0.48 thf(inPowerset,definition,
% 0.27/0.48 ( inPowerset
% 0.27/0.48 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(powersetsubset_type,type,
% 0.27/0.48 powersetsubset: $o ).
% 0.27/0.48
% 0.27/0.48 thf(powersetsubset,definition,
% 0.27/0.48 ( powersetsubset
% 0.27/0.48 = ( ! [A: $i,B: $i] :
% 0.27/0.48 ( ( subset @ A @ B )
% 0.27/0.48 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(sepInPowerset_type,type,
% 0.27/0.48 sepInPowerset: $o ).
% 0.27/0.48
% 0.27/0.48 thf(sepInPowerset,definition,
% 0.27/0.48 ( sepInPowerset
% 0.27/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.48 ( in
% 0.27/0.48 @ ( dsetconstr @ A
% 0.27/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.48 @ ( powerset @ A ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(sepSubset_type,type,
% 0.27/0.48 sepSubset: $o ).
% 0.27/0.48
% 0.27/0.48 thf(sepSubset,definition,
% 0.27/0.48 ( sepSubset
% 0.27/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.27/0.48 ( subset
% 0.27/0.48 @ ( dsetconstr @ A
% 0.27/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.27/0.48 @ A ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(binunion_type,type,
% 0.27/0.48 binunion: $i > $i > $i ).
% 0.27/0.48
% 0.27/0.48 thf(binunionIL_type,type,
% 0.27/0.48 binunionIL: $o ).
% 0.27/0.48
% 0.27/0.48 thf(binunionIL,definition,
% 0.27/0.48 ( binunionIL
% 0.27/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ A )
% 0.27/0.48 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(upairset2IR_type,type,
% 0.27/0.48 upairset2IR: $o ).
% 0.27/0.48
% 0.27/0.48 thf(upairset2IR,definition,
% 0.27/0.48 ( upairset2IR
% 0.27/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(binunionIR_type,type,
% 0.27/0.48 binunionIR: $o ).
% 0.27/0.48
% 0.27/0.48 thf(binunionIR,definition,
% 0.27/0.48 ( binunionIR
% 0.27/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ B )
% 0.27/0.48 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(binunionEcases_type,type,
% 0.27/0.48 binunionEcases: $o ).
% 0.27/0.48
% 0.27/0.48 thf(binunionEcases,definition,
% 0.27/0.48 ( binunionEcases
% 0.27/0.48 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.27/0.48 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.27/0.48 => ( ( ( in @ Xx @ A )
% 0.27/0.48 => Xphi )
% 0.27/0.48 => ( ( ( in @ Xx @ B )
% 0.27/0.48 => Xphi )
% 0.27/0.48 => Xphi ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(binunionE_type,type,
% 0.27/0.48 binunionE: $o ).
% 0.27/0.48
% 0.27/0.48 thf(binunionE,definition,
% 0.27/0.48 ( binunionE
% 0.27/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.27/0.48 => ( ( in @ Xx @ A )
% 0.27/0.48 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(binunionLsub_type,type,
% 0.27/0.48 binunionLsub: $o ).
% 0.27/0.48
% 0.27/0.48 thf(binunionLsub,definition,
% 0.27/0.48 ( binunionLsub
% 0.27/0.48 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(binunionRsub_type,type,
% 0.27/0.48 binunionRsub: $o ).
% 0.27/0.48
% 0.27/0.48 thf(binunionRsub,definition,
% 0.27/0.48 ( binunionRsub
% 0.27/0.48 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(binintersect_type,type,
% 0.27/0.48 binintersect: $i > $i > $i ).
% 0.27/0.48
% 0.27/0.48 thf(binintersectI_type,type,
% 0.27/0.48 binintersectI: $o ).
% 0.27/0.48
% 0.27/0.48 thf(binintersectI,definition,
% 0.27/0.48 ( binintersectI
% 0.27/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ A )
% 0.27/0.48 => ( ( in @ Xx @ B )
% 0.27/0.48 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(binintersectSubset5_type,type,
% 0.27/0.48 binintersectSubset5: $o ).
% 0.27/0.48
% 0.27/0.48 thf(binintersectSubset5,definition,
% 0.27/0.48 ( binintersectSubset5
% 0.27/0.48 = ( ! [A: $i,B: $i,C: $i] :
% 0.27/0.48 ( ( subset @ C @ A )
% 0.27/0.48 => ( ( subset @ C @ B )
% 0.27/0.48 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(binintersectEL_type,type,
% 0.27/0.48 binintersectEL: $o ).
% 0.27/0.48
% 0.27/0.48 thf(binintersectEL,definition,
% 0.27/0.48 ( binintersectEL
% 0.27/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.27/0.48 => ( in @ Xx @ A ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(binintersectLsub_type,type,
% 0.27/0.48 binintersectLsub: $o ).
% 0.27/0.48
% 0.27/0.48 thf(binintersectLsub,definition,
% 0.27/0.48 ( binintersectLsub
% 0.27/0.48 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(binintersectSubset2_type,type,
% 0.27/0.48 binintersectSubset2: $o ).
% 0.27/0.48
% 0.27/0.48 thf(binintersectSubset2,definition,
% 0.27/0.48 ( binintersectSubset2
% 0.27/0.48 = ( ! [A: $i,B: $i] :
% 0.27/0.48 ( ( subset @ A @ B )
% 0.27/0.48 => ( ( binintersect @ A @ B )
% 0.27/0.48 = A ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(binintersectSubset3_type,type,
% 0.27/0.48 binintersectSubset3: $o ).
% 0.27/0.48
% 0.27/0.48 thf(binintersectSubset3,definition,
% 0.27/0.48 ( binintersectSubset3
% 0.27/0.48 = ( ! [A: $i,B: $i] :
% 0.27/0.48 ( ( ( binintersect @ A @ B )
% 0.27/0.48 = B )
% 0.27/0.48 => ( subset @ B @ A ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(binintersectER_type,type,
% 0.27/0.48 binintersectER: $o ).
% 0.27/0.48
% 0.27/0.48 thf(binintersectER,definition,
% 0.27/0.48 ( binintersectER
% 0.27/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.27/0.48 => ( in @ Xx @ B ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(disjointsetsI1_type,type,
% 0.27/0.48 disjointsetsI1: $o ).
% 0.27/0.48
% 0.27/0.48 thf(disjointsetsI1,definition,
% 0.27/0.48 ( disjointsetsI1
% 0.27/0.48 = ( ! [A: $i,B: $i] :
% 0.27/0.48 ( ~ ? [Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ A )
% 0.27/0.48 & ( in @ Xx @ B ) )
% 0.27/0.48 => ( ( binintersect @ A @ B )
% 0.27/0.48 = emptyset ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(binintersectRsub_type,type,
% 0.27/0.48 binintersectRsub: $o ).
% 0.27/0.48
% 0.27/0.48 thf(binintersectRsub,definition,
% 0.27/0.48 ( binintersectRsub
% 0.27/0.48 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(binintersectSubset4_type,type,
% 0.27/0.48 binintersectSubset4: $o ).
% 0.27/0.48
% 0.27/0.48 thf(binintersectSubset4,definition,
% 0.27/0.48 ( binintersectSubset4
% 0.27/0.48 = ( ! [A: $i,B: $i] :
% 0.27/0.48 ( ( subset @ B @ A )
% 0.27/0.48 => ( ( binintersect @ A @ B )
% 0.27/0.48 = B ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(binintersectSubset1_type,type,
% 0.27/0.48 binintersectSubset1: $o ).
% 0.27/0.48
% 0.27/0.48 thf(binintersectSubset1,definition,
% 0.27/0.48 ( binintersectSubset1
% 0.27/0.48 = ( ! [A: $i,B: $i] :
% 0.27/0.48 ( ( ( binintersect @ A @ B )
% 0.27/0.48 = A )
% 0.27/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(bs114d_type,type,
% 0.27/0.48 bs114d: $o ).
% 0.27/0.48
% 0.27/0.48 thf(bs114d,definition,
% 0.27/0.48 ( bs114d
% 0.27/0.48 = ( ! [A: $i,B: $i,C: $i] :
% 0.27/0.48 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.27/0.48 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(regular_type,type,
% 0.27/0.48 regular: $i > $o ).
% 0.27/0.48
% 0.27/0.48 thf(setminus_type,type,
% 0.27/0.48 setminus: $i > $i > $i ).
% 0.27/0.48
% 0.27/0.48 thf(setminusI_type,type,
% 0.27/0.48 setminusI: $o ).
% 0.27/0.48
% 0.27/0.48 thf(setminusI,definition,
% 0.27/0.48 ( setminusI
% 0.27/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ A )
% 0.27/0.48 => ( ~ ( in @ Xx @ B )
% 0.27/0.48 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(setminusEL_type,type,
% 0.27/0.48 setminusEL: $o ).
% 0.27/0.48
% 0.27/0.48 thf(setminusEL,definition,
% 0.27/0.48 ( setminusEL
% 0.27/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.27/0.48 => ( in @ Xx @ A ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(setminusER_type,type,
% 0.27/0.48 setminusER: $o ).
% 0.27/0.48
% 0.27/0.48 thf(setminusER,definition,
% 0.27/0.48 ( setminusER
% 0.27/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.27/0.48 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(setminusSubset2_type,type,
% 0.27/0.48 setminusSubset2: $o ).
% 0.27/0.48
% 0.27/0.48 thf(setminusSubset2,definition,
% 0.27/0.48 ( setminusSubset2
% 0.27/0.48 = ( ! [A: $i,B: $i] :
% 0.27/0.48 ( ( subset @ A @ B )
% 0.27/0.48 => ( ( setminus @ A @ B )
% 0.27/0.48 = emptyset ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(setminusERneg_type,type,
% 0.27/0.48 setminusERneg: $o ).
% 0.27/0.48
% 0.27/0.48 thf(setminusERneg,definition,
% 0.27/0.48 ( setminusERneg
% 0.27/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.48 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.27/0.48 => ( ( in @ Xx @ A )
% 0.27/0.48 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(setminusELneg_type,type,
% 0.27/0.48 setminusELneg: $o ).
% 0.27/0.48
% 0.27/0.48 thf(setminusELneg,definition,
% 0.27/0.48 ( setminusELneg
% 0.27/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.48 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.27/0.48 => ( ~ ( in @ Xx @ B )
% 0.27/0.48 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(setminusILneg_type,type,
% 0.27/0.48 setminusILneg: $o ).
% 0.27/0.48
% 0.27/0.48 thf(setminusILneg,definition,
% 0.27/0.48 ( setminusILneg
% 0.27/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.48 ( ~ ( in @ Xx @ A )
% 0.27/0.48 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(setminusIRneg_type,type,
% 0.27/0.48 setminusIRneg: $o ).
% 0.27/0.48
% 0.27/0.48 thf(setminusIRneg,definition,
% 0.27/0.48 ( setminusIRneg
% 0.27/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.27/0.48 ( ( in @ Xx @ B )
% 0.27/0.48 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(setminusLsub_type,type,
% 0.27/0.48 setminusLsub: $o ).
% 0.27/0.48
% 0.27/0.48 thf(setminusLsub,definition,
% 0.27/0.48 ( setminusLsub
% 0.27/0.48 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.27/0.48
% 0.27/0.48 thf(setminusSubset1,conjecture,
% 0.27/0.48 ( setextAx
% 0.27/0.48 => ( emptysetAx
% 0.27/0.48 => ( setadjoinAx
% 0.27/0.48 => ( powersetAx
% 0.27/0.48 => ( setunionAx
% 0.27/0.48 => ( omega0Ax
% 0.27/0.48 => ( omegaSAx
% 0.27/0.48 => ( omegaIndAx
% 0.27/0.48 => ( replAx
% 0.27/0.48 => ( foundationAx
% 0.27/0.48 => ( wellorderingAx
% 0.27/0.48 => ( descrp
% 0.27/0.48 => ( dsetconstrI
% 0.27/0.48 => ( dsetconstrEL
% 0.27/0.48 => ( dsetconstrER
% 0.27/0.48 => ( exuE1
% 0.27/0.48 => ( prop2setE
% 0.27/0.48 => ( emptysetE
% 0.27/0.48 => ( emptysetimpfalse
% 0.27/0.48 => ( notinemptyset
% 0.27/0.48 => ( exuE3e
% 0.27/0.48 => ( setext
% 0.27/0.48 => ( emptyI
% 0.27/0.48 => ( noeltsimpempty
% 0.27/0.48 => ( setbeta
% 0.27/0.48 => ( nonemptyE1
% 0.27/0.48 => ( nonemptyI
% 0.27/0.48 => ( nonemptyI1
% 0.27/0.48 => ( setadjoinIL
% 0.27/0.48 => ( emptyinunitempty
% 0.27/0.48 => ( setadjoinIR
% 0.27/0.48 => ( setadjoinE
% 0.27/0.48 => ( setadjoinOr
% 0.27/0.48 => ( setoftrueEq
% 0.27/0.48 => ( powersetI
% 0.27/0.48 => ( emptyinPowerset
% 0.27/0.48 => ( emptyInPowerset
% 0.27/0.48 => ( powersetE
% 0.27/0.48 => ( setunionI
% 0.27/0.48 => ( setunionE
% 0.27/0.48 => ( subPowSU
% 0.27/0.48 => ( exuE2
% 0.27/0.48 => ( nonemptyImpWitness
% 0.27/0.48 => ( uniqinunit
% 0.27/0.48 => ( notinsingleton
% 0.27/0.48 => ( eqinunit
% 0.27/0.48 => ( singletonsswitch
% 0.27/0.48 => ( upairsetE
% 0.27/0.48 => ( upairsetIL
% 0.27/0.48 => ( upairsetIR
% 0.27/0.48 => ( emptyE1
% 0.27/0.48 => ( vacuousDall
% 0.27/0.48 => ( quantDeMorgan1
% 0.27/0.48 => ( quantDeMorgan2
% 0.27/0.48 => ( quantDeMorgan3
% 0.27/0.48 => ( quantDeMorgan4
% 0.27/0.48 => ( prop2setI
% 0.27/0.48 => ( prop2set2propI
% 0.27/0.48 => ( notdexE
% 0.27/0.48 => ( notdallE
% 0.27/0.48 => ( exuI1
% 0.27/0.48 => ( exuI3
% 0.27/0.48 => ( exuI2
% 0.27/0.48 => ( inCongP
% 0.27/0.48 => ( in__Cong
% 0.27/0.48 => ( exuE3u
% 0.27/0.48 => ( exu__Cong
% 0.27/0.48 => ( emptyset__Cong
% 0.27/0.48 => ( setadjoin__Cong
% 0.27/0.48 => ( powerset__Cong
% 0.27/0.48 => ( setunion__Cong
% 0.27/0.48 => ( omega__Cong
% 0.27/0.48 => ( exuEu
% 0.27/0.48 => ( descr__Cong
% 0.27/0.48 => ( dsetconstr__Cong
% 0.27/0.48 => ( subsetI1
% 0.27/0.48 => ( eqimpsubset2
% 0.27/0.48 => ( eqimpsubset1
% 0.27/0.48 => ( subsetI2
% 0.27/0.48 => ( emptysetsubset
% 0.27/0.48 => ( subsetE
% 0.27/0.48 => ( subsetE2
% 0.27/0.48 => ( notsubsetI
% 0.27/0.48 => ( notequalI1
% 0.27/0.48 => ( notequalI2
% 0.27/0.48 => ( subsetRefl
% 0.27/0.48 => ( subsetTrans
% 0.27/0.48 => ( setadjoinSub
% 0.27/0.48 => ( setadjoinSub2
% 0.27/0.48 => ( subset2powerset
% 0.27/0.48 => ( setextsub
% 0.27/0.48 => ( subsetemptysetimpeq
% 0.27/0.48 => ( powersetI1
% 0.27/0.48 => ( powersetE1
% 0.27/0.48 => ( inPowerset
% 0.27/0.48 => ( powersetsubset
% 0.27/0.48 => ( sepInPowerset
% 0.27/0.48 => ( sepSubset
% 0.27/0.48 => ( binunionIL
% 0.27/0.48 => ( upairset2IR
% 0.27/0.48 => ( binunionIR
% 0.27/0.48 => ( binunionEcases
% 0.27/0.48 => ( binunionE
% 0.27/0.48 => ( binunionLsub
% 0.27/0.48 => ( binunionRsub
% 0.27/0.48 => ( binintersectI
% 0.27/0.48 => ( binintersectSubset5
% 0.27/0.48 => ( binintersectEL
% 0.27/0.48 => ( binintersectLsub
% 0.27/0.48 => ( binintersectSubset2
% 0.27/0.48 => ( binintersectSubset3
% 0.27/0.48 => ( binintersectER
% 0.27/0.48 => ( disjointsetsI1
% 0.27/0.48 => ( binintersectRsub
% 0.27/0.48 => ( binintersectSubset4
% 0.27/0.48 => ( binintersectSubset1
% 0.27/0.48 => ( bs114d
% 0.27/0.48 => ( setminusI
% 0.27/0.48 => ( setminusEL
% 0.27/0.48 => ( setminusER
% 0.27/0.48 => ( setminusSubset2
% 0.27/0.48 => ( setminusERneg
% 0.27/0.48 => ( setminusELneg
% 0.27/0.48 => ( setminusILneg
% 0.27/0.48 => ( setminusIRneg
% 0.27/0.48 => ( setminusLsub
% 0.27/0.48 => ! [A: $i,B: $i] :
% 0.27/0.48 ( ( ( setminus @ A @ B )
% 0.27/0.48 = emptyset )
% 0.27/0.48 => ( subset @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.48
% 0.27/0.48 %------------------------------------------------------------------------------
% 0.27/0.48 ------------------------
% 2.28/1.46 ---- Embedded in THF ---
% 2.28/1.46 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.28/1.46 %%% Generated on Tue Feb 24 12:29:49 EST 2026
% 2.28/1.46 %%% using '$$dhol' embedding, version 1.3.0.
% 2.28/1.46 %%% Logic specification used:
% 2.28/1.46 %%% thf(spec, logic, $$dhol).
% 2.28/1.46
% 2.28/1.46 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.mU0PE1mI9q/DTF2DTF13954.p
% See solution above
% 2.28/1.46 ------------------------
% 2.28/1.48 ---- Cleaned THF ---
% 2.28/1.48 thf(in_type,type,
% 2.28/1.48 in: $i > $i > $o ).
% 2.28/1.48
% 2.28/1.48 thf(exu_type,type,
% 2.28/1.48 exu: ( $i > $o ) > $o ).
% 2.28/1.48
% 2.28/1.48 thf(exu,definition,
% 2.28/1.48 ( exu
% 2.28/1.48 = ( ^ [Xphi: $i > $o] :
% 2.28/1.48 ? [Xx: $i] :
% 2.28/1.48 ( ( Xphi @ Xx )
% 2.28/1.48 & ! [Xy: $i] :
% 2.28/1.48 ( ( Xphi @ Xy )
% 2.28/1.48 => ( Xx = Xy ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(setextAx_type,type,
% 2.28/1.48 setextAx: $o ).
% 2.28/1.48
% 2.28/1.48 thf(setextAx,definition,
% 2.28/1.48 ( setextAx
% 2.28/1.48 = ( ! [A: $i,B: $i] :
% 2.28/1.48 ( ! [Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ A )
% 2.28/1.48 <=> ( in @ Xx @ B ) )
% 2.28/1.48 => ( A = B ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(emptyset_type,type,
% 2.28/1.48 emptyset: $i ).
% 2.28/1.48
% 2.28/1.48 thf(emptysetAx_type,type,
% 2.28/1.48 emptysetAx: $o ).
% 2.28/1.48
% 2.28/1.48 thf(emptysetAx,definition,
% 2.28/1.48 ( emptysetAx
% 2.28/1.48 = ( ! [Xx: $i] :
% 2.28/1.48 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(setadjoin_type,type,
% 2.28/1.48 setadjoin: $i > $i > $i ).
% 2.28/1.48
% 2.28/1.48 thf(setadjoinAx_type,type,
% 2.28/1.48 setadjoinAx: $o ).
% 2.28/1.48
% 2.28/1.48 thf(setadjoinAx,definition,
% 2.28/1.48 ( setadjoinAx
% 2.28/1.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.28/1.48 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.28/1.48 <=> ( ( Xy = Xx )
% 2.28/1.48 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(powerset_type,type,
% 2.28/1.48 powerset: $i > $i ).
% 2.28/1.48
% 2.28/1.48 thf(powersetAx_type,type,
% 2.28/1.48 powersetAx: $o ).
% 2.28/1.48
% 2.28/1.48 thf(powersetAx,definition,
% 2.28/1.48 ( powersetAx
% 2.28/1.48 = ( ! [A: $i,B: $i] :
% 2.28/1.48 ( ( in @ B @ ( powerset @ A ) )
% 2.28/1.48 <=> ! [Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ B )
% 2.28/1.48 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(setunion_type,type,
% 2.28/1.48 setunion: $i > $i ).
% 2.28/1.48
% 2.28/1.48 thf(setunionAx_type,type,
% 2.28/1.48 setunionAx: $o ).
% 2.28/1.48
% 2.28/1.48 thf(setunionAx,definition,
% 2.28/1.48 ( setunionAx
% 2.28/1.48 = ( ! [A: $i,Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ ( setunion @ A ) )
% 2.28/1.48 <=> ? [B: $i] :
% 2.28/1.48 ( ( in @ Xx @ B )
% 2.28/1.48 & ( in @ B @ A ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(omega_type,type,
% 2.28/1.48 omega: $i ).
% 2.28/1.48
% 2.28/1.48 thf(omega0Ax_type,type,
% 2.28/1.48 omega0Ax: $o ).
% 2.28/1.48
% 2.28/1.48 thf(omega0Ax,definition,
% 2.28/1.48 ( omega0Ax
% 2.28/1.48 = ( in @ emptyset @ omega ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(omegaSAx_type,type,
% 2.28/1.48 omegaSAx: $o ).
% 2.28/1.48
% 2.28/1.48 thf(omegaSAx,definition,
% 2.28/1.48 ( omegaSAx
% 2.28/1.48 = ( ! [Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ omega )
% 2.28/1.48 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(omegaIndAx_type,type,
% 2.28/1.48 omegaIndAx: $o ).
% 2.28/1.48
% 2.28/1.48 thf(omegaIndAx,definition,
% 2.28/1.48 ( omegaIndAx
% 2.28/1.48 = ( ! [A: $i] :
% 2.28/1.48 ( ( ( in @ emptyset @ A )
% 2.28/1.48 & ! [Xx: $i] :
% 2.28/1.48 ( ( ( in @ Xx @ omega )
% 2.28/1.48 & ( in @ Xx @ A ) )
% 2.28/1.48 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.28/1.48 => ! [Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ omega )
% 2.28/1.48 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(replAx_type,type,
% 2.28/1.48 replAx: $o ).
% 2.28/1.48
% 2.28/1.48 thf(replAx,definition,
% 2.28/1.48 ( replAx
% 2.28/1.48 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.28/1.48 ( ! [Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ A )
% 2.28/1.48 => ( exu
% 2.28/1.48 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.28/1.48 => ? [B: $i] :
% 2.28/1.48 ! [Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ B )
% 2.28/1.48 <=> ? [Xy: $i] :
% 2.28/1.48 ( ( in @ Xy @ A )
% 2.28/1.48 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(foundationAx_type,type,
% 2.28/1.48 foundationAx: $o ).
% 2.28/1.48
% 2.28/1.48 thf(foundationAx,definition,
% 2.28/1.48 ( foundationAx
% 2.28/1.48 = ( ! [A: $i] :
% 2.28/1.48 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.28/1.48 => ? [B: $i] :
% 2.28/1.48 ( ( in @ B @ A )
% 2.28/1.48 & ~ ? [Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ B )
% 2.28/1.48 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(wellorderingAx_type,type,
% 2.28/1.48 wellorderingAx: $o ).
% 2.28/1.48
% 2.28/1.48 thf(wellorderingAx,definition,
% 2.28/1.48 ( wellorderingAx
% 2.28/1.48 = ( ! [A: $i] :
% 2.28/1.48 ? [B: $i] :
% 2.28/1.48 ( ! [C: $i] :
% 2.28/1.48 ( ( in @ C @ B )
% 2.28/1.48 => ! [Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ C )
% 2.28/1.48 => ( in @ Xx @ A ) ) )
% 2.28/1.48 & ! [Xx: $i,Xy: $i] :
% 2.28/1.48 ( ( ( in @ Xx @ A )
% 2.28/1.48 & ( in @ Xy @ A ) )
% 2.28/1.48 => ( ! [C: $i] :
% 2.28/1.48 ( ( in @ C @ B )
% 2.28/1.48 => ( ( in @ Xx @ C )
% 2.28/1.48 <=> ( in @ Xy @ C ) ) )
% 2.28/1.48 => ( Xx = Xy ) ) )
% 2.28/1.48 & ! [C: $i,D: $i] :
% 2.28/1.48 ( ( ( in @ C @ B )
% 2.28/1.48 & ( in @ D @ B ) )
% 2.28/1.48 => ( ! [Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ C )
% 2.28/1.48 => ( in @ Xx @ D ) )
% 2.28/1.48 | ! [Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ D )
% 2.28/1.48 => ( in @ Xx @ C ) ) ) )
% 2.28/1.48 & ! [C: $i] :
% 2.28/1.48 ( ( ! [Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ C )
% 2.28/1.48 => ( in @ Xx @ A ) )
% 2.28/1.48 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.28/1.48 => ? [D: $i,Xx: $i] :
% 2.28/1.48 ( ( in @ D @ B )
% 2.28/1.48 & ( in @ Xx @ C )
% 2.28/1.48 & ~ ? [Xy: $i] :
% 2.28/1.48 ( ( in @ Xy @ D )
% 2.28/1.48 & ( in @ Xy @ C ) )
% 2.28/1.48 & ! [E: $i] :
% 2.28/1.48 ( ( in @ E @ B )
% 2.28/1.48 => ( ! [Xy: $i] :
% 2.28/1.48 ( ( in @ Xy @ E )
% 2.28/1.48 => ( in @ Xy @ D ) )
% 2.28/1.48 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(descr_type,type,
% 2.28/1.48 descr: ( $i > $o ) > $i ).
% 2.28/1.48
% 2.28/1.48 thf(descrp_type,type,
% 2.28/1.48 descrp: $o ).
% 2.28/1.48
% 2.28/1.48 thf(descrp,definition,
% 2.28/1.48 ( descrp
% 2.28/1.48 = ( ! [Xphi: $i > $o] :
% 2.28/1.48 ( ( exu
% 2.28/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.28/1.48 => ( Xphi
% 2.28/1.48 @ ( descr
% 2.28/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(dsetconstr_type,type,
% 2.28/1.48 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.28/1.48
% 2.28/1.48 thf(dsetconstrI_type,type,
% 2.28/1.48 dsetconstrI: $o ).
% 2.28/1.48
% 2.28/1.48 thf(dsetconstrI,definition,
% 2.28/1.48 ( dsetconstrI
% 2.28/1.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ A )
% 2.28/1.48 => ( ( Xphi @ Xx )
% 2.28/1.48 => ( in @ Xx
% 2.28/1.48 @ ( dsetconstr @ A
% 2.28/1.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(dsetconstrEL_type,type,
% 2.28/1.48 dsetconstrEL: $o ).
% 2.28/1.48
% 2.28/1.48 thf(dsetconstrEL,definition,
% 2.28/1.48 ( dsetconstrEL
% 2.28/1.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.28/1.48 ( ( in @ Xx
% 2.28/1.48 @ ( dsetconstr @ A
% 2.28/1.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.28/1.48 => ( in @ Xx @ A ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(dsetconstrER_type,type,
% 2.28/1.48 dsetconstrER: $o ).
% 2.28/1.48
% 2.28/1.48 thf(dsetconstrER,definition,
% 2.28/1.48 ( dsetconstrER
% 2.28/1.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.28/1.48 ( ( in @ Xx
% 2.28/1.48 @ ( dsetconstr @ A
% 2.28/1.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.28/1.48 => ( Xphi @ Xx ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(exuE1_type,type,
% 2.28/1.48 exuE1: $o ).
% 2.28/1.48
% 2.28/1.48 thf(exuE1,definition,
% 2.28/1.48 ( exuE1
% 2.28/1.48 = ( ! [Xphi: $i > $o] :
% 2.28/1.48 ( ( exu
% 2.28/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.28/1.48 => ? [Xx: $i] :
% 2.28/1.48 ( ( Xphi @ Xx )
% 2.28/1.48 & ! [Xy: $i] :
% 2.28/1.48 ( ( Xphi @ Xy )
% 2.28/1.48 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(prop2set_type,type,
% 2.28/1.48 prop2set: $o > $i ).
% 2.28/1.48
% 2.28/1.48 thf(prop2setE_type,type,
% 2.28/1.48 prop2setE: $o ).
% 2.28/1.48
% 2.28/1.48 thf(prop2setE,definition,
% 2.28/1.48 ( prop2setE
% 2.28/1.48 = ( ! [Xphi: $o,Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.28/1.48 => Xphi ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(emptysetE_type,type,
% 2.28/1.48 emptysetE: $o ).
% 2.28/1.48
% 2.28/1.48 thf(emptysetE,definition,
% 2.28/1.48 ( emptysetE
% 2.28/1.48 = ( ! [Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ emptyset )
% 2.28/1.48 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(emptysetimpfalse_type,type,
% 2.28/1.48 emptysetimpfalse: $o ).
% 2.28/1.48
% 2.28/1.48 thf(emptysetimpfalse,definition,
% 2.28/1.48 ( emptysetimpfalse
% 2.28/1.48 = ( ! [Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ emptyset )
% 2.28/1.48 => $false ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(notinemptyset_type,type,
% 2.28/1.48 notinemptyset: $o ).
% 2.28/1.48
% 2.28/1.48 thf(notinemptyset,definition,
% 2.28/1.48 ( notinemptyset
% 2.28/1.48 = ( ! [Xx: $i] :
% 2.28/1.48 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(exuE3e_type,type,
% 2.28/1.48 exuE3e: $o ).
% 2.28/1.48
% 2.28/1.48 thf(exuE3e,definition,
% 2.28/1.48 ( exuE3e
% 2.28/1.48 = ( ! [Xphi: $i > $o] :
% 2.28/1.48 ( ( exu
% 2.28/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.28/1.48 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(setext_type,type,
% 2.28/1.48 setext: $o ).
% 2.28/1.48
% 2.28/1.48 thf(setext,definition,
% 2.28/1.48 ( setext
% 2.28/1.48 = ( ! [A: $i,B: $i] :
% 2.28/1.48 ( ! [Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ A )
% 2.28/1.48 => ( in @ Xx @ B ) )
% 2.28/1.48 => ( ! [Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ B )
% 2.28/1.48 => ( in @ Xx @ A ) )
% 2.28/1.48 => ( A = B ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(emptyI_type,type,
% 2.28/1.48 emptyI: $o ).
% 2.28/1.48
% 2.28/1.48 thf(emptyI,definition,
% 2.28/1.48 ( emptyI
% 2.28/1.48 = ( ! [A: $i] :
% 2.28/1.48 ( ! [Xx: $i] :
% 2.28/1.48 ~ ( in @ Xx @ A )
% 2.28/1.48 => ( A = emptyset ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(noeltsimpempty_type,type,
% 2.28/1.48 noeltsimpempty: $o ).
% 2.28/1.48
% 2.28/1.48 thf(noeltsimpempty,definition,
% 2.28/1.48 ( noeltsimpempty
% 2.28/1.48 = ( ! [A: $i] :
% 2.28/1.48 ( ! [Xx: $i] :
% 2.28/1.48 ~ ( in @ Xx @ A )
% 2.28/1.48 => ( A = emptyset ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(setbeta_type,type,
% 2.28/1.48 setbeta: $o ).
% 2.28/1.48
% 2.28/1.48 thf(setbeta,definition,
% 2.28/1.48 ( setbeta
% 2.28/1.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ A )
% 2.28/1.48 => ( ( in @ Xx
% 2.28/1.48 @ ( dsetconstr @ A
% 2.28/1.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.28/1.48 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(nonempty_type,type,
% 2.28/1.48 nonempty: $i > $o ).
% 2.28/1.48
% 2.28/1.48 thf(nonempty,definition,
% 2.28/1.48 ( nonempty
% 2.28/1.48 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(nonemptyE1_type,type,
% 2.28/1.48 nonemptyE1: $o ).
% 2.28/1.48
% 2.28/1.48 thf(nonemptyE1,definition,
% 2.28/1.48 ( nonemptyE1
% 2.28/1.48 = ( ! [A: $i] :
% 2.28/1.48 ( ( nonempty @ A )
% 2.28/1.48 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(nonemptyI_type,type,
% 2.28/1.48 nonemptyI: $o ).
% 2.28/1.48
% 2.28/1.48 thf(nonemptyI,definition,
% 2.28/1.48 ( nonemptyI
% 2.28/1.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ A )
% 2.28/1.48 => ( ( Xphi @ Xx )
% 2.28/1.48 => ( nonempty
% 2.28/1.48 @ ( dsetconstr @ A
% 2.28/1.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(nonemptyI1_type,type,
% 2.28/1.48 nonemptyI1: $o ).
% 2.28/1.48
% 2.28/1.48 thf(nonemptyI1,definition,
% 2.28/1.48 ( nonemptyI1
% 2.28/1.48 = ( ! [A: $i] :
% 2.28/1.48 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.28/1.48 => ( nonempty @ A ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(setadjoinIL_type,type,
% 2.28/1.48 setadjoinIL: $o ).
% 2.28/1.48
% 2.28/1.48 thf(setadjoinIL,definition,
% 2.28/1.48 ( setadjoinIL
% 2.28/1.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(emptyinunitempty_type,type,
% 2.28/1.48 emptyinunitempty: $o ).
% 2.28/1.48
% 2.28/1.48 thf(emptyinunitempty,definition,
% 2.28/1.48 ( emptyinunitempty
% 2.28/1.48 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(setadjoinIR_type,type,
% 2.28/1.48 setadjoinIR: $o ).
% 2.28/1.48
% 2.28/1.48 thf(setadjoinIR,definition,
% 2.28/1.48 ( setadjoinIR
% 2.28/1.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.28/1.48 ( ( in @ Xy @ A )
% 2.28/1.48 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(setadjoinE_type,type,
% 2.28/1.48 setadjoinE: $o ).
% 2.28/1.48
% 2.28/1.48 thf(setadjoinE,definition,
% 2.28/1.48 ( setadjoinE
% 2.28/1.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.28/1.48 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.28/1.48 => ! [Xphi: $o] :
% 2.28/1.48 ( ( ( Xy = Xx )
% 2.28/1.48 => Xphi )
% 2.28/1.48 => ( ( ( in @ Xy @ A )
% 2.28/1.48 => Xphi )
% 2.28/1.48 => Xphi ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(setadjoinOr_type,type,
% 2.28/1.48 setadjoinOr: $o ).
% 2.28/1.48
% 2.28/1.48 thf(setadjoinOr,definition,
% 2.28/1.48 ( setadjoinOr
% 2.28/1.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.28/1.48 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.28/1.48 => ( ( Xy = Xx )
% 2.28/1.48 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(setoftrueEq_type,type,
% 2.28/1.48 setoftrueEq: $o ).
% 2.28/1.48
% 2.28/1.48 thf(setoftrueEq,definition,
% 2.28/1.48 ( setoftrueEq
% 2.28/1.48 = ( ! [A: $i] :
% 2.28/1.48 ( ( dsetconstr @ A
% 2.28/1.48 @ ^ [Xx: $i] : $true )
% 2.28/1.48 = A ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(powersetI_type,type,
% 2.28/1.48 powersetI: $o ).
% 2.28/1.48
% 2.28/1.48 thf(powersetI,definition,
% 2.28/1.48 ( powersetI
% 2.28/1.48 = ( ! [A: $i,B: $i] :
% 2.28/1.48 ( ! [Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ B )
% 2.28/1.48 => ( in @ Xx @ A ) )
% 2.28/1.48 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(emptyinPowerset_type,type,
% 2.28/1.48 emptyinPowerset: $o ).
% 2.28/1.48
% 2.28/1.48 thf(emptyinPowerset,definition,
% 2.28/1.48 ( emptyinPowerset
% 2.28/1.48 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(emptyInPowerset_type,type,
% 2.28/1.48 emptyInPowerset: $o ).
% 2.28/1.48
% 2.28/1.48 thf(emptyInPowerset,definition,
% 2.28/1.48 ( emptyInPowerset
% 2.28/1.48 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(powersetE_type,type,
% 2.28/1.48 powersetE: $o ).
% 2.28/1.48
% 2.28/1.48 thf(powersetE,definition,
% 2.28/1.48 ( powersetE
% 2.28/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.28/1.48 ( ( in @ B @ ( powerset @ A ) )
% 2.28/1.48 => ( ( in @ Xx @ B )
% 2.28/1.48 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(setunionI_type,type,
% 2.28/1.48 setunionI: $o ).
% 2.28/1.48
% 2.28/1.48 thf(setunionI,definition,
% 2.28/1.48 ( setunionI
% 2.28/1.48 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.28/1.48 ( ( in @ Xx @ B )
% 2.28/1.48 => ( ( in @ B @ A )
% 2.28/1.48 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(setunionE_type,type,
% 2.28/1.48 setunionE: $o ).
% 2.28/1.48
% 2.28/1.48 thf(setunionE,definition,
% 2.28/1.48 ( setunionE
% 2.28/1.48 = ( ! [A: $i,Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ ( setunion @ A ) )
% 2.28/1.48 => ! [Xphi: $o] :
% 2.28/1.48 ( ! [B: $i] :
% 2.28/1.48 ( ( in @ Xx @ B )
% 2.28/1.48 => ( ( in @ B @ A )
% 2.28/1.48 => Xphi ) )
% 2.28/1.48 => Xphi ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(subPowSU_type,type,
% 2.28/1.48 subPowSU: $o ).
% 2.28/1.48
% 2.28/1.48 thf(subPowSU,definition,
% 2.28/1.48 ( subPowSU
% 2.28/1.48 = ( ! [A: $i,Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ A )
% 2.28/1.48 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(exuE2_type,type,
% 2.28/1.48 exuE2: $o ).
% 2.28/1.48
% 2.28/1.48 thf(exuE2,definition,
% 2.28/1.48 ( exuE2
% 2.28/1.48 = ( ! [Xphi: $i > $o] :
% 2.28/1.48 ( ( exu
% 2.28/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.28/1.48 => ? [Xx: $i] :
% 2.28/1.48 ! [Xy: $i] :
% 2.28/1.48 ( ( Xphi @ Xy )
% 2.28/1.48 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(nonemptyImpWitness_type,type,
% 2.28/1.48 nonemptyImpWitness: $o ).
