%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU613^1 : 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 : n001.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 09:35:37 AM UTC 2026
% Result : Theorem 28.08s 5.16s
% Output : Refutation 28.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 13
% Syntax : Number of formulae : 72 ( 40 unt; 0 typ; 6 def)
% Number of atoms : 2788 ( 735 equ; 0 cnn)
% Maximal formula atoms : 132 ( 38 avg)
% Number of connectives : 1701 ( 59 ~; 39 |; 397 &; 475 @)
% ( 6 <=>; 692 =>; 0 <=; 0 <~>)
% Maximal formula depth : 139 ( 17 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 243 ( 239 usr; 141 con; 0-4 aty)
% ( 33 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 133 ( 64 ^; 60 !; 9 ?; 133 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_170,type,
sK4: $i > $i > $i ).
thf(func_def_171,type,
sK5: ( $i > $o ) > $i > ( $i > $o ) > $i > $i ).
thf(func_def_172,type,
sK6: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_173,type,
sK7: ( $i > $o ) > $i ).
thf(func_def_174,type,
sK8: ( $i > $o ) > $i ).
thf(func_def_175,type,
sK9: ( $i > $o ) > $i ).
thf(func_def_176,type,
sK10: ( $i > $o ) > $i ).
thf(func_def_177,type,
sK11: ( $i > $o ) > $i ).
thf(func_def_178,type,
sK12: ( $i > $o ) > $i > $i ).
thf(func_def_179,type,
sK13: ( $i > $o ) > $i > $i ).
thf(func_def_180,type,
sK14: $i > ( $i > $o ) > $i ).
thf(func_def_181,type,
sK15: $i > $i > $i ).
thf(func_def_182,type,
sK16: ( $i > $o ) > $i > $i ).
thf(func_def_183,type,
sK17: $i > $i ).
thf(func_def_184,type,
sK18: $i > $i > $i ).
thf(func_def_185,type,
sK19: $i > $i > $i ).
thf(func_def_186,type,
sK20: $i > $i > $i ).
thf(func_def_187,type,
sK21: $i > $i ).
thf(func_def_188,type,
sK22: $i > $i > $i ).
thf(func_def_189,type,
sK23: $i > ( $i > $o ) > $i ).
thf(func_def_190,type,
sK24: ( $i > $o ) > $i > $i ).
thf(func_def_191,type,
sK25: ( $i > $o ) > $i ).
thf(func_def_192,type,
sK26: ( $i > $o ) > $i > $i ).
thf(func_def_194,type,
sK27: ( $i > $i > $o ) > $i > $i ).
thf(func_def_195,type,
sK28: ( $i > $i > $o ) > $i > $i ).
thf(func_def_196,type,
sK29: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_197,type,
sK30: ( $i > $i > $o ) > $i > $i ).
thf(func_def_198,type,
sK31: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_199,type,
sK32: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_200,type,
sK33: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_201,type,
sK34: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_202,type,
sK35: ( $i > $o ) > $i > $i ).
thf(func_def_203,type,
sK36: $i > $i ).
thf(func_def_204,type,
sK37: $i > $o > $i > $i ).
thf(func_def_205,type,
sK38: $i > $i ).
thf(func_def_206,type,
sK39: $i > $i > $i ).
thf(func_def_207,type,
sK40: $i > $i > $i ).
thf(func_def_208,type,
sK41: $i > $i > $i ).
thf(func_def_209,type,
sK42: $i > $i > $i ).
thf(func_def_210,type,
sK43: $i > $i ).
thf(func_def_211,type,
sK44: ( $i > $o ) > $i ).
thf(func_def_212,type,
sK45: ( $i > $o ) > $i > $i ).
thf(func_def_213,type,
sK46: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_214,type,
sK47: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_215,type,
sK48: ( $i > $o ) > $i ).
thf(func_def_216,type,
sK49: ( $i > $o ) > $i > $i ).
thf(func_def_217,type,
sK50: ( $i > $o ) > $i > $i ).
thf(func_def_218,type,
sK51: ( $i > $o ) > $i ).
thf(func_def_219,type,
sK52: ( $i > $o ) > $i > $i ).
thf(func_def_220,type,
sK53: ( $i > $o ) > $i ).
thf(func_def_221,type,
sK54: ( $i > $o ) > $i > $i ).
thf(func_def_222,type,
sK55: ( $i > $o ) > $i > $i ).
thf(func_def_223,type,
sK56: ( $i > $o ) > $i ).
thf(func_def_224,type,
sK57: ( $i > $o ) > $i > $i ).
thf(func_def_225,type,
sK58: ( $i > $o ) > $i > $i ).
thf(func_def_226,type,
sK59: ( $i > $o ) > $i ).
thf(func_def_227,type,
sK60: ( $i > $o ) > $i > $i ).
thf(func_def_228,type,
sK61: ( $i > $o ) > $i > $i ).
thf(func_def_229,type,
sK62: ( $i > $o ) > $i ).
thf(func_def_230,type,
sK63: ( $i > $o ) > $i > $i ).
thf(func_def_231,type,
sK64: ( $i > $o ) > $i > $i ).
thf(func_def_232,type,
sK65: ( $i > $o ) > $i > $i ).
thf(func_def_233,type,
sK66: $i > $i ).
thf(func_def_234,type,
sK67: $i > $i > $i > $i ).
thf(func_def_235,type,
sK68: $i > $i > $i ).
thf(func_def_236,type,
sK69: $i > $i > $i ).
thf(func_def_237,type,
sK70: $i > $i > $i ).
thf(func_def_238,type,
sK71: $i > $i > $i ).
thf(func_def_239,type,
sK72: $i > $i ).
thf(func_def_240,type,
sK73: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_241,type,
sK74: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_242,type,
sK75: ( $i > $o ) > $i > $i ).
thf(func_def_243,type,
sK76: ( $i > $o ) > $i > $i ).
thf(func_def_244,type,
sK77: ( $i > $o ) > $i > $i ).
thf(func_def_245,type,
sK78: ( $i > $o ) > $i > $i ).
thf(func_def_246,type,
sK79: ( $i > $o ) > $i > $i ).
thf(func_def_247,type,
sK80: ( $i > $o ) > $i > $i ).
thf(func_def_248,type,
sK81: ( $i > $o ) > $i > $i ).
thf(func_def_249,type,
sK82: ( $i > $o ) > $i > $i ).
thf(func_def_250,type,
sK83: ( $i > $o ) > $i > $i ).
thf(func_def_251,type,
sK84: $i > ( $i > $o ) > $i ).
thf(func_def_252,type,
sK85: $i > ( $i > $o ) > $i ).
thf(func_def_253,type,
ph86:
!>[X0: $tType] : X0 ).
thf(f7733,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f2377,f2396,f2401,f2407,f2508,f7729,f7730]) ).
thf(f7730,plain,
( ( ( in @ sK0 @ sK2 )
!= $false )
| ( ( in @ sK0 @ sK2 )
!= $true )
| ( $true = $false ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f7729,plain,
( spl3_36
| ~ spl3_22 ),
inference(avatar_split_clause,[status(thm)],[f7715,f2505,f7725]) ).
thf(f7725,definition,
( spl3_36
<=> ( ( in @ sK0 @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_36])],[avatar_definition]) ).
thf(f2505,definition,
( spl3_22
<=> ( $false
= ( in @ sK0 @ ( binunion @ sK1 @ sK2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_22])],[avatar_definition]) ).
thf(f7715,plain,
( ( ( in @ sK0 @ sK2 )
= $false )
| ~ spl3_22 ),
inference(trivial_inequality_removal,[status(thm)],[f7708]) ).
thf(f7708,plain,
( ( ( in @ sK0 @ sK2 )
= $false )
| ( $true = $false )
| ~ spl3_22 ),
inference(superposition,[status(thm)],[f2507,f2269]) ).
thf(f2269,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ ( binunion @ X1 @ X3 ) )
= $true )
| ( ( in @ X2 @ X3 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f2268]) ).
thf(f2268,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X2 @ X3 )
=> ( in @ X2 @ ( binunion @ X1 @ X3 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2267]) ).
thf(f2267,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ X2 @ Y0 )
=> ( in @ X2 @ ( binunion @ X1 @ Y0 ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f2266]) ).
thf(f2266,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ Y0 )
=> ( in @ X2 @ ( binunion @ X1 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2265]) ).
thf(f2265,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( binunion @ X1 @ Y1 ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f2264]) ).
thf(f2264,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( binunion @ X1 @ Y1 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2263]) ).
thf(f2263,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ ( binunion @ Y0 @ Y2 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f738]) ).
thf(f738,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ ( binunion @ Y0 @ Y2 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f600,f455]) ).
thf(f455,plain,
binunionIR = $true,
inference(cnf_transformation,[status(thm)],[f400]) ).
thf(f400,plain,
( ( binintersectSubset1 = $true )
& ( emptyinPowerset = $true )
& ( setminusIRneg = $true )
& ( powersetE = $true )
& ( setext = $true )
& ( disjointsetsI1 = $true )
& ( sepInPowerset = $true )
& ( bs114d = $true )
& ( binintersectRsub = $true )
& ( setminusLsub = $true )
& ( setminusSubset2 = $true )
& ( ( in @ sK0 @ ( symdiff @ sK1 @ sK2 ) )
!= $true )
& ( ( in @ sK0 @ sK2 )
= $true )
& ( ( in @ sK0 @ sK1 )
!= $true )
& ( binintersectLsub = $true )
& ( setadjoinIR = $true )
& ( subPowSU = $true )
& ( replAx = $true )
& ( emptyset__Cong = $true )
& ( emptysetsubset = $true )
& ( uniqinunit = $true )
& ( dsetconstr__Cong = $true )
& ( binunionLsub = $true )
& ( setminusERneg = $true )
& ( quantDeMorgan1 = $true )
& ( subsetE2 = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( exuE1 = $true )
& ( powersetE1 = $true )
& ( emptyinunitempty = $true )
& ( notequalI1 = $true )
& ( notequalI2 = $true )
& ( nonemptyE1 = $true )
& ( binunionE = $true )
& ( exuE2 = $true )
& ( setminusELneg = $true )
& ( in__Cong = $true )
& ( exuI3 = $true )
& ( subsetRefl = $true )
& ( binintersectSubset4 = $true )
& ( exuE3u = $true )
& ( nonemptyI = $true )
& ( subset2powerset = $true )
& ( binintersectSubset5 = $true )
& ( subsetemptysetimpeq = $true )
& ( dsetconstrEL = $true )
& ( setoftrueEq = $true )
& ( powerset__Cong = $true )
& ( singletonsswitch = $true )
& ( notsubsetI = $true )
& ( emptyI = $true )
& ( setadjoinIL = $true )
& ( sepSubset = $true )
& ( inPowerset = $true )
& ( emptysetAx = $true )
& ( subsetI2 = $true )
& ( prop2setE = $true )
& ( setunionI = $true )
& ( binintersectSubset2 = $true )
& ( setextAx = $true )
& ( binunionIL = $true )
& ( setextsub = $true )
& ( setminusILneg = $true )
& ( binunionEcases = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( notinemptyset = $true )
& ( powersetsubset = $true )
& ( exuI1 = $true )
& ( symdiffI1 = $true )
& ( nonemptyI1 = $true )
& ( setadjoinAx = $true )
& ( foundationAx = $true )
& ( setunionAx = $true )
& ( eqimpsubset1 = $true )
& ( wellorderingAx = $true )
& ( emptysetE = $true )
& ( binintersectER = $true )
& ( powersetI = $true )
& ( omega0Ax = $true )
& ( upairsetIL = $true )
& ( omega__Cong = $true )
& ( emptysetimpfalse = $true )
& ( setadjoinOr = $true )
& ( eqinunit = $true )
& ( quantDeMorgan2 = $true )
& ( exuI2 = $true )
& ( setminusEL = $true )
& ( inCongP = $true )
& ( dsetconstrER = $true )
& ( powersetI1 = $true )
& ( exu__Cong = $true )
& ( notinsingleton = $true )
& ( dsetconstrI = $true )
& ( setbeta = $true )
& ( setadjoin__Cong = $true )
& ( binintersectSubset3 = $true )
& ( prop2set2propI = $true )
& ( exuE3e = $true )
& ( descrp = $true )
& ( setunion__Cong = $true )
& ( setadjoinE = $true )
& ( symdiffE = $true )
& ( setadjoinSub2 = $true )
& ( exuEu = $true )
& ( noeltsimpempty = $true )
& ( notdallE = $true )
& ( emptyE1 = $true )
& ( omegaIndAx = $true )
& ( quantDeMorgan3 = $true )
& ( upairsetIR = $true )
& ( upairset2IR = $true )
& ( setminusSubset1 = $true )
& ( nonemptyImpWitness = $true )
& ( subsetI1 = $true )
& ( upairsetE = $true )
& ( subsetTrans = $true )
& ( omegaSAx = $true )
& ( setminusER = $true )
& ( setadjoinSub = $true )
& ( subsetE = $true )
& ( descr__Cong = $true )
& ( binunionIR = $true )
& ( emptyInPowerset = $true )
& ( eqimpsubset2 = $true )
& ( setminusI = $true )
& ( binintersectEL = $true )
& ( powersetAx = $true )
& ( notdexE = $true )
& ( setunionE = $true )
& ( vacuousDall = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f398,f399]) ).
thf(f399,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ ( symdiff @ X1 @ X2 ) ) )
& ( $true
= ( in @ X0 @ X2 ) )
& ( ( in @ X0 @ X1 )
!= $true ) )
=> ( ( ( in @ sK0 @ ( symdiff @ sK1 @ sK2 ) )
!= $true )
& ( ( in @ sK0 @ sK2 )
= $true )
& ( ( in @ sK0 @ sK1 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f398,plain,
( ( binintersectSubset1 = $true )
& ( emptyinPowerset = $true )
& ( setminusIRneg = $true )
& ( powersetE = $true )
& ( setext = $true )
& ( disjointsetsI1 = $true )
& ( sepInPowerset = $true )
& ( bs114d = $true )
& ( binintersectRsub = $true )
& ( setminusLsub = $true )
& ( setminusSubset2 = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ ( symdiff @ X1 @ X2 ) ) )
& ( $true
= ( in @ X0 @ X2 ) )
& ( ( in @ X0 @ X1 )
!= $true ) )
& ( binintersectLsub = $true )
& ( setadjoinIR = $true )
& ( subPowSU = $true )
& ( replAx = $true )
& ( emptyset__Cong = $true )
& ( emptysetsubset = $true )
& ( uniqinunit = $true )
& ( dsetconstr__Cong = $true )
& ( binunionLsub = $true )
& ( setminusERneg = $true )
& ( quantDeMorgan1 = $true )
& ( subsetE2 = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( exuE1 = $true )
& ( powersetE1 = $true )
& ( emptyinunitempty = $true )
& ( notequalI1 = $true )
& ( notequalI2 = $true )
& ( nonemptyE1 = $true )
& ( binunionE = $true )
& ( exuE2 = $true )
& ( setminusELneg = $true )
& ( in__Cong = $true )
& ( exuI3 = $true )
& ( subsetRefl = $true )
& ( binintersectSubset4 = $true )
& ( exuE3u = $true )
& ( nonemptyI = $true )
& ( subset2powerset = $true )
& ( binintersectSubset5 = $true )
& ( subsetemptysetimpeq = $true )
& ( dsetconstrEL = $true )
& ( setoftrueEq = $true )
& ( powerset__Cong = $true )
& ( singletonsswitch = $true )
& ( notsubsetI = $true )
& ( emptyI = $true )
& ( setadjoinIL = $true )
& ( sepSubset = $true )
& ( inPowerset = $true )
& ( emptysetAx = $true )
& ( subsetI2 = $true )
& ( prop2setE = $true )
& ( setunionI = $true )
& ( binintersectSubset2 = $true )
& ( setextAx = $true )
& ( binunionIL = $true )
& ( setextsub = $true )
& ( setminusILneg = $true )
& ( binunionEcases = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( notinemptyset = $true )
& ( powersetsubset = $true )
& ( exuI1 = $true )
& ( symdiffI1 = $true )
& ( nonemptyI1 = $true )
& ( setadjoinAx = $true )
& ( foundationAx = $true )
& ( setunionAx = $true )
& ( eqimpsubset1 = $true )
& ( wellorderingAx = $true )
& ( emptysetE = $true )
& ( binintersectER = $true )
& ( powersetI = $true )
& ( omega0Ax = $true )
& ( upairsetIL = $true )
& ( omega__Cong = $true )
& ( emptysetimpfalse = $true )
& ( setadjoinOr = $true )
& ( eqinunit = $true )
& ( quantDeMorgan2 = $true )
& ( exuI2 = $true )
& ( setminusEL = $true )
& ( inCongP = $true )
& ( dsetconstrER = $true )
& ( powersetI1 = $true )
& ( exu__Cong = $true )
& ( notinsingleton = $true )
& ( dsetconstrI = $true )
& ( setbeta = $true )
& ( setadjoin__Cong = $true )
& ( binintersectSubset3 = $true )
& ( prop2set2propI = $true )
& ( exuE3e = $true )
& ( descrp = $true )
& ( setunion__Cong = $true )
& ( setadjoinE = $true )
& ( symdiffE = $true )
& ( setadjoinSub2 = $true )
& ( exuEu = $true )
& ( noeltsimpempty = $true )
& ( notdallE = $true )
& ( emptyE1 = $true )
& ( omegaIndAx = $true )
& ( quantDeMorgan3 = $true )
& ( upairsetIR = $true )
& ( upairset2IR = $true )
& ( setminusSubset1 = $true )
& ( nonemptyImpWitness = $true )
& ( subsetI1 = $true )
& ( upairsetE = $true )
& ( subsetTrans = $true )
& ( omegaSAx = $true )
& ( setminusER = $true )
& ( setadjoinSub = $true )
& ( subsetE = $true )
& ( descr__Cong = $true )
& ( binunionIR = $true )
& ( emptyInPowerset = $true )
& ( eqimpsubset2 = $true )
& ( setminusI = $true )
& ( binintersectEL = $true )
& ( powersetAx = $true )
& ( notdexE = $true )
& ( setunionE = $true )
& ( vacuousDall = $true ) ),
inference(flattening,[status(thm)],[f397]) ).
thf(f397,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ ( symdiff @ X1 @ X2 ) ) )
& ( $true
= ( in @ X0 @ X2 ) )
& ( ( in @ X0 @ X1 )
!= $true ) )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f396]) ).
thf(f396,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
=> ( ( $true
= ( in @ X0 @ X2 ) )
=> ( $true
= ( in @ X0 @ ( symdiff @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f341]) ).
thf(f341,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
!= $true )
=> ( ( $true
= ( in @ X0 @ X2 ) )
=> ( $true
= ( in @ X0 @ ( symdiff @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f340]) ).
thf(f340,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X0 @ X1 )
=> ( ( in @ X0 @ X2 )
=> ( in @ X0 @ ( symdiff @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f134]) ).
thf(f134,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ! [X1: $i,X3: $i,X4: $i] :
( ~ ( in @ X1 @ X3 )
=> ( ( in @ X1 @ X4 )
=> ( in @ X1 @ ( symdiff @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f133]) ).
thf(f133,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ! [X1: $i,X3: $i,X4: $i] :
( ~ ( in @ X1 @ X3 )
=> ( ( in @ X1 @ X4 )
=> ( in @ X1 @ ( symdiff @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.7X3sL6M5Q7/DTF2THF_23484.p',symdiffI2) ).
thf(f600,plain,
( binunionIR
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ ( binunion @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f215]) ).
thf(f215,plain,
( binunionIR
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ ( binunion @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f214]) ).
thf(f214,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X0 )
=> ( in @ X1 @ ( binunion @ X2 @ X0 ) ) )
= binunionIR ),
inference(rectify,[status(thm)],[f103]) ).
thf(f103,axiom,
! [X4: $i,X1: $i,X3: $i] :
( ( ( in @ X1 @ X4 )
=> ( in @ X1 @ ( binunion @ X3 @ X4 ) ) )
= binunionIR ),
file('/export/starexec/sandbox/tmp/tmp.7X3sL6M5Q7/DTF2THF_23484.p',binunionIR) ).
thf(f2507,plain,
( ( $false
= ( in @ sK0 @ ( binunion @ sK1 @ sK2 ) ) )
| ~ spl3_22 ),
inference(avatar_component_clause,[status(thm)],[f2505]) ).
thf(f2508,plain,
( spl3_22
| spl3_12
| spl3_16 ),
inference(avatar_split_clause,[status(thm)],[f2503,f2393,f2374,f2505]) ).
thf(f2374,definition,
( spl3_12
<=> ( ( in @ sK0 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_12])],[avatar_definition]) ).
thf(f2393,definition,
( spl3_16
<=> ( $true
= ( in @ sK0
@ ( dsetconstr @ ( binunion @ sK1 @ sK2 )
@ ^ [Y0: $i] :
( ~ ( in @ Y0 @ sK2 )
| ~ ( in @ Y0 @ sK1 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_16])],[avatar_definition]) ).
thf(f2503,plain,
( ( $false
= ( in @ sK0 @ ( binunion @ sK1 @ sK2 ) ) )
| spl3_12
| spl3_16 ),
inference(subsumption_resolution,[status(thm)],[f2502,f2376]) ).
thf(f2376,plain,
( ( ( in @ sK0 @ sK1 )
!= $true )
| spl3_12 ),
inference(avatar_component_clause,[status(thm)],[f2374]) ).
thf(f2502,plain,
( ( ( in @ sK0 @ sK1 )
= $true )
| ( $false
= ( in @ sK0 @ ( binunion @ sK1 @ sK2 ) ) )
| spl3_16 ),
inference(not_proxy_clausification,[status(thm)],[f2499]) ).
thf(f2499,plain,
( ( $false
= ( ~ ( in @ sK0 @ sK1 ) ) )
| ( $false
= ( in @ sK0 @ ( binunion @ sK1 @ sK2 ) ) )
| spl3_16 ),
inference(binary_proxy_clausification,[status(thm)],[f2498]) ).
thf(f2498,plain,
( ( $false
= ( in @ sK0 @ ( binunion @ sK1 @ sK2 ) ) )
| ( $false
= ( ~ ( in @ sK0 @ sK2 )
| ~ ( in @ sK0 @ sK1 ) ) )
| spl3_16 ),
inference(beta_eta_normalization,[status(thm)],[f2497]) ).
thf(f2497,plain,
( ( $false
= ( in @ sK0 @ ( binunion @ sK1 @ sK2 ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( in @ Y0 @ sK2 )
| ~ ( in @ Y0 @ sK1 ) )
@ sK0 )
= $false )
| spl3_16 ),
inference(trivial_inequality_removal,[status(thm)],[f2496]) ).
thf(f2496,plain,
( ( ( ^ [Y0: $i] :
( ~ ( in @ Y0 @ sK2 )
| ~ ( in @ Y0 @ sK1 ) )
@ sK0 )
= $false )
| ( $true != $true )
| ( $false
= ( in @ sK0 @ ( binunion @ sK1 @ sK2 ) ) )
| spl3_16 ),
inference(superposition,[status(thm)],[f2395,f1194]) ).
thf(f1194,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( $true
= ( in @ X2 @ ( dsetconstr @ X3 @ X1 ) ) )
| ( ( in @ X2 @ X3 )
= $false )
| ( ( X1 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1193]) ).
thf(f1193,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ( in @ X2 @ X3 )
= $false )
| ( $true
= ( ( X1 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X3 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1192]) ).
thf(f1192,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( $true
= ( ( in @ X2 @ X3 )
=> ( ( X1 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ X3 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1191]) ).
thf(f1191,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ^ [Y0: $i] :
( ( in @ X2 @ Y0 )
=> ( ( X1 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ Y0 @ X1 ) ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f1190]) ).
thf(f1190,plain,
! [X2: $i,X1: $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ Y0 )
=> ( ( X1 @ X2 )
=> ( in @ X2 @ ( dsetconstr @ Y0 @ X1 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1189]) ).
thf(f1189,plain,
! [X2: $i,X1: $i > $o] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ Y1 )
=> ( ( X1 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ Y1 @ X1 ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f1188]) ).
thf(f1188,plain,
! [X1: $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ Y1 )
=> ( ( X1 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ Y1 @ X1 ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1187]) ).
thf(f1187,plain,
! [X1: $i > $o] :
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y2 @ Y0 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f1186]) ).
thf(f1186,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ Y2 @ Y0 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f703]) ).
thf(f703,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( in @ Y1
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f484,f407]) ).
thf(f407,plain,
( dsetconstrI
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( in @ Y1
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f361]) ).
thf(f361,plain,
( dsetconstrI
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( ( Y0 @ Y1 )
=> ( in @ Y1
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f360]) ).
thf(f360,plain,
! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X1 @ X0 )
=> ( ( X2 @ X1 )
=> ( in @ X1
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) )
= dsetconstrI ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,axiom,
! [X3: $i,X1: $i,X0: $i > $o] :
( ( ( in @ X1 @ X3 )
=> ( ( X0 @ X1 )
=> ( in @ X1
@ ( dsetconstr @ X3
@ ^ [X2: $i] : ( X0 @ X2 ) ) ) ) )
= dsetconstrI ),
file('/export/starexec/sandbox/tmp/tmp.7X3sL6M5Q7/DTF2THF_23484.p',dsetconstrI) ).
thf(f484,plain,
dsetconstrI = $true,
inference(cnf_transformation,[status(thm)],[f400]) ).
thf(f2395,plain,
( ( $true
!= ( in @ sK0
@ ( dsetconstr @ ( binunion @ sK1 @ sK2 )
@ ^ [Y0: $i] :
( ~ ( in @ Y0 @ sK2 )
| ~ ( in @ Y0 @ sK1 ) ) ) ) )
| spl3_16 ),
inference(avatar_component_clause,[status(thm)],[f2393]) ).
thf(f2407,plain,
~ spl3_18,
inference(avatar_split_clause,[status(thm)],[f135,f2404]) ).
thf(f2404,definition,
( spl3_18
<=> ( $true = $false ) ),
introduced(definition,[new_symbols(naming,[spl3_18])],[avatar_definition]) ).
thf(f135,plain,
$true != $false,
introduced(definition,[],[fool_axiom]) ).
thf(f2401,plain,
spl3_17,
inference(avatar_split_clause,[status(thm)],[f566,f2398]) ).
thf(f2398,definition,
( spl3_17
<=> ( ( in @ sK0 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_17])],[avatar_definition]) ).
thf(f566,plain,
( ( in @ sK0 @ sK2 )
= $true ),
inference(cnf_transformation,[status(thm)],[f400]) ).
thf(f2396,plain,
~ spl3_16,
inference(avatar_split_clause,[status(thm)],[f1308,f2393]) ).
thf(f1308,plain,
( $true
!= ( in @ sK0
@ ( dsetconstr @ ( binunion @ sK1 @ sK2 )
@ ^ [Y0: $i] :
( ~ ( in @ Y0 @ sK2 )
| ~ ( in @ Y0 @ sK1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f675]) ).
thf(f675,plain,
( ( in @ sK0
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( binunion @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y1 )
| ~ ( in @ Y2 @ Y0 ) ) )
@ sK1
@ sK2 ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f567,f439]) ).
thf(f439,plain,
( symdiff
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( binunion @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y1 )
| ~ ( in @ Y2 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f321]) ).
thf(f321,plain,
( symdiff
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( binunion @ Y0 @ Y1 )
@ ^ [Y2: $i] :
( ~ ( in @ Y2 @ Y1 )
| ~ ( in @ Y2 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f320]) ).
thf(f320,plain,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( binunion @ X0 @ X1 )
@ ^ [X2: $i] :
( ~ ( in @ X2 @ X0 )
| ~ ( in @ X2 @ X1 ) ) ) )
= symdiff ),
inference(rectify,[status(thm)],[f130]) ).
thf(f130,axiom,
( ( ^ [X3: $i,X4: $i] :
( dsetconstr @ ( binunion @ X3 @ X4 )
@ ^ [X1: $i] :
( ~ ( in @ X1 @ X3 )
| ~ ( in @ X1 @ X4 ) ) ) )
= symdiff ),
file('/export/starexec/sandbox/tmp/tmp.7X3sL6M5Q7/DTF2THF_23484.p',symdiff) ).
thf(f567,plain,
( ( in @ sK0 @ ( symdiff @ sK1 @ sK2 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f400]) ).
thf(f2377,plain,
~ spl3_12,
inference(avatar_split_clause,[status(thm)],[f565,f2374]) ).
thf(f565,plain,
( ( in @ sK0 @ sK1 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f400]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU613^1 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n001.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:29:35 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.44 ---- Original DTF file ---
% 0.28/0.44 thf(spec,logic,$$dhol).
% 0.28/0.44 %------------------------------------------------------------------------------
% 0.28/0.44 % File : SEU613^1 : TPTP v9.2.1. Released v3.7.0.
% 0.28/0.44 % Domain : Set Theory
% 0.28/0.44 % Problem : Preliminary Notions - Operations on Sets - Symmetric Difference
% 0.28/0.44 % Version : Especial.
% 0.28/0.44 % English : (! A:i.! B:i.! x:i.~(in x A) -> in x B -> in x (symdiff A B))
% 0.28/0.44
% 0.28/0.44 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.28/0.44 % Source : [Bro08]
% 0.28/0.44 % Names : ZFC115g [Bro08]
% 0.28/0.44
% 0.28/0.44 % Status : Theorem
% 0.28/0.44 % Rating : 0.33 v9.1.0, 0.50 v9.0.0, 0.40 v8.2.0, 0.62 v8.1.0, 0.64 v7.5.0, 0.57 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.86 v5.5.0, 0.83 v5.4.0, 0.60 v5.2.0, 0.80 v5.0.0, 0.60 v4.1.0, 1.00 v3.7.0
% 0.28/0.44 % Syntax : Number of formulae : 282 ( 132 unt; 149 typ; 132 def)
% 0.28/0.44 % Number of atoms : 704 ( 189 equ; 0 cnn)
% 0.28/0.44 % Maximal formula atoms : 132 ( 5 avg)
% 0.28/0.44 % Number of connectives : 1136 ( 45 ~; 7 |; 28 &; 727 @)
% 0.28/0.44 % ( 14 <=>; 315 =>; 0 <=; 0 <~>)
% 0.28/0.44 % Maximal formula depth : 138 ( 2 avg)
% 0.28/0.44 % Number of types : 2 ( 0 usr)
% 0.28/0.44 % Number of type conns : 64 ( 64 >; 0 *; 0 +; 0 <<)
% 0.28/0.44 % Number of symbols : 152 ( 149 usr; 133 con; 0-2 aty)
% 0.28/0.44 % Number of variables : 383 ( 33 ^; 321 !; 29 ?; 383 :)
% 0.28/0.44 % SPC : TH0_THM_EQU_NAR
% 0.28/0.44
% 0.28/0.44 % Comments : http://mathgate.info/detsetitem.php?id=491
% 0.28/0.44 %------------------------------------------------------------------------------
% 0.28/0.44 thf(in_type,type,
% 0.28/0.44 in: $i > $i > $o ).
% 0.28/0.44
% 0.28/0.44 thf(exu_type,type,
% 0.28/0.44 exu: ( $i > $o ) > $o ).
% 0.28/0.44
% 0.28/0.44 thf(exu,definition,
% 0.28/0.44 ( exu
% 0.28/0.44 = ( ^ [Xphi: $i > $o] :
% 0.28/0.44 ? [Xx: $i] :
% 0.28/0.44 ( ( Xphi @ Xx )
% 0.28/0.44 & ! [Xy: $i] :
% 0.28/0.44 ( ( Xphi @ Xy )
% 0.28/0.44 => ( Xx = Xy ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(setextAx_type,type,
% 0.28/0.44 setextAx: $o ).
% 0.28/0.44
% 0.28/0.44 thf(setextAx,definition,
% 0.28/0.44 ( setextAx
% 0.28/0.44 = ( ! [A: $i,B: $i] :
% 0.28/0.44 ( ! [Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ A )
% 0.28/0.44 <=> ( in @ Xx @ B ) )
% 0.28/0.44 => ( A = B ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(emptyset_type,type,
% 0.28/0.44 emptyset: $i ).
% 0.28/0.44
% 0.28/0.44 thf(emptysetAx_type,type,
% 0.28/0.44 emptysetAx: $o ).
% 0.28/0.44
% 0.28/0.44 thf(emptysetAx,definition,
% 0.28/0.44 ( emptysetAx
% 0.28/0.44 = ( ! [Xx: $i] :
% 0.28/0.44 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(setadjoin_type,type,
% 0.28/0.44 setadjoin: $i > $i > $i ).
% 0.28/0.44
% 0.28/0.44 thf(setadjoinAx_type,type,
% 0.28/0.44 setadjoinAx: $o ).
% 0.28/0.44
% 0.28/0.44 thf(setadjoinAx,definition,
% 0.28/0.44 ( setadjoinAx
% 0.28/0.44 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.44 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.44 <=> ( ( Xy = Xx )
% 0.28/0.44 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(powerset_type,type,
% 0.28/0.44 powerset: $i > $i ).
% 0.28/0.44
% 0.28/0.44 thf(powersetAx_type,type,
% 0.28/0.44 powersetAx: $o ).
% 0.28/0.44
% 0.28/0.44 thf(powersetAx,definition,
% 0.28/0.44 ( powersetAx
% 0.28/0.44 = ( ! [A: $i,B: $i] :
% 0.28/0.44 ( ( in @ B @ ( powerset @ A ) )
% 0.28/0.44 <=> ! [Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ B )
% 0.28/0.44 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(setunion_type,type,
% 0.28/0.44 setunion: $i > $i ).
% 0.28/0.44
% 0.28/0.44 thf(setunionAx_type,type,
% 0.28/0.44 setunionAx: $o ).
% 0.28/0.44
% 0.28/0.44 thf(setunionAx,definition,
% 0.28/0.44 ( setunionAx
% 0.28/0.44 = ( ! [A: $i,Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ ( setunion @ A ) )
% 0.28/0.44 <=> ? [B: $i] :
% 0.28/0.44 ( ( in @ Xx @ B )
% 0.28/0.44 & ( in @ B @ A ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(omega_type,type,
% 0.28/0.44 omega: $i ).
% 0.28/0.44
% 0.28/0.44 thf(omega0Ax_type,type,
% 0.28/0.44 omega0Ax: $o ).
% 0.28/0.44
% 0.28/0.44 thf(omega0Ax,definition,
% 0.28/0.44 ( omega0Ax
% 0.28/0.44 = ( in @ emptyset @ omega ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(omegaSAx_type,type,
% 0.28/0.44 omegaSAx: $o ).
% 0.28/0.44
% 0.28/0.44 thf(omegaSAx,definition,
% 0.28/0.44 ( omegaSAx
% 0.28/0.44 = ( ! [Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ omega )
% 0.28/0.44 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(omegaIndAx_type,type,
% 0.28/0.44 omegaIndAx: $o ).
% 0.28/0.44
% 0.28/0.44 thf(omegaIndAx,definition,
% 0.28/0.44 ( omegaIndAx
% 0.28/0.44 = ( ! [A: $i] :
% 0.28/0.44 ( ( ( in @ emptyset @ A )
% 0.28/0.44 & ! [Xx: $i] :
% 0.28/0.44 ( ( ( in @ Xx @ omega )
% 0.28/0.44 & ( in @ Xx @ A ) )
% 0.28/0.44 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.28/0.44 => ! [Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ omega )
% 0.28/0.44 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(replAx_type,type,
% 0.28/0.44 replAx: $o ).
% 0.28/0.44
% 0.28/0.44 thf(replAx,definition,
% 0.28/0.44 ( replAx
% 0.28/0.44 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.28/0.44 ( ! [Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ A )
% 0.28/0.44 => ( exu
% 0.28/0.44 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.28/0.44 => ? [B: $i] :
% 0.28/0.44 ! [Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ B )
% 0.28/0.44 <=> ? [Xy: $i] :
% 0.28/0.44 ( ( in @ Xy @ A )
% 0.28/0.44 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(foundationAx_type,type,
% 0.28/0.44 foundationAx: $o ).
% 0.28/0.44
% 0.28/0.44 thf(foundationAx,definition,
% 0.28/0.44 ( foundationAx
% 0.28/0.44 = ( ! [A: $i] :
% 0.28/0.44 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.28/0.44 => ? [B: $i] :
% 0.28/0.44 ( ( in @ B @ A )
% 0.28/0.44 & ~ ? [Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ B )
% 0.28/0.44 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(wellorderingAx_type,type,
% 0.28/0.44 wellorderingAx: $o ).
