%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU631^1 : 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 : n023.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 09:35:46 AM UTC 2026
% Result : Theorem 27.35s 5.36s
% Output : Refutation 27.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 8
% Syntax : Number of formulae : 74 ( 54 unt; 0 typ; 0 def)
% Number of atoms : 2850 ( 722 equ; 0 cnn)
% Maximal formula atoms : 151 ( 38 avg)
% Number of connectives : 2000 ( 24 ~; 27 |; 494 &; 804 @)
% ( 0 <=>; 605 =>; 0 <=; 0 <~>)
% Maximal formula depth : 159 ( 16 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 268 ( 263 usr; 159 con; 0-4 aty)
% ( 18 !!; 28 ??; 0 @@+; 0 @@-)
% Number of variables : 169 ( 97 ^; 51 !; 21 ?; 169 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_153,type,
iskpair: $i > $o ).
thf(func_def_158,type,
kpair: $i > $i > $i ).
thf(func_def_160,type,
cartprod: $i > $i > $i ).
thf(func_def_190,type,
sP3: $o > $o ).
thf(func_def_191,type,
sP4: $i > $o ).
thf(func_def_192,type,
sP5: $o > $o ).
thf(func_def_193,type,
sP6: $o > $o ).
thf(func_def_194,type,
sK7: $i > $i ).
thf(func_def_195,type,
sK8: $i > $i > $i ).
thf(func_def_196,type,
sK9: $i > $i > $i ).
thf(func_def_197,type,
sK10: $i > $i > $i ).
thf(func_def_198,type,
sK11: $i > $i > $i > $i ).
thf(func_def_199,type,
sK12: $i > ( $i > $o ) > $i ).
thf(func_def_200,type,
sK13: $i > $i > $i ).
thf(func_def_201,type,
sK14: $i > $i > $i ).
thf(func_def_202,type,
sK15: $i > ( $i > $i > $o ) > $i ).
thf(func_def_203,type,
sK16: $i > ( $i > $i > $o ) > $i ).
thf(func_def_204,type,
sK17: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_205,type,
sK18: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_206,type,
sK19: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_207,type,
sK20: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_208,type,
sK21: $i > $i ).
thf(func_def_211,type,
sK22: $o > $i > $i > $i ).
thf(func_def_212,type,
sK23: $i > $i > $i ).
thf(func_def_213,type,
sK24: $i > $i > $i ).
thf(func_def_214,type,
sK25: $i > $i > $i ).
thf(func_def_215,type,
sK26: ( $i > $o ) > $i ).
thf(func_def_216,type,
sK27: ( $i > $o ) > $i > $i ).
thf(func_def_217,type,
sK28: ( $i > $o ) > $i > $i ).
thf(func_def_218,type,
sK29: $i > $i ).
thf(func_def_219,type,
sK30: $i > $i > $i ).
thf(func_def_220,type,
sK31: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_221,type,
sK32: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_222,type,
sK33: $i > ( $i > $o ) > $i ).
thf(func_def_223,type,
sK34: ( $i > $o ) > $i > $i ).
thf(func_def_224,type,
sK35: ( $i > $o ) > $i > $i ).
thf(func_def_225,type,
sK36: $i > ( $i > $o ) > $i ).
thf(func_def_226,type,
sK37: ( $i > $o ) > $i > $i ).
thf(func_def_227,type,
sK38: $i > ( $i > $o ) > $i ).
thf(func_def_228,type,
sK39: ( $i > $o ) > $i > $i ).
thf(func_def_229,type,
sK40: ( $i > $o ) > $i > $i ).
thf(func_def_230,type,
sK41: ( $i > $o ) > $i > $i ).
thf(func_def_231,type,
sK42: $i > ( $i > $o ) > $i ).
thf(func_def_232,type,
sK43: ( $i > $o ) > $i ).
thf(func_def_233,type,
sK44: ( $i > $o ) > $i > $i ).
thf(func_def_234,type,
sK45: ( $i > $o ) > $i ).
thf(func_def_235,type,
sK46: ( $i > $o ) > $i > $i ).
thf(func_def_236,type,
sK47: $i > $i > $i ).
thf(func_def_237,type,
sK48: $i > $i > $i ).
thf(func_def_238,type,
sK49: $i > $i > $i ).
thf(func_def_239,type,
sK50: $i > ( $i > $o ) > $i ).
thf(func_def_240,type,
sK51: $i > $i ).
thf(func_def_241,type,
sK52: $i > $i ).
thf(func_def_242,type,
sK53: $i > $i > $i ).
thf(func_def_243,type,
sK54: $i > ( $i > $o ) > $i ).
thf(func_def_244,type,
sK55: $i > $i > $i ).
thf(func_def_245,type,
sK56: ( $i > $o ) > $i > $i ).
thf(func_def_246,type,
sK57: ( $i > $o ) > $i > $i ).
thf(func_def_247,type,
sK58: $i > $i > $i ).
thf(func_def_248,type,
sK59: ( $i > $o ) > $i ).
thf(func_def_249,type,
sK60: $i > ( $i > $o ) > $i ).
thf(func_def_250,type,
sK61: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_251,type,
sK62: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_252,type,
sK63: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_253,type,
sK64: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_254,type,
sK65: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_255,type,
sK66: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_256,type,
sK67: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_257,type,
sK68: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_258,type,
sK69: ( $i > $o ) > $i ).
thf(func_def_259,type,
sK70: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_260,type,
sK71: $i > ( $i > $o ) > $i ).
thf(func_def_261,type,
sK72: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_262,type,
sK73: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_263,type,
sK74: ( $i > $o ) > $i > $i ).
thf(func_def_264,type,
sK75: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_265,type,
sK76: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_266,type,
sK77: $i > ( $i > $o ) > $i ).
thf(func_def_267,type,
sK78: $i > $i > $i ).
thf(func_def_268,type,
sK79: ( $i > $o ) > $i ).
thf(func_def_269,type,
sK80: ( $i > $o ) > $i ).
thf(func_def_270,type,
sK81: ( $i > $o ) > $i ).
thf(func_def_271,type,
sK82: ( $i > $o ) > $i ).
thf(func_def_272,type,
sK83: $i > $i ).
thf(func_def_273,type,
sK84: ( $i > $o ) > $i > ( $i > $o ) > $i > $i ).
thf(func_def_274,type,
sK85: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_275,type,
sK86: $i > $i ).
thf(func_def_276,type,
sK87: $i > $i > $i ).
thf(func_def_277,type,
sK88: $i > ( $i > $o ) > $i ).
thf(func_def_278,type,
ph89:
!>[X0: $tType] : X0 ).
thf(f4046,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f4045]) ).
thf(f4045,plain,
$false = $true,
inference(forward_demodulation,[status(thm)],[f4044,f932]) ).
thf(f932,plain,
( ( sP6 @ $true )
= $false ),
introduced(definition,[new_symbols(naming,[sP6])],[inequality_splitting_name_introduction]) ).
thf(f4044,plain,
( ( sP6 @ $true )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f4043]) ).
thf(f4043,plain,
( ( ( sP6 @ $true )
= $true )
| ( $false = $true ) ),
inference(forward_demodulation,[status(thm)],[f4042,f931]) ).
thf(f931,plain,
( ( sP5 @ $true )
= $false ),
introduced(definition,[new_symbols(naming,[sP5])],[inequality_splitting_name_introduction]) ).
thf(f4042,plain,
( ( ( sP5 @ $true )
= $true )
| ( ( sP6 @ $true )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f4041,f3971]) ).
thf(f3971,plain,
( ( in @ sK90 @ sK2 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f3970]) ).
thf(f3970,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ sK90 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK90 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK1 )
& ( in @ Y0 @ sK0 ) ) )
& ( in @ sK90 @ sK2 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f3969]) ).
thf(f3969,plain,
( $true
= ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= sK1 )
& ( in @ Y1 @ sK0 ) ) )
& ( in @ Y0 @ sK2 ) )
@ sK90 ) ),
inference(sigma_clausification,[status(thm)],[f3968]) ).
thf(f3968,plain,
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= sK1 )
& ( in @ Y1 @ sK0 ) ) )
& ( in @ Y0 @ sK2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f3967]) ).
thf(f3967,plain,
( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ sK0 ) ) )
& ( in @ Y1 @ sK2 ) ) )
@ sK1 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f3958]) ).
thf(f3958,plain,
( ( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ sK0 ) ) )
& ( in @ Y1 @ sK2 ) ) )
@ sK1 )
= $true )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f1893,f1249]) ).
thf(f1249,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( $false
= ( in @ X1 @ ( dsetconstr @ X2 @ X3 ) ) )
| ( $true
= ( X3 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1248]) ).
thf(f1248,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( $true
= ( ( in @ X1 @ ( dsetconstr @ X2 @ X3 ) )
=> ( X3 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1247]) ).
thf(f1247,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ^ [Y0: $i > $o] :
( ( in @ X1 @ ( dsetconstr @ X2 @ Y0 ) )
=> ( Y0 @ X1 ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f1246]) ).
thf(f1246,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( in @ X1 @ ( dsetconstr @ X2 @ Y0 ) )
=> ( Y0 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1245]) ).
thf(f1245,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f1244]) ).
thf(f1244,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ X1 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1243]) ).
thf(f1243,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ Y2 ) )
=> ( Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f1242]) ).
thf(f1242,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ Y2 ) )
=> ( Y2 @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f881]) ).
thf(f881,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f616,f584]) ).
thf(f584,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f405]) ).
thf(f405,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y0
@ ( dsetconstr @ Y1
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f404]) ).
thf(f404,plain,
! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X0 @ X3 ) ) )
=> ( X0 @ X2 ) )
= dsetconstrER ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,axiom,
! [X0: $i > $o,X3: $i,X1: $i] :
( ( ( in @ X1
@ ( dsetconstr @ X3
@ ^ [X2: $i] : ( X0 @ X2 ) ) )
=> ( X0 @ X1 ) )
= dsetconstrER ),
file('/export/starexec/sandbox/tmp/tmp.X63vARrhRj/DTF2THF_30432.p',dsetconstrER) ).
thf(f616,plain,
dsetconstrER = $true,
inference(cnf_transformation,[status(thm)],[f459]) ).
thf(f459,plain,
( ( singletoninpowunion = $true )
& ( setminusILneg = $true )
& ( kpairp = $true )
& ( binintersectEL = $true )
& ( binunionIL = $true )
& ( exuI1 = $true )
& ( upairinpowunion = $true )
& ( subPowSU = $true )
& ( secondinupair = $true )
& ( setadjoinE = $true )
& ( emptyinunitempty = $true )
& ( binintersectLsub = $true )
& ( notdallE = $true )
& ( emptysetimpfalse = $true )
& ( vacuousDall = $true )
& ! [X3: $i] :
( ! [X4: $i] :
( ( sK1
!= ( kpair @ X3 @ X4 ) )
| ( ( in @ X4 @ sK0 )
!= $true ) )
| ( ( in @ X3 @ sK2 )
!= $true ) )
& ( ( in @ sK1 @ ( cartprod @ sK2 @ sK0 ) )
= $true )
& ( setextAx = $true )
& ( upairsetIL = $true )
& ( setunionE = $true )
& ( symdiffIneg1 = $true )
& ( prop2setI = $true )
& ( setminusEL = $true )
& ( setext = $true )
& ( nonemptyI = $true )
& ( dsetconstrEL = $true )
& ( binunionIR = $true )
& ( ubforcartprodlem2 = $true )
& ( subsetRefl = $true )
& ( nonemptyE1 = $true )
& ( quantDeMorgan1 = $true )
& ( upairsetE = $true )
& ( powerset__Cong = $true )
& ( notequalI1 = $true )
& ( subsetE2 = $true )
& ( setminusERneg = $true )
& ( nonemptyI1 = $true )
& ( quantDeMorgan4 = $true )
& ( subset2powerset = $true )
& ( quantDeMorgan2 = $true )
& ( symdiffI1 = $true )
& ( powersetI = $true )
& ( descrp = $true )
& ( powersetE = $true )
& ( setadjoinIL = $true )
& ( omegaSAx = $true )
& ( quantDeMorgan3 = $true )
& ( notsubsetI = $true )
& ( binintersectI = $true )
& ( binintersectSubset4 = $true )
& ( ubforcartprodlem1 = $true )
& ( emptysetAx = $true )
& ( kpairiskpair = $true )
& ( eqinunit = $true )
& ( setminusSubset2 = $true )
& ( setminusLsub = $true )
& ( binunionE = $true )
& ( setunionAx = $true )
& ( exu__Cong = $true )
& ( setminusELneg = $true )
& ( setminusER = $true )
& ( setbeta = $true )
& ( exuI3 = $true )
& ( binintersectSubset2 = $true )
& ( setukpairIL = $true )
& ( binintersectER = $true )
& ( prop2set2propI = $true )
& ( upairset2E = $true )
& ( binunionEcases = $true )
& ( notdexE = $true )
& ( cartprodpairin = $true )
& ( binintersectSubset3 = $true )
& ( emptyset__Cong = $true )
& ( exuE1 = $true )
& ( powersetAx = $true )
& ( setadjoin__Cong = $true )
& ( binunionLsub = $true )
& ( emptyinPowerset = $true )
& ( descr__Cong = $true )
& ( exuI2 = $true )
& ( setoftrueEq = $true )
& ( binintersectRsub = $true )
& ( setminusSubset1 = $true )
& ( singletoninpowerset = $true )
& ( binintersectSubset1 = $true )
& ( wellorderingAx = $true )
& ( in__Cong = $true )
& ( powersetI1 = $true )
& ( nonemptyImpWitness = $true )
& ( emptysetsubset = $true )
& ( setminusIRneg = $true )
& ( setukpairIR = $true )
& ( foundationAx = $true )
& ( setadjoinOr = $true )
& ( emptyInPowerset = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( uniqinunit = $true )
& ( setadjoinSub = $true )
& ( powersetsubset = $true )
& ( omega__Cong = $true )
& ( singletonsubset = $true )
& ( setadjoinIR = $true )
& ( noeltsimpempty = $true )
& ( binunionRsub = $true )
& ( subsetI1 = $true )
& ( omegaIndAx = $true )
& ( sepInPowerset = $true )
& ( subsetI2 = $true )
& ( omega0Ax = $true )
& ( emptysetE = $true )
& ( binintersectSubset5 = $true )
& ( setunionI = $true )
& ( bs114d = $true )
& ( setunion__Cong = $true )
& ( symdiffIneg2 = $true )
& ( subsetemptysetimpeq = $true )
& ( exuE3u = $true )
& ( emptyI = $true )
& ( upairsubunion = $true )
& ( upairset2IR = $true )
& ( dsetconstrER = $true )
& ( sepSubset = $true )
& ( inCongP = $true )
& ( notinemptyset = $true )
& ( powersetE1 = $true )
& ( notinsingleton = $true )
& ( replAx = $true )
& ( notequalI2 = $true )
& ( singletonsswitch = $true )
& ( exuEu = $true )
& ( subsetTrans = $true )
& ( setminusI = $true )
& ( inPowerset = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( setadjoinAx = $true )
& ( dsetconstrI = $true )
& ( ubforcartprodlem3 = $true )
& ( prop2setE = $true )
& ( setadjoinSub2 = $true )
& ( symdiffI2 = $true )
& ( dsetconstr__Cong = $true )
& ( subsetE = $true )
& ( setextsub = $true )
& ( exuE2 = $true )
& ( symdiffE = $true )
& ( disjointsetsI1 = $true )
& ( exuE3e = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f457,f458]) ).
thf(f458,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( ( kpair @ X3 @ X4 )
!= X1 )
| ( ( in @ X4 @ X0 )
!= $true ) )
| ( ( in @ X3 @ X2 )
!= $true ) )
& ( ( in @ X1 @ ( cartprod @ X2 @ X0 ) )
= $true ) )
=> ( ! [X3: $i] :
( ! [X4: $i] :
( ( sK1
!= ( kpair @ X3 @ X4 ) )
| ( ( in @ X4 @ sK0 )
!= $true ) )
| ( ( in @ X3 @ sK2 )
!= $true ) )
& ( ( in @ sK1 @ ( cartprod @ sK2 @ sK0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f457,plain,
( ( singletoninpowunion = $true )
& ( setminusILneg = $true )
& ( kpairp = $true )
& ( binintersectEL = $true )
& ( binunionIL = $true )
& ( exuI1 = $true )
& ( upairinpowunion = $true )
& ( subPowSU = $true )
& ( secondinupair = $true )
& ( setadjoinE = $true )
& ( emptyinunitempty = $true )
& ( binintersectLsub = $true )
& ( notdallE = $true )
& ( emptysetimpfalse = $true )
& ( vacuousDall = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( ( kpair @ X3 @ X4 )
!= X1 )
| ( ( in @ X4 @ X0 )
!= $true ) )
| ( ( in @ X3 @ X2 )
!= $true ) )
& ( ( in @ X1 @ ( cartprod @ X2 @ X0 ) )
= $true ) )
& ( setextAx = $true )
& ( upairsetIL = $true )
& ( setunionE = $true )
& ( symdiffIneg1 = $true )
& ( prop2setI = $true )
& ( setminusEL = $true )
& ( setext = $true )
& ( nonemptyI = $true )
& ( dsetconstrEL = $true )
& ( binunionIR = $true )
& ( ubforcartprodlem2 = $true )
& ( subsetRefl = $true )
& ( nonemptyE1 = $true )
& ( quantDeMorgan1 = $true )
& ( upairsetE = $true )
& ( powerset__Cong = $true )
& ( notequalI1 = $true )
& ( subsetE2 = $true )
& ( setminusERneg = $true )
& ( nonemptyI1 = $true )
& ( quantDeMorgan4 = $true )
& ( subset2powerset = $true )
& ( quantDeMorgan2 = $true )
& ( symdiffI1 = $true )
& ( powersetI = $true )
& ( descrp = $true )
& ( powersetE = $true )
& ( setadjoinIL = $true )
& ( omegaSAx = $true )
& ( quantDeMorgan3 = $true )
& ( notsubsetI = $true )
& ( binintersectI = $true )
& ( binintersectSubset4 = $true )
& ( ubforcartprodlem1 = $true )
& ( emptysetAx = $true )
& ( kpairiskpair = $true )
& ( eqinunit = $true )
& ( setminusSubset2 = $true )
& ( setminusLsub = $true )
& ( binunionE = $true )
& ( setunionAx = $true )
& ( exu__Cong = $true )
& ( setminusELneg = $true )
& ( setminusER = $true )
& ( setbeta = $true )
& ( exuI3 = $true )
& ( binintersectSubset2 = $true )
& ( setukpairIL = $true )
& ( binintersectER = $true )
& ( prop2set2propI = $true )
& ( upairset2E = $true )
& ( binunionEcases = $true )
& ( notdexE = $true )
& ( cartprodpairin = $true )
& ( binintersectSubset3 = $true )
& ( emptyset__Cong = $true )
& ( exuE1 = $true )
& ( powersetAx = $true )
& ( setadjoin__Cong = $true )
& ( binunionLsub = $true )
& ( emptyinPowerset = $true )
& ( descr__Cong = $true )
& ( exuI2 = $true )
& ( setoftrueEq = $true )
& ( binintersectRsub = $true )
& ( setminusSubset1 = $true )
& ( singletoninpowerset = $true )
& ( binintersectSubset1 = $true )
& ( wellorderingAx = $true )
& ( in__Cong = $true )
& ( powersetI1 = $true )
& ( nonemptyImpWitness = $true )
& ( emptysetsubset = $true )
& ( setminusIRneg = $true )
& ( setukpairIR = $true )
& ( foundationAx = $true )
& ( setadjoinOr = $true )
& ( emptyInPowerset = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( uniqinunit = $true )
& ( setadjoinSub = $true )
& ( powersetsubset = $true )
& ( omega__Cong = $true )
& ( singletonsubset = $true )
& ( setadjoinIR = $true )
& ( noeltsimpempty = $true )
& ( binunionRsub = $true )
& ( subsetI1 = $true )
& ( omegaIndAx = $true )
& ( sepInPowerset = $true )
& ( subsetI2 = $true )
& ( omega0Ax = $true )
& ( emptysetE = $true )
& ( binintersectSubset5 = $true )
& ( setunionI = $true )
& ( bs114d = $true )
& ( setunion__Cong = $true )
& ( symdiffIneg2 = $true )
& ( subsetemptysetimpeq = $true )
& ( exuE3u = $true )
& ( emptyI = $true )
& ( upairsubunion = $true )
& ( upairset2IR = $true )
& ( dsetconstrER = $true )
& ( sepSubset = $true )
& ( inCongP = $true )
& ( notinemptyset = $true )
& ( powersetE1 = $true )
& ( notinsingleton = $true )
& ( replAx = $true )
& ( notequalI2 = $true )
& ( singletonsswitch = $true )
& ( exuEu = $true )
& ( subsetTrans = $true )
& ( setminusI = $true )
& ( inPowerset = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( setadjoinAx = $true )
& ( dsetconstrI = $true )
& ( ubforcartprodlem3 = $true )
& ( prop2setE = $true )
& ( setadjoinSub2 = $true )
& ( symdiffI2 = $true )
& ( dsetconstr__Cong = $true )
& ( subsetE = $true )
& ( setextsub = $true )
& ( exuE2 = $true )
& ( symdiffE = $true )
& ( disjointsetsI1 = $true )
& ( exuE3e = $true ) ),
inference(flattening,[status(thm)],[f456]) ).
thf(f456,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( ( kpair @ X3 @ X4 )
!= X1 )
| ( ( in @ X4 @ X0 )
!= $true ) )
| ( ( in @ X3 @ X2 )
!= $true ) )
& ( ( in @ X1 @ ( cartprod @ X2 @ X0 ) )
= $true ) )
& ( cartprodpairin = $true )
& ( ubforcartprodlem3 = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( upairsubunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f172]) ).
thf(f172,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( cartprod @ X2 @ X0 ) )
= $true )
=> ? [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
& ? [X4: $i] :
( ( ( kpair @ X3 @ X4 )
= X1 )
& ( ( in @ X4 @ X0 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f171]) ).
thf(f171,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( cartprod @ X2 @ X0 ) )
=> ? [X3: $i] :
( ( in @ X3 @ X2 )
& ? [X4: $i] :
( ( ( kpair @ X3 @ X4 )
= X1 )
& ( in @ X4 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f154]) ).
thf(f154,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ! [X4: $i,X10: $i,X3: $i] :
( ( in @ X10 @ ( cartprod @ X3 @ X4 ) )
=> ? [X1: $i] :
( ( in @ X1 @ X3 )
& ? [X2: $i] :
( ( ( kpair @ X1 @ X2 )
= X10 )
& ( in @ X2 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f153]) ).
thf(f153,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ! [X4: $i,X10: $i,X3: $i] :
( ( in @ X10 @ ( cartprod @ X3 @ X4 ) )
=> ? [X1: $i] :
( ( in @ X1 @ X3 )
& ? [X2: $i] :
( ( ( kpair @ X1 @ X2 )
= X10 )
& ( in @ X2 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.X63vARrhRj/DTF2THF_30432.p',cartprodmempair1) ).
thf(f1893,plain,
( ( in @ sK1
@ ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ sK2 @ sK0 ) ) )
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ sK0 ) ) )
& ( in @ Y1 @ sK2 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f793]) ).
thf(f793,plain,
( $true
= ( in @ sK1
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ Y0 @ Y1 ) ) )
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( ?? @ $i
@ ^ [Y4: $i] :
( ( ( ^ [Y5: $i,Y6: $i] : ( setadjoin @ ( setadjoin @ Y5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y5 @ ( setadjoin @ Y6 @ emptyset ) ) @ emptyset ) )
@ Y3
@ Y4 )
= Y2 )
& ( in @ Y4 @ Y1 ) ) )
& ( in @ Y3 @ Y0 ) ) ) )
@ sK2
@ sK0 ) ) ),
inference(definition_unfolding,[status(thm)],[f721,f776]) ).
thf(f776,plain,
( cartprod
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ Y0 @ Y1 ) ) )
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( ?? @ $i
@ ^ [Y4: $i] :
( ( ( ^ [Y5: $i,Y6: $i] : ( setadjoin @ ( setadjoin @ Y5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y5 @ ( setadjoin @ Y6 @ emptyset ) ) @ emptyset ) )
@ Y3
@ Y4 )
= Y2 )
& ( in @ Y4 @ Y1 ) ) )
& ( in @ Y3 @ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f739,f563]) ).
thf(f563,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(cnf_transformation,[status(thm)],[f311]) ).
thf(f311,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(fool_elimination,[status(thm)],[f310]) ).
thf(f310,plain,
( kpair
= ( ^ [X0: $i,X1: $i] : ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(rectify,[status(thm)],[f140]) ).
thf(f140,axiom,
( kpair
= ( ^ [X1: $i,X2: $i] : ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.X63vARrhRj/DTF2THF_30432.p',kpair) ).
thf(f739,plain,
( cartprod
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ Y0 @ Y1 ) ) )
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( ?? @ $i
@ ^ [Y4: $i] :
( ( ( kpair @ Y3 @ Y4 )
= Y2 )
& ( in @ Y4 @ Y1 ) ) )
& ( in @ Y3 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f379]) ).
thf(f379,plain,
( cartprod
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ Y0 @ Y1 ) ) )
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( ?? @ $i
@ ^ [Y4: $i] :
( ( ( kpair @ Y3 @ Y4 )
= Y2 )
& ( in @ Y4 @ Y1 ) ) )
& ( in @ Y3 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f378]) ).
thf(f378,plain,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ X0 @ X1 ) ) )
@ ^ [X2: $i] :
? [X3: $i] :
( ( in @ X3 @ X0 )
& ? [X4: $i] :
( ( in @ X4 @ X1 )
& ( ( kpair @ X3 @ X4 )
= X2 ) ) ) ) )
= cartprod ),
inference(rectify,[status(thm)],[f142]) ).
thf(f142,axiom,
( ( ^ [X3: $i,X4: $i] :
( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ X3 @ X4 ) ) )
@ ^ [X1: $i] :
? [X2: $i] :
( ( in @ X2 @ X3 )
& ? [X8: $i] :
( ( in @ X8 @ X4 )
& ( ( kpair @ X2 @ X8 )
= X1 ) ) ) ) )
= cartprod ),
file('/export/starexec/sandbox/tmp/tmp.X63vARrhRj/DTF2THF_30432.p',cartprod) ).
thf(f721,plain,
( ( in @ sK1 @ ( cartprod @ sK2 @ sK0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f459]) ).
thf(f4041,plain,
( ( ( sP6 @ ( in @ sK90 @ sK2 ) )
= $true )
| ( ( sP5 @ $true )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f4039,f3975]) ).
thf(f3975,plain,
( ( in @ sK91 @ sK0 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f3974]) ).
thf(f3974,plain,
( $true
= ( ( ( setadjoin @ ( setadjoin @ sK90 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK90 @ ( setadjoin @ sK91 @ emptyset ) ) @ emptyset ) )
= sK1 )
& ( in @ sK91 @ sK0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f3973]) ).
thf(f3973,plain,
( ( ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ sK90 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK90 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK1 )
& ( in @ Y0 @ sK0 ) )
@ sK91 )
= $true ),
inference(sigma_clausification,[status(thm)],[f3972]) ).
thf(f3972,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ sK90 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK90 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK1 )
& ( in @ Y0 @ sK0 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f3970]) ).
thf(f4039,plain,
( ( ( sP5 @ ( in @ sK91 @ sK0 ) )
= $true )
| ( ( sP6 @ ( in @ sK90 @ sK2 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f4037]) ).
thf(f4037,plain,
( ( $false = $true )
| ( ( sP5 @ ( in @ sK91 @ sK0 ) )
= $true )
| ( ( sP6 @ ( in @ sK90 @ sK2 ) )
= $true ) ),
inference(superposition,[status(thm)],[f2260,f4005]) ).
thf(f4005,plain,
( ( sP4 @ ( setadjoin @ ( setadjoin @ sK90 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK90 @ ( setadjoin @ sK91 @ emptyset ) ) @ emptyset ) ) )
= $false ),
inference(backward_demodulation,[status(thm)],[f3993,f4004]) ).
thf(f4004,plain,
( ( setadjoin @ ( setadjoin @ sK92 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK92 @ ( setadjoin @ sK93 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK90 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK90 @ ( setadjoin @ sK91 @ emptyset ) ) @ emptyset ) ) ),
inference(backward_demodulation,[status(thm)],[f3989,f3977]) ).
thf(f3977,plain,
( sK1
= ( setadjoin @ ( setadjoin @ sK90 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK90 @ ( setadjoin @ sK91 @ emptyset ) ) @ emptyset ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f3976]) ).
thf(f3976,plain,
( ( ( setadjoin @ ( setadjoin @ sK90 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK90 @ ( setadjoin @ sK91 @ emptyset ) ) @ emptyset ) )
= sK1 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f3974]) ).
thf(f3989,plain,
( ( setadjoin @ ( setadjoin @ sK92 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK92 @ ( setadjoin @ sK93 @ emptyset ) ) @ emptyset ) )
= sK1 ),
inference(equality_proxy_clausification,[status(thm)],[f3988]) ).
thf(f3988,plain,
( $true
= ( ( setadjoin @ ( setadjoin @ sK92 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK92 @ ( setadjoin @ sK93 @ emptyset ) ) @ emptyset ) )
= sK1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f3986]) ).
thf(f3986,plain,
( $true
= ( ( ( setadjoin @ ( setadjoin @ sK92 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK92 @ ( setadjoin @ sK93 @ emptyset ) ) @ emptyset ) )
= sK1 )
& ( in @ sK93 @ sK0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f3985]) ).
thf(f3985,plain,
( $true
= ( ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ sK92 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK92 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK1 )
& ( in @ Y0 @ sK0 ) )
@ sK93 ) ),
inference(sigma_clausification,[status(thm)],[f3984]) ).
thf(f3984,plain,
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ sK92 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK92 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK1 )
& ( in @ Y0 @ sK0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f3982]) ).
thf(f3982,plain,
( $true
= ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ sK92 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK92 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= sK1 )
& ( in @ Y0 @ sK0 ) ) )
& ( in @ sK92 @ sK2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f3981]) ).
thf(f3981,plain,
( $true
= ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= sK1 )
& ( in @ Y1 @ sK0 ) ) )
& ( in @ Y0 @ sK2 ) )
@ sK92 ) ),
inference(sigma_clausification,[status(thm)],[f3980]) ).
thf(f3980,plain,
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= sK1 )
& ( in @ Y1 @ sK0 ) ) )
& ( in @ Y0 @ sK2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f3979]) ).
thf(f3979,plain,
( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ sK0 ) ) )
& ( in @ Y1 @ sK2 ) ) )
@ sK1 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f3962]) ).
thf(f3962,plain,
( ( $false = $true )
| ( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 )
& ( in @ Y2 @ sK0 ) ) )
& ( in @ Y1 @ sK2 ) ) )
@ sK1 )
= $true ) ),
inference(superposition,[status(thm)],[f1249,f1893]) ).
thf(f3993,plain,
( $false
= ( sP4 @ ( setadjoin @ ( setadjoin @ sK92 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK92 @ ( setadjoin @ sK93 @ emptyset ) ) @ emptyset ) ) ) ),
inference(backward_demodulation,[status(thm)],[f930,f3989]) ).
thf(f930,plain,
( $false
= ( sP4 @ sK1 ) ),
introduced(definition,[new_symbols(naming,[sP4])],[inequality_splitting_name_introduction]) ).
thf(f2260,plain,
! [X3: $i,X4: $i] :
( ( $true
= ( sP4 @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) ) )
| ( ( sP5 @ ( in @ X4 @ sK0 ) )
= $true )
| ( $true
= ( sP6 @ ( in @ X3 @ sK2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f933]) ).
thf(f933,plain,
! [X3: $i,X4: $i] :
( ( $true
= ( sP4
@ ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
@ X3
@ X4 ) ) )
| ( $true
= ( sP6 @ ( in @ X3 @ sK2 ) ) )
| ( ( sP5 @ ( in @ X4 @ sK0 ) )
= $true ) ),
inference(inequality_splitting,[status(thm)],[f792,f932,f931,f930]) ).
thf(f792,plain,
! [X3: $i,X4: $i] :
( ( sK1
!= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
@ X3
@ X4 ) )
| ( ( in @ X4 @ sK0 )
!= $true )
| ( ( in @ X3 @ sK2 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f722,f563]) ).
thf(f722,plain,
! [X3: $i,X4: $i] :
( ( sK1
!= ( kpair @ X3 @ X4 ) )
| ( ( in @ X4 @ sK0 )
!= $true )
| ( ( in @ X3 @ sK2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f459]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU631^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n023.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:30:04 EST 2026
% 0.15/0.35 % CPUTime :
% 0.15/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.49 ---- Original DTF file ---
% 0.28/0.49 thf(spec,logic,$$dhol).