% 2.28/1.48
% 2.28/1.48 thf(nonemptyImpWitness,definition,
% 2.28/1.48 ( nonemptyImpWitness
% 2.28/1.48 = ( ! [A: $i] :
% 2.28/1.48 ( ( nonempty @ A )
% 2.28/1.48 => ? [Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ A )
% 2.28/1.48 & $true ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(uniqinunit_type,type,
% 2.28/1.48 uniqinunit: $o ).
% 2.28/1.48
% 2.28/1.48 thf(uniqinunit,definition,
% 2.28/1.48 ( uniqinunit
% 2.28/1.48 = ( ! [Xx: $i,Xy: $i] :
% 2.28/1.48 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.28/1.48 => ( Xx = Xy ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(notinsingleton_type,type,
% 2.28/1.48 notinsingleton: $o ).
% 2.28/1.48
% 2.28/1.48 thf(notinsingleton,definition,
% 2.28/1.48 ( notinsingleton
% 2.28/1.48 = ( ! [Xx: $i,Xy: $i] :
% 2.28/1.48 ( ( Xx != Xy )
% 2.28/1.48 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(eqinunit_type,type,
% 2.28/1.48 eqinunit: $o ).
% 2.28/1.48
% 2.28/1.48 thf(eqinunit,definition,
% 2.28/1.48 ( eqinunit
% 2.28/1.48 = ( ! [Xx: $i,Xy: $i] :
% 2.28/1.48 ( ( Xx = Xy )
% 2.28/1.48 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(singletonsswitch_type,type,
% 2.28/1.48 singletonsswitch: $o ).
% 2.28/1.48
% 2.28/1.48 thf(singletonsswitch,definition,
% 2.28/1.48 ( singletonsswitch
% 2.28/1.48 = ( ! [Xx: $i,Xy: $i] :
% 2.28/1.48 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.28/1.48 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(upairsetE_type,type,
% 2.28/1.48 upairsetE: $o ).
% 2.28/1.48
% 2.28/1.48 thf(upairsetE,definition,
% 2.28/1.48 ( upairsetE
% 2.28/1.48 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.28/1.48 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.28/1.48 => ( ( Xz = Xx )
% 2.28/1.48 | ( Xz = Xy ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(upairsetIL_type,type,
% 2.28/1.48 upairsetIL: $o ).
% 2.28/1.48
% 2.28/1.48 thf(upairsetIL,definition,
% 2.28/1.48 ( upairsetIL
% 2.28/1.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(upairsetIR_type,type,
% 2.28/1.48 upairsetIR: $o ).
% 2.28/1.48
% 2.28/1.48 thf(upairsetIR,definition,
% 2.28/1.48 ( upairsetIR
% 2.28/1.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(emptyE1_type,type,
% 2.28/1.48 emptyE1: $o ).
% 2.28/1.48
% 2.28/1.48 thf(emptyE1,definition,
% 2.28/1.48 ( emptyE1
% 2.28/1.48 = ( ! [A: $i,Xphi: $i > $o] :
% 2.28/1.48 ( ? [Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ A )
% 2.28/1.48 & ( Xphi @ Xx ) )
% 2.28/1.48 => ( ( ( dsetconstr @ A
% 2.28/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.28/1.48 = emptyset )
% 2.28/1.48 => $false ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(vacuousDall_type,type,
% 2.28/1.48 vacuousDall: $o ).
% 2.28/1.48
% 2.28/1.48 thf(vacuousDall,definition,
% 2.28/1.48 ( vacuousDall
% 2.28/1.48 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ emptyset )
% 2.28/1.48 => ( Xphi @ Xx ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(quantDeMorgan1_type,type,
% 2.28/1.48 quantDeMorgan1: $o ).
% 2.28/1.48
% 2.28/1.48 thf(quantDeMorgan1,definition,
% 2.28/1.48 ( quantDeMorgan1
% 2.28/1.48 = ( ! [A: $i,Xphi: $i > $o] :
% 2.28/1.48 ( ~ ! [Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ A )
% 2.28/1.48 => ( Xphi @ Xx ) )
% 2.28/1.48 => ? [Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ A )
% 2.28/1.48 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(quantDeMorgan2_type,type,
% 2.28/1.48 quantDeMorgan2: $o ).
% 2.28/1.48
% 2.28/1.48 thf(quantDeMorgan2,definition,
% 2.28/1.48 ( quantDeMorgan2
% 2.28/1.48 = ( ! [A: $i,Xphi: $i > $o] :
% 2.28/1.48 ( ! [Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ A )
% 2.28/1.48 => ~ ( Xphi @ Xx ) )
% 2.28/1.48 => ~ ? [Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ A )
% 2.28/1.48 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(quantDeMorgan3_type,type,
% 2.28/1.48 quantDeMorgan3: $o ).
% 2.28/1.48
% 2.28/1.48 thf(quantDeMorgan3,definition,
% 2.28/1.48 ( quantDeMorgan3
% 2.28/1.48 = ( ! [A: $i,Xphi: $i > $o] :
% 2.28/1.48 ( ~ ? [Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ A )
% 2.28/1.48 & ( Xphi @ Xx ) )
% 2.28/1.48 => ! [Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ A )
% 2.28/1.48 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(quantDeMorgan4_type,type,
% 2.28/1.48 quantDeMorgan4: $o ).
% 2.28/1.48
% 2.28/1.48 thf(quantDeMorgan4,definition,
% 2.28/1.48 ( quantDeMorgan4
% 2.28/1.48 = ( ! [A: $i,Xphi: $i > $o] :
% 2.28/1.48 ( ? [Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ A )
% 2.28/1.48 & ~ ( Xphi @ Xx ) )
% 2.28/1.48 => ~ ! [Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ A )
% 2.28/1.48 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(prop2setI_type,type,
% 2.28/1.48 prop2setI: $o ).
% 2.28/1.48
% 2.28/1.48 thf(prop2setI,definition,
% 2.28/1.48 ( prop2setI
% 2.28/1.48 = ( ! [Xphi: $o] :
% 2.28/1.48 ( Xphi
% 2.28/1.48 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(set2prop_type,type,
% 2.28/1.48 set2prop: $i > $o ).
% 2.28/1.48
% 2.28/1.48 thf(prop2set2propI_type,type,
% 2.28/1.48 prop2set2propI: $o ).
% 2.28/1.48
% 2.28/1.48 thf(prop2set2propI,definition,
% 2.28/1.48 ( prop2set2propI
% 2.28/1.48 = ( ! [Xphi: $o] :
% 2.28/1.48 ( Xphi
% 2.28/1.48 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(notdexE_type,type,
% 2.28/1.48 notdexE: $o ).
% 2.28/1.48
% 2.28/1.48 thf(notdexE,definition,
% 2.28/1.48 ( notdexE
% 2.28/1.48 = ( ! [A: $i,Xphi: $i > $o] :
% 2.28/1.48 ( ~ ? [Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ A )
% 2.28/1.48 & ( Xphi @ Xx ) )
% 2.28/1.48 => ! [Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ A )
% 2.28/1.48 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(notdallE_type,type,
% 2.28/1.48 notdallE: $o ).
% 2.28/1.48
% 2.28/1.48 thf(notdallE,definition,
% 2.28/1.48 ( notdallE
% 2.28/1.48 = ( ! [A: $i,Xphi: $i > $o] :
% 2.28/1.48 ( ~ ! [Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ A )
% 2.28/1.48 => ( Xphi @ Xx ) )
% 2.28/1.48 => ? [Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ A )
% 2.28/1.48 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(exuI1_type,type,
% 2.28/1.48 exuI1: $o ).
% 2.28/1.48
% 2.28/1.48 thf(exuI1,definition,
% 2.28/1.48 ( exuI1
% 2.28/1.48 = ( ! [Xphi: $i > $o] :
% 2.28/1.48 ( ? [Xx: $i] :
% 2.28/1.48 ( ( Xphi @ Xx )
% 2.28/1.48 & ! [Xy: $i] :
% 2.28/1.48 ( ( Xphi @ Xy )
% 2.28/1.48 => ( Xx = Xy ) ) )
% 2.28/1.48 => ( exu
% 2.28/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(exuI3_type,type,
% 2.28/1.48 exuI3: $o ).
% 2.28/1.48
% 2.28/1.48 thf(exuI3,definition,
% 2.28/1.48 ( exuI3
% 2.28/1.48 = ( ! [Xphi: $i > $o] :
% 2.28/1.48 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.28/1.48 => ( ! [Xx: $i,Xy: $i] :
% 2.28/1.48 ( ( Xphi @ Xx )
% 2.28/1.48 => ( ( Xphi @ Xy )
% 2.28/1.48 => ( Xx = Xy ) ) )
% 2.28/1.48 => ( exu
% 2.28/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(exuI2_type,type,
% 2.28/1.48 exuI2: $o ).
% 2.28/1.48
% 2.28/1.48 thf(exuI2,definition,
% 2.28/1.48 ( exuI2
% 2.28/1.48 = ( ! [Xphi: $i > $o] :
% 2.28/1.48 ( ? [Xx: $i] :
% 2.28/1.48 ! [Xy: $i] :
% 2.28/1.48 ( ( Xphi @ Xy )
% 2.28/1.48 <=> ( Xy = Xx ) )
% 2.28/1.48 => ( exu
% 2.28/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(inCongP_type,type,
% 2.28/1.48 inCongP: $o ).
% 2.28/1.48
% 2.28/1.48 thf(inCongP,definition,
% 2.28/1.48 ( inCongP
% 2.28/1.48 = ( ! [A: $i,B: $i] :
% 2.28/1.48 ( ( A = B )
% 2.28/1.48 => ! [Xx: $i,Xy: $i] :
% 2.28/1.48 ( ( Xx = Xy )
% 2.28/1.48 => ( ( in @ Xx @ A )
% 2.28/1.48 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(in__Cong_type,type,
% 2.28/1.48 in__Cong: $o ).
% 2.28/1.48
% 2.28/1.48 thf(in__Cong,definition,
% 2.28/1.48 ( in__Cong
% 2.28/1.48 = ( ! [A: $i,B: $i] :
% 2.28/1.48 ( ( A = B )
% 2.28/1.48 => ! [Xx: $i,Xy: $i] :
% 2.28/1.48 ( ( Xx = Xy )
% 2.28/1.48 => ( ( in @ Xx @ A )
% 2.28/1.48 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(exuE3u_type,type,
% 2.28/1.48 exuE3u: $o ).
% 2.28/1.48
% 2.28/1.48 thf(exuE3u,definition,
% 2.28/1.48 ( exuE3u
% 2.28/1.48 = ( ! [Xphi: $i > $o] :
% 2.28/1.48 ( ( exu
% 2.28/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.28/1.48 => ! [Xx: $i,Xy: $i] :
% 2.28/1.48 ( ( Xphi @ Xx )
% 2.28/1.48 => ( ( Xphi @ Xy )
% 2.28/1.48 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(exu__Cong_type,type,
% 2.28/1.48 exu__Cong: $o ).
% 2.28/1.48
% 2.28/1.48 thf(exu__Cong,definition,
% 2.28/1.48 ( exu__Cong
% 2.28/1.48 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.28/1.48 ( ! [Xx: $i,Xy: $i] :
% 2.28/1.48 ( ( Xx = Xy )
% 2.28/1.48 => ( ( Xphi @ Xx )
% 2.28/1.48 <=> ( Xpsi @ Xy ) ) )
% 2.28/1.48 => ( ( exu
% 2.28/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.28/1.48 <=> ( exu
% 2.28/1.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(emptyset__Cong_type,type,
% 2.28/1.48 emptyset__Cong: $o ).
% 2.28/1.48
% 2.28/1.48 thf(emptyset__Cong,definition,
% 2.28/1.48 ( emptyset__Cong
% 2.28/1.48 = ( emptyset = emptyset ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(setadjoin__Cong_type,type,
% 2.28/1.48 setadjoin__Cong: $o ).
% 2.28/1.48
% 2.28/1.48 thf(setadjoin__Cong,definition,
% 2.28/1.48 ( setadjoin__Cong
% 2.28/1.48 = ( ! [Xx: $i,Xy: $i] :
% 2.28/1.48 ( ( Xx = Xy )
% 2.28/1.48 => ! [Xz: $i,Xu: $i] :
% 2.28/1.48 ( ( Xz = Xu )
% 2.28/1.48 => ( ( setadjoin @ Xx @ Xz )
% 2.28/1.48 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(powerset__Cong_type,type,
% 2.28/1.48 powerset__Cong: $o ).
% 2.28/1.48
% 2.28/1.48 thf(powerset__Cong,definition,
% 2.28/1.48 ( powerset__Cong
% 2.28/1.48 = ( ! [A: $i,B: $i] :
% 2.28/1.48 ( ( A = B )
% 2.28/1.48 => ( ( powerset @ A )
% 2.28/1.48 = ( powerset @ B ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(setunion__Cong_type,type,
% 2.28/1.48 setunion__Cong: $o ).
% 2.28/1.48
% 2.28/1.48 thf(setunion__Cong,definition,
% 2.28/1.48 ( setunion__Cong
% 2.28/1.48 = ( ! [A: $i,B: $i] :
% 2.28/1.48 ( ( A = B )
% 2.28/1.48 => ( ( setunion @ A )
% 2.28/1.48 = ( setunion @ B ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(omega__Cong_type,type,
% 2.28/1.48 omega__Cong: $o ).
% 2.28/1.48
% 2.28/1.48 thf(omega__Cong,definition,
% 2.28/1.48 ( omega__Cong
% 2.28/1.48 = ( omega = omega ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(exuEu_type,type,
% 2.28/1.48 exuEu: $o ).
% 2.28/1.48
% 2.28/1.48 thf(exuEu,definition,
% 2.28/1.48 ( exuEu
% 2.28/1.48 = ( ! [Xphi: $i > $o] :
% 2.28/1.48 ( ( exu
% 2.28/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.28/1.48 => ! [Xx: $i,Xy: $i] :
% 2.28/1.48 ( ( Xphi @ Xx )
% 2.28/1.48 => ( ( Xphi @ Xy )
% 2.28/1.48 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(descr__Cong_type,type,
% 2.28/1.48 descr__Cong: $o ).
% 2.28/1.48
% 2.28/1.48 thf(descr__Cong,definition,
% 2.28/1.48 ( descr__Cong
% 2.28/1.48 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.28/1.48 ( ! [Xx: $i,Xy: $i] :
% 2.28/1.48 ( ( Xx = Xy )
% 2.28/1.48 => ( ( Xphi @ Xx )
% 2.28/1.48 <=> ( Xpsi @ Xy ) ) )
% 2.28/1.48 => ( ( exu
% 2.28/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.28/1.48 => ( ( exu
% 2.28/1.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.28/1.48 => ( ( descr
% 2.28/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.28/1.48 = ( descr
% 2.28/1.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(dsetconstr__Cong_type,type,
% 2.28/1.48 dsetconstr__Cong: $o ).
% 2.28/1.48
% 2.28/1.48 thf(dsetconstr__Cong,definition,
% 2.28/1.48 ( dsetconstr__Cong
% 2.28/1.48 = ( ! [A: $i,B: $i] :
% 2.28/1.48 ( ( A = B )
% 2.28/1.48 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.28/1.48 ( ! [Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ A )
% 2.28/1.48 => ! [Xy: $i] :
% 2.28/1.48 ( ( in @ Xy @ B )
% 2.28/1.48 => ( ( Xx = Xy )
% 2.28/1.48 => ( ( Xphi @ Xx )
% 2.28/1.48 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.28/1.48 => ( ( dsetconstr @ A
% 2.28/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.28/1.48 = ( dsetconstr @ B
% 2.28/1.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(subset_type,type,
% 2.28/1.48 subset: $i > $i > $o ).
% 2.28/1.48
% 2.28/1.48 thf(disjoint_type,type,
% 2.28/1.48 disjoint: $i > $i > $o ).
% 2.28/1.48
% 2.28/1.48 thf(setsmeet_type,type,
% 2.28/1.48 setsmeet: $i > $i > $o ).
% 2.28/1.48
% 2.28/1.48 thf(subsetI1_type,type,
% 2.28/1.48 subsetI1: $o ).
% 2.28/1.48
% 2.28/1.48 thf(subsetI1,definition,
% 2.28/1.48 ( subsetI1
% 2.28/1.48 = ( ! [A: $i,B: $i] :
% 2.28/1.48 ( ! [Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ A )
% 2.28/1.48 => ( in @ Xx @ B ) )
% 2.28/1.48 => ( subset @ A @ B ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(eqimpsubset2_type,type,
% 2.28/1.48 eqimpsubset2: $o ).
% 2.28/1.48
% 2.28/1.48 thf(eqimpsubset2,definition,
% 2.28/1.48 ( eqimpsubset2
% 2.28/1.48 = ( ! [A: $i,B: $i] :
% 2.28/1.48 ( ( A = B )
% 2.28/1.48 => ( subset @ B @ A ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(eqimpsubset1_type,type,
% 2.28/1.48 eqimpsubset1: $o ).
% 2.28/1.48
% 2.28/1.48 thf(eqimpsubset1,definition,
% 2.28/1.48 ( eqimpsubset1
% 2.28/1.48 = ( ! [A: $i,B: $i] :
% 2.28/1.48 ( ( A = B )
% 2.28/1.48 => ( subset @ A @ B ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(subsetI2_type,type,
% 2.28/1.48 subsetI2: $o ).
% 2.28/1.48
% 2.28/1.48 thf(subsetI2,definition,
% 2.28/1.48 ( subsetI2
% 2.28/1.48 = ( ! [A: $i,B: $i] :
% 2.28/1.48 ( ! [Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ A )
% 2.28/1.48 => ( in @ Xx @ B ) )
% 2.28/1.48 => ( subset @ A @ B ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(emptysetsubset_type,type,
% 2.28/1.48 emptysetsubset: $o ).
% 2.28/1.48
% 2.28/1.48 thf(emptysetsubset,definition,
% 2.28/1.48 ( emptysetsubset
% 2.28/1.48 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(subsetE_type,type,
% 2.28/1.48 subsetE: $o ).
% 2.28/1.48
% 2.28/1.48 thf(subsetE,definition,
% 2.28/1.48 ( subsetE
% 2.28/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.28/1.48 ( ( subset @ A @ B )
% 2.28/1.48 => ( ( in @ Xx @ A )
% 2.28/1.48 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(subsetE2_type,type,
% 2.28/1.48 subsetE2: $o ).
% 2.28/1.48
% 2.28/1.48 thf(subsetE2,definition,
% 2.28/1.48 ( subsetE2
% 2.28/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.28/1.48 ( ( subset @ A @ B )
% 2.28/1.48 => ( ~ ( in @ Xx @ B )
% 2.28/1.48 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(notsubsetI_type,type,
% 2.28/1.48 notsubsetI: $o ).
% 2.28/1.48
% 2.28/1.48 thf(notsubsetI,definition,
% 2.28/1.48 ( notsubsetI
% 2.28/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ A )
% 2.28/1.48 => ( ~ ( in @ Xx @ B )
% 2.28/1.48 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(notequalI1_type,type,
% 2.28/1.48 notequalI1: $o ).
% 2.28/1.48
% 2.28/1.48 thf(notequalI1,definition,
% 2.28/1.48 ( notequalI1
% 2.28/1.48 = ( ! [A: $i,B: $i] :
% 2.28/1.48 ( ~ ( subset @ A @ B )
% 2.28/1.48 => ( A != B ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(notequalI2_type,type,
% 2.28/1.48 notequalI2: $o ).
% 2.28/1.48
% 2.28/1.48 thf(notequalI2,definition,
% 2.28/1.48 ( notequalI2
% 2.28/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ A )
% 2.28/1.48 => ( ~ ( in @ Xx @ B )
% 2.28/1.48 => ( A != B ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(subsetRefl_type,type,
% 2.28/1.48 subsetRefl: $o ).
% 2.28/1.48
% 2.28/1.48 thf(subsetRefl,definition,
% 2.28/1.48 ( subsetRefl
% 2.28/1.48 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(subsetTrans_type,type,
% 2.28/1.48 subsetTrans: $o ).
% 2.28/1.48
% 2.28/1.48 thf(subsetTrans,definition,
% 2.28/1.48 ( subsetTrans
% 2.28/1.48 = ( ! [A: $i,B: $i,C: $i] :
% 2.28/1.48 ( ( subset @ A @ B )
% 2.28/1.48 => ( ( subset @ B @ C )
% 2.28/1.48 => ( subset @ A @ C ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(setadjoinSub_type,type,
% 2.28/1.48 setadjoinSub: $o ).
% 2.28/1.48
% 2.28/1.48 thf(setadjoinSub,definition,
% 2.28/1.48 ( setadjoinSub
% 2.28/1.48 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(setadjoinSub2_type,type,
% 2.28/1.48 setadjoinSub2: $o ).
% 2.28/1.48
% 2.28/1.48 thf(setadjoinSub2,definition,
% 2.28/1.48 ( setadjoinSub2
% 2.28/1.48 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.28/1.48 ( ( subset @ A @ B )
% 2.28/1.48 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(subset2powerset_type,type,
% 2.28/1.48 subset2powerset: $o ).
% 2.28/1.48
% 2.28/1.48 thf(subset2powerset,definition,
% 2.28/1.48 ( subset2powerset
% 2.28/1.48 = ( ! [A: $i,B: $i] :
% 2.28/1.48 ( ( subset @ A @ B )
% 2.28/1.48 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(setextsub_type,type,
% 2.28/1.48 setextsub: $o ).
% 2.28/1.48
% 2.28/1.48 thf(setextsub,definition,
% 2.28/1.48 ( setextsub
% 2.28/1.48 = ( ! [A: $i,B: $i] :
% 2.28/1.48 ( ( subset @ A @ B )
% 2.28/1.48 => ( ( subset @ B @ A )
% 2.28/1.48 => ( A = B ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(subsetemptysetimpeq_type,type,
% 2.28/1.48 subsetemptysetimpeq: $o ).
% 2.28/1.48
% 2.28/1.48 thf(subsetemptysetimpeq,definition,
% 2.28/1.48 ( subsetemptysetimpeq
% 2.28/1.48 = ( ! [A: $i] :
% 2.28/1.48 ( ( subset @ A @ emptyset )
% 2.28/1.48 => ( A = emptyset ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(powersetI1_type,type,
% 2.28/1.48 powersetI1: $o ).
% 2.28/1.48
% 2.28/1.48 thf(powersetI1,definition,
% 2.28/1.48 ( powersetI1
% 2.28/1.48 = ( ! [A: $i,B: $i] :
% 2.28/1.48 ( ( subset @ B @ A )
% 2.28/1.48 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(powersetE1_type,type,
% 2.28/1.48 powersetE1: $o ).
% 2.28/1.48
% 2.28/1.48 thf(powersetE1,definition,
% 2.28/1.48 ( powersetE1
% 2.28/1.48 = ( ! [A: $i,B: $i] :
% 2.28/1.48 ( ( in @ B @ ( powerset @ A ) )
% 2.28/1.48 => ( subset @ B @ A ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(inPowerset_type,type,
% 2.28/1.48 inPowerset: $o ).
% 2.28/1.48
% 2.28/1.48 thf(inPowerset,definition,
% 2.28/1.48 ( inPowerset
% 2.28/1.48 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(powersetsubset_type,type,
% 2.28/1.48 powersetsubset: $o ).
% 2.28/1.48
% 2.28/1.48 thf(powersetsubset,definition,
% 2.28/1.48 ( powersetsubset
% 2.28/1.48 = ( ! [A: $i,B: $i] :
% 2.28/1.48 ( ( subset @ A @ B )
% 2.28/1.48 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(sepInPowerset_type,type,
% 2.28/1.48 sepInPowerset: $o ).
% 2.28/1.48
% 2.28/1.48 thf(sepInPowerset,definition,
% 2.28/1.48 ( sepInPowerset
% 2.28/1.48 = ( ! [A: $i,Xphi: $i > $o] :
% 2.28/1.48 ( in
% 2.28/1.48 @ ( dsetconstr @ A
% 2.28/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.28/1.48 @ ( powerset @ A ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(sepSubset_type,type,
% 2.28/1.48 sepSubset: $o ).
% 2.28/1.48
% 2.28/1.48 thf(sepSubset,definition,
% 2.28/1.48 ( sepSubset
% 2.28/1.48 = ( ! [A: $i,Xphi: $i > $o] :
% 2.28/1.48 ( subset
% 2.28/1.48 @ ( dsetconstr @ A
% 2.28/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.28/1.48 @ A ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(binunion_type,type,
% 2.28/1.48 binunion: $i > $i > $i ).
% 2.28/1.48
% 2.28/1.48 thf(binunionIL_type,type,
% 2.28/1.48 binunionIL: $o ).
% 2.28/1.48
% 2.28/1.48 thf(binunionIL,definition,
% 2.28/1.48 ( binunionIL
% 2.28/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ A )
% 2.28/1.48 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(upairset2IR_type,type,
% 2.28/1.48 upairset2IR: $o ).
% 2.28/1.48
% 2.28/1.48 thf(upairset2IR,definition,
% 2.28/1.48 ( upairset2IR
% 2.28/1.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(binunionIR_type,type,
% 2.28/1.48 binunionIR: $o ).
% 2.28/1.48
% 2.28/1.48 thf(binunionIR,definition,
% 2.28/1.48 ( binunionIR
% 2.28/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ B )
% 2.28/1.48 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(binunionEcases_type,type,
% 2.28/1.48 binunionEcases: $o ).
% 2.28/1.48
% 2.28/1.48 thf(binunionEcases,definition,
% 2.28/1.48 ( binunionEcases
% 2.28/1.48 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.28/1.48 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.28/1.48 => ( ( ( in @ Xx @ A )
% 2.28/1.48 => Xphi )
% 2.28/1.48 => ( ( ( in @ Xx @ B )
% 2.28/1.48 => Xphi )
% 2.28/1.48 => Xphi ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(binunionE_type,type,
% 2.28/1.48 binunionE: $o ).
% 2.28/1.48
% 2.28/1.48 thf(binunionE,definition,
% 2.28/1.48 ( binunionE
% 2.28/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.28/1.48 => ( ( in @ Xx @ A )
% 2.28/1.48 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(binunionLsub_type,type,
% 2.28/1.48 binunionLsub: $o ).
% 2.28/1.48
% 2.28/1.48 thf(binunionLsub,definition,
% 2.28/1.48 ( binunionLsub
% 2.28/1.48 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(binunionRsub_type,type,
% 2.28/1.48 binunionRsub: $o ).
% 2.28/1.48
% 2.28/1.48 thf(binunionRsub,definition,
% 2.28/1.48 ( binunionRsub
% 2.28/1.48 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(binintersect_type,type,
% 2.28/1.48 binintersect: $i > $i > $i ).
% 2.28/1.48
% 2.28/1.48 thf(binintersectI_type,type,
% 2.28/1.48 binintersectI: $o ).
% 2.28/1.48
% 2.28/1.48 thf(binintersectI,definition,
% 2.28/1.48 ( binintersectI
% 2.28/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ A )
% 2.28/1.48 => ( ( in @ Xx @ B )
% 2.28/1.48 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(binintersectSubset5_type,type,
% 2.28/1.48 binintersectSubset5: $o ).
% 2.28/1.48
% 2.28/1.48 thf(binintersectSubset5,definition,
% 2.28/1.48 ( binintersectSubset5
% 2.28/1.48 = ( ! [A: $i,B: $i,C: $i] :
% 2.28/1.48 ( ( subset @ C @ A )
% 2.28/1.48 => ( ( subset @ C @ B )
% 2.28/1.48 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(binintersectEL_type,type,
% 2.28/1.48 binintersectEL: $o ).
% 2.28/1.48
% 2.28/1.48 thf(binintersectEL,definition,
% 2.28/1.48 ( binintersectEL
% 2.28/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.28/1.48 => ( in @ Xx @ A ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(binintersectLsub_type,type,
% 2.28/1.48 binintersectLsub: $o ).
% 2.28/1.48
% 2.28/1.48 thf(binintersectLsub,definition,
% 2.28/1.48 ( binintersectLsub
% 2.28/1.48 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(binintersectSubset2_type,type,
% 2.28/1.48 binintersectSubset2: $o ).
% 2.28/1.48
% 2.28/1.48 thf(binintersectSubset2,definition,
% 2.28/1.48 ( binintersectSubset2
% 2.28/1.48 = ( ! [A: $i,B: $i] :
% 2.28/1.48 ( ( subset @ A @ B )
% 2.28/1.48 => ( ( binintersect @ A @ B )
% 2.28/1.48 = A ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(binintersectSubset3_type,type,
% 2.28/1.48 binintersectSubset3: $o ).
% 2.28/1.48
% 2.28/1.48 thf(binintersectSubset3,definition,
% 2.28/1.48 ( binintersectSubset3
% 2.28/1.48 = ( ! [A: $i,B: $i] :
% 2.28/1.48 ( ( ( binintersect @ A @ B )
% 2.28/1.48 = B )
% 2.28/1.48 => ( subset @ B @ A ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(binintersectER_type,type,
% 2.28/1.48 binintersectER: $o ).
% 2.28/1.48
% 2.28/1.48 thf(binintersectER,definition,
% 2.28/1.48 ( binintersectER
% 2.28/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.28/1.48 => ( in @ Xx @ B ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(disjointsetsI1_type,type,
% 2.28/1.48 disjointsetsI1: $o ).
% 2.28/1.48
% 2.28/1.48 thf(disjointsetsI1,definition,
% 2.28/1.48 ( disjointsetsI1
% 2.28/1.48 = ( ! [A: $i,B: $i] :
% 2.28/1.48 ( ~ ? [Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ A )
% 2.28/1.48 & ( in @ Xx @ B ) )
% 2.28/1.48 => ( ( binintersect @ A @ B )
% 2.28/1.48 = emptyset ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(binintersectRsub_type,type,
% 2.28/1.48 binintersectRsub: $o ).
% 2.28/1.48
% 2.28/1.48 thf(binintersectRsub,definition,
% 2.28/1.48 ( binintersectRsub
% 2.28/1.48 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(binintersectSubset4_type,type,
% 2.28/1.48 binintersectSubset4: $o ).
% 2.28/1.48
% 2.28/1.48 thf(binintersectSubset4,definition,
% 2.28/1.48 ( binintersectSubset4
% 2.28/1.48 = ( ! [A: $i,B: $i] :
% 2.28/1.48 ( ( subset @ B @ A )
% 2.28/1.48 => ( ( binintersect @ A @ B )
% 2.28/1.48 = B ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(binintersectSubset1_type,type,
% 2.28/1.48 binintersectSubset1: $o ).
% 2.28/1.48
% 2.28/1.48 thf(binintersectSubset1,definition,
% 2.28/1.48 ( binintersectSubset1
% 2.28/1.48 = ( ! [A: $i,B: $i] :
% 2.28/1.48 ( ( ( binintersect @ A @ B )
% 2.28/1.48 = A )
% 2.28/1.48 => ( subset @ A @ B ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(bs114d_type,type,
% 2.28/1.48 bs114d: $o ).
% 2.28/1.48
% 2.28/1.48 thf(bs114d,definition,
% 2.28/1.48 ( bs114d
% 2.28/1.48 = ( ! [A: $i,B: $i,C: $i] :
% 2.28/1.48 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.28/1.48 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(regular_type,type,
% 2.28/1.48 regular: $i > $o ).
% 2.28/1.48
% 2.28/1.48 thf(setminus_type,type,
% 2.28/1.48 setminus: $i > $i > $i ).
% 2.28/1.48
% 2.28/1.48 thf(setminusI_type,type,
% 2.28/1.48 setminusI: $o ).
% 2.28/1.48
% 2.28/1.48 thf(setminusI,definition,
% 2.28/1.48 ( setminusI
% 2.28/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ A )
% 2.28/1.48 => ( ~ ( in @ Xx @ B )
% 2.28/1.48 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(setminusEL_type,type,
% 2.28/1.48 setminusEL: $o ).
% 2.28/1.48
% 2.28/1.48 thf(setminusEL,definition,
% 2.28/1.48 ( setminusEL
% 2.28/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.28/1.48 => ( in @ Xx @ A ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(setminusER_type,type,
% 2.28/1.48 setminusER: $o ).
% 2.28/1.48
% 2.28/1.48 thf(setminusER,definition,
% 2.28/1.48 ( setminusER
% 2.28/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.28/1.48 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(setminusSubset2_type,type,
% 2.28/1.48 setminusSubset2: $o ).
% 2.28/1.48
% 2.28/1.48 thf(setminusSubset2,definition,
% 2.28/1.48 ( setminusSubset2
% 2.28/1.48 = ( ! [A: $i,B: $i] :
% 2.28/1.48 ( ( subset @ A @ B )
% 2.28/1.48 => ( ( setminus @ A @ B )
% 2.28/1.48 = emptyset ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(setminusERneg_type,type,
% 2.28/1.48 setminusERneg: $o ).
% 2.28/1.48
% 2.28/1.48 thf(setminusERneg,definition,
% 2.28/1.48 ( setminusERneg
% 2.28/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.28/1.48 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.28/1.48 => ( ( in @ Xx @ A )
% 2.28/1.48 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(setminusELneg_type,type,
% 2.28/1.48 setminusELneg: $o ).
% 2.28/1.48
% 2.28/1.48 thf(setminusELneg,definition,
% 2.28/1.48 ( setminusELneg
% 2.28/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.28/1.48 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.28/1.48 => ( ~ ( in @ Xx @ B )
% 2.28/1.48 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(setminusILneg_type,type,
% 2.28/1.48 setminusILneg: $o ).
% 2.28/1.48
% 2.28/1.48 thf(setminusILneg,definition,
% 2.28/1.48 ( setminusILneg
% 2.28/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.28/1.48 ( ~ ( in @ Xx @ A )
% 2.28/1.48 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(setminusIRneg_type,type,
% 2.28/1.48 setminusIRneg: $o ).
% 2.28/1.48
% 2.28/1.48 thf(setminusIRneg,definition,
% 2.28/1.48 ( setminusIRneg
% 2.28/1.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.28/1.48 ( ( in @ Xx @ B )
% 2.28/1.48 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(setminusLsub_type,type,
% 2.28/1.48 setminusLsub: $o ).
% 2.28/1.48
% 2.28/1.48 thf(setminusLsub,definition,
% 2.28/1.48 ( setminusLsub
% 2.28/1.48 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.28/1.48
% 2.28/1.48 thf(setminusSubset1,conjecture,
% 2.28/1.48 ( setextAx
% 2.28/1.48 => ( emptysetAx
% 2.28/1.48 => ( setadjoinAx
% 2.28/1.48 => ( powersetAx
% 2.28/1.48 => ( setunionAx
% 2.28/1.48 => ( omega0Ax
% 2.28/1.48 => ( omegaSAx
% 2.28/1.48 => ( omegaIndAx
% 2.28/1.48 => ( replAx
% 2.28/1.48 => ( foundationAx
% 2.28/1.48 => ( wellorderingAx
% 2.28/1.48 => ( descrp
% 2.28/1.48 => ( dsetconstrI
% 2.28/1.48 => ( dsetconstrEL
% 2.28/1.48 => ( dsetconstrER
% 2.28/1.48 => ( exuE1
% 2.28/1.48 => ( prop2setE
% 2.28/1.48 => ( emptysetE
% 2.28/1.48 => ( emptysetimpfalse
% 2.28/1.48 => ( notinemptyset
% 2.28/1.48 => ( exuE3e
% 2.28/1.48 => ( setext
% 2.28/1.48 => ( emptyI
% 2.28/1.48 => ( noeltsimpempty
% 2.28/1.48 => ( setbeta
% 2.28/1.48 => ( nonemptyE1
% 2.28/1.48 => ( nonemptyI
% 2.28/1.48 => ( nonemptyI1
% 2.28/1.48 => ( setadjoinIL
% 2.28/1.48 => ( emptyinunitempty
% 2.28/1.48 => ( setadjoinIR
% 2.28/1.48 => ( setadjoinE
% 2.28/1.48 => ( setadjoinOr
% 2.28/1.48 => ( setoftrueEq
% 2.28/1.48 => ( powersetI
% 2.28/1.48 => ( emptyinPowerset
% 2.28/1.48 => ( emptyInPowerset
% 2.28/1.48 => ( powersetE
% 2.28/1.48 => ( setunionI
% 2.28/1.48 => ( setunionE
% 2.28/1.48 => ( subPowSU
% 2.28/1.48 => ( exuE2
% 2.28/1.48 => ( nonemptyImpWitness
% 2.28/1.48 => ( uniqinunit
% 2.28/1.48 => ( notinsingleton
% 2.28/1.48 => ( eqinunit
% 2.28/1.48 => ( singletonsswitch
% 2.28/1.48 => ( upairsetE
% 2.28/1.48 => ( upairsetIL
% 2.28/1.48 => ( upairsetIR
% 2.28/1.48 => ( emptyE1
% 2.28/1.48 => ( vacuousDall
% 2.28/1.48 => ( quantDeMorgan1
% 2.28/1.48 => ( quantDeMorgan2
% 2.28/1.48 => ( quantDeMorgan3
% 2.28/1.48 => ( quantDeMorgan4
% 2.28/1.48 => ( prop2setI
% 2.28/1.48 => ( prop2set2propI
% 2.28/1.48 => ( notdexE
% 2.28/1.48 => ( notdallE
% 2.28/1.48 => ( exuI1
% 2.28/1.48 => ( exuI3
% 2.28/1.48 => ( exuI2
% 2.28/1.48 => ( inCongP
% 2.28/1.48 => ( in__Cong
% 2.28/1.48 => ( exuE3u
% 2.28/1.48 => ( exu__Cong
% 2.28/1.48 => ( emptyset__Cong
% 2.28/1.48 => ( setadjoin__Cong
% 2.28/1.48 => ( powerset__Cong
% 2.28/1.48 => ( setunion__Cong
% 2.28/1.48 => ( omega__Cong
% 2.28/1.48 => ( exuEu
% 2.28/1.48 => ( descr__Cong
% 2.28/1.48 => ( dsetconstr__Cong
% 2.28/1.48 => ( subsetI1
% 2.28/1.48 => ( eqimpsubset2
% 2.28/1.48 => ( eqimpsubset1
% 2.28/1.48 => ( subsetI2
% 2.28/1.48 => ( emptysetsubset
% 2.28/1.48 => ( subsetE
% 2.28/1.48 => ( subsetE2
% 2.28/1.48 => ( notsubsetI
% 2.28/1.48 => ( notequalI1
% 2.28/1.48 => ( notequalI2
% 2.28/1.48 => ( subsetRefl
% 2.28/1.48 => ( subsetTrans
% 2.28/1.48 => ( setadjoinSub
% 2.28/1.48 => ( setadjoinSub2
% 2.28/1.48 => ( subset2powerset
% 2.28/1.48 => ( setextsub
% 2.28/1.48 => ( subsetemptysetimpeq
% 2.28/1.48 => ( powersetI1
% 2.28/1.48 => ( powersetE1
% 2.28/1.48 => ( inPowerset
% 2.28/1.48 => ( powersetsubset
% 2.28/1.48 => ( sepInPowerset
% 2.28/1.48 => ( sepSubset
% 2.28/1.48 => ( binunionIL
% 2.28/1.48 => ( upairset2IR
% 2.28/1.48 => ( binunionIR
% 2.28/1.48 => ( binunionEcases
% 2.28/1.48 => ( binunionE
% 2.28/1.48 => ( binunionLsub
% 2.28/1.48 => ( binunionRsub
% 2.28/1.48 => ( binintersectI
% 2.28/1.48 => ( binintersectSubset5
% 2.28/1.48 => ( binintersectEL
% 2.28/1.48 => ( binintersectLsub
% 2.28/1.48 => ( binintersectSubset2
% 2.28/1.48 => ( binintersectSubset3
% 2.28/1.48 => ( binintersectER
% 2.28/1.48 => ( disjointsetsI1
% 2.28/1.48 => ( binintersectRsub
% 2.28/1.48 => ( binintersectSubset4
% 2.28/1.48 => ( binintersectSubset1
% 2.28/1.48 => ( bs114d
% 2.28/1.48 => ( setminusI
% 2.28/1.48 => ( setminusEL
% 2.28/1.48 => ( setminusER
% 2.28/1.48 => ( setminusSubset2
% 2.28/1.48 => ( setminusERneg
% 2.28/1.48 => ( setminusELneg
% 2.28/1.48 => ( setminusILneg
% 2.28/1.48 => ( setminusIRneg
% 2.28/1.48 => ( setminusLsub
% 2.28/1.48 => ! [A: $i,B: $i] :
% 2.28/1.48 ( ( ( setminus @ A @ B )
% 2.28/1.48 = emptyset )
% 2.28/1.48 => ( subset @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.28/1.48 ------------------------
% 2.28/1.49 % (14223)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13954 for (2999ds/183Mi)
% 2.28/1.49 % (14224)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_13954 for (2999ds/4Mi)
% 2.28/1.49 % (14227)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_13954 for (2999ds/2Mi)
% 2.28/1.49 % (14227)Instruction limit reached!