% 0.28/0.44
% 0.28/0.44 thf(wellorderingAx,definition,
% 0.28/0.44 ( wellorderingAx
% 0.28/0.44 = ( ! [A: $i] :
% 0.28/0.44 ? [B: $i] :
% 0.28/0.44 ( ! [C: $i] :
% 0.28/0.44 ( ( in @ C @ B )
% 0.28/0.44 => ! [Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ C )
% 0.28/0.44 => ( in @ Xx @ A ) ) )
% 0.28/0.44 & ! [Xx: $i,Xy: $i] :
% 0.28/0.44 ( ( ( in @ Xx @ A )
% 0.28/0.44 & ( in @ Xy @ A ) )
% 0.28/0.44 => ( ! [C: $i] :
% 0.28/0.44 ( ( in @ C @ B )
% 0.28/0.44 => ( ( in @ Xx @ C )
% 0.28/0.44 <=> ( in @ Xy @ C ) ) )
% 0.28/0.44 => ( Xx = Xy ) ) )
% 0.28/0.44 & ! [C: $i,D: $i] :
% 0.28/0.44 ( ( ( in @ C @ B )
% 0.28/0.44 & ( in @ D @ B ) )
% 0.28/0.44 => ( ! [Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ C )
% 0.28/0.44 => ( in @ Xx @ D ) )
% 0.28/0.44 | ! [Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ D )
% 0.28/0.44 => ( in @ Xx @ C ) ) ) )
% 0.28/0.44 & ! [C: $i] :
% 0.28/0.44 ( ( ! [Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ C )
% 0.28/0.44 => ( in @ Xx @ A ) )
% 0.28/0.44 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.28/0.44 => ? [D: $i,Xx: $i] :
% 0.28/0.44 ( ( in @ D @ B )
% 0.28/0.44 & ( in @ Xx @ C )
% 0.28/0.44 & ~ ? [Xy: $i] :
% 0.28/0.44 ( ( in @ Xy @ D )
% 0.28/0.44 & ( in @ Xy @ C ) )
% 0.28/0.44 & ! [E: $i] :
% 0.28/0.44 ( ( in @ E @ B )
% 0.28/0.44 => ( ! [Xy: $i] :
% 0.28/0.44 ( ( in @ Xy @ E )
% 0.28/0.44 => ( in @ Xy @ D ) )
% 0.28/0.44 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(descr_type,type,
% 0.28/0.44 descr: ( $i > $o ) > $i ).
% 0.28/0.44
% 0.28/0.44 thf(descrp_type,type,
% 0.28/0.44 descrp: $o ).
% 0.28/0.44
% 0.28/0.44 thf(descrp,definition,
% 0.28/0.44 ( descrp
% 0.28/0.44 = ( ! [Xphi: $i > $o] :
% 0.28/0.44 ( ( exu
% 0.28/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.44 => ( Xphi
% 0.28/0.44 @ ( descr
% 0.28/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(dsetconstr_type,type,
% 0.28/0.44 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.28/0.44
% 0.28/0.44 thf(dsetconstrI_type,type,
% 0.28/0.44 dsetconstrI: $o ).
% 0.28/0.44
% 0.28/0.44 thf(dsetconstrI,definition,
% 0.28/0.44 ( dsetconstrI
% 0.28/0.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ A )
% 0.28/0.44 => ( ( Xphi @ Xx )
% 0.28/0.44 => ( in @ Xx
% 0.28/0.44 @ ( dsetconstr @ A
% 0.28/0.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(dsetconstrEL_type,type,
% 0.28/0.44 dsetconstrEL: $o ).
% 0.28/0.44
% 0.28/0.44 thf(dsetconstrEL,definition,
% 0.28/0.44 ( dsetconstrEL
% 0.28/0.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.44 ( ( in @ Xx
% 0.28/0.44 @ ( dsetconstr @ A
% 0.28/0.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.44 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(dsetconstrER_type,type,
% 0.28/0.44 dsetconstrER: $o ).
% 0.28/0.44
% 0.28/0.44 thf(dsetconstrER,definition,
% 0.28/0.44 ( dsetconstrER
% 0.28/0.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.44 ( ( in @ Xx
% 0.28/0.44 @ ( dsetconstr @ A
% 0.28/0.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.44 => ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(exuE1_type,type,
% 0.28/0.44 exuE1: $o ).
% 0.28/0.44
% 0.28/0.44 thf(exuE1,definition,
% 0.28/0.44 ( exuE1
% 0.28/0.44 = ( ! [Xphi: $i > $o] :
% 0.28/0.44 ( ( exu
% 0.28/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.44 => ? [Xx: $i] :
% 0.28/0.44 ( ( Xphi @ Xx )
% 0.28/0.44 & ! [Xy: $i] :
% 0.28/0.44 ( ( Xphi @ Xy )
% 0.28/0.44 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(prop2set_type,type,
% 0.28/0.44 prop2set: $o > $i ).
% 0.28/0.44
% 0.28/0.44 thf(prop2setE_type,type,
% 0.28/0.44 prop2setE: $o ).
% 0.28/0.44
% 0.28/0.44 thf(prop2setE,definition,
% 0.28/0.44 ( prop2setE
% 0.28/0.44 = ( ! [Xphi: $o,Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.28/0.44 => Xphi ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(emptysetE_type,type,
% 0.28/0.44 emptysetE: $o ).
% 0.28/0.44
% 0.28/0.44 thf(emptysetE,definition,
% 0.28/0.44 ( emptysetE
% 0.28/0.44 = ( ! [Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ emptyset )
% 0.28/0.44 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(emptysetimpfalse_type,type,
% 0.28/0.44 emptysetimpfalse: $o ).
% 0.28/0.44
% 0.28/0.44 thf(emptysetimpfalse,definition,
% 0.28/0.44 ( emptysetimpfalse
% 0.28/0.44 = ( ! [Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ emptyset )
% 0.28/0.44 => $false ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(notinemptyset_type,type,
% 0.28/0.44 notinemptyset: $o ).
% 0.28/0.44
% 0.28/0.44 thf(notinemptyset,definition,
% 0.28/0.44 ( notinemptyset
% 0.28/0.44 = ( ! [Xx: $i] :
% 0.28/0.44 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(exuE3e_type,type,
% 0.28/0.44 exuE3e: $o ).
% 0.28/0.44
% 0.28/0.44 thf(exuE3e,definition,
% 0.28/0.44 ( exuE3e
% 0.28/0.44 = ( ! [Xphi: $i > $o] :
% 0.28/0.44 ( ( exu
% 0.28/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.44 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(setext_type,type,
% 0.28/0.44 setext: $o ).
% 0.28/0.44
% 0.28/0.44 thf(setext,definition,
% 0.28/0.44 ( setext
% 0.28/0.44 = ( ! [A: $i,B: $i] :
% 0.28/0.44 ( ! [Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ A )
% 0.28/0.44 => ( in @ Xx @ B ) )
% 0.28/0.44 => ( ! [Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ B )
% 0.28/0.44 => ( in @ Xx @ A ) )
% 0.28/0.44 => ( A = B ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(emptyI_type,type,
% 0.28/0.44 emptyI: $o ).
% 0.28/0.44
% 0.28/0.44 thf(emptyI,definition,
% 0.28/0.44 ( emptyI
% 0.28/0.44 = ( ! [A: $i] :
% 0.28/0.44 ( ! [Xx: $i] :
% 0.28/0.44 ~ ( in @ Xx @ A )
% 0.28/0.44 => ( A = emptyset ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(noeltsimpempty_type,type,
% 0.28/0.44 noeltsimpempty: $o ).
% 0.28/0.44
% 0.28/0.44 thf(noeltsimpempty,definition,
% 0.28/0.44 ( noeltsimpempty
% 0.28/0.44 = ( ! [A: $i] :
% 0.28/0.44 ( ! [Xx: $i] :
% 0.28/0.44 ~ ( in @ Xx @ A )
% 0.28/0.44 => ( A = emptyset ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(setbeta_type,type,
% 0.28/0.44 setbeta: $o ).
% 0.28/0.44
% 0.28/0.44 thf(setbeta,definition,
% 0.28/0.44 ( setbeta
% 0.28/0.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ A )
% 0.28/0.44 => ( ( in @ Xx
% 0.28/0.44 @ ( dsetconstr @ A
% 0.28/0.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.44 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(nonempty_type,type,
% 0.28/0.44 nonempty: $i > $o ).
% 0.28/0.44
% 0.28/0.44 thf(nonempty,definition,
% 0.28/0.44 ( nonempty
% 0.28/0.44 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(nonemptyE1_type,type,
% 0.28/0.44 nonemptyE1: $o ).
% 0.28/0.44
% 0.28/0.44 thf(nonemptyE1,definition,
% 0.28/0.44 ( nonemptyE1
% 0.28/0.44 = ( ! [A: $i] :
% 0.28/0.44 ( ( nonempty @ A )
% 0.28/0.44 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(nonemptyI_type,type,
% 0.28/0.44 nonemptyI: $o ).
% 0.28/0.44
% 0.28/0.44 thf(nonemptyI,definition,
% 0.28/0.44 ( nonemptyI
% 0.28/0.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ A )
% 0.28/0.44 => ( ( Xphi @ Xx )
% 0.28/0.44 => ( nonempty
% 0.28/0.44 @ ( dsetconstr @ A
% 0.28/0.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(nonemptyI1_type,type,
% 0.28/0.44 nonemptyI1: $o ).
% 0.28/0.44
% 0.28/0.44 thf(nonemptyI1,definition,
% 0.28/0.44 ( nonemptyI1
% 0.28/0.44 = ( ! [A: $i] :
% 0.28/0.44 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.28/0.44 => ( nonempty @ A ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(setadjoinIL_type,type,
% 0.28/0.44 setadjoinIL: $o ).
% 0.28/0.44
% 0.28/0.44 thf(setadjoinIL,definition,
% 0.28/0.44 ( setadjoinIL
% 0.28/0.44 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(emptyinunitempty_type,type,
% 0.28/0.44 emptyinunitempty: $o ).
% 0.28/0.44
% 0.28/0.44 thf(emptyinunitempty,definition,
% 0.28/0.44 ( emptyinunitempty
% 0.28/0.44 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(setadjoinIR_type,type,
% 0.28/0.44 setadjoinIR: $o ).
% 0.28/0.44
% 0.28/0.44 thf(setadjoinIR,definition,
% 0.28/0.44 ( setadjoinIR
% 0.28/0.44 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.44 ( ( in @ Xy @ A )
% 0.28/0.44 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(setadjoinE_type,type,
% 0.28/0.44 setadjoinE: $o ).
% 0.28/0.44
% 0.28/0.44 thf(setadjoinE,definition,
% 0.28/0.44 ( setadjoinE
% 0.28/0.44 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.44 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.44 => ! [Xphi: $o] :
% 0.28/0.44 ( ( ( Xy = Xx )
% 0.28/0.44 => Xphi )
% 0.28/0.44 => ( ( ( in @ Xy @ A )
% 0.28/0.44 => Xphi )
% 0.28/0.44 => Xphi ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(setadjoinOr_type,type,
% 0.28/0.44 setadjoinOr: $o ).
% 0.28/0.44
% 0.28/0.44 thf(setadjoinOr,definition,
% 0.28/0.44 ( setadjoinOr
% 0.28/0.44 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.44 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.44 => ( ( Xy = Xx )
% 0.28/0.44 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(setoftrueEq_type,type,
% 0.28/0.44 setoftrueEq: $o ).
% 0.28/0.44
% 0.28/0.44 thf(setoftrueEq,definition,
% 0.28/0.44 ( setoftrueEq
% 0.28/0.44 = ( ! [A: $i] :
% 0.28/0.44 ( ( dsetconstr @ A
% 0.28/0.44 @ ^ [Xx: $i] : $true )
% 0.28/0.44 = A ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(powersetI_type,type,
% 0.28/0.44 powersetI: $o ).
% 0.28/0.44
% 0.28/0.44 thf(powersetI,definition,
% 0.28/0.44 ( powersetI
% 0.28/0.44 = ( ! [A: $i,B: $i] :
% 0.28/0.44 ( ! [Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ B )
% 0.28/0.44 => ( in @ Xx @ A ) )
% 0.28/0.44 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(emptyinPowerset_type,type,
% 0.28/0.44 emptyinPowerset: $o ).
% 0.28/0.44
% 0.28/0.44 thf(emptyinPowerset,definition,
% 0.28/0.44 ( emptyinPowerset
% 0.28/0.44 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(emptyInPowerset_type,type,
% 0.28/0.44 emptyInPowerset: $o ).
% 0.28/0.44
% 0.28/0.44 thf(emptyInPowerset,definition,
% 0.28/0.44 ( emptyInPowerset
% 0.28/0.44 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(powersetE_type,type,
% 0.28/0.44 powersetE: $o ).
% 0.28/0.44
% 0.28/0.44 thf(powersetE,definition,
% 0.28/0.44 ( powersetE
% 0.28/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.44 ( ( in @ B @ ( powerset @ A ) )
% 0.28/0.44 => ( ( in @ Xx @ B )
% 0.28/0.44 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(setunionI_type,type,
% 0.28/0.44 setunionI: $o ).
% 0.28/0.44
% 0.28/0.44 thf(setunionI,definition,
% 0.28/0.44 ( setunionI
% 0.28/0.44 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.28/0.44 ( ( in @ Xx @ B )
% 0.28/0.44 => ( ( in @ B @ A )
% 0.28/0.44 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(setunionE_type,type,
% 0.28/0.44 setunionE: $o ).
% 0.28/0.44
% 0.28/0.44 thf(setunionE,definition,
% 0.28/0.44 ( setunionE
% 0.28/0.44 = ( ! [A: $i,Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ ( setunion @ A ) )
% 0.28/0.44 => ! [Xphi: $o] :
% 0.28/0.44 ( ! [B: $i] :
% 0.28/0.44 ( ( in @ Xx @ B )
% 0.28/0.44 => ( ( in @ B @ A )
% 0.28/0.44 => Xphi ) )
% 0.28/0.44 => Xphi ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(subPowSU_type,type,
% 0.28/0.44 subPowSU: $o ).
% 0.28/0.44
% 0.28/0.44 thf(subPowSU,definition,
% 0.28/0.44 ( subPowSU
% 0.28/0.44 = ( ! [A: $i,Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ A )
% 0.28/0.44 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(exuE2_type,type,
% 0.28/0.44 exuE2: $o ).
% 0.28/0.44
% 0.28/0.44 thf(exuE2,definition,
% 0.28/0.44 ( exuE2
% 0.28/0.44 = ( ! [Xphi: $i > $o] :
% 0.28/0.44 ( ( exu
% 0.28/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.44 => ? [Xx: $i] :
% 0.28/0.44 ! [Xy: $i] :
% 0.28/0.44 ( ( Xphi @ Xy )
% 0.28/0.44 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(nonemptyImpWitness_type,type,
% 0.28/0.44 nonemptyImpWitness: $o ).
% 0.28/0.44
% 0.28/0.44 thf(nonemptyImpWitness,definition,
% 0.28/0.44 ( nonemptyImpWitness
% 0.28/0.44 = ( ! [A: $i] :
% 0.28/0.44 ( ( nonempty @ A )
% 0.28/0.44 => ? [Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ A )
% 0.28/0.44 & $true ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(uniqinunit_type,type,
% 0.28/0.44 uniqinunit: $o ).
% 0.28/0.44
% 0.28/0.44 thf(uniqinunit,definition,
% 0.28/0.44 ( uniqinunit
% 0.28/0.44 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.44 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.44 => ( Xx = Xy ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(notinsingleton_type,type,
% 0.28/0.44 notinsingleton: $o ).
% 0.28/0.44
% 0.28/0.44 thf(notinsingleton,definition,
% 0.28/0.44 ( notinsingleton
% 0.28/0.44 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.44 ( ( Xx != Xy )
% 0.28/0.44 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(eqinunit_type,type,
% 0.28/0.44 eqinunit: $o ).
% 0.28/0.44
% 0.28/0.44 thf(eqinunit,definition,
% 0.28/0.44 ( eqinunit
% 0.28/0.44 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.44 ( ( Xx = Xy )
% 0.28/0.44 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(singletonsswitch_type,type,
% 0.28/0.44 singletonsswitch: $o ).
% 0.28/0.44
% 0.28/0.44 thf(singletonsswitch,definition,
% 0.28/0.44 ( singletonsswitch
% 0.28/0.44 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.44 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.44 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(upairsetE_type,type,
% 0.28/0.44 upairsetE: $o ).
% 0.28/0.44
% 0.28/0.44 thf(upairsetE,definition,
% 0.28/0.44 ( upairsetE
% 0.28/0.44 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.28/0.44 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.28/0.44 => ( ( Xz = Xx )
% 0.28/0.44 | ( Xz = Xy ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(upairsetIL_type,type,
% 0.28/0.44 upairsetIL: $o ).
% 0.28/0.44
% 0.28/0.44 thf(upairsetIL,definition,
% 0.28/0.44 ( upairsetIL
% 0.28/0.44 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(upairsetIR_type,type,
% 0.28/0.44 upairsetIR: $o ).
% 0.28/0.44
% 0.28/0.44 thf(upairsetIR,definition,
% 0.28/0.44 ( upairsetIR
% 0.28/0.44 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(emptyE1_type,type,
% 0.28/0.44 emptyE1: $o ).
% 0.28/0.44
% 0.28/0.44 thf(emptyE1,definition,
% 0.28/0.44 ( emptyE1
% 0.28/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.44 ( ? [Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ A )
% 0.28/0.44 & ( Xphi @ Xx ) )
% 0.28/0.44 => ( ( ( dsetconstr @ A
% 0.28/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.44 = emptyset )
% 0.28/0.44 => $false ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(vacuousDall_type,type,
% 0.28/0.44 vacuousDall: $o ).
% 0.28/0.44
% 0.28/0.44 thf(vacuousDall,definition,
% 0.28/0.44 ( vacuousDall
% 0.28/0.44 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ emptyset )
% 0.28/0.44 => ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(quantDeMorgan1_type,type,
% 0.28/0.44 quantDeMorgan1: $o ).
% 0.28/0.44
% 0.28/0.44 thf(quantDeMorgan1,definition,
% 0.28/0.44 ( quantDeMorgan1
% 0.28/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.44 ( ~ ! [Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ A )
% 0.28/0.44 => ( Xphi @ Xx ) )
% 0.28/0.44 => ? [Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ A )
% 0.28/0.44 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(quantDeMorgan2_type,type,
% 0.28/0.44 quantDeMorgan2: $o ).
% 0.28/0.44
% 0.28/0.44 thf(quantDeMorgan2,definition,
% 0.28/0.44 ( quantDeMorgan2
% 0.28/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.44 ( ! [Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ A )
% 0.28/0.44 => ~ ( Xphi @ Xx ) )
% 0.28/0.44 => ~ ? [Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ A )
% 0.28/0.44 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(quantDeMorgan3_type,type,
% 0.28/0.44 quantDeMorgan3: $o ).
% 0.28/0.44
% 0.28/0.44 thf(quantDeMorgan3,definition,
% 0.28/0.44 ( quantDeMorgan3
% 0.28/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.44 ( ~ ? [Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ A )
% 0.28/0.44 & ( Xphi @ Xx ) )
% 0.28/0.44 => ! [Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ A )
% 0.28/0.44 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(quantDeMorgan4_type,type,
% 0.28/0.44 quantDeMorgan4: $o ).
% 0.28/0.44
% 0.28/0.44 thf(quantDeMorgan4,definition,
% 0.28/0.44 ( quantDeMorgan4
% 0.28/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.44 ( ? [Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ A )
% 0.28/0.44 & ~ ( Xphi @ Xx ) )
% 0.28/0.44 => ~ ! [Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ A )
% 0.28/0.44 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(prop2setI_type,type,
% 0.28/0.44 prop2setI: $o ).
% 0.28/0.44
% 0.28/0.44 thf(prop2setI,definition,
% 0.28/0.44 ( prop2setI
% 0.28/0.44 = ( ! [Xphi: $o] :
% 0.28/0.44 ( Xphi
% 0.28/0.44 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(set2prop_type,type,
% 0.28/0.44 set2prop: $i > $o ).
% 0.28/0.44
% 0.28/0.44 thf(prop2set2propI_type,type,
% 0.28/0.44 prop2set2propI: $o ).
% 0.28/0.44
% 0.28/0.44 thf(prop2set2propI,definition,
% 0.28/0.44 ( prop2set2propI
% 0.28/0.44 = ( ! [Xphi: $o] :
% 0.28/0.44 ( Xphi
% 0.28/0.44 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(notdexE_type,type,
% 0.28/0.44 notdexE: $o ).
% 0.28/0.44
% 0.28/0.44 thf(notdexE,definition,
% 0.28/0.44 ( notdexE
% 0.28/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.44 ( ~ ? [Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ A )
% 0.28/0.44 & ( Xphi @ Xx ) )
% 0.28/0.44 => ! [Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ A )
% 0.28/0.44 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(notdallE_type,type,
% 0.28/0.44 notdallE: $o ).
% 0.28/0.44
% 0.28/0.44 thf(notdallE,definition,
% 0.28/0.44 ( notdallE
% 0.28/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.44 ( ~ ! [Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ A )
% 0.28/0.44 => ( Xphi @ Xx ) )
% 0.28/0.44 => ? [Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ A )
% 0.28/0.44 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(exuI1_type,type,
% 0.28/0.44 exuI1: $o ).
% 0.28/0.44
% 0.28/0.44 thf(exuI1,definition,
% 0.28/0.44 ( exuI1
% 0.28/0.44 = ( ! [Xphi: $i > $o] :
% 0.28/0.44 ( ? [Xx: $i] :
% 0.28/0.44 ( ( Xphi @ Xx )
% 0.28/0.44 & ! [Xy: $i] :
% 0.28/0.44 ( ( Xphi @ Xy )
% 0.28/0.44 => ( Xx = Xy ) ) )
% 0.28/0.44 => ( exu
% 0.28/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(exuI3_type,type,
% 0.28/0.44 exuI3: $o ).
% 0.28/0.44
% 0.28/0.44 thf(exuI3,definition,
% 0.28/0.44 ( exuI3
% 0.28/0.44 = ( ! [Xphi: $i > $o] :
% 0.28/0.44 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.28/0.44 => ( ! [Xx: $i,Xy: $i] :
% 0.28/0.44 ( ( Xphi @ Xx )
% 0.28/0.44 => ( ( Xphi @ Xy )
% 0.28/0.44 => ( Xx = Xy ) ) )
% 0.28/0.44 => ( exu
% 0.28/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(exuI2_type,type,
% 0.28/0.44 exuI2: $o ).
% 0.28/0.44
% 0.28/0.44 thf(exuI2,definition,
% 0.28/0.44 ( exuI2
% 0.28/0.44 = ( ! [Xphi: $i > $o] :
% 0.28/0.44 ( ? [Xx: $i] :
% 0.28/0.44 ! [Xy: $i] :
% 0.28/0.44 ( ( Xphi @ Xy )
% 0.28/0.44 <=> ( Xy = Xx ) )
% 0.28/0.44 => ( exu
% 0.28/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(inCongP_type,type,
% 0.28/0.44 inCongP: $o ).
% 0.28/0.44
% 0.28/0.44 thf(inCongP,definition,
% 0.28/0.44 ( inCongP
% 0.28/0.44 = ( ! [A: $i,B: $i] :
% 0.28/0.44 ( ( A = B )
% 0.28/0.44 => ! [Xx: $i,Xy: $i] :
% 0.28/0.44 ( ( Xx = Xy )
% 0.28/0.44 => ( ( in @ Xx @ A )
% 0.28/0.44 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(in__Cong_type,type,
% 0.28/0.44 in__Cong: $o ).
% 0.28/0.44
% 0.28/0.44 thf(in__Cong,definition,
% 0.28/0.44 ( in__Cong
% 0.28/0.44 = ( ! [A: $i,B: $i] :
% 0.28/0.44 ( ( A = B )
% 0.28/0.44 => ! [Xx: $i,Xy: $i] :
% 0.28/0.44 ( ( Xx = Xy )
% 0.28/0.44 => ( ( in @ Xx @ A )
% 0.28/0.44 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(exuE3u_type,type,
% 0.28/0.44 exuE3u: $o ).
% 0.28/0.44
% 0.28/0.44 thf(exuE3u,definition,
% 0.28/0.44 ( exuE3u
% 0.28/0.44 = ( ! [Xphi: $i > $o] :
% 0.28/0.44 ( ( exu
% 0.28/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.44 => ! [Xx: $i,Xy: $i] :
% 0.28/0.44 ( ( Xphi @ Xx )
% 0.28/0.44 => ( ( Xphi @ Xy )
% 0.28/0.44 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(exu__Cong_type,type,
% 0.28/0.44 exu__Cong: $o ).
% 0.28/0.44
% 0.28/0.44 thf(exu__Cong,definition,
% 0.28/0.44 ( exu__Cong
% 0.28/0.44 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.28/0.44 ( ! [Xx: $i,Xy: $i] :
% 0.28/0.44 ( ( Xx = Xy )
% 0.28/0.44 => ( ( Xphi @ Xx )
% 0.28/0.44 <=> ( Xpsi @ Xy ) ) )
% 0.28/0.44 => ( ( exu
% 0.28/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.44 <=> ( exu
% 0.28/0.44 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(emptyset__Cong_type,type,
% 0.28/0.44 emptyset__Cong: $o ).
% 0.28/0.44
% 0.28/0.44 thf(emptyset__Cong,definition,
% 0.28/0.44 ( emptyset__Cong
% 0.28/0.44 = ( emptyset = emptyset ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(setadjoin__Cong_type,type,
% 0.28/0.44 setadjoin__Cong: $o ).
% 0.28/0.44
% 0.28/0.44 thf(setadjoin__Cong,definition,
% 0.28/0.44 ( setadjoin__Cong
% 0.28/0.44 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.44 ( ( Xx = Xy )
% 0.28/0.44 => ! [Xz: $i,Xu: $i] :
% 0.28/0.44 ( ( Xz = Xu )
% 0.28/0.44 => ( ( setadjoin @ Xx @ Xz )
% 0.28/0.44 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(powerset__Cong_type,type,
% 0.28/0.44 powerset__Cong: $o ).
% 0.28/0.44
% 0.28/0.44 thf(powerset__Cong,definition,
% 0.28/0.44 ( powerset__Cong
% 0.28/0.44 = ( ! [A: $i,B: $i] :
% 0.28/0.44 ( ( A = B )
% 0.28/0.44 => ( ( powerset @ A )
% 0.28/0.44 = ( powerset @ B ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(setunion__Cong_type,type,
% 0.28/0.44 setunion__Cong: $o ).
% 0.28/0.44
% 0.28/0.44 thf(setunion__Cong,definition,
% 0.28/0.44 ( setunion__Cong
% 0.28/0.44 = ( ! [A: $i,B: $i] :
% 0.28/0.44 ( ( A = B )
% 0.28/0.44 => ( ( setunion @ A )
% 0.28/0.44 = ( setunion @ B ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(omega__Cong_type,type,
% 0.28/0.44 omega__Cong: $o ).
% 0.28/0.44
% 0.28/0.44 thf(omega__Cong,definition,
% 0.28/0.44 ( omega__Cong
% 0.28/0.44 = ( omega = omega ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(exuEu_type,type,
% 0.28/0.44 exuEu: $o ).
% 0.28/0.44
% 0.28/0.44 thf(exuEu,definition,
% 0.28/0.44 ( exuEu
% 0.28/0.44 = ( ! [Xphi: $i > $o] :
% 0.28/0.44 ( ( exu
% 0.28/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.44 => ! [Xx: $i,Xy: $i] :
% 0.28/0.44 ( ( Xphi @ Xx )
% 0.28/0.44 => ( ( Xphi @ Xy )
% 0.28/0.44 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(descr__Cong_type,type,
% 0.28/0.44 descr__Cong: $o ).
% 0.28/0.44
% 0.28/0.44 thf(descr__Cong,definition,
% 0.28/0.44 ( descr__Cong
% 0.28/0.44 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.28/0.44 ( ! [Xx: $i,Xy: $i] :
% 0.28/0.44 ( ( Xx = Xy )
% 0.28/0.44 => ( ( Xphi @ Xx )
% 0.28/0.44 <=> ( Xpsi @ Xy ) ) )
% 0.28/0.44 => ( ( exu
% 0.28/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.44 => ( ( exu
% 0.28/0.44 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.28/0.44 => ( ( descr
% 0.28/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.44 = ( descr
% 0.28/0.44 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(dsetconstr__Cong_type,type,
% 0.28/0.44 dsetconstr__Cong: $o ).
% 0.28/0.44
% 0.28/0.44 thf(dsetconstr__Cong,definition,
% 0.28/0.44 ( dsetconstr__Cong
% 0.28/0.44 = ( ! [A: $i,B: $i] :
% 0.28/0.44 ( ( A = B )
% 0.28/0.44 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.28/0.44 ( ! [Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ A )
% 0.28/0.44 => ! [Xy: $i] :
% 0.28/0.44 ( ( in @ Xy @ B )
% 0.28/0.44 => ( ( Xx = Xy )
% 0.28/0.44 => ( ( Xphi @ Xx )
% 0.28/0.44 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.28/0.44 => ( ( dsetconstr @ A
% 0.28/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.44 = ( dsetconstr @ B
% 0.28/0.44 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(subset_type,type,
% 0.28/0.44 subset: $i > $i > $o ).
% 0.28/0.44
% 0.28/0.44 thf(disjoint_type,type,
% 0.28/0.44 disjoint: $i > $i > $o ).
% 0.28/0.44
% 0.28/0.44 thf(setsmeet_type,type,
% 0.28/0.44 setsmeet: $i > $i > $o ).
% 0.28/0.44
% 0.28/0.44 thf(subsetI1_type,type,
% 0.28/0.44 subsetI1: $o ).
% 0.28/0.44
% 0.28/0.44 thf(subsetI1,definition,
% 0.28/0.44 ( subsetI1
% 0.28/0.44 = ( ! [A: $i,B: $i] :
% 0.28/0.44 ( ! [Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ A )
% 0.28/0.44 => ( in @ Xx @ B ) )
% 0.28/0.44 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(eqimpsubset2_type,type,
% 0.28/0.44 eqimpsubset2: $o ).
% 0.28/0.44
% 0.28/0.44 thf(eqimpsubset2,definition,
% 0.28/0.44 ( eqimpsubset2
% 0.28/0.44 = ( ! [A: $i,B: $i] :
% 0.28/0.44 ( ( A = B )
% 0.28/0.44 => ( subset @ B @ A ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(eqimpsubset1_type,type,
% 0.28/0.44 eqimpsubset1: $o ).
% 0.28/0.44
% 0.28/0.44 thf(eqimpsubset1,definition,
% 0.28/0.44 ( eqimpsubset1
% 0.28/0.44 = ( ! [A: $i,B: $i] :
% 0.28/0.44 ( ( A = B )
% 0.28/0.44 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(subsetI2_type,type,
% 0.28/0.44 subsetI2: $o ).
% 0.28/0.44
% 0.28/0.44 thf(subsetI2,definition,
% 0.28/0.44 ( subsetI2
% 0.28/0.44 = ( ! [A: $i,B: $i] :
% 0.28/0.44 ( ! [Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ A )
% 0.28/0.44 => ( in @ Xx @ B ) )
% 0.28/0.44 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(emptysetsubset_type,type,
% 0.28/0.44 emptysetsubset: $o ).
% 0.28/0.44
% 0.28/0.44 thf(emptysetsubset,definition,
% 0.28/0.44 ( emptysetsubset
% 0.28/0.44 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(subsetE_type,type,
% 0.28/0.44 subsetE: $o ).
% 0.28/0.44
% 0.28/0.44 thf(subsetE,definition,
% 0.28/0.44 ( subsetE
% 0.28/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.44 ( ( subset @ A @ B )
% 0.28/0.44 => ( ( in @ Xx @ A )
% 0.28/0.44 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(subsetE2_type,type,
% 0.28/0.44 subsetE2: $o ).
% 0.28/0.44
% 0.28/0.44 thf(subsetE2,definition,
% 0.28/0.44 ( subsetE2
% 0.28/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.44 ( ( subset @ A @ B )
% 0.28/0.44 => ( ~ ( in @ Xx @ B )
% 0.28/0.44 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(notsubsetI_type,type,
% 0.28/0.44 notsubsetI: $o ).
% 0.28/0.44
% 0.28/0.44 thf(notsubsetI,definition,
% 0.28/0.44 ( notsubsetI
% 0.28/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ A )
% 0.28/0.44 => ( ~ ( in @ Xx @ B )
% 0.28/0.44 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(notequalI1_type,type,
% 0.28/0.44 notequalI1: $o ).
% 0.28/0.44
% 0.28/0.44 thf(notequalI1,definition,
% 0.28/0.44 ( notequalI1
% 0.28/0.44 = ( ! [A: $i,B: $i] :
% 0.28/0.44 ( ~ ( subset @ A @ B )
% 0.28/0.44 => ( A != B ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(notequalI2_type,type,
% 0.28/0.44 notequalI2: $o ).
% 0.28/0.44
% 0.28/0.44 thf(notequalI2,definition,
% 0.28/0.44 ( notequalI2
% 0.28/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ A )
% 0.28/0.44 => ( ~ ( in @ Xx @ B )
% 0.28/0.44 => ( A != B ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(subsetRefl_type,type,
% 0.28/0.44 subsetRefl: $o ).
% 0.28/0.44
% 0.28/0.44 thf(subsetRefl,definition,
% 0.28/0.44 ( subsetRefl
% 0.28/0.44 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(subsetTrans_type,type,
% 0.28/0.44 subsetTrans: $o ).
% 0.28/0.44
% 0.28/0.44 thf(subsetTrans,definition,
% 0.28/0.44 ( subsetTrans
% 0.28/0.44 = ( ! [A: $i,B: $i,C: $i] :
% 0.28/0.44 ( ( subset @ A @ B )
% 0.28/0.44 => ( ( subset @ B @ C )
% 0.28/0.44 => ( subset @ A @ C ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(setadjoinSub_type,type,
% 0.28/0.44 setadjoinSub: $o ).
% 0.28/0.44
% 0.28/0.44 thf(setadjoinSub,definition,
% 0.28/0.44 ( setadjoinSub
% 0.28/0.44 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(setadjoinSub2_type,type,
% 0.28/0.44 setadjoinSub2: $o ).
% 0.28/0.44
% 0.28/0.44 thf(setadjoinSub2,definition,
% 0.28/0.44 ( setadjoinSub2
% 0.28/0.44 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.28/0.44 ( ( subset @ A @ B )
% 0.28/0.44 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(subset2powerset_type,type,
% 0.28/0.44 subset2powerset: $o ).
% 0.28/0.44
% 0.28/0.44 thf(subset2powerset,definition,
% 0.28/0.44 ( subset2powerset
% 0.28/0.44 = ( ! [A: $i,B: $i] :
% 0.28/0.44 ( ( subset @ A @ B )
% 0.28/0.44 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(setextsub_type,type,
% 0.28/0.44 setextsub: $o ).
% 0.28/0.44
% 0.28/0.44 thf(setextsub,definition,
% 0.28/0.44 ( setextsub
% 0.28/0.44 = ( ! [A: $i,B: $i] :
% 0.28/0.44 ( ( subset @ A @ B )
% 0.28/0.44 => ( ( subset @ B @ A )
% 0.28/0.44 => ( A = B ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(subsetemptysetimpeq_type,type,
% 0.28/0.44 subsetemptysetimpeq: $o ).
% 0.28/0.44
% 0.28/0.44 thf(subsetemptysetimpeq,definition,
% 0.28/0.44 ( subsetemptysetimpeq
% 0.28/0.44 = ( ! [A: $i] :
% 0.28/0.44 ( ( subset @ A @ emptyset )
% 0.28/0.44 => ( A = emptyset ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(powersetI1_type,type,
% 0.28/0.44 powersetI1: $o ).
% 0.28/0.44
% 0.28/0.44 thf(powersetI1,definition,
% 0.28/0.44 ( powersetI1
% 0.28/0.44 = ( ! [A: $i,B: $i] :
% 0.28/0.44 ( ( subset @ B @ A )
% 0.28/0.44 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(powersetE1_type,type,
% 0.28/0.44 powersetE1: $o ).
% 0.28/0.44
% 0.28/0.44 thf(powersetE1,definition,
% 0.28/0.44 ( powersetE1
% 0.28/0.44 = ( ! [A: $i,B: $i] :
% 0.28/0.44 ( ( in @ B @ ( powerset @ A ) )
% 0.28/0.44 => ( subset @ B @ A ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(inPowerset_type,type,
% 0.28/0.44 inPowerset: $o ).
% 0.28/0.44
% 0.28/0.44 thf(inPowerset,definition,
% 0.28/0.44 ( inPowerset
% 0.28/0.44 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(powersetsubset_type,type,
% 0.28/0.44 powersetsubset: $o ).
% 0.28/0.44
% 0.28/0.44 thf(powersetsubset,definition,
% 0.28/0.44 ( powersetsubset
% 0.28/0.44 = ( ! [A: $i,B: $i] :
% 0.28/0.44 ( ( subset @ A @ B )
% 0.28/0.44 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(sepInPowerset_type,type,
% 0.28/0.44 sepInPowerset: $o ).
% 0.28/0.44
% 0.28/0.44 thf(sepInPowerset,definition,
% 0.28/0.44 ( sepInPowerset
% 0.28/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.44 ( in
% 0.28/0.44 @ ( dsetconstr @ A
% 0.28/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.44 @ ( powerset @ A ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(sepSubset_type,type,
% 0.28/0.44 sepSubset: $o ).
% 0.28/0.44
% 0.28/0.44 thf(sepSubset,definition,
% 0.28/0.44 ( sepSubset
% 0.28/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.44 ( subset
% 0.28/0.44 @ ( dsetconstr @ A
% 0.28/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.44 @ A ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(binunion_type,type,
% 0.28/0.44 binunion: $i > $i > $i ).
% 0.28/0.44
% 0.28/0.44 thf(binunionIL_type,type,
% 0.28/0.44 binunionIL: $o ).
% 0.28/0.44
% 0.28/0.44 thf(binunionIL,definition,
% 0.28/0.44 ( binunionIL
% 0.28/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ A )
% 0.28/0.44 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(upairset2IR_type,type,
% 0.28/0.44 upairset2IR: $o ).