% 0.28/0.49 %------------------------------------------------------------------------------
% 0.28/0.49 % File : SEU631^1 : TPTP v9.2.1. Released v3.7.0.
% 0.28/0.49 % Domain : Set Theory
% 0.28/0.49 % Problem : Ordered Pairs - Cartesian Products
% 0.28/0.49 % Version : Especial.
% 0.28/0.49 % English : (! A:i.! B:i.! u:i.in u (cartprod A B) -> (? x:i.in x A &
% 0.28/0.49 % (? y:i.in y B & u = kpair x y)))
% 0.28/0.49
% 0.28/0.49 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.28/0.49 % Source : [Bro08]
% 0.28/0.49 % Names : ZFC133g [Bro08]
% 0.28/0.49
% 0.28/0.49 % Status : Theorem
% 0.28/0.49 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.60 v8.2.0, 0.69 v8.1.0, 0.73 v7.5.0, 0.71 v7.4.0, 0.78 v7.2.0, 0.75 v7.0.0, 0.71 v6.4.0, 0.67 v6.3.0, 0.80 v6.2.0, 0.86 v5.5.0, 0.83 v5.4.0, 0.80 v4.1.0, 1.00 v3.7.0
% 0.28/0.49 % Syntax : Number of formulae : 323 ( 152 unt; 170 typ; 152 def)
% 0.28/0.49 % Number of atoms : 807 ( 214 equ; 0 cnn)
% 0.28/0.49 % Maximal formula atoms : 151 ( 5 avg)
% 0.28/0.49 % Number of connectives : 1399 ( 47 ~; 7 |; 34 &; 943 @)
% 0.28/0.49 % ( 14 <=>; 354 =>; 0 <=; 0 <~>)
% 0.28/0.49 % Maximal formula depth : 158 ( 2 avg)
% 0.28/0.49 % Number of types : 2 ( 0 usr)
% 0.28/0.49 % Number of type conns : 69 ( 69 >; 0 *; 0 +; 0 <<)
% 0.28/0.49 % Number of symbols : 173 ( 170 usr; 151 con; 0-2 aty)
% 0.28/0.49 % Number of variables : 445 ( 36 ^; 374 !; 35 ?; 445 :)
% 0.28/0.49 % SPC : TH0_THM_EQU_NAR
% 0.28/0.49
% 0.28/0.49 % Comments : http://mathgate.info/detsetitem.php?id=188
% 0.28/0.49 %------------------------------------------------------------------------------
% 0.28/0.49 thf(in_type,type,
% 0.28/0.49 in: $i > $i > $o ).
% 0.28/0.49
% 0.28/0.49 thf(exu_type,type,
% 0.28/0.49 exu: ( $i > $o ) > $o ).
% 0.28/0.49
% 0.28/0.49 thf(exu,definition,
% 0.28/0.49 ( exu
% 0.28/0.49 = ( ^ [Xphi: $i > $o] :
% 0.28/0.49 ? [Xx: $i] :
% 0.28/0.49 ( ( Xphi @ Xx )
% 0.28/0.49 & ! [Xy: $i] :
% 0.28/0.49 ( ( Xphi @ Xy )
% 0.28/0.49 => ( Xx = Xy ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(setextAx_type,type,
% 0.28/0.49 setextAx: $o ).
% 0.28/0.49
% 0.28/0.49 thf(setextAx,definition,
% 0.28/0.49 ( setextAx
% 0.28/0.49 = ( ! [A: $i,B: $i] :
% 0.28/0.49 ( ! [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 <=> ( in @ Xx @ B ) )
% 0.28/0.49 => ( A = B ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(emptyset_type,type,
% 0.28/0.49 emptyset: $i ).
% 0.28/0.49
% 0.28/0.49 thf(emptysetAx_type,type,
% 0.28/0.49 emptysetAx: $o ).
% 0.28/0.49
% 0.28/0.49 thf(emptysetAx,definition,
% 0.28/0.49 ( emptysetAx
% 0.28/0.49 = ( ! [Xx: $i] :
% 0.28/0.49 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(setadjoin_type,type,
% 0.28/0.49 setadjoin: $i > $i > $i ).
% 0.28/0.49
% 0.28/0.49 thf(setadjoinAx_type,type,
% 0.28/0.49 setadjoinAx: $o ).
% 0.28/0.49
% 0.28/0.49 thf(setadjoinAx,definition,
% 0.28/0.49 ( setadjoinAx
% 0.28/0.49 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.49 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.49 <=> ( ( Xy = Xx )
% 0.28/0.49 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(powerset_type,type,
% 0.28/0.49 powerset: $i > $i ).
% 0.28/0.49
% 0.28/0.49 thf(powersetAx_type,type,
% 0.28/0.49 powersetAx: $o ).
% 0.28/0.49
% 0.28/0.49 thf(powersetAx,definition,
% 0.28/0.49 ( powersetAx
% 0.28/0.49 = ( ! [A: $i,B: $i] :
% 0.28/0.49 ( ( in @ B @ ( powerset @ A ) )
% 0.28/0.49 <=> ! [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ B )
% 0.28/0.49 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(setunion_type,type,
% 0.28/0.49 setunion: $i > $i ).
% 0.28/0.49
% 0.28/0.49 thf(setunionAx_type,type,
% 0.28/0.49 setunionAx: $o ).
% 0.28/0.49
% 0.28/0.49 thf(setunionAx,definition,
% 0.28/0.49 ( setunionAx
% 0.28/0.49 = ( ! [A: $i,Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ ( setunion @ A ) )
% 0.28/0.49 <=> ? [B: $i] :
% 0.28/0.49 ( ( in @ Xx @ B )
% 0.28/0.49 & ( in @ B @ A ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(omega_type,type,
% 0.28/0.49 omega: $i ).
% 0.28/0.49
% 0.28/0.49 thf(omega0Ax_type,type,
% 0.28/0.49 omega0Ax: $o ).
% 0.28/0.49
% 0.28/0.49 thf(omega0Ax,definition,
% 0.28/0.49 ( omega0Ax
% 0.28/0.49 = ( in @ emptyset @ omega ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(omegaSAx_type,type,
% 0.28/0.49 omegaSAx: $o ).
% 0.28/0.49
% 0.28/0.49 thf(omegaSAx,definition,
% 0.28/0.49 ( omegaSAx
% 0.28/0.49 = ( ! [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ omega )
% 0.28/0.49 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(omegaIndAx_type,type,
% 0.28/0.49 omegaIndAx: $o ).
% 0.28/0.49
% 0.28/0.49 thf(omegaIndAx,definition,
% 0.28/0.49 ( omegaIndAx
% 0.28/0.49 = ( ! [A: $i] :
% 0.28/0.49 ( ( ( in @ emptyset @ A )
% 0.28/0.49 & ! [Xx: $i] :
% 0.28/0.49 ( ( ( in @ Xx @ omega )
% 0.28/0.49 & ( in @ Xx @ A ) )
% 0.28/0.49 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.28/0.49 => ! [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ omega )
% 0.28/0.49 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(replAx_type,type,
% 0.28/0.49 replAx: $o ).
% 0.28/0.49
% 0.28/0.49 thf(replAx,definition,
% 0.28/0.49 ( replAx
% 0.28/0.49 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.28/0.49 ( ! [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ( exu
% 0.28/0.49 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.28/0.49 => ? [B: $i] :
% 0.28/0.49 ! [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ B )
% 0.28/0.49 <=> ? [Xy: $i] :
% 0.28/0.49 ( ( in @ Xy @ A )
% 0.28/0.49 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(foundationAx_type,type,
% 0.28/0.49 foundationAx: $o ).
% 0.28/0.49
% 0.28/0.49 thf(foundationAx,definition,
% 0.28/0.49 ( foundationAx
% 0.28/0.49 = ( ! [A: $i] :
% 0.28/0.49 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.28/0.49 => ? [B: $i] :
% 0.28/0.49 ( ( in @ B @ A )
% 0.28/0.49 & ~ ? [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ B )
% 0.28/0.49 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(wellorderingAx_type,type,
% 0.28/0.49 wellorderingAx: $o ).
% 0.28/0.49
% 0.28/0.49 thf(wellorderingAx,definition,
% 0.28/0.49 ( wellorderingAx
% 0.28/0.49 = ( ! [A: $i] :
% 0.28/0.49 ? [B: $i] :
% 0.28/0.49 ( ! [C: $i] :
% 0.28/0.49 ( ( in @ C @ B )
% 0.28/0.49 => ! [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ C )
% 0.28/0.49 => ( in @ Xx @ A ) ) )
% 0.28/0.49 & ! [Xx: $i,Xy: $i] :
% 0.28/0.49 ( ( ( in @ Xx @ A )
% 0.28/0.49 & ( in @ Xy @ A ) )
% 0.28/0.49 => ( ! [C: $i] :
% 0.28/0.49 ( ( in @ C @ B )
% 0.28/0.49 => ( ( in @ Xx @ C )
% 0.28/0.49 <=> ( in @ Xy @ C ) ) )
% 0.28/0.49 => ( Xx = Xy ) ) )
% 0.28/0.49 & ! [C: $i,D: $i] :
% 0.28/0.49 ( ( ( in @ C @ B )
% 0.28/0.49 & ( in @ D @ B ) )
% 0.28/0.49 => ( ! [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ C )
% 0.28/0.49 => ( in @ Xx @ D ) )
% 0.28/0.49 | ! [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ D )
% 0.28/0.49 => ( in @ Xx @ C ) ) ) )
% 0.28/0.49 & ! [C: $i] :
% 0.28/0.49 ( ( ! [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ C )
% 0.28/0.49 => ( in @ Xx @ A ) )
% 0.28/0.49 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.28/0.49 => ? [D: $i,Xx: $i] :
% 0.28/0.49 ( ( in @ D @ B )
% 0.28/0.49 & ( in @ Xx @ C )
% 0.28/0.49 & ~ ? [Xy: $i] :
% 0.28/0.49 ( ( in @ Xy @ D )
% 0.28/0.49 & ( in @ Xy @ C ) )
% 0.28/0.49 & ! [E: $i] :
% 0.28/0.49 ( ( in @ E @ B )
% 0.28/0.49 => ( ! [Xy: $i] :
% 0.28/0.49 ( ( in @ Xy @ E )
% 0.28/0.49 => ( in @ Xy @ D ) )
% 0.28/0.49 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(descr_type,type,
% 0.28/0.49 descr: ( $i > $o ) > $i ).
% 0.28/0.49
% 0.28/0.49 thf(descrp_type,type,
% 0.28/0.49 descrp: $o ).
% 0.28/0.49
% 0.28/0.49 thf(descrp,definition,
% 0.28/0.49 ( descrp
% 0.28/0.49 = ( ! [Xphi: $i > $o] :
% 0.28/0.49 ( ( exu
% 0.28/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.49 => ( Xphi
% 0.28/0.49 @ ( descr
% 0.28/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(dsetconstr_type,type,
% 0.28/0.49 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.28/0.49
% 0.28/0.49 thf(dsetconstrI_type,type,
% 0.28/0.49 dsetconstrI: $o ).
% 0.28/0.49
% 0.28/0.49 thf(dsetconstrI,definition,
% 0.28/0.49 ( dsetconstrI
% 0.28/0.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ( ( Xphi @ Xx )
% 0.28/0.49 => ( in @ Xx
% 0.28/0.49 @ ( dsetconstr @ A
% 0.28/0.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(dsetconstrEL_type,type,
% 0.28/0.49 dsetconstrEL: $o ).
% 0.28/0.49
% 0.28/0.49 thf(dsetconstrEL,definition,
% 0.28/0.49 ( dsetconstrEL
% 0.28/0.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.49 ( ( in @ Xx
% 0.28/0.49 @ ( dsetconstr @ A
% 0.28/0.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.49 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(dsetconstrER_type,type,
% 0.28/0.49 dsetconstrER: $o ).
% 0.28/0.49
% 0.28/0.49 thf(dsetconstrER,definition,
% 0.28/0.49 ( dsetconstrER
% 0.28/0.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.49 ( ( in @ Xx
% 0.28/0.49 @ ( dsetconstr @ A
% 0.28/0.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.49 => ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(exuE1_type,type,
% 0.28/0.49 exuE1: $o ).
% 0.28/0.49
% 0.28/0.49 thf(exuE1,definition,
% 0.28/0.49 ( exuE1
% 0.28/0.49 = ( ! [Xphi: $i > $o] :
% 0.28/0.49 ( ( exu
% 0.28/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.49 => ? [Xx: $i] :
% 0.28/0.49 ( ( Xphi @ Xx )
% 0.28/0.49 & ! [Xy: $i] :
% 0.28/0.49 ( ( Xphi @ Xy )
% 0.28/0.49 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(prop2set_type,type,
% 0.28/0.49 prop2set: $o > $i ).
% 0.28/0.49
% 0.28/0.49 thf(prop2setE_type,type,
% 0.28/0.49 prop2setE: $o ).
% 0.28/0.49
% 0.28/0.49 thf(prop2setE,definition,
% 0.28/0.49 ( prop2setE
% 0.28/0.49 = ( ! [Xphi: $o,Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.28/0.49 => Xphi ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(emptysetE_type,type,
% 0.28/0.49 emptysetE: $o ).
% 0.28/0.49
% 0.28/0.49 thf(emptysetE,definition,
% 0.28/0.49 ( emptysetE
% 0.28/0.49 = ( ! [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ emptyset )
% 0.28/0.49 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(emptysetimpfalse_type,type,
% 0.28/0.49 emptysetimpfalse: $o ).
% 0.28/0.49
% 0.28/0.49 thf(emptysetimpfalse,definition,
% 0.28/0.49 ( emptysetimpfalse
% 0.28/0.49 = ( ! [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ emptyset )
% 0.28/0.49 => $false ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(notinemptyset_type,type,
% 0.28/0.49 notinemptyset: $o ).
% 0.28/0.49
% 0.28/0.49 thf(notinemptyset,definition,
% 0.28/0.49 ( notinemptyset
% 0.28/0.49 = ( ! [Xx: $i] :
% 0.28/0.49 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(exuE3e_type,type,
% 0.28/0.49 exuE3e: $o ).
% 0.28/0.49
% 0.28/0.49 thf(exuE3e,definition,
% 0.28/0.49 ( exuE3e
% 0.28/0.49 = ( ! [Xphi: $i > $o] :
% 0.28/0.49 ( ( exu
% 0.28/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.49 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(setext_type,type,
% 0.28/0.49 setext: $o ).
% 0.28/0.49
% 0.28/0.49 thf(setext,definition,
% 0.28/0.49 ( setext
% 0.28/0.49 = ( ! [A: $i,B: $i] :
% 0.28/0.49 ( ! [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ( in @ Xx @ B ) )
% 0.28/0.49 => ( ! [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ B )
% 0.28/0.49 => ( in @ Xx @ A ) )
% 0.28/0.49 => ( A = B ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(emptyI_type,type,
% 0.28/0.49 emptyI: $o ).
% 0.28/0.49
% 0.28/0.49 thf(emptyI,definition,
% 0.28/0.49 ( emptyI
% 0.28/0.49 = ( ! [A: $i] :
% 0.28/0.49 ( ! [Xx: $i] :
% 0.28/0.49 ~ ( in @ Xx @ A )
% 0.28/0.49 => ( A = emptyset ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(noeltsimpempty_type,type,
% 0.28/0.49 noeltsimpempty: $o ).
% 0.28/0.49
% 0.28/0.49 thf(noeltsimpempty,definition,
% 0.28/0.49 ( noeltsimpempty
% 0.28/0.49 = ( ! [A: $i] :
% 0.28/0.49 ( ! [Xx: $i] :
% 0.28/0.49 ~ ( in @ Xx @ A )
% 0.28/0.49 => ( A = emptyset ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(setbeta_type,type,
% 0.28/0.49 setbeta: $o ).
% 0.28/0.49
% 0.28/0.49 thf(setbeta,definition,
% 0.28/0.49 ( setbeta
% 0.28/0.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ( ( in @ Xx
% 0.28/0.49 @ ( dsetconstr @ A
% 0.28/0.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.49 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(nonempty_type,type,
% 0.28/0.49 nonempty: $i > $o ).
% 0.28/0.49
% 0.28/0.49 thf(nonempty,definition,
% 0.28/0.49 ( nonempty
% 0.28/0.49 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(nonemptyE1_type,type,
% 0.28/0.49 nonemptyE1: $o ).
% 0.28/0.49
% 0.28/0.49 thf(nonemptyE1,definition,
% 0.28/0.49 ( nonemptyE1
% 0.28/0.49 = ( ! [A: $i] :
% 0.28/0.49 ( ( nonempty @ A )
% 0.28/0.49 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(nonemptyI_type,type,
% 0.28/0.49 nonemptyI: $o ).
% 0.28/0.49
% 0.28/0.49 thf(nonemptyI,definition,
% 0.28/0.49 ( nonemptyI
% 0.28/0.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ( ( Xphi @ Xx )
% 0.28/0.49 => ( nonempty
% 0.28/0.49 @ ( dsetconstr @ A
% 0.28/0.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(nonemptyI1_type,type,
% 0.28/0.49 nonemptyI1: $o ).
% 0.28/0.49
% 0.28/0.49 thf(nonemptyI1,definition,
% 0.28/0.49 ( nonemptyI1
% 0.28/0.49 = ( ! [A: $i] :
% 0.28/0.49 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.28/0.49 => ( nonempty @ A ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(setadjoinIL_type,type,
% 0.28/0.49 setadjoinIL: $o ).
% 0.28/0.49
% 0.28/0.49 thf(setadjoinIL,definition,
% 0.28/0.49 ( setadjoinIL
% 0.28/0.49 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(emptyinunitempty_type,type,
% 0.28/0.49 emptyinunitempty: $o ).
% 0.28/0.49
% 0.28/0.49 thf(emptyinunitempty,definition,
% 0.28/0.49 ( emptyinunitempty
% 0.28/0.49 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(setadjoinIR_type,type,
% 0.28/0.49 setadjoinIR: $o ).
% 0.28/0.49
% 0.28/0.49 thf(setadjoinIR,definition,
% 0.28/0.49 ( setadjoinIR
% 0.28/0.49 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.49 ( ( in @ Xy @ A )
% 0.28/0.49 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(setadjoinE_type,type,
% 0.28/0.49 setadjoinE: $o ).
% 0.28/0.49
% 0.28/0.49 thf(setadjoinE,definition,
% 0.28/0.49 ( setadjoinE
% 0.28/0.49 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.49 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.49 => ! [Xphi: $o] :
% 0.28/0.49 ( ( ( Xy = Xx )
% 0.28/0.49 => Xphi )
% 0.28/0.49 => ( ( ( in @ Xy @ A )
% 0.28/0.49 => Xphi )
% 0.28/0.49 => Xphi ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(setadjoinOr_type,type,
% 0.28/0.49 setadjoinOr: $o ).
% 0.28/0.49
% 0.28/0.49 thf(setadjoinOr,definition,
% 0.28/0.49 ( setadjoinOr
% 0.28/0.49 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.49 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.49 => ( ( Xy = Xx )
% 0.28/0.49 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(setoftrueEq_type,type,
% 0.28/0.49 setoftrueEq: $o ).
% 0.28/0.49
% 0.28/0.49 thf(setoftrueEq,definition,
% 0.28/0.49 ( setoftrueEq
% 0.28/0.49 = ( ! [A: $i] :
% 0.28/0.49 ( ( dsetconstr @ A
% 0.28/0.49 @ ^ [Xx: $i] : $true )
% 0.28/0.49 = A ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(powersetI_type,type,
% 0.28/0.49 powersetI: $o ).
% 0.28/0.49
% 0.28/0.49 thf(powersetI,definition,
% 0.28/0.49 ( powersetI
% 0.28/0.49 = ( ! [A: $i,B: $i] :
% 0.28/0.49 ( ! [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ B )
% 0.28/0.49 => ( in @ Xx @ A ) )
% 0.28/0.49 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(emptyinPowerset_type,type,
% 0.28/0.49 emptyinPowerset: $o ).
% 0.28/0.49
% 0.28/0.49 thf(emptyinPowerset,definition,
% 0.28/0.49 ( emptyinPowerset
% 0.28/0.49 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(emptyInPowerset_type,type,
% 0.28/0.49 emptyInPowerset: $o ).
% 0.28/0.49
% 0.28/0.49 thf(emptyInPowerset,definition,
% 0.28/0.49 ( emptyInPowerset
% 0.28/0.49 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(powersetE_type,type,
% 0.28/0.49 powersetE: $o ).
% 0.28/0.49
% 0.28/0.49 thf(powersetE,definition,
% 0.28/0.49 ( powersetE
% 0.28/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.49 ( ( in @ B @ ( powerset @ A ) )
% 0.28/0.49 => ( ( in @ Xx @ B )
% 0.28/0.49 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(setunionI_type,type,
% 0.28/0.49 setunionI: $o ).
% 0.28/0.49
% 0.28/0.49 thf(setunionI,definition,
% 0.28/0.49 ( setunionI
% 0.28/0.49 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.28/0.49 ( ( in @ Xx @ B )
% 0.28/0.49 => ( ( in @ B @ A )
% 0.28/0.49 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(setunionE_type,type,
% 0.28/0.49 setunionE: $o ).
% 0.28/0.49
% 0.28/0.49 thf(setunionE,definition,
% 0.28/0.49 ( setunionE
% 0.28/0.49 = ( ! [A: $i,Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ ( setunion @ A ) )
% 0.28/0.49 => ! [Xphi: $o] :
% 0.28/0.49 ( ! [B: $i] :
% 0.28/0.49 ( ( in @ Xx @ B )
% 0.28/0.49 => ( ( in @ B @ A )
% 0.28/0.49 => Xphi ) )
% 0.28/0.49 => Xphi ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(subPowSU_type,type,
% 0.28/0.49 subPowSU: $o ).
% 0.28/0.49
% 0.28/0.49 thf(subPowSU,definition,
% 0.28/0.49 ( subPowSU
% 0.28/0.49 = ( ! [A: $i,Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(exuE2_type,type,
% 0.28/0.49 exuE2: $o ).
% 0.28/0.49
% 0.28/0.49 thf(exuE2,definition,
% 0.28/0.49 ( exuE2
% 0.28/0.49 = ( ! [Xphi: $i > $o] :
% 0.28/0.49 ( ( exu
% 0.28/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.49 => ? [Xx: $i] :
% 0.28/0.49 ! [Xy: $i] :
% 0.28/0.49 ( ( Xphi @ Xy )
% 0.28/0.49 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(nonemptyImpWitness_type,type,
% 0.28/0.49 nonemptyImpWitness: $o ).
% 0.28/0.49
% 0.28/0.49 thf(nonemptyImpWitness,definition,
% 0.28/0.49 ( nonemptyImpWitness
% 0.28/0.49 = ( ! [A: $i] :
% 0.28/0.49 ( ( nonempty @ A )
% 0.28/0.49 => ? [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 & $true ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(uniqinunit_type,type,
% 0.28/0.49 uniqinunit: $o ).
% 0.28/0.49
% 0.28/0.49 thf(uniqinunit,definition,
% 0.28/0.49 ( uniqinunit
% 0.28/0.49 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.49 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.49 => ( Xx = Xy ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(notinsingleton_type,type,
% 0.28/0.49 notinsingleton: $o ).
% 0.28/0.49
% 0.28/0.49 thf(notinsingleton,definition,
% 0.28/0.49 ( notinsingleton
% 0.28/0.49 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.49 ( ( Xx != Xy )
% 0.28/0.49 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(eqinunit_type,type,
% 0.28/0.49 eqinunit: $o ).
% 0.28/0.49
% 0.28/0.49 thf(eqinunit,definition,
% 0.28/0.49 ( eqinunit
% 0.28/0.49 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.49 ( ( Xx = Xy )
% 0.28/0.49 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(singletonsswitch_type,type,
% 0.28/0.49 singletonsswitch: $o ).
% 0.28/0.49
% 0.28/0.49 thf(singletonsswitch,definition,
% 0.28/0.49 ( singletonsswitch
% 0.28/0.49 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.49 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.49 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(upairsetE_type,type,
% 0.28/0.49 upairsetE: $o ).
% 0.28/0.49
% 0.28/0.49 thf(upairsetE,definition,
% 0.28/0.49 ( upairsetE
% 0.28/0.49 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.28/0.49 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.28/0.49 => ( ( Xz = Xx )
% 0.28/0.49 | ( Xz = Xy ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(upairsetIL_type,type,
% 0.28/0.49 upairsetIL: $o ).
% 0.28/0.49
% 0.28/0.49 thf(upairsetIL,definition,
% 0.28/0.49 ( upairsetIL
% 0.28/0.49 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(upairsetIR_type,type,
% 0.28/0.49 upairsetIR: $o ).
% 0.28/0.49
% 0.28/0.49 thf(upairsetIR,definition,
% 0.28/0.49 ( upairsetIR
% 0.28/0.49 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(emptyE1_type,type,
% 0.28/0.49 emptyE1: $o ).
% 0.28/0.49
% 0.28/0.49 thf(emptyE1,definition,
% 0.28/0.49 ( emptyE1
% 0.28/0.49 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.49 ( ? [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 & ( Xphi @ Xx ) )
% 0.28/0.49 => ( ( ( dsetconstr @ A
% 0.28/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.49 = emptyset )
% 0.28/0.49 => $false ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(vacuousDall_type,type,
% 0.28/0.49 vacuousDall: $o ).
% 0.28/0.49
% 0.28/0.49 thf(vacuousDall,definition,
% 0.28/0.49 ( vacuousDall
% 0.28/0.49 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ emptyset )
% 0.28/0.49 => ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(quantDeMorgan1_type,type,
% 0.28/0.49 quantDeMorgan1: $o ).
% 0.28/0.49
% 0.28/0.49 thf(quantDeMorgan1,definition,
% 0.28/0.49 ( quantDeMorgan1
% 0.28/0.49 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.49 ( ~ ! [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ( Xphi @ Xx ) )
% 0.28/0.49 => ? [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(quantDeMorgan2_type,type,
% 0.28/0.49 quantDeMorgan2: $o ).
% 0.28/0.49
% 0.28/0.49 thf(quantDeMorgan2,definition,
% 0.28/0.49 ( quantDeMorgan2
% 0.28/0.49 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.49 ( ! [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ~ ( Xphi @ Xx ) )
% 0.28/0.49 => ~ ? [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(quantDeMorgan3_type,type,
% 0.28/0.49 quantDeMorgan3: $o ).