% 2.28/1.49 % (14227)------------------------------
% 2.28/1.49 % (14227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.49 % (14227)Termination reason: Unknown
% 2.28/1.49 % (14227)Termination phase: shuffling
% 2.28/1.49
% 2.28/1.49 % (14227)Memory used [KB]: 1151
% 2.28/1.49 % (14227)Time elapsed: 0.002 s
% 2.28/1.49 % (14227)Instructions burned: 3 (million)
% 2.28/1.49 % (14227)------------------------------
% 2.28/1.49 % (14227)------------------------------
% 2.28/1.50 % (14224)Instruction limit reached!
% 2.28/1.50 % (14224)------------------------------
% 2.28/1.50 % (14224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.28/1.50 % (14224)Termination reason: Unknown
% 2.28/1.50 % (14224)Termination phase: shuffling
% 2.28/1.50
% 2.28/1.50 % (14224)Memory used [KB]: 1279
% 2.28/1.50 % (14224)Time elapsed: 0.003 s
% 2.28/1.50 % (14224)Instructions burned: 6 (million)
% 2.28/1.50 % (14224)------------------------------
% 2.28/1.50 % (14224)------------------------------
% 2.47/1.50 % (14225)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_13954 for (2999ds/27Mi)
% 2.47/1.50 % (14226)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13954 for (2999ds/2Mi)
% 2.47/1.50 % (14228)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_13954 for (2999ds/275Mi)
% 2.47/1.50 % (14229)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13954 for (2999ds/18Mi)
% 2.47/1.50 % (14226)Instruction limit reached!
% 2.47/1.50 % (14226)------------------------------
% 2.47/1.50 % (14226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.50 % (14226)Termination reason: Unknown
% 2.47/1.50 % (14226)Termination phase: shuffling
% 2.47/1.50
% 2.47/1.50 % (14226)Memory used [KB]: 1151
% 2.47/1.50 % (14226)Time elapsed: 0.004 s
% 2.47/1.50 % (14226)Instructions burned: 3 (million)
% 2.47/1.50 % (14226)------------------------------
% 2.47/1.50 % (14226)------------------------------
% 2.47/1.51 % (14230)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_13954 for (2999ds/3Mi)
% 2.47/1.51 % (14231)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_13954 for (2999ds/37Mi)
% 2.47/1.51 % (14230)Instruction limit reached!
% 2.47/1.51 % (14230)------------------------------
% 2.47/1.51 % (14230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.51 % (14230)Termination reason: Unknown
% 2.47/1.51 % (14230)Termination phase: shuffling
% 2.47/1.51
% 2.47/1.51 % (14230)Memory used [KB]: 1279
% 2.47/1.51 % (14230)Time elapsed: 0.003 s
% 2.47/1.51 % (14230)Instructions burned: 4 (million)
% 2.47/1.51 % (14230)------------------------------
% 2.47/1.51 % (14230)------------------------------
% 2.47/1.51 % (14229)Instruction limit reached!
% 2.47/1.51 % (14229)------------------------------
% 2.47/1.51 % (14229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.51 % (14229)Termination reason: Unknown
% 2.47/1.51 % (14229)Termination phase: Preprocessing 3
% 2.47/1.51
% 2.47/1.51 % (14229)Memory used [KB]: 1535
% 2.47/1.51 % (14229)Time elapsed: 0.013 s
% 2.47/1.51 % (14229)Instructions burned: 19 (million)
% 2.47/1.51 % (14229)------------------------------
% 2.47/1.51 % (14229)------------------------------
% 2.47/1.51 % (14225)Instruction limit reached!
% 2.47/1.51 % (14225)------------------------------
% 2.47/1.51 % (14225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.51 % (14225)Termination reason: Unknown
% 2.47/1.51 % (14225)Termination phase: Property scanning
% 2.47/1.51
% 2.47/1.51 % (14225)Memory used [KB]: 1535
% 2.47/1.51 % (14225)Time elapsed: 0.016 s
% 2.47/1.51 % (14225)Instructions burned: 28 (million)
% 2.47/1.51 % (14225)------------------------------
% 2.47/1.51 % (14225)------------------------------
% 2.47/1.52 % (14233)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_13954 for (2999ds/3Mi)
% 2.47/1.52 % (14231)Instruction limit reached!
% 2.47/1.52 % (14231)------------------------------
% 2.47/1.52 % (14231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.52 % (14231)Termination reason: Unknown
% 2.47/1.52 % (14231)Termination phase: Property scanning
% 2.47/1.52
% 2.47/1.52 % (14231)Memory used [KB]: 1663
% 2.47/1.52 % (14231)Time elapsed: 0.012 s
% 2.47/1.52 % (14231)Instructions burned: 37 (million)
% 2.47/1.52 % (14231)------------------------------
% 2.47/1.52 % (14231)------------------------------
% 2.47/1.52 % (14233)Instruction limit reached!
% 2.47/1.52 % (14233)------------------------------
% 2.47/1.52 % (14233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.52 % (14233)Termination reason: Unknown
% 2.47/1.52 % (14233)Termination phase: shuffling
% 2.47/1.52
% 2.47/1.52 % (14233)Memory used [KB]: 1279
% 2.47/1.52 % (14233)Time elapsed: 0.003 s
% 2.47/1.52 % (14233)Instructions burned: 6 (million)
% 2.47/1.52 % (14233)------------------------------
% 2.47/1.52 % (14233)------------------------------
% 2.47/1.52 % (14232)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_13954 for (2999ds/15Mi)
% 2.47/1.53 % (14236)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_13954 for (2999ds/16Mi)
% 2.47/1.53 % (14237)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_13954 for (2999ds/3Mi)
% 2.47/1.53 % (14237)Instruction limit reached!
% 2.47/1.53 % (14237)------------------------------
% 2.47/1.53 % (14237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.53 % (14237)Termination reason: Unknown
% 2.47/1.53 % (14237)Termination phase: shuffling
% 2.47/1.53
% 2.47/1.53 % (14237)Memory used [KB]: 1151
% 2.47/1.53 % (14237)Time elapsed: 0.002 s
% 2.47/1.53 % (14237)Instructions burned: 4 (million)
% 2.47/1.53 % (14237)------------------------------
% 2.47/1.53 % (14237)------------------------------
% 2.47/1.53 % (14232)Instruction limit reached!
% 2.47/1.53 % (14232)------------------------------
% 2.47/1.53 % (14232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.53 % (14232)Termination reason: Unknown
% 2.47/1.53 % (14232)Termination phase: Preprocessing 1
% 2.47/1.53
% 2.47/1.53 % (14232)Memory used [KB]: 1407
% 2.47/1.53 % (14232)Time elapsed: 0.011 s
% 2.47/1.53 % (14232)Instructions burned: 16 (million)
% 2.47/1.53 % (14232)------------------------------
% 2.47/1.53 % (14232)------------------------------
% 2.47/1.53 % (14234)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_13954 for (2999ds/1041Mi)
% 2.47/1.53 % (14236)Instruction limit reached!
% 2.47/1.53 % (14236)------------------------------
% 2.47/1.53 % (14236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.53 % (14236)Termination reason: Unknown
% 2.47/1.53 % (14236)Termination phase: shuffling
% 2.47/1.53
% 2.47/1.53 % (14236)Memory used [KB]: 1535
% 2.47/1.53 % (14236)Time elapsed: 0.007 s
% 2.47/1.53 % (14236)Instructions burned: 18 (million)
% 2.47/1.53 % (14236)------------------------------
% 2.47/1.53 % (14236)------------------------------
% 2.47/1.53 % (14235)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_13954 for (2999ds/7Mi)
% 2.47/1.54 % (14235)Instruction limit reached!
% 2.47/1.54 % (14235)------------------------------
% 2.47/1.54 % (14235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.54 % (14235)Termination reason: Unknown
% 2.47/1.54 % (14235)Termination phase: shuffling
% 2.47/1.54
% 2.47/1.54 % (14235)Memory used [KB]: 1279
% 2.47/1.54 % (14235)Time elapsed: 0.006 s
% 2.47/1.54 % (14235)Instructions burned: 8 (million)
% 2.47/1.54 % (14235)------------------------------
% 2.47/1.54 % (14235)------------------------------
% 2.47/1.54 % (14238)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_13954 for (2999ds/3Mi)
% 2.47/1.54 % (14238)Instruction limit reached!
% 2.47/1.54 % (14238)------------------------------
% 2.47/1.54 % (14238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.54 % (14238)Termination reason: Unknown
% 2.47/1.54 % (14238)Termination phase: shuffling
% 2.47/1.54
% 2.47/1.54 % (14238)Memory used [KB]: 1279
% 2.47/1.54 % (14238)Time elapsed: 0.002 s
% 2.47/1.54 % (14238)Instructions burned: 3 (million)
% 2.47/1.54 % (14238)------------------------------
% 2.47/1.54 % (14238)------------------------------
% 2.47/1.54 % (14240)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_13954 for (2999ds/3Mi)
% 2.47/1.54 % (14240)Instruction limit reached!
% 2.47/1.54 % (14240)------------------------------
% 2.47/1.54 % (14240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.54 % (14240)Termination reason: Unknown
% 2.47/1.54 % (14240)Termination phase: shuffling
% 2.47/1.54
% 2.47/1.54 % (14240)Memory used [KB]: 1279
% 2.47/1.54 % (14240)Time elapsed: 0.003 s
% 2.47/1.54 % (14240)Instructions burned: 4 (million)
% 2.47/1.54 % (14240)------------------------------
% 2.47/1.54 % (14240)------------------------------
% 2.47/1.55 % (14239)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_13954 for (2999ds/7Mi)
% 2.47/1.55 % (14242)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_13954 for (2999ds/18Mi)
% 2.47/1.55 % (14223)Instruction limit reached!
% 2.47/1.55 % (14223)------------------------------
% 2.47/1.55 % (14223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.55 % (14223)Termination reason: Unknown
% 2.47/1.55 % (14223)Termination phase: Saturation
% 2.47/1.55
% 2.47/1.55 % (14223)Memory used [KB]: 7036
% 2.47/1.55 % (14223)Time elapsed: 0.057 s
% 2.47/1.55 % (14223)Instructions burned: 183 (million)
% 2.47/1.55 % (14223)------------------------------
% 2.47/1.55 % (14223)------------------------------
% 2.47/1.55 % (14239)Instruction limit reached!
% 2.47/1.55 % (14239)------------------------------
% 2.47/1.55 % (14239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.55 % (14239)Termination reason: Unknown
% 2.47/1.55 % (14239)Termination phase: shuffling
% 2.47/1.55
% 2.47/1.55 % (14239)Memory used [KB]: 1279
% 2.47/1.55 % (14239)Time elapsed: 0.006 s
% 2.47/1.55 % (14239)Instructions burned: 8 (million)
% 2.47/1.55 % (14239)------------------------------
% 2.47/1.55 % (14239)------------------------------
% 2.47/1.55 % (14242)Instruction limit reached!
% 2.47/1.55 % (14242)------------------------------
% 2.47/1.55 % (14242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.55 % (14242)Termination reason: Unknown
% 2.47/1.55 % (14242)Termination phase: shuffling
% 2.47/1.55
% 2.47/1.55 % (14242)Memory used [KB]: 1535
% 2.47/1.55 % (14242)Time elapsed: 0.006 s
% 2.47/1.55 % (14242)Instructions burned: 18 (million)
% 2.47/1.55 % (14242)------------------------------
% 2.47/1.55 % (14242)------------------------------
% 2.47/1.55 % (14243)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_13954 for (2999ds/710Mi)
% 2.47/1.55 % (14241)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_13954 for (2999ds/4Mi)
% 2.47/1.56 % (14241)Instruction limit reached!
% 2.47/1.56 % (14241)------------------------------
% 2.47/1.56 % (14241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.56 % (14241)Termination reason: Unknown
% 2.47/1.56 % (14241)Termination phase: shuffling
% 2.47/1.56
% 2.47/1.56 % (14241)Memory used [KB]: 1279
% 2.47/1.56 % (14241)Time elapsed: 0.004 s
% 2.47/1.56 % (14241)Instructions burned: 5 (million)
% 2.47/1.56 % (14241)------------------------------
% 2.47/1.56 % (14241)------------------------------
% 2.47/1.56 % (14244)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_13954 for (2999ds/6Mi)
% 2.47/1.56 % (14246)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_13954 for (2999ds/21Mi)
% 2.47/1.56 % (14244)Instruction limit reached!
% 2.47/1.56 % (14244)------------------------------
% 2.47/1.56 % (14244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.56 % (14244)Termination reason: Unknown
% 2.47/1.56 % (14244)Termination phase: shuffling
% 2.47/1.56
% 2.47/1.56 % (14244)Memory used [KB]: 1279
% 2.47/1.56 % (14244)Time elapsed: 0.004 s
% 2.47/1.56 % (14244)Instructions burned: 8 (million)
% 2.47/1.56 % (14244)------------------------------
% 2.47/1.56 % (14244)------------------------------
% 2.47/1.57 % (14246)Instruction limit reached!
% 2.47/1.57 % (14246)------------------------------
% 2.47/1.57 % (14246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.57 % (14246)Termination reason: Unknown
% 2.47/1.57 % (14246)Termination phase: Property scanning
% 2.47/1.57
% 2.47/1.57 % (14246)Memory used [KB]: 1535
% 2.47/1.57 % (14246)Time elapsed: 0.007 s
% 2.47/1.57 % (14246)Instructions burned: 22 (million)
% 2.47/1.57 % (14246)------------------------------
% 2.47/1.57 % (14246)------------------------------
% 2.47/1.57 % (14245)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_13954 for (2999ds/902Mi)
% 2.47/1.57 % (14248)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_13954 for (2999ds/6Mi)
% 2.47/1.57 % (14247)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_13954 for (2999ds/5Mi)
% 2.47/1.57 % (14248)Instruction limit reached!
% 2.47/1.57 % (14248)------------------------------
% 2.47/1.57 % (14248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.57 % (14248)Termination reason: Unknown
% 2.47/1.57 % (14248)Termination phase: shuffling
% 2.47/1.57
% 2.47/1.57 % (14248)Memory used [KB]: 1279
% 2.47/1.57 % (14248)Time elapsed: 0.004 s
% 2.47/1.57 % (14248)Instructions burned: 8 (million)
% 2.47/1.57 % (14248)------------------------------
% 2.47/1.57 % (14248)------------------------------
% 2.47/1.58 % (14249)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_13954 for (2999ds/377Mi)
% 2.47/1.58 % (14247)Instruction limit reached!
% 2.47/1.58 % (14247)------------------------------
% 2.47/1.58 % (14247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.58 % (14247)Termination reason: Unknown
% 2.47/1.58 % (14247)Termination phase: shuffling
% 2.47/1.58
% 2.47/1.58 % (14247)Memory used [KB]: 1279
% 2.47/1.58 % (14247)Time elapsed: 0.005 s
% 2.47/1.58 % (14247)Instructions burned: 6 (million)
% 2.47/1.58 % (14247)------------------------------
% 2.47/1.58 % (14247)------------------------------
% 2.47/1.58 % (14250)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_13954 for (2999ds/779Mi)
% 2.47/1.59 % (14251)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_13954 for (2999ds/19Mi)
% 2.47/1.60 % (14251)Instruction limit reached!
% 2.47/1.60 % (14251)------------------------------
% 2.47/1.60 % (14251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.60 % (14251)Termination reason: Unknown
% 2.47/1.60 % (14251)Termination phase: Property scanning
% 2.47/1.60
% 2.47/1.60 % (14251)Memory used [KB]: 1535
% 2.47/1.60 % (14251)Time elapsed: 0.009 s
% 2.47/1.60 % (14251)Instructions burned: 20 (million)
% 2.47/1.60 % (14251)------------------------------
% 2.47/1.60 % (14251)------------------------------
% 2.47/1.61 % (14252)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_13954 for (2998ds/879Mi)
% 2.47/1.64 % (14228)Instruction limit reached!
% 2.47/1.64 % (14228)------------------------------
% 2.47/1.64 % (14228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.64 % (14228)Termination reason: Unknown
% 2.47/1.64 % (14228)Termination phase: Saturation
% 2.47/1.64
% 2.47/1.64 % (14228)Memory used [KB]: 7803
% 2.47/1.64 % (14228)Time elapsed: 0.141 s
% 2.47/1.64 % (14228)Instructions burned: 277 (million)
% 2.47/1.64 % (14228)------------------------------
% 2.47/1.64 % (14228)------------------------------
% 2.47/1.65 % (14253)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_13954 for (2998ds/17Mi)
% 2.47/1.66 % (14253)Instruction limit reached!
% 2.47/1.66 % (14253)------------------------------
% 2.47/1.66 % (14253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.66 % (14253)Termination reason: Unknown
% 2.47/1.66 % (14253)Termination phase: shuffling
% 2.47/1.66
% 2.47/1.66 % (14253)Memory used [KB]: 1535
% 2.47/1.66 % (14253)Time elapsed: 0.007 s
% 2.47/1.66 % (14253)Instructions burned: 18 (million)
% 2.47/1.66 % (14253)------------------------------
% 2.47/1.66 % (14253)------------------------------
% 2.47/1.67 % (14254)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_13954 for (2998ds/3Mi)
% 2.47/1.67 % (14254)Instruction limit reached!
% 2.47/1.67 % (14254)------------------------------
% 2.47/1.67 % (14254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.67 % (14254)Termination reason: Unknown
% 2.47/1.67 % (14254)Termination phase: shuffling
% 2.47/1.67
% 2.47/1.67 % (14254)Memory used [KB]: 1279
% 2.47/1.67 % (14254)Time elapsed: 0.003 s
% 2.47/1.67 % (14254)Instructions burned: 4 (million)
% 2.47/1.67 % (14254)------------------------------
% 2.47/1.67 % (14254)------------------------------
% 2.47/1.68 % (14255)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_13954 for (2998ds/30Mi)
% 2.47/1.69 % (14255)Instruction limit reached!
% 2.47/1.69 % (14255)------------------------------
% 2.47/1.69 % (14255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.69 % (14255)Termination reason: Unknown
% 2.47/1.69 % (14255)Termination phase: Property scanning
% 2.47/1.69
% 2.47/1.69 % (14255)Memory used [KB]: 1663
% 2.47/1.69 % (14255)Time elapsed: 0.011 s
% 2.47/1.69 % (14255)Instructions burned: 33 (million)
% 2.47/1.69 % (14255)------------------------------
% 2.47/1.69 % (14255)------------------------------
% 2.47/1.69 % (14249)Instruction limit reached!
% 2.47/1.69 % (14249)------------------------------
% 2.47/1.69 % (14249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.69 % (14249)Termination reason: Unknown
% 2.47/1.69 % (14249)Termination phase: Saturation
% 2.47/1.69
% 2.47/1.69 % (14249)Memory used [KB]: 7291
% 2.47/1.69 % (14249)Time elapsed: 0.115 s
% 2.47/1.69 % (14249)Instructions burned: 377 (million)
% 2.47/1.69 % (14249)------------------------------
% 2.47/1.69 % (14249)------------------------------
% 2.47/1.70 % (14256)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_13954 for (2998ds/127Mi)
% 2.47/1.70 % (14257)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_13954 for (2998ds/100Mi)
% 2.47/1.73 % (14257)Instruction limit reached!
% 2.47/1.73 % (14257)------------------------------
% 2.47/1.73 % (14257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.73 % (14257)Termination reason: Unknown
% 2.47/1.73 % (14257)Termination phase: Saturation
% 2.47/1.73
% 2.47/1.73 % (14257)Memory used [KB]: 6396
% 2.47/1.73 % (14257)Time elapsed: 0.030 s
% 2.47/1.73 % (14257)Instructions burned: 101 (million)
% 2.47/1.73 % (14257)------------------------------
% 2.47/1.73 % (14257)------------------------------
% 2.47/1.73 % (14256)Instruction limit reached!
% 2.47/1.73 % (14256)------------------------------
% 2.47/1.73 % (14256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.73 % (14256)Termination reason: Unknown
% 2.47/1.73 % (14256)Termination phase: Saturation
% 2.47/1.73
% 2.47/1.73 % (14256)Memory used [KB]: 6780
% 2.47/1.73 % (14256)Time elapsed: 0.038 s
% 2.47/1.73 % (14256)Instructions burned: 127 (million)
% 2.47/1.73 % (14256)------------------------------
% 2.47/1.73 % (14256)------------------------------
% 2.47/1.74 % (14258)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_13954 for (2997ds/3Mi)
% 2.47/1.74 % (14258)Instruction limit reached!
% 2.47/1.74 % (14258)------------------------------
% 2.47/1.74 % (14258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.74 % (14258)Termination reason: Unknown
% 2.47/1.74 % (14258)Termination phase: shuffling
% 2.47/1.74
% 2.47/1.74 % (14258)Memory used [KB]: 1279
% 2.47/1.74 % (14258)Time elapsed: 0.002 s
% 2.47/1.74 % (14258)Instructions burned: 4 (million)
% 2.47/1.74 % (14258)------------------------------
% 2.47/1.74 % (14258)------------------------------
% 2.47/1.74 % (14259)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_13954 for (2997ds/20Mi)
% 2.47/1.75 % (14259)Instruction limit reached!
% 2.47/1.75 % (14259)------------------------------
% 2.47/1.75 % (14259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.75 % (14259)Termination reason: Unknown
% 2.47/1.75 % (14259)Termination phase: SInE selection
% 2.47/1.75
% 2.47/1.75 % (14259)Memory used [KB]: 1407
% 2.47/1.75 % (14259)Time elapsed: 0.008 s
% 2.47/1.75 % (14259)Instructions burned: 20 (million)
% 2.47/1.75 % (14259)------------------------------
% 2.47/1.75 % (14259)------------------------------
% 2.47/1.75 % (14260)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_13954 for (2997ds/86Mi)
% 2.47/1.76 % (14261)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_13954 for (2997ds/107Mi)
% 2.47/1.77 % (14260)Instruction limit reached!
% 2.47/1.77 % (14260)------------------------------
% 2.47/1.77 % (14260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.77 % (14260)Termination reason: Unknown
% 2.47/1.77 % (14260)Termination phase: Saturation
% 2.47/1.77
% 2.47/1.77 % (14260)Memory used [KB]: 6396
% 2.47/1.77 % (14260)Time elapsed: 0.024 s
% 2.47/1.77 % (14260)Instructions burned: 86 (million)
% 2.47/1.77 % (14260)------------------------------
% 2.47/1.77 % (14260)------------------------------
% 2.47/1.78 % (14250)Instruction limit reached!
% 2.47/1.78 % (14250)------------------------------
% 2.47/1.78 % (14250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.78 % (14250)Termination reason: Unknown
% 2.47/1.78 % (14250)Termination phase: Saturation
% 2.47/1.78
% 2.47/1.78 % (14250)Memory used [KB]: 6524
% 2.47/1.78 % (14250)Time elapsed: 0.196 s
% 2.47/1.78 % (14250)Instructions burned: 779 (million)
% 2.47/1.78 % (14250)------------------------------
% 2.47/1.78 % (14250)------------------------------
% 2.47/1.78 % (14262)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_13954 for (2997ds/39Mi)
% 2.47/1.79 % (14263)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_13954 for (2997ds/448Mi)
% 2.47/1.79 % (14243)Instruction limit reached!
% 2.47/1.79 % (14243)------------------------------
% 2.47/1.79 % (14243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.79 % (14243)Termination reason: Unknown
% 2.47/1.79 % (14243)Termination phase: Saturation
% 2.47/1.79
% 2.47/1.79 % (14243)Memory used [KB]: 8699
% 2.47/1.79 % (14243)Time elapsed: 0.238 s
% 2.47/1.79 % (14243)Instructions burned: 712 (million)
% 2.47/1.79 % (14243)------------------------------
% 2.47/1.79 % (14243)------------------------------
% 2.47/1.79 % (14261)Instruction limit reached!
% 2.47/1.79 % (14261)------------------------------
% 2.47/1.79 % (14261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.79 % (14261)Termination reason: Unknown
% 2.47/1.79 % (14261)Termination phase: Saturation
% 2.47/1.79
% 2.47/1.79 % (14261)Memory used [KB]: 6652
% 2.47/1.79 % (14261)Time elapsed: 0.032 s
% 2.47/1.79 % (14261)Instructions burned: 107 (million)
% 2.47/1.79 % (14261)------------------------------
% 2.47/1.79 % (14261)------------------------------
% 2.47/1.79 % (14262)Instruction limit reached!
% 2.47/1.79 % (14262)------------------------------
% 2.47/1.79 % (14262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.79 % (14262)Termination reason: Unknown
% 2.47/1.79 % (14262)Termination phase: Property scanning
% 2.47/1.79
% 2.47/1.79 % (14262)Memory used [KB]: 1663
% 2.47/1.79 % (14262)Time elapsed: 0.011 s
% 2.47/1.79 % (14262)Instructions burned: 40 (million)
% 2.47/1.79 % (14262)------------------------------
% 2.47/1.79 % (14262)------------------------------
% 2.47/1.80 % (14264)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_13954 for (2997ds/46Mi)
% 2.47/1.80 % (14265)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_13954 for (2997ds/98Mi)
% 2.47/1.80 % (14266)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_13954 for (2997ds/507Mi)
% 2.47/1.81 % (14234)Instruction limit reached!
% 2.47/1.81 % (14234)------------------------------
% 2.47/1.81 % (14234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.81 % (14234)Termination reason: Unknown
% 2.47/1.81 % (14234)Termination phase: Saturation
% 2.47/1.81
% 2.47/1.81 % (14234)Memory used [KB]: 8443
% 2.47/1.81 % (14234)Time elapsed: 0.281 s
% 2.47/1.81 % (14234)Instructions burned: 1043 (million)
% 2.47/1.81 % (14234)------------------------------
% 2.47/1.81 % (14234)------------------------------
% 2.47/1.81 % (14264)Instruction limit reached!
% 2.47/1.81 % (14264)------------------------------
% 2.47/1.81 % (14264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.81 % (14264)Termination reason: Unknown
% 2.47/1.81 % (14264)Termination phase: Property scanning
% 2.47/1.81
% 2.47/1.81 % (14264)Memory used [KB]: 1663
% 2.47/1.81 % (14264)Time elapsed: 0.013 s
% 2.47/1.81 % (14264)Instructions burned: 46 (million)
% 2.47/1.81 % (14264)------------------------------
% 2.47/1.81 % (14264)------------------------------
% 2.47/1.82 % (14267)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_13954 for (2996ds/149Mi)
% 2.47/1.82 % (14268)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_13954 for (2996ds/39Mi)
% 2.47/1.83 % (14265)Instruction limit reached!
% 2.47/1.83 % (14265)------------------------------
% 2.47/1.83 % (14265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.83 % (14265)Termination reason: Unknown
% 2.47/1.83 % (14265)Termination phase: Saturation
% 2.47/1.83
% 2.47/1.83 % (14265)Memory used [KB]: 1791
% 2.47/1.83 % (14265)Time elapsed: 0.029 s
% 2.47/1.83 % (14265)Instructions burned: 100 (million)
% 2.47/1.83 % (14265)------------------------------
% 2.47/1.83 % (14265)------------------------------
% 2.47/1.83 % (14268)Instruction limit reached!
% 2.47/1.83 % (14268)------------------------------
% 2.47/1.83 % (14268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.83 % (14268)Termination reason: Unknown
% 2.47/1.83 % (14268)Termination phase: Property scanning
% 2.47/1.83
% 2.47/1.83 % (14268)Memory used [KB]: 1663
% 2.47/1.83 % (14268)Time elapsed: 0.011 s
% 2.47/1.83 % (14268)Instructions burned: 39 (million)
% 2.47/1.83 % (14268)------------------------------
% 2.47/1.83 % (14268)------------------------------
% 2.47/1.84 % (14269)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_13954 for (2996ds/6Mi)
% 2.47/1.84 % (14269)Instruction limit reached!
% 2.47/1.84 % (14269)------------------------------
% 2.47/1.84 % (14269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.84 % (14269)Termination reason: Unknown
% 2.47/1.84 % (14269)Termination phase: shuffling
% 2.47/1.84
% 2.47/1.84 % (14269)Memory used [KB]: 1279
% 2.47/1.84 % (14269)Time elapsed: 0.004 s
% 2.47/1.84 % (14269)Instructions burned: 8 (million)
% 2.47/1.84 % (14269)------------------------------
% 2.47/1.84 % (14269)------------------------------
% 2.47/1.84 % (14270)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_13954 for (2996ds/1087Mi)
% 2.47/1.85 % (14271)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_13954 for (2996ds/47Mi)
% 2.47/1.86 % (14271)Instruction limit reached!
% 2.47/1.86 % (14271)------------------------------
% 2.47/1.86 % (14271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.86 % (14271)Termination reason: Unknown
% 2.47/1.86 % (14271)Termination phase: Property scanning
% 2.47/1.86
% 2.47/1.86 % (14271)Memory used [KB]: 1663
% 2.47/1.86 % (14271)Time elapsed: 0.015 s
% 2.47/1.86 % (14271)Instructions burned: 47 (million)
% 2.47/1.86 % (14271)------------------------------
% 2.47/1.86 % (14271)------------------------------
% 2.47/1.87 % (14267)Instruction limit reached!
% 2.47/1.87 % (14267)------------------------------
% 2.47/1.87 % (14267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.87 % (14267)Termination reason: Unknown
% 2.47/1.87 % (14267)Termination phase: Saturation
% 2.47/1.87
% 2.47/1.87 % (14267)Memory used [KB]: 6908
% 2.47/1.87 % (14267)Time elapsed: 0.049 s
% 2.47/1.87 % (14267)Instructions burned: 151 (million)
% 2.47/1.87 % (14267)------------------------------
% 2.47/1.87 % (14267)------------------------------
% 2.47/1.87 % (14245)Instruction limit reached!
% 2.47/1.87 % (14245)------------------------------
% 2.47/1.87 % (14245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.87 % (14245)Termination reason: Unknown
% 2.47/1.87 % (14245)Termination phase: Saturation
% 2.47/1.87
% 2.47/1.87 % (14245)Memory used [KB]: 9978
% 2.47/1.87 % (14245)Time elapsed: 0.304 s
% 2.47/1.87 % (14245)Instructions burned: 903 (million)
% 2.47/1.87 % (14245)------------------------------
% 2.47/1.87 % (14245)------------------------------
% 2.47/1.87 % (14272)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_13954 for (2996ds/44Mi)
% 2.47/1.88 % (14273)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_13954 for (2996ds/432Mi)
% 2.47/1.88 % (14274)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_13954 for (2996ds/62Mi)
% 2.47/1.89 % (14272)Instruction limit reached!
% 2.47/1.89 % (14272)------------------------------
% 2.47/1.89 % (14272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.89 % (14272)Termination reason: Unknown
% 2.47/1.89 % (14272)Termination phase: Property scanning
% 2.47/1.89
% 2.47/1.89 % (14272)Memory used [KB]: 1663
% 2.47/1.89 % (14272)Time elapsed: 0.013 s
% 2.47/1.89 % (14272)Instructions burned: 45 (million)
% 2.47/1.89 % (14272)------------------------------
% 2.47/1.89 % (14272)------------------------------
% 2.47/1.90 % (14275)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_13954 for (2995ds/31Mi)
% 2.47/1.90 % (14263)Instruction limit reached!
% 2.47/1.90 % (14263)------------------------------
% 2.47/1.90 % (14263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.90 % (14263)Termination reason: Unknown
% 2.47/1.90 % (14263)Termination phase: Saturation
% 2.47/1.90
% 2.47/1.90 % (14263)Memory used [KB]: 6524
% 2.47/1.90 % (14263)Time elapsed: 0.109 s
% 2.47/1.90 % (14263)Instructions burned: 450 (million)
% 2.47/1.90 % (14263)------------------------------
% 2.47/1.90 % (14263)------------------------------
% 2.47/1.90 % (14274)Instruction limit reached!
% 2.47/1.90 % (14274)------------------------------
% 2.47/1.90 % (14274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.90 % (14274)Termination reason: Unknown
% 2.47/1.90 % (14274)Termination phase: Saturation
% 2.47/1.90
% 2.47/1.90 % (14274)Memory used [KB]: 6140
% 2.47/1.90 % (14274)Time elapsed: 0.019 s
% 2.47/1.90 % (14274)Instructions burned: 62 (million)
% 2.47/1.90 % (14274)------------------------------
% 2.47/1.90 % (14274)------------------------------
% 2.47/1.90 % (14252)Instruction limit reached!
% 2.47/1.90 % (14252)------------------------------
% 2.47/1.90 % (14252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.90 % (14252)Termination reason: Unknown
% 2.47/1.90 % (14252)Termination phase: Saturation
% 2.47/1.90
% 2.47/1.90 % (14252)Memory used [KB]: 7931
% 2.47/1.90 % (14252)Time elapsed: 0.293 s
% 2.47/1.90 % (14252)Instructions burned: 881 (million)
% 2.47/1.90 % (14252)------------------------------
% 2.47/1.90 % (14252)------------------------------
% 2.47/1.90 % (14275)Instruction limit reached!
% 2.47/1.90 % (14275)------------------------------
% 2.47/1.90 % (14275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.90 % (14275)Termination reason: Unknown
% 2.47/1.90 % (14275)Termination phase: Property scanning
% 2.47/1.90
% 2.47/1.90 % (14275)Memory used [KB]: 1663
% 2.47/1.90 % (14275)Time elapsed: 0.011 s
% 2.47/1.90 % (14275)Instructions burned: 32 (million)
% 2.47/1.90 % (14275)------------------------------
% 2.47/1.90 % (14275)------------------------------
% 2.47/1.91 % (14276)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_13954 for (2995ds/96Mi)
% 2.47/1.91 % (14277)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_13954 for (2995ds/453Mi)
% 2.47/1.91 % (14278)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_13954 for (2995ds/71Mi)
% 2.47/1.91 % (14279)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_13954 for (2995ds/83Mi)
% 2.47/1.93 % (14278)Instruction limit reached!
% 2.47/1.93 % (14278)------------------------------
% 2.47/1.93 % (14278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.93 % (14278)Termination reason: Unknown
% 2.47/1.93 % (14278)Termination phase: Saturation
% 2.47/1.93
% 2.47/1.93 % (14278)Memory used [KB]: 6268
% 2.47/1.93 % (14278)Time elapsed: 0.022 s
% 2.47/1.93 % (14278)Instructions burned: 71 (million)
% 2.47/1.93 % (14278)------------------------------
% 2.47/1.93 % (14278)------------------------------
% 2.47/1.93 % (14276)Instruction limit reached!
% 2.47/1.93 % (14276)------------------------------
% 2.47/1.93 % (14276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.93 % (14276)Termination reason: Unknown
% 2.47/1.93 % (14276)Termination phase: Saturation
% 2.47/1.93
% 2.47/1.93 % (14276)Memory used [KB]: 6524
% 2.47/1.93 % (14276)Time elapsed: 0.027 s
% 2.47/1.93 % (14276)Instructions burned: 99 (million)
% 2.47/1.93 % (14276)------------------------------
% 2.47/1.93 % (14276)------------------------------
% 2.47/1.94 % (14279)Instruction limit reached!
% 2.47/1.94 % (14279)------------------------------
% 2.47/1.94 % (14279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.94 % (14279)Termination reason: Unknown
% 2.47/1.94 % (14279)Termination phase: Saturation
% 2.47/1.94
% 2.47/1.94 % (14279)Memory used [KB]: 6268
% 2.47/1.94 % (14279)Time elapsed: 0.025 s
% 2.47/1.94 % (14279)Instructions burned: 83 (million)
% 2.47/1.94 % (14279)------------------------------
% 2.47/1.94 % (14279)------------------------------
% 2.47/1.94 % (14280)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_13954 for (2995ds/11Mi)
% 2.47/1.94 % (14281)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_13954 for (2995ds/41Mi)
% 2.47/1.94 % (14280)Instruction limit reached!
% 2.47/1.94 % (14280)------------------------------
% 2.47/1.94 % (14280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.94 % (14280)Termination reason: Unknown
% 2.47/1.94 % (14280)Termination phase: shuffling
% 2.47/1.94
% 2.47/1.94 % (14280)Memory used [KB]: 1407
% 2.47/1.94 % (14280)Time elapsed: 0.005 s
% 2.47/1.94 % (14280)Instructions burned: 12 (million)
% 2.47/1.94 % (14280)------------------------------
% 2.47/1.94 % (14280)------------------------------
% 2.47/1.95 % (14282)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_13954 for (2995ds/6Mi)
% 2.47/1.95 % (14282)Instruction limit reached!
% 2.47/1.95 % (14282)------------------------------
% 2.47/1.95 % (14282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.95 % (14282)Termination reason: Unknown
% 2.47/1.95 % (14282)Termination phase: shuffling
% 2.47/1.95
% 2.47/1.95 % (14282)Memory used [KB]: 1279
% 2.47/1.95 % (14282)Time elapsed: 0.004 s
% 2.47/1.95 % (14282)Instructions burned: 8 (million)
% 2.47/1.95 % (14282)------------------------------
% 2.47/1.95 % (14282)------------------------------
% 2.47/1.95 % (14281)Instruction limit reached!