% 0.28/0.44
% 0.28/0.44 thf(upairset2IR,definition,
% 0.28/0.44 ( upairset2IR
% 0.28/0.44 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(binunionIR_type,type,
% 0.28/0.44 binunionIR: $o ).
% 0.28/0.44
% 0.28/0.44 thf(binunionIR,definition,
% 0.28/0.44 ( binunionIR
% 0.28/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ B )
% 0.28/0.44 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(binunionEcases_type,type,
% 0.28/0.44 binunionEcases: $o ).
% 0.28/0.44
% 0.28/0.44 thf(binunionEcases,definition,
% 0.28/0.44 ( binunionEcases
% 0.28/0.44 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.28/0.44 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.28/0.44 => ( ( ( in @ Xx @ A )
% 0.28/0.44 => Xphi )
% 0.28/0.44 => ( ( ( in @ Xx @ B )
% 0.28/0.44 => Xphi )
% 0.28/0.44 => Xphi ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(binunionE_type,type,
% 0.28/0.44 binunionE: $o ).
% 0.28/0.44
% 0.28/0.44 thf(binunionE,definition,
% 0.28/0.44 ( binunionE
% 0.28/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.28/0.44 => ( ( in @ Xx @ A )
% 0.28/0.44 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(binunionLsub_type,type,
% 0.28/0.44 binunionLsub: $o ).
% 0.28/0.44
% 0.28/0.44 thf(binunionLsub,definition,
% 0.28/0.44 ( binunionLsub
% 0.28/0.44 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(binunionRsub_type,type,
% 0.28/0.44 binunionRsub: $o ).
% 0.28/0.44
% 0.28/0.44 thf(binunionRsub,definition,
% 0.28/0.44 ( binunionRsub
% 0.28/0.44 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(binintersect_type,type,
% 0.28/0.44 binintersect: $i > $i > $i ).
% 0.28/0.44
% 0.28/0.44 thf(binintersectI_type,type,
% 0.28/0.44 binintersectI: $o ).
% 0.28/0.44
% 0.28/0.44 thf(binintersectI,definition,
% 0.28/0.44 ( binintersectI
% 0.28/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ A )
% 0.28/0.44 => ( ( in @ Xx @ B )
% 0.28/0.44 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(binintersectSubset5_type,type,
% 0.28/0.44 binintersectSubset5: $o ).
% 0.28/0.44
% 0.28/0.44 thf(binintersectSubset5,definition,
% 0.28/0.44 ( binintersectSubset5
% 0.28/0.44 = ( ! [A: $i,B: $i,C: $i] :
% 0.28/0.44 ( ( subset @ C @ A )
% 0.28/0.44 => ( ( subset @ C @ B )
% 0.28/0.44 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(binintersectEL_type,type,
% 0.28/0.44 binintersectEL: $o ).
% 0.28/0.44
% 0.28/0.44 thf(binintersectEL,definition,
% 0.28/0.44 ( binintersectEL
% 0.28/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.28/0.44 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(binintersectLsub_type,type,
% 0.28/0.44 binintersectLsub: $o ).
% 0.28/0.44
% 0.28/0.44 thf(binintersectLsub,definition,
% 0.28/0.44 ( binintersectLsub
% 0.28/0.44 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(binintersectSubset2_type,type,
% 0.28/0.44 binintersectSubset2: $o ).
% 0.28/0.44
% 0.28/0.44 thf(binintersectSubset2,definition,
% 0.28/0.44 ( binintersectSubset2
% 0.28/0.44 = ( ! [A: $i,B: $i] :
% 0.28/0.44 ( ( subset @ A @ B )
% 0.28/0.44 => ( ( binintersect @ A @ B )
% 0.28/0.44 = A ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(binintersectSubset3_type,type,
% 0.28/0.44 binintersectSubset3: $o ).
% 0.28/0.44
% 0.28/0.44 thf(binintersectSubset3,definition,
% 0.28/0.44 ( binintersectSubset3
% 0.28/0.44 = ( ! [A: $i,B: $i] :
% 0.28/0.44 ( ( ( binintersect @ A @ B )
% 0.28/0.44 = B )
% 0.28/0.44 => ( subset @ B @ A ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(binintersectER_type,type,
% 0.28/0.44 binintersectER: $o ).
% 0.28/0.44
% 0.28/0.44 thf(binintersectER,definition,
% 0.28/0.44 ( binintersectER
% 0.28/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.28/0.44 => ( in @ Xx @ B ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(disjointsetsI1_type,type,
% 0.28/0.44 disjointsetsI1: $o ).
% 0.28/0.44
% 0.28/0.44 thf(disjointsetsI1,definition,
% 0.28/0.44 ( disjointsetsI1
% 0.28/0.44 = ( ! [A: $i,B: $i] :
% 0.28/0.44 ( ~ ? [Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ A )
% 0.28/0.44 & ( in @ Xx @ B ) )
% 0.28/0.44 => ( ( binintersect @ A @ B )
% 0.28/0.44 = emptyset ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(binintersectRsub_type,type,
% 0.28/0.44 binintersectRsub: $o ).
% 0.28/0.44
% 0.28/0.44 thf(binintersectRsub,definition,
% 0.28/0.44 ( binintersectRsub
% 0.28/0.44 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(binintersectSubset4_type,type,
% 0.28/0.44 binintersectSubset4: $o ).
% 0.28/0.44
% 0.28/0.44 thf(binintersectSubset4,definition,
% 0.28/0.44 ( binintersectSubset4
% 0.28/0.44 = ( ! [A: $i,B: $i] :
% 0.28/0.44 ( ( subset @ B @ A )
% 0.28/0.44 => ( ( binintersect @ A @ B )
% 0.28/0.44 = B ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(binintersectSubset1_type,type,
% 0.28/0.44 binintersectSubset1: $o ).
% 0.28/0.44
% 0.28/0.44 thf(binintersectSubset1,definition,
% 0.28/0.44 ( binintersectSubset1
% 0.28/0.44 = ( ! [A: $i,B: $i] :
% 0.28/0.44 ( ( ( binintersect @ A @ B )
% 0.28/0.44 = A )
% 0.28/0.44 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(bs114d_type,type,
% 0.28/0.44 bs114d: $o ).
% 0.28/0.44
% 0.28/0.44 thf(bs114d,definition,
% 0.28/0.44 ( bs114d
% 0.28/0.44 = ( ! [A: $i,B: $i,C: $i] :
% 0.28/0.44 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.28/0.44 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(regular_type,type,
% 0.28/0.44 regular: $i > $o ).
% 0.28/0.44
% 0.28/0.44 thf(setminus_type,type,
% 0.28/0.44 setminus: $i > $i > $i ).
% 0.28/0.44
% 0.28/0.44 thf(setminusI_type,type,
% 0.28/0.44 setminusI: $o ).
% 0.28/0.44
% 0.28/0.44 thf(setminusI,definition,
% 0.28/0.44 ( setminusI
% 0.28/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ A )
% 0.28/0.44 => ( ~ ( in @ Xx @ B )
% 0.28/0.44 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(setminusEL_type,type,
% 0.28/0.44 setminusEL: $o ).
% 0.28/0.44
% 0.28/0.44 thf(setminusEL,definition,
% 0.28/0.44 ( setminusEL
% 0.28/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.28/0.44 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(setminusER_type,type,
% 0.28/0.44 setminusER: $o ).
% 0.28/0.44
% 0.28/0.44 thf(setminusER,definition,
% 0.28/0.44 ( setminusER
% 0.28/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.28/0.44 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(setminusSubset2_type,type,
% 0.28/0.44 setminusSubset2: $o ).
% 0.28/0.44
% 0.28/0.44 thf(setminusSubset2,definition,
% 0.28/0.44 ( setminusSubset2
% 0.28/0.44 = ( ! [A: $i,B: $i] :
% 0.28/0.44 ( ( subset @ A @ B )
% 0.28/0.44 => ( ( setminus @ A @ B )
% 0.28/0.44 = emptyset ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(setminusERneg_type,type,
% 0.28/0.44 setminusERneg: $o ).
% 0.28/0.44
% 0.28/0.44 thf(setminusERneg,definition,
% 0.28/0.44 ( setminusERneg
% 0.28/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.44 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.28/0.44 => ( ( in @ Xx @ A )
% 0.28/0.44 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(setminusELneg_type,type,
% 0.28/0.44 setminusELneg: $o ).
% 0.28/0.44
% 0.28/0.44 thf(setminusELneg,definition,
% 0.28/0.44 ( setminusELneg
% 0.28/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.44 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.28/0.44 => ( ~ ( in @ Xx @ B )
% 0.28/0.44 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(setminusILneg_type,type,
% 0.28/0.44 setminusILneg: $o ).
% 0.28/0.44
% 0.28/0.44 thf(setminusILneg,definition,
% 0.28/0.44 ( setminusILneg
% 0.28/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.44 ( ~ ( in @ Xx @ A )
% 0.28/0.44 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(setminusIRneg_type,type,
% 0.28/0.44 setminusIRneg: $o ).
% 0.28/0.44
% 0.28/0.44 thf(setminusIRneg,definition,
% 0.28/0.44 ( setminusIRneg
% 0.28/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ B )
% 0.28/0.44 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(setminusLsub_type,type,
% 0.28/0.44 setminusLsub: $o ).
% 0.28/0.44
% 0.28/0.44 thf(setminusLsub,definition,
% 0.28/0.44 ( setminusLsub
% 0.28/0.44 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(setminusSubset1_type,type,
% 0.28/0.44 setminusSubset1: $o ).
% 0.28/0.44
% 0.28/0.44 thf(setminusSubset1,definition,
% 0.28/0.44 ( setminusSubset1
% 0.28/0.44 = ( ! [A: $i,B: $i] :
% 0.28/0.44 ( ( ( setminus @ A @ B )
% 0.28/0.44 = emptyset )
% 0.28/0.44 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(symdiff_type,type,
% 0.28/0.44 symdiff: $i > $i > $i ).
% 0.28/0.44
% 0.28/0.44 thf(symdiff,definition,
% 0.28/0.44 ( symdiff
% 0.28/0.44 = ( ^ [A: $i,B: $i] :
% 0.28/0.44 ( dsetconstr @ ( binunion @ A @ B )
% 0.28/0.44 @ ^ [Xx: $i] :
% 0.28/0.44 ( ~ ( in @ Xx @ A )
% 0.28/0.44 | ~ ( in @ Xx @ B ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(symdiffE_type,type,
% 0.28/0.44 symdiffE: $o ).
% 0.28/0.44
% 0.28/0.44 thf(symdiffE,definition,
% 0.28/0.44 ( symdiffE
% 0.28/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.28/0.44 => ! [Xphi: $o] :
% 0.28/0.44 ( ( ( in @ Xx @ A )
% 0.28/0.44 => ( ~ ( in @ Xx @ B )
% 0.28/0.44 => Xphi ) )
% 0.28/0.44 => ( ( ~ ( in @ Xx @ A )
% 0.28/0.44 => ( ( in @ Xx @ B )
% 0.28/0.44 => Xphi ) )
% 0.28/0.44 => Xphi ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(symdiffI1_type,type,
% 0.28/0.44 symdiffI1: $o ).
% 0.28/0.44
% 0.28/0.44 thf(symdiffI1,definition,
% 0.28/0.44 ( symdiffI1
% 0.28/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.44 ( ( in @ Xx @ A )
% 0.28/0.44 => ( ~ ( in @ Xx @ B )
% 0.28/0.44 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 thf(symdiffI2,conjecture,
% 0.28/0.44 ( setextAx
% 0.28/0.44 => ( emptysetAx
% 0.28/0.44 => ( setadjoinAx
% 0.28/0.44 => ( powersetAx
% 0.28/0.44 => ( setunionAx
% 0.28/0.44 => ( omega0Ax
% 0.28/0.44 => ( omegaSAx
% 0.28/0.44 => ( omegaIndAx
% 0.28/0.44 => ( replAx
% 0.28/0.44 => ( foundationAx
% 0.28/0.44 => ( wellorderingAx
% 0.28/0.44 => ( descrp
% 0.28/0.44 => ( dsetconstrI
% 0.28/0.44 => ( dsetconstrEL
% 0.28/0.44 => ( dsetconstrER
% 0.28/0.44 => ( exuE1
% 0.28/0.44 => ( prop2setE
% 0.28/0.44 => ( emptysetE
% 0.28/0.44 => ( emptysetimpfalse
% 0.28/0.44 => ( notinemptyset
% 0.28/0.44 => ( exuE3e
% 0.28/0.44 => ( setext
% 0.28/0.44 => ( emptyI
% 0.28/0.44 => ( noeltsimpempty
% 0.28/0.44 => ( setbeta
% 0.28/0.44 => ( nonemptyE1
% 0.28/0.44 => ( nonemptyI
% 0.28/0.44 => ( nonemptyI1
% 0.28/0.44 => ( setadjoinIL
% 0.28/0.44 => ( emptyinunitempty
% 0.28/0.44 => ( setadjoinIR
% 0.28/0.44 => ( setadjoinE
% 0.28/0.44 => ( setadjoinOr
% 0.28/0.44 => ( setoftrueEq
% 0.28/0.44 => ( powersetI
% 0.28/0.44 => ( emptyinPowerset
% 0.28/0.44 => ( emptyInPowerset
% 0.28/0.44 => ( powersetE
% 0.28/0.44 => ( setunionI
% 0.28/0.44 => ( setunionE
% 0.28/0.44 => ( subPowSU
% 0.28/0.44 => ( exuE2
% 0.28/0.44 => ( nonemptyImpWitness
% 0.28/0.44 => ( uniqinunit
% 0.28/0.44 => ( notinsingleton
% 0.28/0.44 => ( eqinunit
% 0.28/0.44 => ( singletonsswitch
% 0.28/0.44 => ( upairsetE
% 0.28/0.44 => ( upairsetIL
% 0.28/0.44 => ( upairsetIR
% 0.28/0.44 => ( emptyE1
% 0.28/0.44 => ( vacuousDall
% 0.28/0.44 => ( quantDeMorgan1
% 0.28/0.44 => ( quantDeMorgan2
% 0.28/0.44 => ( quantDeMorgan3
% 0.28/0.44 => ( quantDeMorgan4
% 0.28/0.44 => ( prop2setI
% 0.28/0.44 => ( prop2set2propI
% 0.28/0.44 => ( notdexE
% 0.28/0.44 => ( notdallE
% 0.28/0.44 => ( exuI1
% 0.28/0.44 => ( exuI3
% 0.28/0.44 => ( exuI2
% 0.28/0.44 => ( inCongP
% 0.28/0.44 => ( in__Cong
% 0.28/0.44 => ( exuE3u
% 0.28/0.44 => ( exu__Cong
% 0.28/0.44 => ( emptyset__Cong
% 0.28/0.44 => ( setadjoin__Cong
% 0.28/0.44 => ( powerset__Cong
% 0.28/0.44 => ( setunion__Cong
% 0.28/0.44 => ( omega__Cong
% 0.28/0.44 => ( exuEu
% 0.28/0.44 => ( descr__Cong
% 0.28/0.44 => ( dsetconstr__Cong
% 0.28/0.44 => ( subsetI1
% 0.28/0.44 => ( eqimpsubset2
% 0.28/0.44 => ( eqimpsubset1
% 0.28/0.44 => ( subsetI2
% 0.28/0.44 => ( emptysetsubset
% 0.28/0.44 => ( subsetE
% 0.28/0.44 => ( subsetE2
% 0.28/0.44 => ( notsubsetI
% 0.28/0.44 => ( notequalI1
% 0.28/0.44 => ( notequalI2
% 0.28/0.44 => ( subsetRefl
% 0.28/0.44 => ( subsetTrans
% 0.28/0.44 => ( setadjoinSub
% 0.28/0.44 => ( setadjoinSub2
% 0.28/0.44 => ( subset2powerset
% 0.28/0.44 => ( setextsub
% 0.28/0.44 => ( subsetemptysetimpeq
% 0.28/0.44 => ( powersetI1
% 0.28/0.44 => ( powersetE1
% 0.28/0.44 => ( inPowerset
% 0.28/0.44 => ( powersetsubset
% 0.28/0.44 => ( sepInPowerset
% 0.28/0.44 => ( sepSubset
% 0.28/0.44 => ( binunionIL
% 0.28/0.44 => ( upairset2IR
% 0.28/0.44 => ( binunionIR
% 0.28/0.44 => ( binunionEcases
% 0.28/0.44 => ( binunionE
% 0.28/0.44 => ( binunionLsub
% 0.28/0.44 => ( binunionRsub
% 0.28/0.44 => ( binintersectI
% 0.28/0.44 => ( binintersectSubset5
% 0.28/0.44 => ( binintersectEL
% 0.28/0.44 => ( binintersectLsub
% 0.28/0.44 => ( binintersectSubset2
% 0.28/0.44 => ( binintersectSubset3
% 0.28/0.44 => ( binintersectER
% 0.28/0.44 => ( disjointsetsI1
% 0.28/0.44 => ( binintersectRsub
% 0.28/0.44 => ( binintersectSubset4
% 0.28/0.44 => ( binintersectSubset1
% 0.28/0.44 => ( bs114d
% 0.28/0.44 => ( setminusI
% 0.28/0.44 => ( setminusEL
% 0.28/0.44 => ( setminusER
% 0.28/0.44 => ( setminusSubset2
% 0.28/0.44 => ( setminusERneg
% 0.28/0.44 => ( setminusELneg
% 0.28/0.44 => ( setminusILneg
% 0.28/0.44 => ( setminusIRneg
% 0.28/0.44 => ( setminusLsub
% 0.28/0.44 => ( setminusSubset1
% 0.28/0.44 => ( symdiffE
% 0.28/0.44 => ( symdiffI1
% 0.28/0.44 => ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.44 ( ~ ( in @ Xx @ A )
% 0.28/0.44 => ( ( in @ Xx @ B )
% 0.28/0.44 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.44
% 0.28/0.44 %------------------------------------------------------------------------------
% 0.28/0.44 ------------------------
% 2.43/1.43 ---- Embedded in THF ---
% 2.43/1.43 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.43/1.43 %%% Generated on Tue Feb 24 12:29:36 EST 2026
% 2.43/1.43 %%% using '$$dhol' embedding, version 1.3.0.
% 2.43/1.43 %%% Logic specification used:
% 2.43/1.43 %%% thf(spec, logic, $$dhol).
% 2.43/1.43
% 2.43/1.43 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.7X3sL6M5Q7/DTF2DTF23484.p
% See solution above
% 2.43/1.43 ------------------------
% 2.43/1.46 ---- Cleaned THF ---
% 2.43/1.46 thf(in_type,type,
% 2.43/1.46 in: $i > $i > $o ).
% 2.43/1.46
% 2.43/1.46 thf(exu_type,type,
% 2.43/1.46 exu: ( $i > $o ) > $o ).
% 2.43/1.46
% 2.43/1.46 thf(exu,definition,
% 2.43/1.46 ( exu
% 2.43/1.46 = ( ^ [Xphi: $i > $o] :
% 2.43/1.46 ? [Xx: $i] :
% 2.43/1.46 ( ( Xphi @ Xx )
% 2.43/1.46 & ! [Xy: $i] :
% 2.43/1.46 ( ( Xphi @ Xy )
% 2.43/1.46 => ( Xx = Xy ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(setextAx_type,type,
% 2.43/1.46 setextAx: $o ).
% 2.43/1.46
% 2.43/1.46 thf(setextAx,definition,
% 2.43/1.46 ( setextAx
% 2.43/1.46 = ( ! [A: $i,B: $i] :
% 2.43/1.46 ( ! [Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ A )
% 2.43/1.46 <=> ( in @ Xx @ B ) )
% 2.43/1.46 => ( A = B ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(emptyset_type,type,
% 2.43/1.46 emptyset: $i ).
% 2.43/1.46
% 2.43/1.46 thf(emptysetAx_type,type,
% 2.43/1.46 emptysetAx: $o ).
% 2.43/1.46
% 2.43/1.46 thf(emptysetAx,definition,
% 2.43/1.46 ( emptysetAx
% 2.43/1.46 = ( ! [Xx: $i] :
% 2.43/1.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(setadjoin_type,type,
% 2.43/1.46 setadjoin: $i > $i > $i ).
% 2.43/1.46
% 2.43/1.46 thf(setadjoinAx_type,type,
% 2.43/1.46 setadjoinAx: $o ).
% 2.43/1.46
% 2.43/1.46 thf(setadjoinAx,definition,
% 2.43/1.46 ( setadjoinAx
% 2.43/1.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.43/1.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.43/1.46 <=> ( ( Xy = Xx )
% 2.43/1.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(powerset_type,type,
% 2.43/1.46 powerset: $i > $i ).
% 2.43/1.46
% 2.43/1.46 thf(powersetAx_type,type,
% 2.43/1.46 powersetAx: $o ).
% 2.43/1.46
% 2.43/1.46 thf(powersetAx,definition,
% 2.43/1.46 ( powersetAx
% 2.43/1.46 = ( ! [A: $i,B: $i] :
% 2.43/1.46 ( ( in @ B @ ( powerset @ A ) )
% 2.43/1.46 <=> ! [Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ B )
% 2.43/1.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(setunion_type,type,
% 2.43/1.46 setunion: $i > $i ).
% 2.43/1.46
% 2.43/1.46 thf(setunionAx_type,type,
% 2.43/1.46 setunionAx: $o ).
% 2.43/1.46
% 2.43/1.46 thf(setunionAx,definition,
% 2.43/1.46 ( setunionAx
% 2.43/1.46 = ( ! [A: $i,Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ ( setunion @ A ) )
% 2.43/1.46 <=> ? [B: $i] :
% 2.43/1.46 ( ( in @ Xx @ B )
% 2.43/1.46 & ( in @ B @ A ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(omega_type,type,
% 2.43/1.46 omega: $i ).
% 2.43/1.46
% 2.43/1.46 thf(omega0Ax_type,type,
% 2.43/1.46 omega0Ax: $o ).
% 2.43/1.46
% 2.43/1.46 thf(omega0Ax,definition,
% 2.43/1.46 ( omega0Ax
% 2.43/1.46 = ( in @ emptyset @ omega ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(omegaSAx_type,type,
% 2.43/1.46 omegaSAx: $o ).
% 2.43/1.46
% 2.43/1.46 thf(omegaSAx,definition,
% 2.43/1.46 ( omegaSAx
% 2.43/1.46 = ( ! [Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ omega )
% 2.43/1.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(omegaIndAx_type,type,
% 2.43/1.46 omegaIndAx: $o ).
% 2.43/1.46
% 2.43/1.46 thf(omegaIndAx,definition,
% 2.43/1.46 ( omegaIndAx
% 2.43/1.46 = ( ! [A: $i] :
% 2.43/1.46 ( ( ( in @ emptyset @ A )
% 2.43/1.46 & ! [Xx: $i] :
% 2.43/1.46 ( ( ( in @ Xx @ omega )
% 2.43/1.46 & ( in @ Xx @ A ) )
% 2.43/1.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.43/1.46 => ! [Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ omega )
% 2.43/1.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(replAx_type,type,
% 2.43/1.46 replAx: $o ).
% 2.43/1.46
% 2.43/1.46 thf(replAx,definition,
% 2.43/1.46 ( replAx
% 2.43/1.46 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.43/1.46 ( ! [Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ A )
% 2.43/1.46 => ( exu
% 2.43/1.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.43/1.46 => ? [B: $i] :
% 2.43/1.46 ! [Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ B )
% 2.43/1.46 <=> ? [Xy: $i] :
% 2.43/1.46 ( ( in @ Xy @ A )
% 2.43/1.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(foundationAx_type,type,
% 2.43/1.46 foundationAx: $o ).
% 2.43/1.46
% 2.43/1.46 thf(foundationAx,definition,
% 2.43/1.46 ( foundationAx
% 2.43/1.46 = ( ! [A: $i] :
% 2.43/1.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.43/1.46 => ? [B: $i] :
% 2.43/1.46 ( ( in @ B @ A )
% 2.43/1.46 & ~ ? [Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ B )
% 2.43/1.46 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(wellorderingAx_type,type,
% 2.43/1.46 wellorderingAx: $o ).
% 2.43/1.46
% 2.43/1.46 thf(wellorderingAx,definition,
% 2.43/1.46 ( wellorderingAx
% 2.43/1.46 = ( ! [A: $i] :
% 2.43/1.46 ? [B: $i] :
% 2.43/1.46 ( ! [C: $i] :
% 2.43/1.46 ( ( in @ C @ B )
% 2.43/1.46 => ! [Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ C )
% 2.43/1.46 => ( in @ Xx @ A ) ) )
% 2.43/1.46 & ! [Xx: $i,Xy: $i] :
% 2.43/1.46 ( ( ( in @ Xx @ A )
% 2.43/1.46 & ( in @ Xy @ A ) )
% 2.43/1.46 => ( ! [C: $i] :
% 2.43/1.46 ( ( in @ C @ B )
% 2.43/1.46 => ( ( in @ Xx @ C )
% 2.43/1.46 <=> ( in @ Xy @ C ) ) )
% 2.43/1.46 => ( Xx = Xy ) ) )
% 2.43/1.46 & ! [C: $i,D: $i] :
% 2.43/1.46 ( ( ( in @ C @ B )
% 2.43/1.46 & ( in @ D @ B ) )
% 2.43/1.46 => ( ! [Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ C )
% 2.43/1.46 => ( in @ Xx @ D ) )
% 2.43/1.46 | ! [Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ D )
% 2.43/1.46 => ( in @ Xx @ C ) ) ) )
% 2.43/1.46 & ! [C: $i] :
% 2.43/1.46 ( ( ! [Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ C )
% 2.43/1.46 => ( in @ Xx @ A ) )
% 2.43/1.46 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.43/1.46 => ? [D: $i,Xx: $i] :
% 2.43/1.46 ( ( in @ D @ B )
% 2.43/1.46 & ( in @ Xx @ C )
% 2.43/1.46 & ~ ? [Xy: $i] :
% 2.43/1.46 ( ( in @ Xy @ D )
% 2.43/1.46 & ( in @ Xy @ C ) )
% 2.43/1.46 & ! [E: $i] :
% 2.43/1.46 ( ( in @ E @ B )
% 2.43/1.46 => ( ! [Xy: $i] :
% 2.43/1.46 ( ( in @ Xy @ E )
% 2.43/1.46 => ( in @ Xy @ D ) )
% 2.43/1.46 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(descr_type,type,
% 2.43/1.46 descr: ( $i > $o ) > $i ).
% 2.43/1.46
% 2.43/1.46 thf(descrp_type,type,
% 2.43/1.46 descrp: $o ).
% 2.43/1.46
% 2.43/1.46 thf(descrp,definition,
% 2.43/1.46 ( descrp
% 2.43/1.46 = ( ! [Xphi: $i > $o] :
% 2.43/1.46 ( ( exu
% 2.43/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.43/1.46 => ( Xphi
% 2.43/1.46 @ ( descr
% 2.43/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(dsetconstr_type,type,
% 2.43/1.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.43/1.46
% 2.43/1.46 thf(dsetconstrI_type,type,
% 2.43/1.46 dsetconstrI: $o ).
% 2.43/1.46
% 2.43/1.46 thf(dsetconstrI,definition,
% 2.43/1.46 ( dsetconstrI
% 2.43/1.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ A )
% 2.43/1.46 => ( ( Xphi @ Xx )
% 2.43/1.46 => ( in @ Xx
% 2.43/1.46 @ ( dsetconstr @ A
% 2.43/1.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(dsetconstrEL_type,type,
% 2.43/1.46 dsetconstrEL: $o ).
% 2.43/1.46
% 2.43/1.46 thf(dsetconstrEL,definition,
% 2.43/1.46 ( dsetconstrEL
% 2.43/1.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.43/1.46 ( ( in @ Xx
% 2.43/1.46 @ ( dsetconstr @ A
% 2.43/1.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.43/1.46 => ( in @ Xx @ A ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(dsetconstrER_type,type,
% 2.43/1.46 dsetconstrER: $o ).
% 2.43/1.46
% 2.43/1.46 thf(dsetconstrER,definition,
% 2.43/1.46 ( dsetconstrER
% 2.43/1.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.43/1.46 ( ( in @ Xx
% 2.43/1.46 @ ( dsetconstr @ A
% 2.43/1.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.43/1.46 => ( Xphi @ Xx ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(exuE1_type,type,
% 2.43/1.46 exuE1: $o ).
% 2.43/1.46
% 2.43/1.46 thf(exuE1,definition,
% 2.43/1.46 ( exuE1
% 2.43/1.46 = ( ! [Xphi: $i > $o] :
% 2.43/1.46 ( ( exu
% 2.43/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.43/1.46 => ? [Xx: $i] :
% 2.43/1.46 ( ( Xphi @ Xx )
% 2.43/1.46 & ! [Xy: $i] :
% 2.43/1.46 ( ( Xphi @ Xy )
% 2.43/1.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(prop2set_type,type,
% 2.43/1.46 prop2set: $o > $i ).
% 2.43/1.46
% 2.43/1.46 thf(prop2setE_type,type,
% 2.43/1.46 prop2setE: $o ).
% 2.43/1.46
% 2.43/1.46 thf(prop2setE,definition,
% 2.43/1.46 ( prop2setE
% 2.43/1.46 = ( ! [Xphi: $o,Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.43/1.46 => Xphi ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(emptysetE_type,type,
% 2.43/1.46 emptysetE: $o ).
% 2.43/1.46
% 2.43/1.46 thf(emptysetE,definition,
% 2.43/1.46 ( emptysetE
% 2.43/1.46 = ( ! [Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ emptyset )
% 2.43/1.46 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(emptysetimpfalse_type,type,
% 2.43/1.46 emptysetimpfalse: $o ).
% 2.43/1.46
% 2.43/1.46 thf(emptysetimpfalse,definition,
% 2.43/1.46 ( emptysetimpfalse
% 2.43/1.46 = ( ! [Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ emptyset )
% 2.43/1.46 => $false ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(notinemptyset_type,type,
% 2.43/1.46 notinemptyset: $o ).
% 2.43/1.46
% 2.43/1.46 thf(notinemptyset,definition,
% 2.43/1.46 ( notinemptyset
% 2.43/1.46 = ( ! [Xx: $i] :
% 2.43/1.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(exuE3e_type,type,
% 2.43/1.46 exuE3e: $o ).
% 2.43/1.46
% 2.43/1.46 thf(exuE3e,definition,
% 2.43/1.46 ( exuE3e
% 2.43/1.46 = ( ! [Xphi: $i > $o] :
% 2.43/1.46 ( ( exu
% 2.43/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.43/1.46 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(setext_type,type,
% 2.43/1.46 setext: $o ).
% 2.43/1.46
% 2.43/1.46 thf(setext,definition,
% 2.43/1.46 ( setext
% 2.43/1.46 = ( ! [A: $i,B: $i] :
% 2.43/1.46 ( ! [Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ A )
% 2.43/1.46 => ( in @ Xx @ B ) )
% 2.43/1.46 => ( ! [Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ B )
% 2.43/1.46 => ( in @ Xx @ A ) )
% 2.43/1.46 => ( A = B ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(emptyI_type,type,
% 2.43/1.46 emptyI: $o ).
% 2.43/1.46
% 2.43/1.46 thf(emptyI,definition,
% 2.43/1.46 ( emptyI
% 2.43/1.46 = ( ! [A: $i] :
% 2.43/1.46 ( ! [Xx: $i] :
% 2.43/1.46 ~ ( in @ Xx @ A )
% 2.43/1.46 => ( A = emptyset ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(noeltsimpempty_type,type,
% 2.43/1.46 noeltsimpempty: $o ).
% 2.43/1.46
% 2.43/1.46 thf(noeltsimpempty,definition,
% 2.43/1.46 ( noeltsimpempty
% 2.43/1.46 = ( ! [A: $i] :
% 2.43/1.46 ( ! [Xx: $i] :
% 2.43/1.46 ~ ( in @ Xx @ A )
% 2.43/1.46 => ( A = emptyset ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(setbeta_type,type,
% 2.43/1.46 setbeta: $o ).
% 2.43/1.46
% 2.43/1.46 thf(setbeta,definition,
% 2.43/1.46 ( setbeta
% 2.43/1.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ A )
% 2.43/1.46 => ( ( in @ Xx
% 2.43/1.46 @ ( dsetconstr @ A
% 2.43/1.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.43/1.46 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(nonempty_type,type,
% 2.43/1.46 nonempty: $i > $o ).
% 2.43/1.46
% 2.43/1.46 thf(nonempty,definition,
% 2.43/1.46 ( nonempty
% 2.43/1.46 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(nonemptyE1_type,type,
% 2.43/1.46 nonemptyE1: $o ).
% 2.43/1.46
% 2.43/1.46 thf(nonemptyE1,definition,
% 2.43/1.46 ( nonemptyE1
% 2.43/1.46 = ( ! [A: $i] :
% 2.43/1.46 ( ( nonempty @ A )
% 2.43/1.46 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(nonemptyI_type,type,
% 2.43/1.46 nonemptyI: $o ).
% 2.43/1.46
% 2.43/1.46 thf(nonemptyI,definition,
% 2.43/1.46 ( nonemptyI
% 2.43/1.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ A )
% 2.43/1.46 => ( ( Xphi @ Xx )
% 2.43/1.46 => ( nonempty
% 2.43/1.46 @ ( dsetconstr @ A
% 2.43/1.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(nonemptyI1_type,type,
% 2.43/1.46 nonemptyI1: $o ).
% 2.43/1.46
% 2.43/1.46 thf(nonemptyI1,definition,
% 2.43/1.46 ( nonemptyI1
% 2.43/1.46 = ( ! [A: $i] :
% 2.43/1.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.43/1.46 => ( nonempty @ A ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(setadjoinIL_type,type,
% 2.43/1.46 setadjoinIL: $o ).
% 2.43/1.46
% 2.43/1.46 thf(setadjoinIL,definition,
% 2.43/1.46 ( setadjoinIL
% 2.43/1.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(emptyinunitempty_type,type,
% 2.43/1.46 emptyinunitempty: $o ).
% 2.43/1.46
% 2.43/1.46 thf(emptyinunitempty,definition,
% 2.43/1.46 ( emptyinunitempty
% 2.43/1.46 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(setadjoinIR_type,type,
% 2.43/1.46 setadjoinIR: $o ).
% 2.43/1.46
% 2.43/1.46 thf(setadjoinIR,definition,
% 2.43/1.46 ( setadjoinIR
% 2.43/1.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.43/1.46 ( ( in @ Xy @ A )
% 2.43/1.46 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(setadjoinE_type,type,
% 2.43/1.46 setadjoinE: $o ).
% 2.43/1.46
% 2.43/1.46 thf(setadjoinE,definition,
% 2.43/1.46 ( setadjoinE
% 2.43/1.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.43/1.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.43/1.46 => ! [Xphi: $o] :
% 2.43/1.46 ( ( ( Xy = Xx )
% 2.43/1.46 => Xphi )
% 2.43/1.46 => ( ( ( in @ Xy @ A )
% 2.43/1.46 => Xphi )
% 2.43/1.46 => Xphi ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(setadjoinOr_type,type,
% 2.43/1.46 setadjoinOr: $o ).
% 2.43/1.46
% 2.43/1.46 thf(setadjoinOr,definition,
% 2.43/1.46 ( setadjoinOr
% 2.43/1.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.43/1.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.43/1.46 => ( ( Xy = Xx )
% 2.43/1.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(setoftrueEq_type,type,
% 2.43/1.46 setoftrueEq: $o ).
% 2.43/1.46
% 2.43/1.46 thf(setoftrueEq,definition,
% 2.43/1.46 ( setoftrueEq
% 2.43/1.46 = ( ! [A: $i] :
% 2.43/1.46 ( ( dsetconstr @ A
% 2.43/1.46 @ ^ [Xx: $i] : $true )
% 2.43/1.46 = A ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(powersetI_type,type,
% 2.43/1.46 powersetI: $o ).
% 2.43/1.46
% 2.43/1.46 thf(powersetI,definition,
% 2.43/1.46 ( powersetI
% 2.43/1.46 = ( ! [A: $i,B: $i] :
% 2.43/1.46 ( ! [Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ B )
% 2.43/1.46 => ( in @ Xx @ A ) )
% 2.43/1.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(emptyinPowerset_type,type,
% 2.43/1.46 emptyinPowerset: $o ).
% 2.43/1.46
% 2.43/1.46 thf(emptyinPowerset,definition,
% 2.43/1.46 ( emptyinPowerset
% 2.43/1.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(emptyInPowerset_type,type,
% 2.43/1.46 emptyInPowerset: $o ).
% 2.43/1.46
% 2.43/1.46 thf(emptyInPowerset,definition,
% 2.43/1.46 ( emptyInPowerset
% 2.43/1.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(powersetE_type,type,
% 2.43/1.46 powersetE: $o ).
% 2.43/1.46
% 2.43/1.46 thf(powersetE,definition,
% 2.43/1.46 ( powersetE
% 2.43/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.43/1.46 ( ( in @ B @ ( powerset @ A ) )
% 2.43/1.46 => ( ( in @ Xx @ B )
% 2.43/1.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(setunionI_type,type,
% 2.43/1.46 setunionI: $o ).