% 0.28/0.49
% 0.28/0.49 thf(quantDeMorgan3,definition,
% 0.28/0.49 ( quantDeMorgan3
% 0.28/0.49 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.49 ( ~ ? [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 & ( Xphi @ Xx ) )
% 0.28/0.49 => ! [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(quantDeMorgan4_type,type,
% 0.28/0.49 quantDeMorgan4: $o ).
% 0.28/0.49
% 0.28/0.49 thf(quantDeMorgan4,definition,
% 0.28/0.49 ( quantDeMorgan4
% 0.28/0.49 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.49 ( ? [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 & ~ ( Xphi @ Xx ) )
% 0.28/0.49 => ~ ! [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(prop2setI_type,type,
% 0.28/0.49 prop2setI: $o ).
% 0.28/0.49
% 0.28/0.49 thf(prop2setI,definition,
% 0.28/0.49 ( prop2setI
% 0.28/0.49 = ( ! [Xphi: $o] :
% 0.28/0.49 ( Xphi
% 0.28/0.49 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(set2prop_type,type,
% 0.28/0.49 set2prop: $i > $o ).
% 0.28/0.49
% 0.28/0.49 thf(prop2set2propI_type,type,
% 0.28/0.49 prop2set2propI: $o ).
% 0.28/0.49
% 0.28/0.49 thf(prop2set2propI,definition,
% 0.28/0.49 ( prop2set2propI
% 0.28/0.49 = ( ! [Xphi: $o] :
% 0.28/0.49 ( Xphi
% 0.28/0.49 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(notdexE_type,type,
% 0.28/0.49 notdexE: $o ).
% 0.28/0.49
% 0.28/0.49 thf(notdexE,definition,
% 0.28/0.49 ( notdexE
% 0.28/0.49 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.49 ( ~ ? [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 & ( Xphi @ Xx ) )
% 0.28/0.49 => ! [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(notdallE_type,type,
% 0.28/0.49 notdallE: $o ).
% 0.28/0.49
% 0.28/0.49 thf(notdallE,definition,
% 0.28/0.49 ( notdallE
% 0.28/0.49 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.49 ( ~ ! [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ( Xphi @ Xx ) )
% 0.28/0.49 => ? [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(exuI1_type,type,
% 0.28/0.49 exuI1: $o ).
% 0.28/0.49
% 0.28/0.49 thf(exuI1,definition,
% 0.28/0.49 ( exuI1
% 0.28/0.49 = ( ! [Xphi: $i > $o] :
% 0.28/0.49 ( ? [Xx: $i] :
% 0.28/0.49 ( ( Xphi @ Xx )
% 0.28/0.49 & ! [Xy: $i] :
% 0.28/0.49 ( ( Xphi @ Xy )
% 0.28/0.49 => ( Xx = Xy ) ) )
% 0.28/0.49 => ( exu
% 0.28/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(exuI3_type,type,
% 0.28/0.49 exuI3: $o ).
% 0.28/0.49
% 0.28/0.49 thf(exuI3,definition,
% 0.28/0.49 ( exuI3
% 0.28/0.49 = ( ! [Xphi: $i > $o] :
% 0.28/0.49 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.28/0.49 => ( ! [Xx: $i,Xy: $i] :
% 0.28/0.49 ( ( Xphi @ Xx )
% 0.28/0.49 => ( ( Xphi @ Xy )
% 0.28/0.49 => ( Xx = Xy ) ) )
% 0.28/0.49 => ( exu
% 0.28/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(exuI2_type,type,
% 0.28/0.49 exuI2: $o ).
% 0.28/0.49
% 0.28/0.49 thf(exuI2,definition,
% 0.28/0.49 ( exuI2
% 0.28/0.49 = ( ! [Xphi: $i > $o] :
% 0.28/0.49 ( ? [Xx: $i] :
% 0.28/0.49 ! [Xy: $i] :
% 0.28/0.49 ( ( Xphi @ Xy )
% 0.28/0.49 <=> ( Xy = Xx ) )
% 0.28/0.49 => ( exu
% 0.28/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(inCongP_type,type,
% 0.28/0.49 inCongP: $o ).
% 0.28/0.49
% 0.28/0.49 thf(inCongP,definition,
% 0.28/0.49 ( inCongP
% 0.28/0.49 = ( ! [A: $i,B: $i] :
% 0.28/0.49 ( ( A = B )
% 0.28/0.49 => ! [Xx: $i,Xy: $i] :
% 0.28/0.49 ( ( Xx = Xy )
% 0.28/0.49 => ( ( in @ Xx @ A )
% 0.28/0.49 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(in__Cong_type,type,
% 0.28/0.49 in__Cong: $o ).
% 0.28/0.49
% 0.28/0.49 thf(in__Cong,definition,
% 0.28/0.49 ( in__Cong
% 0.28/0.49 = ( ! [A: $i,B: $i] :
% 0.28/0.49 ( ( A = B )
% 0.28/0.49 => ! [Xx: $i,Xy: $i] :
% 0.28/0.49 ( ( Xx = Xy )
% 0.28/0.49 => ( ( in @ Xx @ A )
% 0.28/0.49 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(exuE3u_type,type,
% 0.28/0.49 exuE3u: $o ).
% 0.28/0.49
% 0.28/0.49 thf(exuE3u,definition,
% 0.28/0.49 ( exuE3u
% 0.28/0.49 = ( ! [Xphi: $i > $o] :
% 0.28/0.49 ( ( exu
% 0.28/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.49 => ! [Xx: $i,Xy: $i] :
% 0.28/0.49 ( ( Xphi @ Xx )
% 0.28/0.49 => ( ( Xphi @ Xy )
% 0.28/0.49 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(exu__Cong_type,type,
% 0.28/0.49 exu__Cong: $o ).
% 0.28/0.49
% 0.28/0.49 thf(exu__Cong,definition,
% 0.28/0.49 ( exu__Cong
% 0.28/0.49 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.28/0.49 ( ! [Xx: $i,Xy: $i] :
% 0.28/0.49 ( ( Xx = Xy )
% 0.28/0.49 => ( ( Xphi @ Xx )
% 0.28/0.49 <=> ( Xpsi @ Xy ) ) )
% 0.28/0.49 => ( ( exu
% 0.28/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.49 <=> ( exu
% 0.28/0.49 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(emptyset__Cong_type,type,
% 0.28/0.49 emptyset__Cong: $o ).
% 0.28/0.49
% 0.28/0.49 thf(emptyset__Cong,definition,
% 0.28/0.49 ( emptyset__Cong
% 0.28/0.49 = ( emptyset = emptyset ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(setadjoin__Cong_type,type,
% 0.28/0.49 setadjoin__Cong: $o ).
% 0.28/0.49
% 0.28/0.49 thf(setadjoin__Cong,definition,
% 0.28/0.49 ( setadjoin__Cong
% 0.28/0.49 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.49 ( ( Xx = Xy )
% 0.28/0.49 => ! [Xz: $i,Xu: $i] :
% 0.28/0.49 ( ( Xz = Xu )
% 0.28/0.49 => ( ( setadjoin @ Xx @ Xz )
% 0.28/0.49 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(powerset__Cong_type,type,
% 0.28/0.49 powerset__Cong: $o ).
% 0.28/0.49
% 0.28/0.49 thf(powerset__Cong,definition,
% 0.28/0.49 ( powerset__Cong
% 0.28/0.49 = ( ! [A: $i,B: $i] :
% 0.28/0.49 ( ( A = B )
% 0.28/0.49 => ( ( powerset @ A )
% 0.28/0.49 = ( powerset @ B ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(setunion__Cong_type,type,
% 0.28/0.49 setunion__Cong: $o ).
% 0.28/0.49
% 0.28/0.49 thf(setunion__Cong,definition,
% 0.28/0.49 ( setunion__Cong
% 0.28/0.49 = ( ! [A: $i,B: $i] :
% 0.28/0.49 ( ( A = B )
% 0.28/0.49 => ( ( setunion @ A )
% 0.28/0.49 = ( setunion @ B ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(omega__Cong_type,type,
% 0.28/0.49 omega__Cong: $o ).
% 0.28/0.49
% 0.28/0.49 thf(omega__Cong,definition,
% 0.28/0.49 ( omega__Cong
% 0.28/0.49 = ( omega = omega ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(exuEu_type,type,
% 0.28/0.49 exuEu: $o ).
% 0.28/0.49
% 0.28/0.49 thf(exuEu,definition,
% 0.28/0.49 ( exuEu
% 0.28/0.49 = ( ! [Xphi: $i > $o] :
% 0.28/0.49 ( ( exu
% 0.28/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.49 => ! [Xx: $i,Xy: $i] :
% 0.28/0.49 ( ( Xphi @ Xx )
% 0.28/0.49 => ( ( Xphi @ Xy )
% 0.28/0.49 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(descr__Cong_type,type,
% 0.28/0.49 descr__Cong: $o ).
% 0.28/0.49
% 0.28/0.49 thf(descr__Cong,definition,
% 0.28/0.49 ( descr__Cong
% 0.28/0.49 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.28/0.49 ( ! [Xx: $i,Xy: $i] :
% 0.28/0.49 ( ( Xx = Xy )
% 0.28/0.49 => ( ( Xphi @ Xx )
% 0.28/0.49 <=> ( Xpsi @ Xy ) ) )
% 0.28/0.49 => ( ( exu
% 0.28/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.49 => ( ( exu
% 0.28/0.49 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.28/0.49 => ( ( descr
% 0.28/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.49 = ( descr
% 0.28/0.49 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(dsetconstr__Cong_type,type,
% 0.28/0.49 dsetconstr__Cong: $o ).
% 0.28/0.49
% 0.28/0.49 thf(dsetconstr__Cong,definition,
% 0.28/0.49 ( dsetconstr__Cong
% 0.28/0.49 = ( ! [A: $i,B: $i] :
% 0.28/0.49 ( ( A = B )
% 0.28/0.49 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.28/0.49 ( ! [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ! [Xy: $i] :
% 0.28/0.49 ( ( in @ Xy @ B )
% 0.28/0.49 => ( ( Xx = Xy )
% 0.28/0.49 => ( ( Xphi @ Xx )
% 0.28/0.49 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.28/0.49 => ( ( dsetconstr @ A
% 0.28/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.49 = ( dsetconstr @ B
% 0.28/0.49 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(subset_type,type,
% 0.28/0.49 subset: $i > $i > $o ).
% 0.28/0.49
% 0.28/0.49 thf(disjoint_type,type,
% 0.28/0.49 disjoint: $i > $i > $o ).
% 0.28/0.49
% 0.28/0.49 thf(setsmeet_type,type,
% 0.28/0.49 setsmeet: $i > $i > $o ).
% 0.28/0.49
% 0.28/0.49 thf(subsetI1_type,type,
% 0.28/0.49 subsetI1: $o ).
% 0.28/0.49
% 0.28/0.49 thf(subsetI1,definition,
% 0.28/0.49 ( subsetI1
% 0.28/0.49 = ( ! [A: $i,B: $i] :
% 0.28/0.49 ( ! [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ( in @ Xx @ B ) )
% 0.28/0.49 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(eqimpsubset2_type,type,
% 0.28/0.49 eqimpsubset2: $o ).
% 0.28/0.49
% 0.28/0.49 thf(eqimpsubset2,definition,
% 0.28/0.49 ( eqimpsubset2
% 0.28/0.49 = ( ! [A: $i,B: $i] :
% 0.28/0.49 ( ( A = B )
% 0.28/0.49 => ( subset @ B @ A ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(eqimpsubset1_type,type,
% 0.28/0.49 eqimpsubset1: $o ).
% 0.28/0.49
% 0.28/0.49 thf(eqimpsubset1,definition,
% 0.28/0.49 ( eqimpsubset1
% 0.28/0.49 = ( ! [A: $i,B: $i] :
% 0.28/0.49 ( ( A = B )
% 0.28/0.49 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(subsetI2_type,type,
% 0.28/0.49 subsetI2: $o ).
% 0.28/0.49
% 0.28/0.49 thf(subsetI2,definition,
% 0.28/0.49 ( subsetI2
% 0.28/0.49 = ( ! [A: $i,B: $i] :
% 0.28/0.49 ( ! [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ( in @ Xx @ B ) )
% 0.28/0.49 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(emptysetsubset_type,type,
% 0.28/0.49 emptysetsubset: $o ).
% 0.28/0.49
% 0.28/0.49 thf(emptysetsubset,definition,
% 0.28/0.49 ( emptysetsubset
% 0.28/0.49 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(subsetE_type,type,
% 0.28/0.49 subsetE: $o ).
% 0.28/0.49
% 0.28/0.49 thf(subsetE,definition,
% 0.28/0.49 ( subsetE
% 0.28/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.49 ( ( subset @ A @ B )
% 0.28/0.49 => ( ( in @ Xx @ A )
% 0.28/0.49 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(subsetE2_type,type,
% 0.28/0.49 subsetE2: $o ).
% 0.28/0.49
% 0.28/0.49 thf(subsetE2,definition,
% 0.28/0.49 ( subsetE2
% 0.28/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.49 ( ( subset @ A @ B )
% 0.28/0.49 => ( ~ ( in @ Xx @ B )
% 0.28/0.49 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(notsubsetI_type,type,
% 0.28/0.49 notsubsetI: $o ).
% 0.28/0.49
% 0.28/0.49 thf(notsubsetI,definition,
% 0.28/0.49 ( notsubsetI
% 0.28/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ( ~ ( in @ Xx @ B )
% 0.28/0.49 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(notequalI1_type,type,
% 0.28/0.49 notequalI1: $o ).
% 0.28/0.49
% 0.28/0.49 thf(notequalI1,definition,
% 0.28/0.49 ( notequalI1
% 0.28/0.49 = ( ! [A: $i,B: $i] :
% 0.28/0.49 ( ~ ( subset @ A @ B )
% 0.28/0.49 => ( A != B ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(notequalI2_type,type,
% 0.28/0.49 notequalI2: $o ).
% 0.28/0.49
% 0.28/0.49 thf(notequalI2,definition,
% 0.28/0.49 ( notequalI2
% 0.28/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ( ~ ( in @ Xx @ B )
% 0.28/0.49 => ( A != B ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(subsetRefl_type,type,
% 0.28/0.49 subsetRefl: $o ).
% 0.28/0.49
% 0.28/0.49 thf(subsetRefl,definition,
% 0.28/0.49 ( subsetRefl
% 0.28/0.49 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(subsetTrans_type,type,
% 0.28/0.49 subsetTrans: $o ).
% 0.28/0.49
% 0.28/0.49 thf(subsetTrans,definition,
% 0.28/0.49 ( subsetTrans
% 0.28/0.49 = ( ! [A: $i,B: $i,C: $i] :
% 0.28/0.49 ( ( subset @ A @ B )
% 0.28/0.49 => ( ( subset @ B @ C )
% 0.28/0.49 => ( subset @ A @ C ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(setadjoinSub_type,type,
% 0.28/0.49 setadjoinSub: $o ).
% 0.28/0.49
% 0.28/0.49 thf(setadjoinSub,definition,
% 0.28/0.49 ( setadjoinSub
% 0.28/0.49 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(setadjoinSub2_type,type,
% 0.28/0.49 setadjoinSub2: $o ).
% 0.28/0.49
% 0.28/0.49 thf(setadjoinSub2,definition,
% 0.28/0.49 ( setadjoinSub2
% 0.28/0.49 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.28/0.49 ( ( subset @ A @ B )
% 0.28/0.49 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(subset2powerset_type,type,
% 0.28/0.49 subset2powerset: $o ).
% 0.28/0.49
% 0.28/0.49 thf(subset2powerset,definition,
% 0.28/0.49 ( subset2powerset
% 0.28/0.49 = ( ! [A: $i,B: $i] :
% 0.28/0.49 ( ( subset @ A @ B )
% 0.28/0.49 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(setextsub_type,type,
% 0.28/0.49 setextsub: $o ).
% 0.28/0.49
% 0.28/0.49 thf(setextsub,definition,
% 0.28/0.49 ( setextsub
% 0.28/0.49 = ( ! [A: $i,B: $i] :
% 0.28/0.49 ( ( subset @ A @ B )
% 0.28/0.49 => ( ( subset @ B @ A )
% 0.28/0.49 => ( A = B ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(subsetemptysetimpeq_type,type,
% 0.28/0.49 subsetemptysetimpeq: $o ).
% 0.28/0.49
% 0.28/0.49 thf(subsetemptysetimpeq,definition,
% 0.28/0.49 ( subsetemptysetimpeq
% 0.28/0.49 = ( ! [A: $i] :
% 0.28/0.49 ( ( subset @ A @ emptyset )
% 0.28/0.49 => ( A = emptyset ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(powersetI1_type,type,
% 0.28/0.49 powersetI1: $o ).
% 0.28/0.49
% 0.28/0.49 thf(powersetI1,definition,
% 0.28/0.49 ( powersetI1
% 0.28/0.49 = ( ! [A: $i,B: $i] :
% 0.28/0.49 ( ( subset @ B @ A )
% 0.28/0.49 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(powersetE1_type,type,
% 0.28/0.49 powersetE1: $o ).
% 0.28/0.49
% 0.28/0.49 thf(powersetE1,definition,
% 0.28/0.49 ( powersetE1
% 0.28/0.49 = ( ! [A: $i,B: $i] :
% 0.28/0.49 ( ( in @ B @ ( powerset @ A ) )
% 0.28/0.49 => ( subset @ B @ A ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(inPowerset_type,type,
% 0.28/0.49 inPowerset: $o ).
% 0.28/0.49
% 0.28/0.49 thf(inPowerset,definition,
% 0.28/0.49 ( inPowerset
% 0.28/0.49 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(powersetsubset_type,type,
% 0.28/0.49 powersetsubset: $o ).
% 0.28/0.49
% 0.28/0.49 thf(powersetsubset,definition,
% 0.28/0.49 ( powersetsubset
% 0.28/0.49 = ( ! [A: $i,B: $i] :
% 0.28/0.49 ( ( subset @ A @ B )
% 0.28/0.49 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(sepInPowerset_type,type,
% 0.28/0.49 sepInPowerset: $o ).
% 0.28/0.49
% 0.28/0.49 thf(sepInPowerset,definition,
% 0.28/0.49 ( sepInPowerset
% 0.28/0.49 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.49 ( in
% 0.28/0.49 @ ( dsetconstr @ A
% 0.28/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.49 @ ( powerset @ A ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(sepSubset_type,type,
% 0.28/0.49 sepSubset: $o ).
% 0.28/0.49
% 0.28/0.49 thf(sepSubset,definition,
% 0.28/0.49 ( sepSubset
% 0.28/0.49 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.49 ( subset
% 0.28/0.49 @ ( dsetconstr @ A
% 0.28/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.49 @ A ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(binunion_type,type,
% 0.28/0.49 binunion: $i > $i > $i ).
% 0.28/0.49
% 0.28/0.49 thf(binunionIL_type,type,
% 0.28/0.49 binunionIL: $o ).
% 0.28/0.49
% 0.28/0.49 thf(binunionIL,definition,
% 0.28/0.49 ( binunionIL
% 0.28/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(upairset2IR_type,type,
% 0.28/0.49 upairset2IR: $o ).
% 0.28/0.49
% 0.28/0.49 thf(upairset2IR,definition,
% 0.28/0.49 ( upairset2IR
% 0.28/0.49 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(binunionIR_type,type,
% 0.28/0.49 binunionIR: $o ).
% 0.28/0.49
% 0.28/0.49 thf(binunionIR,definition,
% 0.28/0.49 ( binunionIR
% 0.28/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ B )
% 0.28/0.49 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(binunionEcases_type,type,
% 0.28/0.49 binunionEcases: $o ).
% 0.28/0.49
% 0.28/0.49 thf(binunionEcases,definition,
% 0.28/0.49 ( binunionEcases
% 0.28/0.49 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.28/0.49 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.28/0.49 => ( ( ( in @ Xx @ A )
% 0.28/0.49 => Xphi )
% 0.28/0.49 => ( ( ( in @ Xx @ B )
% 0.28/0.49 => Xphi )
% 0.28/0.49 => Xphi ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(binunionE_type,type,
% 0.28/0.49 binunionE: $o ).
% 0.28/0.49
% 0.28/0.49 thf(binunionE,definition,
% 0.28/0.49 ( binunionE
% 0.28/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.28/0.49 => ( ( in @ Xx @ A )
% 0.28/0.49 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(binunionLsub_type,type,
% 0.28/0.49 binunionLsub: $o ).
% 0.28/0.49
% 0.28/0.49 thf(binunionLsub,definition,
% 0.28/0.49 ( binunionLsub
% 0.28/0.49 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(binunionRsub_type,type,
% 0.28/0.49 binunionRsub: $o ).
% 0.28/0.49
% 0.28/0.49 thf(binunionRsub,definition,
% 0.28/0.49 ( binunionRsub
% 0.28/0.49 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(binintersect_type,type,
% 0.28/0.49 binintersect: $i > $i > $i ).
% 0.28/0.49
% 0.28/0.49 thf(binintersectI_type,type,
% 0.28/0.49 binintersectI: $o ).
% 0.28/0.49
% 0.28/0.49 thf(binintersectI,definition,
% 0.28/0.49 ( binintersectI
% 0.28/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ( ( in @ Xx @ B )
% 0.28/0.49 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(binintersectSubset5_type,type,
% 0.28/0.49 binintersectSubset5: $o ).
% 0.28/0.49
% 0.28/0.49 thf(binintersectSubset5,definition,
% 0.28/0.49 ( binintersectSubset5
% 0.28/0.49 = ( ! [A: $i,B: $i,C: $i] :
% 0.28/0.49 ( ( subset @ C @ A )
% 0.28/0.49 => ( ( subset @ C @ B )
% 0.28/0.49 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(binintersectEL_type,type,
% 0.28/0.49 binintersectEL: $o ).
% 0.28/0.49
% 0.28/0.49 thf(binintersectEL,definition,
% 0.28/0.49 ( binintersectEL
% 0.28/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.28/0.49 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(binintersectLsub_type,type,
% 0.28/0.49 binintersectLsub: $o ).
% 0.28/0.49
% 0.28/0.49 thf(binintersectLsub,definition,
% 0.28/0.49 ( binintersectLsub
% 0.28/0.49 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(binintersectSubset2_type,type,
% 0.28/0.49 binintersectSubset2: $o ).
% 0.28/0.49
% 0.28/0.49 thf(binintersectSubset2,definition,
% 0.28/0.49 ( binintersectSubset2
% 0.28/0.49 = ( ! [A: $i,B: $i] :
% 0.28/0.49 ( ( subset @ A @ B )
% 0.28/0.49 => ( ( binintersect @ A @ B )
% 0.28/0.49 = A ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(binintersectSubset3_type,type,
% 0.28/0.49 binintersectSubset3: $o ).
% 0.28/0.49
% 0.28/0.49 thf(binintersectSubset3,definition,
% 0.28/0.49 ( binintersectSubset3
% 0.28/0.49 = ( ! [A: $i,B: $i] :
% 0.28/0.49 ( ( ( binintersect @ A @ B )
% 0.28/0.49 = B )
% 0.28/0.49 => ( subset @ B @ A ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(binintersectER_type,type,
% 0.28/0.49 binintersectER: $o ).
% 0.28/0.49
% 0.28/0.49 thf(binintersectER,definition,
% 0.28/0.49 ( binintersectER
% 0.28/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.28/0.49 => ( in @ Xx @ B ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(disjointsetsI1_type,type,
% 0.28/0.49 disjointsetsI1: $o ).
% 0.28/0.49
% 0.28/0.49 thf(disjointsetsI1,definition,
% 0.28/0.49 ( disjointsetsI1
% 0.28/0.49 = ( ! [A: $i,B: $i] :
% 0.28/0.49 ( ~ ? [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 & ( in @ Xx @ B ) )
% 0.28/0.49 => ( ( binintersect @ A @ B )
% 0.28/0.49 = emptyset ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(binintersectRsub_type,type,
% 0.28/0.49 binintersectRsub: $o ).
% 0.28/0.49
% 0.28/0.49 thf(binintersectRsub,definition,
% 0.28/0.49 ( binintersectRsub
% 0.28/0.49 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(binintersectSubset4_type,type,
% 0.28/0.49 binintersectSubset4: $o ).
% 0.28/0.49
% 0.28/0.49 thf(binintersectSubset4,definition,
% 0.28/0.49 ( binintersectSubset4
% 0.28/0.49 = ( ! [A: $i,B: $i] :
% 0.28/0.49 ( ( subset @ B @ A )
% 0.28/0.49 => ( ( binintersect @ A @ B )
% 0.28/0.49 = B ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(binintersectSubset1_type,type,
% 0.28/0.49 binintersectSubset1: $o ).
% 0.28/0.49
% 0.28/0.49 thf(binintersectSubset1,definition,
% 0.28/0.49 ( binintersectSubset1
% 0.28/0.49 = ( ! [A: $i,B: $i] :
% 0.28/0.49 ( ( ( binintersect @ A @ B )
% 0.28/0.49 = A )
% 0.28/0.49 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(bs114d_type,type,
% 0.28/0.49 bs114d: $o ).
% 0.28/0.49
% 0.28/0.49 thf(bs114d,definition,
% 0.28/0.49 ( bs114d
% 0.28/0.49 = ( ! [A: $i,B: $i,C: $i] :
% 0.28/0.49 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.28/0.49 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(regular_type,type,
% 0.28/0.49 regular: $i > $o ).
% 0.28/0.49
% 0.28/0.49 thf(setminus_type,type,
% 0.28/0.49 setminus: $i > $i > $i ).
% 0.28/0.49
% 0.28/0.49 thf(setminusI_type,type,
% 0.28/0.49 setminusI: $o ).
% 0.28/0.49
% 0.28/0.49 thf(setminusI,definition,
% 0.28/0.49 ( setminusI
% 0.28/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ( ~ ( in @ Xx @ B )
% 0.28/0.49 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(setminusEL_type,type,
% 0.28/0.49 setminusEL: $o ).
% 0.28/0.49
% 0.28/0.49 thf(setminusEL,definition,
% 0.28/0.49 ( setminusEL
% 0.28/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.28/0.49 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(setminusER_type,type,
% 0.28/0.49 setminusER: $o ).
% 0.28/0.49
% 0.28/0.49 thf(setminusER,definition,
% 0.28/0.49 ( setminusER
% 0.28/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.28/0.49 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(setminusSubset2_type,type,
% 0.28/0.49 setminusSubset2: $o ).
% 0.28/0.49
% 0.28/0.49 thf(setminusSubset2,definition,
% 0.28/0.49 ( setminusSubset2
% 0.28/0.49 = ( ! [A: $i,B: $i] :
% 0.28/0.49 ( ( subset @ A @ B )
% 0.28/0.49 => ( ( setminus @ A @ B )
% 0.28/0.49 = emptyset ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(setminusERneg_type,type,
% 0.28/0.49 setminusERneg: $o ).
% 0.28/0.49
% 0.28/0.49 thf(setminusERneg,definition,
% 0.28/0.49 ( setminusERneg
% 0.28/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.49 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.28/0.49 => ( ( in @ Xx @ A )
% 0.28/0.49 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(setminusELneg_type,type,
% 0.28/0.49 setminusELneg: $o ).
% 0.28/0.49
% 0.28/0.49 thf(setminusELneg,definition,
% 0.28/0.49 ( setminusELneg
% 0.28/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.49 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.28/0.49 => ( ~ ( in @ Xx @ B )
% 0.28/0.49 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(setminusILneg_type,type,
% 0.28/0.49 setminusILneg: $o ).
% 0.28/0.49
% 0.28/0.49 thf(setminusILneg,definition,
% 0.28/0.49 ( setminusILneg
% 0.28/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.49 ( ~ ( in @ Xx @ A )
% 0.28/0.49 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(setminusIRneg_type,type,
% 0.28/0.49 setminusIRneg: $o ).
% 0.28/0.49
% 0.28/0.49 thf(setminusIRneg,definition,
% 0.28/0.49 ( setminusIRneg
% 0.28/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ B )
% 0.28/0.49 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(setminusLsub_type,type,
% 0.28/0.49 setminusLsub: $o ).
% 0.28/0.49
% 0.28/0.49 thf(setminusLsub,definition,
% 0.28/0.49 ( setminusLsub
% 0.28/0.49 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(setminusSubset1_type,type,
% 0.28/0.49 setminusSubset1: $o ).
% 0.28/0.49
% 0.28/0.49 thf(setminusSubset1,definition,
% 0.28/0.49 ( setminusSubset1
% 0.28/0.49 = ( ! [A: $i,B: $i] :
% 0.28/0.49 ( ( ( setminus @ A @ B )
% 0.28/0.49 = emptyset )
% 0.28/0.49 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(symdiff_type,type,
% 0.28/0.49 symdiff: $i > $i > $i ).
% 0.28/0.49
% 0.28/0.49 thf(symdiffE_type,type,
% 0.28/0.49 symdiffE: $o ).
% 0.28/0.49
% 0.28/0.49 thf(symdiffE,definition,
% 0.28/0.49 ( symdiffE
% 0.28/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.28/0.49 => ! [Xphi: $o] :
% 0.28/0.49 ( ( ( in @ Xx @ A )
% 0.28/0.49 => ( ~ ( in @ Xx @ B )
% 0.28/0.49 => Xphi ) )
% 0.28/0.49 => ( ( ~ ( in @ Xx @ A )
% 0.28/0.49 => ( ( in @ Xx @ B )
% 0.28/0.49 => Xphi ) )
% 0.28/0.49 => Xphi ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(symdiffI1_type,type,
% 0.28/0.49 symdiffI1: $o ).
% 0.28/0.49
% 0.28/0.49 thf(symdiffI1,definition,
% 0.28/0.49 ( symdiffI1
% 0.28/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ( ~ ( in @ Xx @ B )
% 0.28/0.49 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(symdiffI2_type,type,
% 0.28/0.49 symdiffI2: $o ).