% 2.47/1.95 % (14281)------------------------------
% 2.47/1.95 % (14281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.95 % (14281)Termination reason: Unknown
% 2.47/1.95 % (14281)Termination phase: Function definition elimination
% 2.47/1.95
% 2.47/1.95 % (14281)Memory used [KB]: 1663
% 2.47/1.95 % (14281)Time elapsed: 0.012 s
% 2.47/1.95 % (14281)Instructions burned: 44 (million)
% 2.47/1.95 % (14281)------------------------------
% 2.47/1.95 % (14281)------------------------------
% 2.47/1.95 % (14283)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_13954 for (2995ds/150Mi)
% 2.47/1.96 % (14266)Instruction limit reached!
% 2.47/1.96 % (14266)------------------------------
% 2.47/1.96 % (14266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.96 % (14266)Termination reason: Unknown
% 2.47/1.96 % (14266)Termination phase: Saturation
% 2.47/1.96
% 2.47/1.96 % (14266)Memory used [KB]: 7164
% 2.47/1.96 % (14266)Time elapsed: 0.176 s
% 2.47/1.96 % (14266)Instructions burned: 509 (million)
% 2.47/1.96 % (14266)------------------------------
% 2.47/1.96 % (14266)------------------------------
% 2.47/1.96 % (14284)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_13954 for (2995ds/343Mi)
% 2.47/1.96 % (14285)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_13954 for (2995ds/109Mi)
% 2.47/1.97 % (14286)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_13954 for (2995ds/253Mi)
% 2.47/1.99 % (14273)Instruction limit reached!
% 2.47/1.99 % (14273)------------------------------
% 2.47/1.99 % (14273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.99 % (14273)Termination reason: Unknown
% 2.47/1.99 % (14273)Termination phase: Saturation
% 2.47/1.99
% 2.47/1.99 % (14273)Memory used [KB]: 2686
% 2.47/1.99 % (14273)Time elapsed: 0.114 s
% 2.47/1.99 % (14273)Instructions burned: 432 (million)
% 2.47/1.99 % (14273)------------------------------
% 2.47/1.99 % (14273)------------------------------
% 2.47/1.99 % (14285)Instruction limit reached!
% 2.47/1.99 % (14285)------------------------------
% 2.47/1.99 % (14285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.99 % (14285)Termination reason: Unknown
% 2.47/1.99 % (14285)Termination phase: Saturation
% 2.47/1.99
% 2.47/1.99 % (14285)Memory used [KB]: 6652
% 2.47/1.99 % (14285)Time elapsed: 0.031 s
% 2.47/1.99 % (14285)Instructions burned: 109 (million)
% 2.47/1.99 % (14285)------------------------------
% 2.47/1.99 % (14285)------------------------------
% 2.47/2.00 % (14287)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_13954 for (2994ds/140Mi)
% 2.47/2.00 % (14283)Instruction limit reached!
% 2.47/2.00 % (14283)------------------------------
% 2.47/2.00 % (14283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/2.00 % (14283)Termination reason: Unknown
% 2.47/2.00 % (14283)Termination phase: Saturation
% 2.47/2.00
% 2.47/2.00 % (14283)Memory used [KB]: 7419
% 2.47/2.00 % (14283)Time elapsed: 0.048 s
% 2.47/2.00 % (14283)Instructions burned: 152 (million)
% 2.47/2.00 % (14283)------------------------------
% 2.47/2.00 % (14283)------------------------------
% 2.47/2.00 % (14288)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_13954 for (2994ds/614Mi)
% 2.47/2.01 % (14289)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_13954 for (2994ds/202Mi)
% 6.09/2.02 % (14277)Instruction limit reached!
% 6.09/2.02 % (14277)------------------------------
% 6.09/2.02 % (14277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.09/2.02 % (14277)Termination reason: Unknown
% 6.09/2.02 % (14277)Termination phase: Saturation
% 6.09/2.02
% 6.09/2.02 % (14277)Memory used [KB]: 6268
% 6.09/2.02 % (14277)Time elapsed: 0.113 s
% 6.09/2.02 % (14277)Instructions burned: 455 (million)
% 6.09/2.02 % (14277)------------------------------
% 6.09/2.02 % (14277)------------------------------
% 6.09/2.03 % (14290)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_13954 for (2994ds/339Mi)
% 6.09/2.04 % (14287)Instruction limit reached!
% 6.09/2.04 % (14287)------------------------------
% 6.09/2.04 % (14287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.09/2.04 % (14287)Termination reason: Unknown
% 6.09/2.04 % (14287)Termination phase: Saturation
% 6.09/2.04
% 6.09/2.04 % (14287)Memory used [KB]: 6396
% 6.09/2.04 % (14287)Time elapsed: 0.039 s
% 6.09/2.04 % (14287)Instructions burned: 142 (million)
% 6.09/2.04 % (14287)------------------------------
% 6.09/2.04 % (14287)------------------------------
% 6.09/2.04 % (14286)Instruction limit reached!
% 6.09/2.04 % (14286)------------------------------
% 6.09/2.04 % (14286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.09/2.04 % (14286)Termination reason: Unknown
% 6.09/2.04 % (14286)Termination phase: Saturation
% 6.09/2.04
% 6.09/2.04 % (14286)Memory used [KB]: 7803
% 6.09/2.04 % (14286)Time elapsed: 0.079 s
% 6.09/2.04 % (14286)Instructions burned: 255 (million)
% 6.09/2.04 % (14286)------------------------------
% 6.09/2.04 % (14286)------------------------------
% 6.09/2.05 % (14291)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_13954 for (2994ds/283Mi)
% 6.09/2.05 % (14292)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_13954 for (2994ds/134Mi)
% 6.09/2.06 % (14284)Instruction limit reached!
% 6.09/2.06 % (14284)------------------------------
% 6.09/2.06 % (14284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.09/2.06 % (14284)Termination reason: Unknown
% 6.09/2.06 % (14284)Termination phase: Saturation
% 6.09/2.06
% 6.09/2.06 % (14284)Memory used [KB]: 7419
% 6.09/2.06 % (14284)Time elapsed: 0.106 s
% 6.09/2.06 % (14284)Instructions burned: 343 (million)
% 6.09/2.06 % (14284)------------------------------
% 6.09/2.06 % (14284)------------------------------
% 6.09/2.07 % (14289)Instruction limit reached!
% 6.09/2.07 % (14289)------------------------------
% 6.09/2.07 % (14289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.09/2.07 % (14289)Termination reason: Unknown
% 6.09/2.07 % (14289)Termination phase: Saturation
% 6.09/2.07
% 6.09/2.07 % (14289)Memory used [KB]: 7803
% 6.09/2.07 % (14289)Time elapsed: 0.063 s
% 6.09/2.07 % (14289)Instructions burned: 203 (million)
% 6.09/2.07 % (14289)------------------------------
% 6.09/2.07 % (14289)------------------------------
% 6.09/2.07 % (14293)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_13954 for (2994ds/298Mi)
% 6.09/2.08 % (14294)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_13954 for (2994ds/192Mi)
% 6.09/2.09 % (14292)Instruction limit reached!
% 6.09/2.09 % (14292)------------------------------
% 6.09/2.09 % (14292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.09/2.09 % (14292)Termination reason: Unknown
% 6.09/2.09 % (14292)Termination phase: Saturation
% 6.09/2.09
% 6.09/2.09 % (14292)Memory used [KB]: 6908
% 6.09/2.09 % (14292)Time elapsed: 0.038 s
% 6.09/2.09 % (14292)Instructions burned: 136 (million)
% 6.09/2.09 % (14292)------------------------------
% 6.09/2.09 % (14292)------------------------------
% 6.09/2.10 % (14295)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_13954 for (2994ds/258Mi)
% 6.56/2.12 % (14291)Instruction limit reached!
% 6.56/2.12 % (14291)------------------------------
% 6.56/2.12 % (14291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.56/2.12 % (14291)Termination reason: Unknown
% 6.56/2.12 % (14291)Termination phase: Saturation
% 6.56/2.12
% 6.56/2.12 % (14291)Memory used [KB]: 8827
% 6.56/2.12 % (14291)Time elapsed: 0.073 s
% 6.56/2.12 % (14291)Instructions burned: 285 (million)
% 6.56/2.12 % (14291)------------------------------
% 6.56/2.12 % (14291)------------------------------
% 6.56/2.13 % (14296)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_13954 for (2993ds/90Mi)
% 6.56/2.13 % (14290)Instruction limit reached!
% 6.56/2.13 % (14290)------------------------------
% 6.56/2.13 % (14290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.56/2.13 % (14290)Termination reason: Unknown
% 6.56/2.13 % (14290)Termination phase: Saturation
% 6.56/2.13
% 6.56/2.13 % (14290)Memory used [KB]: 7547
% 6.56/2.13 % (14290)Time elapsed: 0.102 s
% 6.56/2.13 % (14290)Instructions burned: 340 (million)
% 6.56/2.13 % (14290)------------------------------
% 6.56/2.13 % (14290)------------------------------
% 6.56/2.14 % (14294)Instruction limit reached!
% 6.56/2.14 % (14294)------------------------------
% 6.56/2.14 % (14294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.56/2.14 % (14294)Termination reason: Unknown
% 6.56/2.14 % (14294)Termination phase: Saturation
% 6.56/2.14
% 6.56/2.14 % (14294)Memory used [KB]: 7164
% 6.56/2.14 % (14294)Time elapsed: 0.057 s
% 6.56/2.14 % (14294)Instructions burned: 192 (million)
% 6.56/2.14 % (14294)------------------------------
% 6.56/2.14 % (14294)------------------------------
% 6.56/2.14 % (14297)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_13954 for (2993ds/231Mi)
% 6.56/2.15 % (14298)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_13954 for (2993ds/458Mi)
% 6.56/2.15 % (14293)Instruction limit reached!
% 6.56/2.15 % (14293)------------------------------
% 6.56/2.15 % (14293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.56/2.15 % (14293)Termination reason: Unknown
% 6.56/2.15 % (14293)Termination phase: Saturation
% 6.56/2.15
% 6.56/2.15 % (14293)Memory used [KB]: 6396
% 6.56/2.15 % (14293)Time elapsed: 0.078 s
% 6.56/2.15 % (14293)Instructions burned: 301 (million)
% 6.56/2.15 % (14293)------------------------------
% 6.56/2.15 % (14293)------------------------------
% 6.56/2.15 % (14296)Instruction limit reached!
% 6.56/2.15 % (14296)------------------------------
% 6.56/2.15 % (14296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.56/2.15 % (14296)Termination reason: Unknown
% 6.56/2.15 % (14296)Termination phase: Saturation
% 6.56/2.15
% 6.56/2.15 % (14296)Memory used [KB]: 6652
% 6.56/2.15 % (14296)Time elapsed: 0.025 s
% 6.56/2.15 % (14296)Instructions burned: 91 (million)
% 6.56/2.15 % (14296)------------------------------
% 6.56/2.15 % (14296)------------------------------
% 6.56/2.16 % (14299)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_13954 for (2993ds/31Mi)
% 6.56/2.16 % (14300)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_13954 for (2993ds/297Mi)
% 6.56/2.17 % (14299)Instruction limit reached!
% 6.56/2.17 % (14299)------------------------------
% 6.56/2.17 % (14299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.56/2.17 % (14299)Termination reason: Unknown
% 6.56/2.17 % (14299)Termination phase: Property scanning
% 6.56/2.17
% 6.56/2.17 % (14299)Memory used [KB]: 1663
% 6.56/2.17 % (14299)Time elapsed: 0.010 s
% 6.56/2.17 % (14299)Instructions burned: 32 (million)
% 6.56/2.17 % (14299)------------------------------
% 6.56/2.17 % (14299)------------------------------
% 6.56/2.18 % (14295)Instruction limit reached!
% 6.56/2.18 % (14295)------------------------------
% 6.56/2.18 % (14295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.56/2.18 % (14295)Termination reason: Unknown
% 6.56/2.18 % (14295)Termination phase: Saturation
% 6.56/2.18
% 6.56/2.18 % (14295)Memory used [KB]: 7164
% 6.56/2.18 % (14295)Time elapsed: 0.099 s
% 6.56/2.18 % (14295)Instructions burned: 259 (million)
% 6.56/2.18 % (14295)------------------------------
% 6.56/2.18 % (14295)------------------------------
% 6.56/2.18 % (14301)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_13954 for (2993ds/987Mi)
% 6.56/2.19 % (14302)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_13954 for (2993ds/182Mi)
% 6.56/2.19 % (14288)Instruction limit reached!
% 6.56/2.19 % (14288)------------------------------
% 6.56/2.19 % (14288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.56/2.19 % (14288)Termination reason: Unknown
% 6.56/2.19 % (14288)Termination phase: Saturation
% 6.56/2.19
% 6.56/2.19 % (14288)Memory used [KB]: 8059
% 6.56/2.19 % (14288)Time elapsed: 0.187 s
% 6.56/2.19 % (14288)Instructions burned: 614 (million)
% 6.56/2.19 % (14288)------------------------------
% 6.56/2.19 % (14288)------------------------------
% 7.22/2.20 % (14303)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_13954 for (2992ds/182Mi)
% 7.22/2.21 % (14297)Instruction limit reached!
% 7.22/2.21 % (14297)------------------------------
% 7.22/2.21 % (14297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.22/2.21 % (14297)Termination reason: Unknown
% 7.22/2.21 % (14297)Termination phase: Saturation
% 7.22/2.21
% 7.22/2.21 % (14297)Memory used [KB]: 9850
% 7.22/2.21 % (14297)Time elapsed: 0.088 s
% 7.22/2.21 % (14297)Instructions burned: 231 (million)
% 7.22/2.21 % (14297)------------------------------
% 7.22/2.21 % (14297)------------------------------
% 7.22/2.22 % (14304)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_13954 for (2992ds/154Mi)
% 7.22/2.24 % (14300)Instruction limit reached!
% 7.22/2.24 % (14300)------------------------------
% 7.22/2.24 % (14300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.22/2.24 % (14300)Termination reason: Unknown
% 7.22/2.24 % (14300)Termination phase: Saturation
% 7.22/2.24
% 7.22/2.24 % (14300)Memory used [KB]: 7803
% 7.22/2.24 % (14300)Time elapsed: 0.075 s
% 7.22/2.24 % (14300)Instructions burned: 301 (million)
% 7.22/2.24 % (14300)------------------------------
% 7.22/2.24 % (14300)------------------------------
% 7.22/2.24 % (14302)Instruction limit reached!
% 7.22/2.24 % (14302)------------------------------
% 7.22/2.24 % (14302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.22/2.24 % (14302)Termination reason: Unknown
% 7.22/2.24 % (14302)Termination phase: Saturation
% 7.22/2.24
% 7.22/2.24 % (14302)Memory used [KB]: 7036
% 7.22/2.24 % (14302)Time elapsed: 0.053 s
% 7.22/2.24 % (14302)Instructions burned: 183 (million)
% 7.22/2.24 % (14302)------------------------------
% 7.22/2.24 % (14302)------------------------------
% 7.22/2.25 % (14305)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_13954 for (2992ds/79Mi)
% 7.22/2.25 % (14306)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_13954 for (2992ds/216Mi)
% 7.22/2.25 % (14270)Instruction limit reached!
% 7.22/2.25 % (14270)------------------------------
% 7.22/2.25 % (14270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.22/2.25 % (14270)Termination reason: Unknown
% 7.22/2.25 % (14270)Termination phase: Saturation
% 7.22/2.25
% 7.22/2.25 % (14270)Memory used [KB]: 9850
% 7.22/2.25 % (14270)Time elapsed: 0.412 s
% 7.22/2.25 % (14270)Instructions burned: 1088 (million)
% 7.22/2.25 % (14270)------------------------------
% 7.22/2.25 % (14270)------------------------------
% 7.22/2.25 % (14304)Instruction limit reached!
% 7.22/2.25 % (14304)------------------------------
% 7.22/2.25 % (14304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.22/2.25 % (14304)Termination reason: Unknown
% 7.22/2.25 % (14304)Termination phase: Saturation
% 7.22/2.25
% 7.22/2.25 % (14304)Memory used [KB]: 6268
% 7.22/2.25 % (14304)Time elapsed: 0.039 s
% 7.22/2.25 % (14304)Instructions burned: 154 (million)
% 7.22/2.25 % (14304)------------------------------
% 7.22/2.25 % (14304)------------------------------
% 7.22/2.25 % (14303)Instruction limit reached!
% 7.22/2.25 % (14303)------------------------------
% 7.22/2.25 % (14303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.22/2.25 % (14303)Termination reason: Unknown
% 7.22/2.25 % (14303)Termination phase: Saturation
% 7.22/2.25
% 7.22/2.25 % (14303)Memory used [KB]: 8827
% 7.22/2.25 % (14303)Time elapsed: 0.058 s
% 7.22/2.25 % (14303)Instructions burned: 182 (million)
% 7.22/2.25 % (14303)------------------------------
% 7.22/2.25 % (14303)------------------------------
% 7.22/2.26 % (14308)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_13954 for (2992ds/922Mi)
% 7.22/2.26 % (14307)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_13954 for (2992ds/114Mi)
% 7.22/2.26 % (14309)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_13954 for (2992ds/182Mi)
% 7.22/2.27 % (14305)Instruction limit reached!
% 7.22/2.27 % (14305)------------------------------
% 7.22/2.27 % (14305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.22/2.27 % (14305)Termination reason: Unknown
% 7.22/2.27 % (14305)Termination phase: Saturation
% 7.22/2.27
% 7.22/2.27 % (14305)Memory used [KB]: 6396
% 7.22/2.27 % (14305)Time elapsed: 0.022 s
% 7.22/2.27 % (14305)Instructions burned: 79 (million)
% 7.22/2.27 % (14305)------------------------------
% 7.22/2.27 % (14305)------------------------------
% 7.22/2.28 % (14310)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_13954 for (2992ds/164Mi)
% 7.22/2.29 % (14298)Instruction limit reached!
% 7.22/2.29 % (14298)------------------------------
% 7.22/2.29 % (14298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.22/2.29 % (14298)Termination reason: Unknown
% 7.22/2.29 % (14298)Termination phase: Saturation
% 7.22/2.29
% 7.22/2.29 % (14298)Memory used [KB]: 7803
% 7.22/2.29 % (14298)Time elapsed: 0.164 s
% 7.22/2.29 % (14298)Instructions burned: 461 (million)
% 7.22/2.29 % (14298)------------------------------
% 7.22/2.29 % (14298)------------------------------
% 7.22/2.30 % (14307)Instruction limit reached!
% 7.22/2.30 % (14307)------------------------------
% 7.22/2.30 % (14307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.22/2.30 % (14307)Termination reason: Unknown
% 7.22/2.30 % (14307)Termination phase: Saturation
% 7.22/2.30
% 7.22/2.30 % (14307)Memory used [KB]: 6652
% 7.22/2.30 % (14307)Time elapsed: 0.035 s
% 7.22/2.30 % (14307)Instructions burned: 115 (million)
% 7.22/2.30 % (14307)------------------------------
% 7.22/2.30 % (14307)------------------------------
% 7.85/2.30 % (14311)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_13954 for (2991ds/50Mi)
% 7.85/2.30 % (14306)Instruction limit reached!
% 7.85/2.30 % (14306)------------------------------
% 7.85/2.30 % (14306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.85/2.30 % (14306)Termination reason: Unknown
% 7.85/2.30 % (14306)Termination phase: Saturation
% 7.85/2.30
% 7.85/2.30 % (14306)Memory used [KB]: 7036
% 7.85/2.30 % (14306)Time elapsed: 0.056 s
% 7.85/2.30 % (14306)Instructions burned: 219 (million)
% 7.85/2.30 % (14306)------------------------------
% 7.85/2.30 % (14306)------------------------------
% 7.85/2.31 % (14312)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_13954 for (2991ds/368Mi)
% 7.85/2.31 % (14309)Instruction limit reached!
% 7.85/2.31 % (14309)------------------------------
% 7.85/2.31 % (14309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.85/2.31 % (14309)Termination reason: Unknown
% 7.85/2.31 % (14309)Termination phase: Saturation
% 7.85/2.31
% 7.85/2.31 % (14309)Memory used [KB]: 6396
% 7.85/2.31 % (14309)Time elapsed: 0.047 s
% 7.85/2.31 % (14309)Instructions burned: 184 (million)
% 7.85/2.31 % (14309)------------------------------
% 7.85/2.31 % (14309)------------------------------
% 7.85/2.31 % (14311)Instruction limit reached!
% 7.85/2.31 % (14311)------------------------------
% 7.85/2.31 % (14311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.85/2.31 % (14311)Termination reason: Unknown
% 7.85/2.31 % (14311)Termination phase: Property scanning
% 7.85/2.31
% 7.85/2.31 % (14311)Memory used [KB]: 1663
% 7.85/2.31 % (14311)Time elapsed: 0.014 s
% 7.85/2.31 % (14311)Instructions burned: 52 (million)
% 7.85/2.31 % (14311)------------------------------
% 7.85/2.31 % (14311)------------------------------
% 7.85/2.31 % (14313)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_13954 for (2991ds/1021Mi)
% 7.85/2.32 % (14314)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_13954 for (2991ds/267Mi)
% 7.85/2.32 % (14315)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_13954 for (2991ds/204Mi)
% 7.85/2.32 % (14310)Instruction limit reached!
% 7.85/2.32 % (14310)------------------------------
% 7.85/2.32 % (14310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.85/2.32 % (14310)Termination reason: Unknown
% 7.85/2.32 % (14310)Termination phase: Saturation
% 7.85/2.32
% 7.85/2.32 % (14310)Memory used [KB]: 2174
% 7.85/2.32 % (14310)Time elapsed: 0.048 s
% 7.85/2.32 % (14310)Instructions burned: 165 (million)
% 7.85/2.32 % (14310)------------------------------
% 7.85/2.32 % (14310)------------------------------
% 7.85/2.33 % (14316)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_13954 for (2991ds/26Mi)
% 7.85/2.34 % (14316)Instruction limit reached!
% 7.85/2.34 % (14316)------------------------------
% 7.85/2.34 % (14316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.85/2.34 % (14316)Termination reason: Unknown
% 7.85/2.34 % (14316)Termination phase: Property scanning
% 7.85/2.34
% 7.85/2.34 % (14316)Memory used [KB]: 1663
% 7.85/2.34 % (14316)Time elapsed: 0.008 s
% 7.85/2.34 % (14316)Instructions burned: 28 (million)
% 7.85/2.34 % (14316)------------------------------
% 7.85/2.34 % (14316)------------------------------
% 7.85/2.35 % (14317)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_13954 for (2991ds/53Mi)
% 7.85/2.36 % (14317)Instruction limit reached!
% 7.85/2.36 % (14317)------------------------------
% 7.85/2.36 % (14317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.85/2.36 % (14317)Termination reason: Unknown
% 7.85/2.36 % (14317)Termination phase: Property scanning
% 7.85/2.36
% 7.85/2.36 % (14317)Memory used [KB]: 1663
% 7.85/2.36 % (14317)Time elapsed: 0.015 s
% 7.85/2.36 % (14317)Instructions burned: 56 (million)
% 7.85/2.36 % (14317)------------------------------
% 7.85/2.36 % (14317)------------------------------
% 7.85/2.37 % (14319)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_13954 for (2991ds/4436Mi)
% 7.85/2.38 % (14315)Instruction limit reached!
% 7.85/2.38 % (14315)------------------------------
% 7.85/2.38 % (14315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.85/2.38 % (14315)Termination reason: Unknown
% 7.85/2.38 % (14315)Termination phase: Saturation
% 7.85/2.38
% 7.85/2.38 % (14315)Memory used [KB]: 7036
% 7.85/2.38 % (14315)Time elapsed: 0.059 s
% 7.85/2.38 % (14315)Instructions burned: 204 (million)
% 7.85/2.38 % (14315)------------------------------
% 7.85/2.38 % (14315)------------------------------
% 7.85/2.39 % (14314)Instruction limit reached!
% 7.85/2.39 % (14314)------------------------------
% 7.85/2.39 % (14314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.85/2.39 % (14314)Termination reason: Unknown
% 7.85/2.39 % (14314)Termination phase: Saturation
% 7.85/2.39
% 7.85/2.39 % (14314)Memory used [KB]: 8827
% 7.85/2.39 % (14314)Time elapsed: 0.068 s
% 7.85/2.39 % (14314)Instructions burned: 270 (million)
% 7.85/2.39 % (14314)------------------------------
% 7.85/2.39 % (14314)------------------------------
% 7.85/2.39 % (14320)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_13954 for (2991ds/1539Mi)
% 7.85/2.40 % (14321)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_13954 for (2991ds/408Mi)
% 8.23/2.41 % (14301)Instruction limit reached!
% 8.23/2.41 % (14301)------------------------------
% 8.23/2.41 % (14301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.23/2.41 % (14301)Termination reason: Unknown
% 8.23/2.41 % (14301)Termination phase: Saturation
% 8.23/2.41
% 8.23/2.41 % (14301)Memory used [KB]: 8699
% 8.23/2.41 % (14301)Time elapsed: 0.257 s
% 8.23/2.41 % (14301)Instructions burned: 989 (million)
% 8.23/2.41 % (14301)------------------------------
% 8.23/2.41 % (14301)------------------------------
% 8.23/2.42 % (14322)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_13954 for (2990ds/5205Mi)
% 8.23/2.42 % (14312)Instruction limit reached!
% 8.23/2.42 % (14312)------------------------------
% 8.23/2.42 % (14312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.23/2.42 % (14312)Termination reason: Unknown
% 8.23/2.42 % (14312)Termination phase: Saturation
% 8.23/2.42
% 8.23/2.42 % (14312)Memory used [KB]: 7419
% 8.23/2.42 % (14312)Time elapsed: 0.119 s
% 8.23/2.42 % (14312)Instructions burned: 368 (million)
% 8.23/2.42 % (14312)------------------------------
% 8.23/2.42 % (14312)------------------------------
% 8.23/2.43 % (14323)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_13954 for (2990ds/1913Mi)
% 8.60/2.53 % (14321)Instruction limit reached!
% 8.60/2.53 % (14321)------------------------------
% 8.60/2.53 % (14321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.60/2.53 % (14321)Termination reason: Unknown
% 8.60/2.53 % (14321)Termination phase: Saturation
% 8.60/2.53
% 8.60/2.53 % (14321)Memory used [KB]: 8955
% 8.60/2.53 % (14321)Time elapsed: 0.133 s
% 8.60/2.53 % (14321)Instructions burned: 409 (million)
% 8.60/2.53 % (14321)------------------------------
% 8.60/2.53 % (14321)------------------------------
% 8.60/2.54 % (14324)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_13954 for (2989ds/4350Mi)
% 8.60/2.55 % (14308)Instruction limit reached!
% 8.60/2.55 % (14308)------------------------------
% 8.60/2.55 % (14308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.60/2.55 % (14308)Termination reason: Unknown
% 8.60/2.55 % (14308)Termination phase: Saturation
% 8.60/2.55
% 8.60/2.55 % (14308)Memory used [KB]: 9466
% 8.60/2.55 % (14308)Time elapsed: 0.292 s
% 8.60/2.55 % (14308)Instructions burned: 924 (million)
% 8.60/2.55 % (14308)------------------------------
% 8.60/2.55 % (14308)------------------------------
% 8.60/2.56 % (14325)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_13954 for (2989ds/68Mi)
% 8.60/2.58 % (14325)Instruction limit reached!
% 8.60/2.58 % (14325)------------------------------
% 8.60/2.58 % (14325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.60/2.58 % (14325)Termination reason: Unknown
% 8.60/2.58 % (14325)Termination phase: Saturation
% 8.60/2.58
% 8.60/2.58 % (14325)Memory used [KB]: 6268
% 8.60/2.58 % (14325)Time elapsed: 0.019 s
% 8.60/2.58 % (14325)Instructions burned: 71 (million)
% 8.60/2.58 % (14325)------------------------------
% 8.60/2.58 % (14325)------------------------------
% 8.60/2.59 % (14326)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_13954 for (2989ds/358Mi)
% 9.08/2.64 % (14313)Instruction limit reached!
% 9.08/2.64 % (14313)------------------------------
% 9.08/2.64 % (14313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.08/2.64 % (14313)Termination reason: Unknown
% 9.08/2.64 % (14313)Termination phase: Saturation
% 9.08/2.64
% 9.08/2.64 % (14313)Memory used [KB]: 9722
% 9.08/2.64 % (14313)Time elapsed: 0.327 s
% 9.08/2.64 % (14313)Instructions burned: 1022 (million)
% 9.08/2.64 % (14313)------------------------------
% 9.08/2.64 % (14313)------------------------------
% 9.08/2.65 % (14327)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_13954 for (2988ds/31Mi)
% 9.08/2.66 % (14327)Instruction limit reached!
% 9.08/2.66 % (14327)------------------------------
% 9.08/2.66 % (14327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.08/2.66 % (14327)Termination reason: Unknown
% 9.08/2.66 % (14327)Termination phase: Property scanning
% 9.08/2.66
% 9.08/2.66 % (14327)Memory used [KB]: 1663
% 9.08/2.66 % (14327)Time elapsed: 0.010 s
% 9.08/2.66 % (14327)Instructions burned: 34 (million)
% 9.08/2.66 % (14327)------------------------------
% 9.08/2.66 % (14327)------------------------------
% 9.08/2.67 % (14328)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_13954 for (2988ds/279Mi)
% 9.43/2.70 % (14326)Instruction limit reached!
% 9.43/2.70 % (14326)------------------------------
% 9.43/2.70 % (14326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.43/2.70 % (14326)Termination reason: Unknown
% 9.43/2.70 % (14326)Termination phase: Saturation
% 9.43/2.70
% 9.43/2.70 % (14326)Memory used [KB]: 7291
% 9.43/2.70 % (14326)Time elapsed: 0.109 s
% 9.43/2.70 % (14326)Instructions burned: 359 (million)
% 9.43/2.70 % (14326)------------------------------
% 9.43/2.70 % (14326)------------------------------
% 9.43/2.71 % (14329)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_13954 for (2987ds/258Mi)
% 9.43/2.73 % (14328)Instruction limit reached!
% 9.43/2.73 % (14328)------------------------------
% 9.43/2.73 % (14328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.43/2.73 % (14328)Termination reason: Unknown
% 9.43/2.73 % (14328)Termination phase: Saturation
% 9.43/2.73
% 9.43/2.73 % (14328)Memory used [KB]: 6524
% 9.43/2.73 % (14328)Time elapsed: 0.067 s
% 9.43/2.73 % (14328)Instructions burned: 279 (million)
% 9.43/2.73 % (14328)------------------------------
% 9.43/2.73 % (14328)------------------------------
% 9.43/2.74 % (14330)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_13954 for (2987ds/26Mi)
% 9.43/2.75 % (14330)Instruction limit reached!
% 9.43/2.75 % (14330)------------------------------
% 9.43/2.75 % (14330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.43/2.75 % (14330)Termination reason: Unknown
% 9.43/2.75 % (14330)Termination phase: Property scanning
% 9.43/2.75
% 9.43/2.75 % (14330)Memory used [KB]: 1663
% 9.43/2.75 % (14330)Time elapsed: 0.008 s
% 9.43/2.75 % (14330)Instructions burned: 26 (million)
% 9.43/2.75 % (14330)------------------------------
% 9.43/2.75 % (14330)------------------------------
% 9.43/2.76 % (14331)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_13954 for (2987ds/995Mi)
% 9.43/2.78 % (14329)Instruction limit reached!
% 9.43/2.78 % (14329)------------------------------
% 9.43/2.78 % (14329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.43/2.78 % (14329)Termination reason: Unknown
% 9.43/2.78 % (14329)Termination phase: Saturation
% 9.43/2.78
% 9.43/2.78 % (14329)Memory used [KB]: 7547
% 9.43/2.78 % (14329)Time elapsed: 0.072 s
% 9.43/2.78 % (14329)Instructions burned: 260 (million)
% 9.43/2.78 % (14329)------------------------------
% 9.43/2.78 % (14329)------------------------------
% 9.43/2.79 % (14332)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_13954 for (2987ds/373Mi)
% 9.73/2.87 % (14320)Instruction limit reached!
% 9.73/2.87 % (14320)------------------------------
% 9.73/2.87 % (14320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.73/2.87 % (14320)Termination reason: Unknown
% 9.73/2.87 % (14320)Termination phase: Saturation
% 9.73/2.87
% 9.73/2.87 % (14320)Memory used [KB]: 8571
% 9.73/2.87 % (14320)Time elapsed: 0.486 s
% 9.73/2.87 % (14320)Instructions burned: 1541 (million)
% 9.73/2.87 % (14320)------------------------------
% 9.73/2.87 % (14320)------------------------------
% 9.73/2.88 % (14333)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_13954 for (2986ds/253Mi)
% 10.22/2.90 % (14332)Instruction limit reached!
% 10.22/2.90 % (14332)------------------------------
% 10.22/2.90 % (14332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.22/2.90 % (14332)Termination reason: Unknown
% 10.22/2.90 % (14332)Termination phase: Saturation
% 10.22/2.90
% 10.22/2.90 % (14332)Memory used [KB]: 7164
% 10.22/2.90 % (14332)Time elapsed: 0.117 s
% 10.22/2.90 % (14332)Instructions burned: 373 (million)
% 10.22/2.90 % (14332)------------------------------
% 10.22/2.90 % (14332)------------------------------
% 10.22/2.91 % (14334)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_13954 for (2985ds/832Mi)
% 10.22/2.94 % (14333)Instruction limit reached!
% 10.22/2.94 % (14333)------------------------------
% 10.22/2.94 % (14333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.22/2.94 % (14333)Termination reason: Unknown
% 10.22/2.94 % (14333)Termination phase: Saturation
% 10.22/2.94
% 10.22/2.94 % (14333)Memory used [KB]: 6268
% 10.22/2.94 % (14333)Time elapsed: 0.062 s
% 10.22/2.94 % (14333)Instructions burned: 254 (million)
% 10.22/2.94 % (14333)------------------------------
% 10.22/2.94 % (14333)------------------------------
% 10.22/2.95 % (14335)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_13954 for (2985ds/668Mi)
% 10.22/3.00 % (14331)Instruction limit reached!
% 10.22/3.00 % (14331)------------------------------
% 10.22/3.00 % (14331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.22/3.00 % (14331)Termination reason: Unknown
% 10.22/3.00 % (14331)Termination phase: Saturation
% 10.22/3.00
% 10.22/3.00 % (14331)Memory used [KB]: 8315
% 10.22/3.00 % (14331)Time elapsed: 0.246 s
% 10.22/3.00 % (14331)Instructions burned: 998 (million)
% 10.22/3.00 % (14331)------------------------------
% 10.22/3.00 % (14331)------------------------------
% 10.22/3.01 % (14323)Instruction limit reached!
% 10.22/3.01 % (14323)------------------------------
% 10.22/3.01 % (14323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.22/3.01 % (14323)Termination reason: Unknown
% 10.22/3.01 % (14323)Termination phase: Saturation
% 10.22/3.01
% 10.22/3.01 % (14323)Memory used [KB]: 3326
% 10.22/3.01 % (14323)Time elapsed: 0.578 s
% 10.22/3.01 % (14323)Instructions burned: 1915 (million)
% 10.22/3.01 % (14323)------------------------------
% 10.22/3.01 % (14323)------------------------------
% 10.22/3.01 % (14336)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_13954 for (2984ds/40Mi)
% 10.22/3.02 % (14337)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_13954 for (2984ds/294Mi)
% 10.22/3.02 % (14336)Instruction limit reached!
% 10.22/3.02 % (14336)------------------------------
% 10.22/3.02 % (14336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.22/3.02 % (14336)Termination reason: Unknown
% 10.22/3.02 % (14336)Termination phase: Function definition elimination
% 10.22/3.02
% 10.22/3.02 % (14336)Memory used [KB]: 1663
% 10.22/3.02 % (14336)Time elapsed: 0.012 s
% 10.22/3.02 % (14336)Instructions burned: 43 (million)
% 10.22/3.02 % (14336)------------------------------
% 10.22/3.02 % (14336)------------------------------
% 13.16/3.03 % (14338)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_13954 for (2984ds/187Mi)
% 13.16/3.09 % (14338)Instruction limit reached!
% 13.16/3.09 % (14338)------------------------------
% 13.16/3.09 % (14338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.16/3.09 % (14338)Termination reason: Unknown
% 13.16/3.09 % (14338)Termination phase: Saturation
% 13.16/3.09
% 13.16/3.09 % (14338)Memory used [KB]: 7036
% 13.16/3.09 % (14338)Time elapsed: 0.075 s
% 13.16/3.09 % (14338)Instructions burned: 187 (million)
% 13.16/3.09 % (14338)------------------------------
% 13.16/3.09 % (14338)------------------------------
% 13.16/3.09 % (14337)Instruction limit reached!
% 13.16/3.09 % (14337)------------------------------
% 13.16/3.09 % (14337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.16/3.09 % (14337)Termination reason: Unknown
% 13.16/3.09 % (14337)Termination phase: Saturation
% 13.16/3.09
% 13.16/3.09 % (14337)Memory used [KB]: 6268
% 13.16/3.09 % (14337)Time elapsed: 0.075 s
% 13.16/3.09 % (14337)Instructions burned: 295 (million)
% 13.16/3.09 % (14337)------------------------------
% 13.16/3.09 % (14337)------------------------------
% 13.16/3.10 % (14339)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_13954 for (2984ds/371Mi)
% 13.16/3.10 % (14340)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_13954 for (2984ds/1827Mi)
% 13.16/3.12 % (14335)Instruction limit reached!
% 13.16/3.12 % (14335)------------------------------
% 13.16/3.12 % (14335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.16/3.12 % (14335)Termination reason: Unknown
% 13.16/3.12 % (14335)Termination phase: Saturation
% 13.16/3.12
% 13.16/3.12 % (14335)Memory used [KB]: 12920
% 13.16/3.12 % (14335)Time elapsed: 0.164 s
% 13.16/3.12 % (14335)Instructions burned: 671 (million)
% 13.16/3.12 % (14335)------------------------------
% 13.16/3.12 % (14335)------------------------------
% 13.85/3.13 % (14341)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_13954 for (2983ds/70Mi)
% 13.85/3.14 % (14341)Instruction limit reached!