% 2.43/1.46
% 2.43/1.46 thf(setunionI,definition,
% 2.43/1.46 ( setunionI
% 2.43/1.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.43/1.46 ( ( in @ Xx @ B )
% 2.43/1.46 => ( ( in @ B @ A )
% 2.43/1.46 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(setunionE_type,type,
% 2.43/1.46 setunionE: $o ).
% 2.43/1.46
% 2.43/1.46 thf(setunionE,definition,
% 2.43/1.46 ( setunionE
% 2.43/1.46 = ( ! [A: $i,Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ ( setunion @ A ) )
% 2.43/1.46 => ! [Xphi: $o] :
% 2.43/1.46 ( ! [B: $i] :
% 2.43/1.46 ( ( in @ Xx @ B )
% 2.43/1.46 => ( ( in @ B @ A )
% 2.43/1.46 => Xphi ) )
% 2.43/1.46 => Xphi ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(subPowSU_type,type,
% 2.43/1.46 subPowSU: $o ).
% 2.43/1.46
% 2.43/1.46 thf(subPowSU,definition,
% 2.43/1.46 ( subPowSU
% 2.43/1.46 = ( ! [A: $i,Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ A )
% 2.43/1.46 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(exuE2_type,type,
% 2.43/1.46 exuE2: $o ).
% 2.43/1.46
% 2.43/1.46 thf(exuE2,definition,
% 2.43/1.46 ( exuE2
% 2.43/1.46 = ( ! [Xphi: $i > $o] :
% 2.43/1.46 ( ( exu
% 2.43/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.43/1.46 => ? [Xx: $i] :
% 2.43/1.46 ! [Xy: $i] :
% 2.43/1.46 ( ( Xphi @ Xy )
% 2.43/1.46 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(nonemptyImpWitness_type,type,
% 2.43/1.46 nonemptyImpWitness: $o ).
% 2.43/1.46
% 2.43/1.46 thf(nonemptyImpWitness,definition,
% 2.43/1.46 ( nonemptyImpWitness
% 2.43/1.46 = ( ! [A: $i] :
% 2.43/1.46 ( ( nonempty @ A )
% 2.43/1.46 => ? [Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ A )
% 2.43/1.46 & $true ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(uniqinunit_type,type,
% 2.43/1.46 uniqinunit: $o ).
% 2.43/1.46
% 2.43/1.46 thf(uniqinunit,definition,
% 2.43/1.46 ( uniqinunit
% 2.43/1.46 = ( ! [Xx: $i,Xy: $i] :
% 2.43/1.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.43/1.46 => ( Xx = Xy ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(notinsingleton_type,type,
% 2.43/1.46 notinsingleton: $o ).
% 2.43/1.46
% 2.43/1.46 thf(notinsingleton,definition,
% 2.43/1.46 ( notinsingleton
% 2.43/1.46 = ( ! [Xx: $i,Xy: $i] :
% 2.43/1.46 ( ( Xx != Xy )
% 2.43/1.46 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(eqinunit_type,type,
% 2.43/1.46 eqinunit: $o ).
% 2.43/1.46
% 2.43/1.46 thf(eqinunit,definition,
% 2.43/1.46 ( eqinunit
% 2.43/1.46 = ( ! [Xx: $i,Xy: $i] :
% 2.43/1.46 ( ( Xx = Xy )
% 2.43/1.46 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(singletonsswitch_type,type,
% 2.43/1.46 singletonsswitch: $o ).
% 2.43/1.46
% 2.43/1.46 thf(singletonsswitch,definition,
% 2.43/1.46 ( singletonsswitch
% 2.43/1.46 = ( ! [Xx: $i,Xy: $i] :
% 2.43/1.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.43/1.46 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(upairsetE_type,type,
% 2.43/1.46 upairsetE: $o ).
% 2.43/1.46
% 2.43/1.46 thf(upairsetE,definition,
% 2.43/1.46 ( upairsetE
% 2.43/1.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.43/1.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.43/1.46 => ( ( Xz = Xx )
% 2.43/1.46 | ( Xz = Xy ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(upairsetIL_type,type,
% 2.43/1.46 upairsetIL: $o ).
% 2.43/1.46
% 2.43/1.46 thf(upairsetIL,definition,
% 2.43/1.46 ( upairsetIL
% 2.43/1.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(upairsetIR_type,type,
% 2.43/1.46 upairsetIR: $o ).
% 2.43/1.46
% 2.43/1.46 thf(upairsetIR,definition,
% 2.43/1.46 ( upairsetIR
% 2.43/1.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(emptyE1_type,type,
% 2.43/1.46 emptyE1: $o ).
% 2.43/1.46
% 2.43/1.46 thf(emptyE1,definition,
% 2.43/1.46 ( emptyE1
% 2.43/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.43/1.46 ( ? [Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ A )
% 2.43/1.46 & ( Xphi @ Xx ) )
% 2.43/1.46 => ( ( ( dsetconstr @ A
% 2.43/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.43/1.46 = emptyset )
% 2.43/1.46 => $false ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(vacuousDall_type,type,
% 2.43/1.46 vacuousDall: $o ).
% 2.43/1.46
% 2.43/1.46 thf(vacuousDall,definition,
% 2.43/1.46 ( vacuousDall
% 2.43/1.46 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ emptyset )
% 2.43/1.46 => ( Xphi @ Xx ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(quantDeMorgan1_type,type,
% 2.43/1.46 quantDeMorgan1: $o ).
% 2.43/1.46
% 2.43/1.46 thf(quantDeMorgan1,definition,
% 2.43/1.46 ( quantDeMorgan1
% 2.43/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.43/1.46 ( ~ ! [Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ A )
% 2.43/1.46 => ( Xphi @ Xx ) )
% 2.43/1.46 => ? [Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ A )
% 2.43/1.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(quantDeMorgan2_type,type,
% 2.43/1.46 quantDeMorgan2: $o ).
% 2.43/1.46
% 2.43/1.46 thf(quantDeMorgan2,definition,
% 2.43/1.46 ( quantDeMorgan2
% 2.43/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.43/1.46 ( ! [Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ A )
% 2.43/1.46 => ~ ( Xphi @ Xx ) )
% 2.43/1.46 => ~ ? [Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ A )
% 2.43/1.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(quantDeMorgan3_type,type,
% 2.43/1.46 quantDeMorgan3: $o ).
% 2.43/1.46
% 2.43/1.46 thf(quantDeMorgan3,definition,
% 2.43/1.46 ( quantDeMorgan3
% 2.43/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.43/1.46 ( ~ ? [Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ A )
% 2.43/1.46 & ( Xphi @ Xx ) )
% 2.43/1.46 => ! [Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ A )
% 2.43/1.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(quantDeMorgan4_type,type,
% 2.43/1.46 quantDeMorgan4: $o ).
% 2.43/1.46
% 2.43/1.46 thf(quantDeMorgan4,definition,
% 2.43/1.46 ( quantDeMorgan4
% 2.43/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.43/1.46 ( ? [Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ A )
% 2.43/1.46 & ~ ( Xphi @ Xx ) )
% 2.43/1.46 => ~ ! [Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ A )
% 2.43/1.46 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(prop2setI_type,type,
% 2.43/1.46 prop2setI: $o ).
% 2.43/1.46
% 2.43/1.46 thf(prop2setI,definition,
% 2.43/1.46 ( prop2setI
% 2.43/1.46 = ( ! [Xphi: $o] :
% 2.43/1.46 ( Xphi
% 2.43/1.46 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(set2prop_type,type,
% 2.43/1.46 set2prop: $i > $o ).
% 2.43/1.46
% 2.43/1.46 thf(prop2set2propI_type,type,
% 2.43/1.46 prop2set2propI: $o ).
% 2.43/1.46
% 2.43/1.46 thf(prop2set2propI,definition,
% 2.43/1.46 ( prop2set2propI
% 2.43/1.46 = ( ! [Xphi: $o] :
% 2.43/1.46 ( Xphi
% 2.43/1.46 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(notdexE_type,type,
% 2.43/1.46 notdexE: $o ).
% 2.43/1.46
% 2.43/1.46 thf(notdexE,definition,
% 2.43/1.46 ( notdexE
% 2.43/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.43/1.46 ( ~ ? [Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ A )
% 2.43/1.46 & ( Xphi @ Xx ) )
% 2.43/1.46 => ! [Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ A )
% 2.43/1.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(notdallE_type,type,
% 2.43/1.46 notdallE: $o ).
% 2.43/1.46
% 2.43/1.46 thf(notdallE,definition,
% 2.43/1.46 ( notdallE
% 2.43/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.43/1.46 ( ~ ! [Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ A )
% 2.43/1.46 => ( Xphi @ Xx ) )
% 2.43/1.46 => ? [Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ A )
% 2.43/1.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(exuI1_type,type,
% 2.43/1.46 exuI1: $o ).
% 2.43/1.46
% 2.43/1.46 thf(exuI1,definition,
% 2.43/1.46 ( exuI1
% 2.43/1.46 = ( ! [Xphi: $i > $o] :
% 2.43/1.46 ( ? [Xx: $i] :
% 2.43/1.46 ( ( Xphi @ Xx )
% 2.43/1.46 & ! [Xy: $i] :
% 2.43/1.46 ( ( Xphi @ Xy )
% 2.43/1.46 => ( Xx = Xy ) ) )
% 2.43/1.46 => ( exu
% 2.43/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(exuI3_type,type,
% 2.43/1.46 exuI3: $o ).
% 2.43/1.46
% 2.43/1.46 thf(exuI3,definition,
% 2.43/1.46 ( exuI3
% 2.43/1.46 = ( ! [Xphi: $i > $o] :
% 2.43/1.46 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.43/1.46 => ( ! [Xx: $i,Xy: $i] :
% 2.43/1.46 ( ( Xphi @ Xx )
% 2.43/1.46 => ( ( Xphi @ Xy )
% 2.43/1.46 => ( Xx = Xy ) ) )
% 2.43/1.46 => ( exu
% 2.43/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(exuI2_type,type,
% 2.43/1.46 exuI2: $o ).
% 2.43/1.46
% 2.43/1.46 thf(exuI2,definition,
% 2.43/1.46 ( exuI2
% 2.43/1.46 = ( ! [Xphi: $i > $o] :
% 2.43/1.46 ( ? [Xx: $i] :
% 2.43/1.46 ! [Xy: $i] :
% 2.43/1.46 ( ( Xphi @ Xy )
% 2.43/1.46 <=> ( Xy = Xx ) )
% 2.43/1.46 => ( exu
% 2.43/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(inCongP_type,type,
% 2.43/1.46 inCongP: $o ).
% 2.43/1.46
% 2.43/1.46 thf(inCongP,definition,
% 2.43/1.46 ( inCongP
% 2.43/1.46 = ( ! [A: $i,B: $i] :
% 2.43/1.46 ( ( A = B )
% 2.43/1.46 => ! [Xx: $i,Xy: $i] :
% 2.43/1.46 ( ( Xx = Xy )
% 2.43/1.46 => ( ( in @ Xx @ A )
% 2.43/1.46 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(in__Cong_type,type,
% 2.43/1.46 in__Cong: $o ).
% 2.43/1.46
% 2.43/1.46 thf(in__Cong,definition,
% 2.43/1.46 ( in__Cong
% 2.43/1.46 = ( ! [A: $i,B: $i] :
% 2.43/1.46 ( ( A = B )
% 2.43/1.46 => ! [Xx: $i,Xy: $i] :
% 2.43/1.46 ( ( Xx = Xy )
% 2.43/1.46 => ( ( in @ Xx @ A )
% 2.43/1.46 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(exuE3u_type,type,
% 2.43/1.46 exuE3u: $o ).
% 2.43/1.46
% 2.43/1.46 thf(exuE3u,definition,
% 2.43/1.46 ( exuE3u
% 2.43/1.46 = ( ! [Xphi: $i > $o] :
% 2.43/1.46 ( ( exu
% 2.43/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.43/1.46 => ! [Xx: $i,Xy: $i] :
% 2.43/1.46 ( ( Xphi @ Xx )
% 2.43/1.46 => ( ( Xphi @ Xy )
% 2.43/1.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(exu__Cong_type,type,
% 2.43/1.46 exu__Cong: $o ).
% 2.43/1.46
% 2.43/1.46 thf(exu__Cong,definition,
% 2.43/1.46 ( exu__Cong
% 2.43/1.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.43/1.46 ( ! [Xx: $i,Xy: $i] :
% 2.43/1.46 ( ( Xx = Xy )
% 2.43/1.46 => ( ( Xphi @ Xx )
% 2.43/1.46 <=> ( Xpsi @ Xy ) ) )
% 2.43/1.46 => ( ( exu
% 2.43/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.43/1.46 <=> ( exu
% 2.43/1.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(emptyset__Cong_type,type,
% 2.43/1.46 emptyset__Cong: $o ).
% 2.43/1.46
% 2.43/1.46 thf(emptyset__Cong,definition,
% 2.43/1.46 ( emptyset__Cong
% 2.43/1.46 = ( emptyset = emptyset ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(setadjoin__Cong_type,type,
% 2.43/1.46 setadjoin__Cong: $o ).
% 2.43/1.46
% 2.43/1.46 thf(setadjoin__Cong,definition,
% 2.43/1.46 ( setadjoin__Cong
% 2.43/1.46 = ( ! [Xx: $i,Xy: $i] :
% 2.43/1.46 ( ( Xx = Xy )
% 2.43/1.46 => ! [Xz: $i,Xu: $i] :
% 2.43/1.46 ( ( Xz = Xu )
% 2.43/1.46 => ( ( setadjoin @ Xx @ Xz )
% 2.43/1.46 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(powerset__Cong_type,type,
% 2.43/1.46 powerset__Cong: $o ).
% 2.43/1.46
% 2.43/1.46 thf(powerset__Cong,definition,
% 2.43/1.46 ( powerset__Cong
% 2.43/1.46 = ( ! [A: $i,B: $i] :
% 2.43/1.46 ( ( A = B )
% 2.43/1.46 => ( ( powerset @ A )
% 2.43/1.46 = ( powerset @ B ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(setunion__Cong_type,type,
% 2.43/1.46 setunion__Cong: $o ).
% 2.43/1.46
% 2.43/1.46 thf(setunion__Cong,definition,
% 2.43/1.46 ( setunion__Cong
% 2.43/1.46 = ( ! [A: $i,B: $i] :
% 2.43/1.46 ( ( A = B )
% 2.43/1.46 => ( ( setunion @ A )
% 2.43/1.46 = ( setunion @ B ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(omega__Cong_type,type,
% 2.43/1.46 omega__Cong: $o ).
% 2.43/1.46
% 2.43/1.46 thf(omega__Cong,definition,
% 2.43/1.46 ( omega__Cong
% 2.43/1.46 = ( omega = omega ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(exuEu_type,type,
% 2.43/1.46 exuEu: $o ).
% 2.43/1.46
% 2.43/1.46 thf(exuEu,definition,
% 2.43/1.46 ( exuEu
% 2.43/1.46 = ( ! [Xphi: $i > $o] :
% 2.43/1.46 ( ( exu
% 2.43/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.43/1.46 => ! [Xx: $i,Xy: $i] :
% 2.43/1.46 ( ( Xphi @ Xx )
% 2.43/1.46 => ( ( Xphi @ Xy )
% 2.43/1.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(descr__Cong_type,type,
% 2.43/1.46 descr__Cong: $o ).
% 2.43/1.46
% 2.43/1.46 thf(descr__Cong,definition,
% 2.43/1.46 ( descr__Cong
% 2.43/1.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.43/1.46 ( ! [Xx: $i,Xy: $i] :
% 2.43/1.46 ( ( Xx = Xy )
% 2.43/1.46 => ( ( Xphi @ Xx )
% 2.43/1.46 <=> ( Xpsi @ Xy ) ) )
% 2.43/1.46 => ( ( exu
% 2.43/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.43/1.46 => ( ( exu
% 2.43/1.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.43/1.46 => ( ( descr
% 2.43/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.43/1.46 = ( descr
% 2.43/1.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(dsetconstr__Cong_type,type,
% 2.43/1.46 dsetconstr__Cong: $o ).
% 2.43/1.46
% 2.43/1.46 thf(dsetconstr__Cong,definition,
% 2.43/1.46 ( dsetconstr__Cong
% 2.43/1.46 = ( ! [A: $i,B: $i] :
% 2.43/1.46 ( ( A = B )
% 2.43/1.46 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.43/1.46 ( ! [Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ A )
% 2.43/1.46 => ! [Xy: $i] :
% 2.43/1.46 ( ( in @ Xy @ B )
% 2.43/1.46 => ( ( Xx = Xy )
% 2.43/1.46 => ( ( Xphi @ Xx )
% 2.43/1.46 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.43/1.46 => ( ( dsetconstr @ A
% 2.43/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.43/1.46 = ( dsetconstr @ B
% 2.43/1.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(subset_type,type,
% 2.43/1.46 subset: $i > $i > $o ).
% 2.43/1.46
% 2.43/1.46 thf(disjoint_type,type,
% 2.43/1.46 disjoint: $i > $i > $o ).
% 2.43/1.46
% 2.43/1.46 thf(setsmeet_type,type,
% 2.43/1.46 setsmeet: $i > $i > $o ).
% 2.43/1.46
% 2.43/1.46 thf(subsetI1_type,type,
% 2.43/1.46 subsetI1: $o ).
% 2.43/1.46
% 2.43/1.46 thf(subsetI1,definition,
% 2.43/1.46 ( subsetI1
% 2.43/1.46 = ( ! [A: $i,B: $i] :
% 2.43/1.46 ( ! [Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ A )
% 2.43/1.46 => ( in @ Xx @ B ) )
% 2.43/1.46 => ( subset @ A @ B ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(eqimpsubset2_type,type,
% 2.43/1.46 eqimpsubset2: $o ).
% 2.43/1.46
% 2.43/1.46 thf(eqimpsubset2,definition,
% 2.43/1.46 ( eqimpsubset2
% 2.43/1.46 = ( ! [A: $i,B: $i] :
% 2.43/1.46 ( ( A = B )
% 2.43/1.46 => ( subset @ B @ A ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(eqimpsubset1_type,type,
% 2.43/1.46 eqimpsubset1: $o ).
% 2.43/1.46
% 2.43/1.46 thf(eqimpsubset1,definition,
% 2.43/1.46 ( eqimpsubset1
% 2.43/1.46 = ( ! [A: $i,B: $i] :
% 2.43/1.46 ( ( A = B )
% 2.43/1.46 => ( subset @ A @ B ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(subsetI2_type,type,
% 2.43/1.46 subsetI2: $o ).
% 2.43/1.46
% 2.43/1.46 thf(subsetI2,definition,
% 2.43/1.46 ( subsetI2
% 2.43/1.46 = ( ! [A: $i,B: $i] :
% 2.43/1.46 ( ! [Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ A )
% 2.43/1.46 => ( in @ Xx @ B ) )
% 2.43/1.46 => ( subset @ A @ B ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(emptysetsubset_type,type,
% 2.43/1.46 emptysetsubset: $o ).
% 2.43/1.46
% 2.43/1.46 thf(emptysetsubset,definition,
% 2.43/1.46 ( emptysetsubset
% 2.43/1.46 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(subsetE_type,type,
% 2.43/1.46 subsetE: $o ).
% 2.43/1.46
% 2.43/1.46 thf(subsetE,definition,
% 2.43/1.46 ( subsetE
% 2.43/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.43/1.46 ( ( subset @ A @ B )
% 2.43/1.46 => ( ( in @ Xx @ A )
% 2.43/1.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(subsetE2_type,type,
% 2.43/1.46 subsetE2: $o ).
% 2.43/1.46
% 2.43/1.46 thf(subsetE2,definition,
% 2.43/1.46 ( subsetE2
% 2.43/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.43/1.46 ( ( subset @ A @ B )
% 2.43/1.46 => ( ~ ( in @ Xx @ B )
% 2.43/1.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(notsubsetI_type,type,
% 2.43/1.46 notsubsetI: $o ).
% 2.43/1.46
% 2.43/1.46 thf(notsubsetI,definition,
% 2.43/1.46 ( notsubsetI
% 2.43/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ A )
% 2.43/1.46 => ( ~ ( in @ Xx @ B )
% 2.43/1.46 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(notequalI1_type,type,
% 2.43/1.46 notequalI1: $o ).
% 2.43/1.46
% 2.43/1.46 thf(notequalI1,definition,
% 2.43/1.46 ( notequalI1
% 2.43/1.46 = ( ! [A: $i,B: $i] :
% 2.43/1.46 ( ~ ( subset @ A @ B )
% 2.43/1.46 => ( A != B ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(notequalI2_type,type,
% 2.43/1.46 notequalI2: $o ).
% 2.43/1.46
% 2.43/1.46 thf(notequalI2,definition,
% 2.43/1.46 ( notequalI2
% 2.43/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ A )
% 2.43/1.46 => ( ~ ( in @ Xx @ B )
% 2.43/1.46 => ( A != B ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(subsetRefl_type,type,
% 2.43/1.46 subsetRefl: $o ).
% 2.43/1.46
% 2.43/1.46 thf(subsetRefl,definition,
% 2.43/1.46 ( subsetRefl
% 2.43/1.46 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(subsetTrans_type,type,
% 2.43/1.46 subsetTrans: $o ).
% 2.43/1.46
% 2.43/1.46 thf(subsetTrans,definition,
% 2.43/1.46 ( subsetTrans
% 2.43/1.46 = ( ! [A: $i,B: $i,C: $i] :
% 2.43/1.46 ( ( subset @ A @ B )
% 2.43/1.46 => ( ( subset @ B @ C )
% 2.43/1.46 => ( subset @ A @ C ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(setadjoinSub_type,type,
% 2.43/1.46 setadjoinSub: $o ).
% 2.43/1.46
% 2.43/1.46 thf(setadjoinSub,definition,
% 2.43/1.46 ( setadjoinSub
% 2.43/1.46 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(setadjoinSub2_type,type,
% 2.43/1.46 setadjoinSub2: $o ).
% 2.43/1.46
% 2.43/1.46 thf(setadjoinSub2,definition,
% 2.43/1.46 ( setadjoinSub2
% 2.43/1.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.43/1.46 ( ( subset @ A @ B )
% 2.43/1.46 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(subset2powerset_type,type,
% 2.43/1.46 subset2powerset: $o ).
% 2.43/1.46
% 2.43/1.46 thf(subset2powerset,definition,
% 2.43/1.46 ( subset2powerset
% 2.43/1.46 = ( ! [A: $i,B: $i] :
% 2.43/1.46 ( ( subset @ A @ B )
% 2.43/1.46 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(setextsub_type,type,
% 2.43/1.46 setextsub: $o ).
% 2.43/1.46
% 2.43/1.46 thf(setextsub,definition,
% 2.43/1.46 ( setextsub
% 2.43/1.46 = ( ! [A: $i,B: $i] :
% 2.43/1.46 ( ( subset @ A @ B )
% 2.43/1.46 => ( ( subset @ B @ A )
% 2.43/1.46 => ( A = B ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(subsetemptysetimpeq_type,type,
% 2.43/1.46 subsetemptysetimpeq: $o ).
% 2.43/1.46
% 2.43/1.46 thf(subsetemptysetimpeq,definition,
% 2.43/1.46 ( subsetemptysetimpeq
% 2.43/1.46 = ( ! [A: $i] :
% 2.43/1.46 ( ( subset @ A @ emptyset )
% 2.43/1.46 => ( A = emptyset ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(powersetI1_type,type,
% 2.43/1.46 powersetI1: $o ).
% 2.43/1.46
% 2.43/1.46 thf(powersetI1,definition,
% 2.43/1.46 ( powersetI1
% 2.43/1.46 = ( ! [A: $i,B: $i] :
% 2.43/1.46 ( ( subset @ B @ A )
% 2.43/1.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(powersetE1_type,type,
% 2.43/1.46 powersetE1: $o ).
% 2.43/1.46
% 2.43/1.46 thf(powersetE1,definition,
% 2.43/1.46 ( powersetE1
% 2.43/1.46 = ( ! [A: $i,B: $i] :
% 2.43/1.46 ( ( in @ B @ ( powerset @ A ) )
% 2.43/1.46 => ( subset @ B @ A ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(inPowerset_type,type,
% 2.43/1.46 inPowerset: $o ).
% 2.43/1.46
% 2.43/1.46 thf(inPowerset,definition,
% 2.43/1.46 ( inPowerset
% 2.43/1.46 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(powersetsubset_type,type,
% 2.43/1.46 powersetsubset: $o ).
% 2.43/1.46
% 2.43/1.46 thf(powersetsubset,definition,
% 2.43/1.46 ( powersetsubset
% 2.43/1.46 = ( ! [A: $i,B: $i] :
% 2.43/1.46 ( ( subset @ A @ B )
% 2.43/1.46 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(sepInPowerset_type,type,
% 2.43/1.46 sepInPowerset: $o ).
% 2.43/1.46
% 2.43/1.46 thf(sepInPowerset,definition,
% 2.43/1.46 ( sepInPowerset
% 2.43/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.43/1.46 ( in
% 2.43/1.46 @ ( dsetconstr @ A
% 2.43/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.43/1.46 @ ( powerset @ A ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(sepSubset_type,type,
% 2.43/1.46 sepSubset: $o ).
% 2.43/1.46
% 2.43/1.46 thf(sepSubset,definition,
% 2.43/1.46 ( sepSubset
% 2.43/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.43/1.46 ( subset
% 2.43/1.46 @ ( dsetconstr @ A
% 2.43/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.43/1.46 @ A ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(binunion_type,type,
% 2.43/1.46 binunion: $i > $i > $i ).
% 2.43/1.46
% 2.43/1.46 thf(binunionIL_type,type,
% 2.43/1.46 binunionIL: $o ).
% 2.43/1.46
% 2.43/1.46 thf(binunionIL,definition,
% 2.43/1.46 ( binunionIL
% 2.43/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ A )
% 2.43/1.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(upairset2IR_type,type,
% 2.43/1.46 upairset2IR: $o ).
% 2.43/1.46
% 2.43/1.46 thf(upairset2IR,definition,
% 2.43/1.46 ( upairset2IR
% 2.43/1.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(binunionIR_type,type,
% 2.43/1.46 binunionIR: $o ).
% 2.43/1.46
% 2.43/1.46 thf(binunionIR,definition,
% 2.43/1.46 ( binunionIR
% 2.43/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ B )
% 2.43/1.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(binunionEcases_type,type,
% 2.43/1.46 binunionEcases: $o ).
% 2.43/1.46
% 2.43/1.46 thf(binunionEcases,definition,
% 2.43/1.46 ( binunionEcases
% 2.43/1.46 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.43/1.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.43/1.46 => ( ( ( in @ Xx @ A )
% 2.43/1.46 => Xphi )
% 2.43/1.46 => ( ( ( in @ Xx @ B )
% 2.43/1.46 => Xphi )
% 2.43/1.46 => Xphi ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(binunionE_type,type,
% 2.43/1.46 binunionE: $o ).
% 2.43/1.46
% 2.43/1.46 thf(binunionE,definition,
% 2.43/1.46 ( binunionE
% 2.43/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.43/1.46 => ( ( in @ Xx @ A )
% 2.43/1.46 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(binunionLsub_type,type,
% 2.43/1.46 binunionLsub: $o ).
% 2.43/1.46
% 2.43/1.46 thf(binunionLsub,definition,
% 2.43/1.46 ( binunionLsub
% 2.43/1.46 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(binunionRsub_type,type,
% 2.43/1.46 binunionRsub: $o ).
% 2.43/1.46
% 2.43/1.46 thf(binunionRsub,definition,
% 2.43/1.46 ( binunionRsub
% 2.43/1.46 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(binintersect_type,type,
% 2.43/1.46 binintersect: $i > $i > $i ).
% 2.43/1.46
% 2.43/1.46 thf(binintersectI_type,type,
% 2.43/1.46 binintersectI: $o ).
% 2.43/1.46
% 2.43/1.46 thf(binintersectI,definition,
% 2.43/1.46 ( binintersectI
% 2.43/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ A )
% 2.43/1.46 => ( ( in @ Xx @ B )
% 2.43/1.46 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(binintersectSubset5_type,type,
% 2.43/1.46 binintersectSubset5: $o ).
% 2.43/1.46
% 2.43/1.46 thf(binintersectSubset5,definition,
% 2.43/1.46 ( binintersectSubset5
% 2.43/1.46 = ( ! [A: $i,B: $i,C: $i] :
% 2.43/1.46 ( ( subset @ C @ A )
% 2.43/1.46 => ( ( subset @ C @ B )
% 2.43/1.46 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(binintersectEL_type,type,
% 2.43/1.46 binintersectEL: $o ).
% 2.43/1.46
% 2.43/1.46 thf(binintersectEL,definition,
% 2.43/1.46 ( binintersectEL
% 2.43/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.43/1.46 => ( in @ Xx @ A ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(binintersectLsub_type,type,
% 2.43/1.46 binintersectLsub: $o ).
% 2.43/1.46
% 2.43/1.46 thf(binintersectLsub,definition,
% 2.43/1.46 ( binintersectLsub
% 2.43/1.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(binintersectSubset2_type,type,
% 2.43/1.46 binintersectSubset2: $o ).
% 2.43/1.46
% 2.43/1.46 thf(binintersectSubset2,definition,
% 2.43/1.46 ( binintersectSubset2
% 2.43/1.46 = ( ! [A: $i,B: $i] :
% 2.43/1.46 ( ( subset @ A @ B )
% 2.43/1.46 => ( ( binintersect @ A @ B )
% 2.43/1.46 = A ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(binintersectSubset3_type,type,
% 2.43/1.46 binintersectSubset3: $o ).
% 2.43/1.46
% 2.43/1.46 thf(binintersectSubset3,definition,
% 2.43/1.46 ( binintersectSubset3
% 2.43/1.46 = ( ! [A: $i,B: $i] :
% 2.43/1.46 ( ( ( binintersect @ A @ B )
% 2.43/1.46 = B )
% 2.43/1.46 => ( subset @ B @ A ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(binintersectER_type,type,
% 2.43/1.46 binintersectER: $o ).
% 2.43/1.46
% 2.43/1.46 thf(binintersectER,definition,
% 2.43/1.46 ( binintersectER
% 2.43/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.43/1.46 => ( in @ Xx @ B ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(disjointsetsI1_type,type,
% 2.43/1.46 disjointsetsI1: $o ).
% 2.43/1.46
% 2.43/1.46 thf(disjointsetsI1,definition,
% 2.43/1.46 ( disjointsetsI1
% 2.43/1.46 = ( ! [A: $i,B: $i] :
% 2.43/1.46 ( ~ ? [Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ A )
% 2.43/1.46 & ( in @ Xx @ B ) )
% 2.43/1.46 => ( ( binintersect @ A @ B )
% 2.43/1.46 = emptyset ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(binintersectRsub_type,type,
% 2.43/1.46 binintersectRsub: $o ).
% 2.43/1.46
% 2.43/1.46 thf(binintersectRsub,definition,
% 2.43/1.46 ( binintersectRsub
% 2.43/1.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(binintersectSubset4_type,type,
% 2.43/1.46 binintersectSubset4: $o ).
% 2.43/1.46
% 2.43/1.46 thf(binintersectSubset4,definition,
% 2.43/1.46 ( binintersectSubset4
% 2.43/1.46 = ( ! [A: $i,B: $i] :
% 2.43/1.46 ( ( subset @ B @ A )
% 2.43/1.46 => ( ( binintersect @ A @ B )
% 2.43/1.46 = B ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(binintersectSubset1_type,type,
% 2.43/1.46 binintersectSubset1: $o ).
% 2.43/1.46
% 2.43/1.46 thf(binintersectSubset1,definition,
% 2.43/1.46 ( binintersectSubset1
% 2.43/1.46 = ( ! [A: $i,B: $i] :
% 2.43/1.46 ( ( ( binintersect @ A @ B )
% 2.43/1.46 = A )
% 2.43/1.46 => ( subset @ A @ B ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(bs114d_type,type,
% 2.43/1.46 bs114d: $o ).
% 2.43/1.46
% 2.43/1.46 thf(bs114d,definition,
% 2.43/1.46 ( bs114d
% 2.43/1.46 = ( ! [A: $i,B: $i,C: $i] :
% 2.43/1.46 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.43/1.46 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(regular_type,type,
% 2.43/1.46 regular: $i > $o ).
% 2.43/1.46
% 2.43/1.46 thf(setminus_type,type,
% 2.43/1.46 setminus: $i > $i > $i ).
% 2.43/1.46
% 2.43/1.46 thf(setminusI_type,type,
% 2.43/1.46 setminusI: $o ).
% 2.43/1.46
% 2.43/1.46 thf(setminusI,definition,
% 2.43/1.46 ( setminusI
% 2.43/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ A )
% 2.43/1.46 => ( ~ ( in @ Xx @ B )
% 2.43/1.46 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(setminusEL_type,type,
% 2.43/1.46 setminusEL: $o ).
% 2.43/1.46
% 2.43/1.46 thf(setminusEL,definition,
% 2.43/1.46 ( setminusEL
% 2.43/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.43/1.46 => ( in @ Xx @ A ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(setminusER_type,type,
% 2.43/1.46 setminusER: $o ).
% 2.43/1.46
% 2.43/1.46 thf(setminusER,definition,
% 2.43/1.46 ( setminusER
% 2.43/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.43/1.46 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(setminusSubset2_type,type,
% 2.43/1.46 setminusSubset2: $o ).
% 2.43/1.46
% 2.43/1.46 thf(setminusSubset2,definition,
% 2.43/1.46 ( setminusSubset2
% 2.43/1.46 = ( ! [A: $i,B: $i] :
% 2.43/1.46 ( ( subset @ A @ B )
% 2.43/1.46 => ( ( setminus @ A @ B )
% 2.43/1.46 = emptyset ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(setminusERneg_type,type,
% 2.43/1.46 setminusERneg: $o ).
% 2.43/1.46
% 2.43/1.46 thf(setminusERneg,definition,
% 2.43/1.46 ( setminusERneg
% 2.43/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.43/1.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.43/1.46 => ( ( in @ Xx @ A )
% 2.43/1.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(setminusELneg_type,type,
% 2.43/1.46 setminusELneg: $o ).
% 2.43/1.46
% 2.43/1.46 thf(setminusELneg,definition,
% 2.43/1.46 ( setminusELneg
% 2.43/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.43/1.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.43/1.46 => ( ~ ( in @ Xx @ B )
% 2.43/1.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(setminusILneg_type,type,
% 2.43/1.46 setminusILneg: $o ).
% 2.43/1.46
% 2.43/1.46 thf(setminusILneg,definition,
% 2.43/1.46 ( setminusILneg
% 2.43/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.43/1.46 ( ~ ( in @ Xx @ A )
% 2.43/1.46 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(setminusIRneg_type,type,
% 2.43/1.46 setminusIRneg: $o ).
% 2.43/1.46
% 2.43/1.46 thf(setminusIRneg,definition,
% 2.43/1.46 ( setminusIRneg
% 2.43/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ B )
% 2.43/1.46 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(setminusLsub_type,type,
% 2.43/1.46 setminusLsub: $o ).
% 2.43/1.46
% 2.43/1.46 thf(setminusLsub,definition,
% 2.43/1.46 ( setminusLsub
% 2.43/1.46 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(setminusSubset1_type,type,
% 2.43/1.46 setminusSubset1: $o ).
% 2.43/1.46
% 2.43/1.46 thf(setminusSubset1,definition,
% 2.43/1.46 ( setminusSubset1
% 2.43/1.46 = ( ! [A: $i,B: $i] :
% 2.43/1.46 ( ( ( setminus @ A @ B )
% 2.43/1.46 = emptyset )
% 2.43/1.46 => ( subset @ A @ B ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(symdiff_type,type,
% 2.43/1.46 symdiff: $i > $i > $i ).
% 2.43/1.46
% 2.43/1.46 thf(symdiff,definition,
% 2.43/1.46 ( symdiff
% 2.43/1.46 = ( ^ [A: $i,B: $i] :
% 2.43/1.46 ( dsetconstr @ ( binunion @ A @ B )
% 2.43/1.46 @ ^ [Xx: $i] :
% 2.43/1.46 ( ~ ( in @ Xx @ A )
% 2.43/1.46 | ~ ( in @ Xx @ B ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(symdiffE_type,type,
% 2.43/1.46 symdiffE: $o ).
% 2.43/1.46
% 2.43/1.46 thf(symdiffE,definition,
% 2.43/1.46 ( symdiffE
% 2.43/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.43/1.46 => ! [Xphi: $o] :
% 2.43/1.46 ( ( ( in @ Xx @ A )
% 2.43/1.46 => ( ~ ( in @ Xx @ B )
% 2.43/1.46 => Xphi ) )
% 2.43/1.46 => ( ( ~ ( in @ Xx @ A )
% 2.43/1.46 => ( ( in @ Xx @ B )
% 2.43/1.46 => Xphi ) )
% 2.43/1.46 => Xphi ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(symdiffI1_type,type,
% 2.43/1.46 symdiffI1: $o ).