% 0.28/0.49
% 0.28/0.49 thf(symdiffI2,definition,
% 0.28/0.49 ( symdiffI2
% 0.28/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.49 ( ~ ( in @ Xx @ A )
% 0.28/0.49 => ( ( in @ Xx @ B )
% 0.28/0.49 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(symdiffIneg1_type,type,
% 0.28/0.49 symdiffIneg1: $o ).
% 0.28/0.49
% 0.28/0.49 thf(symdiffIneg1,definition,
% 0.28/0.49 ( symdiffIneg1
% 0.28/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ( ( in @ Xx @ B )
% 0.28/0.49 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(symdiffIneg2_type,type,
% 0.28/0.49 symdiffIneg2: $o ).
% 0.28/0.49
% 0.28/0.49 thf(symdiffIneg2,definition,
% 0.28/0.49 ( symdiffIneg2
% 0.28/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.49 ( ~ ( in @ Xx @ A )
% 0.28/0.49 => ( ~ ( in @ Xx @ B )
% 0.28/0.49 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(iskpair_type,type,
% 0.28/0.49 iskpair: $i > $o ).
% 0.28/0.49
% 0.28/0.49 thf(iskpair,definition,
% 0.28/0.49 ( iskpair
% 0.28/0.49 = ( ^ [A: $i] :
% 0.28/0.49 ? [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ ( setunion @ A ) )
% 0.28/0.49 & ? [Xy: $i] :
% 0.28/0.49 ( ( in @ Xy @ ( setunion @ A ) )
% 0.28/0.49 & ( A
% 0.28/0.49 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(secondinupair_type,type,
% 0.28/0.49 secondinupair: $o ).
% 0.28/0.49
% 0.28/0.49 thf(secondinupair,definition,
% 0.28/0.49 ( secondinupair
% 0.28/0.49 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(setukpairIL_type,type,
% 0.28/0.49 setukpairIL: $o ).
% 0.28/0.49
% 0.28/0.49 thf(setukpairIL,definition,
% 0.28/0.49 ( setukpairIL
% 0.28/0.49 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(setukpairIR_type,type,
% 0.28/0.49 setukpairIR: $o ).
% 0.28/0.49
% 0.28/0.49 thf(setukpairIR,definition,
% 0.28/0.49 ( setukpairIR
% 0.28/0.49 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(kpairiskpair_type,type,
% 0.28/0.49 kpairiskpair: $o ).
% 0.28/0.49
% 0.28/0.49 thf(kpairiskpair,definition,
% 0.28/0.49 ( kpairiskpair
% 0.28/0.49 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(kpair_type,type,
% 0.28/0.49 kpair: $i > $i > $i ).
% 0.28/0.49
% 0.28/0.49 thf(kpair,definition,
% 0.28/0.49 ( kpair
% 0.28/0.49 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(kpairp_type,type,
% 0.28/0.49 kpairp: $o ).
% 0.28/0.49
% 0.28/0.49 thf(kpairp,definition,
% 0.28/0.49 ( kpairp
% 0.28/0.49 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(cartprod_type,type,
% 0.28/0.49 cartprod: $i > $i > $i ).
% 0.28/0.49
% 0.28/0.49 thf(cartprod,definition,
% 0.28/0.49 ( cartprod
% 0.28/0.49 = ( ^ [A: $i,B: $i] :
% 0.28/0.49 ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) )
% 0.28/0.49 @ ^ [Xx: $i] :
% 0.28/0.49 ? [Xy: $i] :
% 0.28/0.49 ( ( in @ Xy @ A )
% 0.28/0.49 & ? [Xz: $i] :
% 0.28/0.49 ( ( in @ Xz @ B )
% 0.28/0.49 & ( Xx
% 0.28/0.49 = ( kpair @ Xy @ Xz ) ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(singletonsubset_type,type,
% 0.28/0.49 singletonsubset: $o ).
% 0.28/0.49
% 0.28/0.49 thf(singletonsubset,definition,
% 0.28/0.49 ( singletonsubset
% 0.28/0.49 = ( ! [A: $i,Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(singletoninpowerset_type,type,
% 0.28/0.49 singletoninpowerset: $o ).
% 0.28/0.49
% 0.28/0.49 thf(singletoninpowerset,definition,
% 0.28/0.49 ( singletoninpowerset
% 0.28/0.49 = ( ! [A: $i,Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(singletoninpowunion_type,type,
% 0.28/0.49 singletoninpowunion: $o ).
% 0.28/0.49
% 0.28/0.49 thf(singletoninpowunion,definition,
% 0.28/0.49 ( singletoninpowunion
% 0.28/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(upairset2E_type,type,
% 0.28/0.49 upairset2E: $o ).
% 0.28/0.49
% 0.28/0.49 thf(upairset2E,definition,
% 0.28/0.49 ( upairset2E
% 0.28/0.49 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.28/0.49 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.28/0.49 => ( ( Xz = Xx )
% 0.28/0.49 | ( Xz = Xy ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(upairsubunion_type,type,
% 0.28/0.49 upairsubunion: $o ).
% 0.28/0.49
% 0.28/0.49 thf(upairsubunion,definition,
% 0.28/0.49 ( upairsubunion
% 0.28/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ! [Xy: $i] :
% 0.28/0.49 ( ( in @ Xy @ B )
% 0.28/0.49 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(upairinpowunion_type,type,
% 0.28/0.49 upairinpowunion: $o ).
% 0.28/0.49
% 0.28/0.49 thf(upairinpowunion,definition,
% 0.28/0.49 ( upairinpowunion
% 0.28/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ! [Xy: $i] :
% 0.28/0.49 ( ( in @ Xy @ B )
% 0.28/0.49 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(ubforcartprodlem1_type,type,
% 0.28/0.49 ubforcartprodlem1: $o ).
% 0.28/0.49
% 0.28/0.49 thf(ubforcartprodlem1,definition,
% 0.28/0.49 ( ubforcartprodlem1
% 0.28/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ! [Xy: $i] :
% 0.28/0.49 ( ( in @ Xy @ B )
% 0.28/0.49 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(ubforcartprodlem2_type,type,
% 0.28/0.49 ubforcartprodlem2: $o ).
% 0.28/0.49
% 0.28/0.49 thf(ubforcartprodlem2,definition,
% 0.28/0.49 ( ubforcartprodlem2
% 0.28/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ! [Xy: $i] :
% 0.28/0.49 ( ( in @ Xy @ B )
% 0.28/0.49 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(ubforcartprodlem3_type,type,
% 0.28/0.49 ubforcartprodlem3: $o ).
% 0.28/0.49
% 0.28/0.49 thf(ubforcartprodlem3,definition,
% 0.28/0.49 ( ubforcartprodlem3
% 0.28/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ! [Xy: $i] :
% 0.28/0.49 ( ( in @ Xy @ B )
% 0.28/0.49 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(cartprodpairin_type,type,
% 0.28/0.49 cartprodpairin: $o ).
% 0.28/0.49
% 0.28/0.49 thf(cartprodpairin,definition,
% 0.28/0.49 ( cartprodpairin
% 0.28/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 => ! [Xy: $i] :
% 0.28/0.49 ( ( in @ Xy @ B )
% 0.28/0.49 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 thf(cartprodmempair1,conjecture,
% 0.28/0.49 ( setextAx
% 0.28/0.49 => ( emptysetAx
% 0.28/0.49 => ( setadjoinAx
% 0.28/0.49 => ( powersetAx
% 0.28/0.49 => ( setunionAx
% 0.28/0.49 => ( omega0Ax
% 0.28/0.49 => ( omegaSAx
% 0.28/0.49 => ( omegaIndAx
% 0.28/0.49 => ( replAx
% 0.28/0.49 => ( foundationAx
% 0.28/0.49 => ( wellorderingAx
% 0.28/0.49 => ( descrp
% 0.28/0.49 => ( dsetconstrI
% 0.28/0.49 => ( dsetconstrEL
% 0.28/0.49 => ( dsetconstrER
% 0.28/0.49 => ( exuE1
% 0.28/0.49 => ( prop2setE
% 0.28/0.49 => ( emptysetE
% 0.28/0.49 => ( emptysetimpfalse
% 0.28/0.49 => ( notinemptyset
% 0.28/0.49 => ( exuE3e
% 0.28/0.49 => ( setext
% 0.28/0.49 => ( emptyI
% 0.28/0.49 => ( noeltsimpempty
% 0.28/0.49 => ( setbeta
% 0.28/0.49 => ( nonemptyE1
% 0.28/0.49 => ( nonemptyI
% 0.28/0.49 => ( nonemptyI1
% 0.28/0.49 => ( setadjoinIL
% 0.28/0.49 => ( emptyinunitempty
% 0.28/0.49 => ( setadjoinIR
% 0.28/0.49 => ( setadjoinE
% 0.28/0.49 => ( setadjoinOr
% 0.28/0.49 => ( setoftrueEq
% 0.28/0.49 => ( powersetI
% 0.28/0.49 => ( emptyinPowerset
% 0.28/0.49 => ( emptyInPowerset
% 0.28/0.49 => ( powersetE
% 0.28/0.49 => ( setunionI
% 0.28/0.49 => ( setunionE
% 0.28/0.49 => ( subPowSU
% 0.28/0.49 => ( exuE2
% 0.28/0.49 => ( nonemptyImpWitness
% 0.28/0.49 => ( uniqinunit
% 0.28/0.49 => ( notinsingleton
% 0.28/0.49 => ( eqinunit
% 0.28/0.49 => ( singletonsswitch
% 0.28/0.49 => ( upairsetE
% 0.28/0.49 => ( upairsetIL
% 0.28/0.49 => ( upairsetIR
% 0.28/0.49 => ( emptyE1
% 0.28/0.49 => ( vacuousDall
% 0.28/0.49 => ( quantDeMorgan1
% 0.28/0.49 => ( quantDeMorgan2
% 0.28/0.49 => ( quantDeMorgan3
% 0.28/0.49 => ( quantDeMorgan4
% 0.28/0.49 => ( prop2setI
% 0.28/0.49 => ( prop2set2propI
% 0.28/0.49 => ( notdexE
% 0.28/0.49 => ( notdallE
% 0.28/0.49 => ( exuI1
% 0.28/0.49 => ( exuI3
% 0.28/0.49 => ( exuI2
% 0.28/0.49 => ( inCongP
% 0.28/0.49 => ( in__Cong
% 0.28/0.49 => ( exuE3u
% 0.28/0.49 => ( exu__Cong
% 0.28/0.49 => ( emptyset__Cong
% 0.28/0.49 => ( setadjoin__Cong
% 0.28/0.49 => ( powerset__Cong
% 0.28/0.49 => ( setunion__Cong
% 0.28/0.49 => ( omega__Cong
% 0.28/0.49 => ( exuEu
% 0.28/0.49 => ( descr__Cong
% 0.28/0.49 => ( dsetconstr__Cong
% 0.28/0.49 => ( subsetI1
% 0.28/0.49 => ( eqimpsubset2
% 0.28/0.49 => ( eqimpsubset1
% 0.28/0.49 => ( subsetI2
% 0.28/0.49 => ( emptysetsubset
% 0.28/0.49 => ( subsetE
% 0.28/0.49 => ( subsetE2
% 0.28/0.49 => ( notsubsetI
% 0.28/0.49 => ( notequalI1
% 0.28/0.49 => ( notequalI2
% 0.28/0.49 => ( subsetRefl
% 0.28/0.49 => ( subsetTrans
% 0.28/0.49 => ( setadjoinSub
% 0.28/0.49 => ( setadjoinSub2
% 0.28/0.49 => ( subset2powerset
% 0.28/0.49 => ( setextsub
% 0.28/0.49 => ( subsetemptysetimpeq
% 0.28/0.49 => ( powersetI1
% 0.28/0.49 => ( powersetE1
% 0.28/0.49 => ( inPowerset
% 0.28/0.49 => ( powersetsubset
% 0.28/0.49 => ( sepInPowerset
% 0.28/0.49 => ( sepSubset
% 0.28/0.49 => ( binunionIL
% 0.28/0.49 => ( upairset2IR
% 0.28/0.49 => ( binunionIR
% 0.28/0.49 => ( binunionEcases
% 0.28/0.49 => ( binunionE
% 0.28/0.49 => ( binunionLsub
% 0.28/0.49 => ( binunionRsub
% 0.28/0.49 => ( binintersectI
% 0.28/0.49 => ( binintersectSubset5
% 0.28/0.49 => ( binintersectEL
% 0.28/0.49 => ( binintersectLsub
% 0.28/0.49 => ( binintersectSubset2
% 0.28/0.49 => ( binintersectSubset3
% 0.28/0.49 => ( binintersectER
% 0.28/0.49 => ( disjointsetsI1
% 0.28/0.49 => ( binintersectRsub
% 0.28/0.49 => ( binintersectSubset4
% 0.28/0.49 => ( binintersectSubset1
% 0.28/0.49 => ( bs114d
% 0.28/0.49 => ( setminusI
% 0.28/0.49 => ( setminusEL
% 0.28/0.49 => ( setminusER
% 0.28/0.49 => ( setminusSubset2
% 0.28/0.49 => ( setminusERneg
% 0.28/0.49 => ( setminusELneg
% 0.28/0.49 => ( setminusILneg
% 0.28/0.49 => ( setminusIRneg
% 0.28/0.49 => ( setminusLsub
% 0.28/0.49 => ( setminusSubset1
% 0.28/0.49 => ( symdiffE
% 0.28/0.49 => ( symdiffI1
% 0.28/0.49 => ( symdiffI2
% 0.28/0.49 => ( symdiffIneg1
% 0.28/0.49 => ( symdiffIneg2
% 0.28/0.49 => ( secondinupair
% 0.28/0.49 => ( setukpairIL
% 0.28/0.49 => ( setukpairIR
% 0.28/0.49 => ( kpairiskpair
% 0.28/0.49 => ( kpairp
% 0.28/0.49 => ( singletonsubset
% 0.28/0.49 => ( singletoninpowerset
% 0.28/0.49 => ( singletoninpowunion
% 0.28/0.49 => ( upairset2E
% 0.28/0.49 => ( upairsubunion
% 0.28/0.49 => ( upairinpowunion
% 0.28/0.49 => ( ubforcartprodlem1
% 0.28/0.49 => ( ubforcartprodlem2
% 0.28/0.49 => ( ubforcartprodlem3
% 0.28/0.49 => ( cartprodpairin
% 0.28/0.49 => ! [A: $i,B: $i,Xu: $i] :
% 0.28/0.49 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.28/0.49 => ? [Xx: $i] :
% 0.28/0.49 ( ( in @ Xx @ A )
% 0.28/0.49 & ? [Xy: $i] :
% 0.28/0.49 ( ( in @ Xy @ B )
% 0.28/0.49 & ( Xu
% 0.28/0.49 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.49
% 0.28/0.49 %------------------------------------------------------------------------------
% 0.28/0.49 ------------------------
% 0.32/1.70 ---- Embedded in THF ---
% 0.32/1.70 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.32/1.70 %%% Generated on Tue Feb 24 12:30:05 EST 2026
% 0.32/1.70 %%% using '$$dhol' embedding, version 1.3.0.
% 0.32/1.70 %%% Logic specification used:
% 0.32/1.70 %%% thf(spec, logic, $$dhol).
% 0.32/1.70
% 0.32/1.70 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.X63vARrhRj/DTF2DTF30432.p
% See solution above
% 0.32/1.70 ------------------------
% 0.32/1.73 ---- Cleaned THF ---
% 0.32/1.73 thf(in_type,type,
% 0.32/1.73 in: $i > $i > $o ).
% 0.32/1.73
% 0.32/1.73 thf(exu_type,type,
% 0.32/1.73 exu: ( $i > $o ) > $o ).
% 0.32/1.73
% 0.32/1.73 thf(exu,definition,
% 0.32/1.73 ( exu
% 0.32/1.73 = ( ^ [Xphi: $i > $o] :
% 0.32/1.73 ? [Xx: $i] :
% 0.32/1.73 ( ( Xphi @ Xx )
% 0.32/1.73 & ! [Xy: $i] :
% 0.32/1.73 ( ( Xphi @ Xy )
% 0.32/1.73 => ( Xx = Xy ) ) ) ) ) ).
% 0.32/1.73
% 0.32/1.73 thf(setextAx_type,type,
% 0.32/1.73 setextAx: $o ).
% 0.32/1.73
% 0.32/1.73 thf(setextAx,definition,
% 0.32/1.73 ( setextAx
% 0.32/1.73 = ( ! [A: $i,B: $i] :
% 0.32/1.73 ( ! [Xx: $i] :
% 0.32/1.73 ( ( in @ Xx @ A )
% 0.32/1.73 <=> ( in @ Xx @ B ) )
% 0.32/1.73 => ( A = B ) ) ) ) ).
% 0.32/1.73
% 0.32/1.73 thf(emptyset_type,type,
% 0.32/1.73 emptyset: $i ).
% 0.32/1.73
% 0.32/1.73 thf(emptysetAx_type,type,
% 0.32/1.73 emptysetAx: $o ).
% 0.32/1.73
% 0.32/1.73 thf(emptysetAx,definition,
% 0.32/1.73 ( emptysetAx
% 0.32/1.73 = ( ! [Xx: $i] :
% 0.32/1.73 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.32/1.73
% 0.32/1.73 thf(setadjoin_type,type,
% 0.32/1.73 setadjoin: $i > $i > $i ).
% 0.32/1.73
% 0.32/1.73 thf(setadjoinAx_type,type,
% 0.32/1.73 setadjoinAx: $o ).
% 0.32/1.73
% 0.32/1.73 thf(setadjoinAx,definition,
% 0.32/1.73 ( setadjoinAx
% 0.32/1.73 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.32/1.73 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.32/1.73 <=> ( ( Xy = Xx )
% 0.32/1.73 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.32/1.73
% 0.32/1.73 thf(powerset_type,type,
% 0.32/1.73 powerset: $i > $i ).
% 0.32/1.73
% 0.32/1.73 thf(powersetAx_type,type,
% 0.32/1.73 powersetAx: $o ).
% 0.32/1.73
% 0.32/1.73 thf(powersetAx,definition,
% 0.32/1.73 ( powersetAx
% 0.32/1.73 = ( ! [A: $i,B: $i] :
% 0.32/1.73 ( ( in @ B @ ( powerset @ A ) )
% 0.32/1.73 <=> ! [Xx: $i] :
% 0.32/1.73 ( ( in @ Xx @ B )
% 0.32/1.73 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.32/1.73
% 0.32/1.73 thf(setunion_type,type,
% 0.32/1.73 setunion: $i > $i ).
% 0.32/1.73
% 0.32/1.73 thf(setunionAx_type,type,
% 0.32/1.73 setunionAx: $o ).
% 0.32/1.73
% 0.32/1.73 thf(setunionAx,definition,
% 0.32/1.73 ( setunionAx
% 0.32/1.73 = ( ! [A: $i,Xx: $i] :
% 0.32/1.73 ( ( in @ Xx @ ( setunion @ A ) )
% 0.32/1.73 <=> ? [B: $i] :
% 0.32/1.73 ( ( in @ Xx @ B )
% 0.32/1.73 & ( in @ B @ A ) ) ) ) ) ).
% 0.32/1.73
% 0.32/1.73 thf(omega_type,type,
% 0.32/1.73 omega: $i ).
% 0.32/1.73
% 0.32/1.73 thf(omega0Ax_type,type,
% 0.32/1.73 omega0Ax: $o ).
% 0.32/1.73
% 0.32/1.73 thf(omega0Ax,definition,
% 0.32/1.73 ( omega0Ax
% 0.32/1.73 = ( in @ emptyset @ omega ) ) ).
% 0.32/1.73
% 0.32/1.73 thf(omegaSAx_type,type,
% 0.32/1.73 omegaSAx: $o ).
% 0.32/1.73
% 0.32/1.73 thf(omegaSAx,definition,
% 0.32/1.73 ( omegaSAx
% 0.32/1.73 = ( ! [Xx: $i] :
% 0.32/1.73 ( ( in @ Xx @ omega )
% 0.32/1.73 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.32/1.73
% 0.32/1.73 thf(omegaIndAx_type,type,
% 0.32/1.73 omegaIndAx: $o ).
% 0.32/1.73
% 0.32/1.73 thf(omegaIndAx,definition,
% 0.32/1.73 ( omegaIndAx
% 0.32/1.73 = ( ! [A: $i] :
% 0.32/1.73 ( ( ( in @ emptyset @ A )
% 0.32/1.73 & ! [Xx: $i] :
% 0.32/1.73 ( ( ( in @ Xx @ omega )
% 0.32/1.73 & ( in @ Xx @ A ) )
% 0.32/1.73 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.32/1.73 => ! [Xx: $i] :
% 0.32/1.73 ( ( in @ Xx @ omega )
% 0.32/1.73 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.32/1.73
% 0.32/1.73 thf(replAx_type,type,
% 0.32/1.73 replAx: $o ).
% 0.32/1.73
% 0.32/1.73 thf(replAx,definition,
% 0.32/1.73 ( replAx
% 0.32/1.73 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.32/1.73 ( ! [Xx: $i] :
% 0.32/1.73 ( ( in @ Xx @ A )
% 0.32/1.73 => ( exu
% 0.32/1.73 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.32/1.73 => ? [B: $i] :
% 0.32/1.73 ! [Xx: $i] :
% 0.32/1.73 ( ( in @ Xx @ B )
% 0.32/1.73 <=> ? [Xy: $i] :
% 0.32/1.73 ( ( in @ Xy @ A )
% 0.32/1.73 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.32/1.73
% 0.32/1.73 thf(foundationAx_type,type,
% 0.32/1.73 foundationAx: $o ).
% 0.32/1.73
% 0.32/1.73 thf(foundationAx,definition,
% 0.32/1.73 ( foundationAx
% 0.32/1.73 = ( ! [A: $i] :
% 0.32/1.73 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.32/1.73 => ? [B: $i] :
% 0.32/1.73 ( ( in @ B @ A )
% 0.32/1.73 & ~ ? [Xx: $i] :
% 0.32/1.73 ( ( in @ Xx @ B )
% 0.32/1.73 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.32/1.73
% 0.32/1.73 thf(wellorderingAx_type,type,
% 0.32/1.73 wellorderingAx: $o ).
% 0.32/1.73
% 0.32/1.73 thf(wellorderingAx,definition,
% 0.32/1.73 ( wellorderingAx
% 0.32/1.73 = ( ! [A: $i] :
% 0.32/1.73 ? [B: $i] :
% 0.32/1.73 ( ! [C: $i] :
% 0.32/1.73 ( ( in @ C @ B )
% 0.32/1.73 => ! [Xx: $i] :
% 0.32/1.73 ( ( in @ Xx @ C )
% 0.32/1.73 => ( in @ Xx @ A ) ) )
% 0.32/1.73 & ! [Xx: $i,Xy: $i] :
% 0.32/1.73 ( ( ( in @ Xx @ A )
% 0.32/1.73 & ( in @ Xy @ A ) )
% 0.32/1.73 => ( ! [C: $i] :
% 0.32/1.73 ( ( in @ C @ B )
% 0.32/1.73 => ( ( in @ Xx @ C )
% 0.32/1.73 <=> ( in @ Xy @ C ) ) )
% 0.32/1.73 => ( Xx = Xy ) ) )
% 0.32/1.73 & ! [C: $i,D: $i] :
% 0.32/1.73 ( ( ( in @ C @ B )
% 0.32/1.73 & ( in @ D @ B ) )
% 0.32/1.73 => ( ! [Xx: $i] :
% 0.32/1.73 ( ( in @ Xx @ C )
% 0.32/1.73 => ( in @ Xx @ D ) )
% 0.32/1.73 | ! [Xx: $i] :
% 0.32/1.73 ( ( in @ Xx @ D )
% 0.32/1.73 => ( in @ Xx @ C ) ) ) )
% 0.32/1.73 & ! [C: $i] :
% 0.32/1.73 ( ( ! [Xx: $i] :
% 0.32/1.73 ( ( in @ Xx @ C )
% 0.32/1.73 => ( in @ Xx @ A ) )
% 0.32/1.73 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.32/1.73 => ? [D: $i,Xx: $i] :
% 0.32/1.73 ( ( in @ D @ B )
% 0.32/1.73 & ( in @ Xx @ C )
% 0.32/1.73 & ~ ? [Xy: $i] :
% 0.32/1.73 ( ( in @ Xy @ D )
% 0.32/1.73 & ( in @ Xy @ C ) )
% 0.32/1.73 & ! [E: $i] :
% 0.32/1.73 ( ( in @ E @ B )
% 0.32/1.73 => ( ! [Xy: $i] :
% 0.32/1.73 ( ( in @ Xy @ E )
% 0.32/1.73 => ( in @ Xy @ D ) )
% 0.32/1.73 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.32/1.73
% 0.32/1.73 thf(descr_type,type,
% 0.32/1.73 descr: ( $i > $o ) > $i ).
% 0.32/1.73
% 0.32/1.73 thf(descrp_type,type,
% 0.32/1.73 descrp: $o ).
% 0.32/1.73
% 0.32/1.73 thf(descrp,definition,
% 0.32/1.73 ( descrp
% 0.32/1.73 = ( ! [Xphi: $i > $o] :
% 0.32/1.73 ( ( exu
% 0.32/1.73 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/1.73 => ( Xphi
% 0.32/1.73 @ ( descr
% 0.32/1.73 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(dsetconstr_type,type,
% 0.32/1.74 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.32/1.74
% 0.32/1.74 thf(dsetconstrI_type,type,
% 0.32/1.74 dsetconstrI: $o ).
% 0.32/1.74
% 0.32/1.74 thf(dsetconstrI,definition,
% 0.32/1.74 ( dsetconstrI
% 0.32/1.74 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 => ( ( Xphi @ Xx )
% 0.32/1.74 => ( in @ Xx
% 0.32/1.74 @ ( dsetconstr @ A
% 0.32/1.74 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(dsetconstrEL_type,type,
% 0.32/1.74 dsetconstrEL: $o ).
% 0.32/1.74
% 0.32/1.74 thf(dsetconstrEL,definition,
% 0.32/1.74 ( dsetconstrEL
% 0.32/1.74 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.32/1.74 ( ( in @ Xx
% 0.32/1.74 @ ( dsetconstr @ A
% 0.32/1.74 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.32/1.74 => ( in @ Xx @ A ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(dsetconstrER_type,type,
% 0.32/1.74 dsetconstrER: $o ).
% 0.32/1.74
% 0.32/1.74 thf(dsetconstrER,definition,
% 0.32/1.74 ( dsetconstrER
% 0.32/1.74 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.32/1.74 ( ( in @ Xx
% 0.32/1.74 @ ( dsetconstr @ A
% 0.32/1.74 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.32/1.74 => ( Xphi @ Xx ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(exuE1_type,type,
% 0.32/1.74 exuE1: $o ).
% 0.32/1.74
% 0.32/1.74 thf(exuE1,definition,
% 0.32/1.74 ( exuE1
% 0.32/1.74 = ( ! [Xphi: $i > $o] :
% 0.32/1.74 ( ( exu
% 0.32/1.74 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/1.74 => ? [Xx: $i] :
% 0.32/1.74 ( ( Xphi @ Xx )
% 0.32/1.74 & ! [Xy: $i] :
% 0.32/1.74 ( ( Xphi @ Xy )
% 0.32/1.74 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(prop2set_type,type,
% 0.32/1.74 prop2set: $o > $i ).
% 0.32/1.74
% 0.32/1.74 thf(prop2setE_type,type,
% 0.32/1.74 prop2setE: $o ).
% 0.32/1.74
% 0.32/1.74 thf(prop2setE,definition,
% 0.32/1.74 ( prop2setE
% 0.32/1.74 = ( ! [Xphi: $o,Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.32/1.74 => Xphi ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(emptysetE_type,type,
% 0.32/1.74 emptysetE: $o ).
% 0.32/1.74
% 0.32/1.74 thf(emptysetE,definition,
% 0.32/1.74 ( emptysetE
% 0.32/1.74 = ( ! [Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ emptyset )
% 0.32/1.74 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(emptysetimpfalse_type,type,
% 0.32/1.74 emptysetimpfalse: $o ).
% 0.32/1.74
% 0.32/1.74 thf(emptysetimpfalse,definition,
% 0.32/1.74 ( emptysetimpfalse
% 0.32/1.74 = ( ! [Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ emptyset )
% 0.32/1.74 => $false ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(notinemptyset_type,type,
% 0.32/1.74 notinemptyset: $o ).
% 0.32/1.74
% 0.32/1.74 thf(notinemptyset,definition,
% 0.32/1.74 ( notinemptyset
% 0.32/1.74 = ( ! [Xx: $i] :
% 0.32/1.74 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(exuE3e_type,type,
% 0.32/1.74 exuE3e: $o ).
% 0.32/1.74
% 0.32/1.74 thf(exuE3e,definition,
% 0.32/1.74 ( exuE3e
% 0.32/1.74 = ( ! [Xphi: $i > $o] :
% 0.32/1.74 ( ( exu
% 0.32/1.74 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/1.74 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(setext_type,type,
% 0.32/1.74 setext: $o ).
% 0.32/1.74
% 0.32/1.74 thf(setext,definition,
% 0.32/1.74 ( setext
% 0.32/1.74 = ( ! [A: $i,B: $i] :
% 0.32/1.74 ( ! [Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 => ( in @ Xx @ B ) )
% 0.32/1.74 => ( ! [Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ B )
% 0.32/1.74 => ( in @ Xx @ A ) )
% 0.32/1.74 => ( A = B ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(emptyI_type,type,
% 0.32/1.74 emptyI: $o ).