% 13.85/3.14 % (14341)------------------------------
% 13.85/3.14 % (14341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.85/3.14 % (14341)Termination reason: Unknown
% 13.85/3.14 % (14341)Termination phase: Saturation
% 13.85/3.14
% 13.85/3.14 % (14341)Memory used [KB]: 1791
% 13.85/3.14 % (14341)Time elapsed: 0.019 s
% 13.85/3.14 % (14341)Instructions burned: 72 (million)
% 13.85/3.14 % (14341)------------------------------
% 13.85/3.14 % (14341)------------------------------
% 13.85/3.15 % (14342)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_13954 for (2983ds/316Mi)
% 13.85/3.17 % (14334)Instruction limit reached!
% 13.85/3.17 % (14334)------------------------------
% 13.85/3.17 % (14334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.85/3.17 % (14334)Termination reason: Unknown
% 13.85/3.17 % (14334)Termination phase: Saturation
% 13.85/3.17
% 13.85/3.17 % (14334)Memory used [KB]: 9338
% 13.85/3.17 % (14334)Time elapsed: 0.256 s
% 13.85/3.17 % (14334)Instructions burned: 834 (million)
% 13.85/3.17 % (14334)------------------------------
% 13.85/3.17 % (14334)------------------------------
% 13.85/3.18 % (14343)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_13954 for (2983ds/932Mi)
% 14.16/3.21 % (14339)Instruction limit reached!
% 14.16/3.21 % (14339)------------------------------
% 14.16/3.21 % (14339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.16/3.21 % (14339)Termination reason: Unknown
% 14.16/3.21 % (14339)Termination phase: Saturation
% 14.16/3.21
% 14.16/3.21 % (14339)Memory used [KB]: 7291
% 14.16/3.21 % (14339)Time elapsed: 0.113 s
% 14.16/3.21 % (14339)Instructions burned: 373 (million)
% 14.16/3.21 % (14339)------------------------------
% 14.16/3.21 % (14339)------------------------------
% 14.16/3.22 % (14344)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_13954 for (2982ds/4714Mi)
% 14.16/3.23 % (14342)Instruction limit reached!
% 14.16/3.23 % (14342)------------------------------
% 14.16/3.23 % (14342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.16/3.23 % (14342)Termination reason: Unknown
% 14.16/3.23 % (14342)Termination phase: Saturation
% 14.16/3.23
% 14.16/3.23 % (14342)Memory used [KB]: 7164
% 14.16/3.23 % (14342)Time elapsed: 0.080 s
% 14.16/3.23 % (14342)Instructions burned: 316 (million)
% 14.16/3.23 % (14342)------------------------------
% 14.16/3.23 % (14342)------------------------------
% 14.16/3.24 % (14345)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_13954 for (2982ds/8250Mi)
% 14.97/3.41 % (14343)Instruction limit reached!
% 14.97/3.41 % (14343)------------------------------
% 14.97/3.41 % (14343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.97/3.41 % (14343)Termination reason: Unknown
% 14.97/3.41 % (14343)Termination phase: Saturation
% 14.97/3.41
% 14.97/3.41 % (14343)Memory used [KB]: 9083
% 14.97/3.41 % (14343)Time elapsed: 0.228 s
% 14.97/3.41 % (14343)Instructions burned: 933 (million)
% 14.97/3.41 % (14343)------------------------------
% 14.97/3.41 % (14343)------------------------------
% 14.97/3.42 % (14346)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_13954 for (2980ds/770Mi)
% 15.82/3.63 % (14346)Instruction limit reached!
% 15.82/3.63 % (14346)------------------------------
% 15.82/3.63 % (14346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.82/3.63 % (14346)Termination reason: Unknown
% 15.82/3.63 % (14346)Termination phase: Saturation
% 15.82/3.63
% 15.82/3.63 % (14346)Memory used [KB]: 6652
% 15.82/3.63 % (14346)Time elapsed: 0.215 s
% 15.82/3.63 % (14346)Instructions burned: 773 (million)
% 15.82/3.63 % (14346)------------------------------
% 15.82/3.63 % (14346)------------------------------
% 15.82/3.64 % (14347)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_13954 for (2978ds/794Mi)
% 15.82/3.66 % (14340)Instruction limit reached!
% 15.82/3.66 % (14340)------------------------------
% 15.82/3.66 % (14340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.82/3.66 % (14340)Termination reason: Unknown
% 15.82/3.66 % (14340)Termination phase: Saturation
% 15.82/3.66
% 15.82/3.66 % (14340)Memory used [KB]: 14711
% 15.82/3.66 % (14340)Time elapsed: 0.578 s
% 15.82/3.66 % (14340)Instructions burned: 1829 (million)
% 15.82/3.66 % (14340)------------------------------
% 15.82/3.66 % (14340)------------------------------
% 15.82/3.67 % (14348)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_13954 for (2978ds/464Mi)
% 15.82/3.67 % (14322)Instruction limit reached!
% 15.82/3.67 % (14322)------------------------------
% 15.82/3.67 % (14322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.82/3.67 % (14322)Termination reason: Unknown
% 15.82/3.67 % (14322)Termination phase: Saturation
% 15.82/3.67
% 15.82/3.67 % (14322)Memory used [KB]: 10874
% 15.82/3.67 % (14322)Time elapsed: 1.249 s
% 15.82/3.67 % (14322)Instructions burned: 5207 (million)
% 15.82/3.67 % (14322)------------------------------
% 15.82/3.67 % (14322)------------------------------
% 15.82/3.68 % (14349)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_13954 for (2978ds/1376Mi)
% 16.89/3.77 % (14319)Instruction limit reached!
% 16.89/3.77 % (14319)------------------------------
% 16.89/3.77 % (14319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.89/3.77 % (14319)Termination reason: Unknown
% 16.89/3.77 % (14319)Termination phase: Saturation
% 16.89/3.77
% 16.89/3.77 % (14319)Memory used [KB]: 15863
% 16.89/3.77 % (14319)Time elapsed: 1.400 s
% 16.89/3.77 % (14319)Instructions burned: 4439 (million)
% 16.89/3.77 % (14319)------------------------------
% 16.89/3.77 % (14319)------------------------------
% 16.89/3.78 % (14350)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_13954 for (2977ds/906Mi)
% 17.08/3.81 % (14348)Instruction limit reached!
% 17.08/3.81 % (14348)------------------------------
% 17.08/3.81 % (14348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.08/3.81 % (14348)Termination reason: Unknown
% 17.08/3.81 % (14348)Termination phase: Saturation
% 17.08/3.81
% 17.08/3.81 % (14348)Memory used [KB]: 7675
% 17.08/3.81 % (14348)Time elapsed: 0.142 s
% 17.08/3.81 % (14348)Instructions burned: 465 (million)
% 17.08/3.81 % (14348)------------------------------
% 17.08/3.81 % (14348)------------------------------
% 17.08/3.82 % (14351)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_13954 for (2976ds/434Mi)
% 17.08/3.85 % (14324)Instruction limit reached!
% 17.08/3.85 % (14324)------------------------------
% 17.08/3.85 % (14324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.08/3.85 % (14324)Termination reason: Unknown
% 17.08/3.85 % (14324)Termination phase: Saturation
% 17.08/3.85
% 17.08/3.85 % (14324)Memory used [KB]: 10234
% 17.08/3.85 % (14324)Time elapsed: 1.319 s
% 17.08/3.85 % (14324)Instructions burned: 4351 (million)
% 17.08/3.85 % (14324)------------------------------
% 17.08/3.85 % (14324)------------------------------
% 17.08/3.86 % (14352)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_13954 for (2976ds/865Mi)
% 17.08/3.89 % (14347)Instruction limit reached!
% 17.08/3.89 % (14347)------------------------------
% 17.08/3.89 % (14347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.08/3.89 % (14347)Termination reason: Unknown
% 17.08/3.89 % (14347)Termination phase: Saturation
% 17.08/3.89
% 17.08/3.89 % (14347)Memory used [KB]: 3709
% 17.08/3.89 % (14347)Time elapsed: 0.249 s
% 17.08/3.89 % (14347)Instructions burned: 796 (million)
% 17.08/3.89 % (14347)------------------------------
% 17.08/3.89 % (14347)------------------------------
% 17.55/3.90 % (14353)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_13954 for (2975ds/593Mi)
% 17.55/3.95 % (14351)Instruction limit reached!
% 17.55/3.95 % (14351)------------------------------
% 17.55/3.95 % (14351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.55/3.95 % (14351)Termination reason: Unknown
% 17.55/3.95 % (14351)Termination phase: Saturation
% 17.55/3.95
% 17.55/3.95 % (14351)Memory used [KB]: 8571
% 17.55/3.95 % (14351)Time elapsed: 0.131 s
% 17.55/3.95 % (14351)Instructions burned: 436 (million)
% 17.55/3.95 % (14351)------------------------------
% 17.55/3.95 % (14351)------------------------------
% 17.55/3.96 % (14354)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_13954 for (2975ds/443Mi)
% 17.55/4.02 % (14349)Instruction limit reached!
% 17.55/4.02 % (14349)------------------------------
% 17.55/4.02 % (14349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.55/4.02 % (14349)Termination reason: Unknown
% 17.55/4.02 % (14349)Termination phase: Saturation
% 17.55/4.02
% 17.55/4.02 % (14349)Memory used [KB]: 7931
% 17.55/4.02 % (14349)Time elapsed: 0.344 s
% 17.55/4.02 % (14349)Instructions burned: 1378 (million)
% 17.55/4.02 % (14349)------------------------------
% 17.55/4.02 % (14349)------------------------------
% 20.21/4.03 % (14353)Instruction limit reached!
% 20.21/4.03 % (14353)------------------------------
% 20.21/4.03 % (14353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.21/4.03 % (14353)Termination reason: Unknown
% 20.21/4.03 % (14353)Termination phase: Saturation
% 20.21/4.03
% 20.21/4.03 % (14353)Memory used [KB]: 6524
% 20.21/4.03 % (14353)Time elapsed: 0.137 s
% 20.21/4.03 % (14353)Instructions burned: 593 (million)
% 20.21/4.03 % (14353)------------------------------
% 20.21/4.03 % (14353)------------------------------
% 20.21/4.03 % (14355)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_13954 for (2974ds/594Mi)
% 20.21/4.04 % (14350)Instruction limit reached!
% 20.21/4.04 % (14350)------------------------------
% 20.21/4.04 % (14350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.21/4.04 % (14350)Termination reason: Unknown
% 20.21/4.04 % (14350)Termination phase: Saturation
% 20.21/4.04
% 20.21/4.04 % (14350)Memory used [KB]: 9850
% 20.21/4.04 % (14350)Time elapsed: 0.255 s
% 20.21/4.04 % (14350)Instructions burned: 909 (million)
% 20.21/4.04 % (14350)------------------------------
% 20.21/4.04 % (14350)------------------------------
% 20.21/4.04 % (14356)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_13954 for (2974ds/327Mi)
% 20.21/4.04 % (14357)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_13954 for (2974ds/5411Mi)
% 20.21/4.09 % (14354)Instruction limit reached!
% 20.21/4.09 % (14354)------------------------------
% 20.21/4.09 % (14354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.21/4.09 % (14354)Termination reason: Unknown
% 20.21/4.09 % (14354)Termination phase: Saturation
% 20.21/4.09
% 20.21/4.09 % (14354)Memory used [KB]: 7419
% 20.21/4.09 % (14354)Time elapsed: 0.135 s
% 20.21/4.09 % (14354)Instructions burned: 445 (million)
% 20.21/4.09 % (14354)------------------------------
% 20.21/4.09 % (14354)------------------------------
% 20.21/4.09 % (14352)Instruction limit reached!
% 20.21/4.09 % (14352)------------------------------
% 20.21/4.09 % (14352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.21/4.09 % (14352)Termination reason: Unknown
% 20.21/4.09 % (14352)Termination phase: Saturation
% 20.21/4.09
% 20.21/4.09 % (14352)Memory used [KB]: 7291
% 20.21/4.09 % (14352)Time elapsed: 0.230 s
% 20.21/4.09 % (14352)Instructions burned: 867 (million)
% 20.21/4.09 % (14352)------------------------------
% 20.21/4.09 % (14352)------------------------------
% 20.21/4.10 % (14358)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_13954 for (2974ds/1762Mi)
% 20.21/4.10 % (14359)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_13954 for (2974ds/96Mi)
% 20.64/4.13 % (14359)Instruction limit reached!
% 20.64/4.13 % (14359)------------------------------
% 20.64/4.13 % (14359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.64/4.13 % (14359)Termination reason: Unknown
% 20.64/4.13 % (14359)Termination phase: Saturation
% 20.64/4.13
% 20.64/4.13 % (14359)Memory used [KB]: 6268
% 20.64/4.13 % (14359)Time elapsed: 0.025 s
% 20.64/4.13 % (14359)Instructions burned: 96 (million)
% 20.64/4.13 % (14359)------------------------------
% 20.64/4.13 % (14359)------------------------------
% 20.64/4.14 % (14360)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_13954 for (2973ds/503Mi)
% 20.64/4.15 % (14356)Instruction limit reached!
% 20.64/4.15 % (14356)------------------------------
% 20.64/4.15 % (14356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.64/4.15 % (14356)Termination reason: Unknown
% 20.64/4.15 % (14356)Termination phase: Saturation
% 20.64/4.15
% 20.64/4.15 % (14356)Memory used [KB]: 8827
% 20.64/4.15 % (14356)Time elapsed: 0.106 s
% 20.64/4.15 % (14356)Instructions burned: 328 (million)
% 20.64/4.15 % (14356)------------------------------
% 20.64/4.15 % (14356)------------------------------
% 20.64/4.16 % (14361)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_13954 for (2973ds/90Mi)
% 20.64/4.18 % (14361)Instruction limit reached!
% 20.64/4.18 % (14361)------------------------------
% 20.64/4.18 % (14361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.64/4.18 % (14361)Termination reason: Unknown
% 20.64/4.18 % (14361)Termination phase: Saturation
% 20.64/4.18
% 20.64/4.18 % (14361)Memory used [KB]: 6652
% 20.64/4.18 % (14361)Time elapsed: 0.025 s
% 20.64/4.18 % (14361)Instructions burned: 90 (million)
% 20.64/4.18 % (14361)------------------------------
% 20.64/4.18 % (14361)------------------------------
% 20.64/4.19 % (14362)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_13954 for (2973ds/593Mi)
% 20.96/4.21 % (14355)Instruction limit reached!
% 20.96/4.21 % (14355)------------------------------
% 20.96/4.21 % (14355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.96/4.21 % (14355)Termination reason: Unknown
% 20.96/4.21 % (14355)Termination phase: Saturation
% 20.96/4.21
% 20.96/4.21 % (14355)Memory used [KB]: 7419
% 20.96/4.21 % (14355)Time elapsed: 0.181 s
% 20.96/4.21 % (14355)Instructions burned: 595 (million)
% 20.96/4.21 % (14355)------------------------------
% 20.96/4.21 % (14355)------------------------------
% 20.96/4.22 % (14363)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_13954 for (2972ds/1512Mi)
% 20.96/4.28 % (14344)Instruction limit reached!
% 20.96/4.28 % (14344)------------------------------
% 20.96/4.28 % (14344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.96/4.28 % (14344)Termination reason: Unknown
% 20.96/4.28 % (14344)Termination phase: Saturation
% 20.96/4.28
% 20.96/4.28 % (14344)Memory used [KB]: 6908
% 20.96/4.28 % (14344)Time elapsed: 1.064 s
% 20.96/4.28 % (14344)Instructions burned: 4714 (million)
% 20.96/4.28 % (14344)------------------------------
% 20.96/4.28 % (14344)------------------------------
% 20.96/4.29 % (14364)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_13954 for (2972ds/569Mi)
% 20.96/4.29 % (14360)Instruction limit reached!
% 20.96/4.29 % (14360)------------------------------
% 20.96/4.29 % (14360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.96/4.29 % (14360)Termination reason: Unknown
% 20.96/4.29 % (14360)Termination phase: Saturation
% 20.96/4.29
% 20.96/4.29 % (14360)Memory used [KB]: 7419
% 20.96/4.29 % (14360)Time elapsed: 0.178 s
% 20.96/4.29 % (14360)Instructions burned: 505 (million)
% 20.96/4.29 % (14360)------------------------------
% 20.96/4.29 % (14360)------------------------------
% 21.50/4.30 % (14365)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_13954 for (2972ds/501Mi)
% 21.50/4.37 % (14362)Instruction limit reached!
% 21.50/4.37 % (14362)------------------------------
% 21.50/4.37 % (14362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.50/4.37 % (14362)Termination reason: Unknown
% 21.50/4.37 % (14362)Termination phase: Saturation
% 21.50/4.37
% 21.50/4.37 % (14362)Memory used [KB]: 7675
% 21.50/4.37 % (14362)Time elapsed: 0.205 s
% 21.50/4.37 % (14362)Instructions burned: 593 (million)
% 21.50/4.37 % (14362)------------------------------
% 21.50/4.37 % (14362)------------------------------
% 21.50/4.38 % (14366)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_13954 for (2971ds/562Mi)
% 21.79/4.43 % (14364)Instruction limit reached!
% 21.79/4.43 % (14364)------------------------------
% 21.79/4.43 % (14364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.79/4.43 % (14364)Termination reason: Unknown
% 21.79/4.43 % (14364)Termination phase: Saturation
% 21.79/4.43
% 21.79/4.43 % (14364)Memory used [KB]: 8187
% 21.79/4.43 % (14364)Time elapsed: 0.139 s
% 21.79/4.43 % (14364)Instructions burned: 571 (million)
% 21.79/4.43 % (14364)------------------------------
% 21.79/4.43 % (14364)------------------------------
% 21.79/4.44 % (14367)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_13954 for (2970ds/406Mi)
% 21.79/4.45 % (14365)Instruction limit reached!
% 21.79/4.45 % (14365)------------------------------
% 21.79/4.45 % (14365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.79/4.45 % (14365)Termination reason: Unknown
% 21.79/4.45 % (14365)Termination phase: Saturation
% 21.79/4.45
% 21.79/4.45 % (14365)Memory used [KB]: 8443
% 21.79/4.45 % (14365)Time elapsed: 0.175 s
% 21.79/4.45 % (14365)Instructions burned: 502 (million)
% 21.79/4.45 % (14365)------------------------------
% 21.79/4.45 % (14365)------------------------------
% 21.79/4.46 % (14368)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_13954 for (2970ds/582Mi)
% 22.21/4.50 % (14367)Refutation not found, incomplete strategy
% 22.21/4.50 % (14367)------------------------------
% 22.21/4.50 % (14367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.21/4.50 % (14367)Termination reason: Refutation not found, incomplete strategy
% 22.21/4.50
% 22.21/4.50
% 22.21/4.50 % (14367)Memory used [KB]: 6524
% 22.21/4.50 % (14367)Time elapsed: 0.061 s
% 22.21/4.50 % (14367)Instructions burned: 218 (million)
% 22.21/4.50 % (14367)------------------------------
% 22.21/4.50 % (14367)------------------------------
% 22.21/4.51 % (14369)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_13954 for (2969ds/456Mi)
% 22.21/4.54 % (14358)Instruction limit reached!
% 22.21/4.54 % (14358)------------------------------
% 22.21/4.54 % (14358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.21/4.54 % (14358)Termination reason: Unknown
% 22.21/4.54 % (14358)Termination phase: Saturation
% 22.21/4.54
% 22.21/4.54 % (14358)Memory used [KB]: 10106
% 22.21/4.54 % (14358)Time elapsed: 0.444 s
% 22.21/4.54 % (14358)Instructions burned: 1763 (million)
% 22.21/4.54 % (14358)------------------------------
% 22.21/4.54 % (14358)------------------------------
% 22.21/4.55 % (14366)Instruction limit reached!
% 22.21/4.55 % (14366)------------------------------
% 22.21/4.55 % (14366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.21/4.55 % (14366)Termination reason: Unknown
% 22.21/4.55 % (14366)Termination phase: Saturation
% 22.21/4.55
% 22.21/4.55 % (14366)Memory used [KB]: 7547
% 22.21/4.55 % (14366)Time elapsed: 0.198 s
% 22.21/4.55 % (14366)Instructions burned: 563 (million)
% 22.21/4.55 % (14366)------------------------------
% 22.21/4.55 % (14366)------------------------------
% 22.21/4.55 % (14370)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_13954 for (2969ds/393Mi)
% 22.21/4.56 % (14371)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_13954 for (2969ds/1335Mi)
% 23.02/4.65 % (14369)Instruction limit reached!
% 23.02/4.65 % (14369)------------------------------
% 23.02/4.65 % (14369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.02/4.65 % (14369)Termination reason: Unknown
% 23.02/4.65 % (14369)Termination phase: Saturation
% 23.02/4.65
% 23.02/4.65 % (14369)Memory used [KB]: 7291
% 23.02/4.65 % (14369)Time elapsed: 0.143 s
% 23.02/4.65 % (14369)Instructions burned: 458 (million)
% 23.02/4.65 % (14369)------------------------------
% 23.02/4.65 % (14369)------------------------------
% 23.02/4.65 % (14368)Instruction limit reached!
% 23.02/4.65 % (14368)------------------------------
% 23.02/4.65 % (14368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.02/4.65 % (14368)Termination reason: Unknown
% 23.02/4.65 % (14368)Termination phase: Saturation
% 23.02/4.65
% 23.02/4.65 % (14368)Memory used [KB]: 8443
% 23.02/4.65 % (14368)Time elapsed: 0.188 s
% 23.02/4.65 % (14368)Instructions burned: 584 (million)
% 23.02/4.65 % (14368)------------------------------
% 23.02/4.65 % (14368)------------------------------
% 23.02/4.66 % (14372)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_13954 for (2968ds/3373Mi)
% 23.02/4.66 % (14373)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_13954 for (2968ds/474Mi)
% 23.02/4.68 % (14370)Instruction limit reached!
% 23.02/4.68 % (14370)------------------------------
% 23.02/4.68 % (14370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.02/4.68 % (14370)Termination reason: Unknown
% 23.02/4.68 % (14370)Termination phase: Saturation
% 23.02/4.68
% 23.02/4.68 % (14370)Memory used [KB]: 7931
% 23.02/4.68 % (14370)Time elapsed: 0.123 s
% 23.02/4.68 % (14370)Instructions burned: 396 (million)
% 23.02/4.68 % (14370)------------------------------
% 23.02/4.68 % (14370)------------------------------
% 23.02/4.69 % (14374)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_13954 for (2968ds/157Mi)
% 23.60/4.71 % (14363)Instruction limit reached!
% 23.60/4.71 % (14363)------------------------------
% 23.60/4.71 % (14363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.60/4.71 % (14363)Termination reason: Unknown
% 23.60/4.71 % (14363)Termination phase: Saturation
% 23.60/4.71
% 23.60/4.71 % (14363)Memory used [KB]: 11257
% 23.60/4.71 % (14363)Time elapsed: 0.511 s
% 23.60/4.71 % (14363)Instructions burned: 1514 (million)
% 23.60/4.71 % (14363)------------------------------
% 23.60/4.71 % (14363)------------------------------
% 23.60/4.72 % (14375)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_13954 for (2967ds/590Mi)
% 23.60/4.72 % (14374)Instruction limit reached!
% 23.60/4.72 % (14374)------------------------------
% 23.60/4.72 % (14374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.60/4.72 % (14374)Termination reason: Unknown
% 23.60/4.72 % (14374)Termination phase: Saturation
% 23.60/4.72
% 23.60/4.72 % (14374)Memory used [KB]: 6268
% 23.60/4.72 % (14374)Time elapsed: 0.040 s
% 23.60/4.72 % (14374)Instructions burned: 158 (million)
% 23.60/4.72 % (14374)------------------------------
% 23.60/4.72 % (14374)------------------------------
% 23.60/4.73 % (14376)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_13954 for (2967ds/104Mi)
% 23.60/4.76 % (14376)Instruction limit reached!
% 23.60/4.76 % (14376)------------------------------
% 23.60/4.76 % (14376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.60/4.76 % (14376)Termination reason: Unknown
% 23.60/4.76 % (14376)Termination phase: Saturation
% 23.60/4.76
% 23.60/4.76 % (14376)Memory used [KB]: 6780
% 23.60/4.76 % (14376)Time elapsed: 0.030 s
% 23.60/4.76 % (14376)Instructions burned: 105 (million)
% 23.60/4.76 % (14376)------------------------------
% 23.60/4.76 % (14376)------------------------------
% 23.60/4.77 % (14377)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_13954 for (2967ds/414Mi)
% 23.60/4.77 % (14373)Instruction limit reached!
% 23.60/4.77 % (14373)------------------------------
% 23.60/4.77 % (14373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.60/4.77 % (14373)Termination reason: Unknown
% 23.60/4.77 % (14373)Termination phase: Saturation
% 23.60/4.77
% 23.60/4.77 % (14373)Memory used [KB]: 8443
% 23.60/4.77 % (14373)Time elapsed: 0.116 s
% 23.60/4.77 % (14373)Instructions burned: 474 (million)
% 23.60/4.77 % (14373)------------------------------
% 23.60/4.77 % (14373)------------------------------
% 23.60/4.78 % (14378)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_13954 for (2967ds/715Mi)
% 24.41/4.87 % (14377)Instruction limit reached!
% 24.41/4.87 % (14377)------------------------------
% 24.41/4.87 % (14377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.41/4.87 % (14377)Termination reason: Unknown
% 24.41/4.87 % (14377)Termination phase: Saturation
% 24.41/4.87
% 24.41/4.87 % (14377)Memory used [KB]: 6268
% 24.41/4.87 % (14377)Time elapsed: 0.099 s
% 24.41/4.87 % (14377)Instructions burned: 414 (million)
% 24.41/4.87 % (14377)------------------------------
% 24.41/4.87 % (14377)------------------------------
% 24.41/4.88 % (14379)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_13954 for (2966ds/961Mi)
% 24.41/4.89 % (14375)Instruction limit reached!
% 24.41/4.89 % (14375)------------------------------
% 24.41/4.89 % (14375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.41/4.89 % (14375)Termination reason: Unknown
% 24.41/4.89 % (14375)Termination phase: Saturation
% 24.41/4.89
% 24.41/4.89 % (14375)Memory used [KB]: 7931
% 24.41/4.89 % (14375)Time elapsed: 0.175 s
% 24.41/4.89 % (14375)Instructions burned: 590 (million)
% 24.41/4.89 % (14375)------------------------------
% 24.41/4.89 % (14375)------------------------------
% 24.80/4.90 % (14380)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_13954 for (2965ds/1213Mi)
% 24.80/4.92 % (14371)Instruction limit reached!
% 24.80/4.92 % (14371)------------------------------
% 24.80/4.92 % (14371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.80/4.92 % (14371)Termination reason: Unknown
% 24.80/4.92 % (14371)Termination phase: Saturation
% 24.80/4.92
% 24.80/4.92 % (14371)Memory used [KB]: 7419
% 24.80/4.92 % (14371)Time elapsed: 0.362 s
% 24.80/4.92 % (14371)Instructions burned: 1337 (million)
% 24.80/4.92 % (14371)------------------------------
% 24.80/4.92 % (14371)------------------------------
% 24.80/4.93 % (14381)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_13954 for (2965ds/1979Mi)
% 24.80/5.00 % (14378)Instruction limit reached!
% 24.80/5.00 % (14378)------------------------------
% 24.80/5.00 % (14378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.80/5.00 % (14378)Termination reason: Unknown
% 24.80/5.00 % (14378)Termination phase: Saturation
% 24.80/5.00
% 24.80/5.00 % (14378)Memory used [KB]: 3326
% 24.80/5.00 % (14378)Time elapsed: 0.218 s
% 24.80/5.00 % (14378)Instructions burned: 717 (million)
% 24.80/5.00 % (14378)------------------------------
% 24.80/5.00 % (14378)------------------------------
% 24.80/5.01 % (14382)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_13954 for (2964ds/481Mi)
% 27.86/5.13 % (14382)Instruction limit reached!
% 27.86/5.13 % (14382)------------------------------
% 27.86/5.13 % (14382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.86/5.13 % (14382)Termination reason: Unknown
% 27.86/5.13 % (14382)Termination phase: Saturation
% 27.86/5.13
% 27.86/5.13 % (14382)Memory used [KB]: 8571
% 27.86/5.13 % (14382)Time elapsed: 0.117 s
% 27.86/5.13 % (14382)Instructions burned: 481 (million)
% 27.86/5.13 % (14382)------------------------------
% 27.86/5.13 % (14382)------------------------------
% 27.86/5.14 % (14383)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_13954 for (2963ds/783Mi)
% 27.86/5.18 % (14379)Instruction limit reached!
% 27.86/5.18 % (14379)------------------------------
% 27.86/5.18 % (14379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.86/5.18 % (14379)Termination reason: Unknown
% 27.86/5.18 % (14379)Termination phase: Saturation
% 27.86/5.18
% 27.86/5.18 % (14379)Memory used [KB]: 7675
% 27.86/5.18 % (14379)Time elapsed: 0.297 s
% 27.86/5.18 % (14379)Instructions burned: 961 (million)
% 27.86/5.18 % (14379)------------------------------
% 27.86/5.18 % (14379)------------------------------
% 27.86/5.19 % (14384)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_13954 for (2963ds/432Mi)
% 28.41/5.28 % (14380)Instruction limit reached!
% 28.41/5.28 % (14380)------------------------------
% 28.41/5.28 % (14380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.41/5.28 % (14380)Termination reason: Unknown
% 28.41/5.28 % (14380)Termination phase: Saturation
% 28.41/5.28
% 28.41/5.28 % (14380)Memory used [KB]: 10746
% 28.41/5.28 % (14380)Time elapsed: 0.375 s
% 28.41/5.28 % (14380)Instructions burned: 1213 (million)
% 28.41/5.28 % (14380)------------------------------
% 28.41/5.28 % (14380)------------------------------
% 28.41/5.29 % (14385)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_13954 for (2962ds/1670Mi)
% 28.89/5.31 % (14384)Instruction limit reached!
% 28.89/5.31 % (14384)------------------------------
% 28.89/5.31 % (14384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.89/5.31 % (14384)Termination reason: Unknown
% 28.89/5.31 % (14384)Termination phase: Saturation
% 28.89/5.31
% 28.89/5.31 % (14384)Memory used [KB]: 7291
% 28.89/5.31 % (14384)Time elapsed: 0.130 s
% 28.89/5.31 % (14384)Instructions burned: 434 (million)
% 28.89/5.31 % (14384)------------------------------
% 28.89/5.31 % (14384)------------------------------
% 28.89/5.32 % (14386)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_13954 for (2961ds/90Mi)
% 28.89/5.35 % (14386)Instruction limit reached!
% 28.89/5.35 % (14386)------------------------------
% 28.89/5.35 % (14386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.89/5.35 % (14386)Termination reason: Unknown
% 28.89/5.35 % (14386)Termination phase: Saturation
% 28.89/5.35
% 28.89/5.35 % (14386)Memory used [KB]: 6524
% 28.89/5.35 % (14386)Time elapsed: 0.025 s
% 28.89/5.35 % (14386)Instructions burned: 90 (million)
% 28.89/5.35 % (14386)------------------------------
% 28.89/5.35 % (14386)------------------------------
% 28.89/5.36 % (14387)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_13954 for (2961ds/346Mi)
% 28.89/5.38 % (14383)Instruction limit reached!
% 28.89/5.38 % (14383)------------------------------
% 28.89/5.38 % (14383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.89/5.38 % (14383)Termination reason: Unknown
% 28.89/5.38 % (14383)Termination phase: Saturation
% 28.89/5.38
% 28.89/5.38 % (14383)Memory used [KB]: 9083
% 28.89/5.38 % (14383)Time elapsed: 0.244 s
% 28.89/5.38 % (14383)Instructions burned: 783 (million)
% 28.89/5.38 % (14383)------------------------------
% 28.89/5.38 % (14383)------------------------------
% 28.89/5.39 % (14388)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_13954 for (2961ds/401Mi)
% 29.73/5.44 % (14387)Instruction limit reached!
% 29.73/5.44 % (14387)------------------------------
% 29.73/5.44 % (14387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.73/5.44 % (14387)Termination reason: Unknown
% 29.73/5.44 % (14387)Termination phase: Saturation
% 29.73/5.44
% 29.73/5.44 % (14387)Memory used [KB]: 8443
% 29.73/5.44 % (14387)Time elapsed: 0.084 s
% 29.73/5.44 % (14387)Instructions burned: 347 (million)
% 29.73/5.44 % (14387)------------------------------
% 29.73/5.44 % (14387)------------------------------
% 29.73/5.45 % (14389)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_13954 for (2960ds/6454Mi)
% 29.73/5.48 % (14388)Instruction limit reached!
% 29.73/5.48 % (14388)------------------------------
% 29.73/5.48 % (14388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.73/5.48 % (14388)Termination reason: Unknown
% 29.73/5.48 % (14388)Termination phase: Saturation
% 29.73/5.48
% 29.73/5.48 % (14388)Memory used [KB]: 6524
% 29.73/5.48 % (14388)Time elapsed: 0.094 s
% 29.73/5.48 % (14388)Instructions burned: 403 (million)
% 29.73/5.48 % (14388)------------------------------
% 29.73/5.48 % (14388)------------------------------
% 29.73/5.49 % (14390)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_13954 for (2960ds/283Mi)
% 30.32/5.50 % (14381)Instruction limit reached!
% 30.32/5.50 % (14381)------------------------------
% 30.32/5.50 % (14381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.32/5.50 % (14381)Termination reason: Unknown
% 30.32/5.50 % (14381)Termination phase: Saturation
% 30.32/5.50
% 30.32/5.50 % (14381)Memory used [KB]: 8059
% 30.32/5.50 % (14381)Time elapsed: 0.566 s
% 30.32/5.50 % (14381)Instructions burned: 1979 (million)
% 30.32/5.50 % (14381)------------------------------
% 30.32/5.50 % (14381)------------------------------
% 30.32/5.51 % (14391)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_13954 for (2959ds/865Mi)
% 30.32/5.58 % (14390)Instruction limit reached!
% 30.32/5.58 % (14390)------------------------------
% 30.32/5.58 % (14390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.32/5.58 % (14390)Termination reason: Unknown
% 30.32/5.58 % (14390)Termination phase: Saturation
% 30.32/5.58
% 30.32/5.58 % (14390)Memory used [KB]: 7291
% 30.32/5.58 % (14390)Time elapsed: 0.108 s
% 30.32/5.58 % (14390)Instructions burned: 284 (million)
% 30.32/5.58 % (14390)------------------------------
% 30.32/5.58 % (14390)------------------------------
% 30.32/5.59 % (14392)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_13954 for (2959ds/4528Mi)
% 30.72/5.63 % (14392)Refutation not found, incomplete strategy
% 30.72/5.63 % (14392)------------------------------
% 30.72/5.63 % (14392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.72/5.63 % (14392)Termination reason: Refutation not found, incomplete strategy
% 30.72/5.63
% 30.72/5.63
% 30.72/5.63 % (14392)Memory used [KB]: 1791
% 30.72/5.63 % (14392)Time elapsed: 0.043 s
% 30.72/5.63 % (14392)Instructions burned: 161 (million)
% 30.72/5.63 % (14392)------------------------------
% 30.72/5.63 % (14392)------------------------------
% 30.72/5.64 % (14393)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_13954 for (2958ds/1001Mi)
% 30.72/5.69 % (14372)Instruction limit reached!
% 30.72/5.69 % (14372)------------------------------
% 30.72/5.69 % (14372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.72/5.69 % (14372)Termination reason: Unknown
% 30.72/5.69 % (14372)Termination phase: Saturation
% 30.72/5.69
% 30.72/5.69 % (14372)Memory used [KB]: 10746
% 30.72/5.69 % (14372)Time elapsed: 1.031 s
% 30.72/5.69 % (14372)Instructions burned: 3374 (million)
% 30.72/5.69 % (14372)------------------------------
% 30.72/5.69 % (14372)------------------------------
% 31.06/5.70 % (14394)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_13954 for (2957ds/102Mi)
% 31.06/5.70 % (14385)Instruction limit reached!
% 31.06/5.70 % (14385)------------------------------
% 31.06/5.70 % (14385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.06/5.70 % (14385)Termination reason: Unknown
% 31.06/5.70 % (14385)Termination phase: Saturation
% 31.06/5.70
% 31.06/5.70 % (14385)Memory used [KB]: 9083
% 31.06/5.70 % (14385)Time elapsed: 0.413 s
% 31.06/5.70 % (14385)Instructions burned: 1672 (million)
% 31.06/5.70 % (14385)------------------------------
% 31.06/5.70 % (14385)------------------------------
% 31.06/5.71 % (14395)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_13954 for (2957ds/952Mi)
% 31.06/5.73 % (14394)Instruction limit reached!
% 31.06/5.73 % (14394)------------------------------
% 31.06/5.73 % (14394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.06/5.73 % (14394)Termination reason: Unknown
% 31.06/5.73 % (14394)Termination phase: Saturation
% 31.06/5.73
% 31.06/5.73 % (14394)Memory used [KB]: 6396
% 31.06/5.73 % (14394)Time elapsed: 0.030 s
% 31.06/5.73 % (14394)Instructions burned: 104 (million)
% 31.06/5.73 % (14394)------------------------------
% 31.06/5.73 % (14394)------------------------------
% 31.06/5.73 % (14357)Refutation not found, non-redundant clauses discarded% (14357)------------------------------
% 31.06/5.73 % (14357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.06/5.73 % (14357)Termination reason: Refutation not found, non-redundant clauses discarded
% 31.06/5.73
% 31.06/5.73 % (14357)Memory used [KB]: 15863
% 31.06/5.73 % (14357)Time elapsed: 1.684 s
% 31.06/5.73 % (14357)Instructions burned: 5371 (million)
% 31.06/5.73 % (14357)------------------------------
% 31.06/5.73 % (14357)------------------------------
% 31.06/5.74 % (14396)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_13954 for (2957ds/578Mi)
% 31.06/5.74 % (14397)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_13954 for (2957ds/643Mi)
% 31.06/5.76 % (14391)Instruction limit reached!
% 31.06/5.76 % (14391)------------------------------
% 31.06/5.76 % (14391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.06/5.76 % (14391)Termination reason: Unknown
% 31.06/5.76 % (14391)Termination phase: Saturation
% 31.06/5.76
% 31.06/5.76 % (14391)Memory used [KB]: 7803
% 31.06/5.76 % (14391)Time elapsed: 0.278 s
% 31.06/5.76 % (14391)Instructions burned: 865 (million)
% 31.06/5.76 % (14391)------------------------------
% 31.06/5.76 % (14391)------------------------------
% 31.06/5.77 % (14398)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_13954 for (2957ds/865Mi)
% 31.95/5.87 % (14396)Instruction limit reached!
% 31.95/5.87 % (14396)------------------------------
% 31.95/5.87 % (14396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.95/5.87 % (14396)Termination reason: Unknown
% 31.95/5.87 % (14396)Termination phase: Saturation
% 31.95/5.87
% 31.95/5.87 % (14396)Memory used [KB]: 7547
% 31.95/5.87 % (14396)Time elapsed: 0.134 s
% 31.95/5.87 % (14396)Instructions burned: 578 (million)
% 31.95/5.87 % (14396)------------------------------
% 31.95/5.87 % (14396)------------------------------
% 31.95/5.88 % (14345)Instruction limit reached!