% 2.43/1.46
% 2.43/1.46 thf(symdiffI1,definition,
% 2.43/1.46 ( symdiffI1
% 2.43/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.43/1.46 ( ( in @ Xx @ A )
% 2.43/1.46 => ( ~ ( in @ Xx @ B )
% 2.43/1.46 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.43/1.46
% 2.43/1.46 thf(symdiffI2,conjecture,
% 2.43/1.46 ( setextAx
% 2.43/1.46 => ( emptysetAx
% 2.43/1.46 => ( setadjoinAx
% 2.43/1.46 => ( powersetAx
% 2.43/1.46 => ( setunionAx
% 2.43/1.46 => ( omega0Ax
% 2.43/1.46 => ( omegaSAx
% 2.43/1.46 => ( omegaIndAx
% 2.43/1.46 => ( replAx
% 2.43/1.46 => ( foundationAx
% 2.43/1.46 => ( wellorderingAx
% 2.43/1.46 => ( descrp
% 2.43/1.46 => ( dsetconstrI
% 2.43/1.46 => ( dsetconstrEL
% 2.43/1.46 => ( dsetconstrER
% 2.43/1.46 => ( exuE1
% 2.43/1.46 => ( prop2setE
% 2.43/1.46 => ( emptysetE
% 2.43/1.46 => ( emptysetimpfalse
% 2.43/1.46 => ( notinemptyset
% 2.43/1.46 => ( exuE3e
% 2.43/1.46 => ( setext
% 2.43/1.46 => ( emptyI
% 2.43/1.46 => ( noeltsimpempty
% 2.43/1.46 => ( setbeta
% 2.43/1.46 => ( nonemptyE1
% 2.43/1.46 => ( nonemptyI
% 2.43/1.46 => ( nonemptyI1
% 2.43/1.46 => ( setadjoinIL
% 2.43/1.46 => ( emptyinunitempty
% 2.43/1.46 => ( setadjoinIR
% 2.43/1.46 => ( setadjoinE
% 2.43/1.46 => ( setadjoinOr
% 2.43/1.46 => ( setoftrueEq
% 2.43/1.46 => ( powersetI
% 2.43/1.46 => ( emptyinPowerset
% 2.43/1.46 => ( emptyInPowerset
% 2.43/1.46 => ( powersetE
% 2.43/1.46 => ( setunionI
% 2.43/1.46 => ( setunionE
% 2.43/1.46 => ( subPowSU
% 2.43/1.46 => ( exuE2
% 2.43/1.46 => ( nonemptyImpWitness
% 2.43/1.46 => ( uniqinunit
% 2.43/1.46 => ( notinsingleton
% 2.43/1.46 => ( eqinunit
% 2.43/1.46 => ( singletonsswitch
% 2.43/1.46 => ( upairsetE
% 2.43/1.46 => ( upairsetIL
% 2.43/1.46 => ( upairsetIR
% 2.43/1.46 => ( emptyE1
% 2.43/1.46 => ( vacuousDall
% 2.43/1.46 => ( quantDeMorgan1
% 2.43/1.46 => ( quantDeMorgan2
% 2.43/1.46 => ( quantDeMorgan3
% 2.43/1.46 => ( quantDeMorgan4
% 2.43/1.46 => ( prop2setI
% 2.43/1.46 => ( prop2set2propI
% 2.43/1.46 => ( notdexE
% 2.43/1.46 => ( notdallE
% 2.43/1.46 => ( exuI1
% 2.43/1.46 => ( exuI3
% 2.43/1.46 => ( exuI2
% 2.43/1.46 => ( inCongP
% 2.43/1.46 => ( in__Cong
% 2.43/1.46 => ( exuE3u
% 2.43/1.46 => ( exu__Cong
% 2.43/1.46 => ( emptyset__Cong
% 2.43/1.46 => ( setadjoin__Cong
% 2.43/1.46 => ( powerset__Cong
% 2.43/1.46 => ( setunion__Cong
% 2.43/1.46 => ( omega__Cong
% 2.43/1.46 => ( exuEu
% 2.43/1.46 => ( descr__Cong
% 2.43/1.46 => ( dsetconstr__Cong
% 2.43/1.46 => ( subsetI1
% 2.43/1.46 => ( eqimpsubset2
% 2.43/1.46 => ( eqimpsubset1
% 2.43/1.46 => ( subsetI2
% 2.43/1.46 => ( emptysetsubset
% 2.43/1.46 => ( subsetE
% 2.43/1.46 => ( subsetE2
% 2.43/1.46 => ( notsubsetI
% 2.43/1.46 => ( notequalI1
% 2.43/1.46 => ( notequalI2
% 2.43/1.46 => ( subsetRefl
% 2.43/1.46 => ( subsetTrans
% 2.43/1.47 => ( setadjoinSub
% 2.43/1.47 => ( setadjoinSub2
% 2.43/1.47 => ( subset2powerset
% 2.43/1.47 => ( setextsub
% 2.43/1.47 => ( subsetemptysetimpeq
% 2.43/1.47 => ( powersetI1
% 2.43/1.47 => ( powersetE1
% 2.43/1.47 => ( inPowerset
% 2.43/1.47 => ( powersetsubset
% 2.43/1.47 => ( sepInPowerset
% 2.43/1.47 => ( sepSubset
% 2.43/1.47 => ( binunionIL
% 2.43/1.47 => ( upairset2IR
% 2.43/1.47 => ( binunionIR
% 2.43/1.47 => ( binunionEcases
% 2.43/1.47 => ( binunionE
% 2.43/1.47 => ( binunionLsub
% 2.43/1.47 => ( binunionRsub
% 2.43/1.47 => ( binintersectI
% 2.43/1.47 => ( binintersectSubset5
% 2.43/1.47 => ( binintersectEL
% 2.43/1.47 => ( binintersectLsub
% 2.43/1.47 => ( binintersectSubset2
% 2.43/1.47 => ( binintersectSubset3
% 2.43/1.47 => ( binintersectER
% 2.43/1.47 => ( disjointsetsI1
% 2.43/1.47 => ( binintersectRsub
% 2.43/1.47 => ( binintersectSubset4
% 2.43/1.47 => ( binintersectSubset1
% 2.43/1.47 => ( bs114d
% 2.43/1.47 => ( setminusI
% 2.43/1.47 => ( setminusEL
% 2.43/1.47 => ( setminusER
% 2.43/1.47 => ( setminusSubset2
% 2.43/1.47 => ( setminusERneg
% 2.43/1.47 => ( setminusELneg
% 2.43/1.47 => ( setminusILneg
% 2.43/1.47 => ( setminusIRneg
% 2.43/1.47 => ( setminusLsub
% 2.43/1.47 => ( setminusSubset1
% 2.43/1.47 => ( symdiffE
% 2.43/1.47 => ( symdiffI1
% 2.43/1.47 => ! [A: $i,B: $i,Xx: $i] :
% 2.43/1.47 ( ~ ( in @ Xx @ A )
% 2.43/1.47 => ( ( in @ Xx @ B )
% 2.43/1.47 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.43/1.47 ------------------------
% 2.43/1.48 % (23816)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_23484 for (2999ds/27Mi)
% 2.43/1.48 % (23818)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_23484 for (2999ds/2Mi)
% 2.43/1.48 % (23818)Instruction limit reached!
% 2.43/1.48 % (23818)------------------------------
% 2.43/1.48 % (23818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.48 % (23818)Termination reason: Unknown
% 2.43/1.48 % (23818)Termination phase: shuffling
% 2.43/1.48
% 2.43/1.48 % (23818)Memory used [KB]: 1279
% 2.43/1.48 % (23818)Time elapsed: 0.002 s
% 2.43/1.48 % (23818)Instructions burned: 3 (million)
% 2.43/1.48 % (23818)------------------------------
% 2.43/1.48 % (23818)------------------------------
% 2.43/1.49 % (23814)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23484 for (2999ds/183Mi)
% 2.43/1.49 % (23815)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_23484 for (2999ds/4Mi)
% 2.43/1.49 % (23819)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_23484 for (2999ds/275Mi)
% 2.43/1.49 % (23817)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23484 for (2999ds/2Mi)
% 2.43/1.49 % (23820)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23484 for (2999ds/18Mi)
% 2.43/1.49 % (23816)Instruction limit reached!
% 2.43/1.49 % (23816)------------------------------
% 2.43/1.49 % (23816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.49 % (23816)Termination reason: Unknown
% 2.43/1.49 % (23816)Termination phase: Preprocessing 1
% 2.43/1.49
% 2.43/1.49 % (23816)Memory used [KB]: 1663
% 2.43/1.49 % (23816)Time elapsed: 0.010 s
% 2.43/1.49 % (23816)Instructions burned: 31 (million)
% 2.43/1.49 % (23816)------------------------------
% 2.43/1.49 % (23816)------------------------------
% 2.43/1.49 % (23817)Instruction limit reached!
% 2.43/1.49 % (23817)------------------------------
% 2.43/1.49 % (23817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.49 % (23817)Termination reason: Unknown
% 2.43/1.49 % (23817)Termination phase: shuffling
% 2.43/1.49
% 2.43/1.49 % (23817)Memory used [KB]: 1279
% 2.43/1.49 % (23817)Time elapsed: 0.004 s
% 2.43/1.49 % (23817)Instructions burned: 3 (million)
% 2.43/1.49 % (23817)------------------------------
% 2.43/1.49 % (23817)------------------------------
% 2.43/1.49 % (23815)Instruction limit reached!
% 2.43/1.49 % (23815)------------------------------
% 2.43/1.49 % (23815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.49 % (23815)Termination reason: Unknown
% 2.43/1.49 % (23815)Termination phase: shuffling
% 2.43/1.49
% 2.43/1.49 % (23815)Memory used [KB]: 1279
% 2.43/1.49 % (23815)Time elapsed: 0.005 s
% 2.43/1.49 % (23815)Instructions burned: 5 (million)
% 2.43/1.49 % (23815)------------------------------
% 2.43/1.49 % (23815)------------------------------
% 2.43/1.49 % (23821)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_23484 for (2999ds/3Mi)
% 2.43/1.50 % (23821)Instruction limit reached!
% 2.43/1.50 % (23821)------------------------------
% 2.43/1.50 % (23821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.50 % (23821)Termination reason: Unknown
% 2.43/1.50 % (23821)Termination phase: shuffling
% 2.43/1.50
% 2.43/1.50 % (23821)Memory used [KB]: 1279
% 2.43/1.50 % (23821)Time elapsed: 0.003 s
% 2.43/1.50 % (23821)Instructions burned: 4 (million)
% 2.43/1.50 % (23821)------------------------------
% 2.43/1.50 % (23821)------------------------------
% 2.54/1.50 % (23822)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_23484 for (2999ds/37Mi)
% 2.54/1.50 % (23820)Instruction limit reached!
% 2.54/1.50 % (23820)------------------------------
% 2.54/1.50 % (23820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.50 % (23820)Termination reason: Unknown
% 2.54/1.50 % (23820)Termination phase: Preprocessing 3
% 2.54/1.50
% 2.54/1.50 % (23820)Memory used [KB]: 1535
% 2.54/1.50 % (23820)Time elapsed: 0.013 s
% 2.54/1.50 % (23820)Instructions burned: 19 (million)
% 2.54/1.50 % (23820)------------------------------
% 2.54/1.50 % (23820)------------------------------
% 2.54/1.51 % (23825)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_23484 for (2999ds/1041Mi)
% 2.54/1.51 % (23823)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_23484 for (2999ds/15Mi)
% 2.54/1.51 % (23824)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_23484 for (2999ds/3Mi)
% 2.54/1.51 % (23822)Instruction limit reached!
% 2.54/1.51 % (23822)------------------------------
% 2.54/1.51 % (23822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.51 % (23822)Termination reason: Unknown
% 2.54/1.51 % (23822)Termination phase: Property scanning
% 2.54/1.51
% 2.54/1.51 % (23822)Memory used [KB]: 1663
% 2.54/1.51 % (23822)Time elapsed: 0.011 s
% 2.54/1.51 % (23822)Instructions burned: 39 (million)
% 2.54/1.51 % (23822)------------------------------
% 2.54/1.51 % (23822)------------------------------
% 2.54/1.51 % (23824)Instruction limit reached!
% 2.54/1.51 % (23824)------------------------------
% 2.54/1.51 % (23824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.51 % (23824)Termination reason: Unknown
% 2.54/1.51 % (23824)Termination phase: shuffling
% 2.54/1.51
% 2.54/1.51 % (23824)Memory used [KB]: 1151
% 2.54/1.51 % (23824)Time elapsed: 0.003 s
% 2.54/1.51 % (23824)Instructions burned: 3 (million)
% 2.54/1.51 % (23824)------------------------------
% 2.54/1.51 % (23824)------------------------------
% 2.54/1.52 % (23823)Instruction limit reached!
% 2.54/1.52 % (23823)------------------------------
% 2.54/1.52 % (23823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.52 % (23823)Termination reason: Unknown
% 2.54/1.52 % (23823)Termination phase: Preprocessing 1
% 2.54/1.52
% 2.54/1.52 % (23823)Memory used [KB]: 1407
% 2.54/1.52 % (23823)Time elapsed: 0.011 s
% 2.54/1.52 % (23823)Instructions burned: 16 (million)
% 2.54/1.52 % (23823)------------------------------
% 2.54/1.52 % (23823)------------------------------
% 2.54/1.52 % (23826)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_23484 for (2999ds/7Mi)
% 2.54/1.52 % (23827)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_23484 for (2999ds/16Mi)
% 2.54/1.52 % (23826)Instruction limit reached!
% 2.54/1.52 % (23826)------------------------------
% 2.54/1.52 % (23826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.52 % (23826)Termination reason: Unknown
% 2.54/1.52 % (23826)Termination phase: shuffling
% 2.54/1.52
% 2.54/1.52 % (23826)Memory used [KB]: 1279
% 2.54/1.52 % (23826)Time elapsed: 0.006 s
% 2.54/1.52 % (23826)Instructions burned: 8 (million)
% 2.54/1.52 % (23826)------------------------------
% 2.54/1.52 % (23826)------------------------------
% 2.54/1.52 % (23828)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_23484 for (2999ds/3Mi)
% 2.54/1.53 % (23827)Instruction limit reached!
% 2.54/1.53 % (23827)------------------------------
% 2.54/1.53 % (23827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.53 % (23827)Termination reason: Unknown
% 2.54/1.53 % (23827)Termination phase: shuffling
% 2.54/1.53
% 2.54/1.53 % (23827)Memory used [KB]: 1535
% 2.54/1.53 % (23827)Time elapsed: 0.006 s
% 2.54/1.53 % (23827)Instructions burned: 18 (million)
% 2.54/1.53 % (23827)------------------------------
% 2.54/1.53 % (23827)------------------------------
% 2.54/1.53 % (23828)Instruction limit reached!
% 2.54/1.53 % (23828)------------------------------
% 2.54/1.53 % (23828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.53 % (23828)Termination reason: Unknown
% 2.54/1.53 % (23828)Termination phase: shuffling
% 2.54/1.53
% 2.54/1.53 % (23828)Memory used [KB]: 1151
% 2.54/1.53 % (23828)Time elapsed: 0.002 s
% 2.54/1.53 % (23828)Instructions burned: 3 (million)
% 2.54/1.53 % (23828)------------------------------
% 2.54/1.53 % (23828)------------------------------
% 2.54/1.53 % (23832)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_23484 for (2999ds/4Mi)
% 2.54/1.54 % (23831)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_23484 for (2999ds/3Mi)
% 2.54/1.54 % (23832)Instruction limit reached!
% 2.54/1.54 % (23832)------------------------------
% 2.54/1.54 % (23832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.54 % (23832)Termination reason: Unknown
% 2.54/1.54 % (23832)Termination phase: shuffling
% 2.54/1.54
% 2.54/1.54 % (23832)Memory used [KB]: 1279
% 2.54/1.54 % (23832)Time elapsed: 0.002 s
% 2.54/1.54 % (23832)Instructions burned: 4 (million)
% 2.54/1.54 % (23832)------------------------------
% 2.54/1.54 % (23832)------------------------------
% 2.54/1.54 % (23831)Instruction limit reached!
% 2.54/1.54 % (23831)------------------------------
% 2.54/1.54 % (23831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.54 % (23831)Termination reason: Unknown
% 2.54/1.54 % (23831)Termination phase: shuffling
% 2.54/1.54
% 2.54/1.54 % (23831)Memory used [KB]: 1279
% 2.54/1.54 % (23831)Time elapsed: 0.002 s
% 2.54/1.54 % (23831)Instructions burned: 4 (million)
% 2.54/1.54 % (23831)------------------------------
% 2.54/1.54 % (23831)------------------------------
% 2.54/1.54 % (23829)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_23484 for (2999ds/3Mi)
% 2.54/1.54 % (23829)Instruction limit reached!
% 2.54/1.54 % (23829)------------------------------
% 2.54/1.54 % (23829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.54 % (23829)Termination reason: Unknown
% 2.54/1.54 % (23829)Termination phase: shuffling
% 2.54/1.54
% 2.54/1.54 % (23829)Memory used [KB]: 1279
% 2.54/1.54 % (23829)Time elapsed: 0.004 s
% 2.54/1.54 % (23829)Instructions burned: 4 (million)
% 2.54/1.54 % (23829)------------------------------
% 2.54/1.54 % (23829)------------------------------
% 2.54/1.54 % (23830)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_23484 for (2999ds/7Mi)
% 2.54/1.54 % (23830)Instruction limit reached!
% 2.54/1.54 % (23830)------------------------------
% 2.54/1.54 % (23830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.54 % (23830)Termination reason: Unknown
% 2.54/1.54 % (23830)Termination phase: shuffling
% 2.54/1.54
% 2.54/1.54 % (23830)Memory used [KB]: 1279
% 2.54/1.54 % (23830)Time elapsed: 0.006 s
% 2.54/1.54 % (23830)Instructions burned: 8 (million)
% 2.54/1.54 % (23830)------------------------------
% 2.54/1.54 % (23830)------------------------------
% 2.54/1.54 % (23833)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_23484 for (2999ds/18Mi)
% 2.54/1.55 % (23834)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_23484 for (2999ds/710Mi)
% 2.54/1.55 % (23833)Instruction limit reached!
% 2.54/1.55 % (23833)------------------------------
% 2.54/1.55 % (23833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.55 % (23833)Termination reason: Unknown
% 2.54/1.55 % (23833)Termination phase: shuffling
% 2.54/1.55
% 2.54/1.55 % (23833)Memory used [KB]: 1535
% 2.54/1.55 % (23833)Time elapsed: 0.006 s
% 2.54/1.55 % (23833)Instructions burned: 18 (million)
% 2.54/1.55 % (23833)------------------------------
% 2.54/1.55 % (23833)------------------------------
% 2.54/1.55 % (23835)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_23484 for (2999ds/6Mi)
% 2.54/1.55 % (23835)Instruction limit reached!
% 2.54/1.55 % (23835)------------------------------
% 2.54/1.55 % (23835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.55 % (23835)Termination reason: Unknown
% 2.54/1.55 % (23835)Termination phase: shuffling
% 2.54/1.55
% 2.54/1.55 % (23835)Memory used [KB]: 1279
% 2.54/1.55 % (23835)Time elapsed: 0.003 s
% 2.54/1.55 % (23835)Instructions burned: 7 (million)
% 2.54/1.55 % (23835)------------------------------
% 2.54/1.55 % (23835)------------------------------
% 2.54/1.56 % (23837)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_23484 for (2999ds/21Mi)
% 2.54/1.56 % (23836)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_23484 for (2999ds/902Mi)
% 2.54/1.56 % (23838)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_23484 for (2999ds/5Mi)
% 2.54/1.57 % (23837)Instruction limit reached!
% 2.54/1.57 % (23837)------------------------------
% 2.54/1.57 % (23837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.57 % (23837)Termination reason: Unknown
% 2.54/1.57 % (23837)Termination phase: Property scanning
% 2.54/1.57
% 2.54/1.57 % (23837)Memory used [KB]: 1663
% 2.54/1.57 % (23837)Time elapsed: 0.007 s
% 2.54/1.57 % (23837)Instructions burned: 22 (million)
% 2.54/1.57 % (23837)------------------------------
% 2.54/1.57 % (23837)------------------------------
% 2.54/1.57 % (23838)Instruction limit reached!
% 2.54/1.57 % (23838)------------------------------
% 2.54/1.57 % (23838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.57 % (23838)Termination reason: Unknown
% 2.54/1.57 % (23838)Termination phase: shuffling
% 2.54/1.57
% 2.54/1.57 % (23838)Memory used [KB]: 1279
% 2.54/1.57 % (23838)Time elapsed: 0.004 s
% 2.54/1.57 % (23838)Instructions burned: 8 (million)
% 2.54/1.57 % (23838)------------------------------
% 2.54/1.57 % (23838)------------------------------
% 2.54/1.57 % (23839)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_23484 for (2999ds/6Mi)
% 2.54/1.58 % (23840)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_23484 for (2999ds/377Mi)
% 2.54/1.58 % (23839)Instruction limit reached!
% 2.54/1.58 % (23839)------------------------------
% 2.54/1.58 % (23839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.58 % (23839)Termination reason: Unknown
% 2.54/1.58 % (23839)Termination phase: shuffling
% 2.54/1.58
% 2.54/1.58 % (23839)Memory used [KB]: 1279
% 2.54/1.58 % (23839)Time elapsed: 0.003 s
% 2.54/1.58 % (23839)Instructions burned: 8 (million)
% 2.54/1.58 % (23839)------------------------------
% 2.54/1.58 % (23839)------------------------------
% 2.54/1.59 % (23841)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_23484 for (2998ds/779Mi)
% 2.54/1.59 % (23814)Instruction limit reached!
% 2.54/1.59 % (23814)------------------------------
% 2.54/1.59 % (23814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.59 % (23814)Termination reason: Unknown
% 2.54/1.59 % (23814)Termination phase: Saturation
% 2.54/1.59
% 2.54/1.59 % (23814)Memory used [KB]: 7036
% 2.54/1.59 % (23814)Time elapsed: 0.099 s
% 2.54/1.59 % (23814)Instructions burned: 184 (million)
% 2.54/1.59 % (23814)------------------------------
% 2.54/1.59 % (23814)------------------------------
% 2.54/1.59 % (23819)Instruction limit reached!
% 2.54/1.59 % (23819)------------------------------
% 2.54/1.59 % (23819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.59 % (23819)Termination reason: Unknown
% 2.54/1.59 % (23819)Termination phase: Saturation
% 2.54/1.59
% 2.54/1.59 % (23819)Memory used [KB]: 7803
% 2.54/1.59 % (23819)Time elapsed: 0.101 s
% 2.54/1.59 % (23819)Instructions burned: 276 (million)
% 2.54/1.59 % (23819)------------------------------
% 2.54/1.59 % (23819)------------------------------
% 2.54/1.60 % (23843)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_23484 for (2998ds/879Mi)
% 2.54/1.60 % (23842)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_23484 for (2998ds/19Mi)
% 2.54/1.60 % (23842)Instruction limit reached!
% 2.54/1.60 % (23842)------------------------------
% 2.54/1.60 % (23842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.60 % (23842)Termination reason: Unknown
% 2.54/1.60 % (23842)Termination phase: shuffling
% 2.54/1.60
% 2.54/1.60 % (23842)Memory used [KB]: 1535
% 2.54/1.60 % (23842)Time elapsed: 0.007 s
% 2.54/1.60 % (23842)Instructions burned: 19 (million)
% 2.54/1.60 % (23842)------------------------------
% 2.54/1.60 % (23842)------------------------------
% 2.54/1.62 % (23844)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_23484 for (2998ds/17Mi)
% 2.54/1.62 % (23844)Instruction limit reached!
% 2.54/1.62 % (23844)------------------------------
% 2.54/1.62 % (23844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.62 % (23844)Termination reason: Unknown
% 2.54/1.62 % (23844)Termination phase: shuffling
% 2.54/1.62
% 2.54/1.62 % (23844)Memory used [KB]: 1535
% 2.54/1.62 % (23844)Time elapsed: 0.007 s
% 2.54/1.62 % (23844)Instructions burned: 18 (million)
% 2.54/1.62 % (23844)------------------------------
% 2.54/1.62 % (23844)------------------------------
% 2.54/1.63 % (23845)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_23484 for (2998ds/3Mi)
% 2.54/1.63 % (23845)Instruction limit reached!
% 2.54/1.63 % (23845)------------------------------
% 2.54/1.63 % (23845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.63 % (23845)Termination reason: Unknown
% 2.54/1.63 % (23845)Termination phase: shuffling
% 2.54/1.63
% 2.54/1.63 % (23845)Memory used [KB]: 1279
% 2.54/1.63 % (23845)Time elapsed: 0.003 s
% 2.54/1.63 % (23845)Instructions burned: 4 (million)
% 2.54/1.63 % (23845)------------------------------
% 2.54/1.63 % (23845)------------------------------
% 2.54/1.64 % (23846)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_23484 for (2998ds/30Mi)
% 2.54/1.65 % (23846)Instruction limit reached!
% 2.54/1.65 % (23846)------------------------------
% 2.54/1.65 % (23846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.65 % (23846)Termination reason: Unknown
% 2.54/1.65 % (23846)Termination phase: Property scanning
% 2.54/1.65
% 2.54/1.65 % (23846)Memory used [KB]: 1663
% 2.54/1.65 % (23846)Time elapsed: 0.011 s
% 2.54/1.65 % (23846)Instructions burned: 32 (million)
% 2.54/1.65 % (23846)------------------------------
% 2.54/1.65 % (23846)------------------------------
% 2.54/1.66 % (23847)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_23484 for (2998ds/127Mi)
% 2.54/1.70 % (23840)Instruction limit reached!
% 2.54/1.70 % (23840)------------------------------
% 2.54/1.70 % (23840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.70 % (23840)Termination reason: Unknown
% 2.54/1.70 % (23840)Termination phase: Saturation
% 2.54/1.70
% 2.54/1.70 % (23840)Memory used [KB]: 7291
% 2.54/1.70 % (23840)Time elapsed: 0.123 s
% 2.54/1.70 % (23840)Instructions burned: 377 (million)
% 2.54/1.70 % (23840)------------------------------
% 2.54/1.70 % (23840)------------------------------
% 2.54/1.70 % (23847)Instruction limit reached!
% 2.54/1.70 % (23847)------------------------------
% 2.54/1.70 % (23847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.70 % (23847)Termination reason: Unknown
% 2.54/1.70 % (23847)Termination phase: Saturation
% 2.54/1.70
% 2.54/1.70 % (23847)Memory used [KB]: 6780
% 2.54/1.70 % (23847)Time elapsed: 0.039 s
% 2.54/1.70 % (23847)Instructions burned: 129 (million)
% 2.54/1.70 % (23847)------------------------------
% 2.54/1.70 % (23847)------------------------------
% 2.54/1.71 % (23848)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_23484 for (2997ds/100Mi)
% 2.54/1.71 % (23849)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_23484 for (2997ds/3Mi)
% 2.54/1.71 % (23849)Instruction limit reached!
% 2.54/1.71 % (23849)------------------------------
% 2.54/1.71 % (23849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.71 % (23849)Termination reason: Unknown
% 2.54/1.71 % (23849)Termination phase: shuffling
% 2.54/1.71
% 2.54/1.71 % (23849)Memory used [KB]: 1279
% 2.54/1.71 % (23849)Time elapsed: 0.003 s
% 2.54/1.71 % (23849)Instructions burned: 4 (million)
% 2.54/1.71 % (23849)------------------------------
% 2.54/1.71 % (23849)------------------------------
% 2.54/1.72 % (23850)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_23484 for (2997ds/20Mi)
% 2.54/1.73 % (23850)Instruction limit reached!
% 2.54/1.73 % (23850)------------------------------
% 2.54/1.73 % (23850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.73 % (23850)Termination reason: Unknown
% 2.54/1.73 % (23850)Termination phase: SInE selection
% 2.54/1.73
% 2.54/1.73 % (23850)Memory used [KB]: 1407
% 2.54/1.73 % (23850)Time elapsed: 0.008 s
% 2.54/1.73 % (23850)Instructions burned: 20 (million)
% 2.54/1.73 % (23850)------------------------------
% 2.54/1.73 % (23850)------------------------------
% 2.54/1.74 % (23851)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_23484 for (2997ds/86Mi)
% 2.54/1.74 % (23848)Instruction limit reached!
% 2.54/1.74 % (23848)------------------------------
% 2.54/1.74 % (23848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.74 % (23848)Termination reason: Unknown
% 2.54/1.74 % (23848)Termination phase: Saturation
% 2.54/1.74
% 2.54/1.74 % (23848)Memory used [KB]: 6396
% 2.54/1.74 % (23848)Time elapsed: 0.032 s
% 2.54/1.74 % (23848)Instructions burned: 102 (million)
% 2.54/1.74 % (23848)------------------------------
% 2.54/1.74 % (23848)------------------------------
% 2.54/1.75 % (23852)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_23484 for (2997ds/107Mi)
% 2.54/1.76 % (23851)Instruction limit reached!
% 2.54/1.76 % (23851)------------------------------
% 2.54/1.76 % (23851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.76 % (23851)Termination reason: Unknown
% 2.54/1.76 % (23851)Termination phase: Saturation
% 2.54/1.76
% 2.54/1.76 % (23851)Memory used [KB]: 6524
% 2.54/1.76 % (23851)Time elapsed: 0.026 s
% 2.54/1.76 % (23851)Instructions burned: 86 (million)
% 2.54/1.76 % (23851)------------------------------
% 2.54/1.76 % (23851)------------------------------
% 2.54/1.77 % (23825)Instruction limit reached!
% 2.54/1.77 % (23825)------------------------------
% 2.54/1.77 % (23825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.77 % (23825)Termination reason: Unknown
% 2.54/1.77 % (23825)Termination phase: Saturation
% 2.54/1.77
% 2.54/1.77 % (23825)Memory used [KB]: 8443
% 2.54/1.77 % (23825)Time elapsed: 0.262 s
% 2.54/1.77 % (23825)Instructions burned: 1044 (million)
% 2.54/1.77 % (23825)------------------------------
% 2.54/1.77 % (23825)------------------------------
% 2.54/1.77 % (23841)Instruction limit reached!
% 2.54/1.77 % (23841)------------------------------
% 2.54/1.77 % (23841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.77 % (23841)Termination reason: Unknown
% 2.54/1.77 % (23841)Termination phase: Saturation
% 2.54/1.77
% 2.54/1.77 % (23841)Memory used [KB]: 6524
% 2.54/1.77 % (23841)Time elapsed: 0.182 s
% 2.54/1.77 % (23841)Instructions burned: 782 (million)
% 2.54/1.77 % (23841)------------------------------
% 2.54/1.77 % (23841)------------------------------
% 2.54/1.77 % (23853)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_23484 for (2997ds/39Mi)
% 2.54/1.78 % (23854)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_23484 for (2997ds/448Mi)
% 2.54/1.78 % (23855)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_23484 for (2997ds/46Mi)
% 2.54/1.78 % (23852)Instruction limit reached!
% 2.54/1.78 % (23852)------------------------------
% 2.54/1.78 % (23852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.78 % (23852)Termination reason: Unknown
% 2.54/1.78 % (23852)Termination phase: Saturation
% 2.54/1.78
% 2.54/1.78 % (23852)Memory used [KB]: 6652
% 2.54/1.78 % (23852)Time elapsed: 0.033 s
% 2.54/1.78 % (23852)Instructions burned: 110 (million)
% 2.54/1.78 % (23852)------------------------------
% 2.54/1.78 % (23852)------------------------------
% 2.54/1.78 % (23853)Instruction limit reached!
% 2.54/1.78 % (23853)------------------------------
% 2.54/1.78 % (23853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.78 % (23853)Termination reason: Unknown
% 2.54/1.78 % (23853)Termination phase: Property scanning
% 2.54/1.78
% 2.54/1.78 % (23853)Memory used [KB]: 1663
% 2.54/1.78 % (23853)Time elapsed: 0.013 s
% 2.54/1.78 % (23853)Instructions burned: 41 (million)
% 2.54/1.78 % (23853)------------------------------
% 2.54/1.78 % (23853)------------------------------
% 2.54/1.79 % (23834)Instruction limit reached!
% 2.54/1.79 % (23834)------------------------------
% 2.54/1.79 % (23834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.79 % (23834)Termination reason: Unknown
% 2.54/1.79 % (23834)Termination phase: Saturation
% 2.54/1.79
% 2.54/1.79 % (23834)Memory used [KB]: 9338
% 2.54/1.79 % (23834)Time elapsed: 0.242 s
% 2.54/1.79 % (23834)Instructions burned: 712 (million)
% 2.54/1.79 % (23834)------------------------------
% 2.54/1.79 % (23834)------------------------------
% 2.54/1.79 % (23855)Instruction limit reached!
% 2.54/1.79 % (23855)------------------------------
% 2.54/1.79 % (23855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.79 % (23855)Termination reason: Unknown
% 2.54/1.79 % (23855)Termination phase: Property scanning
% 2.54/1.79
% 2.54/1.79 % (23855)Memory used [KB]: 1663
% 2.54/1.79 % (23855)Time elapsed: 0.013 s
% 2.54/1.79 % (23855)Instructions burned: 46 (million)
% 2.54/1.79 % (23855)------------------------------
% 2.54/1.79 % (23855)------------------------------
% 2.54/1.79 % (23856)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_23484 for (2997ds/98Mi)
% 2.54/1.79 % (23857)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_23484 for (2996ds/507Mi)
% 2.54/1.80 % (23858)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_23484 for (2996ds/149Mi)
% 2.54/1.80 % (23859)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_23484 for (2996ds/39Mi)
% 2.54/1.81 % (23859)Instruction limit reached!
% 2.54/1.81 % (23859)------------------------------
% 2.54/1.81 % (23859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.81 % (23859)Termination reason: Unknown
% 2.54/1.81 % (23859)Termination phase: Property scanning
% 2.54/1.81
% 2.54/1.81 % (23859)Memory used [KB]: 1663
% 2.54/1.81 % (23859)Time elapsed: 0.012 s
% 2.54/1.81 % (23859)Instructions burned: 42 (million)
% 2.54/1.81 % (23859)------------------------------
% 2.54/1.81 % (23859)------------------------------
% 2.54/1.82 % (23856)Instruction limit reached!
% 2.54/1.82 % (23856)------------------------------
% 2.54/1.82 % (23856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.82 % (23856)Termination reason: Unknown
% 2.54/1.82 % (23856)Termination phase: Saturation
% 2.54/1.82
% 2.54/1.82 % (23856)Memory used [KB]: 1791
% 2.54/1.82 % (23856)Time elapsed: 0.029 s
% 2.54/1.82 % (23856)Instructions burned: 100 (million)
% 2.54/1.82 % (23856)------------------------------
% 2.54/1.82 % (23856)------------------------------
% 2.54/1.82 % (23860)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_23484 for (2996ds/6Mi)
% 2.54/1.82 % (23860)Instruction limit reached!
% 2.54/1.82 % (23860)------------------------------
% 2.54/1.82 % (23860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.82 % (23860)Termination reason: Unknown
% 2.54/1.82 % (23860)Termination phase: shuffling
% 2.54/1.82
% 2.54/1.82 % (23860)Memory used [KB]: 1279
% 2.54/1.82 % (23860)Time elapsed: 0.003 s
% 2.54/1.82 % (23860)Instructions burned: 8 (million)
% 2.54/1.82 % (23860)------------------------------
% 2.54/1.82 % (23860)------------------------------
% 2.54/1.83 % (23861)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_23484 for (2996ds/1087Mi)
% 2.54/1.83 % (23862)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_23484 for (2996ds/47Mi)
% 2.54/1.84 % (23862)Instruction limit reached!
% 2.54/1.84 % (23862)------------------------------
% 2.54/1.84 % (23862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.84 % (23862)Termination reason: Unknown
% 2.54/1.84 % (23862)Termination phase: Function definition elimination
% 2.54/1.84
% 2.54/1.84 % (23862)Memory used [KB]: 1791
% 2.54/1.84 % (23862)Time elapsed: 0.013 s
% 2.54/1.84 % (23862)Instructions burned: 47 (million)
% 2.54/1.84 % (23862)------------------------------
% 2.54/1.84 % (23862)------------------------------
% 2.54/1.84 % (23858)Instruction limit reached!
% 2.54/1.84 % (23858)------------------------------
% 2.54/1.84 % (23858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.84 % (23858)Termination reason: Unknown
% 2.54/1.84 % (23858)Termination phase: Saturation
% 2.54/1.84
% 2.54/1.84 % (23858)Memory used [KB]: 6908
% 2.54/1.84 % (23858)Time elapsed: 0.071 s
% 2.54/1.84 % (23858)Instructions burned: 149 (million)
% 2.54/1.84 % (23858)------------------------------
% 2.54/1.84 % (23858)------------------------------
% 2.54/1.85 % (23863)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_23484 for (2996ds/44Mi)
% 2.54/1.85 % (23864)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_23484 for (2996ds/432Mi)
% 2.54/1.86 % (23863)Instruction limit reached!
% 2.54/1.86 % (23863)------------------------------
% 2.54/1.86 % (23863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.86 % (23863)Termination reason: Unknown
% 2.54/1.86 % (23863)Termination phase: Property scanning
% 2.54/1.86
% 2.54/1.86 % (23863)Memory used [KB]: 1663
% 2.54/1.86 % (23863)Time elapsed: 0.013 s
% 2.54/1.86 % (23863)Instructions burned: 46 (million)
% 2.54/1.86 % (23863)------------------------------
% 2.54/1.86 % (23863)------------------------------
% 2.54/1.87 % (23843)Instruction limit reached!