% 0.32/1.74
% 0.32/1.74 thf(emptyI,definition,
% 0.32/1.74 ( emptyI
% 0.32/1.74 = ( ! [A: $i] :
% 0.32/1.74 ( ! [Xx: $i] :
% 0.32/1.74 ~ ( in @ Xx @ A )
% 0.32/1.74 => ( A = emptyset ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(noeltsimpempty_type,type,
% 0.32/1.74 noeltsimpempty: $o ).
% 0.32/1.74
% 0.32/1.74 thf(noeltsimpempty,definition,
% 0.32/1.74 ( noeltsimpempty
% 0.32/1.74 = ( ! [A: $i] :
% 0.32/1.74 ( ! [Xx: $i] :
% 0.32/1.74 ~ ( in @ Xx @ A )
% 0.32/1.74 => ( A = emptyset ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(setbeta_type,type,
% 0.32/1.74 setbeta: $o ).
% 0.32/1.74
% 0.32/1.74 thf(setbeta,definition,
% 0.32/1.74 ( setbeta
% 0.32/1.74 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 => ( ( in @ Xx
% 0.32/1.74 @ ( dsetconstr @ A
% 0.32/1.74 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.32/1.74 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(nonempty_type,type,
% 0.32/1.74 nonempty: $i > $o ).
% 0.32/1.74
% 0.32/1.74 thf(nonempty,definition,
% 0.32/1.74 ( nonempty
% 0.32/1.74 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(nonemptyE1_type,type,
% 0.32/1.74 nonemptyE1: $o ).
% 0.32/1.74
% 0.32/1.74 thf(nonemptyE1,definition,
% 0.32/1.74 ( nonemptyE1
% 0.32/1.74 = ( ! [A: $i] :
% 0.32/1.74 ( ( nonempty @ A )
% 0.32/1.74 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(nonemptyI_type,type,
% 0.32/1.74 nonemptyI: $o ).
% 0.32/1.74
% 0.32/1.74 thf(nonemptyI,definition,
% 0.32/1.74 ( nonemptyI
% 0.32/1.74 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 => ( ( Xphi @ Xx )
% 0.32/1.74 => ( nonempty
% 0.32/1.74 @ ( dsetconstr @ A
% 0.32/1.74 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(nonemptyI1_type,type,
% 0.32/1.74 nonemptyI1: $o ).
% 0.32/1.74
% 0.32/1.74 thf(nonemptyI1,definition,
% 0.32/1.74 ( nonemptyI1
% 0.32/1.74 = ( ! [A: $i] :
% 0.32/1.74 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.32/1.74 => ( nonempty @ A ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(setadjoinIL_type,type,
% 0.32/1.74 setadjoinIL: $o ).
% 0.32/1.74
% 0.32/1.74 thf(setadjoinIL,definition,
% 0.32/1.74 ( setadjoinIL
% 0.32/1.74 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(emptyinunitempty_type,type,
% 0.32/1.74 emptyinunitempty: $o ).
% 0.32/1.74
% 0.32/1.74 thf(emptyinunitempty,definition,
% 0.32/1.74 ( emptyinunitempty
% 0.32/1.74 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(setadjoinIR_type,type,
% 0.32/1.74 setadjoinIR: $o ).
% 0.32/1.74
% 0.32/1.74 thf(setadjoinIR,definition,
% 0.32/1.74 ( setadjoinIR
% 0.32/1.74 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.32/1.74 ( ( in @ Xy @ A )
% 0.32/1.74 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(setadjoinE_type,type,
% 0.32/1.74 setadjoinE: $o ).
% 0.32/1.74
% 0.32/1.74 thf(setadjoinE,definition,
% 0.32/1.74 ( setadjoinE
% 0.32/1.74 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.32/1.74 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.32/1.74 => ! [Xphi: $o] :
% 0.32/1.74 ( ( ( Xy = Xx )
% 0.32/1.74 => Xphi )
% 0.32/1.74 => ( ( ( in @ Xy @ A )
% 0.32/1.74 => Xphi )
% 0.32/1.74 => Xphi ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(setadjoinOr_type,type,
% 0.32/1.74 setadjoinOr: $o ).
% 0.32/1.74
% 0.32/1.74 thf(setadjoinOr,definition,
% 0.32/1.74 ( setadjoinOr
% 0.32/1.74 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.32/1.74 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.32/1.74 => ( ( Xy = Xx )
% 0.32/1.74 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(setoftrueEq_type,type,
% 0.32/1.74 setoftrueEq: $o ).
% 0.32/1.74
% 0.32/1.74 thf(setoftrueEq,definition,
% 0.32/1.74 ( setoftrueEq
% 0.32/1.74 = ( ! [A: $i] :
% 0.32/1.74 ( ( dsetconstr @ A
% 0.32/1.74 @ ^ [Xx: $i] : $true )
% 0.32/1.74 = A ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(powersetI_type,type,
% 0.32/1.74 powersetI: $o ).
% 0.32/1.74
% 0.32/1.74 thf(powersetI,definition,
% 0.32/1.74 ( powersetI
% 0.32/1.74 = ( ! [A: $i,B: $i] :
% 0.32/1.74 ( ! [Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ B )
% 0.32/1.74 => ( in @ Xx @ A ) )
% 0.32/1.74 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(emptyinPowerset_type,type,
% 0.32/1.74 emptyinPowerset: $o ).
% 0.32/1.74
% 0.32/1.74 thf(emptyinPowerset,definition,
% 0.32/1.74 ( emptyinPowerset
% 0.32/1.74 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(emptyInPowerset_type,type,
% 0.32/1.74 emptyInPowerset: $o ).
% 0.32/1.74
% 0.32/1.74 thf(emptyInPowerset,definition,
% 0.32/1.74 ( emptyInPowerset
% 0.32/1.74 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(powersetE_type,type,
% 0.32/1.74 powersetE: $o ).
% 0.32/1.74
% 0.32/1.74 thf(powersetE,definition,
% 0.32/1.74 ( powersetE
% 0.32/1.74 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/1.74 ( ( in @ B @ ( powerset @ A ) )
% 0.32/1.74 => ( ( in @ Xx @ B )
% 0.32/1.74 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(setunionI_type,type,
% 0.32/1.74 setunionI: $o ).
% 0.32/1.74
% 0.32/1.74 thf(setunionI,definition,
% 0.32/1.74 ( setunionI
% 0.32/1.74 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.32/1.74 ( ( in @ Xx @ B )
% 0.32/1.74 => ( ( in @ B @ A )
% 0.32/1.74 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(setunionE_type,type,
% 0.32/1.74 setunionE: $o ).
% 0.32/1.74
% 0.32/1.74 thf(setunionE,definition,
% 0.32/1.74 ( setunionE
% 0.32/1.74 = ( ! [A: $i,Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ ( setunion @ A ) )
% 0.32/1.74 => ! [Xphi: $o] :
% 0.32/1.74 ( ! [B: $i] :
% 0.32/1.74 ( ( in @ Xx @ B )
% 0.32/1.74 => ( ( in @ B @ A )
% 0.32/1.74 => Xphi ) )
% 0.32/1.74 => Xphi ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(subPowSU_type,type,
% 0.32/1.74 subPowSU: $o ).
% 0.32/1.74
% 0.32/1.74 thf(subPowSU,definition,
% 0.32/1.74 ( subPowSU
% 0.32/1.74 = ( ! [A: $i,Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(exuE2_type,type,
% 0.32/1.74 exuE2: $o ).
% 0.32/1.74
% 0.32/1.74 thf(exuE2,definition,
% 0.32/1.74 ( exuE2
% 0.32/1.74 = ( ! [Xphi: $i > $o] :
% 0.32/1.74 ( ( exu
% 0.32/1.74 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/1.74 => ? [Xx: $i] :
% 0.32/1.74 ! [Xy: $i] :
% 0.32/1.74 ( ( Xphi @ Xy )
% 0.32/1.74 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(nonemptyImpWitness_type,type,
% 0.32/1.74 nonemptyImpWitness: $o ).
% 0.32/1.74
% 0.32/1.74 thf(nonemptyImpWitness,definition,
% 0.32/1.74 ( nonemptyImpWitness
% 0.32/1.74 = ( ! [A: $i] :
% 0.32/1.74 ( ( nonempty @ A )
% 0.32/1.74 => ? [Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 & $true ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(uniqinunit_type,type,
% 0.32/1.74 uniqinunit: $o ).
% 0.32/1.74
% 0.32/1.74 thf(uniqinunit,definition,
% 0.32/1.74 ( uniqinunit
% 0.32/1.74 = ( ! [Xx: $i,Xy: $i] :
% 0.32/1.74 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.32/1.74 => ( Xx = Xy ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(notinsingleton_type,type,
% 0.32/1.74 notinsingleton: $o ).
% 0.32/1.74
% 0.32/1.74 thf(notinsingleton,definition,
% 0.32/1.74 ( notinsingleton
% 0.32/1.74 = ( ! [Xx: $i,Xy: $i] :
% 0.32/1.74 ( ( Xx != Xy )
% 0.32/1.74 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(eqinunit_type,type,
% 0.32/1.74 eqinunit: $o ).
% 0.32/1.74
% 0.32/1.74 thf(eqinunit,definition,
% 0.32/1.74 ( eqinunit
% 0.32/1.74 = ( ! [Xx: $i,Xy: $i] :
% 0.32/1.74 ( ( Xx = Xy )
% 0.32/1.74 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(singletonsswitch_type,type,
% 0.32/1.74 singletonsswitch: $o ).
% 0.32/1.74
% 0.32/1.74 thf(singletonsswitch,definition,
% 0.32/1.74 ( singletonsswitch
% 0.32/1.74 = ( ! [Xx: $i,Xy: $i] :
% 0.32/1.74 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.32/1.74 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(upairsetE_type,type,
% 0.32/1.74 upairsetE: $o ).
% 0.32/1.74
% 0.32/1.74 thf(upairsetE,definition,
% 0.32/1.74 ( upairsetE
% 0.32/1.74 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.32/1.74 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.32/1.74 => ( ( Xz = Xx )
% 0.32/1.74 | ( Xz = Xy ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(upairsetIL_type,type,
% 0.32/1.74 upairsetIL: $o ).
% 0.32/1.74
% 0.32/1.74 thf(upairsetIL,definition,
% 0.32/1.74 ( upairsetIL
% 0.32/1.74 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(upairsetIR_type,type,
% 0.32/1.74 upairsetIR: $o ).
% 0.32/1.74
% 0.32/1.74 thf(upairsetIR,definition,
% 0.32/1.74 ( upairsetIR
% 0.32/1.74 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(emptyE1_type,type,
% 0.32/1.74 emptyE1: $o ).
% 0.32/1.74
% 0.32/1.74 thf(emptyE1,definition,
% 0.32/1.74 ( emptyE1
% 0.32/1.74 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/1.74 ( ? [Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 & ( Xphi @ Xx ) )
% 0.32/1.74 => ( ( ( dsetconstr @ A
% 0.32/1.74 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/1.74 = emptyset )
% 0.32/1.74 => $false ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(vacuousDall_type,type,
% 0.32/1.74 vacuousDall: $o ).
% 0.32/1.74
% 0.32/1.74 thf(vacuousDall,definition,
% 0.32/1.74 ( vacuousDall
% 0.32/1.74 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ emptyset )
% 0.32/1.74 => ( Xphi @ Xx ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(quantDeMorgan1_type,type,
% 0.32/1.74 quantDeMorgan1: $o ).
% 0.32/1.74
% 0.32/1.74 thf(quantDeMorgan1,definition,
% 0.32/1.74 ( quantDeMorgan1
% 0.32/1.74 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/1.74 ( ~ ! [Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 => ( Xphi @ Xx ) )
% 0.32/1.74 => ? [Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(quantDeMorgan2_type,type,
% 0.32/1.74 quantDeMorgan2: $o ).
% 0.32/1.74
% 0.32/1.74 thf(quantDeMorgan2,definition,
% 0.32/1.74 ( quantDeMorgan2
% 0.32/1.74 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/1.74 ( ! [Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 => ~ ( Xphi @ Xx ) )
% 0.32/1.74 => ~ ? [Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(quantDeMorgan3_type,type,
% 0.32/1.74 quantDeMorgan3: $o ).
% 0.32/1.74
% 0.32/1.74 thf(quantDeMorgan3,definition,
% 0.32/1.74 ( quantDeMorgan3
% 0.32/1.74 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/1.74 ( ~ ? [Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 & ( Xphi @ Xx ) )
% 0.32/1.74 => ! [Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(quantDeMorgan4_type,type,
% 0.32/1.74 quantDeMorgan4: $o ).
% 0.32/1.74
% 0.32/1.74 thf(quantDeMorgan4,definition,
% 0.32/1.74 ( quantDeMorgan4
% 0.32/1.74 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/1.74 ( ? [Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 & ~ ( Xphi @ Xx ) )
% 0.32/1.74 => ~ ! [Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(prop2setI_type,type,
% 0.32/1.74 prop2setI: $o ).
% 0.32/1.74
% 0.32/1.74 thf(prop2setI,definition,
% 0.32/1.74 ( prop2setI
% 0.32/1.74 = ( ! [Xphi: $o] :
% 0.32/1.74 ( Xphi
% 0.32/1.74 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(set2prop_type,type,
% 0.32/1.74 set2prop: $i > $o ).
% 0.32/1.74
% 0.32/1.74 thf(prop2set2propI_type,type,
% 0.32/1.74 prop2set2propI: $o ).
% 0.32/1.74
% 0.32/1.74 thf(prop2set2propI,definition,
% 0.32/1.74 ( prop2set2propI
% 0.32/1.74 = ( ! [Xphi: $o] :
% 0.32/1.74 ( Xphi
% 0.32/1.74 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(notdexE_type,type,
% 0.32/1.74 notdexE: $o ).
% 0.32/1.74
% 0.32/1.74 thf(notdexE,definition,
% 0.32/1.74 ( notdexE
% 0.32/1.74 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/1.74 ( ~ ? [Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 & ( Xphi @ Xx ) )
% 0.32/1.74 => ! [Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(notdallE_type,type,
% 0.32/1.74 notdallE: $o ).
% 0.32/1.74
% 0.32/1.74 thf(notdallE,definition,
% 0.32/1.74 ( notdallE
% 0.32/1.74 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/1.74 ( ~ ! [Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 => ( Xphi @ Xx ) )
% 0.32/1.74 => ? [Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(exuI1_type,type,
% 0.32/1.74 exuI1: $o ).
% 0.32/1.74
% 0.32/1.74 thf(exuI1,definition,
% 0.32/1.74 ( exuI1
% 0.32/1.74 = ( ! [Xphi: $i > $o] :
% 0.32/1.74 ( ? [Xx: $i] :
% 0.32/1.74 ( ( Xphi @ Xx )
% 0.32/1.74 & ! [Xy: $i] :
% 0.32/1.74 ( ( Xphi @ Xy )
% 0.32/1.74 => ( Xx = Xy ) ) )
% 0.32/1.74 => ( exu
% 0.32/1.74 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(exuI3_type,type,
% 0.32/1.74 exuI3: $o ).
% 0.32/1.74
% 0.32/1.74 thf(exuI3,definition,
% 0.32/1.74 ( exuI3
% 0.32/1.74 = ( ! [Xphi: $i > $o] :
% 0.32/1.74 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.32/1.74 => ( ! [Xx: $i,Xy: $i] :
% 0.32/1.74 ( ( Xphi @ Xx )
% 0.32/1.74 => ( ( Xphi @ Xy )
% 0.32/1.74 => ( Xx = Xy ) ) )
% 0.32/1.74 => ( exu
% 0.32/1.74 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(exuI2_type,type,
% 0.32/1.74 exuI2: $o ).
% 0.32/1.74
% 0.32/1.74 thf(exuI2,definition,
% 0.32/1.74 ( exuI2
% 0.32/1.74 = ( ! [Xphi: $i > $o] :
% 0.32/1.74 ( ? [Xx: $i] :
% 0.32/1.74 ! [Xy: $i] :
% 0.32/1.74 ( ( Xphi @ Xy )
% 0.32/1.74 <=> ( Xy = Xx ) )
% 0.32/1.74 => ( exu
% 0.32/1.74 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(inCongP_type,type,
% 0.32/1.74 inCongP: $o ).
% 0.32/1.74
% 0.32/1.74 thf(inCongP,definition,
% 0.32/1.74 ( inCongP
% 0.32/1.74 = ( ! [A: $i,B: $i] :
% 0.32/1.74 ( ( A = B )
% 0.32/1.74 => ! [Xx: $i,Xy: $i] :
% 0.32/1.74 ( ( Xx = Xy )
% 0.32/1.74 => ( ( in @ Xx @ A )
% 0.32/1.74 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(in__Cong_type,type,
% 0.32/1.74 in__Cong: $o ).
% 0.32/1.74
% 0.32/1.74 thf(in__Cong,definition,
% 0.32/1.74 ( in__Cong
% 0.32/1.74 = ( ! [A: $i,B: $i] :
% 0.32/1.74 ( ( A = B )
% 0.32/1.74 => ! [Xx: $i,Xy: $i] :
% 0.32/1.74 ( ( Xx = Xy )
% 0.32/1.74 => ( ( in @ Xx @ A )
% 0.32/1.74 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(exuE3u_type,type,
% 0.32/1.74 exuE3u: $o ).
% 0.32/1.74
% 0.32/1.74 thf(exuE3u,definition,
% 0.32/1.74 ( exuE3u
% 0.32/1.74 = ( ! [Xphi: $i > $o] :
% 0.32/1.74 ( ( exu
% 0.32/1.74 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/1.74 => ! [Xx: $i,Xy: $i] :
% 0.32/1.74 ( ( Xphi @ Xx )
% 0.32/1.74 => ( ( Xphi @ Xy )
% 0.32/1.74 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(exu__Cong_type,type,
% 0.32/1.74 exu__Cong: $o ).
% 0.32/1.74
% 0.32/1.74 thf(exu__Cong,definition,
% 0.32/1.74 ( exu__Cong
% 0.32/1.74 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.32/1.74 ( ! [Xx: $i,Xy: $i] :
% 0.32/1.74 ( ( Xx = Xy )
% 0.32/1.74 => ( ( Xphi @ Xx )
% 0.32/1.74 <=> ( Xpsi @ Xy ) ) )
% 0.32/1.74 => ( ( exu
% 0.32/1.74 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/1.74 <=> ( exu
% 0.32/1.74 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(emptyset__Cong_type,type,
% 0.32/1.74 emptyset__Cong: $o ).
% 0.32/1.74
% 0.32/1.74 thf(emptyset__Cong,definition,
% 0.32/1.74 ( emptyset__Cong
% 0.32/1.74 = ( emptyset = emptyset ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(setadjoin__Cong_type,type,
% 0.32/1.74 setadjoin__Cong: $o ).
% 0.32/1.74
% 0.32/1.74 thf(setadjoin__Cong,definition,
% 0.32/1.74 ( setadjoin__Cong
% 0.32/1.74 = ( ! [Xx: $i,Xy: $i] :
% 0.32/1.74 ( ( Xx = Xy )
% 0.32/1.74 => ! [Xz: $i,Xu: $i] :
% 0.32/1.74 ( ( Xz = Xu )
% 0.32/1.74 => ( ( setadjoin @ Xx @ Xz )
% 0.32/1.74 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(powerset__Cong_type,type,
% 0.32/1.74 powerset__Cong: $o ).
% 0.32/1.74
% 0.32/1.74 thf(powerset__Cong,definition,
% 0.32/1.74 ( powerset__Cong
% 0.32/1.74 = ( ! [A: $i,B: $i] :
% 0.32/1.74 ( ( A = B )
% 0.32/1.74 => ( ( powerset @ A )
% 0.32/1.74 = ( powerset @ B ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(setunion__Cong_type,type,
% 0.32/1.74 setunion__Cong: $o ).
% 0.32/1.74
% 0.32/1.74 thf(setunion__Cong,definition,
% 0.32/1.74 ( setunion__Cong
% 0.32/1.74 = ( ! [A: $i,B: $i] :
% 0.32/1.74 ( ( A = B )
% 0.32/1.74 => ( ( setunion @ A )
% 0.32/1.74 = ( setunion @ B ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(omega__Cong_type,type,
% 0.32/1.74 omega__Cong: $o ).
% 0.32/1.74
% 0.32/1.74 thf(omega__Cong,definition,
% 0.32/1.74 ( omega__Cong
% 0.32/1.74 = ( omega = omega ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(exuEu_type,type,
% 0.32/1.74 exuEu: $o ).
% 0.32/1.74
% 0.32/1.74 thf(exuEu,definition,
% 0.32/1.74 ( exuEu
% 0.32/1.74 = ( ! [Xphi: $i > $o] :
% 0.32/1.74 ( ( exu
% 0.32/1.74 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/1.74 => ! [Xx: $i,Xy: $i] :
% 0.32/1.74 ( ( Xphi @ Xx )
% 0.32/1.74 => ( ( Xphi @ Xy )
% 0.32/1.74 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(descr__Cong_type,type,
% 0.32/1.74 descr__Cong: $o ).
% 0.32/1.74
% 0.32/1.74 thf(descr__Cong,definition,
% 0.32/1.74 ( descr__Cong
% 0.32/1.74 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.32/1.74 ( ! [Xx: $i,Xy: $i] :
% 0.32/1.74 ( ( Xx = Xy )
% 0.32/1.74 => ( ( Xphi @ Xx )
% 0.32/1.74 <=> ( Xpsi @ Xy ) ) )
% 0.32/1.74 => ( ( exu
% 0.32/1.74 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/1.74 => ( ( exu
% 0.32/1.74 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.32/1.74 => ( ( descr
% 0.32/1.74 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/1.74 = ( descr
% 0.32/1.74 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(dsetconstr__Cong_type,type,
% 0.32/1.74 dsetconstr__Cong: $o ).
% 0.32/1.74
% 0.32/1.74 thf(dsetconstr__Cong,definition,
% 0.32/1.74 ( dsetconstr__Cong
% 0.32/1.74 = ( ! [A: $i,B: $i] :
% 0.32/1.74 ( ( A = B )
% 0.32/1.74 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.32/1.74 ( ! [Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 => ! [Xy: $i] :
% 0.32/1.74 ( ( in @ Xy @ B )
% 0.32/1.74 => ( ( Xx = Xy )
% 0.32/1.74 => ( ( Xphi @ Xx )
% 0.32/1.74 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.32/1.74 => ( ( dsetconstr @ A
% 0.32/1.74 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/1.74 = ( dsetconstr @ B
% 0.32/1.74 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(subset_type,type,
% 0.32/1.74 subset: $i > $i > $o ).
% 0.32/1.74
% 0.32/1.74 thf(disjoint_type,type,
% 0.32/1.74 disjoint: $i > $i > $o ).
% 0.32/1.74
% 0.32/1.74 thf(setsmeet_type,type,
% 0.32/1.74 setsmeet: $i > $i > $o ).
% 0.32/1.74
% 0.32/1.74 thf(subsetI1_type,type,
% 0.32/1.74 subsetI1: $o ).
% 0.32/1.74
% 0.32/1.74 thf(subsetI1,definition,
% 0.32/1.74 ( subsetI1
% 0.32/1.74 = ( ! [A: $i,B: $i] :
% 0.32/1.74 ( ! [Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 => ( in @ Xx @ B ) )
% 0.32/1.74 => ( subset @ A @ B ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(eqimpsubset2_type,type,
% 0.32/1.74 eqimpsubset2: $o ).
% 0.32/1.74
% 0.32/1.74 thf(eqimpsubset2,definition,
% 0.32/1.74 ( eqimpsubset2
% 0.32/1.74 = ( ! [A: $i,B: $i] :
% 0.32/1.74 ( ( A = B )
% 0.32/1.74 => ( subset @ B @ A ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(eqimpsubset1_type,type,
% 0.32/1.74 eqimpsubset1: $o ).
% 0.32/1.74
% 0.32/1.74 thf(eqimpsubset1,definition,
% 0.32/1.74 ( eqimpsubset1
% 0.32/1.74 = ( ! [A: $i,B: $i] :
% 0.32/1.74 ( ( A = B )
% 0.32/1.74 => ( subset @ A @ B ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(subsetI2_type,type,
% 0.32/1.74 subsetI2: $o ).
% 0.32/1.74
% 0.32/1.74 thf(subsetI2,definition,
% 0.32/1.74 ( subsetI2
% 0.32/1.74 = ( ! [A: $i,B: $i] :
% 0.32/1.74 ( ! [Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 => ( in @ Xx @ B ) )
% 0.32/1.74 => ( subset @ A @ B ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(emptysetsubset_type,type,
% 0.32/1.74 emptysetsubset: $o ).
% 0.32/1.74
% 0.32/1.74 thf(emptysetsubset,definition,
% 0.32/1.74 ( emptysetsubset
% 0.32/1.74 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(subsetE_type,type,
% 0.32/1.74 subsetE: $o ).
% 0.32/1.74
% 0.32/1.74 thf(subsetE,definition,
% 0.32/1.74 ( subsetE
% 0.32/1.74 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/1.74 ( ( subset @ A @ B )
% 0.32/1.74 => ( ( in @ Xx @ A )
% 0.32/1.74 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(subsetE2_type,type,
% 0.32/1.74 subsetE2: $o ).
% 0.32/1.74
% 0.32/1.74 thf(subsetE2,definition,
% 0.32/1.74 ( subsetE2
% 0.32/1.74 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/1.74 ( ( subset @ A @ B )
% 0.32/1.74 => ( ~ ( in @ Xx @ B )
% 0.32/1.74 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(notsubsetI_type,type,
% 0.32/1.74 notsubsetI: $o ).
% 0.32/1.74
% 0.32/1.74 thf(notsubsetI,definition,
% 0.32/1.74 ( notsubsetI
% 0.32/1.74 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 => ( ~ ( in @ Xx @ B )
% 0.32/1.74 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(notequalI1_type,type,
% 0.32/1.74 notequalI1: $o ).
% 0.32/1.74
% 0.32/1.74 thf(notequalI1,definition,
% 0.32/1.74 ( notequalI1
% 0.32/1.74 = ( ! [A: $i,B: $i] :
% 0.32/1.74 ( ~ ( subset @ A @ B )
% 0.32/1.74 => ( A != B ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(notequalI2_type,type,
% 0.32/1.74 notequalI2: $o ).
% 0.32/1.74
% 0.32/1.74 thf(notequalI2,definition,
% 0.32/1.74 ( notequalI2
% 0.32/1.74 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 => ( ~ ( in @ Xx @ B )
% 0.32/1.74 => ( A != B ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(subsetRefl_type,type,
% 0.32/1.74 subsetRefl: $o ).
% 0.32/1.74
% 0.32/1.74 thf(subsetRefl,definition,
% 0.32/1.74 ( subsetRefl
% 0.32/1.74 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(subsetTrans_type,type,
% 0.32/1.74 subsetTrans: $o ).
% 0.32/1.74
% 0.32/1.74 thf(subsetTrans,definition,
% 0.32/1.74 ( subsetTrans
% 0.32/1.74 = ( ! [A: $i,B: $i,C: $i] :
% 0.32/1.74 ( ( subset @ A @ B )
% 0.32/1.74 => ( ( subset @ B @ C )
% 0.32/1.74 => ( subset @ A @ C ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(setadjoinSub_type,type,
% 0.32/1.74 setadjoinSub: $o ).
% 0.32/1.74
% 0.32/1.74 thf(setadjoinSub,definition,
% 0.32/1.74 ( setadjoinSub
% 0.32/1.74 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(setadjoinSub2_type,type,
% 0.32/1.74 setadjoinSub2: $o ).
% 0.32/1.74
% 0.32/1.74 thf(setadjoinSub2,definition,
% 0.32/1.74 ( setadjoinSub2
% 0.32/1.74 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.32/1.74 ( ( subset @ A @ B )
% 0.32/1.74 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(subset2powerset_type,type,
% 0.32/1.74 subset2powerset: $o ).
% 0.32/1.74
% 0.32/1.74 thf(subset2powerset,definition,
% 0.32/1.74 ( subset2powerset
% 0.32/1.74 = ( ! [A: $i,B: $i] :
% 0.32/1.74 ( ( subset @ A @ B )
% 0.32/1.74 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(setextsub_type,type,
% 0.32/1.74 setextsub: $o ).
% 0.32/1.74
% 0.32/1.74 thf(setextsub,definition,
% 0.32/1.74 ( setextsub
% 0.32/1.74 = ( ! [A: $i,B: $i] :
% 0.32/1.74 ( ( subset @ A @ B )
% 0.32/1.74 => ( ( subset @ B @ A )
% 0.32/1.74 => ( A = B ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(subsetemptysetimpeq_type,type,
% 0.32/1.74 subsetemptysetimpeq: $o ).
% 0.32/1.74
% 0.32/1.74 thf(subsetemptysetimpeq,definition,
% 0.32/1.74 ( subsetemptysetimpeq
% 0.32/1.74 = ( ! [A: $i] :
% 0.32/1.74 ( ( subset @ A @ emptyset )
% 0.32/1.74 => ( A = emptyset ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(powersetI1_type,type,
% 0.32/1.74 powersetI1: $o ).
% 0.32/1.74
% 0.32/1.74 thf(powersetI1,definition,
% 0.32/1.74 ( powersetI1
% 0.32/1.74 = ( ! [A: $i,B: $i] :
% 0.32/1.74 ( ( subset @ B @ A )
% 0.32/1.74 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(powersetE1_type,type,
% 0.32/1.74 powersetE1: $o ).
% 0.32/1.74
% 0.32/1.74 thf(powersetE1,definition,
% 0.32/1.74 ( powersetE1
% 0.32/1.74 = ( ! [A: $i,B: $i] :
% 0.32/1.74 ( ( in @ B @ ( powerset @ A ) )
% 0.32/1.74 => ( subset @ B @ A ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(inPowerset_type,type,
% 0.32/1.74 inPowerset: $o ).