% 31.95/5.88 % (14345)------------------------------
% 31.95/5.88 % (14345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.95/5.88 % (14345)Termination reason: Unknown
% 31.95/5.88 % (14345)Termination phase: Saturation
% 31.95/5.88
% 31.95/5.88 % (14345)Memory used [KB]: 26737
% 31.95/5.88 % (14345)Time elapsed: 2.635 s
% 31.95/5.88 % (14345)Instructions burned: 8250 (million)
% 31.95/5.88 % (14345)------------------------------
% 31.95/5.88 % (14345)------------------------------
% 31.95/5.88 % (14399)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_13954 for (2956ds/1174Mi)
% 31.95/5.89 % (14400)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_13954 for (2956ds/644Mi)
% 31.95/5.89 % (14397)Instruction limit reached!
% 31.95/5.89 % (14397)------------------------------
% 31.95/5.89 % (14397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.95/5.89 % (14397)Termination reason: Unknown
% 31.95/5.89 % (14397)Termination phase: Saturation
% 31.95/5.89
% 31.95/5.89 % (14397)Memory used [KB]: 8187
% 31.95/5.89 % (14397)Time elapsed: 0.155 s
% 31.95/5.89 % (14397)Instructions burned: 646 (million)
% 31.95/5.89 % (14397)------------------------------
% 31.95/5.89 % (14397)------------------------------
% 32.33/5.90 % (14401)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_13954 for (2955ds/1201Mi)
% 32.33/5.95 % (14393)Instruction limit reached!
% 32.33/5.95 % (14393)------------------------------
% 32.33/5.95 % (14393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.33/5.95 % (14393)Termination reason: Unknown
% 32.33/5.95 % (14393)Termination phase: Saturation
% 32.33/5.95
% 32.33/5.95 % (14393)Memory used [KB]: 9338
% 32.33/5.95 % (14393)Time elapsed: 0.316 s
% 32.33/5.95 % (14393)Instructions burned: 1002 (million)
% 32.33/5.95 % (14393)------------------------------
% 32.33/5.95 % (14393)------------------------------
% 32.33/5.96 % (14402)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_13954 for (2955ds/1046Mi)
% 32.33/6.01 % (14395)Instruction limit reached!
% 32.33/6.01 % (14395)------------------------------
% 32.33/6.01 % (14395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.33/6.01 % (14395)Termination reason: Unknown
% 32.33/6.01 % (14395)Termination phase: Saturation
% 32.33/6.01
% 32.33/6.01 % (14395)Memory used [KB]: 8443
% 32.33/6.01 % (14395)Time elapsed: 0.298 s
% 32.33/6.01 % (14395)Instructions burned: 954 (million)
% 32.33/6.01 % (14395)------------------------------
% 32.33/6.01 % (14395)------------------------------
% 32.33/6.01 % (14398)Instruction limit reached!
% 32.33/6.01 % (14398)------------------------------
% 32.33/6.01 % (14398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.33/6.01 % (14398)Termination reason: Unknown
% 32.33/6.01 % (14398)Termination phase: Saturation
% 32.33/6.01
% 32.33/6.01 % (14398)Memory used [KB]: 6652
% 32.33/6.01 % (14398)Time elapsed: 0.240 s
% 32.33/6.01 % (14398)Instructions burned: 865 (million)
% 32.33/6.01 % (14398)------------------------------
% 32.33/6.01 % (14398)------------------------------
% 32.33/6.02 % (14403)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_13954 for (2954ds/222Mi)
% 32.33/6.02 % (14404)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_13954 for (2954ds/68Mi)
% 34.24/6.04 % (14404)Instruction limit reached!
% 34.24/6.04 % (14404)------------------------------
% 34.24/6.04 % (14404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.24/6.04 % (14404)Termination reason: Unknown
% 34.24/6.04 % (14404)Termination phase: Saturation
% 34.24/6.04
% 34.24/6.04 % (14404)Memory used [KB]: 6268
% 34.24/6.04 % (14404)Time elapsed: 0.019 s
% 34.24/6.04 % (14404)Instructions burned: 70 (million)
% 34.24/6.04 % (14404)------------------------------
% 34.24/6.04 % (14404)------------------------------
% 34.24/6.05 % (14405)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_13954 for (2954ds/454Mi)
% 34.24/6.07 % (14403)Instruction limit reached!
% 34.24/6.07 % (14403)------------------------------
% 34.24/6.07 % (14403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.24/6.07 % (14403)Termination reason: Unknown
% 34.24/6.07 % (14403)Termination phase: Saturation
% 34.24/6.07
% 34.24/6.07 % (14403)Memory used [KB]: 6268
% 34.24/6.07 % (14403)Time elapsed: 0.055 s
% 34.24/6.07 % (14403)Instructions burned: 224 (million)
% 34.24/6.07 % (14403)------------------------------
% 34.24/6.07 % (14403)------------------------------
% 34.24/6.08 % (14406)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_13954 for (2954ds/360Mi)
% 34.24/6.08 % (14400)Instruction limit reached!
% 34.24/6.08 % (14400)------------------------------
% 34.24/6.08 % (14400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.24/6.08 % (14400)Termination reason: Unknown
% 34.24/6.08 % (14400)Termination phase: Saturation
% 34.24/6.08
% 34.24/6.08 % (14400)Memory used [KB]: 6908
% 34.24/6.08 % (14400)Time elapsed: 0.196 s
% 34.24/6.08 % (14400)Instructions burned: 644 (million)
% 34.24/6.08 % (14400)------------------------------
% 34.24/6.08 % (14400)------------------------------
% 34.24/6.09 % (14407)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_13954 for (2954ds/157Mi)
% 34.82/6.13 % (14407)Instruction limit reached!
% 34.82/6.13 % (14407)------------------------------
% 34.82/6.13 % (14407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.82/6.13 % (14407)Termination reason: Unknown
% 34.82/6.13 % (14407)Termination phase: Saturation
% 34.82/6.13
% 34.82/6.13 % (14407)Memory used [KB]: 6268
% 34.82/6.13 % (14407)Time elapsed: 0.040 s
% 34.82/6.13 % (14407)Instructions burned: 159 (million)
% 34.82/6.13 % (14407)------------------------------
% 34.82/6.13 % (14407)------------------------------
% 34.82/6.14 % (14408)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_13954 for (2953ds/5061Mi)
% 34.82/6.16 % (14405)Instruction limit reached!
% 34.82/6.16 % (14405)------------------------------
% 34.82/6.16 % (14405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.82/6.16 % (14405)Termination reason: Unknown
% 34.82/6.16 % (14405)Termination phase: Saturation
% 34.82/6.16
% 34.82/6.16 % (14405)Memory used [KB]: 12920
% 34.82/6.16 % (14405)Time elapsed: 0.111 s
% 34.82/6.16 % (14405)Instructions burned: 456 (million)
% 34.82/6.16 % (14405)------------------------------
% 34.82/6.16 % (14405)------------------------------
% 34.82/6.16 % (14406)Instruction limit reached!
% 34.82/6.16 % (14406)------------------------------
% 34.82/6.16 % (14406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.82/6.16 % (14406)Termination reason: Unknown
% 34.82/6.16 % (14406)Termination phase: Saturation
% 34.82/6.16
% 34.82/6.16 % (14406)Memory used [KB]: 6524
% 34.82/6.16 % (14406)Time elapsed: 0.086 s
% 34.82/6.16 % (14406)Instructions burned: 360 (million)
% 34.82/6.16 % (14406)------------------------------
% 34.82/6.16 % (14406)------------------------------
% 34.82/6.17 % (14409)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_13954 for (2953ds/2401Mi)
% 34.82/6.17 % (14410)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_13954 for (2953ds/5798Mi)
% 35.39/6.22 % (14402)Instruction limit reached!
% 35.39/6.22 % (14402)------------------------------
% 35.39/6.22 % (14402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.39/6.22 % (14402)Termination reason: Unknown
% 35.39/6.22 % (14402)Termination phase: Saturation
% 35.39/6.22
% 35.39/6.22 % (14402)Memory used [KB]: 6652
% 35.39/6.22 % (14402)Time elapsed: 0.255 s
% 35.39/6.22 % (14402)Instructions burned: 1046 (million)
% 35.39/6.22 % (14402)------------------------------
% 35.39/6.22 % (14402)------------------------------
% 35.39/6.23 % (14411)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_13954 for (2952ds/346Mi)
% 35.39/6.24 % (14399)Instruction limit reached!
% 35.39/6.24 % (14399)------------------------------
% 35.39/6.24 % (14399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.39/6.24 % (14399)Termination reason: Unknown
% 35.39/6.24 % (14399)Termination phase: Saturation
% 35.39/6.24
% 35.39/6.24 % (14399)Memory used [KB]: 8059
% 35.39/6.24 % (14399)Time elapsed: 0.365 s
% 35.39/6.24 % (14399)Instructions burned: 1174 (million)
% 35.39/6.24 % (14399)------------------------------
% 35.39/6.24 % (14399)------------------------------
% 35.39/6.25 % (14412)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_13954 for (2952ds/1321Mi)
% 35.39/6.27 % (14401)Instruction limit reached!
% 35.39/6.27 % (14401)------------------------------
% 35.39/6.27 % (14401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.39/6.27 % (14401)Termination reason: Unknown
% 35.39/6.27 % (14401)Termination phase: Saturation
% 35.39/6.27
% 35.39/6.27 % (14401)Memory used [KB]: 9466
% 35.39/6.27 % (14401)Time elapsed: 0.369 s
% 35.39/6.27 % (14401)Instructions burned: 1201 (million)
% 35.39/6.27 % (14401)------------------------------
% 35.39/6.27 % (14401)------------------------------
% 35.39/6.29 % (14413)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_13954 for (2952ds/1312Mi)
% 35.66/6.31 % (14411)Instruction limit reached!
% 35.66/6.31 % (14411)------------------------------
% 35.66/6.31 % (14411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.66/6.31 % (14411)Termination reason: Unknown
% 35.66/6.31 % (14411)Termination phase: Saturation
% 35.66/6.31
% 35.66/6.31 % (14411)Memory used [KB]: 8443
% 35.66/6.31 % (14411)Time elapsed: 0.085 s
% 35.66/6.31 % (14411)Instructions burned: 346 (million)
% 35.66/6.31 % (14411)------------------------------
% 35.66/6.31 % (14411)------------------------------
% 35.66/6.32 % (14414)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_13954 for (2951ds/672Mi)
% 35.95/6.52 % (14414)Instruction limit reached!
% 35.95/6.52 % (14414)------------------------------
% 35.95/6.52 % (14414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.95/6.52 % (14414)Termination reason: Unknown
% 35.95/6.52 % (14414)Termination phase: Saturation
% 35.95/6.52
% 35.95/6.52 % (14414)Memory used [KB]: 8955
% 35.95/6.52 % (14414)Time elapsed: 0.228 s
% 35.95/6.52 % (14414)Instructions burned: 674 (million)
% 35.95/6.52 % (14414)------------------------------
% 35.95/6.52 % (14414)------------------------------
% 35.95/6.54 % (14415)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_13954 for (2949ds/1897Mi)
% 36.27/6.66 % (14412)Refutation not found, non-redundant clauses discarded% (14412)------------------------------
% 36.27/6.66 % (14412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.27/6.66 % (14412)Termination reason: Refutation not found, non-redundant clauses discarded
% 36.27/6.66
% 36.27/6.66 % (14412)Memory used [KB]: 5500
% 36.27/6.66 % (14412)Time elapsed: 0.428 s
% 36.27/6.66 % (14412)Instructions burned: 1319 (million)
% 36.27/6.66 % (14412)------------------------------
% 36.27/6.66 % (14412)------------------------------
% 36.27/6.67 % (14416)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_13954 for (2948ds/1202Mi)
% 36.78/6.71 % (14413)Instruction limit reached!
% 36.78/6.71 % (14413)------------------------------
% 36.78/6.71 % (14413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.78/6.71 % (14413)Termination reason: Unknown
% 36.78/6.71 % (14413)Termination phase: Saturation
% 36.78/6.71
% 36.78/6.71 % (14413)Memory used [KB]: 8955
% 36.78/6.71 % (14413)Time elapsed: 0.428 s
% 36.78/6.71 % (14413)Instructions burned: 1313 (million)
% 36.78/6.71 % (14413)------------------------------
% 36.78/6.71 % (14413)------------------------------
% 36.78/6.72 % (14417)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_13954 for (2947ds/1493Mi)
% 37.44/6.91 % (14409)Instruction limit reached!
% 37.44/6.91 % (14409)------------------------------
% 37.44/6.91 % (14409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.44/6.91 % (14409)Termination reason: Unknown
% 37.44/6.91 % (14409)Termination phase: Saturation
% 37.44/6.91
% 37.44/6.91 % (14409)Memory used [KB]: 7675
% 37.44/6.91 % (14409)Time elapsed: 0.742 s
% 37.44/6.91 % (14409)Instructions burned: 2401 (million)
% 37.44/6.91 % (14409)------------------------------
% 37.44/6.91 % (14409)------------------------------
% 37.44/6.92 % (14418)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_13954 for (2945ds/7679Mi)
% 41.19/7.02 % (14416)Instruction limit reached!
% 41.19/7.02 % (14416)------------------------------
% 41.19/7.02 % (14416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.19/7.02 % (14416)Termination reason: Unknown
% 41.19/7.02 % (14416)Termination phase: Saturation
% 41.19/7.02
% 41.19/7.02 % (14416)Memory used [KB]: 5628
% 41.19/7.02 % (14416)Time elapsed: 0.373 s
% 41.19/7.02 % (14416)Instructions burned: 1203 (million)
% 41.19/7.02 % (14416)------------------------------
% 41.19/7.02 % (14416)------------------------------
% 41.19/7.03 % (14419)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_13954 for (2944ds/340Mi)
% 41.81/7.13 % (14415)Instruction limit reached!
% 41.81/7.13 % (14415)------------------------------
% 41.81/7.13 % (14415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.81/7.13 % (14415)Termination reason: Unknown
% 41.81/7.13 % (14415)Termination phase: Saturation
% 41.81/7.13
% 41.81/7.13 % (14415)Memory used [KB]: 10490
% 41.81/7.13 % (14415)Time elapsed: 0.617 s
% 41.81/7.13 % (14415)Instructions burned: 1898 (million)
% 41.81/7.13 % (14415)------------------------------
% 41.81/7.13 % (14415)------------------------------
% 41.81/7.13 % (14419)Instruction limit reached!
% 41.81/7.13 % (14419)------------------------------
% 41.81/7.13 % (14419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.81/7.13 % (14419)Termination reason: Unknown
% 41.81/7.13 % (14419)Termination phase: Saturation
% 41.81/7.13
% 41.81/7.13 % (14419)Memory used [KB]: 8443
% 41.81/7.13 % (14419)Time elapsed: 0.106 s
% 41.81/7.13 % (14419)Instructions burned: 340 (million)
% 41.81/7.13 % (14419)------------------------------
% 41.81/7.13 % (14419)------------------------------
% 41.81/7.14 % (14420)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_13954 for (2943ds/3672Mi)
% 41.81/7.14 % (14421)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_13954 for (2943ds/1535Mi)
% 41.81/7.15 % (14417)Instruction limit reached!
% 41.81/7.15 % (14417)------------------------------
% 41.81/7.15 % (14417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.81/7.15 % (14417)Termination reason: Unknown
% 41.81/7.15 % (14417)Termination phase: Saturation
% 41.81/7.15
% 41.81/7.15 % (14417)Memory used [KB]: 7419
% 41.81/7.15 % (14417)Time elapsed: 0.449 s
% 41.81/7.15 % (14417)Instructions burned: 1495 (million)
% 41.81/7.15 % (14417)------------------------------
% 41.81/7.15 % (14417)------------------------------
% 41.81/7.16 % (14422)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_13954 for (2943ds/4637Mi)
% 43.16/7.43 % (14389)Instruction limit reached!
% 43.16/7.43 % (14389)------------------------------
% 43.16/7.43 % (14389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.16/7.43 % (14389)Termination reason: Unknown
% 43.16/7.43 % (14389)Termination phase: Saturation
% 43.16/7.43
% 43.16/7.43 % (14389)Memory used [KB]: 9466
% 43.16/7.43 % (14389)Time elapsed: 2.001 s
% 43.16/7.43 % (14389)Instructions burned: 6455 (million)
% 43.16/7.43 % (14389)------------------------------
% 43.16/7.43 % (14389)------------------------------
% 43.16/7.44 % (14423)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_13954 for (2940ds/3174Mi)
% 43.51/7.53 % (14421)Instruction limit reached!
% 43.51/7.53 % (14421)------------------------------
% 43.51/7.53 % (14421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.51/7.53 % (14421)Termination reason: Unknown
% 43.51/7.53 % (14421)Termination phase: Saturation
% 43.51/7.53
% 43.51/7.53 % (14421)Memory used [KB]: 9722
% 43.51/7.53 % (14421)Time elapsed: 0.385 s
% 43.51/7.53 % (14421)Instructions burned: 1539 (million)
% 43.51/7.53 % (14421)------------------------------
% 43.51/7.53 % (14421)------------------------------
% 43.51/7.54 % (14424)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_13954 for (2939ds/307Mi)
% 43.51/7.59 % (14408)Instruction limit reached!
% 43.51/7.59 % (14408)------------------------------
% 43.51/7.59 % (14408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.51/7.59 % (14408)Termination reason: Unknown
% 43.51/7.59 % (14408)Termination phase: Saturation
% 43.51/7.59
% 43.51/7.59 % (14408)Memory used [KB]: 8699
% 43.51/7.59 % (14408)Time elapsed: 1.452 s
% 43.51/7.59 % (14408)Instructions burned: 5061 (million)
% 43.51/7.59 % (14408)------------------------------
% 43.51/7.59 % (14408)------------------------------
% 44.20/7.60 % (14425)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_13954 for (2938ds/3619Mi)
% 44.20/7.61 % (14424)Instruction limit reached!
% 44.20/7.61 % (14424)------------------------------
% 44.20/7.61 % (14424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.20/7.61 % (14424)Termination reason: Unknown
% 44.20/7.61 % (14424)Termination phase: Saturation
% 44.20/7.61
% 44.20/7.61 % (14424)Memory used [KB]: 6268
% 44.20/7.61 % (14424)Time elapsed: 0.075 s
% 44.20/7.61 % (14424)Instructions burned: 307 (million)
% 44.20/7.61 % (14424)------------------------------
% 44.20/7.61 % (14424)------------------------------
% 44.20/7.62 % (14426)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_13954 for (2938ds/2325Mi)
% 44.90/7.98 % (14410)Instruction limit reached!
% 44.90/7.98 % (14410)------------------------------
% 44.90/7.98 % (14410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.90/7.98 % (14410)Termination reason: Unknown
% 44.90/7.98 % (14410)Termination phase: Saturation
% 44.90/7.98
% 44.90/7.98 % (14410)Memory used [KB]: 12153
% 44.90/7.98 % (14410)Time elapsed: 1.808 s
% 44.90/7.98 % (14410)Instructions burned: 5798 (million)
% 44.90/7.98 % (14410)------------------------------
% 44.90/7.98 % (14410)------------------------------
% 44.90/7.99 % (14427)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_13954 for (2935ds/2341Mi)
% 50.23/8.31 % (14426)Refutation not found, non-redundant clauses discarded% (14426)------------------------------
% 50.23/8.31 % (14426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.23/8.31 % (14426)Termination reason: Refutation not found, non-redundant clauses discarded
% 50.23/8.31
% 50.23/8.31 % (14426)Memory used [KB]: 12409
% 50.23/8.31 % (14426)Time elapsed: 0.689 s
% 50.23/8.31 % (14426)Instructions burned: 2231 (million)
% 50.23/8.31 % (14426)------------------------------
% 50.23/8.31 % (14426)------------------------------
% 50.23/8.31 % (14420)Instruction limit reached!
% 50.23/8.31 % (14420)------------------------------
% 50.23/8.31 % (14420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.23/8.31 % (14420)Termination reason: Unknown
% 50.23/8.31 % (14420)Termination phase: Saturation
% 50.23/8.31
% 50.23/8.31 % (14420)Memory used [KB]: 10746
% 50.23/8.31 % (14420)Time elapsed: 1.172 s
% 50.23/8.31 % (14420)Instructions burned: 3673 (million)
% 50.23/8.31 % (14420)------------------------------
% 50.23/8.31 % (14420)------------------------------
% 50.23/8.32 % (14428)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_13954 for (2931ds/7257Mi)
% 50.23/8.32 % (14429)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_13954 for (2931ds/3710Mi)
% 50.23/8.36 % (14425)First to succeed.
% 50.23/8.36 % (14425)Refutation found. Thanks to Tanya!
% 50.23/8.36 % SZS status Theorem for DTF2THF_13954
% 50.23/8.36 % SZS output start Proof for DTF2THF_13954
% 50.23/8.36 thf(func_def_0, type, in: $i > $i > $o).
% 50.23/8.36 thf(func_def_1, type, exu: ($i > $o) > $o).
% 50.23/8.36 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 50.23/8.36 thf(func_def_8, type, powerset: $i > $i).
% 50.23/8.36 thf(func_def_10, type, setunion: $i > $i).
% 50.23/8.36 thf(func_def_19, type, descr: ($i > $o) > $i).
% 50.23/8.36 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 50.23/8.36 thf(func_def_26, type, prop2set: $o > $i).
% 50.23/8.36 thf(func_def_36, type, nonempty: $i > $o).
% 50.23/8.36 thf(func_def_69, type, set2prop: $i > $o).
% 50.23/8.36 thf(func_def_88, type, subset: $i > $i > $o).
% 50.23/8.36 thf(func_def_89, type, disjoint: $i > $i > $o).
% 50.23/8.36 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 50.23/8.36 thf(func_def_114, type, binunion: $i > $i > $i).
% 50.23/8.36 thf(func_def_122, type, binintersect: $i > $i > $i).
% 50.23/8.36 thf(func_def_135, type, regular: $i > $o).
% 50.23/8.36 thf(func_def_136, type, setminus: $i > $i > $i).
% 50.23/8.36 thf(func_def_159, type, sP1: $i > $i > $o).
% 50.23/8.36 thf(func_def_160, type, sP2: $i > $o).
% 50.23/8.36 thf(func_def_161, type, sP3: $i > $i > $o).
% 50.23/8.36 thf(func_def_162, type, sP4: $i > $i > $o).
% 50.23/8.36 thf(func_def_171, type, sK13: $i > $i).
% 50.23/8.36 thf(func_def_175, type, sK17: $i > $i > $i).
% 50.23/8.36 thf(func_def_182, type, sK24: $i > $o).
% 50.23/8.36 thf(func_def_183, type, sK25: ($i > $o) > $i).
% 50.23/8.36 thf(func_def_184, type, sK26: $i > $o).
% 50.23/8.36 thf(func_def_185, type, sK27: $i > $o).
% 50.23/8.36 thf(func_def_186, type, sK28: ($i > $o) > ($i > $o) > $i).
% 50.23/8.36 thf(func_def_187, type, sK29: ($i > $o) > ($i > $o) > $i).
% 50.23/8.36 thf(func_def_203, type, sK45: $i > $o).
% 50.23/8.36 thf(func_def_205, type, sK47: $i > ($i > $o) > $i).
% 50.23/8.36 thf(func_def_206, type, sK48: $i > $i > $o).
% 50.23/8.36 thf(func_def_208, type, sK50: $i > $i).
% 50.23/8.36 thf(func_def_209, type, sK51: $i > $i).
% 50.23/8.36 thf(func_def_210, type, sK52: $i > ($i > $i > $o) > $i).
% 50.23/8.36 thf(func_def_211, type, sK53: $i > $i > ($i > $i > $o) > $i).
% 50.23/8.36 thf(func_def_212, type, sK54: $i > ($i > $i > $o) > $i).
% 50.23/8.36 thf(func_def_216, type, sK58: $i > $o).
% 50.23/8.36 thf(func_def_228, type, sK70: $i > $o).
% 50.23/8.36 thf(func_def_235, type, sK77: $i > $o).
% 50.23/8.36 thf(func_def_241, type, sK83: $i > $i).
% 50.23/8.36 thf(func_def_246, type, sK88: ($i > $o) > ($i > $o) > $i).
% 50.23/8.36 thf(func_def_247, type, sK89: ($i > $o) > ($i > $o) > $i).
% 50.23/8.36 thf(func_def_248, type, sK90: $i > $o).
% 50.23/8.36 thf(func_def_249, type, sK91: $i > $o).
% 50.23/8.36 thf(func_def_268, type, sK110: $i > $o).
% 50.23/8.36 thf(func_def_269, type, sK111: $i > $i).
% 50.23/8.36 thf(func_def_270, type, sK112: ($i > $o) > $i).
% 50.23/8.36 thf(func_def_276, type, sK118: $i > $i).
% 50.23/8.36 thf(func_def_278, type, sK120: $i > $i).
% 50.23/8.36 thf(func_def_279, type, sK121: $i > $o).
% 50.23/8.36 thf(func_def_281, type, sK123: ($i > $o) > $i).
% 50.23/8.36 thf(func_def_282, type, sK124: ($i > $o) > $i).
% 50.23/8.36 thf(func_def_293, type, sK135: $i > $i > $i).
% 50.23/8.36 thf(func_def_301, type, sK143: $i > ($i > $o) > $i).
% 50.23/8.36 thf(func_def_302, type, sK144: $i > $o).
% 50.23/8.36 thf(func_def_306, type, sK148: $i > $o).
% 50.23/8.36 thf(func_def_309, type, sK151: $i > $o).
% 50.23/8.36 thf(func_def_312, type, sK154: $i > $i > $i).
% 50.23/8.36 thf(func_def_323, type, sK165: $i > $i).
% 50.23/8.36 thf(func_def_328, type, sK170: $i > $i).
% 50.23/8.36 thf(func_def_343, type, sK185: $i > $o).
% 50.23/8.36 thf(func_def_346, type, sK188: $i > ($i > $o) > $i).
% 50.23/8.36 thf(func_def_348, type, sK190: $i > $o).
% 50.23/8.36 thf(func_def_351, type, sK193: $i > ($i > $o) > $i).
% 50.23/8.36 thf(func_def_352, type, sK194: $i > $o).
% 50.23/8.36 thf(func_def_367, type, sK209: $i > $o).
% 50.23/8.36 thf(func_def_368, type, sK210: $i > $i).
% 50.23/8.36 thf(func_def_369, type, sK211: ($i > $o) > $i).
% 50.23/8.36 thf(func_def_370, type, sK212: $i > $i > $i).
% 50.23/8.36 thf(func_def_371, type, sK213: $i > $i > $i).
% 50.23/8.36 thf(func_def_372, type, sK214: $i > $i > $i).
% 50.23/8.36 thf(func_def_373, type, sK215: $i > $i > $i).
% 50.23/8.36 thf(func_def_374, type, sK216: $i > $i > $i > $i).
% 50.23/8.36 thf(func_def_375, type, sK217: $i > $i).
% 50.23/8.36 thf(func_def_376, type, sK218: $i > $i).
% 50.23/8.36 thf(func_def_377, type, sK219: $i > $i).
% 50.23/8.36 thf(func_def_378, type, sK220: $i > $i).
% 50.23/8.36 thf(func_def_379, type, sK221: $i > $i > $i > $i).
% 50.23/8.36 thf(func_def_380, type, sK222: $i > $i > $i > $i).
% 50.23/8.36 thf(func_def_381, type, sK223: $i > $i > $i).
% 50.23/8.36 thf(func_def_382, type, sK224: $i > $i > $i).
% 50.23/8.36 thf(func_def_383, type, sK225: $i > $i > $i).
% 50.23/8.36 thf(func_def_384, type, sK226: $i > $i).
% 50.23/8.36 thf(func_def_385, type, sK227: $i > $i > $i).
% 50.23/8.36 thf(func_def_387, type, sK229: $i > $i).
% 50.23/8.36 thf(func_def_388, type, sK230: $i > $i).
% 50.23/8.36 thf(func_def_389, type, sK231: $i > $i > $i).
% 50.23/8.36 thf(func_def_395, type, sK237: $i > $o).
% 50.23/8.36 thf(func_def_396, type, sK238: $i > $o).
% 50.23/8.36 thf(func_def_399, type, sK241: $i > $o).
% 50.23/8.36 thf(func_def_402, type, sK244: $i > ($i > $o) > $i).
% 50.23/8.36 thf(func_def_406, type, sK248: $o > $i > $i > $i).
% 50.23/8.36 thf(func_def_412, type, sK254: $i > $o).
% 50.23/8.36 thf(func_def_414, type, sK256: ($i > $o) > $i > $i).
% 50.23/8.36 thf(func_def_417, type, sK259: ($i > $o) > ($i > $o) > $i > $i > $i).
% 50.23/8.36 thf(func_def_418, type, sK260: ($i > $o) > ($i > $o) > $i > $i > $i).
% 50.23/8.36 thf(func_def_421, type, sK263: $i > $o).
% 50.23/8.36 thf(func_def_422, type, sK264: $i > $o).
% 50.23/8.36 thf(func_def_424, type, sK266: $i > $o).
% 50.23/8.36 thf(func_def_426, type, sK268: ($i > $o) > $i > $i).
% 50.23/8.36 thf(func_def_432, type, sK274: ($i > $o) > $i > $i).
% 50.23/8.36 thf(func_def_434, type, sK276: $i > $o).
% 50.23/8.36 thf(func_def_438, type, sK280: $i > $i > $i).
% 50.23/8.36 thf(func_def_456, type, sK298: $i > $o).
% 50.23/8.36 thf(func_def_460, type, sK302: $i > $o).
% 50.23/8.36 thf(func_def_463, type, sK305: $i > $i).
% 50.23/8.36 thf(func_def_469, type, sK311: $i > $i > $i).
% 50.23/8.36 thf(func_def_470, type, sK312: $i > $i > $i).
% 50.23/8.36 thf(func_def_476, type, sK318: $i > $i > $i).
% 50.23/8.36 thf(func_def_482, type, sK324: $i > $i > $i).
% 50.23/8.36 thf(func_def_486, type, sK328: $i > $o).
% 50.23/8.36 thf(func_def_497, type, sK339: $i > $o).
% 50.23/8.36 thf(func_def_505, type, ph347: !>[X0: $tType]:(X0)).
% 50.23/8.36 thf(f28469,plain,(
% 50.23/8.36 $false),
% 50.23/8.36 inference(avatar_sat_refutation,[status(thm)],[f6193,f16383,f17386,f26817,f28373,f28459])).
% 50.23/8.36 thf(f28459,plain,(
% 50.23/8.36 spl346_51 | ~spl346_71),
% 50.23/8.36 inference(avatar_split_clause,[status(thm)],[f28458,f5891,f4972])).
% 50.23/8.36 thf(f4972,definition,(
% 50.23/8.36 spl346_51 <=> ($true = (subset @ sK56 @ sK55))),
% 50.23/8.36 introduced(definition,[new_symbols(naming,[spl346_51])],[avatar_definition])).
% 50.23/8.36 thf(f5891,definition,(
% 50.23/8.36 spl346_71 <=> ! [X0 : $i] : (($true = (subset @ X0 @ sK55)) | ($true != (in @ (sK280 @ X0 @ sK55) @ sK56)))),
% 50.23/8.36 introduced(definition,[new_symbols(naming,[spl346_71])],[avatar_definition])).
% 50.23/8.36 thf(f28458,plain,(
% 50.23/8.36 ($true = (subset @ sK56 @ sK55)) | ~spl346_71),
% 50.23/8.36 inference(trivial_inequality_removal,[status(thm)],[f28457])).
% 50.23/8.36 thf(f28457,plain,(
% 50.23/8.36 ($true = (subset @ sK56 @ sK55)) | ($true != $true) | ~spl346_71),
% 50.23/8.36 inference(forward_demodulation,[status(thm)],[f28453,f1273])).
% 50.23/8.36 thf(f1273,plain,(
% 50.23/8.36 (subsetI2 = $true)),
% 50.23/8.36 inference(cnf_transformation,[status(thm)],[f635])).
% 50.23/8.36 thf(f635,plain,(
% 50.23/8.36 (setextsub = $true) & (powersetI = $true) & (emptysetAx = $true) & (setadjoinIL = $true) & (dsetconstrI = $true) & (setadjoinIR = $true) & (descrp = $true) & (exuEu = $true) & (replAx = $true) & (notsubsetI = $true) & (setadjoinSub = $true) & (binunionEcases = $true) & (exuI1 = $true) & (exuE1 = $true) & (noeltsimpempty = $true) & (setminusEL = $true) & (emptyE1 = $true) & (dsetconstrEL = $true) & (binintersectRsub = $true) & (singletonsswitch = $true) & (binunionE = $true) & (binunionLsub = $true) & (binunionIR = $true) & (setadjoinSub2 = $true) & (subPowSU = $true) & (bs114d = $true) & (exuE3u = $true) & (omega0Ax = $true) & (setunionAx = $true) & (binintersectSubset2 = $true) & (upairsetIR = $true) & (setext = $true) & (foundationAx = $true) & (uniqinunit = $true) & (setminusILneg = $true) & (omegaSAx = $true) & (emptyInPowerset = $true) & (quantDeMorgan2 = $true) & (eqimpsubset2 = $true) & (descr__Cong = $true) & (upairsetIL = $true) & (binintersectLsub = $true) & (nonemptyE1 = $true) & (nonemptyI = $true) & (subsetE = $true) & (emptyinunitempty = $true) & (powersetE1 = $true) & (setunion__Cong = $true) & (quantDeMorgan1 = $true) & (exuI3 = $true) & (eqimpsubset1 = $true) & (setminusLsub = $true) & (upairsetE = $true) & (subsetRefl = $true) & (nonemptyI1 = $true) & (upairset2IR = $true) & (omega__Cong = $true) & (vacuousDall = $true) & (subsetI2 = $true) & (notinemptyset = $true) & (powerset__Cong = $true) & (exu__Cong = $true) & (setadjoinOr = $true) & (setminusSubset2 = $true) & (emptyI = $true) & (binintersectSubset4 = $true) & (powersetAx = $true) & (disjointsetsI1 = $true) & (emptyset__Cong = $true) & (powersetsubset = $true) & (nonemptyImpWitness = $true) & (binintersectSubset1 = $true) & (setminusELneg = $true) & (setminusI = $true) & (emptyinPowerset = $true) & (setextAx = $true) & (quantDeMorgan4 = $true) & (setminusIRneg = $true) & (binintersectER = $true) & (dsetconstr__Cong = $true) & (setadjoinAx = $true) & (notequalI1 = $true) & (binintersectEL = $true) & (dsetconstrER = $true) & (prop2setI = $true) & (sepInPowerset = $true) & (setoftrueEq = $true) & (prop2set2propI = $true) & (subsetTrans = $true) & (binintersectSubset5 = $true) & (subsetI1 = $true) & (in__Cong = $true) & (wellorderingAx = $true) & (emptysetimpfalse = $true) & (powersetE = $true) & (binunionRsub = $true) & (exuI2 = $true) & (inPowerset = $true) & (subsetE2 = $true) & (eqinunit = $true) & (emptysetsubset = $true) & (setbeta = $true) & (notdallE = $true) & (prop2setE = $true) & (quantDeMorgan3 = $true) & (subsetemptysetimpeq = $true) & (exuE2 = $true) & (notequalI2 = $true) & ((emptyset = (setminus @ sK56 @ sK55)) & ($true != (subset @ sK56 @ sK55))) & (setminusER = $true) & (binunionIL = $true) & (subset2powerset = $true) & (notinsingleton = $true) & (notdexE = $true) & (setunionI = $true) & (binintersectSubset3 = $true) & (setadjoinE = $true) & (inCongP = $true) & (setminusERneg = $true) & (emptysetE = $true) & (omegaIndAx = $true) & (powersetI1 = $true) & (exuE3e = $true) & (setadjoin__Cong = $true) & (binintersectI = $true) & (setunionE = $true) & (sepSubset = $true)),
% 50.23/8.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK55,sK56])],[f453,f634])).
% 50.23/8.36 thf(f634,plain,(
% 50.23/8.36 ? [X0 : $i,X1 : $i] : ((emptyset = (setminus @ X1 @ X0)) & ((subset @ X1 @ X0) != $true)) => ((emptyset = (setminus @ sK56 @ sK55)) & ($true != (subset @ sK56 @ sK55)))),
% 50.23/8.36 introduced(definition,[],[choice_axiom])).
% 50.23/8.36 thf(f453,plain,(
% 50.23/8.36 (setextsub = $true) & (powersetI = $true) & (emptysetAx = $true) & (setadjoinIL = $true) & (dsetconstrI = $true) & (setadjoinIR = $true) & (descrp = $true) & (exuEu = $true) & (replAx = $true) & (notsubsetI = $true) & (setadjoinSub = $true) & (binunionEcases = $true) & (exuI1 = $true) & (exuE1 = $true) & (noeltsimpempty = $true) & (setminusEL = $true) & (emptyE1 = $true) & (dsetconstrEL = $true) & (binintersectRsub = $true) & (singletonsswitch = $true) & (binunionE = $true) & (binunionLsub = $true) & (binunionIR = $true) & (setadjoinSub2 = $true) & (subPowSU = $true) & (bs114d = $true) & (exuE3u = $true) & (omega0Ax = $true) & (setunionAx = $true) & (binintersectSubset2 = $true) & (upairsetIR = $true) & (setext = $true) & (foundationAx = $true) & (uniqinunit = $true) & (setminusILneg = $true) & (omegaSAx = $true) & (emptyInPowerset = $true) & (quantDeMorgan2 = $true) & (eqimpsubset2 = $true) & (descr__Cong = $true) & (upairsetIL = $true) & (binintersectLsub = $true) & (nonemptyE1 = $true) & (nonemptyI = $true) & (subsetE = $true) & (emptyinunitempty = $true) & (powersetE1 = $true) & (setunion__Cong = $true) & (quantDeMorgan1 = $true) & (exuI3 = $true) & (eqimpsubset1 = $true) & (setminusLsub = $true) & (upairsetE = $true) & (subsetRefl = $true) & (nonemptyI1 = $true) & (upairset2IR = $true) & (omega__Cong = $true) & (vacuousDall = $true) & (subsetI2 = $true) & (notinemptyset = $true) & (powerset__Cong = $true) & (exu__Cong = $true) & (setadjoinOr = $true) & (setminusSubset2 = $true) & (emptyI = $true) & (binintersectSubset4 = $true) & (powersetAx = $true) & (disjointsetsI1 = $true) & (emptyset__Cong = $true) & (powersetsubset = $true) & (nonemptyImpWitness = $true) & (binintersectSubset1 = $true) & (setminusELneg = $true) & (setminusI = $true) & (emptyinPowerset = $true) & (setextAx = $true) & (quantDeMorgan4 = $true) & (setminusIRneg = $true) & (binintersectER = $true) & (dsetconstr__Cong = $true) & (setadjoinAx = $true) & (notequalI1 = $true) & (binintersectEL = $true) & (dsetconstrER = $true) & (prop2setI = $true) & (sepInPowerset = $true) & (setoftrueEq = $true) & (prop2set2propI = $true) & (subsetTrans = $true) & (binintersectSubset5 = $true) & (subsetI1 = $true) & (in__Cong = $true) & (wellorderingAx = $true) & (emptysetimpfalse = $true) & (powersetE = $true) & (binunionRsub = $true) & (exuI2 = $true) & (inPowerset = $true) & (subsetE2 = $true) & (eqinunit = $true) & (emptysetsubset = $true) & (setbeta = $true) & (notdallE = $true) & (prop2setE = $true) & (quantDeMorgan3 = $true) & (subsetemptysetimpeq = $true) & (exuE2 = $true) & (notequalI2 = $true) & ? [X0 : $i,X1 : $i] : ((emptyset = (setminus @ X1 @ X0)) & ((subset @ X1 @ X0) != $true)) & (setminusER = $true) & (binunionIL = $true) & (subset2powerset = $true) & (notinsingleton = $true) & (notdexE = $true) & (setunionI = $true) & (binintersectSubset3 = $true) & (setadjoinE = $true) & (inCongP = $true) & (setminusERneg = $true) & (emptysetE = $true) & (omegaIndAx = $true) & (powersetI1 = $true) & (exuE3e = $true) & (setadjoin__Cong = $true) & (binintersectI = $true) & (setunionE = $true) & (sepSubset = $true)),
% 50.23/8.36 inference(flattening,[status(thm)],[f452])).