% 2.54/1.87 % (23843)------------------------------
% 2.54/1.87 % (23843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.87 % (23843)Termination reason: Unknown
% 2.54/1.87 % (23843)Termination phase: Saturation
% 2.54/1.87
% 2.54/1.87 % (23843)Memory used [KB]: 8059
% 2.54/1.87 % (23843)Time elapsed: 0.272 s
% 2.54/1.87 % (23843)Instructions burned: 879 (million)
% 2.54/1.87 % (23843)------------------------------
% 2.54/1.87 % (23843)------------------------------
% 2.54/1.87 % (23836)Instruction limit reached!
% 2.54/1.87 % (23836)------------------------------
% 2.54/1.87 % (23836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.87 % (23836)Termination reason: Unknown
% 2.54/1.87 % (23836)Termination phase: Saturation
% 2.54/1.87
% 2.54/1.87 % (23836)Memory used [KB]: 10234
% 2.54/1.87 % (23836)Time elapsed: 0.311 s
% 2.54/1.87 % (23836)Instructions burned: 904 (million)
% 2.54/1.87 % (23836)------------------------------
% 2.54/1.87 % (23836)------------------------------
% 2.54/1.87 % (23865)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_23484 for (2995ds/62Mi)
% 2.54/1.88 % (23866)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_23484 for (2995ds/31Mi)
% 2.54/1.88 % (23867)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_23484 for (2995ds/96Mi)
% 2.54/1.88 % (23854)Instruction limit reached!
% 2.54/1.88 % (23854)------------------------------
% 2.54/1.88 % (23854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.88 % (23854)Termination reason: Unknown
% 2.54/1.88 % (23854)Termination phase: Saturation
% 2.54/1.88
% 2.54/1.88 % (23854)Memory used [KB]: 6524
% 2.54/1.88 % (23854)Time elapsed: 0.107 s
% 2.54/1.88 % (23854)Instructions burned: 452 (million)
% 2.54/1.88 % (23854)------------------------------
% 2.54/1.88 % (23854)------------------------------
% 2.54/1.89 % (23865)Instruction limit reached!
% 2.54/1.89 % (23865)------------------------------
% 2.54/1.89 % (23865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.89 % (23865)Termination reason: Unknown
% 2.54/1.89 % (23865)Termination phase: Saturation
% 2.54/1.89
% 2.54/1.89 % (23865)Memory used [KB]: 6140
% 2.54/1.89 % (23865)Time elapsed: 0.017 s
% 2.54/1.89 % (23865)Instructions burned: 63 (million)
% 2.54/1.89 % (23865)------------------------------
% 2.54/1.89 % (23865)------------------------------
% 2.54/1.89 % (23866)Instruction limit reached!
% 2.54/1.89 % (23866)------------------------------
% 2.54/1.89 % (23866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.89 % (23866)Termination reason: Unknown
% 2.54/1.89 % (23866)Termination phase: Property scanning
% 2.54/1.89
% 2.54/1.89 % (23866)Memory used [KB]: 1663
% 2.54/1.89 % (23866)Time elapsed: 0.010 s
% 2.54/1.89 % (23866)Instructions burned: 33 (million)
% 2.54/1.89 % (23866)------------------------------
% 2.54/1.89 % (23866)------------------------------
% 2.54/1.89 % (23868)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_23484 for (2995ds/453Mi)
% 2.54/1.90 % (23869)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_23484 for (2995ds/71Mi)
% 2.54/1.90 % (23870)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_23484 for (2995ds/83Mi)
% 2.54/1.91 % (23867)Instruction limit reached!
% 2.54/1.91 % (23867)------------------------------
% 2.54/1.91 % (23867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.91 % (23867)Termination reason: Unknown
% 2.54/1.91 % (23867)Termination phase: Saturation
% 2.54/1.91
% 2.54/1.91 % (23867)Memory used [KB]: 6396
% 2.54/1.91 % (23867)Time elapsed: 0.029 s
% 2.54/1.91 % (23867)Instructions burned: 96 (million)
% 2.54/1.91 % (23867)------------------------------
% 2.54/1.91 % (23867)------------------------------
% 2.54/1.92 % (23869)Instruction limit reached!
% 2.54/1.92 % (23869)------------------------------
% 2.54/1.92 % (23869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.92 % (23869)Termination reason: Unknown
% 2.54/1.92 % (23869)Termination phase: Saturation
% 2.54/1.92
% 2.54/1.92 % (23869)Memory used [KB]: 6268
% 2.54/1.92 % (23869)Time elapsed: 0.020 s
% 2.54/1.92 % (23869)Instructions burned: 72 (million)
% 2.54/1.92 % (23869)------------------------------
% 2.54/1.92 % (23869)------------------------------
% 2.54/1.92 % (23871)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_23484 for (2995ds/11Mi)
% 2.54/1.92 % (23870)Instruction limit reached!
% 2.54/1.92 % (23870)------------------------------
% 2.54/1.92 % (23870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.92 % (23870)Termination reason: Unknown
% 2.54/1.92 % (23870)Termination phase: Saturation
% 2.54/1.92
% 2.54/1.92 % (23870)Memory used [KB]: 6268
% 2.54/1.92 % (23870)Time elapsed: 0.023 s
% 2.54/1.92 % (23870)Instructions burned: 84 (million)
% 2.54/1.92 % (23870)------------------------------
% 2.54/1.92 % (23870)------------------------------
% 2.54/1.92 % (23871)Instruction limit reached!
% 2.54/1.92 % (23871)------------------------------
% 2.54/1.92 % (23871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.92 % (23871)Termination reason: Unknown
% 2.54/1.92 % (23871)Termination phase: shuffling
% 2.54/1.92
% 2.54/1.92 % (23871)Memory used [KB]: 1407
% 2.54/1.92 % (23871)Time elapsed: 0.005 s
% 2.54/1.92 % (23871)Instructions burned: 12 (million)
% 2.54/1.92 % (23871)------------------------------
% 2.54/1.92 % (23871)------------------------------
% 2.54/1.93 % (23872)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_23484 for (2995ds/41Mi)
% 2.54/1.93 % (23873)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_23484 for (2995ds/6Mi)
% 2.54/1.93 % (23873)Instruction limit reached!
% 2.54/1.93 % (23873)------------------------------
% 2.54/1.93 % (23873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.93 % (23873)Termination reason: Unknown
% 2.54/1.93 % (23873)Termination phase: shuffling
% 2.54/1.93
% 2.54/1.93 % (23873)Memory used [KB]: 1279
% 2.54/1.93 % (23873)Time elapsed: 0.003 s
% 2.54/1.93 % (23873)Instructions burned: 7 (million)
% 2.54/1.93 % (23873)------------------------------
% 2.54/1.93 % (23873)------------------------------
% 2.54/1.93 % (23874)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_23484 for (2995ds/150Mi)
% 2.54/1.94 % (23872)Instruction limit reached!
% 2.54/1.94 % (23872)------------------------------
% 2.54/1.94 % (23872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.94 % (23872)Termination reason: Unknown
% 2.54/1.94 % (23872)Termination phase: Property scanning
% 2.54/1.94
% 2.54/1.94 % (23872)Memory used [KB]: 1663
% 2.54/1.94 % (23872)Time elapsed: 0.012 s
% 2.54/1.94 % (23872)Instructions burned: 43 (million)
% 2.54/1.94 % (23872)------------------------------
% 2.54/1.94 % (23872)------------------------------
% 2.54/1.94 % (23875)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_23484 for (2995ds/343Mi)
% 2.54/1.95 % (23876)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_23484 for (2995ds/109Mi)
% 2.54/1.95 % (23857)Instruction limit reached!
% 2.54/1.95 % (23857)------------------------------
% 2.54/1.95 % (23857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.95 % (23857)Termination reason: Unknown
% 2.54/1.95 % (23857)Termination phase: Saturation
% 2.54/1.95
% 2.54/1.95 % (23857)Memory used [KB]: 7164
% 2.54/1.95 % (23857)Time elapsed: 0.185 s
% 2.54/1.95 % (23857)Instructions burned: 508 (million)
% 2.54/1.95 % (23857)------------------------------
% 2.54/1.95 % (23857)------------------------------
% 2.54/1.96 % (23864)Instruction limit reached!
% 2.54/1.96 % (23864)------------------------------
% 2.54/1.96 % (23864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.96 % (23864)Termination reason: Unknown
% 2.54/1.96 % (23864)Termination phase: Saturation
% 2.54/1.96
% 2.54/1.96 % (23864)Memory used [KB]: 2942
% 2.54/1.96 % (23864)Time elapsed: 0.109 s
% 2.54/1.96 % (23864)Instructions burned: 432 (million)
% 2.54/1.96 % (23864)------------------------------
% 2.54/1.96 % (23864)------------------------------
% 2.54/1.96 % (23878)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_23484 for (2995ds/253Mi)
% 2.54/1.97 % (23879)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_23484 for (2995ds/140Mi)
% 2.54/1.98 % (23876)Instruction limit reached!
% 2.54/1.98 % (23876)------------------------------
% 2.54/1.98 % (23876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.98 % (23876)Termination reason: Unknown
% 2.54/1.98 % (23876)Termination phase: Saturation
% 2.54/1.98
% 2.54/1.98 % (23876)Memory used [KB]: 6652
% 2.54/1.98 % (23876)Time elapsed: 0.030 s
% 2.54/1.98 % (23876)Instructions burned: 110 (million)
% 2.54/1.98 % (23876)------------------------------
% 2.54/1.98 % (23876)------------------------------
% 2.54/1.98 % (23874)Instruction limit reached!
% 2.54/1.98 % (23874)------------------------------
% 2.54/1.98 % (23874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.98 % (23874)Termination reason: Unknown
% 2.54/1.98 % (23874)Termination phase: Saturation
% 2.54/1.98
% 2.54/1.98 % (23874)Memory used [KB]: 7547
% 2.54/1.98 % (23874)Time elapsed: 0.047 s
% 2.54/1.98 % (23874)Instructions burned: 152 (million)
% 2.54/1.98 % (23874)------------------------------
% 2.54/1.98 % (23874)------------------------------
% 2.54/1.98 % (23880)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_23484 for (2994ds/614Mi)
% 2.54/1.99 % (23881)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_23484 for (2994ds/202Mi)
% 2.54/2.00 % (23868)Instruction limit reached!
% 2.54/2.00 % (23868)------------------------------
% 2.54/2.00 % (23868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/2.00 % (23868)Termination reason: Unknown
% 2.54/2.00 % (23868)Termination phase: Saturation
% 2.54/2.00
% 2.54/2.00 % (23868)Memory used [KB]: 6524
% 2.54/2.00 % (23868)Time elapsed: 0.111 s
% 2.54/2.00 % (23868)Instructions burned: 456 (million)
% 2.54/2.00 % (23868)------------------------------
% 2.54/2.00 % (23868)------------------------------
% 2.54/2.01 % (23879)Instruction limit reached!
% 2.54/2.01 % (23879)------------------------------
% 2.54/2.01 % (23879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/2.01 % (23879)Termination reason: Unknown
% 2.54/2.01 % (23879)Termination phase: Saturation
% 2.54/2.01
% 2.54/2.01 % (23879)Memory used [KB]: 6396
% 2.54/2.01 % (23879)Time elapsed: 0.039 s
% 2.54/2.01 % (23879)Instructions burned: 143 (million)
% 2.54/2.01 % (23879)------------------------------
% 2.54/2.01 % (23879)------------------------------
% 2.54/2.01 % (23882)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_23484 for (2994ds/339Mi)
% 2.54/2.02 % (23883)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_23484 for (2994ds/283Mi)
% 6.32/2.04 % (23878)Instruction limit reached!
% 6.32/2.04 % (23878)------------------------------
% 6.32/2.04 % (23878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.32/2.04 % (23878)Termination reason: Unknown
% 6.32/2.04 % (23878)Termination phase: Saturation
% 6.32/2.04
% 6.32/2.04 % (23878)Memory used [KB]: 7931
% 6.32/2.04 % (23878)Time elapsed: 0.078 s
% 6.32/2.04 % (23878)Instructions burned: 254 (million)
% 6.32/2.04 % (23878)------------------------------
% 6.32/2.04 % (23878)------------------------------
% 6.32/2.04 % (23875)Instruction limit reached!
% 6.32/2.04 % (23875)------------------------------
% 6.32/2.04 % (23875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.32/2.04 % (23875)Termination reason: Unknown
% 6.32/2.04 % (23875)Termination phase: Saturation
% 6.32/2.04
% 6.32/2.04 % (23875)Memory used [KB]: 7291
% 6.32/2.04 % (23875)Time elapsed: 0.101 s
% 6.32/2.04 % (23875)Instructions burned: 343 (million)
% 6.32/2.04 % (23875)------------------------------
% 6.32/2.04 % (23875)------------------------------
% 6.32/2.05 % (23881)Instruction limit reached!
% 6.32/2.05 % (23881)------------------------------
% 6.32/2.05 % (23881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.32/2.05 % (23881)Termination reason: Unknown
% 6.32/2.05 % (23881)Termination phase: Saturation
% 6.32/2.05
% 6.32/2.05 % (23881)Memory used [KB]: 7803
% 6.32/2.05 % (23881)Time elapsed: 0.063 s
% 6.32/2.05 % (23881)Instructions burned: 204 (million)
% 6.32/2.05 % (23881)------------------------------
% 6.32/2.05 % (23881)------------------------------
% 6.32/2.05 % (23884)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_23484 for (2994ds/134Mi)
% 6.32/2.05 % (23885)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_23484 for (2994ds/298Mi)
% 6.32/2.06 % (23886)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_23484 for (2994ds/192Mi)
% 6.32/2.09 % (23884)Instruction limit reached!
% 6.32/2.09 % (23884)------------------------------
% 6.32/2.09 % (23884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.32/2.09 % (23884)Termination reason: Unknown
% 6.32/2.09 % (23884)Termination phase: Saturation
% 6.32/2.09
% 6.32/2.09 % (23884)Memory used [KB]: 6780
% 6.32/2.09 % (23884)Time elapsed: 0.039 s
% 6.32/2.09 % (23884)Instructions burned: 137 (million)
% 6.32/2.09 % (23884)------------------------------
% 6.32/2.09 % (23884)------------------------------
% 6.32/2.09 % (23883)Instruction limit reached!
% 6.32/2.09 % (23883)------------------------------
% 6.32/2.09 % (23883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.32/2.09 % (23883)Termination reason: Unknown
% 6.32/2.09 % (23883)Termination phase: Saturation
% 6.32/2.09
% 6.32/2.09 % (23883)Memory used [KB]: 8827
% 6.32/2.09 % (23883)Time elapsed: 0.074 s
% 6.32/2.09 % (23883)Instructions burned: 285 (million)
% 6.32/2.09 % (23883)------------------------------
% 6.32/2.09 % (23883)------------------------------
% 6.32/2.10 % (23887)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_23484 for (2993ds/258Mi)
% 6.32/2.10 % (23888)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_23484 for (2993ds/90Mi)
% 6.32/2.11 % (23882)Instruction limit reached!
% 6.32/2.11 % (23882)------------------------------
% 6.32/2.11 % (23882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.32/2.11 % (23882)Termination reason: Unknown
% 6.32/2.11 % (23882)Termination phase: Saturation
% 6.32/2.11
% 6.32/2.11 % (23882)Memory used [KB]: 7547
% 6.32/2.11 % (23882)Time elapsed: 0.102 s
% 6.32/2.11 % (23882)Instructions burned: 339 (million)
% 6.32/2.11 % (23882)------------------------------
% 6.32/2.11 % (23882)------------------------------
% 6.32/2.12 % (23886)Instruction limit reached!
% 6.32/2.12 % (23886)------------------------------
% 6.32/2.12 % (23886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.32/2.12 % (23886)Termination reason: Unknown
% 6.32/2.12 % (23886)Termination phase: Saturation
% 6.32/2.12
% 6.32/2.12 % (23886)Memory used [KB]: 7164
% 6.32/2.12 % (23886)Time elapsed: 0.057 s
% 6.32/2.12 % (23886)Instructions burned: 194 (million)
% 6.32/2.12 % (23886)------------------------------
% 6.32/2.12 % (23886)------------------------------
% 6.32/2.12 % (23889)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_23484 for (2993ds/231Mi)
% 6.91/2.12 % (23890)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_23484 for (2993ds/458Mi)
% 6.91/2.13 % (23888)Instruction limit reached!
% 6.91/2.13 % (23888)------------------------------
% 6.91/2.13 % (23888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.91/2.13 % (23888)Termination reason: Unknown
% 6.91/2.13 % (23888)Termination phase: Saturation
% 6.91/2.13
% 6.91/2.13 % (23888)Memory used [KB]: 6652
% 6.91/2.13 % (23888)Time elapsed: 0.025 s
% 6.91/2.13 % (23888)Instructions burned: 90 (million)
% 6.91/2.13 % (23888)------------------------------
% 6.91/2.13 % (23888)------------------------------
% 6.91/2.13 % (23885)Instruction limit reached!
% 6.91/2.13 % (23885)------------------------------
% 6.91/2.13 % (23885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.91/2.13 % (23885)Termination reason: Unknown
% 6.91/2.13 % (23885)Termination phase: Saturation
% 6.91/2.13
% 6.91/2.13 % (23885)Memory used [KB]: 6396
% 6.91/2.13 % (23885)Time elapsed: 0.078 s
% 6.91/2.13 % (23885)Instructions burned: 298 (million)
% 6.91/2.13 % (23885)------------------------------
% 6.91/2.13 % (23885)------------------------------
% 6.91/2.14 % (23891)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_23484 for (2993ds/31Mi)
% 6.91/2.14 % (23892)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_23484 for (2993ds/297Mi)
% 6.91/2.14 % (23891)Instruction limit reached!
% 6.91/2.14 % (23891)------------------------------
% 6.91/2.14 % (23891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.91/2.14 % (23891)Termination reason: Unknown
% 6.91/2.14 % (23891)Termination phase: Property scanning
% 6.91/2.14
% 6.91/2.14 % (23891)Memory used [KB]: 1663
% 6.91/2.14 % (23891)Time elapsed: 0.010 s
% 6.91/2.14 % (23891)Instructions burned: 34 (million)
% 6.91/2.14 % (23891)------------------------------
% 6.91/2.14 % (23891)------------------------------
% 6.91/2.15 % (23893)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_23484 for (2993ds/987Mi)
% 6.91/2.17 % (23887)Instruction limit reached!
% 6.91/2.17 % (23887)------------------------------
% 6.91/2.17 % (23887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.91/2.17 % (23887)Termination reason: Unknown
% 6.91/2.17 % (23887)Termination phase: Saturation
% 6.91/2.17
% 6.91/2.17 % (23887)Memory used [KB]: 7164
% 6.91/2.17 % (23887)Time elapsed: 0.097 s
% 6.91/2.17 % (23887)Instructions burned: 258 (million)
% 6.91/2.17 % (23887)------------------------------
% 6.91/2.17 % (23887)------------------------------
% 6.91/2.17 % (23880)Instruction limit reached!
% 6.91/2.17 % (23880)------------------------------
% 6.91/2.17 % (23880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.91/2.17 % (23880)Termination reason: Unknown
% 6.91/2.17 % (23880)Termination phase: Saturation
% 6.91/2.17
% 6.91/2.17 % (23880)Memory used [KB]: 8187
% 6.91/2.17 % (23880)Time elapsed: 0.189 s
% 6.91/2.17 % (23880)Instructions burned: 615 (million)
% 6.91/2.17 % (23880)------------------------------
% 6.91/2.17 % (23880)------------------------------
% 6.91/2.17 % (23861)Instruction limit reached!
% 6.91/2.17 % (23861)------------------------------
% 6.91/2.17 % (23861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.91/2.17 % (23861)Termination reason: Unknown
% 6.91/2.17 % (23861)Termination phase: Saturation
% 6.91/2.17
% 6.91/2.17 % (23861)Memory used [KB]: 10362
% 6.91/2.17 % (23861)Time elapsed: 0.349 s
% 6.91/2.17 % (23861)Instructions burned: 1088 (million)
% 6.91/2.17 % (23861)------------------------------
% 6.91/2.17 % (23861)------------------------------
% 6.91/2.18 % (23894)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_23484 for (2992ds/182Mi)
% 6.91/2.18 % (23895)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_23484 for (2992ds/182Mi)
% 6.91/2.18 % (23896)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_23484 for (2992ds/154Mi)
% 6.91/2.19 % (23889)Instruction limit reached!
% 6.91/2.19 % (23889)------------------------------
% 6.91/2.19 % (23889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.91/2.19 % (23889)Termination reason: Unknown
% 6.91/2.19 % (23889)Termination phase: Saturation
% 6.91/2.19
% 6.91/2.19 % (23889)Memory used [KB]: 10106
% 6.91/2.19 % (23889)Time elapsed: 0.088 s
% 6.91/2.19 % (23889)Instructions burned: 232 (million)
% 6.91/2.19 % (23889)------------------------------
% 6.91/2.19 % (23889)------------------------------
% 7.34/2.20 % (23897)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_23484 for (2992ds/79Mi)
% 7.34/2.21 % (23892)Instruction limit reached!
% 7.34/2.21 % (23892)------------------------------
% 7.34/2.21 % (23892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.34/2.21 % (23892)Termination reason: Unknown
% 7.34/2.21 % (23892)Termination phase: Saturation
% 7.34/2.21
% 7.34/2.21 % (23892)Memory used [KB]: 8059
% 7.34/2.21 % (23892)Time elapsed: 0.095 s
% 7.34/2.21 % (23892)Instructions burned: 297 (million)
% 7.34/2.21 % (23892)------------------------------
% 7.34/2.21 % (23892)------------------------------
% 7.34/2.22 % (23897)Instruction limit reached!
% 7.34/2.22 % (23897)------------------------------
% 7.34/2.22 % (23897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.34/2.22 % (23897)Termination reason: Unknown
% 7.34/2.22 % (23897)Termination phase: Saturation
% 7.34/2.22
% 7.34/2.22 % (23897)Memory used [KB]: 6396
% 7.34/2.22 % (23897)Time elapsed: 0.022 s
% 7.34/2.22 % (23897)Instructions burned: 80 (million)
% 7.34/2.22 % (23897)------------------------------
% 7.34/2.22 % (23897)------------------------------
% 7.34/2.22 % (23898)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_23484 for (2992ds/216Mi)
% 7.34/2.22 % (23896)Instruction limit reached!
% 7.34/2.22 % (23896)------------------------------
% 7.34/2.22 % (23896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.34/2.22 % (23896)Termination reason: Unknown
% 7.34/2.22 % (23896)Termination phase: Saturation
% 7.34/2.22
% 7.34/2.22 % (23896)Memory used [KB]: 6524
% 7.34/2.22 % (23896)Time elapsed: 0.040 s
% 7.34/2.22 % (23896)Instructions burned: 156 (million)
% 7.34/2.22 % (23896)------------------------------
% 7.34/2.22 % (23896)------------------------------
% 7.34/2.23 % (23899)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_23484 for (2992ds/114Mi)
% 7.34/2.23 % (23900)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_23484 for (2992ds/922Mi)
% 7.34/2.23 % (23894)Instruction limit reached!
% 7.34/2.23 % (23894)------------------------------
% 7.34/2.23 % (23894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.34/2.23 % (23894)Termination reason: Unknown
% 7.34/2.23 % (23894)Termination phase: Saturation
% 7.34/2.23
% 7.34/2.23 % (23894)Memory used [KB]: 7036
% 7.34/2.23 % (23894)Time elapsed: 0.053 s
% 7.34/2.23 % (23894)Instructions burned: 183 (million)
% 7.34/2.23 % (23894)------------------------------
% 7.34/2.23 % (23894)------------------------------
% 7.34/2.24 % (23895)Instruction limit reached!
% 7.34/2.24 % (23895)------------------------------
% 7.34/2.24 % (23895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.34/2.24 % (23895)Termination reason: Unknown
% 7.34/2.24 % (23895)Termination phase: Saturation
% 7.34/2.24
% 7.34/2.24 % (23895)Memory used [KB]: 8955
% 7.34/2.24 % (23895)Time elapsed: 0.057 s
% 7.34/2.24 % (23895)Instructions burned: 182 (million)
% 7.34/2.24 % (23895)------------------------------
% 7.34/2.24 % (23895)------------------------------
% 7.34/2.24 % (23901)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_23484 for (2992ds/182Mi)
% 7.34/2.25 % (23902)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_23484 for (2992ds/164Mi)
% 7.34/2.26 % (23899)Instruction limit reached!
% 7.34/2.26 % (23899)------------------------------
% 7.34/2.26 % (23899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.34/2.26 % (23899)Termination reason: Unknown
% 7.34/2.26 % (23899)Termination phase: Saturation
% 7.34/2.26
% 7.34/2.26 % (23899)Memory used [KB]: 6780
% 7.34/2.26 % (23899)Time elapsed: 0.032 s
% 7.34/2.26 % (23899)Instructions burned: 115 (million)
% 7.34/2.26 % (23899)------------------------------
% 7.34/2.26 % (23899)------------------------------
% 7.34/2.26 % (23890)Instruction limit reached!
% 7.34/2.26 % (23890)------------------------------
% 7.34/2.26 % (23890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.34/2.26 % (23890)Termination reason: Unknown
% 7.34/2.26 % (23890)Termination phase: Saturation
% 7.34/2.26
% 7.34/2.26 % (23890)Memory used [KB]: 7931
% 7.34/2.26 % (23890)Time elapsed: 0.161 s
% 7.34/2.26 % (23890)Instructions burned: 459 (million)
% 7.34/2.26 % (23890)------------------------------
% 7.34/2.26 % (23890)------------------------------
% 7.34/2.27 % (23903)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_23484 for (2992ds/50Mi)
% 7.34/2.27 % (23904)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_23484 for (2992ds/368Mi)
% 7.34/2.27 % (23898)Instruction limit reached!
% 7.34/2.27 % (23898)------------------------------
% 7.34/2.27 % (23898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.34/2.27 % (23898)Termination reason: Unknown
% 7.34/2.27 % (23898)Termination phase: Saturation
% 7.34/2.27
% 7.34/2.27 % (23898)Memory used [KB]: 6908
% 7.34/2.27 % (23898)Time elapsed: 0.055 s
% 7.34/2.27 % (23898)Instructions burned: 217 (million)
% 7.34/2.27 % (23898)------------------------------
% 7.34/2.27 % (23898)------------------------------
% 7.34/2.28 % (23903)Instruction limit reached!
% 7.34/2.28 % (23903)------------------------------
% 7.34/2.28 % (23903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.34/2.28 % (23903)Termination reason: Unknown
% 7.34/2.28 % (23903)Termination phase: Property scanning
% 7.34/2.28
% 7.34/2.28 % (23903)Memory used [KB]: 1663
% 7.34/2.28 % (23903)Time elapsed: 0.014 s
% 7.34/2.28 % (23903)Instructions burned: 50 (million)
% 7.34/2.28 % (23903)------------------------------
% 7.34/2.28 % (23903)------------------------------
% 7.34/2.28 % (23905)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_23484 for (2991ds/1021Mi)
% 7.34/2.29 % (23901)Instruction limit reached!
% 7.34/2.29 % (23901)------------------------------
% 7.34/2.29 % (23901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.34/2.29 % (23901)Termination reason: Unknown
% 7.34/2.29 % (23901)Termination phase: Saturation
% 7.34/2.29
% 7.34/2.29 % (23901)Memory used [KB]: 6524
% 7.34/2.29 % (23901)Time elapsed: 0.047 s
% 7.34/2.29 % (23901)Instructions burned: 183 (million)
% 7.34/2.29 % (23901)------------------------------
% 7.34/2.29 % (23901)------------------------------
% 7.34/2.29 % (23906)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_23484 for (2991ds/267Mi)
% 7.34/2.29 % (23902)Instruction limit reached!
% 7.34/2.29 % (23902)------------------------------
% 7.34/2.29 % (23902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.34/2.29 % (23902)Termination reason: Unknown
% 7.34/2.29 % (23902)Termination phase: Saturation
% 7.34/2.29
% 7.34/2.29 % (23902)Memory used [KB]: 2174
% 7.34/2.29 % (23902)Time elapsed: 0.047 s
% 7.34/2.29 % (23902)Instructions burned: 164 (million)
% 7.34/2.29 % (23902)------------------------------
% 7.34/2.29 % (23902)------------------------------
% 8.00/2.30 % (23907)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_23484 for (2991ds/204Mi)
% 8.00/2.30 % (23908)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_23484 for (2991ds/26Mi)
% 8.00/2.31 % (23908)Instruction limit reached!
% 8.00/2.31 % (23908)------------------------------
% 8.00/2.31 % (23908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.00/2.31 % (23908)Termination reason: Unknown
% 8.00/2.31 % (23908)Termination phase: Property scanning
% 8.00/2.31
% 8.00/2.31 % (23908)Memory used [KB]: 1663
% 8.00/2.31 % (23908)Time elapsed: 0.008 s
% 8.00/2.31 % (23908)Instructions burned: 27 (million)
% 8.00/2.31 % (23908)------------------------------
% 8.00/2.31 % (23908)------------------------------
% 8.00/2.32 % (23909)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_23484 for (2991ds/53Mi)
% 8.00/2.33 % (23909)Instruction limit reached!
% 8.00/2.33 % (23909)------------------------------
% 8.00/2.33 % (23909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.00/2.33 % (23909)Termination reason: Unknown
% 8.00/2.33 % (23909)Termination phase: Property scanning
% 8.00/2.33
% 8.00/2.33 % (23909)Memory used [KB]: 1663
% 8.00/2.33 % (23909)Time elapsed: 0.016 s
% 8.00/2.33 % (23909)Instructions burned: 57 (million)
% 8.00/2.33 % (23909)------------------------------
% 8.00/2.33 % (23909)------------------------------
% 8.00/2.34 % (23910)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_23484 for (2991ds/4436Mi)
% 8.00/2.36 % (23907)Instruction limit reached!
% 8.00/2.36 % (23907)------------------------------
% 8.00/2.36 % (23907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.00/2.36 % (23907)Termination reason: Unknown
% 8.00/2.36 % (23907)Termination phase: Saturation
% 8.00/2.36
% 8.00/2.36 % (23907)Memory used [KB]: 7036
% 8.00/2.36 % (23907)Time elapsed: 0.060 s
% 8.00/2.36 % (23907)Instructions burned: 205 (million)
% 8.00/2.36 % (23907)------------------------------
% 8.00/2.36 % (23907)------------------------------
% 8.00/2.36 % (23906)Instruction limit reached!
% 8.00/2.36 % (23906)------------------------------
% 8.00/2.36 % (23906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.00/2.36 % (23906)Termination reason: Unknown
% 8.00/2.36 % (23906)Termination phase: Saturation
% 8.00/2.36
% 8.00/2.36 % (23906)Memory used [KB]: 8955
% 8.00/2.36 % (23906)Time elapsed: 0.069 s
% 8.00/2.36 % (23906)Instructions burned: 270 (million)
% 8.00/2.36 % (23906)------------------------------
% 8.00/2.36 % (23906)------------------------------
% 8.00/2.37 % (23911)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_23484 for (2991ds/1539Mi)
% 8.00/2.37 % (23912)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_23484 for (2991ds/408Mi)
% 8.00/2.38 % (23904)Instruction limit reached!
% 8.00/2.38 % (23904)------------------------------
% 8.00/2.38 % (23904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.00/2.38 % (23904)Termination reason: Unknown
% 8.00/2.38 % (23904)Termination phase: Saturation
% 8.00/2.38
% 8.00/2.38 % (23904)Memory used [KB]: 7419
% 8.00/2.38 % (23904)Time elapsed: 0.111 s
% 8.00/2.38 % (23904)Instructions burned: 371 (million)
% 8.00/2.38 % (23904)------------------------------
% 8.00/2.38 % (23904)------------------------------
% 8.00/2.39 % (23893)Instruction limit reached!
% 8.00/2.39 % (23893)------------------------------
% 8.00/2.39 % (23893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.00/2.39 % (23893)Termination reason: Unknown
% 8.00/2.39 % (23893)Termination phase: Saturation
% 8.00/2.39
% 8.00/2.39 % (23893)Memory used [KB]: 8699
% 8.00/2.39 % (23893)Time elapsed: 0.261 s
% 8.00/2.39 % (23893)Instructions burned: 989 (million)
% 8.00/2.39 % (23893)------------------------------
% 8.00/2.39 % (23893)------------------------------
% 8.00/2.39 % (23913)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_23484 for (2990ds/5205Mi)
% 8.56/2.40 % (23914)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_23484 for (2990ds/1913Mi)
% 8.57/2.50 % (23912)Instruction limit reached!
% 8.57/2.50 % (23912)------------------------------
% 8.57/2.50 % (23912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.57/2.50 % (23912)Termination reason: Unknown
% 8.57/2.50 % (23912)Termination phase: Saturation
% 8.57/2.50
% 8.57/2.50 % (23912)Memory used [KB]: 8955
% 8.57/2.50 % (23912)Time elapsed: 0.129 s
% 8.57/2.50 % (23912)Instructions burned: 408 (million)
% 8.57/2.50 % (23912)------------------------------
% 8.57/2.50 % (23912)------------------------------
% 8.57/2.51 % (23915)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_23484 for (2989ds/4350Mi)
% 8.57/2.52 % (23900)Instruction limit reached!
% 8.57/2.52 % (23900)------------------------------
% 8.57/2.52 % (23900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.57/2.52 % (23900)Termination reason: Unknown
% 8.57/2.52 % (23900)Termination phase: Saturation
% 8.57/2.52
% 8.57/2.52 % (23900)Memory used [KB]: 9083
% 8.57/2.52 % (23900)Time elapsed: 0.291 s
% 8.57/2.52 % (23900)Instructions burned: 922 (million)
% 8.57/2.52 % (23900)------------------------------
% 8.57/2.52 % (23900)------------------------------
% 8.57/2.53 % (23916)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_23484 for (2989ds/68Mi)
% 8.57/2.55 % (23916)Instruction limit reached!
% 8.57/2.55 % (23916)------------------------------
% 8.57/2.55 % (23916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.57/2.55 % (23916)Termination reason: Unknown
% 8.57/2.55 % (23916)Termination phase: Saturation
% 8.57/2.55
% 8.57/2.55 % (23916)Memory used [KB]: 6268
% 8.57/2.55 % (23916)Time elapsed: 0.019 s
% 8.57/2.55 % (23916)Instructions burned: 70 (million)
% 8.57/2.55 % (23916)------------------------------
% 8.57/2.55 % (23916)------------------------------
% 8.57/2.56 % (23917)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_23484 for (2989ds/358Mi)
% 9.04/2.61 % (23905)Instruction limit reached!
% 9.04/2.61 % (23905)------------------------------
% 9.04/2.61 % (23905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.04/2.61 % (23905)Termination reason: Unknown
% 9.04/2.61 % (23905)Termination phase: Saturation
% 9.04/2.61
% 9.04/2.61 % (23905)Memory used [KB]: 9594
% 9.04/2.61 % (23905)Time elapsed: 0.323 s
% 9.04/2.61 % (23905)Instructions burned: 1022 (million)
% 9.04/2.61 % (23905)------------------------------
% 9.04/2.61 % (23905)------------------------------
% 9.04/2.61 % (23918)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_23484 for (2988ds/31Mi)
% 9.04/2.62 % (23918)Instruction limit reached!
% 9.04/2.62 % (23918)------------------------------
% 9.04/2.62 % (23918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.04/2.62 % (23918)Termination reason: Unknown
% 9.04/2.62 % (23918)Termination phase: Property scanning
% 9.04/2.62
% 9.04/2.62 % (23918)Memory used [KB]: 1663
% 9.04/2.62 % (23918)Time elapsed: 0.010 s
% 9.04/2.62 % (23918)Instructions burned: 33 (million)
% 9.04/2.62 % (23918)------------------------------
% 9.04/2.62 % (23918)------------------------------
% 9.04/2.63 % (23919)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_23484 for (2988ds/279Mi)
% 9.04/2.67 % (23917)Instruction limit reached!
% 9.04/2.67 % (23917)------------------------------
% 9.04/2.67 % (23917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.04/2.67 % (23917)Termination reason: Unknown
% 9.04/2.67 % (23917)Termination phase: Saturation
% 9.04/2.67
% 9.04/2.67 % (23917)Memory used [KB]: 7291
% 9.04/2.67 % (23917)Time elapsed: 0.109 s
% 9.04/2.67 % (23917)Instructions burned: 361 (million)
% 9.04/2.67 % (23917)------------------------------
% 9.04/2.67 % (23917)------------------------------
% 9.04/2.68 % (23920)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_23484 for (2988ds/258Mi)
% 9.51/2.70 % (23919)Instruction limit reached!
% 9.51/2.70 % (23919)------------------------------
% 9.51/2.70 % (23919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.51/2.70 % (23919)Termination reason: Unknown
% 9.51/2.70 % (23919)Termination phase: Saturation
% 9.51/2.70
% 9.51/2.70 % (23919)Memory used [KB]: 6524
% 9.51/2.70 % (23919)Time elapsed: 0.069 s
% 9.51/2.70 % (23919)Instructions burned: 280 (million)
% 9.51/2.70 % (23919)------------------------------
% 9.51/2.70 % (23919)------------------------------
% 9.51/2.71 % (23921)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_23484 for (2987ds/26Mi)
% 9.51/2.72 % (23921)Instruction limit reached!