% 0.32/1.74
% 0.32/1.74 thf(inPowerset,definition,
% 0.32/1.74 ( inPowerset
% 0.32/1.74 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(powersetsubset_type,type,
% 0.32/1.74 powersetsubset: $o ).
% 0.32/1.74
% 0.32/1.74 thf(powersetsubset,definition,
% 0.32/1.74 ( powersetsubset
% 0.32/1.74 = ( ! [A: $i,B: $i] :
% 0.32/1.74 ( ( subset @ A @ B )
% 0.32/1.74 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(sepInPowerset_type,type,
% 0.32/1.74 sepInPowerset: $o ).
% 0.32/1.74
% 0.32/1.74 thf(sepInPowerset,definition,
% 0.32/1.74 ( sepInPowerset
% 0.32/1.74 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/1.74 ( in
% 0.32/1.74 @ ( dsetconstr @ A
% 0.32/1.74 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/1.74 @ ( powerset @ A ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(sepSubset_type,type,
% 0.32/1.74 sepSubset: $o ).
% 0.32/1.74
% 0.32/1.74 thf(sepSubset,definition,
% 0.32/1.74 ( sepSubset
% 0.32/1.74 = ( ! [A: $i,Xphi: $i > $o] :
% 0.32/1.74 ( subset
% 0.32/1.74 @ ( dsetconstr @ A
% 0.32/1.74 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.32/1.74 @ A ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(binunion_type,type,
% 0.32/1.74 binunion: $i > $i > $i ).
% 0.32/1.74
% 0.32/1.74 thf(binunionIL_type,type,
% 0.32/1.74 binunionIL: $o ).
% 0.32/1.74
% 0.32/1.74 thf(binunionIL,definition,
% 0.32/1.74 ( binunionIL
% 0.32/1.74 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(upairset2IR_type,type,
% 0.32/1.74 upairset2IR: $o ).
% 0.32/1.74
% 0.32/1.74 thf(upairset2IR,definition,
% 0.32/1.74 ( upairset2IR
% 0.32/1.74 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(binunionIR_type,type,
% 0.32/1.74 binunionIR: $o ).
% 0.32/1.74
% 0.32/1.74 thf(binunionIR,definition,
% 0.32/1.74 ( binunionIR
% 0.32/1.74 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ B )
% 0.32/1.74 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(binunionEcases_type,type,
% 0.32/1.74 binunionEcases: $o ).
% 0.32/1.74
% 0.32/1.74 thf(binunionEcases,definition,
% 0.32/1.74 ( binunionEcases
% 0.32/1.74 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.32/1.74 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.32/1.74 => ( ( ( in @ Xx @ A )
% 0.32/1.74 => Xphi )
% 0.32/1.74 => ( ( ( in @ Xx @ B )
% 0.32/1.74 => Xphi )
% 0.32/1.74 => Xphi ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(binunionE_type,type,
% 0.32/1.74 binunionE: $o ).
% 0.32/1.74
% 0.32/1.74 thf(binunionE,definition,
% 0.32/1.74 ( binunionE
% 0.32/1.74 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.32/1.74 => ( ( in @ Xx @ A )
% 0.32/1.74 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(binunionLsub_type,type,
% 0.32/1.74 binunionLsub: $o ).
% 0.32/1.74
% 0.32/1.74 thf(binunionLsub,definition,
% 0.32/1.74 ( binunionLsub
% 0.32/1.74 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(binunionRsub_type,type,
% 0.32/1.74 binunionRsub: $o ).
% 0.32/1.74
% 0.32/1.74 thf(binunionRsub,definition,
% 0.32/1.74 ( binunionRsub
% 0.32/1.74 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(binintersect_type,type,
% 0.32/1.74 binintersect: $i > $i > $i ).
% 0.32/1.74
% 0.32/1.74 thf(binintersectI_type,type,
% 0.32/1.74 binintersectI: $o ).
% 0.32/1.74
% 0.32/1.74 thf(binintersectI,definition,
% 0.32/1.74 ( binintersectI
% 0.32/1.74 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 => ( ( in @ Xx @ B )
% 0.32/1.74 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(binintersectSubset5_type,type,
% 0.32/1.74 binintersectSubset5: $o ).
% 0.32/1.74
% 0.32/1.74 thf(binintersectSubset5,definition,
% 0.32/1.74 ( binintersectSubset5
% 0.32/1.74 = ( ! [A: $i,B: $i,C: $i] :
% 0.32/1.74 ( ( subset @ C @ A )
% 0.32/1.74 => ( ( subset @ C @ B )
% 0.32/1.74 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(binintersectEL_type,type,
% 0.32/1.74 binintersectEL: $o ).
% 0.32/1.74
% 0.32/1.74 thf(binintersectEL,definition,
% 0.32/1.74 ( binintersectEL
% 0.32/1.74 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.32/1.74 => ( in @ Xx @ A ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(binintersectLsub_type,type,
% 0.32/1.74 binintersectLsub: $o ).
% 0.32/1.74
% 0.32/1.74 thf(binintersectLsub,definition,
% 0.32/1.74 ( binintersectLsub
% 0.32/1.74 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(binintersectSubset2_type,type,
% 0.32/1.74 binintersectSubset2: $o ).
% 0.32/1.74
% 0.32/1.74 thf(binintersectSubset2,definition,
% 0.32/1.74 ( binintersectSubset2
% 0.32/1.74 = ( ! [A: $i,B: $i] :
% 0.32/1.74 ( ( subset @ A @ B )
% 0.32/1.74 => ( ( binintersect @ A @ B )
% 0.32/1.74 = A ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(binintersectSubset3_type,type,
% 0.32/1.74 binintersectSubset3: $o ).
% 0.32/1.74
% 0.32/1.74 thf(binintersectSubset3,definition,
% 0.32/1.74 ( binintersectSubset3
% 0.32/1.74 = ( ! [A: $i,B: $i] :
% 0.32/1.74 ( ( ( binintersect @ A @ B )
% 0.32/1.74 = B )
% 0.32/1.74 => ( subset @ B @ A ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(binintersectER_type,type,
% 0.32/1.74 binintersectER: $o ).
% 0.32/1.74
% 0.32/1.74 thf(binintersectER,definition,
% 0.32/1.74 ( binintersectER
% 0.32/1.74 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.32/1.74 => ( in @ Xx @ B ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(disjointsetsI1_type,type,
% 0.32/1.74 disjointsetsI1: $o ).
% 0.32/1.74
% 0.32/1.74 thf(disjointsetsI1,definition,
% 0.32/1.74 ( disjointsetsI1
% 0.32/1.74 = ( ! [A: $i,B: $i] :
% 0.32/1.74 ( ~ ? [Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 & ( in @ Xx @ B ) )
% 0.32/1.74 => ( ( binintersect @ A @ B )
% 0.32/1.74 = emptyset ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(binintersectRsub_type,type,
% 0.32/1.74 binintersectRsub: $o ).
% 0.32/1.74
% 0.32/1.74 thf(binintersectRsub,definition,
% 0.32/1.74 ( binintersectRsub
% 0.32/1.74 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(binintersectSubset4_type,type,
% 0.32/1.74 binintersectSubset4: $o ).
% 0.32/1.74
% 0.32/1.74 thf(binintersectSubset4,definition,
% 0.32/1.74 ( binintersectSubset4
% 0.32/1.74 = ( ! [A: $i,B: $i] :
% 0.32/1.74 ( ( subset @ B @ A )
% 0.32/1.74 => ( ( binintersect @ A @ B )
% 0.32/1.74 = B ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(binintersectSubset1_type,type,
% 0.32/1.74 binintersectSubset1: $o ).
% 0.32/1.74
% 0.32/1.74 thf(binintersectSubset1,definition,
% 0.32/1.74 ( binintersectSubset1
% 0.32/1.74 = ( ! [A: $i,B: $i] :
% 0.32/1.74 ( ( ( binintersect @ A @ B )
% 0.32/1.74 = A )
% 0.32/1.74 => ( subset @ A @ B ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(bs114d_type,type,
% 0.32/1.74 bs114d: $o ).
% 0.32/1.74
% 0.32/1.74 thf(bs114d,definition,
% 0.32/1.74 ( bs114d
% 0.32/1.74 = ( ! [A: $i,B: $i,C: $i] :
% 0.32/1.74 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.32/1.74 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(regular_type,type,
% 0.32/1.74 regular: $i > $o ).
% 0.32/1.74
% 0.32/1.74 thf(setminus_type,type,
% 0.32/1.74 setminus: $i > $i > $i ).
% 0.32/1.74
% 0.32/1.74 thf(setminusI_type,type,
% 0.32/1.74 setminusI: $o ).
% 0.32/1.74
% 0.32/1.74 thf(setminusI,definition,
% 0.32/1.74 ( setminusI
% 0.32/1.74 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 => ( ~ ( in @ Xx @ B )
% 0.32/1.74 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(setminusEL_type,type,
% 0.32/1.74 setminusEL: $o ).
% 0.32/1.74
% 0.32/1.74 thf(setminusEL,definition,
% 0.32/1.74 ( setminusEL
% 0.32/1.74 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.32/1.74 => ( in @ Xx @ A ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(setminusER_type,type,
% 0.32/1.74 setminusER: $o ).
% 0.32/1.74
% 0.32/1.74 thf(setminusER,definition,
% 0.32/1.74 ( setminusER
% 0.32/1.74 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.32/1.74 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(setminusSubset2_type,type,
% 0.32/1.74 setminusSubset2: $o ).
% 0.32/1.74
% 0.32/1.74 thf(setminusSubset2,definition,
% 0.32/1.74 ( setminusSubset2
% 0.32/1.74 = ( ! [A: $i,B: $i] :
% 0.32/1.74 ( ( subset @ A @ B )
% 0.32/1.74 => ( ( setminus @ A @ B )
% 0.32/1.74 = emptyset ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(setminusERneg_type,type,
% 0.32/1.74 setminusERneg: $o ).
% 0.32/1.74
% 0.32/1.74 thf(setminusERneg,definition,
% 0.32/1.74 ( setminusERneg
% 0.32/1.74 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/1.74 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.32/1.74 => ( ( in @ Xx @ A )
% 0.32/1.74 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(setminusELneg_type,type,
% 0.32/1.74 setminusELneg: $o ).
% 0.32/1.74
% 0.32/1.74 thf(setminusELneg,definition,
% 0.32/1.74 ( setminusELneg
% 0.32/1.74 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/1.74 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.32/1.74 => ( ~ ( in @ Xx @ B )
% 0.32/1.74 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(setminusILneg_type,type,
% 0.32/1.74 setminusILneg: $o ).
% 0.32/1.74
% 0.32/1.74 thf(setminusILneg,definition,
% 0.32/1.74 ( setminusILneg
% 0.32/1.74 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/1.74 ( ~ ( in @ Xx @ A )
% 0.32/1.74 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(setminusIRneg_type,type,
% 0.32/1.74 setminusIRneg: $o ).
% 0.32/1.74
% 0.32/1.74 thf(setminusIRneg,definition,
% 0.32/1.74 ( setminusIRneg
% 0.32/1.74 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ B )
% 0.32/1.74 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(setminusLsub_type,type,
% 0.32/1.74 setminusLsub: $o ).
% 0.32/1.74
% 0.32/1.74 thf(setminusLsub,definition,
% 0.32/1.74 ( setminusLsub
% 0.32/1.74 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(setminusSubset1_type,type,
% 0.32/1.74 setminusSubset1: $o ).
% 0.32/1.74
% 0.32/1.74 thf(setminusSubset1,definition,
% 0.32/1.74 ( setminusSubset1
% 0.32/1.74 = ( ! [A: $i,B: $i] :
% 0.32/1.74 ( ( ( setminus @ A @ B )
% 0.32/1.74 = emptyset )
% 0.32/1.74 => ( subset @ A @ B ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(symdiff_type,type,
% 0.32/1.74 symdiff: $i > $i > $i ).
% 0.32/1.74
% 0.32/1.74 thf(symdiffE_type,type,
% 0.32/1.74 symdiffE: $o ).
% 0.32/1.74
% 0.32/1.74 thf(symdiffE,definition,
% 0.32/1.74 ( symdiffE
% 0.32/1.74 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.32/1.74 => ! [Xphi: $o] :
% 0.32/1.74 ( ( ( in @ Xx @ A )
% 0.32/1.74 => ( ~ ( in @ Xx @ B )
% 0.32/1.74 => Xphi ) )
% 0.32/1.74 => ( ( ~ ( in @ Xx @ A )
% 0.32/1.74 => ( ( in @ Xx @ B )
% 0.32/1.74 => Xphi ) )
% 0.32/1.74 => Xphi ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(symdiffI1_type,type,
% 0.32/1.74 symdiffI1: $o ).
% 0.32/1.74
% 0.32/1.74 thf(symdiffI1,definition,
% 0.32/1.74 ( symdiffI1
% 0.32/1.74 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 => ( ~ ( in @ Xx @ B )
% 0.32/1.74 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(symdiffI2_type,type,
% 0.32/1.74 symdiffI2: $o ).
% 0.32/1.74
% 0.32/1.74 thf(symdiffI2,definition,
% 0.32/1.74 ( symdiffI2
% 0.32/1.74 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/1.74 ( ~ ( in @ Xx @ A )
% 0.32/1.74 => ( ( in @ Xx @ B )
% 0.32/1.74 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(symdiffIneg1_type,type,
% 0.32/1.74 symdiffIneg1: $o ).
% 0.32/1.74
% 0.32/1.74 thf(symdiffIneg1,definition,
% 0.32/1.74 ( symdiffIneg1
% 0.32/1.74 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 => ( ( in @ Xx @ B )
% 0.32/1.74 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(symdiffIneg2_type,type,
% 0.32/1.74 symdiffIneg2: $o ).
% 0.32/1.74
% 0.32/1.74 thf(symdiffIneg2,definition,
% 0.32/1.74 ( symdiffIneg2
% 0.32/1.74 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/1.74 ( ~ ( in @ Xx @ A )
% 0.32/1.74 => ( ~ ( in @ Xx @ B )
% 0.32/1.74 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(iskpair_type,type,
% 0.32/1.74 iskpair: $i > $o ).
% 0.32/1.74
% 0.32/1.74 thf(iskpair,definition,
% 0.32/1.74 ( iskpair
% 0.32/1.74 = ( ^ [A: $i] :
% 0.32/1.74 ? [Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ ( setunion @ A ) )
% 0.32/1.74 & ? [Xy: $i] :
% 0.32/1.74 ( ( in @ Xy @ ( setunion @ A ) )
% 0.32/1.74 & ( A
% 0.32/1.74 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(secondinupair_type,type,
% 0.32/1.74 secondinupair: $o ).
% 0.32/1.74
% 0.32/1.74 thf(secondinupair,definition,
% 0.32/1.74 ( secondinupair
% 0.32/1.74 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(setukpairIL_type,type,
% 0.32/1.74 setukpairIL: $o ).
% 0.32/1.74
% 0.32/1.74 thf(setukpairIL,definition,
% 0.32/1.74 ( setukpairIL
% 0.32/1.74 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(setukpairIR_type,type,
% 0.32/1.74 setukpairIR: $o ).
% 0.32/1.74
% 0.32/1.74 thf(setukpairIR,definition,
% 0.32/1.74 ( setukpairIR
% 0.32/1.74 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(kpairiskpair_type,type,
% 0.32/1.74 kpairiskpair: $o ).
% 0.32/1.74
% 0.32/1.74 thf(kpairiskpair,definition,
% 0.32/1.74 ( kpairiskpair
% 0.32/1.74 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(kpair_type,type,
% 0.32/1.74 kpair: $i > $i > $i ).
% 0.32/1.74
% 0.32/1.74 thf(kpair,definition,
% 0.32/1.74 ( kpair
% 0.32/1.74 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(kpairp_type,type,
% 0.32/1.74 kpairp: $o ).
% 0.32/1.74
% 0.32/1.74 thf(kpairp,definition,
% 0.32/1.74 ( kpairp
% 0.32/1.74 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(cartprod_type,type,
% 0.32/1.74 cartprod: $i > $i > $i ).
% 0.32/1.74
% 0.32/1.74 thf(cartprod,definition,
% 0.32/1.74 ( cartprod
% 0.32/1.74 = ( ^ [A: $i,B: $i] :
% 0.32/1.74 ( dsetconstr @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) )
% 0.32/1.74 @ ^ [Xx: $i] :
% 0.32/1.74 ? [Xy: $i] :
% 0.32/1.74 ( ( in @ Xy @ A )
% 0.32/1.74 & ? [Xz: $i] :
% 0.32/1.74 ( ( in @ Xz @ B )
% 0.32/1.74 & ( Xx
% 0.32/1.74 = ( kpair @ Xy @ Xz ) ) ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(singletonsubset_type,type,
% 0.32/1.74 singletonsubset: $o ).
% 0.32/1.74
% 0.32/1.74 thf(singletonsubset,definition,
% 0.32/1.74 ( singletonsubset
% 0.32/1.74 = ( ! [A: $i,Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(singletoninpowerset_type,type,
% 0.32/1.74 singletoninpowerset: $o ).
% 0.32/1.74
% 0.32/1.74 thf(singletoninpowerset,definition,
% 0.32/1.74 ( singletoninpowerset
% 0.32/1.74 = ( ! [A: $i,Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(singletoninpowunion_type,type,
% 0.32/1.74 singletoninpowunion: $o ).
% 0.32/1.74
% 0.32/1.74 thf(singletoninpowunion,definition,
% 0.32/1.74 ( singletoninpowunion
% 0.32/1.74 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(upairset2E_type,type,
% 0.32/1.74 upairset2E: $o ).
% 0.32/1.74
% 0.32/1.74 thf(upairset2E,definition,
% 0.32/1.74 ( upairset2E
% 0.32/1.74 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.32/1.74 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.32/1.74 => ( ( Xz = Xx )
% 0.32/1.74 | ( Xz = Xy ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(upairsubunion_type,type,
% 0.32/1.74 upairsubunion: $o ).
% 0.32/1.74
% 0.32/1.74 thf(upairsubunion,definition,
% 0.32/1.74 ( upairsubunion
% 0.32/1.74 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 => ! [Xy: $i] :
% 0.32/1.74 ( ( in @ Xy @ B )
% 0.32/1.74 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(upairinpowunion_type,type,
% 0.32/1.74 upairinpowunion: $o ).
% 0.32/1.74
% 0.32/1.74 thf(upairinpowunion,definition,
% 0.32/1.74 ( upairinpowunion
% 0.32/1.74 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 => ! [Xy: $i] :
% 0.32/1.74 ( ( in @ Xy @ B )
% 0.32/1.74 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(ubforcartprodlem1_type,type,
% 0.32/1.74 ubforcartprodlem1: $o ).
% 0.32/1.74
% 0.32/1.74 thf(ubforcartprodlem1,definition,
% 0.32/1.74 ( ubforcartprodlem1
% 0.32/1.74 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 => ! [Xy: $i] :
% 0.32/1.74 ( ( in @ Xy @ B )
% 0.32/1.74 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(ubforcartprodlem2_type,type,
% 0.32/1.74 ubforcartprodlem2: $o ).
% 0.32/1.74
% 0.32/1.74 thf(ubforcartprodlem2,definition,
% 0.32/1.74 ( ubforcartprodlem2
% 0.32/1.74 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 => ! [Xy: $i] :
% 0.32/1.74 ( ( in @ Xy @ B )
% 0.32/1.74 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(ubforcartprodlem3_type,type,
% 0.32/1.74 ubforcartprodlem3: $o ).
% 0.32/1.74
% 0.32/1.74 thf(ubforcartprodlem3,definition,
% 0.32/1.74 ( ubforcartprodlem3
% 0.32/1.74 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 => ! [Xy: $i] :
% 0.32/1.74 ( ( in @ Xy @ B )
% 0.32/1.74 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(cartprodpairin_type,type,
% 0.32/1.74 cartprodpairin: $o ).
% 0.32/1.74
% 0.32/1.74 thf(cartprodpairin,definition,
% 0.32/1.74 ( cartprodpairin
% 0.32/1.74 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 => ! [Xy: $i] :
% 0.32/1.74 ( ( in @ Xy @ B )
% 0.32/1.74 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.32/1.74
% 0.32/1.74 thf(cartprodmempair1,conjecture,
% 0.32/1.74 ( setextAx
% 0.32/1.74 => ( emptysetAx
% 0.32/1.74 => ( setadjoinAx
% 0.32/1.74 => ( powersetAx
% 0.32/1.74 => ( setunionAx
% 0.32/1.74 => ( omega0Ax
% 0.32/1.74 => ( omegaSAx
% 0.32/1.74 => ( omegaIndAx
% 0.32/1.74 => ( replAx
% 0.32/1.74 => ( foundationAx
% 0.32/1.74 => ( wellorderingAx
% 0.32/1.74 => ( descrp
% 0.32/1.74 => ( dsetconstrI
% 0.32/1.74 => ( dsetconstrEL
% 0.32/1.74 => ( dsetconstrER
% 0.32/1.74 => ( exuE1
% 0.32/1.74 => ( prop2setE
% 0.32/1.74 => ( emptysetE
% 0.32/1.74 => ( emptysetimpfalse
% 0.32/1.74 => ( notinemptyset
% 0.32/1.74 => ( exuE3e
% 0.32/1.74 => ( setext
% 0.32/1.74 => ( emptyI
% 0.32/1.74 => ( noeltsimpempty
% 0.32/1.74 => ( setbeta
% 0.32/1.74 => ( nonemptyE1
% 0.32/1.74 => ( nonemptyI
% 0.32/1.74 => ( nonemptyI1
% 0.32/1.74 => ( setadjoinIL
% 0.32/1.74 => ( emptyinunitempty
% 0.32/1.74 => ( setadjoinIR
% 0.32/1.74 => ( setadjoinE
% 0.32/1.74 => ( setadjoinOr
% 0.32/1.74 => ( setoftrueEq
% 0.32/1.74 => ( powersetI
% 0.32/1.74 => ( emptyinPowerset
% 0.32/1.74 => ( emptyInPowerset
% 0.32/1.74 => ( powersetE
% 0.32/1.74 => ( setunionI
% 0.32/1.74 => ( setunionE
% 0.32/1.74 => ( subPowSU
% 0.32/1.74 => ( exuE2
% 0.32/1.74 => ( nonemptyImpWitness
% 0.32/1.74 => ( uniqinunit
% 0.32/1.74 => ( notinsingleton
% 0.32/1.74 => ( eqinunit
% 0.32/1.74 => ( singletonsswitch
% 0.32/1.74 => ( upairsetE
% 0.32/1.74 => ( upairsetIL
% 0.32/1.74 => ( upairsetIR
% 0.32/1.74 => ( emptyE1
% 0.32/1.74 => ( vacuousDall
% 0.32/1.74 => ( quantDeMorgan1
% 0.32/1.74 => ( quantDeMorgan2
% 0.32/1.74 => ( quantDeMorgan3
% 0.32/1.74 => ( quantDeMorgan4
% 0.32/1.74 => ( prop2setI
% 0.32/1.74 => ( prop2set2propI
% 0.32/1.74 => ( notdexE
% 0.32/1.74 => ( notdallE
% 0.32/1.74 => ( exuI1
% 0.32/1.74 => ( exuI3
% 0.32/1.74 => ( exuI2
% 0.32/1.74 => ( inCongP
% 0.32/1.74 => ( in__Cong
% 0.32/1.74 => ( exuE3u
% 0.32/1.74 => ( exu__Cong
% 0.32/1.74 => ( emptyset__Cong
% 0.32/1.74 => ( setadjoin__Cong
% 0.32/1.74 => ( powerset__Cong
% 0.32/1.74 => ( setunion__Cong
% 0.32/1.74 => ( omega__Cong
% 0.32/1.74 => ( exuEu
% 0.32/1.74 => ( descr__Cong
% 0.32/1.74 => ( dsetconstr__Cong
% 0.32/1.74 => ( subsetI1
% 0.32/1.74 => ( eqimpsubset2
% 0.32/1.74 => ( eqimpsubset1
% 0.32/1.74 => ( subsetI2
% 0.32/1.74 => ( emptysetsubset
% 0.32/1.74 => ( subsetE
% 0.32/1.74 => ( subsetE2
% 0.32/1.74 => ( notsubsetI
% 0.32/1.74 => ( notequalI1
% 0.32/1.74 => ( notequalI2
% 0.32/1.74 => ( subsetRefl
% 0.32/1.74 => ( subsetTrans
% 0.32/1.74 => ( setadjoinSub
% 0.32/1.74 => ( setadjoinSub2
% 0.32/1.74 => ( subset2powerset
% 0.32/1.74 => ( setextsub
% 0.32/1.74 => ( subsetemptysetimpeq
% 0.32/1.74 => ( powersetI1
% 0.32/1.74 => ( powersetE1
% 0.32/1.74 => ( inPowerset
% 0.32/1.74 => ( powersetsubset
% 0.32/1.74 => ( sepInPowerset
% 0.32/1.74 => ( sepSubset
% 0.32/1.74 => ( binunionIL
% 0.32/1.74 => ( upairset2IR
% 0.32/1.74 => ( binunionIR
% 0.32/1.74 => ( binunionEcases
% 0.32/1.74 => ( binunionE
% 0.32/1.74 => ( binunionLsub
% 0.32/1.74 => ( binunionRsub
% 0.32/1.74 => ( binintersectI
% 0.32/1.74 => ( binintersectSubset5
% 0.32/1.74 => ( binintersectEL
% 0.32/1.74 => ( binintersectLsub
% 0.32/1.74 => ( binintersectSubset2
% 0.32/1.74 => ( binintersectSubset3
% 0.32/1.74 => ( binintersectER
% 0.32/1.74 => ( disjointsetsI1
% 0.32/1.74 => ( binintersectRsub
% 0.32/1.74 => ( binintersectSubset4
% 0.32/1.74 => ( binintersectSubset1
% 0.32/1.74 => ( bs114d
% 0.32/1.74 => ( setminusI
% 0.32/1.74 => ( setminusEL
% 0.32/1.74 => ( setminusER
% 0.32/1.74 => ( setminusSubset2
% 0.32/1.74 => ( setminusERneg
% 0.32/1.74 => ( setminusELneg
% 0.32/1.74 => ( setminusILneg
% 0.32/1.74 => ( setminusIRneg
% 0.32/1.74 => ( setminusLsub
% 0.32/1.74 => ( setminusSubset1
% 0.32/1.74 => ( symdiffE
% 0.32/1.74 => ( symdiffI1
% 0.32/1.74 => ( symdiffI2
% 0.32/1.74 => ( symdiffIneg1
% 0.32/1.74 => ( symdiffIneg2
% 0.32/1.74 => ( secondinupair
% 0.32/1.74 => ( setukpairIL
% 0.32/1.74 => ( setukpairIR
% 0.32/1.74 => ( kpairiskpair
% 0.32/1.74 => ( kpairp
% 0.32/1.74 => ( singletonsubset
% 0.32/1.74 => ( singletoninpowerset
% 0.32/1.74 => ( singletoninpowunion
% 0.32/1.74 => ( upairset2E
% 0.32/1.74 => ( upairsubunion
% 0.32/1.74 => ( upairinpowunion
% 0.32/1.74 => ( ubforcartprodlem1
% 0.32/1.74 => ( ubforcartprodlem2
% 0.32/1.74 => ( ubforcartprodlem3
% 0.32/1.74 => ( cartprodpairin
% 0.32/1.74 => ! [A: $i,B: $i,Xu: $i] :
% 0.32/1.74 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.32/1.74 => ? [Xx: $i] :
% 0.32/1.74 ( ( in @ Xx @ A )
% 0.32/1.74 & ? [Xy: $i] :
% 0.32/1.74 ( ( in @ Xy @ B )
% 0.32/1.74 & ( Xu
% 0.32/1.74 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.32/1.74 ------------------------
% 0.32/1.76 % (30536)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_30432 for (2999ds/275Mi)
% 0.32/1.76 % (30535)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_30432 for (2999ds/2Mi)
% 0.32/1.76 % (30534)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30432 for (2999ds/2Mi)
% 0.32/1.76 % (30531)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30432 for (2999ds/183Mi)
% 0.32/1.76 % (30537)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30432 for (2999ds/18Mi)
% 0.32/1.76 % (30533)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_30432 for (2999ds/27Mi)
% 0.32/1.76 % (30532)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_30432 for (2999ds/4Mi)
% 0.32/1.77 % (30534)Instruction limit reached!
% 0.32/1.77 % (30534)------------------------------
% 0.32/1.77 % (30534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.77 % (30534)Termination reason: Unknown
% 0.32/1.77 % (30534)Termination phase: shuffling
% 0.32/1.77
% 0.32/1.77 % (30535)Instruction limit reached!
% 0.32/1.77 % (30535)------------------------------
% 0.32/1.77 % (30535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.77 % (30535)Termination reason: Unknown
% 0.32/1.77 % (30535)Termination phase: shuffling
% 0.32/1.77
% 0.32/1.77 % (30535)Memory used [KB]: 1279
% 0.32/1.77 % (30535)Time elapsed: 0.003 s
% 0.32/1.77 % (30535)Instructions burned: 3 (million)
% 0.32/1.77 % (30535)------------------------------
% 0.32/1.77 % (30535)------------------------------
% 0.32/1.77 % (30534)Memory used [KB]: 1279
% 0.32/1.77 % (30534)Time elapsed: 0.003 s
% 0.32/1.77 % (30534)Instructions burned: 3 (million)
% 0.32/1.77 % (30534)------------------------------
% 0.32/1.77 % (30534)------------------------------
% 0.32/1.77 % (30532)Instruction limit reached!