% 50.23/8.36 thf(f452,plain,(
% 50.23/8.36 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : ((emptyset = (setminus @ X1 @ X0)) & ((subset @ X1 @ X0) != $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)),
% 50.23/8.36 inference(ennf_transformation,[status(thm)],[f369])).
% 50.23/8.36 thf(f369,plain,(
% 50.23/8.36 ~((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) => ! [X0 : $i,X1 : $i] : ((emptyset = (setminus @ X1 @ X0)) => ((subset @ X1 @ X0) = $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 50.23/8.36 inference(fool_elimination,[status(thm)],[f368])).
% 50.23/8.36 thf(f368,plain,(
% 50.23/8.36 ~(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 => ! [X0 : $i,X1 : $i] : ((emptyset = (setminus @ X1 @ X0)) => (subset @ X1 @ X0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 50.23/8.36 inference(rectify,[status(thm)],[f130])).
% 50.23/8.36 thf(f130,negated_conjecture,(
% 50.23/8.36 ~(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 => ! [X4 : $i,X3 : $i] : ((emptyset = (setminus @ X3 @ X4)) => (subset @ X3 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 50.23/8.36 inference(negated_conjecture,[status(cth)],[f129])).
% 50.23/8.36 thf(f129,conjecture,(
% 50.23/8.36 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 => ! [X4 : $i,X3 : $i] : ((emptyset = (setminus @ X3 @ X4)) => (subset @ X3 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 50.23/8.36 file('/export/starexec/sandbox/tmp/tmp.mU0PE1mI9q/DTF2THF_13954.p',setminusSubset1)).
% 50.23/8.36 thf(f28453,plain,(
% 50.23/8.36 (subsetI2 != $true) | ($true = (subset @ sK56 @ sK55)) | ~spl346_71),
% 50.23/8.36 inference(trivial_inequality_removal,[status(thm)],[f28452])).
% 50.23/8.36 thf(f28452,plain,(
% 50.23/8.36 (subsetI2 != $true) | ($true = (subset @ sK56 @ sK55)) | ($true != $true) | ~spl346_71),
% 50.23/8.36 inference(duplicate_literal_removal,[status(thm)],[f28434])).
% 50.23/8.36 thf(f28434,plain,(
% 50.23/8.36 (subsetI2 != $true) | ($true != $true) | ($true = (subset @ sK56 @ sK55)) | ($true = (subset @ sK56 @ sK55)) | ~spl346_71),
% 50.23/8.36 inference(superposition,[status(thm)],[f5892,f1662])).
% 50.23/8.36 thf(f1662,plain,(
% 50.23/8.36 ( ! [X0 : $i,X1 : $i] : (($true = (in @ (sK280 @ X1 @ X0) @ X1)) | (subsetI2 != $true) | ((subset @ X1 @ X0) = $true)) )),
% 50.23/8.36 inference(cnf_transformation,[status(thm)],[f1020])).
% 50.23/8.36 thf(f1020,plain,(
% 50.23/8.36 (! [X0 : $i,X1 : $i] : ((($true = (in @ (sK280 @ X1 @ X0) @ X1)) & ((in @ (sK280 @ X1 @ X0) @ X0) != $true)) | ((subset @ X1 @ X0) = $true)) | (subsetI2 != $true)) & ((subsetI2 = $true) | (! [X5 : $i] : (((in @ X5 @ sK282) != $true) | ($true = (in @ X5 @ sK281))) & ($true != (subset @ sK282 @ sK281))))),
% 50.23/8.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK280,sK281,sK282])],[f1017,f1019,f1018])).
% 50.23/8.36 thf(f1018,plain,(
% 50.23/8.36 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (in @ X2 @ X1)) & ($true != (in @ X2 @ X0))) => (($true = (in @ (sK280 @ X1 @ X0) @ X1)) & ((in @ (sK280 @ X1 @ X0) @ X0) != $true)))),
% 50.23/8.36 introduced(definition,[],[choice_axiom])).
% 50.23/8.36 thf(f1019,plain,(
% 50.23/8.36 ? [X3 : $i,X4 : $i] : (! [X5 : $i] : (((in @ X5 @ X4) != $true) | ($true = (in @ X5 @ X3))) & ((subset @ X4 @ X3) != $true)) => (! [X5 : $i] : (((in @ X5 @ sK282) != $true) | ($true = (in @ X5 @ sK281))) & ($true != (subset @ sK282 @ sK281)))),
% 50.23/8.36 introduced(definition,[],[choice_axiom])).
% 50.23/8.36 thf(f1017,plain,(
% 50.23/8.36 (! [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (in @ X2 @ X1)) & ($true != (in @ X2 @ X0))) | ((subset @ X1 @ X0) = $true)) | (subsetI2 != $true)) & ((subsetI2 = $true) | ? [X3 : $i,X4 : $i] : (! [X5 : $i] : (((in @ X5 @ X4) != $true) | ($true = (in @ X5 @ X3))) & ((subset @ X4 @ X3) != $true)))),
% 50.23/8.36 inference(rectify,[status(thm)],[f1016])).
% 50.23/8.36 thf(f1016,plain,(
% 50.23/8.36 (! [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (in @ X2 @ X1)) & ($true != (in @ X2 @ X0))) | ((subset @ X1 @ X0) = $true)) | (subsetI2 != $true)) & ((subsetI2 = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true != (in @ X2 @ X1)) | ($true = (in @ X2 @ X0))) & ((subset @ X1 @ X0) != $true)))),
% 50.23/8.36 inference(nnf_transformation,[status(thm)],[f445])).
% 50.23/8.36 thf(f445,plain,(
% 50.23/8.36 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (in @ X2 @ X1)) & ($true != (in @ X2 @ X0))) | ((subset @ X1 @ X0) = $true)) <=> (subsetI2 = $true)),
% 50.23/8.36 inference(ennf_transformation,[status(thm)],[f200])).
% 50.23/8.36 thf(f200,plain,(
% 50.23/8.36 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true = (in @ X2 @ X1)) => ($true = (in @ X2 @ X0))) => ((subset @ X1 @ X0) = $true)) <=> (subsetI2 = $true)),
% 50.23/8.36 inference(fool_elimination,[status(thm)],[f199])).
% 50.23/8.36 thf(f199,plain,(
% 50.23/8.36 (subsetI2 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)))),
% 50.23/8.36 inference(rectify,[status(thm)],[f81])).
% 50.23/8.36 thf(f81,axiom,(
% 50.23/8.36 (subsetI2 = ! [X4 : $i,X3 : $i] : (! [X1 : $i] : ((in @ X1 @ X3) => (in @ X1 @ X4)) => (subset @ X3 @ X4)))),
% 50.23/8.36 file('/export/starexec/sandbox/tmp/tmp.mU0PE1mI9q/DTF2THF_13954.p',subsetI2)).
% 50.23/8.36 thf(f5892,plain,(
% 50.23/8.36 ( ! [X0 : $i] : (($true != (in @ (sK280 @ X0 @ sK55) @ sK56)) | ($true = (subset @ X0 @ sK55))) ) | ~spl346_71),
% 50.23/8.36 inference(avatar_component_clause,[status(thm)],[f5891])).
% 50.23/8.36 thf(f28373,plain,(
% 50.23/8.36 spl346_36),
% 50.23/8.36 inference(avatar_split_clause,[status(thm)],[f28263,f2341])).
% 50.23/8.36 thf(f2341,definition,(
% 50.23/8.36 spl346_36 <=> ! [X0 : $i] : ((in @ X0 @ emptyset) != $true)),
% 50.23/8.36 introduced(definition,[new_symbols(naming,[spl346_36])],[avatar_definition])).
% 50.23/8.36 thf(f28263,plain,(
% 50.23/8.36 ( ! [X0 : $i] : (((in @ X0 @ emptyset) != $true)) )),
% 50.23/8.36 inference(duplicate_literal_removal,[status(thm)],[f28194])).
% 50.23/8.36 thf(f28194,plain,(
% 50.23/8.36 ( ! [X0 : $i] : (((in @ X0 @ emptyset) != $true) | ((in @ X0 @ emptyset) != $true)) )),
% 50.23/8.36 inference(superposition,[status(thm)],[f4566,f3898])).
% 50.23/8.36 thf(f3898,plain,(
% 50.23/8.36 (emptyset = (binintersect @ sK55 @ emptyset))),
% 50.23/8.36 inference(trivial_inequality_removal,[status(thm)],[f3897])).
% 50.23/8.36 thf(f3897,plain,(
% 50.23/8.36 (emptyset = (binintersect @ sK55 @ emptyset)) | ($true != $true)),
% 50.23/8.36 inference(forward_demodulation,[status(thm)],[f3885,f1264])).
% 50.23/8.36 thf(f1264,plain,(
% 50.23/8.36 (disjointsetsI1 = $true)),
% 50.23/8.36 inference(cnf_transformation,[status(thm)],[f635])).
% 50.23/8.36 thf(f3885,plain,(
% 50.23/8.36 (disjointsetsI1 != $true) | (emptyset = (binintersect @ sK55 @ emptyset))),
% 50.23/8.36 inference(trivial_inequality_removal,[status(thm)],[f3884])).
% 50.23/8.36 thf(f3884,plain,(
% 50.23/8.36 (emptyset = (binintersect @ sK55 @ emptyset)) | (disjointsetsI1 != $true) | ($true != $true)),
% 50.23/8.36 inference(duplicate_literal_removal,[status(thm)],[f3878])).
% 50.23/8.36 thf(f3878,plain,(
% 50.23/8.36 (disjointsetsI1 != $true) | (emptyset = (binintersect @ sK55 @ emptyset)) | (emptyset = (binintersect @ sK55 @ emptyset)) | ($true != $true)),
% 50.23/8.36 inference(superposition,[status(thm)],[f2526,f1479])).
% 50.23/8.36 thf(f1479,plain,(
% 50.23/8.36 ( ! [X0 : $i,X1 : $i] : (((in @ (sK154 @ X1 @ X0) @ X0) = $true) | (disjointsetsI1 != $true) | (emptyset = (binintersect @ X1 @ X0))) )),
% 50.23/8.36 inference(cnf_transformation,[status(thm)],[f813])).
% 50.23/8.36 thf(f813,plain,(
% 50.23/8.36 (! [X0 : $i,X1 : $i] : ((((in @ (sK154 @ X1 @ X0) @ X0) = $true) & ($true = (in @ (sK154 @ X1 @ X0) @ X1))) | (emptyset = (binintersect @ X1 @ X0))) | (disjointsetsI1 != $true)) & ((disjointsetsI1 = $true) | (! [X5 : $i] : (($true != (in @ X5 @ sK155)) | ($true != (in @ X5 @ sK156))) & (emptyset != (binintersect @ sK156 @ sK155))))),
% 50.23/8.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK154,sK155,sK156])],[f810,f812,f811])).
% 50.23/8.36 thf(f811,plain,(
% 50.23/8.36 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (in @ X2 @ X0)) & ($true = (in @ X2 @ X1))) => (((in @ (sK154 @ X1 @ X0) @ X0) = $true) & ($true = (in @ (sK154 @ X1 @ X0) @ X1))))),
% 50.23/8.36 introduced(definition,[],[choice_axiom])).
% 50.23/8.36 thf(f812,plain,(
% 50.23/8.36 ? [X3 : $i,X4 : $i] : (! [X5 : $i] : (($true != (in @ X5 @ X3)) | ((in @ X5 @ X4) != $true)) & (emptyset != (binintersect @ X4 @ X3))) => (! [X5 : $i] : (($true != (in @ X5 @ sK155)) | ($true != (in @ X5 @ sK156))) & (emptyset != (binintersect @ sK156 @ sK155)))),
% 50.23/8.36 introduced(definition,[],[choice_axiom])).
% 50.23/8.36 thf(f810,plain,(
% 50.23/8.36 (! [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (in @ X2 @ X0)) & ($true = (in @ X2 @ X1))) | (emptyset = (binintersect @ X1 @ X0))) | (disjointsetsI1 != $true)) & ((disjointsetsI1 = $true) | ? [X3 : $i,X4 : $i] : (! [X5 : $i] : (($true != (in @ X5 @ X3)) | ((in @ X5 @ X4) != $true)) & (emptyset != (binintersect @ X4 @ X3))))),
% 50.23/8.36 inference(rectify,[status(thm)],[f809])).
% 50.23/8.36 thf(f809,plain,(
% 50.23/8.36 (! [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (in @ X2 @ X0)) & ($true = (in @ X2 @ X1))) | (emptyset = (binintersect @ X1 @ X0))) | (disjointsetsI1 != $true)) & ((disjointsetsI1 = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : (($true != (in @ X2 @ X0)) | ($true != (in @ X2 @ X1))) & (emptyset != (binintersect @ X1 @ X0))))),
% 50.23/8.36 inference(nnf_transformation,[status(thm)],[f446])).
% 50.23/8.36 thf(f446,plain,(
% 50.23/8.36 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : (($true = (in @ X2 @ X0)) & ($true = (in @ X2 @ X1))) | (emptyset = (binintersect @ X1 @ X0))) <=> (disjointsetsI1 = $true)),
% 50.23/8.36 inference(ennf_transformation,[status(thm)],[f268])).
% 50.23/8.36 thf(f268,plain,(
% 50.23/8.36 ! [X0 : $i,X1 : $i] : (~? [X2 : $i] : (($true = (in @ X2 @ X0)) & ($true = (in @ X2 @ X1))) => (emptyset = (binintersect @ X1 @ X0))) <=> (disjointsetsI1 = $true)),
% 50.23/8.36 inference(fool_elimination,[status(thm)],[f267])).
% 50.23/8.36 thf(f267,plain,(
% 50.23/8.36 (disjointsetsI1 = ! [X0 : $i,X1 : $i] : (~? [X2 : $i] : ((in @ X2 @ X0) & (in @ X2 @ X1)) => (emptyset = (binintersect @ X1 @ X0))))),
% 50.23/8.36 inference(rectify,[status(thm)],[f115])).
% 50.23/8.36 thf(f115,axiom,(
% 50.23/8.36 (disjointsetsI1 = ! [X4 : $i,X3 : $i] : (~? [X1 : $i] : ((in @ X1 @ X4) & (in @ X1 @ X3)) => (emptyset = (binintersect @ X3 @ X4))))),
% 50.23/8.36 file('/export/starexec/sandbox/tmp/tmp.mU0PE1mI9q/DTF2THF_13954.p',disjointsetsI1)).
% 50.23/8.36 thf(f2526,plain,(
% 50.23/8.36 ( ! [X0 : $i] : (($true != (in @ (sK154 @ sK55 @ X0) @ emptyset)) | (emptyset = (binintersect @ sK55 @ X0))) )),
% 50.23/8.36 inference(trivial_inequality_removal,[status(thm)],[f2525])).
% 50.23/8.36 thf(f2525,plain,(
% 50.23/8.36 ( ! [X0 : $i] : (($true != $true) | ($true != (in @ (sK154 @ sK55 @ X0) @ emptyset)) | (emptyset = (binintersect @ sK55 @ X0))) )),
% 50.23/8.36 inference(forward_demodulation,[status(thm)],[f2505,f1264])).
% 50.23/8.36 thf(f2505,plain,(
% 50.23/8.36 ( ! [X0 : $i] : ((disjointsetsI1 != $true) | (emptyset = (binintersect @ sK55 @ X0)) | ($true != (in @ (sK154 @ sK55 @ X0) @ emptyset))) )),
% 50.23/8.36 inference(trivial_inequality_removal,[status(thm)],[f2431])).
% 50.23/8.36 thf(f2431,plain,(
% 50.23/8.36 ( ! [X0 : $i] : (($true != (in @ (sK154 @ sK55 @ X0) @ emptyset)) | (emptyset = (binintersect @ sK55 @ X0)) | (disjointsetsI1 != $true) | ($true != $true)) )),
% 50.23/8.36 inference(superposition,[status(thm)],[f1880,f1478])).
% 50.23/8.36 thf(f1478,plain,(
% 50.23/8.36 ( ! [X0 : $i,X1 : $i] : (($true = (in @ (sK154 @ X1 @ X0) @ X1)) | (disjointsetsI1 != $true) | (emptyset = (binintersect @ X1 @ X0))) )),
% 50.23/8.36 inference(cnf_transformation,[status(thm)],[f813])).
% 50.23/8.36 thf(f1880,plain,(
% 50.23/8.36 ( ! [X0 : $i] : (((in @ X0 @ sK55) != $true) | ((in @ X0 @ emptyset) != $true)) )),
% 50.23/8.36 inference(trivial_inequality_removal,[status(thm)],[f1879])).
% 50.23/8.36 thf(f1879,plain,(
% 50.23/8.36 ( ! [X0 : $i] : (((in @ X0 @ emptyset) != $true) | ((in @ X0 @ sK55) != $true) | ($true != $true)) )),
% 50.23/8.36 inference(forward_demodulation,[status(thm)],[f1866,f1221])).
% 50.23/8.36 thf(f1221,plain,(
% 50.23/8.36 (setminusER = $true)),
% 50.23/8.36 inference(cnf_transformation,[status(thm)],[f635])).
% 50.23/8.36 thf(f1866,plain,(
% 50.23/8.36 ( ! [X0 : $i] : ((setminusER != $true) | ((in @ X0 @ sK55) != $true) | ((in @ X0 @ emptyset) != $true)) )),
% 50.23/8.36 inference(superposition,[status(thm)],[f1682,f1223])).
% 50.23/8.36 thf(f1223,plain,(
% 50.23/8.36 (emptyset = (setminus @ sK56 @ sK55))),
% 50.23/8.36 inference(cnf_transformation,[status(thm)],[f635])).
% 50.23/8.36 thf(f1682,plain,(
% 50.23/8.36 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X1 @ (setminus @ X0 @ X2))) | (setminusER != $true) | ($true != (in @ X1 @ X2))) )),
% 50.23/8.36 inference(cnf_transformation,[status(thm)],[f1045])).
% 50.23/8.36 thf(f1045,plain,(
% 50.23/8.36 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ (setminus @ X0 @ X2))) | ($true != (in @ X1 @ X2))) | (setminusER != $true)) & ((setminusER = $true) | (($true = (in @ sK293 @ (setminus @ sK292 @ sK294))) & ($true = (in @ sK293 @ sK294))))),
% 50.23/8.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK292,sK293,sK294])],[f1043,f1044])).
% 50.23/8.36 thf(f1044,plain,(
% 50.23/8.36 ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (setminus @ X3 @ X5)) = $true) & ($true = (in @ X4 @ X5))) => (($true = (in @ sK293 @ (setminus @ sK292 @ sK294))) & ($true = (in @ sK293 @ sK294)))),
% 50.23/8.36 introduced(definition,[],[choice_axiom])).
% 50.23/8.36 thf(f1043,plain,(
% 50.23/8.36 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ (setminus @ X0 @ X2))) | ($true != (in @ X1 @ X2))) | (setminusER != $true)) & ((setminusER = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (setminus @ X3 @ X5)) = $true) & ($true = (in @ X4 @ X5))))),
% 50.23/8.36 inference(rectify,[status(thm)],[f1042])).
% 50.23/8.36 thf(f1042,plain,(
% 50.23/8.36 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ (setminus @ X0 @ X2))) | ($true != (in @ X1 @ X2))) | (setminusER != $true)) & ((setminusER = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (setminus @ X0 @ X2))) & ($true = (in @ X1 @ X2))))),
% 50.23/8.36 inference(nnf_transformation,[status(thm)],[f481])).
% 50.23/8.36 thf(f481,plain,(
% 50.23/8.36 ! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ (setminus @ X0 @ X2))) | ($true != (in @ X1 @ X2))) <=> (setminusER = $true)),
% 50.23/8.36 inference(ennf_transformation,[status(thm)],[f402])).
% 50.23/8.36 thf(f402,plain,(
% 50.23/8.36 (setminusER = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (setminus @ X0 @ X2))) => ($true != (in @ X1 @ X2)))),
% 50.23/8.36 inference(flattening,[status(thm)],[f272])).
% 50.23/8.36 thf(f272,plain,(
% 50.23/8.36 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (setminus @ X0 @ X2))) => ~($true = (in @ X1 @ X2))) <=> (setminusER = $true)),
% 50.23/8.36 inference(fool_elimination,[status(thm)],[f271])).
% 50.23/8.36 thf(f271,plain,(
% 50.23/8.36 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (setminus @ X0 @ X2)) => ~(in @ X1 @ X2)) = setminusER)),
% 50.23/8.36 inference(rectify,[status(thm)],[f122])).
% 50.23/8.36 thf(f122,axiom,(
% 50.23/8.36 (! [X3 : $i,X1 : $i,X4 : $i] : ((in @ X1 @ (setminus @ X3 @ X4)) => ~(in @ X1 @ X4)) = setminusER)),
% 50.23/8.36 file('/export/starexec/sandbox/tmp/tmp.mU0PE1mI9q/DTF2THF_13954.p',setminusER)).
% 50.23/8.36 thf(f4566,plain,(
% 50.23/8.36 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (binintersect @ sK55 @ X0))) | ((in @ X1 @ emptyset) != $true)) )),
% 50.23/8.36 inference(trivial_inequality_removal,[status(thm)],[f4565])).
% 50.23/8.36 thf(f4565,plain,(
% 50.23/8.36 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true != (in @ X1 @ (binintersect @ sK55 @ X0))) | ((in @ X1 @ emptyset) != $true)) )),
% 50.23/8.36 inference(forward_demodulation,[status(thm)],[f4523,f1290])).
% 50.23/8.36 thf(f1290,plain,(
% 50.23/8.36 (binintersectLsub = $true)),
% 50.23/8.36 inference(cnf_transformation,[status(thm)],[f635])).
% 50.23/8.36 thf(f4523,plain,(
% 50.23/8.36 ( ! [X0 : $i,X1 : $i] : ((binintersectLsub != $true) | ((in @ X1 @ emptyset) != $true) | ($true != (in @ X1 @ (binintersect @ sK55 @ X0)))) )),
% 50.23/8.36 inference(trivial_inequality_removal,[status(thm)],[f4518])).
% 50.23/8.36 thf(f4518,plain,(
% 50.23/8.36 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ emptyset) != $true) | ($true != $true) | (binintersectLsub != $true) | ($true != (in @ X1 @ (binintersect @ sK55 @ X0)))) )),
% 50.23/8.36 inference(superposition,[status(thm)],[f2577,f1357])).
% 50.23/8.36 thf(f1357,plain,(
% 50.23/8.36 ( ! [X0 : $i,X1 : $i] : (((subset @ (binintersect @ X1 @ X0) @ X1) = $true) | (binintersectLsub != $true)) )),
% 50.23/8.36 inference(cnf_transformation,[status(thm)],[f668])).
% 50.23/8.36 thf(f668,plain,(
% 50.23/8.36 (! [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X1 @ X0) @ X1) = $true) | (binintersectLsub != $true)) & ((binintersectLsub = $true) | ($true != (subset @ (binintersect @ sK73 @ sK72) @ sK73)))),
% 50.23/8.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK72,sK73])],[f666,f667])).
% 50.23/8.36 thf(f667,plain,(
% 50.23/8.36 ? [X2 : $i,X3 : $i] : ($true != (subset @ (binintersect @ X3 @ X2) @ X3)) => ($true != (subset @ (binintersect @ sK73 @ sK72) @ sK73))),
% 50.23/8.36 introduced(definition,[],[choice_axiom])).
% 50.23/8.36 thf(f666,plain,(
% 50.23/8.36 (! [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X1 @ X0) @ X1) = $true) | (binintersectLsub != $true)) & ((binintersectLsub = $true) | ? [X2 : $i,X3 : $i] : ($true != (subset @ (binintersect @ X3 @ X2) @ X3)))),
% 50.23/8.36 inference(rectify,[status(thm)],[f665])).
% 50.23/8.36 thf(f665,plain,(
% 50.23/8.36 (! [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X1 @ X0) @ X1) = $true) | (binintersectLsub != $true)) & ((binintersectLsub = $true) | ? [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X1 @ X0) @ X1) != $true))),
% 50.23/8.36 inference(nnf_transformation,[status(thm)],[f141])).
% 50.23/8.36 thf(f141,plain,(
% 50.23/8.36 ! [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X1 @ X0) @ X1) = $true) <=> (binintersectLsub = $true)),
% 50.23/8.36 inference(fool_elimination,[status(thm)],[f140])).
% 50.23/8.36 thf(f140,plain,(
% 50.23/8.36 (binintersectLsub = ! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X1 @ X0) @ X1))),
% 50.23/8.36 inference(rectify,[status(thm)],[f111])).
% 50.23/8.36 thf(f111,axiom,(
% 50.23/8.36 (binintersectLsub = ! [X4 : $i,X3 : $i] : (subset @ (binintersect @ X3 @ X4) @ X3))),
% 50.23/8.36 file('/export/starexec/sandbox/tmp/tmp.mU0PE1mI9q/DTF2THF_13954.p',binintersectLsub)).
% 50.23/8.36 thf(f2577,plain,(
% 50.23/8.36 ( ! [X0 : $i,X1 : $i] : (($true != (subset @ X1 @ sK55)) | ((in @ X0 @ emptyset) != $true) | ($true != (in @ X0 @ X1))) )),
% 50.23/8.36 inference(trivial_inequality_removal,[status(thm)],[f2576])).
% 50.23/8.36 thf(f2576,plain,(
% 50.23/8.36 ( ! [X0 : $i,X1 : $i] : (($true != (subset @ X1 @ sK55)) | ((in @ X0 @ emptyset) != $true) | ($true != $true) | ($true != (in @ X0 @ X1))) )),
% 50.23/8.36 inference(forward_demodulation,[status(thm)],[f2475,f1322])).
% 50.23/8.36 thf(f1322,plain,(
% 50.23/8.36 (notsubsetI = $true)),
% 50.23/8.36 inference(cnf_transformation,[status(thm)],[f635])).
% 50.23/8.36 thf(f2475,plain,(
% 50.23/8.36 ( ! [X0 : $i,X1 : $i] : ((notsubsetI != $true) | ((in @ X0 @ emptyset) != $true) | ($true != (in @ X0 @ X1)) | ($true != (subset @ X1 @ sK55))) )),
% 50.23/8.36 inference(trivial_inequality_removal,[status(thm)],[f2418])).
% 50.23/8.36 thf(f2418,plain,(
% 50.23/8.36 ( ! [X0 : $i,X1 : $i] : (($true != (subset @ X1 @ sK55)) | ($true != (in @ X0 @ X1)) | ((in @ X0 @ emptyset) != $true) | (notsubsetI != $true) | ($true != $true)) )),
% 50.23/8.36 inference(superposition,[status(thm)],[f1880,f1394])).
% 50.23/8.36 thf(f1394,plain,(
% 50.23/8.36 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X2 @ X0)) | (notsubsetI != $true) | ((subset @ X1 @ X0) != $true) | ($true != (in @ X2 @ X1))) )),
% 50.23/8.36 inference(cnf_transformation,[status(thm)],[f711])).
% 50.23/8.36 thf(f711,plain,(
% 50.23/8.36 (! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X1 @ X0) != $true) | ($true = (in @ X2 @ X0)) | ($true != (in @ X2 @ X1))) | (notsubsetI != $true)) & ((notsubsetI = $true) | (($true = (subset @ sK100 @ sK99)) & ((in @ sK101 @ sK99) != $true) & ($true = (in @ sK101 @ sK100))))),
% 50.23/8.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK99,sK100,sK101])],[f709,f710])).
% 50.23/8.36 thf(f710,plain,(
% 50.23/8.36 ? [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X4 @ X3) = $true) & ($true != (in @ X5 @ X3)) & ((in @ X5 @ X4) = $true)) => (($true = (subset @ sK100 @ sK99)) & ((in @ sK101 @ sK99) != $true) & ($true = (in @ sK101 @ sK100)))),
% 50.23/8.36 introduced(definition,[],[choice_axiom])).
% 50.23/8.36 thf(f709,plain,(
% 50.23/8.36 (! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X1 @ X0) != $true) | ($true = (in @ X2 @ X0)) | ($true != (in @ X2 @ X1))) | (notsubsetI != $true)) & ((notsubsetI = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X4 @ X3) = $true) & ($true != (in @ X5 @ X3)) & ((in @ X5 @ X4) = $true)))),
% 50.23/8.37 inference(rectify,[status(thm)],[f708])).
% 50.23/8.37 thf(f708,plain,(
% 50.23/8.37 (! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X1 @ X0) != $true) | ($true = (in @ X2 @ X0)) | ($true != (in @ X2 @ X1))) | (notsubsetI != $true)) & ((notsubsetI = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X1 @ X0) = $true) & ($true != (in @ X2 @ X0)) & ($true = (in @ X2 @ X1))))),
% 50.23/8.37 inference(nnf_transformation,[status(thm)],[f538])).
% 50.23/8.37 thf(f538,plain,(
% 50.23/8.37 ! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X1 @ X0) != $true) | ($true = (in @ X2 @ X0)) | ($true != (in @ X2 @ X1))) <=> (notsubsetI = $true)),
% 50.23/8.37 inference(flattening,[status(thm)],[f537])).
% 50.23/8.37 thf(f537,plain,(
% 50.23/8.37 (notsubsetI = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : ((((subset @ X1 @ X0) != $true) | ($true = (in @ X2 @ X0))) | ($true != (in @ X2 @ X1)))),
% 50.23/8.37 inference(ennf_transformation,[status(thm)],[f392])).
% 50.23/8.37 thf(f392,plain,(
% 50.23/8.37 (notsubsetI = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ X1)) => (($true != (in @ X2 @ X0)) => ((subset @ X1 @ X0) != $true)))),
% 50.23/8.37 inference(flattening,[status(thm)],[f188])).
% 50.23/8.37 thf(f188,plain,(
% 50.23/8.37 (notsubsetI = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ X1)) => (~($true = (in @ X2 @ X0)) => ~((subset @ X1 @ X0) = $true)))),
% 50.23/8.37 inference(fool_elimination,[status(thm)],[f187])).
% 50.23/8.37 thf(f187,plain,(
% 50.23/8.37 (notsubsetI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => (~(in @ X2 @ X0) => ~(subset @ X1 @ X0))))),
% 50.23/8.37 inference(rectify,[status(thm)],[f85])).
% 50.23/8.37 thf(f85,axiom,(
% 50.23/8.37 (notsubsetI = ! [X4 : $i,X3 : $i,X1 : $i] : ((in @ X1 @ X3) => (~(in @ X1 @ X4) => ~(subset @ X3 @ X4))))),
% 50.23/8.37 file('/export/starexec/sandbox/tmp/tmp.mU0PE1mI9q/DTF2THF_13954.p',notsubsetI)).
% 50.23/8.37 thf(f26817,plain,(
% 50.23/8.37 ~spl346_51),
% 50.23/8.37 inference(avatar_split_clause,[status(thm)],[f3903,f4972])).
% 50.23/8.37 thf(f3903,plain,(
% 50.23/8.37 ($true != (subset @ sK56 @ sK55))),
% 50.23/8.37 inference(trivial_inequality_removal,[status(thm)],[f3902])).
% 50.23/8.37 thf(f3902,plain,(
% 50.23/8.37 ($true != $true) | ($true != (subset @ sK56 @ sK55))),
% 50.23/8.37 inference(forward_demodulation,[status(thm)],[f3901,f1266])).
% 50.23/8.37 thf(f1266,plain,(
% 50.23/8.37 (binintersectSubset4 = $true)),
% 50.23/8.37 inference(cnf_transformation,[status(thm)],[f635])).
% 50.23/8.37 thf(f3901,plain,(
% 50.23/8.37 ($true != (subset @ sK56 @ sK55)) | (binintersectSubset4 != $true)),
% 50.23/8.37 inference(trivial_inequality_removal,[status(thm)],[f3900])).
% 50.23/8.37 thf(f3900,plain,(
% 50.23/8.37 ($true != (subset @ sK56 @ sK55)) | (binintersectSubset4 != $true) | (sK56 != sK56)),
% 50.23/8.37 inference(superposition,[status(thm)],[f2808,f1702])).
% 50.23/8.37 thf(f1702,plain,(
% 50.23/8.37 ( ! [X2 : $i,X3 : $i] : (((binintersect @ X2 @ X3) = X3) | (binintersectSubset4 != $true) | ($true != (subset @ X3 @ X2))) )),
% 50.23/8.37 inference(cnf_transformation,[status(thm)],[f1071])).
% 50.23/8.37 thf(f1071,plain,(
% 50.23/8.37 ((binintersectSubset4 = $true) | (((binintersect @ sK308 @ sK309) != sK309) & ($true = (subset @ sK309 @ sK308)))) & (! [X2 : $i,X3 : $i] : (((binintersect @ X2 @ X3) = X3) | ($true != (subset @ X3 @ X2))) | (binintersectSubset4 != $true))),
% 50.23/8.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK308,sK309])],[f1069,f1070])).
% 50.23/8.37 thf(f1070,plain,(
% 50.23/8.37 ? [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) != X1) & ((subset @ X1 @ X0) = $true)) => (((binintersect @ sK308 @ sK309) != sK309) & ($true = (subset @ sK309 @ sK308)))),
% 50.23/8.37 introduced(definition,[],[choice_axiom])).
% 50.23/8.37 thf(f1069,plain,(
% 50.23/8.37 ((binintersectSubset4 = $true) | ? [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) != X1) & ((subset @ X1 @ X0) = $true))) & (! [X2 : $i,X3 : $i] : (((binintersect @ X2 @ X3) = X3) | ($true != (subset @ X3 @ X2))) | (binintersectSubset4 != $true))),
% 50.23/8.37 inference(rectify,[status(thm)],[f1068])).
% 50.23/8.37 thf(f1068,plain,(
% 50.23/8.37 ((binintersectSubset4 = $true) | ? [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) != X1) & ((subset @ X1 @ X0) = $true))) & (! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = X1) | ((subset @ X1 @ X0) != $true)) | (binintersectSubset4 != $true))),
% 50.23/8.37 inference(nnf_transformation,[status(thm)],[f497])).
% 50.23/8.37 thf(f497,plain,(
% 50.23/8.37 (binintersectSubset4 = $true) <=> ! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = X1) | ((subset @ X1 @ X0) != $true))),
% 50.23/8.37 inference(ennf_transformation,[status(thm)],[f171])).
% 50.23/8.37 thf(f171,plain,(
% 50.23/8.37 ! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) = $true) => ((binintersect @ X0 @ X1) = X1)) <=> (binintersectSubset4 = $true)),
% 50.23/8.37 inference(fool_elimination,[status(thm)],[f170])).
% 50.23/8.37 thf(f170,plain,(
% 50.23/8.37 (binintersectSubset4 = ! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => ((binintersect @ X0 @ X1) = X1)))),
% 50.23/8.37 inference(rectify,[status(thm)],[f117])).
% 50.23/8.37 thf(f117,axiom,(
% 50.23/8.37 (binintersectSubset4 = ! [X3 : $i,X4 : $i] : ((subset @ X4 @ X3) => ((binintersect @ X3 @ X4) = X4)))),
% 50.23/8.37 file('/export/starexec/sandbox/tmp/tmp.mU0PE1mI9q/DTF2THF_13954.p',binintersectSubset4)).
% 50.23/8.37 thf(f2808,plain,(
% 50.23/8.37 ((binintersect @ sK55 @ sK56) != sK56)),
% 50.23/8.37 inference(trivial_inequality_removal,[status(thm)],[f2807])).
% 50.23/8.37 thf(f2807,plain,(
% 50.23/8.37 ((binintersect @ sK55 @ sK56) != sK56) | ($true != $true)),
% 50.23/8.37 inference(forward_demodulation,[status(thm)],[f2806,f1215])).
% 50.23/8.37 thf(f1215,plain,(
% 50.23/8.37 (binintersectSubset3 = $true)),
% 50.23/8.37 inference(cnf_transformation,[status(thm)],[f635])).
% 50.23/8.37 thf(f2806,plain,(
% 50.23/8.37 (binintersectSubset3 != $true) | ((binintersect @ sK55 @ sK56) != sK56)),
% 50.23/8.37 inference(trivial_inequality_removal,[status(thm)],[f2802])).
% 50.23/8.37 thf(f2802,plain,(
% 50.23/8.37 ((binintersect @ sK55 @ sK56) != sK56) | ($true != $true) | (binintersectSubset3 != $true)),
% 50.23/8.37 inference(superposition,[status(thm)],[f1994,f1629])).
% 50.23/8.37 thf(f1629,plain,(
% 50.23/8.37 ( ! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) = $true) | (binintersectSubset3 != $true) | ((binintersect @ X0 @ X1) != X1)) )),
% 50.23/8.37 inference(cnf_transformation,[status(thm)],[f980])).
% 50.23/8.37 thf(f980,plain,(
% 50.23/8.37 (! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) != X1) | ((subset @ X1 @ X0) = $true)) | (binintersectSubset3 != $true)) & ((binintersectSubset3 = $true) | ((sK258 = (binintersect @ sK257 @ sK258)) & ($true != (subset @ sK258 @ sK257))))),
% 50.23/8.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK257,sK258])],[f978,f979])).