% 9.51/2.72 % (23921)------------------------------
% 9.51/2.72 % (23921)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.51/2.72 % (23921)Termination reason: Unknown
% 9.51/2.72 % (23921)Termination phase: Property scanning
% 9.51/2.72
% 9.51/2.72 % (23921)Memory used [KB]: 1535
% 9.51/2.72 % (23921)Time elapsed: 0.008 s
% 9.51/2.72 % (23921)Instructions burned: 27 (million)
% 9.51/2.72 % (23921)------------------------------
% 9.51/2.72 % (23921)------------------------------
% 9.51/2.73 % (23922)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_23484 for (2987ds/995Mi)
% 9.51/2.73 % (23911)Instruction limit reached!
% 9.51/2.73 % (23911)------------------------------
% 9.51/2.73 % (23911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.51/2.73 % (23911)Termination reason: Unknown
% 9.51/2.73 % (23911)Termination phase: Saturation
% 9.51/2.73
% 9.51/2.73 % (23911)Memory used [KB]: 7675
% 9.51/2.73 % (23911)Time elapsed: 0.368 s
% 9.51/2.73 % (23911)Instructions burned: 1539 (million)
% 9.51/2.73 % (23911)------------------------------
% 9.51/2.73 % (23911)------------------------------
% 9.51/2.74 % (23923)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_23484 for (2987ds/373Mi)
% 9.51/2.75 % (23920)Instruction limit reached!
% 9.51/2.75 % (23920)------------------------------
% 9.51/2.75 % (23920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.51/2.75 % (23920)Termination reason: Unknown
% 9.51/2.75 % (23920)Termination phase: Saturation
% 9.51/2.75
% 9.51/2.75 % (23920)Memory used [KB]: 7547
% 9.51/2.75 % (23920)Time elapsed: 0.072 s
% 9.51/2.75 % (23920)Instructions burned: 258 (million)
% 9.51/2.75 % (23920)------------------------------
% 9.51/2.75 % (23920)------------------------------
% 9.51/2.76 % (23924)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_23484 for (2987ds/253Mi)
% 10.06/2.82 % (23924)Instruction limit reached!
% 10.06/2.82 % (23924)------------------------------
% 10.06/2.82 % (23924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.06/2.82 % (23924)Termination reason: Unknown
% 10.06/2.82 % (23924)Termination phase: Saturation
% 10.06/2.82
% 10.06/2.82 % (23924)Memory used [KB]: 6524
% 10.06/2.82 % (23924)Time elapsed: 0.066 s
% 10.06/2.82 % (23924)Instructions burned: 254 (million)
% 10.06/2.82 % (23924)------------------------------
% 10.06/2.82 % (23924)------------------------------
% 10.06/2.83 % (23925)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_23484 for (2986ds/832Mi)
% 10.06/2.86 % (23923)Instruction limit reached!
% 10.06/2.86 % (23923)------------------------------
% 10.06/2.86 % (23923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.06/2.86 % (23923)Termination reason: Unknown
% 10.06/2.86 % (23923)Termination phase: Saturation
% 10.06/2.86
% 10.06/2.86 % (23923)Memory used [KB]: 7419
% 10.06/2.86 % (23923)Time elapsed: 0.118 s
% 10.06/2.86 % (23923)Instructions burned: 374 (million)
% 10.06/2.86 % (23923)------------------------------
% 10.06/2.86 % (23923)------------------------------
% 10.06/2.87 % (23926)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_23484 for (2986ds/668Mi)
% 10.26/2.96 % (23922)Instruction limit reached!
% 10.26/2.96 % (23922)------------------------------
% 10.26/2.96 % (23922)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.26/2.96 % (23922)Termination reason: Unknown
% 10.26/2.96 % (23922)Termination phase: Saturation
% 10.26/2.96
% 10.26/2.96 % (23922)Memory used [KB]: 8443
% 10.26/2.96 % (23922)Time elapsed: 0.239 s
% 10.26/2.96 % (23922)Instructions burned: 997 (million)
% 10.26/2.96 % (23922)------------------------------
% 10.26/2.96 % (23922)------------------------------
% 10.26/2.97 % (23927)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_23484 for (2985ds/40Mi)
% 10.26/2.98 % (23914)Instruction limit reached!
% 10.26/2.98 % (23914)------------------------------
% 10.26/2.98 % (23914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.26/2.98 % (23914)Termination reason: Unknown
% 10.26/2.98 % (23914)Termination phase: Saturation
% 10.26/2.98
% 10.26/2.98 % (23914)Memory used [KB]: 3582
% 10.26/2.98 % (23914)Time elapsed: 0.581 s
% 10.26/2.98 % (23914)Instructions burned: 1913 (million)
% 10.26/2.98 % (23914)------------------------------
% 10.26/2.98 % (23914)------------------------------
% 10.26/2.99 % (23927)Instruction limit reached!
% 10.26/2.99 % (23927)------------------------------
% 10.26/2.99 % (23927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.26/2.99 % (23927)Termination reason: Unknown
% 10.26/2.99 % (23927)Termination phase: Property scanning
% 10.26/2.99
% 10.26/2.99 % (23927)Memory used [KB]: 1663
% 10.26/2.99 % (23927)Time elapsed: 0.012 s
% 10.26/2.99 % (23927)Instructions burned: 42 (million)
% 10.26/2.99 % (23927)------------------------------
% 10.26/2.99 % (23927)------------------------------
% 10.26/2.99 % (23928)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_23484 for (2984ds/294Mi)
% 10.26/3.00 % (23929)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_23484 for (2984ds/187Mi)
% 13.36/3.03 % (23926)Instruction limit reached!
% 13.36/3.03 % (23926)------------------------------
% 13.36/3.03 % (23926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.36/3.03 % (23926)Termination reason: Unknown
% 13.36/3.03 % (23926)Termination phase: Saturation
% 13.36/3.03
% 13.36/3.03 % (23926)Memory used [KB]: 13048
% 13.36/3.03 % (23926)Time elapsed: 0.163 s
% 13.36/3.03 % (23926)Instructions burned: 668 (million)
% 13.36/3.03 % (23926)------------------------------
% 13.36/3.03 % (23926)------------------------------
% 13.36/3.04 % (23930)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_23484 for (2984ds/371Mi)
% 13.36/3.05 % (23929)Instruction limit reached!
% 13.36/3.05 % (23929)------------------------------
% 13.36/3.05 % (23929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.36/3.05 % (23929)Termination reason: Unknown
% 13.36/3.05 % (23929)Termination phase: Saturation
% 13.36/3.05
% 13.36/3.05 % (23929)Memory used [KB]: 7164
% 13.36/3.05 % (23929)Time elapsed: 0.077 s
% 13.36/3.05 % (23929)Instructions burned: 188 (million)
% 13.36/3.05 % (23929)------------------------------
% 13.36/3.05 % (23929)------------------------------
% 13.36/3.06 % (23931)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_23484 for (2984ds/1827Mi)
% 13.36/3.07 % (23928)Instruction limit reached!
% 13.36/3.07 % (23928)------------------------------
% 13.36/3.07 % (23928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.36/3.07 % (23928)Termination reason: Unknown
% 13.36/3.07 % (23928)Termination phase: Saturation
% 13.36/3.07
% 13.36/3.07 % (23928)Memory used [KB]: 6268
% 13.36/3.07 % (23928)Time elapsed: 0.076 s
% 13.36/3.07 % (23928)Instructions burned: 295 (million)
% 13.36/3.07 % (23928)------------------------------
% 13.36/3.07 % (23928)------------------------------
% 13.36/3.08 % (23932)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_23484 for (2983ds/70Mi)
% 13.36/3.09 % (23925)Instruction limit reached!
% 13.36/3.09 % (23925)------------------------------
% 13.36/3.09 % (23925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.36/3.09 % (23925)Termination reason: Unknown
% 13.36/3.09 % (23925)Termination phase: Saturation
% 13.36/3.09
% 13.36/3.09 % (23925)Memory used [KB]: 8699
% 13.36/3.09 % (23925)Time elapsed: 0.258 s
% 13.36/3.09 % (23925)Instructions burned: 834 (million)
% 13.36/3.09 % (23925)------------------------------
% 13.36/3.09 % (23925)------------------------------
% 13.36/3.09 % (23932)Instruction limit reached!
% 13.36/3.09 % (23932)------------------------------
% 13.36/3.09 % (23932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.36/3.09 % (23932)Termination reason: Unknown
% 13.36/3.09 % (23932)Termination phase: Saturation
% 13.36/3.09
% 13.36/3.09 % (23932)Memory used [KB]: 1791
% 13.36/3.09 % (23932)Time elapsed: 0.019 s
% 13.36/3.09 % (23932)Instructions burned: 71 (million)
% 13.36/3.09 % (23932)------------------------------
% 13.36/3.09 % (23932)------------------------------
% 13.36/3.10 % (23933)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_23484 for (2983ds/316Mi)
% 13.36/3.10 % (23934)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_23484 for (2983ds/932Mi)
% 13.87/3.15 % (23930)Instruction limit reached!
% 13.87/3.15 % (23930)------------------------------
% 13.87/3.15 % (23930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.87/3.15 % (23930)Termination reason: Unknown
% 13.87/3.15 % (23930)Termination phase: Saturation
% 13.87/3.15
% 13.87/3.15 % (23930)Memory used [KB]: 7419
% 13.87/3.15 % (23930)Time elapsed: 0.112 s
% 13.87/3.15 % (23930)Instructions burned: 372 (million)
% 13.87/3.15 % (23930)------------------------------
% 13.87/3.15 % (23930)------------------------------
% 13.87/3.16 % (23935)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_23484 for (2983ds/4714Mi)
% 13.87/3.18 % (23933)Instruction limit reached!
% 13.87/3.18 % (23933)------------------------------
% 13.87/3.18 % (23933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.87/3.18 % (23933)Termination reason: Unknown
% 13.87/3.18 % (23933)Termination phase: Saturation
% 13.87/3.18
% 13.87/3.18 % (23933)Memory used [KB]: 7164
% 13.87/3.18 % (23933)Time elapsed: 0.080 s
% 13.87/3.18 % (23933)Instructions burned: 319 (million)
% 13.87/3.18 % (23933)------------------------------
% 13.87/3.18 % (23933)------------------------------
% 13.87/3.19 % (23936)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_23484 for (2982ds/8250Mi)
% 14.59/3.33 % (23934)Instruction limit reached!
% 14.59/3.33 % (23934)------------------------------
% 14.59/3.33 % (23934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.59/3.33 % (23934)Termination reason: Unknown
% 14.59/3.33 % (23934)Termination phase: Saturation
% 14.59/3.33
% 14.59/3.33 % (23934)Memory used [KB]: 9338
% 14.59/3.33 % (23934)Time elapsed: 0.231 s
% 14.59/3.33 % (23934)Instructions burned: 932 (million)
% 14.59/3.33 % (23934)------------------------------
% 14.59/3.33 % (23934)------------------------------
% 14.59/3.34 % (23938)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_23484 for (2981ds/770Mi)
% 15.43/3.55 % (23938)Instruction limit reached!
% 15.43/3.55 % (23938)------------------------------
% 15.43/3.55 % (23938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.43/3.55 % (23938)Termination reason: Unknown
% 15.43/3.55 % (23938)Termination phase: Saturation
% 15.43/3.55
% 15.43/3.55 % (23938)Memory used [KB]: 6652
% 15.43/3.55 % (23938)Time elapsed: 0.211 s
% 15.43/3.55 % (23938)Instructions burned: 771 (million)
% 15.43/3.55 % (23938)------------------------------
% 15.43/3.55 % (23938)------------------------------
% 15.43/3.56 % (23939)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_23484 for (2979ds/794Mi)
% 15.96/3.60 % (23931)Instruction limit reached!
% 15.96/3.60 % (23931)------------------------------
% 15.96/3.60 % (23931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.96/3.60 % (23931)Termination reason: Unknown
% 15.96/3.60 % (23931)Termination phase: Saturation
% 15.96/3.60
% 15.96/3.60 % (23931)Memory used [KB]: 15351
% 15.96/3.60 % (23931)Time elapsed: 0.545 s
% 15.96/3.60 % (23931)Instructions burned: 1830 (million)
% 15.96/3.60 % (23931)------------------------------
% 15.96/3.60 % (23931)------------------------------
% 15.96/3.61 % (23940)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_23484 for (2978ds/464Mi)
% 15.96/3.65 % (23913)Instruction limit reached!
% 15.96/3.65 % (23913)------------------------------
% 15.96/3.65 % (23913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.96/3.65 % (23913)Termination reason: Unknown
% 15.96/3.65 % (23913)Termination phase: Saturation
% 15.96/3.65
% 15.96/3.65 % (23913)Memory used [KB]: 11129
% 15.96/3.65 % (23913)Time elapsed: 1.264 s
% 15.96/3.65 % (23913)Instructions burned: 5207 (million)
% 15.96/3.65 % (23913)------------------------------
% 15.96/3.65 % (23913)------------------------------
% 15.96/3.66 % (23941)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_23484 for (2978ds/1376Mi)
% 16.79/3.75 % (23910)Instruction limit reached!
% 16.79/3.75 % (23910)------------------------------
% 16.79/3.75 % (23910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.79/3.75 % (23910)Termination reason: Unknown
% 16.79/3.75 % (23910)Termination phase: Saturation
% 16.79/3.75
% 16.79/3.75 % (23910)Memory used [KB]: 14967
% 16.79/3.75 % (23910)Time elapsed: 1.404 s
% 16.79/3.75 % (23910)Instructions burned: 4438 (million)
% 16.79/3.75 % (23910)------------------------------
% 16.79/3.75 % (23910)------------------------------
% 16.79/3.75 % (23940)Instruction limit reached!
% 16.79/3.75 % (23940)------------------------------
% 16.79/3.75 % (23940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.79/3.75 % (23940)Termination reason: Unknown
% 16.79/3.75 % (23940)Termination phase: Saturation
% 16.79/3.75
% 16.79/3.75 % (23940)Memory used [KB]: 7419
% 16.79/3.75 % (23940)Time elapsed: 0.142 s
% 16.79/3.75 % (23940)Instructions burned: 464 (million)
% 16.79/3.75 % (23940)------------------------------
% 16.79/3.75 % (23940)------------------------------
% 16.79/3.76 % (23942)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_23484 for (2977ds/906Mi)
% 16.79/3.76 % (23943)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_23484 for (2977ds/434Mi)
% 17.10/3.81 % (23939)Instruction limit reached!
% 17.10/3.81 % (23939)------------------------------
% 17.10/3.81 % (23939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.10/3.81 % (23939)Termination reason: Unknown
% 17.10/3.81 % (23939)Termination phase: Saturation
% 17.10/3.81
% 17.10/3.81 % (23939)Memory used [KB]: 3837
% 17.10/3.81 % (23939)Time elapsed: 0.247 s
% 17.10/3.81 % (23939)Instructions burned: 796 (million)
% 17.10/3.81 % (23939)------------------------------
% 17.10/3.81 % (23939)------------------------------
% 17.10/3.81 % (23915)Instruction limit reached!
% 17.10/3.81 % (23915)------------------------------
% 17.10/3.81 % (23915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.10/3.81 % (23915)Termination reason: Unknown
% 17.10/3.81 % (23915)Termination phase: Saturation
% 17.10/3.81
% 17.10/3.81 % (23915)Memory used [KB]: 10746
% 17.10/3.81 % (23915)Time elapsed: 1.309 s
% 17.10/3.81 % (23915)Instructions burned: 4352 (million)
% 17.10/3.81 % (23915)------------------------------
% 17.10/3.81 % (23915)------------------------------
% 17.10/3.82 % (23944)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_23484 for (2976ds/865Mi)
% 17.10/3.82 % (23945)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_23484 for (2976ds/593Mi)
% 17.10/3.89 % (23943)Instruction limit reached!
% 17.10/3.89 % (23943)------------------------------
% 17.10/3.89 % (23943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.10/3.89 % (23943)Termination reason: Unknown
% 17.10/3.89 % (23943)Termination phase: Saturation
% 17.10/3.89
% 17.10/3.89 % (23943)Memory used [KB]: 8699
% 17.10/3.89 % (23943)Time elapsed: 0.130 s
% 17.10/3.89 % (23943)Instructions burned: 434 (million)
% 17.10/3.89 % (23943)------------------------------
% 17.10/3.89 % (23943)------------------------------
% 17.52/3.90 % (23946)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_23484 for (2975ds/443Mi)
% 17.52/3.96 % (23945)Instruction limit reached!
% 17.52/3.96 % (23945)------------------------------
% 17.52/3.96 % (23945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.52/3.96 % (23945)Termination reason: Unknown
% 17.52/3.96 % (23945)Termination phase: Saturation
% 17.52/3.96
% 17.52/3.96 % (23945)Memory used [KB]: 6524
% 17.52/3.96 % (23945)Time elapsed: 0.141 s
% 17.52/3.96 % (23945)Instructions burned: 595 (million)
% 17.52/3.96 % (23945)------------------------------
% 17.52/3.96 % (23945)------------------------------
% 17.52/3.97 % (23947)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_23484 for (2975ds/594Mi)
% 17.52/4.01 % (23941)Instruction limit reached!
% 17.52/4.01 % (23941)------------------------------
% 17.52/4.01 % (23941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.52/4.01 % (23941)Termination reason: Unknown
% 17.52/4.01 % (23941)Termination phase: Saturation
% 17.52/4.01
% 17.52/4.01 % (23941)Memory used [KB]: 7803
% 17.52/4.01 % (23941)Time elapsed: 0.346 s
% 17.52/4.01 % (23941)Instructions burned: 1377 (million)
% 17.52/4.01 % (23941)------------------------------
% 17.52/4.01 % (23941)------------------------------
% 17.52/4.02 % (23948)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_23484 for (2974ds/327Mi)
% 17.52/4.02 % (23942)Instruction limit reached!
% 17.52/4.02 % (23942)------------------------------
% 17.52/4.02 % (23942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.52/4.02 % (23942)Termination reason: Unknown
% 17.52/4.02 % (23942)Termination phase: Saturation
% 17.52/4.02
% 17.52/4.02 % (23942)Memory used [KB]: 9594
% 17.52/4.02 % (23942)Time elapsed: 0.267 s
% 17.52/4.02 % (23942)Instructions burned: 907 (million)
% 17.52/4.02 % (23942)------------------------------
% 17.52/4.02 % (23942)------------------------------
% 20.38/4.03 % (23949)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_23484 for (2974ds/5411Mi)
% 20.38/4.04 % (23946)Instruction limit reached!
% 20.38/4.04 % (23946)------------------------------
% 20.38/4.04 % (23946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.38/4.04 % (23946)Termination reason: Unknown
% 20.38/4.04 % (23946)Termination phase: Saturation
% 20.38/4.04
% 20.38/4.04 % (23946)Memory used [KB]: 7547
% 20.38/4.04 % (23946)Time elapsed: 0.136 s
% 20.38/4.04 % (23946)Instructions burned: 444 (million)
% 20.38/4.04 % (23946)------------------------------
% 20.38/4.04 % (23946)------------------------------
% 20.38/4.05 % (23950)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_23484 for (2974ds/1762Mi)
% 20.38/4.06 % (23944)Instruction limit reached!
% 20.38/4.06 % (23944)------------------------------
% 20.38/4.06 % (23944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.38/4.06 % (23944)Termination reason: Unknown
% 20.38/4.06 % (23944)Termination phase: Saturation
% 20.38/4.06
% 20.38/4.06 % (23944)Memory used [KB]: 7675
% 20.38/4.06 % (23944)Time elapsed: 0.240 s
% 20.38/4.06 % (23944)Instructions burned: 867 (million)
% 20.38/4.06 % (23944)------------------------------
% 20.38/4.06 % (23944)------------------------------
% 20.38/4.07 % (23951)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_23484 for (2974ds/96Mi)
% 20.38/4.09 % (23951)Instruction limit reached!
% 20.38/4.09 % (23951)------------------------------
% 20.38/4.09 % (23951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.38/4.09 % (23951)Termination reason: Unknown
% 20.38/4.09 % (23951)Termination phase: Saturation
% 20.38/4.09
% 20.38/4.09 % (23951)Memory used [KB]: 6268
% 20.38/4.09 % (23951)Time elapsed: 0.025 s
% 20.38/4.09 % (23951)Instructions burned: 96 (million)
% 20.38/4.09 % (23951)------------------------------
% 20.38/4.09 % (23951)------------------------------
% 20.38/4.10 % (23952)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_23484 for (2973ds/503Mi)
% 20.38/4.12 % (23948)Instruction limit reached!
% 20.38/4.12 % (23948)------------------------------
% 20.38/4.12 % (23948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.38/4.12 % (23948)Termination reason: Unknown
% 20.38/4.12 % (23948)Termination phase: Saturation
% 20.38/4.12
% 20.38/4.12 % (23948)Memory used [KB]: 8955
% 20.38/4.12 % (23948)Time elapsed: 0.105 s
% 20.38/4.12 % (23948)Instructions burned: 327 (million)
% 20.38/4.12 % (23948)------------------------------
% 20.38/4.12 % (23948)------------------------------
% 20.90/4.13 % (23953)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_23484 for (2973ds/90Mi)
% 20.90/4.15 % (23947)Instruction limit reached!
% 20.90/4.15 % (23947)------------------------------
% 20.90/4.15 % (23947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.90/4.15 % (23947)Termination reason: Unknown
% 20.90/4.15 % (23947)Termination phase: Saturation
% 20.90/4.15
% 20.90/4.15 % (23947)Memory used [KB]: 7803
% 20.90/4.15 % (23947)Time elapsed: 0.180 s
% 20.90/4.15 % (23947)Instructions burned: 596 (million)
% 20.90/4.15 % (23947)------------------------------
% 20.90/4.15 % (23947)------------------------------
% 20.90/4.16 % (23953)Instruction limit reached!
% 20.90/4.16 % (23953)------------------------------
% 20.90/4.16 % (23953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.90/4.16 % (23953)Termination reason: Unknown
% 20.90/4.16 % (23953)Termination phase: Saturation
% 20.90/4.16
% 20.90/4.16 % (23953)Memory used [KB]: 6652
% 20.90/4.16 % (23953)Time elapsed: 0.026 s
% 20.90/4.16 % (23953)Instructions burned: 90 (million)
% 20.90/4.16 % (23953)------------------------------
% 20.90/4.16 % (23953)------------------------------
% 20.90/4.16 % (23954)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_23484 for (2973ds/593Mi)
% 20.90/4.17 % (23955)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_23484 for (2973ds/1512Mi)
% 21.12/4.20 % (23935)Instruction limit reached!
% 21.12/4.20 % (23935)------------------------------
% 21.12/4.20 % (23935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.12/4.20 % (23935)Termination reason: Unknown
% 21.12/4.20 % (23935)Termination phase: Saturation
% 21.12/4.20
% 21.12/4.20 % (23935)Memory used [KB]: 6908
% 21.12/4.20 % (23935)Time elapsed: 1.058 s
% 21.12/4.20 % (23935)Instructions burned: 4714 (million)
% 21.12/4.20 % (23935)------------------------------
% 21.12/4.20 % (23935)------------------------------
% 21.12/4.21 % (23956)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_23484 for (2972ds/569Mi)
% 21.12/4.25 % (23952)Refutation not found, non-redundant clauses discarded% (23952)------------------------------
% 21.12/4.25 % (23952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.12/4.25 % (23952)Termination reason: Refutation not found, non-redundant clauses discarded
% 21.12/4.25
% 21.12/4.25 % (23952)Memory used [KB]: 7675
% 21.12/4.25 % (23952)Time elapsed: 0.168 s
% 21.12/4.25 % (23952)Instructions burned: 472 (million)
% 21.12/4.25 % (23952)------------------------------
% 21.12/4.25 % (23952)------------------------------
% 21.12/4.26 % (23957)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_23484 for (2972ds/501Mi)
% 21.39/4.35 % (23954)Instruction limit reached!
% 21.39/4.35 % (23954)------------------------------
% 21.39/4.35 % (23954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.39/4.35 % (23954)Termination reason: Unknown
% 21.39/4.35 % (23954)Termination phase: Saturation
% 21.39/4.35
% 21.39/4.35 % (23954)Memory used [KB]: 7675
% 21.39/4.35 % (23954)Time elapsed: 0.209 s
% 21.39/4.35 % (23954)Instructions burned: 594 (million)
% 21.39/4.35 % (23954)------------------------------
% 21.39/4.35 % (23954)------------------------------
% 21.39/4.35 % (23956)Instruction limit reached!
% 21.39/4.35 % (23956)------------------------------
% 21.39/4.35 % (23956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.39/4.35 % (23956)Termination reason: Unknown
% 21.39/4.35 % (23956)Termination phase: Saturation
% 21.39/4.35
% 21.39/4.35 % (23956)Memory used [KB]: 8443
% 21.39/4.35 % (23956)Time elapsed: 0.147 s
% 21.39/4.35 % (23956)Instructions burned: 572 (million)
% 21.39/4.35 % (23956)------------------------------
% 21.39/4.35 % (23956)------------------------------
% 21.39/4.36 % (23958)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_23484 for (2971ds/562Mi)
% 21.39/4.36 % (23959)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_23484 for (2971ds/406Mi)
% 21.85/4.41 % (23957)Instruction limit reached!
% 21.85/4.41 % (23957)------------------------------
% 21.85/4.41 % (23957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.85/4.41 % (23957)Termination reason: Unknown
% 21.85/4.41 % (23957)Termination phase: Saturation
% 21.85/4.41
% 21.85/4.41 % (23957)Memory used [KB]: 8443
% 21.85/4.41 % (23957)Time elapsed: 0.158 s
% 21.85/4.41 % (23957)Instructions burned: 502 (million)
% 21.85/4.41 % (23957)------------------------------
% 21.85/4.41 % (23957)------------------------------
% 21.85/4.42 % (23960)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_23484 for (2970ds/582Mi)
% 21.85/4.43 % (23959)Refutation not found, incomplete strategy
% 21.85/4.43 % (23959)------------------------------
% 21.85/4.43 % (23959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.85/4.43 % (23959)Termination reason: Refutation not found, incomplete strategy
% 21.85/4.43
% 21.85/4.43
% 21.85/4.43 % (23959)Memory used [KB]: 6524
% 21.85/4.43 % (23959)Time elapsed: 0.064 s
% 21.85/4.43 % (23959)Instructions burned: 232 (million)
% 21.85/4.43 % (23959)------------------------------
% 21.85/4.43 % (23959)------------------------------
% 21.85/4.44 % (23961)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_23484 for (2970ds/456Mi)
% 22.19/4.50 % (23950)Instruction limit reached!
% 22.19/4.50 % (23950)------------------------------
% 22.19/4.50 % (23950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.19/4.50 % (23950)Termination reason: Unknown
% 22.19/4.50 % (23950)Termination phase: Saturation
% 22.19/4.50
% 22.19/4.50 % (23950)Memory used [KB]: 10106
% 22.19/4.50 % (23950)Time elapsed: 0.453 s
% 22.19/4.50 % (23950)Instructions burned: 1764 (million)
% 22.19/4.50 % (23950)------------------------------
% 22.19/4.50 % (23950)------------------------------
% 22.19/4.51 % (23963)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_23484 for (2969ds/393Mi)
% 22.19/4.53 % (23958)Instruction limit reached!
% 22.19/4.53 % (23958)------------------------------
% 22.19/4.53 % (23958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.19/4.53 % (23958)Termination reason: Unknown
% 22.19/4.53 % (23958)Termination phase: Saturation
% 22.19/4.53
% 22.19/4.53 % (23958)Memory used [KB]: 7547
% 22.19/4.53 % (23958)Time elapsed: 0.174 s
% 22.19/4.53 % (23958)Instructions burned: 562 (million)
% 22.19/4.53 % (23958)------------------------------
% 22.19/4.53 % (23958)------------------------------
% 22.19/4.54 % (23964)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_23484 for (2969ds/1335Mi)
% 22.19/4.58 % (23961)Instruction limit reached!
% 22.19/4.58 % (23961)------------------------------
% 22.19/4.58 % (23961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.19/4.58 % (23961)Termination reason: Unknown
% 22.19/4.58 % (23961)Termination phase: Saturation
% 22.19/4.58
% 22.19/4.58 % (23961)Memory used [KB]: 7803
% 22.19/4.58 % (23961)Time elapsed: 0.141 s
% 22.19/4.58 % (23961)Instructions burned: 458 (million)
% 22.19/4.58 % (23961)------------------------------
% 22.19/4.58 % (23961)------------------------------
% 22.19/4.59 % (23965)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_23484 for (2968ds/3373Mi)
% 23.08/4.61 % (23960)Instruction limit reached!
% 23.08/4.61 % (23960)------------------------------
% 23.08/4.61 % (23960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.08/4.61 % (23960)Termination reason: Unknown
% 23.08/4.61 % (23960)Termination phase: Saturation
% 23.08/4.61
% 23.08/4.61 % (23960)Memory used [KB]: 8699
% 23.08/4.61 % (23960)Time elapsed: 0.184 s
% 23.08/4.61 % (23960)Instructions burned: 584 (million)
% 23.08/4.61 % (23960)------------------------------
% 23.08/4.61 % (23960)------------------------------
% 23.08/4.62 % (23966)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_23484 for (2968ds/474Mi)
% 23.08/4.62 % (23963)Instruction limit reached!
% 23.08/4.62 % (23963)------------------------------
% 23.08/4.62 % (23963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.08/4.62 % (23963)Termination reason: Unknown
% 23.08/4.62 % (23963)Termination phase: Saturation
% 23.08/4.62
% 23.08/4.62 % (23963)Memory used [KB]: 8059
% 23.08/4.62 % (23963)Time elapsed: 0.117 s
% 23.08/4.62 % (23963)Instructions burned: 393 (million)
% 23.08/4.62 % (23963)------------------------------
% 23.08/4.62 % (23963)------------------------------
% 23.08/4.63 % (23967)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_23484 for (2968ds/157Mi)
% 23.08/4.65 % (23955)Instruction limit reached!
% 23.08/4.65 % (23955)------------------------------
% 23.08/4.65 % (23955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.08/4.65 % (23955)Termination reason: Unknown
% 23.08/4.65 % (23955)Termination phase: Saturation
% 23.08/4.65
% 23.08/4.65 % (23955)Memory used [KB]: 12281
% 23.08/4.65 % (23955)Time elapsed: 0.508 s
% 23.08/4.65 % (23955)Instructions burned: 1514 (million)
% 23.08/4.65 % (23955)------------------------------
% 23.08/4.65 % (23955)------------------------------
% 23.08/4.66 % (23968)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_23484 for (2968ds/590Mi)
% 23.08/4.67 % (23967)Instruction limit reached!
% 23.08/4.67 % (23967)------------------------------
% 23.08/4.67 % (23967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.08/4.67 % (23967)Termination reason: Unknown
% 23.08/4.67 % (23967)Termination phase: Saturation
% 23.08/4.67
% 23.08/4.67 % (23967)Memory used [KB]: 6524
% 23.08/4.67 % (23967)Time elapsed: 0.041 s
% 23.08/4.67 % (23967)Instructions burned: 160 (million)
% 23.08/4.67 % (23967)------------------------------
% 23.08/4.67 % (23967)------------------------------
% 23.08/4.68 % (23969)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_23484 for (2967ds/104Mi)
% 24.05/4.71 % (23969)Instruction limit reached!
% 24.05/4.71 % (23969)------------------------------
% 24.05/4.71 % (23969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.05/4.71 % (23969)Termination reason: Unknown
% 24.05/4.71 % (23969)Termination phase: Saturation
% 24.05/4.71
% 24.05/4.71 % (23969)Memory used [KB]: 6780
% 24.05/4.71 % (23969)Time elapsed: 0.029 s
% 24.05/4.71 % (23969)Instructions burned: 106 (million)
% 24.05/4.71 % (23969)------------------------------
% 24.05/4.71 % (23969)------------------------------
% 24.05/4.72 % (23970)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_23484 for (2967ds/414Mi)
% 24.05/4.73 % (23966)Instruction limit reached!
% 24.05/4.73 % (23966)------------------------------
% 24.05/4.73 % (23966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.05/4.73 % (23966)Termination reason: Unknown
% 24.05/4.73 % (23966)Termination phase: Saturation
% 24.05/4.73
% 24.05/4.73 % (23966)Memory used [KB]: 8699
% 24.05/4.73 % (23966)Time elapsed: 0.115 s
% 24.05/4.73 % (23966)Instructions burned: 474 (million)
% 24.05/4.73 % (23966)------------------------------
% 24.05/4.73 % (23966)------------------------------
% 24.05/4.74 % (23971)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_23484 for (2967ds/715Mi)
% 24.31/4.83 % (23970)Instruction limit reached!
% 24.31/4.83 % (23970)------------------------------
% 24.31/4.83 % (23970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.31/4.83 % (23970)Termination reason: Unknown
% 24.31/4.83 % (23970)Termination phase: Saturation
% 24.31/4.83
% 24.31/4.83 % (23970)Memory used [KB]: 6524
% 24.31/4.83 % (23970)Time elapsed: 0.105 s
% 24.31/4.83 % (23970)Instructions burned: 416 (million)
% 24.31/4.83 % (23970)------------------------------
% 24.31/4.83 % (23970)------------------------------
% 24.31/4.83 % (23972)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_23484 for (2966ds/961Mi)
% 24.31/4.84 % (23968)Instruction limit reached!
% 24.31/4.84 % (23968)------------------------------
% 24.31/4.84 % (23968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.31/4.84 % (23968)Termination reason: Unknown
% 24.31/4.84 % (23968)Termination phase: Saturation
% 24.31/4.84
% 24.31/4.84 % (23968)Memory used [KB]: 8955
% 24.31/4.84 % (23968)Time elapsed: 0.177 s
% 24.31/4.84 % (23968)Instructions burned: 591 (million)
% 24.31/4.84 % (23968)------------------------------
% 24.31/4.84 % (23968)------------------------------
% 24.31/4.85 % (23973)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_23484 for (2966ds/1213Mi)
% 24.71/4.91 % (23964)Refutation not found, non-redundant clauses discarded% (23964)------------------------------
% 24.71/4.91 % (23964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.71/4.91 % (23964)Termination reason: Refutation not found, non-redundant clauses discarded
% 24.71/4.91
% 24.71/4.91 % (23964)Memory used [KB]: 7547
% 24.71/4.91 % (23964)Time elapsed: 0.366 s
% 24.71/4.91 % (23964)Instructions burned: 1321 (million)
% 24.71/4.91 % (23964)------------------------------
% 24.71/4.91 % (23964)------------------------------
% 24.71/4.92 % (23974)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_23484 for (2965ds/1979Mi)
% 24.71/4.96 % (23971)Instruction limit reached!
% 24.71/4.96 % (23971)------------------------------
% 24.71/4.96 % (23971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.71/4.96 % (23971)Termination reason: Unknown
% 24.71/4.96 % (23971)Termination phase: Saturation
% 24.71/4.96
% 24.71/4.96 % (23971)Memory used [KB]: 3582
% 24.71/4.96 % (23971)Time elapsed: 0.221 s
% 24.71/4.96 % (23971)Instructions burned: 715 (million)
% 24.71/4.96 % (23971)------------------------------
% 24.71/4.96 % (23971)------------------------------
% 24.71/4.97 % (23975)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_23484 for (2965ds/481Mi)
% 27.40/5.08 % (23975)Instruction limit reached!
% 27.40/5.08 % (23975)------------------------------
% 27.40/5.08 % (23975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.40/5.08 % (23975)Termination reason: Unknown
% 27.40/5.08 % (23975)Termination phase: Saturation
% 27.40/5.08
% 27.40/5.08 % (23975)Memory used [KB]: 8443
% 27.40/5.08 % (23975)Time elapsed: 0.117 s
% 27.40/5.08 % (23975)Instructions burned: 482 (million)
% 27.40/5.08 % (23975)------------------------------
% 27.40/5.08 % (23975)------------------------------
% 27.40/5.09 % (23976)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_23484 for (2963ds/783Mi)
% 28.08/5.13 % (23972)Instruction limit reached!
% 28.08/5.13 % (23972)------------------------------
% 28.08/5.13 % (23972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.08/5.13 % (23972)Termination reason: Unknown
% 28.08/5.13 % (23972)Termination phase: Saturation
% 28.08/5.13
% 28.08/5.13 % (23972)Memory used [KB]: 8187
% 28.08/5.13 % (23972)Time elapsed: 0.297 s
% 28.08/5.13 % (23972)Instructions burned: 961 (million)
% 28.08/5.13 % (23972)------------------------------
% 28.08/5.13 % (23972)------------------------------
% 28.08/5.14 % (23977)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_23484 for (2963ds/432Mi)
% 28.08/5.16 % (23965)First to succeed.
% 28.08/5.16 % (23965)Refutation found. Thanks to Tanya!
% 28.08/5.16 % SZS status Theorem for DTF2THF_23484
% 28.08/5.16 % SZS output start Proof for DTF2THF_23484
% 28.08/5.16 thf(func_def_0, type, in: $i > $i > $o).
% 28.08/5.16 thf(func_def_1, type, exu: ($i > $o) > $o).
% 28.08/5.16 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 28.08/5.16 thf(func_def_8, type, powerset: $i > $i).
% 28.08/5.16 thf(func_def_10, type, setunion: $i > $i).
% 28.08/5.16 thf(func_def_19, type, descr: ($i > $o) > $i).
% 28.08/5.16 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 28.08/5.16 thf(func_def_26, type, prop2set: $o > $i).