% 0.32/1.77 % (30532)------------------------------
% 0.32/1.77 % (30532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.77 % (30532)Termination reason: Unknown
% 0.32/1.77 % (30532)Termination phase: shuffling
% 0.32/1.77
% 0.32/1.77 % (30532)Memory used [KB]: 1279
% 0.32/1.77 % (30532)Time elapsed: 0.004 s
% 0.32/1.77 % (30532)Instructions burned: 4 (million)
% 0.32/1.77 % (30532)------------------------------
% 0.32/1.77 % (30532)------------------------------
% 0.32/1.77 % (30537)Instruction limit reached!
% 0.32/1.77 % (30537)------------------------------
% 0.32/1.77 % (30537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.77 % (30537)Termination reason: Unknown
% 0.32/1.77 % (30537)Termination phase: Property scanning
% 0.32/1.77
% 0.32/1.77 % (30537)Memory used [KB]: 1535
% 0.32/1.77 % (30537)Time elapsed: 0.010 s
% 0.32/1.77 % (30537)Instructions burned: 18 (million)
% 0.32/1.77 % (30537)------------------------------
% 0.32/1.77 % (30537)------------------------------
% 0.32/1.78 % (30533)Instruction limit reached!
% 0.32/1.78 % (30533)------------------------------
% 0.32/1.78 % (30533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.78 % (30533)Termination reason: Unknown
% 0.32/1.78 % (30533)Termination phase: Property scanning
% 0.32/1.78
% 0.32/1.78 % (30533)Memory used [KB]: 1663
% 0.32/1.78 % (30533)Time elapsed: 0.015 s
% 0.32/1.78 % (30533)Instructions burned: 28 (million)
% 0.32/1.78 % (30533)------------------------------
% 0.32/1.78 % (30533)------------------------------
% 0.32/1.78 % (30539)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_30432 for (2999ds/37Mi)
% 0.32/1.78 % (30538)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30432 for (2999ds/3Mi)
% 0.32/1.78 % (30540)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_30432 for (2999ds/15Mi)
% 0.32/1.78 % (30538)Instruction limit reached!
% 0.32/1.78 % (30538)------------------------------
% 0.32/1.78 % (30538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.78 % (30538)Termination reason: Unknown
% 0.32/1.78 % (30538)Termination phase: shuffling
% 0.32/1.78
% 0.32/1.78 % (30538)Memory used [KB]: 1279
% 0.32/1.78 % (30538)Time elapsed: 0.003 s
% 0.32/1.78 % (30538)Instructions burned: 3 (million)
% 0.32/1.78 % (30538)------------------------------
% 0.32/1.78 % (30538)------------------------------
% 0.32/1.79 % (30541)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_30432 for (2999ds/3Mi)
% 0.32/1.79 % (30540)Instruction limit reached!
% 0.32/1.79 % (30540)------------------------------
% 0.32/1.79 % (30540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.79 % (30540)Termination reason: Unknown
% 0.32/1.79 % (30540)Termination phase: Property scanning
% 0.32/1.79
% 0.32/1.79 % (30540)Memory used [KB]: 1535
% 0.32/1.79 % (30540)Time elapsed: 0.009 s
% 0.32/1.79 % (30540)Instructions burned: 16 (million)
% 0.32/1.79 % (30540)------------------------------
% 0.32/1.79 % (30540)------------------------------
% 0.32/1.79 % (30541)Instruction limit reached!
% 0.32/1.79 % (30541)------------------------------
% 0.32/1.79 % (30541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.79 % (30541)Termination reason: Unknown
% 0.32/1.79 % (30541)Termination phase: shuffling
% 0.32/1.79
% 0.32/1.79 % (30541)Memory used [KB]: 1279
% 0.32/1.79 % (30541)Time elapsed: 0.003 s
% 0.32/1.79 % (30541)Instructions burned: 3 (million)
% 0.32/1.79 % (30541)------------------------------
% 0.32/1.79 % (30541)------------------------------
% 0.32/1.79 % (30542)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_30432 for (2999ds/1041Mi)
% 2.83/1.80 % (30539)Instruction limit reached!
% 2.83/1.80 % (30539)------------------------------
% 2.83/1.80 % (30539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.80 % (30539)Termination reason: Unknown
% 2.83/1.80 % (30539)Termination phase: Property scanning
% 2.83/1.80
% 2.83/1.80 % (30539)Memory used [KB]: 1791
% 2.83/1.80 % (30539)Time elapsed: 0.018 s
% 2.83/1.80 % (30539)Instructions burned: 38 (million)
% 2.83/1.80 % (30539)------------------------------
% 2.83/1.80 % (30539)------------------------------
% 2.83/1.80 % (30543)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_30432 for (2999ds/7Mi)
% 2.83/1.80 % (30543)Instruction limit reached!
% 2.83/1.80 % (30543)------------------------------
% 2.83/1.80 % (30543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.80 % (30543)Termination reason: Unknown
% 2.83/1.80 % (30543)Termination phase: shuffling
% 2.83/1.80
% 2.83/1.80 % (30543)Memory used [KB]: 1407
% 2.83/1.80 % (30543)Time elapsed: 0.005 s
% 2.83/1.80 % (30543)Instructions burned: 7 (million)
% 2.83/1.80 % (30543)------------------------------
% 2.83/1.80 % (30543)------------------------------
% 2.83/1.81 % (30544)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_30432 for (2999ds/16Mi)
% 2.83/1.81 % (30545)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_30432 for (2999ds/3Mi)
% 2.83/1.81 % (30545)Instruction limit reached!
% 2.83/1.81 % (30545)------------------------------
% 2.83/1.81 % (30545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.81 % (30545)Termination reason: Unknown
% 2.83/1.81 % (30545)Termination phase: shuffling
% 2.83/1.81
% 2.83/1.81 % (30545)Memory used [KB]: 1279
% 2.83/1.81 % (30545)Time elapsed: 0.003 s
% 2.83/1.81 % (30545)Instructions burned: 3 (million)
% 2.83/1.81 % (30545)------------------------------
% 2.83/1.81 % (30545)------------------------------
% 2.83/1.81 % (30546)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_30432 for (2999ds/3Mi)
% 2.83/1.81 % (30544)Instruction limit reached!
% 2.83/1.81 % (30544)------------------------------
% 2.83/1.81 % (30544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.81 % (30544)Termination reason: Unknown
% 2.83/1.81 % (30544)Termination phase: shuffling
% 2.83/1.81
% 2.83/1.81 % (30544)Memory used [KB]: 1663
% 2.83/1.81 % (30544)Time elapsed: 0.010 s
% 2.83/1.81 % (30544)Instructions burned: 17 (million)
% 2.83/1.81 % (30544)------------------------------
% 2.83/1.81 % (30544)------------------------------
% 2.83/1.82 % (30546)Instruction limit reached!
% 2.83/1.82 % (30546)------------------------------
% 2.83/1.82 % (30546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.82 % (30546)Termination reason: Unknown
% 2.83/1.82 % (30546)Termination phase: shuffling
% 2.83/1.82
% 2.83/1.82 % (30546)Memory used [KB]: 1279
% 2.83/1.82 % (30546)Time elapsed: 0.004 s
% 2.83/1.82 % (30546)Instructions burned: 4 (million)
% 2.83/1.82 % (30546)------------------------------
% 2.83/1.82 % (30546)------------------------------
% 2.83/1.82 % (30547)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_30432 for (2999ds/7Mi)
% 2.83/1.82 % (30547)Instruction limit reached!
% 2.83/1.82 % (30547)------------------------------
% 2.83/1.82 % (30547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.82 % (30547)Termination reason: Unknown
% 2.83/1.82 % (30547)Termination phase: shuffling
% 2.83/1.82
% 2.83/1.82 % (30547)Memory used [KB]: 1407
% 2.83/1.82 % (30547)Time elapsed: 0.005 s
% 2.83/1.82 % (30547)Instructions burned: 7 (million)
% 2.83/1.82 % (30547)------------------------------
% 2.83/1.82 % (30547)------------------------------
% 2.83/1.82 % (30548)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_30432 for (2999ds/3Mi)
% 2.83/1.82 % (30548)Instruction limit reached!
% 2.83/1.82 % (30548)------------------------------
% 2.83/1.82 % (30548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.82 % (30548)Termination reason: Unknown
% 2.83/1.83 % (30548)Termination phase: shuffling
% 2.83/1.83
% 2.83/1.83 % (30548)Memory used [KB]: 1279
% 2.83/1.83 % (30548)Time elapsed: 0.003 s
% 2.83/1.83 % (30548)Instructions burned: 3 (million)
% 2.83/1.83 % (30548)------------------------------
% 2.83/1.83 % (30548)------------------------------
% 2.83/1.83 % (30549)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_30432 for (2999ds/4Mi)
% 2.83/1.83 % (30550)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_30432 for (2999ds/18Mi)
% 2.83/1.83 % (30549)Instruction limit reached!
% 2.83/1.83 % (30549)------------------------------
% 2.83/1.83 % (30549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.83 % (30549)Termination reason: Unknown
% 2.83/1.83 % (30549)Termination phase: shuffling
% 2.83/1.83
% 2.83/1.83 % (30549)Memory used [KB]: 1279
% 2.83/1.83 % (30549)Time elapsed: 0.004 s
% 2.83/1.83 % (30549)Instructions burned: 5 (million)
% 2.83/1.83 % (30549)------------------------------
% 2.83/1.83 % (30549)------------------------------
% 2.83/1.84 % (30551)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_30432 for (2999ds/710Mi)
% 2.83/1.84 % (30550)Instruction limit reached!
% 2.83/1.84 % (30550)------------------------------
% 2.83/1.84 % (30550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.84 % (30550)Termination reason: Unknown
% 2.83/1.84 % (30550)Termination phase: shuffling
% 2.83/1.84
% 2.83/1.84 % (30550)Memory used [KB]: 1663
% 2.83/1.84 % (30550)Time elapsed: 0.010 s
% 2.83/1.84 % (30550)Instructions burned: 18 (million)
% 2.83/1.84 % (30550)------------------------------
% 2.83/1.84 % (30550)------------------------------
% 2.83/1.84 % (30552)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_30432 for (2999ds/6Mi)
% 2.83/1.84 % (30552)Instruction limit reached!
% 2.83/1.84 % (30552)------------------------------
% 2.83/1.84 % (30552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.84 % (30552)Termination reason: Unknown
% 2.83/1.84 % (30552)Termination phase: shuffling
% 2.83/1.84
% 2.83/1.84 % (30552)Memory used [KB]: 1279
% 2.83/1.84 % (30552)Time elapsed: 0.004 s
% 2.83/1.84 % (30552)Instructions burned: 6 (million)
% 2.83/1.84 % (30552)------------------------------
% 2.83/1.84 % (30552)------------------------------
% 2.83/1.85 % (30553)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_30432 for (2999ds/902Mi)
% 2.83/1.85 % (30531)Instruction limit reached!
% 2.83/1.85 % (30531)------------------------------
% 2.83/1.85 % (30531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.85 % (30531)Termination reason: Unknown
% 2.83/1.85 % (30531)Termination phase: Saturation
% 2.83/1.85
% 2.83/1.85 % (30531)Memory used [KB]: 7164
% 2.83/1.85 % (30531)Time elapsed: 0.087 s
% 2.83/1.85 % (30531)Instructions burned: 183 (million)
% 2.83/1.85 % (30531)------------------------------
% 2.83/1.85 % (30531)------------------------------
% 2.83/1.86 % (30554)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_30432 for (2999ds/21Mi)
% 2.83/1.86 % (30555)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_30432 for (2999ds/5Mi)
% 2.83/1.86 % (30555)Instruction limit reached!
% 2.83/1.86 % (30555)------------------------------
% 2.83/1.86 % (30555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.86 % (30555)Termination reason: Unknown
% 2.83/1.86 % (30555)Termination phase: shuffling
% 2.83/1.86
% 2.83/1.86 % (30555)Memory used [KB]: 1279
% 2.83/1.86 % (30555)Time elapsed: 0.004 s
% 2.83/1.86 % (30555)Instructions burned: 6 (million)
% 2.83/1.86 % (30555)------------------------------
% 2.83/1.86 % (30555)------------------------------
% 2.83/1.86 % (30554)Instruction limit reached!
% 2.83/1.86 % (30554)------------------------------
% 2.83/1.86 % (30554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.86 % (30554)Termination reason: Unknown
% 2.83/1.86 % (30554)Termination phase: shuffling
% 2.83/1.86
% 2.83/1.86 % (30554)Memory used [KB]: 1663
% 2.83/1.86 % (30554)Time elapsed: 0.011 s
% 2.83/1.86 % (30554)Instructions burned: 22 (million)
% 2.83/1.86 % (30554)------------------------------
% 2.83/1.86 % (30554)------------------------------
% 2.83/1.87 % (30556)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_30432 for (2998ds/6Mi)
% 2.83/1.87 % (30556)Instruction limit reached!
% 2.83/1.87 % (30556)------------------------------
% 2.83/1.87 % (30556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.87 % (30556)Termination reason: Unknown
% 2.83/1.87 % (30556)Termination phase: shuffling
% 2.83/1.87
% 2.83/1.87 % (30556)Memory used [KB]: 1407
% 2.83/1.87 % (30556)Time elapsed: 0.005 s
% 2.83/1.87 % (30556)Instructions burned: 7 (million)
% 2.83/1.87 % (30556)------------------------------
% 2.83/1.87 % (30556)------------------------------
% 2.83/1.88 % (30557)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_30432 for (2998ds/377Mi)
% 2.83/1.88 % (30558)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_30432 for (2998ds/779Mi)
% 2.83/1.88 % (30559)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_30432 for (2998ds/19Mi)
% 2.83/1.89 % (30559)Instruction limit reached!
% 2.83/1.89 % (30559)------------------------------
% 2.83/1.89 % (30559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.89 % (30559)Termination reason: Unknown
% 2.83/1.89 % (30559)Termination phase: shuffling
% 2.83/1.89
% 2.83/1.89 % (30559)Memory used [KB]: 1663
% 2.83/1.89 % (30559)Time elapsed: 0.010 s
% 2.83/1.89 % (30559)Instructions burned: 19 (million)
% 2.83/1.89 % (30559)------------------------------
% 2.83/1.89 % (30559)------------------------------
% 2.83/1.90 % (30536)Instruction limit reached!
% 2.83/1.90 % (30536)------------------------------
% 2.83/1.90 % (30536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.90 % (30536)Termination reason: Unknown
% 2.83/1.90 % (30536)Termination phase: Saturation
% 2.83/1.90
% 2.83/1.90 % (30536)Memory used [KB]: 8059
% 2.83/1.90 % (30536)Time elapsed: 0.139 s
% 2.83/1.90 % (30536)Instructions burned: 275 (million)
% 2.83/1.90 % (30536)------------------------------
% 2.83/1.90 % (30536)------------------------------
% 2.83/1.91 % (30560)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_30432 for (2998ds/879Mi)
% 2.83/1.92 % (30561)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_30432 for (2998ds/17Mi)
% 2.83/1.93 % (30561)Instruction limit reached!
% 2.83/1.93 % (30561)------------------------------
% 2.83/1.93 % (30561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.93 % (30561)Termination reason: Unknown
% 2.83/1.93 % (30561)Termination phase: shuffling
% 2.83/1.93
% 2.83/1.93 % (30561)Memory used [KB]: 1535
% 2.83/1.93 % (30561)Time elapsed: 0.010 s
% 2.83/1.93 % (30561)Instructions burned: 17 (million)
% 2.83/1.93 % (30561)------------------------------
% 2.83/1.93 % (30561)------------------------------
% 2.83/1.93 % (30553)Refutation not found, incomplete strategy
% 2.83/1.93 % (30553)------------------------------
% 2.83/1.93 % (30553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.93 % (30553)Termination reason: Refutation not found, incomplete strategy
% 2.83/1.93
% 2.83/1.93
% 2.83/1.93 % (30553)Memory used [KB]: 7675
% 2.83/1.93 % (30553)Time elapsed: 0.079 s
% 2.83/1.93 % (30553)Instructions burned: 157 (million)
% 2.83/1.93 % (30553)------------------------------
% 2.83/1.93 % (30553)------------------------------
% 2.83/1.94 % (30562)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_30432 for (2998ds/3Mi)
% 2.83/1.94 % (30563)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_30432 for (2998ds/30Mi)
% 2.83/1.94 % (30562)Instruction limit reached!
% 2.83/1.94 % (30562)------------------------------
% 2.83/1.94 % (30562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.94 % (30562)Termination reason: Unknown
% 2.83/1.94 % (30562)Termination phase: shuffling
% 2.83/1.94
% 2.83/1.94 % (30562)Memory used [KB]: 1279
% 2.83/1.94 % (30562)Time elapsed: 0.004 s
% 2.83/1.94 % (30562)Instructions burned: 5 (million)
% 2.83/1.94 % (30562)------------------------------
% 2.83/1.94 % (30562)------------------------------
% 2.83/1.96 % (30563)Instruction limit reached!
% 2.83/1.96 % (30563)------------------------------
% 2.83/1.96 % (30563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.96 % (30563)Termination reason: Unknown
% 2.83/1.96 % (30563)Termination phase: Property scanning
% 2.83/1.96
% 2.83/1.96 % (30563)Memory used [KB]: 1791
% 2.83/1.96 % (30563)Time elapsed: 0.015 s
% 2.83/1.96 % (30563)Instructions burned: 30 (million)
% 2.83/1.96 % (30563)------------------------------
% 2.83/1.96 % (30563)------------------------------
% 2.83/1.96 % (30564)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_30432 for (2997ds/127Mi)
% 2.83/1.97 % (30565)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_30432 for (2997ds/100Mi)
% 2.83/2.02 % (30564)Instruction limit reached!
% 2.83/2.02 % (30564)------------------------------
% 2.83/2.02 % (30564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/2.02 % (30564)Termination reason: Unknown
% 2.83/2.02 % (30564)Termination phase: Saturation
% 2.83/2.02
% 2.83/2.02 % (30564)Memory used [KB]: 6780
% 2.83/2.02 % (30564)Time elapsed: 0.059 s
% 2.83/2.02 % (30564)Instructions burned: 127 (million)
% 2.83/2.02 % (30564)------------------------------
% 2.83/2.02 % (30564)------------------------------
% 2.83/2.02 % (30565)Instruction limit reached!
% 2.83/2.02 % (30565)------------------------------
% 2.83/2.02 % (30565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/2.02 % (30565)Termination reason: Unknown
% 2.83/2.02 % (30565)Termination phase: Saturation
% 2.83/2.02
% 2.83/2.02 % (30565)Memory used [KB]: 6524
% 2.83/2.02 % (30565)Time elapsed: 0.049 s
% 2.83/2.02 % (30565)Instructions burned: 101 (million)
% 2.83/2.02 % (30565)------------------------------
% 2.83/2.02 % (30565)------------------------------
% 4.72/2.03 % (30566)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_30432 for (2997ds/3Mi)
% 4.72/2.04 % (30566)Instruction limit reached!
% 4.72/2.04 % (30566)------------------------------
% 4.72/2.04 % (30566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.72/2.04 % (30566)Termination reason: Unknown
% 4.72/2.04 % (30566)Termination phase: shuffling
% 4.72/2.04
% 4.72/2.04 % (30566)Memory used [KB]: 1279
% 4.72/2.04 % (30566)Time elapsed: 0.004 s
% 4.72/2.04 % (30566)Instructions burned: 4 (million)
% 4.72/2.04 % (30566)------------------------------
% 4.72/2.04 % (30566)------------------------------
% 4.72/2.04 % (30567)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_30432 for (2997ds/20Mi)
% 4.72/2.05 % (30567)Instruction limit reached!
% 4.72/2.05 % (30567)------------------------------
% 4.72/2.05 % (30567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.72/2.05 % (30567)Termination reason: Unknown
% 4.72/2.05 % (30567)Termination phase: SInE selection
% 4.72/2.05
% 4.72/2.05 % (30567)Memory used [KB]: 1535
% 4.72/2.05 % (30567)Time elapsed: 0.012 s
% 4.72/2.05 % (30567)Instructions burned: 21 (million)
% 4.72/2.05 % (30567)------------------------------
% 4.72/2.05 % (30567)------------------------------
% 4.72/2.05 % (30568)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_30432 for (2997ds/86Mi)
% 4.72/2.06 % (30557)Instruction limit reached!
% 4.72/2.06 % (30557)------------------------------
% 4.72/2.06 % (30557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.72/2.06 % (30557)Termination reason: Unknown
% 4.72/2.06 % (30557)Termination phase: Saturation
% 4.72/2.06
% 4.72/2.06 % (30557)Memory used [KB]: 7803
% 4.72/2.06 % (30557)Time elapsed: 0.182 s
% 4.72/2.06 % (30557)Instructions burned: 378 (million)
% 4.72/2.06 % (30557)------------------------------
% 4.72/2.06 % (30557)------------------------------
% 4.72/2.06 % (30569)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_30432 for (2996ds/107Mi)
% 4.72/2.08 % (30570)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_30432 for (2996ds/39Mi)
% 4.72/2.09 % (30568)Instruction limit reached!
% 4.72/2.09 % (30568)------------------------------
% 4.72/2.09 % (30568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.72/2.09 % (30568)Termination reason: Unknown
% 4.72/2.09 % (30568)Termination phase: Saturation
% 4.72/2.09
% 4.72/2.09 % (30568)Memory used [KB]: 6524
% 4.72/2.09 % (30568)Time elapsed: 0.040 s
% 4.72/2.09 % (30568)Instructions burned: 86 (million)
% 4.72/2.09 % (30568)------------------------------
% 4.72/2.09 % (30568)------------------------------
% 4.72/2.09 % (30570)Instruction limit reached!
% 4.72/2.09 % (30570)------------------------------
% 4.72/2.09 % (30570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.72/2.09 % (30570)Termination reason: Unknown
% 4.72/2.09 % (30570)Termination phase: Property scanning
% 4.72/2.09
% 4.72/2.09 % (30570)Memory used [KB]: 1791
% 4.72/2.09 % (30570)Time elapsed: 0.020 s
% 4.72/2.09 % (30570)Instructions burned: 41 (million)
% 4.72/2.09 % (30570)------------------------------
% 4.72/2.09 % (30570)------------------------------
% 4.72/2.11 % (30571)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_30432 for (2996ds/448Mi)
% 4.72/2.11 % (30572)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_30432 for (2996ds/46Mi)
% 4.72/2.11 % (30569)Instruction limit reached!
% 4.72/2.11 % (30569)------------------------------
% 4.72/2.11 % (30569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.72/2.11 % (30569)Termination reason: Unknown
% 4.72/2.11 % (30569)Termination phase: Saturation
% 4.72/2.11
% 4.72/2.11 % (30569)Memory used [KB]: 6652
% 4.72/2.11 % (30569)Time elapsed: 0.049 s
% 4.72/2.11 % (30569)Instructions burned: 107 (million)
% 4.72/2.11 % (30569)------------------------------
% 4.72/2.11 % (30569)------------------------------
% 5.35/2.13 % (30573)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_30432 for (2996ds/98Mi)
% 5.35/2.13 % (30572)Instruction limit reached!
% 5.35/2.13 % (30572)------------------------------
% 5.35/2.13 % (30572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.35/2.13 % (30572)Termination reason: Unknown
% 5.35/2.13 % (30572)Termination phase: Property scanning
% 5.35/2.13
% 5.35/2.13 % (30572)Memory used [KB]: 1791
% 5.35/2.13 % (30572)Time elapsed: 0.022 s
% 5.35/2.13 % (30572)Instructions burned: 47 (million)
% 5.35/2.13 % (30572)------------------------------
% 5.35/2.13 % (30572)------------------------------
% 5.35/2.15 % (30574)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_30432 for (2996ds/507Mi)
% 5.35/2.17 % (30573)Instruction limit reached!
% 5.35/2.17 % (30573)------------------------------
% 5.35/2.17 % (30573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.35/2.17 % (30573)Termination reason: Unknown
% 5.35/2.17 % (30573)Termination phase: Saturation
% 5.35/2.17
% 5.35/2.17 % (30573)Memory used [KB]: 2046
% 5.35/2.17 % (30573)Time elapsed: 0.044 s
% 5.35/2.17 % (30573)Instructions burned: 98 (million)
% 5.35/2.17 % (30573)------------------------------
% 5.35/2.17 % (30573)------------------------------
% 5.35/2.17 % (30558)Instruction limit reached!
% 5.35/2.17 % (30558)------------------------------
% 5.35/2.17 % (30558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.35/2.17 % (30558)Termination reason: Unknown
% 5.35/2.17 % (30558)Termination phase: Saturation
% 5.35/2.17
% 5.35/2.17 % (30558)Memory used [KB]: 6652
% 5.35/2.17 % (30558)Time elapsed: 0.293 s
% 5.35/2.17 % (30558)Instructions burned: 780 (million)
% 5.35/2.17 % (30558)------------------------------
% 5.35/2.17 % (30558)------------------------------
% 5.35/2.18 % (30542)Instruction limit reached!
% 5.35/2.18 % (30542)------------------------------
% 5.35/2.18 % (30542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.35/2.18 % (30542)Termination reason: Unknown
% 5.35/2.18 % (30542)Termination phase: Saturation
% 5.35/2.18
% 5.35/2.18 % (30542)Memory used [KB]: 9083
% 5.35/2.18 % (30542)Time elapsed: 0.387 s
% 5.35/2.18 % (30542)Instructions burned: 1043 (million)
% 5.35/2.18 % (30542)------------------------------
% 5.35/2.18 % (30542)------------------------------
% 5.35/2.18 % (30551)Refutation not found, non-redundant clauses discarded% (30551)------------------------------
% 5.35/2.18 % (30551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.35/2.18 % (30551)Termination reason: Refutation not found, non-redundant clauses discarded
% 5.35/2.18
% 5.35/2.18 % (30551)Memory used [KB]: 9338
% 5.35/2.18 % (30551)Time elapsed: 0.348 s
% 5.35/2.18 % (30551)Instructions burned: 682 (million)
% 5.35/2.18 % (30551)------------------------------
% 5.35/2.18 % (30551)------------------------------
% 5.35/2.19 % (30575)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_30432 for (2995ds/149Mi)
% 5.35/2.19 % (30576)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_30432 for (2995ds/39Mi)
% 5.35/2.20 % (30577)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_30432 for (2995ds/6Mi)
% 5.70/2.20 % (30577)Instruction limit reached!
% 5.70/2.20 % (30577)------------------------------
% 5.70/2.20 % (30577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.20 % (30577)Termination reason: Unknown
% 5.70/2.20 % (30577)Termination phase: shuffling
% 5.70/2.20
% 5.70/2.20 % (30577)Memory used [KB]: 1407
% 5.70/2.20 % (30577)Time elapsed: 0.005 s
% 5.70/2.20 % (30577)Instructions burned: 7 (million)
% 5.70/2.20 % (30577)------------------------------
% 5.70/2.20 % (30577)------------------------------
% 5.70/2.20 % (30578)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_30432 for (2995ds/1087Mi)
% 5.70/2.21 % (30576)Instruction limit reached!
% 5.70/2.21 % (30576)------------------------------
% 5.70/2.21 % (30576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.21 % (30576)Termination reason: Unknown
% 5.70/2.21 % (30576)Termination phase: Property scanning
% 5.70/2.21
% 5.70/2.21 % (30576)Memory used [KB]: 1791
% 5.70/2.21 % (30576)Time elapsed: 0.020 s
% 5.70/2.21 % (30576)Instructions burned: 41 (million)
% 5.70/2.21 % (30576)------------------------------
% 5.70/2.21 % (30576)------------------------------
% 5.70/2.22 % (30579)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_30432 for (2995ds/47Mi)
% 5.70/2.22 % (30580)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_30432 for (2995ds/44Mi)
% 5.70/2.24 % (30579)Instruction limit reached!
% 5.70/2.24 % (30579)------------------------------
% 5.70/2.24 % (30579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.24 % (30579)Termination reason: Unknown
% 5.70/2.24 % (30579)Termination phase: Property scanning
% 5.70/2.24
% 5.70/2.24 % (30579)Memory used [KB]: 1791
% 5.70/2.24 % (30579)Time elapsed: 0.023 s
% 5.70/2.24 % (30579)Instructions burned: 48 (million)
% 5.70/2.24 % (30579)------------------------------
% 5.70/2.24 % (30579)------------------------------
% 5.70/2.24 % (30580)Instruction limit reached!
% 5.70/2.24 % (30580)------------------------------
% 5.70/2.24 % (30580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.24 % (30580)Termination reason: Unknown
% 5.70/2.24 % (30580)Termination phase: SInE selection
% 5.70/2.24
% 5.70/2.24 % (30580)Memory used [KB]: 1663
% 5.70/2.24 % (30580)Time elapsed: 0.022 s
% 5.70/2.24 % (30580)Instructions burned: 45 (million)
% 5.70/2.24 % (30580)------------------------------
% 5.70/2.24 % (30580)------------------------------
% 5.70/2.25 % (30581)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_30432 for (2995ds/432Mi)
% 5.70/2.26 % (30575)Instruction limit reached!
% 5.70/2.26 % (30575)------------------------------
% 5.70/2.26 % (30575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.26 % (30575)Termination reason: Unknown
% 5.70/2.26 % (30575)Termination phase: Saturation
% 5.70/2.26
% 5.70/2.26 % (30575)Memory used [KB]: 7036
% 5.70/2.26 % (30575)Time elapsed: 0.074 s
% 5.70/2.26 % (30575)Instructions burned: 149 (million)
% 5.70/2.26 % (30575)------------------------------
% 5.70/2.26 % (30575)------------------------------
% 5.70/2.26 % (30582)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_30432 for (2995ds/62Mi)
% 5.70/2.28 % (30583)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_30432 for (2994ds/31Mi)
% 5.70/2.29 % (30571)Instruction limit reached!