% 50.23/8.37 thf(f979,plain,(
% 50.23/8.37 ? [X2 : $i,X3 : $i] : (((binintersect @ X2 @ X3) = X3) & ($true != (subset @ X3 @ X2))) => ((sK258 = (binintersect @ sK257 @ sK258)) & ($true != (subset @ sK258 @ sK257)))),
% 50.23/8.37 introduced(definition,[],[choice_axiom])).
% 50.23/8.37 thf(f978,plain,(
% 50.23/8.37 (! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) != X1) | ((subset @ X1 @ X0) = $true)) | (binintersectSubset3 != $true)) & ((binintersectSubset3 = $true) | ? [X2 : $i,X3 : $i] : (((binintersect @ X2 @ X3) = X3) & ($true != (subset @ X3 @ X2))))),
% 50.23/8.37 inference(rectify,[status(thm)],[f977])).
% 50.23/8.37 thf(f977,plain,(
% 50.23/8.37 (! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) != X1) | ((subset @ X1 @ X0) = $true)) | (binintersectSubset3 != $true)) & ((binintersectSubset3 = $true) | ? [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = X1) & ((subset @ X1 @ X0) != $true)))),
% 50.23/8.37 inference(nnf_transformation,[status(thm)],[f484])).
% 50.23/8.37 thf(f484,plain,(
% 50.23/8.37 ! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) != X1) | ((subset @ X1 @ X0) = $true)) <=> (binintersectSubset3 = $true)),
% 50.23/8.37 inference(ennf_transformation,[status(thm)],[f260])).
% 50.23/8.37 thf(f260,plain,(
% 50.23/8.37 ! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = X1) => ((subset @ X1 @ X0) = $true)) <=> (binintersectSubset3 = $true)),
% 50.23/8.37 inference(fool_elimination,[status(thm)],[f259])).
% 50.23/8.37 thf(f259,plain,(
% 50.23/8.37 (! [X0 : $i,X1 : $i] : (((binintersect @ X0 @ X1) = X1) => (subset @ X1 @ X0)) = binintersectSubset3)),
% 50.23/8.37 inference(rectify,[status(thm)],[f113])).
% 50.23/8.37 thf(f113,axiom,(
% 50.23/8.37 (! [X3 : $i,X4 : $i] : (((binintersect @ X3 @ X4) = X4) => (subset @ X4 @ X3)) = binintersectSubset3)),
% 50.23/8.37 file('/export/starexec/sandbox/tmp/tmp.mU0PE1mI9q/DTF2THF_13954.p',binintersectSubset3)).
% 50.23/8.37 thf(f1994,plain,(
% 50.23/8.37 ($true != (subset @ sK56 @ sK55))),
% 50.23/8.37 inference(trivial_inequality_removal,[status(thm)],[f1993])).
% 50.23/8.37 thf(f1993,plain,(
% 50.23/8.37 ($true != $true) | ($true != (subset @ sK56 @ sK55))),
% 50.23/8.37 inference(forward_demodulation,[status(thm)],[f1960,f1281])).
% 50.23/8.37 thf(f1281,plain,(
% 50.23/8.37 (eqimpsubset1 = $true)),
% 50.23/8.37 inference(cnf_transformation,[status(thm)],[f635])).
% 50.23/8.37 thf(f1960,plain,(
% 50.23/8.37 ($true != (subset @ sK56 @ sK55)) | (eqimpsubset1 != $true)),
% 50.23/8.37 inference(trivial_inequality_removal,[status(thm)],[f1925])).
% 50.23/8.37 thf(f1925,plain,(
% 50.23/8.37 (eqimpsubset1 != $true) | ($true != (subset @ sK56 @ sK55)) | ($true != $true)),
% 50.23/8.37 inference(superposition,[status(thm)],[f1856,f1763])).
% 50.23/8.37 thf(f1763,plain,(
% 50.23/8.37 ( ! [X3 : $i] : (((subset @ X3 @ X3) = $true) | (eqimpsubset1 != $true)) )),
% 50.23/8.37 inference(equality_resolution,[status(thm)],[f1443])).
% 50.23/8.37 thf(f1443,plain,(
% 50.23/8.37 ( ! [X2 : $i,X3 : $i] : (($true = (subset @ X3 @ X2)) | (X2 != X3) | (eqimpsubset1 != $true)) )),
% 50.23/8.37 inference(cnf_transformation,[status(thm)],[f772])).
% 50.23/8.37 thf(f772,plain,(
% 50.23/8.37 ((eqimpsubset1 = $true) | (((subset @ sK134 @ sK133) != $true) & (sK134 = sK133))) & (! [X2 : $i,X3 : $i] : (($true = (subset @ X3 @ X2)) | (X2 != X3)) | (eqimpsubset1 != $true))),
% 50.23/8.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK133,sK134])],[f770,f771])).
% 50.23/8.37 thf(f771,plain,(
% 50.23/8.37 ? [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) & (X0 = X1)) => (((subset @ sK134 @ sK133) != $true) & (sK134 = sK133))),
% 50.23/8.37 introduced(definition,[],[choice_axiom])).
% 50.23/8.37 thf(f770,plain,(
% 50.23/8.37 ((eqimpsubset1 = $true) | ? [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) & (X0 = X1))) & (! [X2 : $i,X3 : $i] : (($true = (subset @ X3 @ X2)) | (X2 != X3)) | (eqimpsubset1 != $true))),
% 50.23/8.37 inference(rectify,[status(thm)],[f769])).
% 50.23/8.37 thf(f769,plain,(
% 50.23/8.37 ((eqimpsubset1 = $true) | ? [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) & (X0 = X1))) & (! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) = $true) | (X0 != X1)) | (eqimpsubset1 != $true))),
% 50.23/8.37 inference(nnf_transformation,[status(thm)],[f423])).
% 50.23/8.37 thf(f423,plain,(
% 50.23/8.37 (eqimpsubset1 = $true) <=> ! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) = $true) | (X0 != X1))),
% 50.23/8.37 inference(ennf_transformation,[status(thm)],[f143])).
% 50.23/8.37 thf(f143,plain,(
% 50.23/8.37 ! [X0 : $i,X1 : $i] : ((X0 = X1) => ((subset @ X1 @ X0) = $true)) <=> (eqimpsubset1 = $true)),
% 50.23/8.37 inference(fool_elimination,[status(thm)],[f142])).
% 50.23/8.37 thf(f142,plain,(
% 50.23/8.37 (! [X0 : $i,X1 : $i] : ((X0 = X1) => (subset @ X1 @ X0)) = eqimpsubset1)),
% 50.23/8.37 inference(rectify,[status(thm)],[f80])).
% 50.23/8.37 thf(f80,axiom,(
% 50.23/8.37 (! [X4 : $i,X3 : $i] : ((X3 = X4) => (subset @ X3 @ X4)) = eqimpsubset1)),
% 50.23/8.37 file('/export/starexec/sandbox/tmp/tmp.mU0PE1mI9q/DTF2THF_13954.p',eqimpsubset1)).
% 50.23/8.37 thf(f1856,plain,(
% 50.23/8.37 ( ! [X0 : $i] : (($true != (subset @ sK56 @ X0)) | ($true != (subset @ X0 @ sK55))) )),
% 50.23/8.37 inference(trivial_inequality_removal,[status(thm)],[f1855])).
% 50.23/8.37 thf(f1855,plain,(
% 50.23/8.37 ( ! [X0 : $i] : (($true != (subset @ sK56 @ X0)) | ($true != (subset @ X0 @ sK55)) | ($true != $true)) )),
% 50.23/8.37 inference(forward_demodulation,[status(thm)],[f1851,f1243])).
% 50.23/8.37 thf(f1243,plain,(
% 50.23/8.37 (subsetTrans = $true)),
% 50.23/8.37 inference(cnf_transformation,[status(thm)],[f635])).
% 50.23/8.37 thf(f1851,plain,(
% 50.23/8.37 ( ! [X0 : $i] : (($true != (subset @ X0 @ sK55)) | (subsetTrans != $true) | ($true != (subset @ sK56 @ X0))) )),
% 50.23/8.37 inference(trivial_inequality_removal,[status(thm)],[f1849])).
% 50.23/8.37 thf(f1849,plain,(
% 50.23/8.37 ( ! [X0 : $i] : (($true != $true) | ($true != (subset @ X0 @ sK55)) | ($true != (subset @ sK56 @ X0)) | (subsetTrans != $true)) )),
% 50.23/8.37 inference(superposition,[status(thm)],[f1222,f1735])).
% 50.23/8.37 thf(f1735,plain,(
% 50.23/8.37 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X4 @ X5) = $true) | (subsetTrans != $true) | ((subset @ X4 @ X3) != $true) | ((subset @ X3 @ X5) != $true)) )),
% 50.23/8.37 inference(cnf_transformation,[status(thm)],[f1116])).
% 50.23/8.37 thf(f1116,plain,(
% 50.23/8.37 ((subsetTrans = $true) | (($true = (subset @ sK330 @ sK329)) & ($true != (subset @ sK330 @ sK331)) & ($true = (subset @ sK329 @ sK331)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X4 @ X3) != $true) | ((subset @ X4 @ X5) = $true) | ((subset @ X3 @ X5) != $true)) | (subsetTrans != $true))),
% 50.23/8.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK329,sK330,sK331])],[f1114,f1115])).
% 50.23/8.37 thf(f1115,plain,(
% 50.23/8.37 ? [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X1 @ X0) = $true) & ($true != (subset @ X1 @ X2)) & ($true = (subset @ X0 @ X2))) => (($true = (subset @ sK330 @ sK329)) & ($true != (subset @ sK330 @ sK331)) & ($true = (subset @ sK329 @ sK331)))),
% 50.23/8.37 introduced(definition,[],[choice_axiom])).
% 50.23/8.37 thf(f1114,plain,(
% 50.23/8.37 ((subsetTrans = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X1 @ X0) = $true) & ($true != (subset @ X1 @ X2)) & ($true = (subset @ X0 @ X2)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X4 @ X3) != $true) | ((subset @ X4 @ X5) = $true) | ((subset @ X3 @ X5) != $true)) | (subsetTrans != $true))),
% 50.23/8.37 inference(rectify,[status(thm)],[f1113])).
% 50.23/8.37 thf(f1113,plain,(
% 50.23/8.37 ((subsetTrans = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X1 @ X0) = $true) & ($true != (subset @ X1 @ X2)) & ($true = (subset @ X0 @ X2)))) & (! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X1 @ X0) != $true) | ($true = (subset @ X1 @ X2)) | ($true != (subset @ X0 @ X2))) | (subsetTrans != $true))),
% 50.23/8.37 inference(nnf_transformation,[status(thm)],[f522])).
% 50.23/8.37 thf(f522,plain,(
% 50.23/8.37 (subsetTrans = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X1 @ X0) != $true) | ($true = (subset @ X1 @ X2)) | ($true != (subset @ X0 @ X2)))),
% 50.23/8.37 inference(flattening,[status(thm)],[f521])).
% 50.23/8.37 thf(f521,plain,(
% 50.23/8.37 (subsetTrans = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : ((($true = (subset @ X1 @ X2)) | ($true != (subset @ X0 @ X2))) | ((subset @ X1 @ X0) != $true))),
% 50.23/8.37 inference(ennf_transformation,[status(thm)],[f256])).
% 50.23/8.37 thf(f256,plain,(
% 50.23/8.37 (subsetTrans = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X1 @ X0) = $true) => (($true = (subset @ X0 @ X2)) => ($true = (subset @ X1 @ X2))))),
% 50.23/8.37 inference(fool_elimination,[status(thm)],[f255])).
% 50.23/8.37 thf(f255,plain,(
% 50.23/8.37 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X1 @ X0) => ((subset @ X0 @ X2) => (subset @ X1 @ X2))) = subsetTrans)),
% 50.23/8.37 inference(rectify,[status(thm)],[f89])).
% 50.23/8.37 thf(f89,axiom,(
% 50.23/8.37 (! [X4 : $i,X3 : $i,X5 : $i] : ((subset @ X3 @ X4) => ((subset @ X4 @ X5) => (subset @ X3 @ X5))) = subsetTrans)),
% 50.23/8.37 file('/export/starexec/sandbox/tmp/tmp.mU0PE1mI9q/DTF2THF_13954.p',subsetTrans)).
% 50.23/8.37 thf(f1222,plain,(
% 50.23/8.37 ($true != (subset @ sK56 @ sK55))),
% 50.23/8.37 inference(cnf_transformation,[status(thm)],[f635])).
% 50.23/8.37 thf(f17386,plain,(
% 50.23/8.37 ~spl346_5),
% 50.23/8.37 inference(avatar_contradiction_clause,[status(thm)],[f17385])).
% 50.23/8.37 thf(f17385,plain,(
% 50.23/8.37 $false | ~spl346_5),
% 50.23/8.37 inference(trivial_inequality_removal,[status(thm)],[f17384])).
% 50.23/8.37 thf(f17384,plain,(
% 50.23/8.37 ($true != $true) | ~spl346_5),
% 50.23/8.37 inference(superposition,[status(thm)],[f17245,f1250])).
% 50.23/8.37 thf(f1250,plain,(
% 50.23/8.37 (notequalI1 = $true)),
% 50.23/8.37 inference(cnf_transformation,[status(thm)],[f635])).
% 50.23/8.37 thf(f17245,plain,(
% 50.23/8.37 (notequalI1 != $true) | ~spl346_5),
% 50.23/8.37 inference(trivial_inequality_removal,[status(thm)],[f17229])).
% 50.23/8.37 thf(f17229,plain,(
% 50.23/8.37 ($true != $true) | (notequalI1 != $true) | ~spl346_5),
% 50.23/8.37 inference(superposition,[status(thm)],[f1970,f1771])).
% 50.23/8.37 thf(f1771,plain,(
% 50.23/8.37 ( ! [X1 : $i] : (($true = (subset @ X1 @ X1)) | (notequalI1 != $true)) )),
% 50.23/8.37 inference(equality_resolution,[status(thm)],[f1543])).
% 50.23/8.37 thf(f1543,plain,(
% 50.23/8.37 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ X0 @ X1)) | (X0 != X1) | (notequalI1 != $true)) )),
% 50.23/8.37 inference(cnf_transformation,[status(thm)],[f898])).
% 50.23/8.37 thf(f898,plain,(
% 50.23/8.37 (! [X0 : $i,X1 : $i] : (($true = (subset @ X0 @ X1)) | (X0 != X1)) | (notequalI1 != $true)) & ((notequalI1 = $true) | (((subset @ sK205 @ sK206) != $true) & (sK205 = sK206)))),
% 50.23/8.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK205,sK206])],[f896,f897])).
% 50.23/8.37 thf(f897,plain,(
% 50.23/8.37 ? [X2 : $i,X3 : $i] : (($true != (subset @ X2 @ X3)) & (X2 = X3)) => (((subset @ sK205 @ sK206) != $true) & (sK205 = sK206))),
% 50.23/8.37 introduced(definition,[],[choice_axiom])).
% 50.23/8.37 thf(f896,plain,(
% 50.23/8.37 (! [X0 : $i,X1 : $i] : (($true = (subset @ X0 @ X1)) | (X0 != X1)) | (notequalI1 != $true)) & ((notequalI1 = $true) | ? [X2 : $i,X3 : $i] : (($true != (subset @ X2 @ X3)) & (X2 = X3)))),
% 50.23/8.37 inference(rectify,[status(thm)],[f895])).
% 50.23/8.37 thf(f895,plain,(
% 50.23/8.37 (! [X0 : $i,X1 : $i] : (($true = (subset @ X0 @ X1)) | (X0 != X1)) | (notequalI1 != $true)) & ((notequalI1 = $true) | ? [X0 : $i,X1 : $i] : (($true != (subset @ X0 @ X1)) & (X0 = X1)))),
% 50.23/8.37 inference(nnf_transformation,[status(thm)],[f416])).
% 50.23/8.37 thf(f416,plain,(
% 50.23/8.37 ! [X0 : $i,X1 : $i] : (($true = (subset @ X0 @ X1)) | (X0 != X1)) <=> (notequalI1 = $true)),
% 50.23/8.37 inference(ennf_transformation,[status(thm)],[f399])).
% 50.23/8.37 thf(f399,plain,(
% 50.23/8.37 (notequalI1 = $true) <=> ! [X0 : $i,X1 : $i] : (($true != (subset @ X0 @ X1)) => (X0 != X1))),
% 50.23/8.37 inference(flattening,[status(thm)],[f242])).
% 50.23/8.37 thf(f242,plain,(
% 50.23/8.37 ! [X0 : $i,X1 : $i] : (~($true = (subset @ X0 @ X1)) => (X0 != X1)) <=> (notequalI1 = $true)),
% 50.23/8.37 inference(fool_elimination,[status(thm)],[f241])).
% 50.23/8.37 thf(f241,plain,(
% 50.23/8.37 (! [X0 : $i,X1 : $i] : (~(subset @ X0 @ X1) => (X0 != X1)) = notequalI1)),
% 50.23/8.37 inference(rectify,[status(thm)],[f86])).
% 50.23/8.37 thf(f86,axiom,(
% 50.23/8.37 (! [X3 : $i,X4 : $i] : (~(subset @ X3 @ X4) => (X3 != X4)) = notequalI1)),
% 50.23/8.37 file('/export/starexec/sandbox/tmp/tmp.mU0PE1mI9q/DTF2THF_13954.p',notequalI1)).
% 50.23/8.37 thf(f1970,plain,(
% 50.23/8.37 ( ! [X0 : $i] : (($true != (subset @ sK56 @ X0))) ) | ~spl346_5),
% 50.23/8.37 inference(avatar_component_clause,[status(thm)],[f1969])).
% 50.23/8.37 thf(f1969,definition,(
% 50.23/8.37 spl346_5 <=> ! [X0 : $i] : ($true != (subset @ sK56 @ X0))),
% 50.23/8.37 introduced(definition,[new_symbols(naming,[spl346_5])],[avatar_definition])).
% 50.23/8.37 thf(f16383,plain,(
% 50.23/8.37 spl346_5 | ~spl346_45),
% 50.23/8.37 inference(avatar_split_clause,[status(thm)],[f15852,f2980,f1969])).
% 50.23/8.37 thf(f2980,definition,(
% 50.23/8.37 spl346_45 <=> ! [X0 : $o] : ($true = X0)),
% 50.23/8.37 introduced(definition,[new_symbols(naming,[spl346_45])],[avatar_definition])).
% 50.23/8.37 thf(f15852,plain,(
% 50.23/8.37 ( ! [X1 : $i] : (($true != (subset @ sK56 @ X1))) ) | ~spl346_45),
% 50.23/8.37 inference(trivial_inequality_removal,[status(thm)],[f15721])).
% 50.23/8.37 thf(f15721,plain,(
% 50.23/8.37 ( ! [X1 : $i] : (($true != $true) | ($true != (subset @ sK56 @ X1))) ) | ~spl346_45),
% 50.23/8.37 inference(superposition,[status(thm)],[f2029,f2981])).
% 50.23/8.37 thf(f2981,plain,(
% 50.23/8.37 ( ! [X0 : $o] : (($true = X0)) ) | ~spl346_45),
% 50.23/8.37 inference(avatar_component_clause,[status(thm)],[f2980])).
% 50.23/8.37 thf(f2029,plain,(
% 50.23/8.37 ( ! [X0 : $i,X1 : $i] : (($true != (subset @ (setadjoin @ X0 @ X1) @ sK55)) | ($true != (subset @ sK56 @ X1))) )),
% 50.23/8.37 inference(trivial_inequality_removal,[status(thm)],[f2028])).
% 50.23/8.37 thf(f2028,plain,(
% 50.23/8.37 ( ! [X0 : $i,X1 : $i] : (($true != (subset @ (setadjoin @ X0 @ X1) @ sK55)) | ($true != (subset @ sK56 @ X1)) | ($true != $true)) )),
% 50.23/8.37 inference(forward_demodulation,[status(thm)],[f1952,f1308])).
% 50.23/8.37 thf(f1308,plain,(
% 50.23/8.37 (setadjoinSub2 = $true)),
% 50.23/8.37 inference(cnf_transformation,[status(thm)],[f635])).
% 50.23/8.37 thf(f1952,plain,(
% 50.23/8.37 ( ! [X0 : $i,X1 : $i] : (($true != (subset @ sK56 @ X1)) | ($true != (subset @ (setadjoin @ X0 @ X1) @ sK55)) | (setadjoinSub2 != $true)) )),
% 50.23/8.37 inference(trivial_inequality_removal,[status(thm)],[f1922])).
% 50.23/8.37 thf(f1922,plain,(
% 50.23/8.37 ( ! [X0 : $i,X1 : $i] : ((setadjoinSub2 != $true) | ($true != (subset @ sK56 @ X1)) | ($true != $true) | ($true != (subset @ (setadjoin @ X0 @ X1) @ sK55))) )),
% 50.23/8.37 inference(superposition,[status(thm)],[f1856,f1175])).
% 50.23/8.37 thf(f1175,plain,(
% 50.23/8.37 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = (subset @ X5 @ (setadjoin @ X3 @ X4))) | ((subset @ X5 @ X4) != $true) | (setadjoinSub2 != $true)) )),
% 50.23/8.37 inference(cnf_transformation,[status(thm)],[f605])).
% 50.23/8.37 thf(f605,plain,(
% 50.23/8.37 ((setadjoinSub2 = $true) | (((subset @ sK37 @ (setadjoin @ sK35 @ sK36)) != $true) & ($true = (subset @ sK37 @ sK36)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true = (subset @ X5 @ (setadjoin @ X3 @ X4))) | ((subset @ X5 @ X4) != $true)) | (setadjoinSub2 != $true))),
% 50.23/8.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK35,sK36,sK37])],[f603,f604])).
% 50.23/8.37 thf(f604,plain,(
% 50.23/8.37 ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (subset @ X2 @ (setadjoin @ X0 @ X1))) & ((subset @ X2 @ X1) = $true)) => (((subset @ sK37 @ (setadjoin @ sK35 @ sK36)) != $true) & ($true = (subset @ sK37 @ sK36)))),
% 50.23/8.37 introduced(definition,[],[choice_axiom])).
% 50.23/8.37 thf(f603,plain,(
% 50.23/8.37 ((setadjoinSub2 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (subset @ X2 @ (setadjoin @ X0 @ X1))) & ((subset @ X2 @ X1) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true = (subset @ X5 @ (setadjoin @ X3 @ X4))) | ((subset @ X5 @ X4) != $true)) | (setadjoinSub2 != $true))),
% 50.23/8.37 inference(rectify,[status(thm)],[f602])).
% 50.23/8.37 thf(f602,plain,(
% 50.23/8.37 ((setadjoinSub2 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (subset @ X2 @ (setadjoin @ X0 @ X1))) & ((subset @ X2 @ X1) = $true))) & (! [X0 : $i,X1 : $i,X2 : $i] : (($true = (subset @ X2 @ (setadjoin @ X0 @ X1))) | ((subset @ X2 @ X1) != $true)) | (setadjoinSub2 != $true))),
% 50.23/8.37 inference(nnf_transformation,[status(thm)],[f516])).
% 50.23/8.37 thf(f516,plain,(
% 50.23/8.37 (setadjoinSub2 = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (subset @ X2 @ (setadjoin @ X0 @ X1))) | ((subset @ X2 @ X1) != $true))),
% 50.23/8.37 inference(ennf_transformation,[status(thm)],[f240])).
% 50.23/8.37 thf(f240,plain,(
% 50.23/8.37 ! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X2 @ X1) = $true) => ($true = (subset @ X2 @ (setadjoin @ X0 @ X1)))) <=> (setadjoinSub2 = $true)),
% 50.23/8.37 inference(fool_elimination,[status(thm)],[f239])).
% 50.23/8.37 thf(f239,plain,(
% 50.23/8.37 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X2 @ X1) => (subset @ X2 @ (setadjoin @ X0 @ X1))) = setadjoinSub2)),
% 50.23/8.37 inference(rectify,[status(thm)],[f91])).
% 50.23/8.37 thf(f91,axiom,(
% 50.23/8.37 (! [X1 : $i,X4 : $i,X3 : $i] : ((subset @ X3 @ X4) => (subset @ X3 @ (setadjoin @ X1 @ X4))) = setadjoinSub2)),
% 50.23/8.37 file('/export/starexec/sandbox/tmp/tmp.mU0PE1mI9q/DTF2THF_13954.p',setadjoinSub2)).
% 50.23/8.37 thf(f6193,plain,(
% 50.23/8.37 spl346_71 | spl346_45 | ~spl346_36),
% 50.23/8.37 inference(avatar_split_clause,[status(thm)],[f6192,f2341,f2980,f5891])).
% 50.23/8.37 thf(f6192,plain,(
% 50.23/8.37 ( ! [X0 : $i,X1 : $o] : (($true = (subset @ X0 @ sK55)) | ($true != (in @ (sK280 @ X0 @ sK55) @ sK56)) | ($true = X1)) ) | ~spl346_36),
% 50.23/8.37 inference(trivial_inequality_removal,[status(thm)],[f6191])).
% 50.23/8.37 thf(f6191,plain,(
% 50.23/8.37 ( ! [X0 : $i,X1 : $o] : (($true = (subset @ X0 @ sK55)) | ($true != (in @ (sK280 @ X0 @ sK55) @ sK56)) | ($true != $true) | ($true = X1)) ) | ~spl346_36),
% 50.23/8.37 inference(forward_demodulation,[status(thm)],[f6166,f4166])).
% 50.23/8.37 thf(f4166,plain,(
% 50.23/8.37 (emptysetE = $true) | ~spl346_36),
% 50.23/8.37 inference(trivial_inequality_removal,[status(thm)],[f4153])).
% 50.23/8.37 thf(f4153,plain,(
% 50.23/8.37 (emptysetE = $true) | ($true != $true) | ~spl346_36),
% 50.23/8.37 inference(superposition,[status(thm)],[f2342,f1404])).
% 50.23/8.37 thf(f1404,plain,(
% 50.23/8.37 ($true = (in @ sK106 @ emptyset)) | (emptysetE = $true)),
% 50.23/8.37 inference(cnf_transformation,[status(thm)],[f724])).
% 50.23/8.37 thf(f724,plain,(
% 50.23/8.37 ((emptysetE = $true) | (($true = (in @ sK106 @ emptyset)) & ($true != sK107))) & (! [X2 : $i] : (((in @ X2 @ emptyset) != $true) | ! [X3 : $o] : ($true = X3)) | (emptysetE != $true))),
% 50.23/8.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK106,sK107])],[f721,f723,f722])).
% 50.23/8.37 thf(f722,plain,(
% 50.23/8.37 ? [X0 : $i] : (((in @ X0 @ emptyset) = $true) & ? [X1 : $o] : ($true != X1)) => (($true = (in @ sK106 @ emptyset)) & ? [X1 : $o] : ($true != X1))),
% 50.23/8.37 introduced(definition,[],[choice_axiom])).
% 50.23/8.37 thf(f723,plain,(
% 50.23/8.37 ? [X1 : $o] : ($true != X1) => ($true != sK107)),
% 50.23/8.37 introduced(definition,[],[choice_axiom])).
% 50.23/8.37 thf(f721,plain,(
% 50.23/8.37 ((emptysetE = $true) | ? [X0 : $i] : (((in @ X0 @ emptyset) = $true) & ? [X1 : $o] : ($true != X1))) & (! [X2 : $i] : (((in @ X2 @ emptyset) != $true) | ! [X3 : $o] : ($true = X3)) | (emptysetE != $true))),
% 50.23/8.37 inference(rectify,[status(thm)],[f720])).
% 50.23/8.37 thf(f720,plain,(
% 50.23/8.37 ((emptysetE = $true) | ? [X0 : $i] : (((in @ X0 @ emptyset) = $true) & ? [X1 : $o] : ($true != X1))) & (! [X0 : $i] : (((in @ X0 @ emptyset) != $true) | ! [X1 : $o] : ($true = X1)) | (emptysetE != $true))),
% 50.23/8.37 inference(nnf_transformation,[status(thm)],[f424])).
% 50.23/8.37 thf(f424,plain,(
% 50.23/8.37 (emptysetE = $true) <=> ! [X0 : $i] : (((in @ X0 @ emptyset) != $true) | ! [X1 : $o] : ($true = X1))),
% 50.23/8.37 inference(ennf_transformation,[status(thm)],[f274])).
% 50.23/8.37 thf(f274,plain,(
% 50.23/8.37 (emptysetE = $true) <=> ! [X0 : $i] : (((in @ X0 @ emptyset) = $true) => ! [X1 : $o] : ($true = X1))),
% 50.23/8.37 inference(fool_elimination,[status(thm)],[f273])).
% 50.23/8.37 thf(f273,plain,(
% 50.23/8.37 (emptysetE = ! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 50.23/8.37 inference(rectify,[status(thm)],[f19])).
% 50.23/8.37 thf(f19,axiom,(
% 50.23/8.37 (emptysetE = ! [X1 : $i] : ((in @ X1 @ emptyset) => ! [X0 : $o] : X0))),
% 50.23/8.37 file('/export/starexec/sandbox/tmp/tmp.mU0PE1mI9q/DTF2THF_13954.p',emptysetE)).
% 50.23/8.37 thf(f2342,plain,(
% 50.23/8.37 ( ! [X0 : $i] : (((in @ X0 @ emptyset) != $true)) ) | ~spl346_36),
% 50.23/8.37 inference(avatar_component_clause,[status(thm)],[f2341])).
% 50.23/8.37 thf(f6166,plain,(
% 50.23/8.37 ( ! [X0 : $i,X1 : $o] : (($true != (in @ (sK280 @ X0 @ sK55) @ sK56)) | ($true = (subset @ X0 @ sK55)) | ($true = X1) | (emptysetE != $true)) )),
% 50.23/8.37 inference(trivial_inequality_removal,[status(thm)],[f6159])).
% 50.23/8.37 thf(f6159,plain,(
% 50.23/8.37 ( ! [X0 : $i,X1 : $o] : (($true = (subset @ X0 @ sK55)) | ($true != (in @ (sK280 @ X0 @ sK55) @ sK56)) | ($true = X1) | ($true != $true) | (emptysetE != $true)) )),
% 50.23/8.37 inference(superposition,[status(thm)],[f1402,f2733])).
% 50.23/8.37 thf(f2733,plain,(
% 50.23/8.37 ( ! [X0 : $i] : (((in @ (sK280 @ X0 @ sK55) @ emptyset) = $true) | ($true = (subset @ X0 @ sK55)) | ($true != (in @ (sK280 @ X0 @ sK55) @ sK56))) )),
% 50.23/8.37 inference(trivial_inequality_removal,[status(thm)],[f2732])).
% 50.23/8.37 thf(f2732,plain,(
% 50.23/8.37 ( ! [X0 : $i] : (($true != (in @ (sK280 @ X0 @ sK55) @ sK56)) | ((in @ (sK280 @ X0 @ sK55) @ emptyset) = $true) | ($true = (subset @ X0 @ sK55)) | ($true != $true)) )),
% 50.23/8.37 inference(forward_demodulation,[status(thm)],[f2722,f1273])).
% 50.23/8.37 thf(f2722,plain,(
% 50.23/8.37 ( ! [X0 : $i] : ((subsetI2 != $true) | ((in @ (sK280 @ X0 @ sK55) @ emptyset) = $true) | ($true = (subset @ X0 @ sK55)) | ($true != (in @ (sK280 @ X0 @ sK55) @ sK56))) )),
% 50.23/8.37 inference(trivial_inequality_removal,[status(thm)],[f2710])).
% 50.23/8.37 thf(f2710,plain,(
% 50.23/8.37 ( ! [X0 : $i] : (($true = (subset @ X0 @ sK55)) | (subsetI2 != $true) | ($true != (in @ (sK280 @ X0 @ sK55) @ sK56)) | ((in @ (sK280 @ X0 @ sK55) @ emptyset) = $true) | ($true != $true)) )),
% 50.23/8.37 inference(superposition,[status(thm)],[f1661,f1882])).
% 50.23/8.37 thf(f1882,plain,(
% 50.23/8.37 ( ! [X0 : $i] : (((in @ X0 @ sK55) = $true) | ($true != (in @ X0 @ sK56)) | ((in @ X0 @ emptyset) = $true)) )),
% 50.23/8.37 inference(trivial_inequality_removal,[status(thm)],[f1881])).
% 50.23/8.37 thf(f1881,plain,(
% 50.23/8.37 ( ! [X0 : $i] : (($true != $true) | ((in @ X0 @ emptyset) = $true) | ((in @ X0 @ sK55) = $true) | ($true != (in @ X0 @ sK56))) )),
% 50.23/8.37 inference(forward_demodulation,[status(thm)],[f1865,f1258])).
% 50.23/8.37 thf(f1258,plain,(
% 50.23/8.37 (setminusI = $true)),
% 50.23/8.37 inference(cnf_transformation,[status(thm)],[f635])).
% 50.23/8.37 thf(f1865,plain,(
% 50.23/8.37 ( ! [X0 : $i] : ((setminusI != $true) | ($true != (in @ X0 @ sK56)) | ((in @ X0 @ sK55) = $true) | ((in @ X0 @ emptyset) = $true)) )),
% 50.23/8.37 inference(superposition,[status(thm)],[f1647,f1223])).
% 50.23/8.37 thf(f1647,plain,(
% 50.23/8.37 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (setminus @ X3 @ X5)) = $true) | ($true = (in @ X4 @ X5)) | ((in @ X4 @ X3) != $true) | (setminusI != $true)) )),
% 50.23/8.37 inference(cnf_transformation,[status(thm)],[f1005])).
% 50.23/8.37 thf(f1005,plain,(
% 50.23/8.37 ((setminusI = $true) | (($true = (in @ sK272 @ sK271)) & ($true != (in @ sK272 @ sK273)) & ($true != (in @ sK272 @ (setminus @ sK271 @ sK273))))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ X3) != $true) | ($true = (in @ X4 @ X5)) | ((in @ X4 @ (setminus @ X3 @ X5)) = $true)) | (setminusI != $true))),
% 50.23/8.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK271,sK272,sK273])],[f1003,f1004])).
% 50.23/8.37 thf(f1004,plain,(
% 50.23/8.37 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X0)) & ($true != (in @ X1 @ X2)) & ($true != (in @ X1 @ (setminus @ X0 @ X2)))) => (($true = (in @ sK272 @ sK271)) & ($true != (in @ sK272 @ sK273)) & ($true != (in @ sK272 @ (setminus @ sK271 @ sK273))))),
% 50.23/8.37 introduced(definition,[],[choice_axiom])).
% 50.23/8.37 thf(f1003,plain,(
% 50.23/8.37 ((setminusI = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X0)) & ($true != (in @ X1 @ X2)) & ($true != (in @ X1 @ (setminus @ X0 @ X2))))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ X3) != $true) | ($true = (in @ X4 @ X5)) | ((in @ X4 @ (setminus @ X3 @ X5)) = $true)) | (setminusI != $true))),
% 50.23/8.37 inference(rectify,[status(thm)],[f1002])).
% 50.23/8.37 thf(f1002,plain,(
% 50.23/8.37 ((setminusI = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X0)) & ($true != (in @ X1 @ X2)) & ($true != (in @ X1 @ (setminus @ X0 @ X2))))) & (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ X0)) | ($true = (in @ X1 @ X2)) | ($true = (in @ X1 @ (setminus @ X0 @ X2)))) | (setminusI != $true))),
% 50.23/8.37 inference(nnf_transformation,[status(thm)],[f419])).
% 50.23/8.37 thf(f419,plain,(
% 50.23/8.37 (setminusI = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ X0)) | ($true = (in @ X1 @ X2)) | ($true = (in @ X1 @ (setminus @ X0 @ X2))))),
% 50.23/8.37 inference(flattening,[status(thm)],[f418])).
% 50.23/8.37 thf(f418,plain,(
% 50.23/8.37 ! [X0 : $i,X1 : $i,X2 : $i] : ((($true = (in @ X1 @ (setminus @ X0 @ X2))) | ($true = (in @ X1 @ X2))) | ($true != (in @ X1 @ X0))) <=> (setminusI = $true)),
% 50.23/8.37 inference(ennf_transformation,[status(thm)],[f397])).
% 50.23/8.37 thf(f397,plain,(
% 50.23/8.37 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X0)) => (($true != (in @ X1 @ X2)) => ($true = (in @ X1 @ (setminus @ X0 @ X2))))) <=> (setminusI = $true)),
% 50.23/8.37 inference(flattening,[status(thm)],[f232])).
% 50.23/8.37 thf(f232,plain,(
% 50.23/8.37 (setminusI = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X0)) => (~($true = (in @ X1 @ X2)) => ($true = (in @ X1 @ (setminus @ X0 @ X2)))))),
% 50.23/8.37 inference(fool_elimination,[status(thm)],[f231])).
% 50.23/8.37 thf(f231,plain,(
% 50.23/8.37 (setminusI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X0) => (~(in @ X1 @ X2) => (in @ X1 @ (setminus @ X0 @ X2)))))),
% 50.23/8.37 inference(rectify,[status(thm)],[f120])).
% 50.23/8.37 thf(f120,axiom,(
% 50.23/8.37 (setminusI = ! [X3 : $i,X1 : $i,X4 : $i] : ((in @ X1 @ X3) => (~(in @ X1 @ X4) => (in @ X1 @ (setminus @ X3 @ X4)))))),
% 50.23/8.37 file('/export/starexec/sandbox/tmp/tmp.mU0PE1mI9q/DTF2THF_13954.p',setminusI)).
% 50.23/8.37 thf(f1661,plain,(
% 50.23/8.37 ( ! [X0 : $i,X1 : $i] : (((in @ (sK280 @ X1 @ X0) @ X0) != $true) | ((subset @ X1 @ X0) = $true) | (subsetI2 != $true)) )),
% 50.23/8.37 inference(cnf_transformation,[status(thm)],[f1020])).
% 50.23/8.37 thf(f1402,plain,(
% 50.23/8.37 ( ! [X2 : $i,X3 : $o] : (((in @ X2 @ emptyset) != $true) | (emptysetE != $true) | ($true = X3)) )),
% 50.23/8.37 inference(cnf_transformation,[status(thm)],[f724])).
% 50.23/8.37 % SZS output end Proof for DTF2THF_13954
% 50.23/8.37 % (14425)------------------------------
% 50.23/8.37 % (14425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.23/8.37 % (14425)Termination reason: Refutation
% 50.23/8.37
% 50.23/8.37 % (14425)Memory used [KB]: 15607
% 50.23/8.37 % (14425)Time elapsed: 0.763 s
% 50.23/8.37 % (14425)Instructions burned: 2482 (million)
% 50.23/8.37 % (14425)------------------------------
% 50.23/8.37 % (14425)------------------------------
% 50.23/8.37 % (14222)Success in time 6.868 s
%------------------------------------------------------------------------------