% 28.08/5.16 thf(func_def_36, type, nonempty: $i > $o).
% 28.08/5.16 thf(func_def_69, type, set2prop: $i > $o).
% 28.08/5.16 thf(func_def_88, type, subset: $i > $i > $o).
% 28.08/5.16 thf(func_def_89, type, disjoint: $i > $i > $o).
% 28.08/5.16 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 28.08/5.16 thf(func_def_114, type, binunion: $i > $i > $i).
% 28.08/5.16 thf(func_def_122, type, binintersect: $i > $i > $i).
% 28.08/5.16 thf(func_def_135, type, regular: $i > $o).
% 28.08/5.16 thf(func_def_136, type, setminus: $i > $i > $i).
% 28.08/5.16 thf(func_def_147, type, symdiff: $i > $i > $i).
% 28.08/5.16 thf(func_def_170, type, sK4: $i > $i > $i).
% 28.08/5.16 thf(func_def_171, type, sK5: ($i > $o) > $i > ($i > $o) > $i > $i).
% 28.08/5.16 thf(func_def_172, type, sK6: $i > $i > ($i > $o) > ($i > $o) > $i).
% 28.08/5.16 thf(func_def_173, type, sK7: ($i > $o) > $i).
% 28.08/5.16 thf(func_def_174, type, sK8: ($i > $o) > $i).
% 28.08/5.16 thf(func_def_175, type, sK9: ($i > $o) > $i).
% 28.08/5.16 thf(func_def_176, type, sK10: ($i > $o) > $i).
% 28.08/5.16 thf(func_def_177, type, sK11: ($i > $o) > $i).
% 28.08/5.16 thf(func_def_178, type, sK12: ($i > $o) > $i > $i).
% 28.08/5.16 thf(func_def_179, type, sK13: ($i > $o) > $i > $i).
% 28.08/5.16 thf(func_def_180, type, sK14: $i > ($i > $o) > $i).
% 28.08/5.16 thf(func_def_181, type, sK15: $i > $i > $i).
% 28.08/5.16 thf(func_def_182, type, sK16: ($i > $o) > $i > $i).
% 28.08/5.16 thf(func_def_183, type, sK17: $i > $i).
% 28.08/5.16 thf(func_def_184, type, sK18: $i > $i > $i).
% 28.08/5.16 thf(func_def_185, type, sK19: $i > $i > $i).
% 28.08/5.16 thf(func_def_186, type, sK20: $i > $i > $i).
% 28.08/5.16 thf(func_def_187, type, sK21: $i > $i).
% 28.08/5.16 thf(func_def_188, type, sK22: $i > $i > $i).
% 28.08/5.16 thf(func_def_189, type, sK23: $i > ($i > $o) > $i).
% 28.08/5.16 thf(func_def_190, type, sK24: ($i > $o) > $i > $i).
% 28.08/5.16 thf(func_def_191, type, sK25: ($i > $o) > $i).
% 28.08/5.16 thf(func_def_192, type, sK26: ($i > $o) > $i > $i).
% 28.08/5.16 thf(func_def_194, type, sK27: ($i > $i > $o) > $i > $i).
% 28.08/5.16 thf(func_def_195, type, sK28: ($i > $i > $o) > $i > $i).
% 28.08/5.16 thf(func_def_196, type, sK29: ($i > $i > $o) > $i > $i > $i).
% 28.08/5.16 thf(func_def_197, type, sK30: ($i > $i > $o) > $i > $i).
% 28.08/5.16 thf(func_def_198, type, sK31: ($i > $i > $o) > $i > $i > $i).
% 28.08/5.16 thf(func_def_199, type, sK32: ($i > $i > $o) > $i > $i > $i).
% 28.08/5.16 thf(func_def_200, type, sK33: ($i > $i > $o) > $i > $i > $i).
% 28.08/5.16 thf(func_def_201, type, sK34: ($i > $i > $o) > $i > $i > $i).
% 28.08/5.16 thf(func_def_202, type, sK35: ($i > $o) > $i > $i).
% 28.08/5.16 thf(func_def_203, type, sK36: $i > $i).
% 28.08/5.16 thf(func_def_204, type, sK37: $i > $o > $i > $i).
% 28.08/5.16 thf(func_def_205, type, sK38: $i > $i).
% 28.08/5.16 thf(func_def_206, type, sK39: $i > $i > $i).
% 28.08/5.16 thf(func_def_207, type, sK40: $i > $i > $i).
% 28.08/5.16 thf(func_def_208, type, sK41: $i > $i > $i).
% 28.08/5.16 thf(func_def_209, type, sK42: $i > $i > $i).
% 28.08/5.16 thf(func_def_210, type, sK43: $i > $i).
% 28.08/5.16 thf(func_def_211, type, sK44: ($i > $o) > $i).
% 28.08/5.16 thf(func_def_212, type, sK45: ($i > $o) > $i > $i).
% 28.08/5.16 thf(func_def_213, type, sK46: ($i > $o) > ($i > $o) > $i).
% 28.08/5.16 thf(func_def_214, type, sK47: ($i > $o) > ($i > $o) > $i).
% 28.08/5.16 thf(func_def_215, type, sK48: ($i > $o) > $i).
% 28.08/5.16 thf(func_def_216, type, sK49: ($i > $o) > $i > $i).
% 28.08/5.16 thf(func_def_217, type, sK50: ($i > $o) > $i > $i).
% 28.08/5.16 thf(func_def_218, type, sK51: ($i > $o) > $i).
% 28.08/5.16 thf(func_def_219, type, sK52: ($i > $o) > $i > $i).
% 28.08/5.16 thf(func_def_220, type, sK53: ($i > $o) > $i).
% 28.08/5.16 thf(func_def_221, type, sK54: ($i > $o) > $i > $i).
% 28.08/5.16 thf(func_def_222, type, sK55: ($i > $o) > $i > $i).
% 28.08/5.16 thf(func_def_223, type, sK56: ($i > $o) > $i).
% 28.08/5.16 thf(func_def_224, type, sK57: ($i > $o) > $i > $i).
% 28.08/5.16 thf(func_def_225, type, sK58: ($i > $o) > $i > $i).
% 28.08/5.16 thf(func_def_226, type, sK59: ($i > $o) > $i).
% 28.08/5.16 thf(func_def_227, type, sK60: ($i > $o) > $i > $i).
% 28.08/5.16 thf(func_def_228, type, sK61: ($i > $o) > $i > $i).
% 28.08/5.16 thf(func_def_229, type, sK62: ($i > $o) > $i).
% 28.08/5.16 thf(func_def_230, type, sK63: ($i > $o) > $i > $i).
% 28.08/5.16 thf(func_def_231, type, sK64: ($i > $o) > $i > $i).
% 28.08/5.16 thf(func_def_232, type, sK65: ($i > $o) > $i > $i).
% 28.08/5.16 thf(func_def_233, type, sK66: $i > $i).
% 28.08/5.16 thf(func_def_234, type, sK67: $i > $i > $i > $i).
% 28.08/5.16 thf(func_def_235, type, sK68: $i > $i > $i).
% 28.08/5.16 thf(func_def_236, type, sK69: $i > $i > $i).
% 28.08/5.16 thf(func_def_237, type, sK70: $i > $i > $i).
% 28.08/5.16 thf(func_def_238, type, sK71: $i > $i > $i).
% 28.08/5.16 thf(func_def_239, type, sK72: $i > $i).
% 28.08/5.16 thf(func_def_240, type, sK73: ($i > $o) > ($i > $o) > $i).
% 28.08/5.16 thf(func_def_241, type, sK74: ($i > $o) > ($i > $o) > $i).
% 28.08/5.16 thf(func_def_242, type, sK75: ($i > $o) > $i > $i).
% 28.08/5.16 thf(func_def_243, type, sK76: ($i > $o) > $i > $i).
% 28.08/5.16 thf(func_def_244, type, sK77: ($i > $o) > $i > $i).
% 28.08/5.16 thf(func_def_245, type, sK78: ($i > $o) > $i > $i).
% 28.08/5.16 thf(func_def_246, type, sK79: ($i > $o) > $i > $i).
% 28.08/5.16 thf(func_def_247, type, sK80: ($i > $o) > $i > $i).
% 28.08/5.16 thf(func_def_248, type, sK81: ($i > $o) > $i > $i).
% 28.08/5.16 thf(func_def_249, type, sK82: ($i > $o) > $i > $i).
% 28.08/5.16 thf(func_def_250, type, sK83: ($i > $o) > $i > $i).
% 28.08/5.16 thf(func_def_251, type, sK84: $i > ($i > $o) > $i).
% 28.08/5.16 thf(func_def_252, type, sK85: $i > ($i > $o) > $i).
% 28.08/5.16 thf(func_def_253, type, ph86: !>[X0: $tType]:(X0)).
% 28.08/5.16 thf(f7733,plain,(
% 28.08/5.16 $false),
% 28.08/5.16 inference(avatar_sat_refutation,[status(thm)],[f2377,f2396,f2401,f2407,f2508,f7729,f7730])).
% 28.08/5.16 thf(f7730,plain,(
% 28.08/5.16 ((in @ sK0 @ sK2) != $false) | ((in @ sK0 @ sK2) != $true) | ($true = $false)),
% 28.08/5.16 introduced(definition,[],[theory_tautology_sat_conflict])).
% 28.08/5.16 thf(f7729,plain,(
% 28.08/5.16 spl3_36 | ~spl3_22),
% 28.08/5.16 inference(avatar_split_clause,[status(thm)],[f7715,f2505,f7725])).
% 28.08/5.16 thf(f7725,definition,(
% 28.08/5.16 spl3_36 <=> ((in @ sK0 @ sK2) = $false)),
% 28.08/5.16 introduced(definition,[new_symbols(naming,[spl3_36])],[avatar_definition])).
% 28.08/5.16 thf(f2505,definition,(
% 28.08/5.16 spl3_22 <=> ($false = (in @ sK0 @ (binunion @ sK1 @ sK2)))),
% 28.08/5.16 introduced(definition,[new_symbols(naming,[spl3_22])],[avatar_definition])).
% 28.08/5.16 thf(f7715,plain,(
% 28.08/5.16 ((in @ sK0 @ sK2) = $false) | ~spl3_22),
% 28.08/5.16 inference(trivial_inequality_removal,[status(thm)],[f7708])).
% 28.08/5.16 thf(f7708,plain,(
% 28.08/5.16 ((in @ sK0 @ sK2) = $false) | ($true = $false) | ~spl3_22),
% 28.08/5.16 inference(superposition,[status(thm)],[f2507,f2269])).
% 28.08/5.16 thf(f2269,plain,(
% 28.08/5.16 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X2 @ (binunion @ X1 @ X3)) = $true) | ((in @ X2 @ X3) = $false)) )),
% 28.08/5.16 inference(binary_proxy_clausification,[status(thm)],[f2268])).
% 28.08/5.16 thf(f2268,plain,(
% 28.08/5.16 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X2 @ X3) => (in @ X2 @ (binunion @ X1 @ X3))))) )),
% 28.08/5.16 inference(beta_eta_normalization,[status(thm)],[f2267])).
% 28.08/5.16 thf(f2267,plain,(
% 28.08/5.16 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ X2 @ Y0) => (in @ X2 @ (binunion @ X1 @ Y0)))) @ X3) = $true)) )),
% 28.08/5.16 inference(pi_clausification,[status(thm)],[f2266])).
% 28.08/5.16 thf(f2266,plain,(
% 28.08/5.16 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ Y0) => (in @ X2 @ (binunion @ X1 @ Y0))))))) )),
% 28.08/5.16 inference(beta_eta_normalization,[status(thm)],[f2265])).
% 28.08/5.16 thf(f2265,plain,(
% 28.08/5.16 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ X1 @ Y1)))))) @ X2) = $true)) )),
% 28.08/5.16 inference(pi_clausification,[status(thm)],[f2264])).
% 28.08/5.16 thf(f2264,plain,(
% 28.08/5.16 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ X1 @ Y1))))))) = $true)) )),
% 28.08/5.16 inference(beta_eta_normalization,[status(thm)],[f2263])).
% 28.08/5.16 thf(f2263,plain,(
% 28.08/5.16 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (binunion @ Y0 @ Y2)))))))) @ X1))) )),
% 28.08/5.16 inference(pi_clausification,[status(thm)],[f738])).
% 28.08/5.16 thf(f738,plain,(
% 28.08/5.16 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (binunion @ Y0 @ Y2))))))))) = $true)),
% 28.08/5.16 inference(definition_unfolding,[status(thm)],[f600,f455])).
% 28.08/5.16 thf(f455,plain,(
% 28.08/5.16 (binunionIR = $true)),
% 28.08/5.16 inference(cnf_transformation,[status(thm)],[f400])).
% 28.08/5.16 thf(f400,plain,(
% 28.08/5.16 (binintersectSubset1 = $true) & (emptyinPowerset = $true) & (setminusIRneg = $true) & (powersetE = $true) & (setext = $true) & (disjointsetsI1 = $true) & (sepInPowerset = $true) & (bs114d = $true) & (binintersectRsub = $true) & (setminusLsub = $true) & (setminusSubset2 = $true) & (((in @ sK0 @ (symdiff @ sK1 @ sK2)) != $true) & ((in @ sK0 @ sK2) = $true) & ((in @ sK0 @ sK1) != $true)) & (binintersectLsub = $true) & (setadjoinIR = $true) & (subPowSU = $true) & (replAx = $true) & (emptyset__Cong = $true) & (emptysetsubset = $true) & (uniqinunit = $true) & (dsetconstr__Cong = $true) & (binunionLsub = $true) & (setminusERneg = $true) & (quantDeMorgan1 = $true) & (subsetE2 = $true) & (prop2setI = $true) & (quantDeMorgan4 = $true) & (exuE1 = $true) & (powersetE1 = $true) & (emptyinunitempty = $true) & (notequalI1 = $true) & (notequalI2 = $true) & (nonemptyE1 = $true) & (binunionE = $true) & (exuE2 = $true) & (setminusELneg = $true) & (in__Cong = $true) & (exuI3 = $true) & (subsetRefl = $true) & (binintersectSubset4 = $true) & (exuE3u = $true) & (nonemptyI = $true) & (subset2powerset = $true) & (binintersectSubset5 = $true) & (subsetemptysetimpeq = $true) & (dsetconstrEL = $true) & (setoftrueEq = $true) & (powerset__Cong = $true) & (singletonsswitch = $true) & (notsubsetI = $true) & (emptyI = $true) & (setadjoinIL = $true) & (sepSubset = $true) & (inPowerset = $true) & (emptysetAx = $true) & (subsetI2 = $true) & (prop2setE = $true) & (setunionI = $true) & (binintersectSubset2 = $true) & (setextAx = $true) & (binunionIL = $true) & (setextsub = $true) & (setminusILneg = $true) & (binunionEcases = $true) & (binintersectI = $true) & (binunionRsub = $true) & (notinemptyset = $true) & (powersetsubset = $true) & (exuI1 = $true) & (symdiffI1 = $true) & (nonemptyI1 = $true) & (setadjoinAx = $true) & (foundationAx = $true) & (setunionAx = $true) & (eqimpsubset1 = $true) & (wellorderingAx = $true) & (emptysetE = $true) & (binintersectER = $true) & (powersetI = $true) & (omega0Ax = $true) & (upairsetIL = $true) & (omega__Cong = $true) & (emptysetimpfalse = $true) & (setadjoinOr = $true) & (eqinunit = $true) & (quantDeMorgan2 = $true) & (exuI2 = $true) & (setminusEL = $true) & (inCongP = $true) & (dsetconstrER = $true) & (powersetI1 = $true) & (exu__Cong = $true) & (notinsingleton = $true) & (dsetconstrI = $true) & (setbeta = $true) & (setadjoin__Cong = $true) & (binintersectSubset3 = $true) & (prop2set2propI = $true) & (exuE3e = $true) & (descrp = $true) & (setunion__Cong = $true) & (setadjoinE = $true) & (symdiffE = $true) & (setadjoinSub2 = $true) & (exuEu = $true) & (noeltsimpempty = $true) & (notdallE = $true) & (emptyE1 = $true) & (omegaIndAx = $true) & (quantDeMorgan3 = $true) & (upairsetIR = $true) & (upairset2IR = $true) & (setminusSubset1 = $true) & (nonemptyImpWitness = $true) & (subsetI1 = $true) & (upairsetE = $true) & (subsetTrans = $true) & (omegaSAx = $true) & (setminusER = $true) & (setadjoinSub = $true) & (subsetE = $true) & (descr__Cong = $true) & (binunionIR = $true) & (emptyInPowerset = $true) & (eqimpsubset2 = $true) & (setminusI = $true) & (binintersectEL = $true) & (powersetAx = $true) & (notdexE = $true) & (setunionE = $true) & (vacuousDall = $true)),
% 28.08/5.16 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f398,f399])).
% 28.08/5.16 thf(f399,plain,(
% 28.08/5.16 ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ (symdiff @ X1 @ X2))) & ($true = (in @ X0 @ X2)) & ((in @ X0 @ X1) != $true)) => (((in @ sK0 @ (symdiff @ sK1 @ sK2)) != $true) & ((in @ sK0 @ sK2) = $true) & ((in @ sK0 @ sK1) != $true))),
% 28.08/5.16 introduced(definition,[],[choice_axiom])).
% 28.08/5.16 thf(f398,plain,(
% 28.08/5.16 (binintersectSubset1 = $true) & (emptyinPowerset = $true) & (setminusIRneg = $true) & (powersetE = $true) & (setext = $true) & (disjointsetsI1 = $true) & (sepInPowerset = $true) & (bs114d = $true) & (binintersectRsub = $true) & (setminusLsub = $true) & (setminusSubset2 = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ (symdiff @ X1 @ X2))) & ($true = (in @ X0 @ X2)) & ((in @ X0 @ X1) != $true)) & (binintersectLsub = $true) & (setadjoinIR = $true) & (subPowSU = $true) & (replAx = $true) & (emptyset__Cong = $true) & (emptysetsubset = $true) & (uniqinunit = $true) & (dsetconstr__Cong = $true) & (binunionLsub = $true) & (setminusERneg = $true) & (quantDeMorgan1 = $true) & (subsetE2 = $true) & (prop2setI = $true) & (quantDeMorgan4 = $true) & (exuE1 = $true) & (powersetE1 = $true) & (emptyinunitempty = $true) & (notequalI1 = $true) & (notequalI2 = $true) & (nonemptyE1 = $true) & (binunionE = $true) & (exuE2 = $true) & (setminusELneg = $true) & (in__Cong = $true) & (exuI3 = $true) & (subsetRefl = $true) & (binintersectSubset4 = $true) & (exuE3u = $true) & (nonemptyI = $true) & (subset2powerset = $true) & (binintersectSubset5 = $true) & (subsetemptysetimpeq = $true) & (dsetconstrEL = $true) & (setoftrueEq = $true) & (powerset__Cong = $true) & (singletonsswitch = $true) & (notsubsetI = $true) & (emptyI = $true) & (setadjoinIL = $true) & (sepSubset = $true) & (inPowerset = $true) & (emptysetAx = $true) & (subsetI2 = $true) & (prop2setE = $true) & (setunionI = $true) & (binintersectSubset2 = $true) & (setextAx = $true) & (binunionIL = $true) & (setextsub = $true) & (setminusILneg = $true) & (binunionEcases = $true) & (binintersectI = $true) & (binunionRsub = $true) & (notinemptyset = $true) & (powersetsubset = $true) & (exuI1 = $true) & (symdiffI1 = $true) & (nonemptyI1 = $true) & (setadjoinAx = $true) & (foundationAx = $true) & (setunionAx = $true) & (eqimpsubset1 = $true) & (wellorderingAx = $true) & (emptysetE = $true) & (binintersectER = $true) & (powersetI = $true) & (omega0Ax = $true) & (upairsetIL = $true) & (omega__Cong = $true) & (emptysetimpfalse = $true) & (setadjoinOr = $true) & (eqinunit = $true) & (quantDeMorgan2 = $true) & (exuI2 = $true) & (setminusEL = $true) & (inCongP = $true) & (dsetconstrER = $true) & (powersetI1 = $true) & (exu__Cong = $true) & (notinsingleton = $true) & (dsetconstrI = $true) & (setbeta = $true) & (setadjoin__Cong = $true) & (binintersectSubset3 = $true) & (prop2set2propI = $true) & (exuE3e = $true) & (descrp = $true) & (setunion__Cong = $true) & (setadjoinE = $true) & (symdiffE = $true) & (setadjoinSub2 = $true) & (exuEu = $true) & (noeltsimpempty = $true) & (notdallE = $true) & (emptyE1 = $true) & (omegaIndAx = $true) & (quantDeMorgan3 = $true) & (upairsetIR = $true) & (upairset2IR = $true) & (setminusSubset1 = $true) & (nonemptyImpWitness = $true) & (subsetI1 = $true) & (upairsetE = $true) & (subsetTrans = $true) & (omegaSAx = $true) & (setminusER = $true) & (setadjoinSub = $true) & (subsetE = $true) & (descr__Cong = $true) & (binunionIR = $true) & (emptyInPowerset = $true) & (eqimpsubset2 = $true) & (setminusI = $true) & (binintersectEL = $true) & (powersetAx = $true) & (notdexE = $true) & (setunionE = $true) & (vacuousDall = $true)),
% 28.08/5.16 inference(flattening,[status(thm)],[f397])).
% 28.08/5.16 thf(f397,plain,(
% 28.08/5.16 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : ((($true != (in @ X0 @ (symdiff @ X1 @ X2))) & ($true = (in @ X0 @ X2))) & ((in @ X0 @ X1) != $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 28.08/5.16 inference(ennf_transformation,[status(thm)],[f396])).
% 28.08/5.16 thf(f396,plain,(
% 28.08/5.16 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) != $true) => (($true = (in @ X0 @ X2)) => ($true = (in @ X0 @ (symdiff @ X1 @ X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 28.08/5.16 inference(flattening,[status(thm)],[f341])).
% 28.08/5.16 thf(f341,plain,(
% 28.08/5.16 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (~((in @ X0 @ X1) = $true) => (($true = (in @ X0 @ X2)) => ($true = (in @ X0 @ (symdiff @ X1 @ X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 28.08/5.16 inference(fool_elimination,[status(thm)],[f340])).
% 28.08/5.16 thf(f340,plain,(
% 28.08/5.16 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => ! [X0 : $i,X1 : $i,X2 : $i] : (~(in @ X0 @ X1) => ((in @ X0 @ X2) => (in @ X0 @ (symdiff @ X1 @ X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 28.08/5.16 inference(rectify,[status(thm)],[f134])).
% 28.08/5.16 thf(f134,negated_conjecture,(
% 28.08/5.16 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => ! [X1 : $i,X3 : $i,X4 : $i] : (~(in @ X1 @ X3) => ((in @ X1 @ X4) => (in @ X1 @ (symdiff @ X3 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 28.08/5.16 inference(negated_conjecture,[status(cth)],[f133])).
% 28.08/5.16 thf(f133,conjecture,(
% 28.08/5.16 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => ! [X1 : $i,X3 : $i,X4 : $i] : (~(in @ X1 @ X3) => ((in @ X1 @ X4) => (in @ X1 @ (symdiff @ X3 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 28.08/5.16 file('/export/starexec/sandbox/tmp/tmp.7X3sL6M5Q7/DTF2THF_23484.p',symdiffI2)).
% 28.08/5.16 thf(f600,plain,(
% 28.08/5.16 (binunionIR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (binunion @ Y0 @ Y2))))))))))),
% 28.08/5.16 inference(cnf_transformation,[status(thm)],[f215])).
% 28.08/5.16 thf(f215,plain,(
% 28.08/5.16 (binunionIR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (binunion @ Y0 @ Y2))))))))))),
% 28.08/5.16 inference(fool_elimination,[status(thm)],[f214])).
% 28.08/5.16 thf(f214,plain,(
% 28.08/5.16 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X0) => (in @ X1 @ (binunion @ X2 @ X0))) = binunionIR)),
% 28.08/5.16 inference(rectify,[status(thm)],[f103])).
% 28.08/5.16 thf(f103,axiom,(
% 28.08/5.16 (! [X4 : $i,X1 : $i,X3 : $i] : ((in @ X1 @ X4) => (in @ X1 @ (binunion @ X3 @ X4))) = binunionIR)),
% 28.08/5.16 file('/export/starexec/sandbox/tmp/tmp.7X3sL6M5Q7/DTF2THF_23484.p',binunionIR)).
% 28.08/5.16 thf(f2507,plain,(
% 28.08/5.16 ($false = (in @ sK0 @ (binunion @ sK1 @ sK2))) | ~spl3_22),
% 28.08/5.16 inference(avatar_component_clause,[status(thm)],[f2505])).
% 28.08/5.16 thf(f2508,plain,(
% 28.08/5.16 spl3_22 | spl3_12 | spl3_16),
% 28.08/5.16 inference(avatar_split_clause,[status(thm)],[f2503,f2393,f2374,f2505])).
% 28.08/5.16 thf(f2374,definition,(
% 28.08/5.16 spl3_12 <=> ((in @ sK0 @ sK1) = $true)),
% 28.08/5.16 introduced(definition,[new_symbols(naming,[spl3_12])],[avatar_definition])).
% 28.08/5.16 thf(f2393,definition,(
% 28.08/5.16 spl3_16 <=> ($true = (in @ sK0 @ (dsetconstr @ (binunion @ sK1 @ sK2) @ (^[Y0 : $i]: ((~ (in @ Y0 @ sK2)) | (~ (in @ Y0 @ sK1)))))))),
% 28.08/5.16 introduced(definition,[new_symbols(naming,[spl3_16])],[avatar_definition])).
% 28.08/5.16 thf(f2503,plain,(
% 28.08/5.16 ($false = (in @ sK0 @ (binunion @ sK1 @ sK2))) | (spl3_12 | spl3_16)),
% 28.08/5.16 inference(subsumption_resolution,[status(thm)],[f2502,f2376])).
% 28.08/5.16 thf(f2376,plain,(
% 28.08/5.16 ((in @ sK0 @ sK1) != $true) | spl3_12),
% 28.08/5.16 inference(avatar_component_clause,[status(thm)],[f2374])).
% 28.08/5.16 thf(f2502,plain,(
% 28.08/5.16 ((in @ sK0 @ sK1) = $true) | ($false = (in @ sK0 @ (binunion @ sK1 @ sK2))) | spl3_16),
% 28.08/5.16 inference(not_proxy_clausification,[status(thm)],[f2499])).
% 28.08/5.16 thf(f2499,plain,(
% 28.08/5.16 ($false = (~ (in @ sK0 @ sK1))) | ($false = (in @ sK0 @ (binunion @ sK1 @ sK2))) | spl3_16),
% 28.08/5.16 inference(binary_proxy_clausification,[status(thm)],[f2498])).
% 28.08/5.16 thf(f2498,plain,(
% 28.08/5.16 ($false = (in @ sK0 @ (binunion @ sK1 @ sK2))) | ($false = ((~ (in @ sK0 @ sK2)) | (~ (in @ sK0 @ sK1)))) | spl3_16),
% 28.08/5.16 inference(beta_eta_normalization,[status(thm)],[f2497])).
% 28.08/5.16 thf(f2497,plain,(
% 28.08/5.16 ($false = (in @ sK0 @ (binunion @ sK1 @ sK2))) | (((^[Y0 : $i]: ((~ (in @ Y0 @ sK2)) | (~ (in @ Y0 @ sK1)))) @ sK0) = $false) | spl3_16),
% 28.08/5.16 inference(trivial_inequality_removal,[status(thm)],[f2496])).
% 28.08/5.16 thf(f2496,plain,(
% 28.08/5.16 (((^[Y0 : $i]: ((~ (in @ Y0 @ sK2)) | (~ (in @ Y0 @ sK1)))) @ sK0) = $false) | ($true != $true) | ($false = (in @ sK0 @ (binunion @ sK1 @ sK2))) | spl3_16),
% 28.08/5.16 inference(superposition,[status(thm)],[f2395,f1194])).
% 28.08/5.16 thf(f1194,plain,(
% 28.08/5.16 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (($true = (in @ X2 @ (dsetconstr @ X3 @ X1))) | ((in @ X2 @ X3) = $false) | ((X1 @ X2) = $false)) )),
% 28.08/5.16 inference(binary_proxy_clausification,[status(thm)],[f1193])).
% 28.08/5.16 thf(f1193,plain,(
% 28.08/5.16 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (((in @ X2 @ X3) = $false) | ($true = ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X3 @ X1))))) )),
% 28.08/5.16 inference(binary_proxy_clausification,[status(thm)],[f1192])).
% 28.08/5.16 thf(f1192,plain,(
% 28.08/5.16 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (($true = ((in @ X2 @ X3) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X3 @ X1)))))) )),
% 28.08/5.16 inference(beta_eta_normalization,[status(thm)],[f1191])).
% 28.08/5.16 thf(f1191,plain,(
% 28.08/5.16 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : ((((^[Y0 : $i]: ((in @ X2 @ Y0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ Y0 @ X1))))) @ X3) = $true)) )),
% 28.08/5.16 inference(pi_clausification,[status(thm)],[f1190])).
% 28.08/5.16 thf(f1190,plain,(
% 28.08/5.16 ( ! [X2 : $i,X1 : $i > $o] : (((!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ Y0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ Y0 @ X1)))))) = $true)) )),
% 28.08/5.16 inference(beta_eta_normalization,[status(thm)],[f1189])).
% 28.08/5.16 thf(f1189,plain,(
% 28.08/5.16 ( ! [X2 : $i,X1 : $i > $o] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => ((X1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ X1))))))) @ X2) = $true)) )),
% 28.08/5.16 inference(pi_clausification,[status(thm)],[f1188])).
% 28.08/5.16 thf(f1188,plain,(
% 28.08/5.16 ( ! [X1 : $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => ((X1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ X1)))))))) = $true)) )),
% 28.08/5.16 inference(beta_eta_normalization,[status(thm)],[f1187])).
% 28.08/5.16 thf(f1187,plain,(
% 28.08/5.16 ( ! [X1 : $i > $o] : ((((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) => (in @ Y1 @ (dsetconstr @ Y2 @ Y0))))))))) @ X1) = $true)) )),
% 28.08/5.16 inference(pi_clausification,[status(thm)],[f1186])).
% 28.08/5.16 thf(f1186,plain,(
% 28.08/5.16 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) => (in @ Y1 @ (dsetconstr @ Y2 @ Y0)))))))))) = $true)),
% 28.08/5.16 inference(beta_eta_normalization,[status(thm)],[f703])).
% 28.08/5.16 thf(f703,plain,(
% 28.08/5.16 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) => (in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))) = $true)),
% 28.08/5.16 inference(definition_unfolding,[status(thm)],[f484,f407])).
% 28.08/5.16 thf(f407,plain,(
% 28.08/5.16 (dsetconstrI = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) => (in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))),
% 28.08/5.16 inference(cnf_transformation,[status(thm)],[f361])).
% 28.08/5.16 thf(f361,plain,(
% 28.08/5.16 (dsetconstrI = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) => (in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))),
% 28.08/5.16 inference(fool_elimination,[status(thm)],[f360])).
% 28.08/5.16 thf(f360,plain,(
% 28.08/5.16 (! [X0 : $i,X1 : $i,X2 : $i > $o] : ((in @ X1 @ X0) => ((X2 @ X1) => (in @ X1 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X2 @ X3)))))) = dsetconstrI)),
% 28.08/5.16 inference(rectify,[status(thm)],[f14])).
% 28.08/5.16 thf(f14,axiom,(
% 28.08/5.16 (! [X3 : $i,X1 : $i,X0 : $i > $o] : ((in @ X1 @ X3) => ((X0 @ X1) => (in @ X1 @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))))) = dsetconstrI)),
% 28.08/5.16 file('/export/starexec/sandbox/tmp/tmp.7X3sL6M5Q7/DTF2THF_23484.p',dsetconstrI)).
% 28.08/5.16 thf(f484,plain,(
% 28.08/5.16 (dsetconstrI = $true)),
% 28.08/5.16 inference(cnf_transformation,[status(thm)],[f400])).
% 28.08/5.16 thf(f2395,plain,(
% 28.08/5.16 ($true != (in @ sK0 @ (dsetconstr @ (binunion @ sK1 @ sK2) @ (^[Y0 : $i]: ((~ (in @ Y0 @ sK2)) | (~ (in @ Y0 @ sK1))))))) | spl3_16),
% 28.08/5.16 inference(avatar_component_clause,[status(thm)],[f2393])).
% 28.08/5.16 thf(f2407,plain,(
% 28.08/5.16 ~spl3_18),
% 28.08/5.16 inference(avatar_split_clause,[status(thm)],[f135,f2404])).
% 28.08/5.16 thf(f2404,definition,(
% 28.08/5.16 spl3_18 <=> ($true = $false)),
% 28.08/5.16 introduced(definition,[new_symbols(naming,[spl3_18])],[avatar_definition])).
% 28.08/5.16 thf(f135,plain,(
% 28.08/5.16 ($true != $false)),
% 28.08/5.16 introduced(definition,[],[fool_axiom])).
% 28.08/5.16 thf(f2401,plain,(
% 28.08/5.16 spl3_17),
% 28.08/5.16 inference(avatar_split_clause,[status(thm)],[f566,f2398])).
% 28.08/5.16 thf(f2398,definition,(
% 28.08/5.16 spl3_17 <=> ((in @ sK0 @ sK2) = $true)),
% 28.08/5.16 introduced(definition,[new_symbols(naming,[spl3_17])],[avatar_definition])).
% 28.08/5.16 thf(f566,plain,(
% 28.08/5.16 ((in @ sK0 @ sK2) = $true)),
% 28.08/5.16 inference(cnf_transformation,[status(thm)],[f400])).
% 28.08/5.16 thf(f2396,plain,(
% 28.08/5.16 ~spl3_16),
% 28.08/5.16 inference(avatar_split_clause,[status(thm)],[f1308,f2393])).
% 28.08/5.16 thf(f1308,plain,(
% 28.08/5.16 ($true != (in @ sK0 @ (dsetconstr @ (binunion @ sK1 @ sK2) @ (^[Y0 : $i]: ((~ (in @ Y0 @ sK2)) | (~ (in @ Y0 @ sK1)))))))),
% 28.08/5.16 inference(beta_eta_normalization,[status(thm)],[f675])).
% 28.08/5.16 thf(f675,plain,(
% 28.08/5.16 ((in @ sK0 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (binunion @ Y0 @ Y1) @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) | (~ (in @ Y2 @ Y0)))))))) @ sK1 @ sK2)) != $true)),
% 28.08/5.16 inference(definition_unfolding,[status(thm)],[f567,f439])).
% 28.08/5.16 thf(f439,plain,(
% 28.08/5.16 (symdiff = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (binunion @ Y0 @ Y1) @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) | (~ (in @ Y2 @ Y0)))))))))),
% 28.08/5.16 inference(cnf_transformation,[status(thm)],[f321])).
% 28.08/5.16 thf(f321,plain,(
% 28.08/5.16 (symdiff = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (binunion @ Y0 @ Y1) @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) | (~ (in @ Y2 @ Y0)))))))))),
% 28.08/5.16 inference(fool_elimination,[status(thm)],[f320])).
% 28.08/5.16 thf(f320,plain,(
% 28.08/5.16 ((^[X0 : $i, X1 : $i] : (dsetconstr @ (binunion @ X0 @ X1) @ (^[X2 : $i] : (~(in @ X2 @ X0) | ~(in @ X2 @ X1))))) = symdiff)),
% 28.08/5.16 inference(rectify,[status(thm)],[f130])).
% 28.08/5.16 thf(f130,axiom,(
% 28.08/5.16 ((^[X3 : $i, X4 : $i] : (dsetconstr @ (binunion @ X3 @ X4) @ (^[X1 : $i] : (~(in @ X1 @ X3) | ~(in @ X1 @ X4))))) = symdiff)),
% 28.08/5.16 file('/export/starexec/sandbox/tmp/tmp.7X3sL6M5Q7/DTF2THF_23484.p',symdiff)).
% 28.08/5.16 thf(f567,plain,(
% 28.08/5.16 ((in @ sK0 @ (symdiff @ sK1 @ sK2)) != $true)),
% 28.08/5.16 inference(cnf_transformation,[status(thm)],[f400])).
% 28.08/5.16 thf(f2377,plain,(
% 28.08/5.16 ~spl3_12),
% 28.08/5.16 inference(avatar_split_clause,[status(thm)],[f565,f2374])).
% 28.08/5.16 thf(f565,plain,(
% 28.08/5.16 ((in @ sK0 @ sK1) != $true)),
% 28.08/5.16 inference(cnf_transformation,[status(thm)],[f400])).
% 28.08/5.16 % SZS output end Proof for DTF2THF_23484
% 28.08/5.16 % (23965)------------------------------
% 28.08/5.16 % (23965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.08/5.16 % (23965)Termination reason: Refutation
% 28.08/5.16
% 28.08/5.16 % (23965)Memory used [KB]: 9594
% 28.08/5.16 % (23965)Time elapsed: 0.573 s
% 28.08/5.16 % (23965)Instructions burned: 1860 (million)
% 28.08/5.16 % (23965)------------------------------
% 28.08/5.16 % (23965)------------------------------
% 28.08/5.16 % (23813)Success in time 3.699 s
%------------------------------------------------------------------------------