% 5.70/2.29 % (30571)------------------------------
% 5.70/2.29 % (30571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.29 % (30571)Termination reason: Unknown
% 5.70/2.29 % (30571)Termination phase: Saturation
% 5.70/2.29
% 5.70/2.29 % (30571)Memory used [KB]: 6652
% 5.70/2.29 % (30571)Time elapsed: 0.179 s
% 5.70/2.29 % (30571)Instructions burned: 450 (million)
% 5.70/2.29 % (30571)------------------------------
% 5.70/2.29 % (30571)------------------------------
% 5.70/2.29 % (30582)Instruction limit reached!
% 5.70/2.29 % (30582)------------------------------
% 5.70/2.29 % (30582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.29 % (30582)Termination reason: Unknown
% 5.70/2.29 % (30582)Termination phase: Property scanning
% 5.70/2.29
% 5.70/2.29 % (30582)Memory used [KB]: 1791
% 5.70/2.29 % (30582)Time elapsed: 0.029 s
% 5.70/2.29 % (30582)Instructions burned: 63 (million)
% 5.70/2.29 % (30582)------------------------------
% 5.70/2.29 % (30582)------------------------------
% 5.70/2.29 % (30583)Instruction limit reached!
% 5.70/2.29 % (30583)------------------------------
% 5.70/2.29 % (30583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.29 % (30583)Termination reason: Unknown
% 5.70/2.29 % (30583)Termination phase: Property scanning
% 5.70/2.29
% 5.70/2.29 % (30583)Memory used [KB]: 1663
% 5.70/2.29 % (30583)Time elapsed: 0.016 s
% 5.70/2.29 % (30583)Instructions burned: 31 (million)
% 5.70/2.29 % (30583)------------------------------
% 5.70/2.29 % (30583)------------------------------
% 6.29/2.30 % (30584)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_30432 for (2994ds/96Mi)
% 6.29/2.30 % (30585)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_30432 for (2994ds/453Mi)
% 6.29/2.31 % (30586)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_30432 for (2994ds/71Mi)
% 6.29/2.34 % (30586)Instruction limit reached!
% 6.29/2.34 % (30586)------------------------------
% 6.29/2.34 % (30586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.34 % (30586)Termination reason: Unknown
% 6.29/2.34 % (30586)Termination phase: Property scanning
% 6.29/2.34
% 6.29/2.34 % (30586)Memory used [KB]: 1918
% 6.29/2.34 % (30586)Time elapsed: 0.033 s
% 6.29/2.34 % (30586)Instructions burned: 71 (million)
% 6.29/2.34 % (30586)------------------------------
% 6.29/2.34 % (30586)------------------------------
% 6.29/2.34 % (30584)Instruction limit reached!
% 6.29/2.34 % (30584)------------------------------
% 6.29/2.34 % (30584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.34 % (30584)Termination reason: Unknown
% 6.29/2.34 % (30584)Termination phase: Saturation
% 6.29/2.34
% 6.29/2.35 % (30584)Memory used [KB]: 6780
% 6.29/2.35 % (30584)Time elapsed: 0.045 s
% 6.29/2.35 % (30584)Instructions burned: 96 (million)
% 6.29/2.35 % (30584)------------------------------
% 6.29/2.35 % (30584)------------------------------
% 6.29/2.36 % (30587)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_30432 for (2994ds/83Mi)
% 6.29/2.36 % (30560)Instruction limit reached!
% 6.29/2.36 % (30560)------------------------------
% 6.29/2.36 % (30560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.36 % (30560)Termination reason: Unknown
% 6.29/2.36 % (30560)Termination phase: Saturation
% 6.29/2.36
% 6.29/2.36 % (30560)Memory used [KB]: 8187
% 6.29/2.36 % (30560)Time elapsed: 0.470 s
% 6.29/2.36 % (30560)Instructions burned: 879 (million)
% 6.29/2.36 % (30560)------------------------------
% 6.29/2.36 % (30560)------------------------------
% 6.29/2.36 % (30588)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_30432 for (2994ds/11Mi)
% 6.29/2.37 % (30588)Instruction limit reached!
% 6.29/2.37 % (30588)------------------------------
% 6.29/2.37 % (30588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.37 % (30588)Termination reason: Unknown
% 6.29/2.37 % (30588)Termination phase: shuffling
% 6.29/2.37
% 6.29/2.37 % (30588)Memory used [KB]: 1407
% 6.29/2.37 % (30588)Time elapsed: 0.007 s
% 6.29/2.37 % (30588)Instructions burned: 12 (million)
% 6.29/2.37 % (30588)------------------------------
% 6.29/2.37 % (30588)------------------------------
% 6.29/2.37 % (30589)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_30432 for (2993ds/41Mi)
% 6.29/2.38 % (30590)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_30432 for (2993ds/6Mi)
% 6.29/2.39 % (30590)Instruction limit reached!
% 6.29/2.39 % (30590)------------------------------
% 6.29/2.39 % (30590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.39 % (30590)Termination reason: Unknown
% 6.29/2.39 % (30590)Termination phase: shuffling
% 6.29/2.39
% 6.29/2.39 % (30590)Memory used [KB]: 1407
% 6.29/2.39 % (30590)Time elapsed: 0.005 s
% 6.29/2.39 % (30590)Instructions burned: 7 (million)
% 6.29/2.39 % (30590)------------------------------
% 6.29/2.39 % (30590)------------------------------
% 6.29/2.39 % (30587)Instruction limit reached!
% 6.29/2.39 % (30587)------------------------------
% 6.29/2.39 % (30587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.39 % (30587)Termination reason: Unknown
% 6.29/2.39 % (30587)Termination phase: Saturation
% 6.29/2.39
% 6.29/2.39 % (30587)Memory used [KB]: 6396
% 6.29/2.39 % (30587)Time elapsed: 0.038 s
% 6.29/2.39 % (30587)Instructions burned: 84 (million)
% 6.29/2.39 % (30587)------------------------------
% 6.29/2.39 % (30587)------------------------------
% 6.29/2.39 % (30589)Instruction limit reached!
% 6.29/2.39 % (30589)------------------------------
% 6.29/2.39 % (30589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.39 % (30589)Termination reason: Unknown
% 6.29/2.39 % (30589)Termination phase: Property scanning
% 6.29/2.39
% 6.29/2.39 % (30589)Memory used [KB]: 1791
% 6.29/2.39 % (30589)Time elapsed: 0.020 s
% 6.29/2.39 % (30589)Instructions burned: 41 (million)
% 6.29/2.39 % (30589)------------------------------
% 6.29/2.39 % (30589)------------------------------
% 6.29/2.39 % (30574)Instruction limit reached!
% 6.29/2.39 % (30574)------------------------------
% 6.29/2.39 % (30574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.39 % (30574)Termination reason: Unknown
% 6.29/2.39 % (30574)Termination phase: Saturation
% 6.29/2.39
% 6.29/2.39 % (30574)Memory used [KB]: 7291
% 6.29/2.39 % (30574)Time elapsed: 0.248 s
% 6.29/2.39 % (30574)Instructions burned: 507 (million)
% 6.29/2.39 % (30574)------------------------------
% 6.29/2.39 % (30574)------------------------------
% 6.86/2.40 % (30591)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_30432 for (2993ds/150Mi)
% 6.86/2.41 % (30592)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_30432 for (2993ds/343Mi)
% 6.86/2.41 % (30593)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_30432 for (2993ds/109Mi)
% 6.86/2.41 % (30594)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_30432 for (2993ds/253Mi)
% 6.86/2.42 % (30581)Instruction limit reached!
% 6.86/2.42 % (30581)------------------------------
% 6.86/2.42 % (30581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.42 % (30581)Termination reason: Unknown
% 6.86/2.42 % (30581)Termination phase: Saturation
% 6.86/2.42
% 6.86/2.42 % (30581)Memory used [KB]: 2942
% 6.86/2.42 % (30581)Time elapsed: 0.172 s
% 6.86/2.42 % (30581)Instructions burned: 432 (million)
% 6.86/2.42 % (30581)------------------------------
% 6.86/2.42 % (30581)------------------------------
% 6.86/2.44 % (30595)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_30432 for (2993ds/140Mi)
% 6.86/2.46 % (30593)Instruction limit reached!
% 6.86/2.46 % (30593)------------------------------
% 6.86/2.46 % (30593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.46 % (30593)Termination reason: Unknown
% 6.86/2.46 % (30593)Termination phase: Saturation
% 6.86/2.46
% 6.86/2.46 % (30593)Memory used [KB]: 6652
% 6.86/2.46 % (30593)Time elapsed: 0.051 s
% 6.86/2.46 % (30593)Instructions burned: 109 (million)
% 6.86/2.46 % (30593)------------------------------
% 6.86/2.46 % (30593)------------------------------
% 6.86/2.47 % (30596)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_30432 for (2992ds/614Mi)
% 6.86/2.47 % (30591)Instruction limit reached!
% 6.86/2.47 % (30591)------------------------------
% 6.86/2.47 % (30591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.47 % (30591)Termination reason: Unknown
% 6.86/2.47 % (30591)Termination phase: Saturation
% 6.86/2.47
% 6.86/2.47 % (30591)Memory used [KB]: 7803
% 6.86/2.47 % (30591)Time elapsed: 0.074 s
% 6.86/2.47 % (30591)Instructions burned: 151 (million)
% 6.86/2.47 % (30591)------------------------------
% 6.86/2.47 % (30591)------------------------------
% 6.86/2.48 % (30585)Instruction limit reached!
% 6.86/2.48 % (30585)------------------------------
% 6.86/2.48 % (30585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.48 % (30585)Termination reason: Unknown
% 6.86/2.48 % (30585)Termination phase: Saturation
% 6.86/2.48
% 6.86/2.48 % (30585)Memory used [KB]: 6524
% 6.86/2.48 % (30585)Time elapsed: 0.181 s
% 6.86/2.48 % (30585)Instructions burned: 455 (million)
% 6.86/2.48 % (30585)------------------------------
% 6.86/2.48 % (30585)------------------------------
% 6.86/2.49 % (30597)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_30432 for (2992ds/202Mi)
% 7.40/2.50 % (30598)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_30432 for (2992ds/339Mi)
% 7.40/2.50 % (30595)Instruction limit reached!
% 7.40/2.50 % (30595)------------------------------
% 7.40/2.50 % (30595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.40/2.50 % (30595)Termination reason: Unknown
% 7.40/2.50 % (30595)Termination phase: Saturation
% 7.40/2.50
% 7.40/2.50 % (30595)Memory used [KB]: 6524
% 7.40/2.50 % (30595)Time elapsed: 0.088 s
% 7.40/2.50 % (30595)Instructions burned: 140 (million)
% 7.40/2.50 % (30595)------------------------------
% 7.40/2.50 % (30595)------------------------------
% 7.40/2.52 % (30599)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_30432 for (2992ds/283Mi)
% 7.40/2.53 % (30594)Instruction limit reached!
% 7.40/2.53 % (30594)------------------------------
% 7.40/2.53 % (30594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.40/2.53 % (30594)Termination reason: Unknown
% 7.40/2.53 % (30594)Termination phase: Saturation
% 7.40/2.53
% 7.40/2.53 % (30594)Memory used [KB]: 8059
% 7.40/2.53 % (30594)Time elapsed: 0.146 s
% 7.40/2.53 % (30594)Instructions burned: 254 (million)
% 7.40/2.53 % (30594)------------------------------
% 7.40/2.53 % (30594)------------------------------
% 7.40/2.55 % (30600)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_30432 for (2992ds/134Mi)
% 7.40/2.57 % (30592)Instruction limit reached!
% 7.40/2.57 % (30592)------------------------------
% 7.40/2.57 % (30592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.40/2.57 % (30592)Termination reason: Unknown
% 7.40/2.57 % (30592)Termination phase: Saturation
% 7.40/2.57
% 7.40/2.57 % (30592)Memory used [KB]: 7675
% 7.40/2.57 % (30592)Time elapsed: 0.165 s
% 7.40/2.57 % (30592)Instructions burned: 344 (million)
% 7.40/2.57 % (30592)------------------------------
% 7.40/2.57 % (30592)------------------------------
% 7.40/2.59 % (30601)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_30432 for (2991ds/298Mi)
% 7.40/2.59 % (30597)Instruction limit reached!
% 7.40/2.59 % (30597)------------------------------
% 7.40/2.59 % (30597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.40/2.59 % (30597)Termination reason: Unknown
% 7.40/2.59 % (30597)Termination phase: Saturation
% 7.40/2.59
% 7.40/2.59 % (30597)Memory used [KB]: 8315
% 7.40/2.59 % (30597)Time elapsed: 0.103 s
% 7.40/2.59 % (30597)Instructions burned: 203 (million)
% 7.40/2.59 % (30597)------------------------------
% 7.40/2.59 % (30597)------------------------------
% 7.92/2.61 % (30602)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_30432 for (2991ds/192Mi)
% 7.92/2.61 % (30600)Instruction limit reached!
% 7.92/2.61 % (30600)------------------------------
% 7.92/2.61 % (30600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.92/2.61 % (30600)Termination reason: Unknown
% 7.92/2.61 % (30600)Termination phase: Saturation
% 7.92/2.61
% 7.92/2.61 % (30600)Memory used [KB]: 6908
% 7.92/2.61 % (30600)Time elapsed: 0.063 s
% 7.92/2.61 % (30600)Instructions burned: 134 (million)
% 7.92/2.61 % (30600)------------------------------
% 7.92/2.61 % (30600)------------------------------
% 7.92/2.63 % (30603)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_30432 for (2991ds/258Mi)
% 7.92/2.63 % (30599)Instruction limit reached!
% 7.92/2.63 % (30599)------------------------------
% 7.92/2.63 % (30599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.92/2.63 % (30599)Termination reason: Unknown
% 7.92/2.63 % (30599)Termination phase: Saturation
% 7.92/2.63
% 7.92/2.63 % (30599)Memory used [KB]: 9083
% 7.92/2.63 % (30599)Time elapsed: 0.114 s
% 7.92/2.63 % (30599)Instructions burned: 283 (million)
% 7.92/2.63 % (30599)------------------------------
% 7.92/2.63 % (30599)------------------------------
% 7.92/2.65 % (30604)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_30432 for (2991ds/90Mi)
% 7.92/2.66 % (30598)Instruction limit reached!
% 7.92/2.66 % (30598)------------------------------
% 7.92/2.66 % (30598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.92/2.66 % (30598)Termination reason: Unknown
% 7.92/2.66 % (30598)Termination phase: Saturation
% 7.92/2.66
% 7.92/2.66 % (30598)Memory used [KB]: 7675
% 7.92/2.66 % (30598)Time elapsed: 0.165 s
% 7.92/2.66 % (30598)Instructions burned: 339 (million)
% 7.92/2.66 % (30598)------------------------------
% 7.92/2.66 % (30598)------------------------------
% 7.92/2.68 % (30605)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_30432 for (2990ds/231Mi)
% 7.92/2.69 % (30604)Instruction limit reached!
% 7.92/2.69 % (30604)------------------------------
% 7.92/2.69 % (30604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.92/2.69 % (30604)Termination reason: Unknown
% 7.92/2.69 % (30604)Termination phase: Saturation
% 7.92/2.69
% 7.92/2.69 % (30604)Memory used [KB]: 6908
% 7.92/2.69 % (30604)Time elapsed: 0.043 s
% 7.92/2.69 % (30604)Instructions burned: 91 (million)
% 7.92/2.69 % (30604)------------------------------
% 7.92/2.69 % (30604)------------------------------
% 8.36/2.70 % (30602)Instruction limit reached!
% 8.36/2.70 % (30602)------------------------------
% 8.36/2.70 % (30602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.36/2.70 % (30602)Termination reason: Unknown
% 8.36/2.70 % (30602)Termination phase: Saturation
% 8.36/2.70
% 8.36/2.70 % (30602)Memory used [KB]: 7291
% 8.36/2.70 % (30602)Time elapsed: 0.091 s
% 8.36/2.70 % (30602)Instructions burned: 193 (million)
% 8.36/2.70 % (30602)------------------------------
% 8.36/2.70 % (30602)------------------------------
% 8.36/2.71 % (30606)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_30432 for (2990ds/458Mi)
% 8.36/2.71 % (30601)Instruction limit reached!
% 8.36/2.71 % (30601)------------------------------
% 8.36/2.71 % (30601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.36/2.71 % (30601)Termination reason: Unknown
% 8.36/2.71 % (30601)Termination phase: Saturation
% 8.36/2.71
% 8.36/2.71 % (30601)Memory used [KB]: 6524
% 8.36/2.71 % (30601)Time elapsed: 0.126 s
% 8.36/2.71 % (30601)Instructions burned: 299 (million)
% 8.36/2.71 % (30601)------------------------------
% 8.36/2.71 % (30601)------------------------------
% 8.36/2.72 % (30607)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_30432 for (2990ds/31Mi)
% 8.36/2.73 % (30608)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_30432 for (2990ds/297Mi)
% 8.36/2.73 % (30607)Instruction limit reached!
% 8.36/2.73 % (30607)------------------------------
% 8.36/2.73 % (30607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.36/2.73 % (30607)Termination reason: Unknown
% 8.36/2.73 % (30607)Termination phase: Property scanning
% 8.36/2.73
% 8.36/2.73 % (30607)Memory used [KB]: 1663
% 8.36/2.73 % (30607)Time elapsed: 0.016 s
% 8.36/2.73 % (30607)Instructions burned: 32 (million)
% 8.36/2.73 % (30607)------------------------------
% 8.36/2.73 % (30607)------------------------------
% 8.36/2.75 % (30609)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_30432 for (2990ds/987Mi)
% 8.36/2.75 % (30603)Instruction limit reached!
% 8.36/2.75 % (30603)------------------------------
% 8.36/2.75 % (30603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.36/2.75 % (30603)Termination reason: Unknown
% 8.36/2.75 % (30603)Termination phase: Saturation
% 8.36/2.75
% 8.36/2.75 % (30603)Memory used [KB]: 7419
% 8.36/2.75 % (30603)Time elapsed: 0.124 s
% 8.36/2.75 % (30603)Instructions burned: 258 (million)
% 8.36/2.75 % (30603)------------------------------
% 8.36/2.75 % (30603)------------------------------
% 8.36/2.75 % (30578)Instruction limit reached!
% 8.36/2.75 % (30578)------------------------------
% 8.36/2.75 % (30578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.36/2.75 % (30578)Termination reason: Unknown
% 8.36/2.75 % (30578)Termination phase: Saturation
% 8.36/2.75
% 8.36/2.75 % (30578)Memory used [KB]: 9978
% 8.36/2.75 % (30578)Time elapsed: 0.551 s
% 8.36/2.75 % (30578)Instructions burned: 1087 (million)
% 8.36/2.75 % (30578)------------------------------
% 8.36/2.75 % (30578)------------------------------
% 8.36/2.77 % (30610)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_30432 for (2989ds/182Mi)
% 8.36/2.77 % (30611)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_30432 for (2989ds/182Mi)
% 8.36/2.77 % (30596)Instruction limit reached!
% 8.36/2.77 % (30596)------------------------------
% 8.36/2.77 % (30596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.36/2.77 % (30596)Termination reason: Unknown
% 8.36/2.77 % (30596)Termination phase: Saturation
% 8.36/2.77
% 8.36/2.77 % (30596)Memory used [KB]: 8315
% 8.36/2.77 % (30596)Time elapsed: 0.319 s
% 8.36/2.77 % (30596)Instructions burned: 615 (million)
% 8.36/2.77 % (30596)------------------------------
% 8.36/2.77 % (30596)------------------------------
% 8.36/2.79 % (30612)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_30432 for (2989ds/154Mi)
% 8.36/2.79 % (30605)Instruction limit reached!
% 8.36/2.79 % (30605)------------------------------
% 8.36/2.79 % (30605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.36/2.79 % (30605)Termination reason: Unknown
% 8.36/2.79 % (30605)Termination phase: Saturation
% 8.36/2.79
% 8.36/2.79 % (30605)Memory used [KB]: 10618
% 8.36/2.79 % (30605)Time elapsed: 0.114 s
% 8.36/2.79 % (30605)Instructions burned: 231 (million)
% 8.36/2.79 % (30605)------------------------------
% 8.36/2.79 % (30605)------------------------------
% 9.78/2.81 % (30613)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_30432 for (2989ds/79Mi)
% 9.78/2.84 % (30613)Instruction limit reached!
% 9.78/2.84 % (30613)------------------------------
% 9.78/2.84 % (30613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.78/2.84 % (30613)Termination reason: Unknown
% 9.78/2.84 % (30613)Termination phase: Saturation
% 9.78/2.84
% 9.78/2.84 % (30613)Memory used [KB]: 6396
% 9.78/2.84 % (30613)Time elapsed: 0.038 s
% 9.78/2.84 % (30613)Instructions burned: 80 (million)
% 9.78/2.84 % (30613)------------------------------
% 9.78/2.84 % (30613)------------------------------
% 9.78/2.85 % (30608)Instruction limit reached!
% 9.78/2.85 % (30608)------------------------------
% 9.78/2.85 % (30608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.78/2.85 % (30608)Termination reason: Unknown
% 9.78/2.85 % (30608)Termination phase: Saturation
% 9.78/2.85
% 9.78/2.85 % (30608)Memory used [KB]: 8187
% 9.78/2.85 % (30608)Time elapsed: 0.118 s
% 9.78/2.85 % (30608)Instructions burned: 297 (million)
% 9.78/2.85 % (30608)------------------------------
% 9.78/2.85 % (30608)------------------------------
% 9.78/2.85 % (30610)Instruction limit reached!
% 9.78/2.85 % (30610)------------------------------
% 9.78/2.85 % (30610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.78/2.85 % (30610)Termination reason: Unknown
% 9.78/2.85 % (30610)Termination phase: Saturation
% 9.78/2.85
% 9.78/2.85 % (30610)Memory used [KB]: 7164
% 9.78/2.85 % (30610)Time elapsed: 0.086 s
% 9.78/2.85 % (30610)Instructions burned: 182 (million)
% 9.78/2.85 % (30610)------------------------------
% 9.78/2.85 % (30610)------------------------------
% 9.78/2.85 % (30612)Instruction limit reached!
% 9.78/2.85 % (30612)------------------------------
% 9.78/2.85 % (30612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.78/2.85 % (30612)Termination reason: Unknown
% 9.78/2.85 % (30612)Termination phase: Saturation
% 9.78/2.85
% 9.78/2.85 % (30612)Memory used [KB]: 6524
% 9.78/2.85 % (30612)Time elapsed: 0.067 s
% 9.78/2.85 % (30612)Instructions burned: 155 (million)
% 9.78/2.85 % (30612)------------------------------
% 9.78/2.85 % (30612)------------------------------
% 9.78/2.86 % (30611)Instruction limit reached!
% 9.78/2.86 % (30611)------------------------------
% 9.78/2.86 % (30611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.78/2.86 % (30611)Termination reason: Unknown
% 9.78/2.86 % (30611)Termination phase: Saturation
% 9.78/2.86
% 9.78/2.86 % (30611)Memory used [KB]: 9338
% 9.78/2.86 % (30611)Time elapsed: 0.091 s
% 9.78/2.86 % (30611)Instructions burned: 182 (million)
% 9.78/2.86 % (30611)------------------------------
% 9.78/2.86 % (30611)------------------------------
% 9.78/2.86 % (30614)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_30432 for (2988ds/216Mi)
% 9.78/2.86 % (30615)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_30432 for (2988ds/114Mi)
% 9.78/2.87 % (30617)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_30432 for (2988ds/182Mi)
% 9.78/2.87 % (30616)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_30432 for (2988ds/922Mi)
% 9.78/2.87 % (30618)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_30432 for (2988ds/164Mi)
% 10.26/2.91 % (30615)Instruction limit reached!
% 10.26/2.91 % (30615)------------------------------
% 10.26/2.91 % (30615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.26/2.91 % (30615)Termination reason: Unknown
% 10.26/2.91 % (30615)Termination phase: Saturation
% 10.26/2.91
% 10.26/2.91 % (30615)Memory used [KB]: 6780
% 10.26/2.91 % (30615)Time elapsed: 0.053 s
% 10.26/2.91 % (30615)Instructions burned: 114 (million)
% 10.26/2.91 % (30615)------------------------------
% 10.26/2.91 % (30615)------------------------------
% 10.26/2.93 % (30619)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_30432 for (2988ds/50Mi)
% 10.26/2.93 % (30606)Instruction limit reached!
% 10.26/2.93 % (30606)------------------------------
% 10.26/2.93 % (30606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.26/2.93 % (30606)Termination reason: Unknown
% 10.26/2.93 % (30606)Termination phase: Saturation
% 10.26/2.93
% 10.26/2.93 % (30606)Memory used [KB]: 7803
% 10.26/2.93 % (30606)Time elapsed: 0.225 s
% 10.26/2.93 % (30606)Instructions burned: 458 (million)
% 10.26/2.93 % (30606)------------------------------
% 10.26/2.93 % (30606)------------------------------
% 10.26/2.94 % (30617)Instruction limit reached!
% 10.26/2.94 % (30617)------------------------------
% 10.26/2.94 % (30617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.26/2.94 % (30617)Termination reason: Unknown
% 10.26/2.94 % (30617)Termination phase: Saturation
% 10.26/2.94
% 10.26/2.94 % (30617)Memory used [KB]: 6524
% 10.26/2.94 % (30617)Time elapsed: 0.075 s
% 10.26/2.94 % (30617)Instructions burned: 184 (million)
% 10.26/2.94 % (30617)------------------------------
% 10.26/2.94 % (30617)------------------------------
% 10.26/2.95 % (30614)Instruction limit reached!
% 10.26/2.95 % (30614)------------------------------
% 10.26/2.95 % (30614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.26/2.95 % (30614)Termination reason: Unknown
% 10.26/2.95 % (30614)Termination phase: Saturation
% 10.26/2.95
% 10.26/2.95 % (30614)Memory used [KB]: 6652
% 10.26/2.95 % (30614)Time elapsed: 0.087 s
% 10.26/2.95 % (30614)Instructions burned: 217 (million)
% 10.26/2.95 % (30614)------------------------------
% 10.26/2.95 % (30614)------------------------------
% 10.26/2.95 % (30618)Instruction limit reached!
% 10.26/2.95 % (30618)------------------------------
% 10.26/2.95 % (30618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.26/2.95 % (30618)Termination reason: Unknown
% 10.26/2.95 % (30618)Termination phase: Saturation
% 10.26/2.95
% 10.26/2.95 % (30618)Memory used [KB]: 2302
% 10.26/2.95 % (30618)Time elapsed: 0.075 s
% 10.26/2.95 % (30618)Instructions burned: 164 (million)
% 10.26/2.95 % (30618)------------------------------
% 10.26/2.95 % (30618)------------------------------
% 10.26/2.95 % (30620)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_30432 for (2988ds/368Mi)
% 10.26/2.95 % (30619)Instruction limit reached!
% 10.26/2.95 % (30619)------------------------------
% 10.26/2.95 % (30619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.26/2.95 % (30619)Termination reason: Unknown
% 10.26/2.95 % (30619)Termination phase: Property scanning
% 10.26/2.95
% 10.26/2.95 % (30619)Memory used [KB]: 1791
% 10.26/2.95 % (30619)Time elapsed: 0.025 s
% 10.26/2.95 % (30619)Instructions burned: 51 (million)
% 10.26/2.95 % (30619)------------------------------
% 10.26/2.95 % (30619)------------------------------
% 10.26/2.95 % (30621)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_30432 for (2988ds/1021Mi)
% 10.26/2.96 % (30623)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_30432 for (2988ds/204Mi)
% 10.26/2.96 % (30622)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_30432 for (2988ds/267Mi)
% 10.26/2.97 % (30624)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_30432 for (2987ds/26Mi)
% 10.26/2.98 % (30624)Instruction limit reached!
% 10.26/2.98 % (30624)------------------------------
% 10.26/2.98 % (30624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.26/2.98 % (30624)Termination reason: Unknown
% 10.26/2.98 % (30624)Termination phase: Property scanning
% 10.26/2.98
% 10.26/2.98 % (30624)Memory used [KB]: 1663
% 10.26/2.98 % (30624)Time elapsed: 0.014 s
% 10.26/2.98 % (30624)Instructions burned: 27 (million)
% 10.26/2.98 % (30624)------------------------------
% 10.26/2.98 % (30624)------------------------------
% 10.26/3.00 % (30625)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_30432 for (2987ds/53Mi)
% 10.26/3.02 % (30625)Instruction limit reached!
% 10.26/3.02 % (30625)------------------------------
% 10.26/3.02 % (30625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.26/3.02 % (30625)Termination reason: Unknown
% 10.26/3.02 % (30625)Termination phase: Function definition elimination
% 10.26/3.02
% 10.26/3.02 % (30625)Memory used [KB]: 1791
% 10.26/3.02 % (30625)Time elapsed: 0.026 s
% 10.26/3.02 % (30625)Instructions burned: 54 (million)
% 10.26/3.02 % (30625)------------------------------
% 10.26/3.02 % (30625)------------------------------
% 11.71/3.04 % (30626)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_30432 for (2987ds/4436Mi)
% 11.71/3.06 % (30623)Instruction limit reached!
% 11.71/3.06 % (30623)------------------------------
% 11.71/3.06 % (30623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.71/3.06 % (30623)Termination reason: Unknown
% 11.71/3.06 % (30623)Termination phase: Saturation
% 11.71/3.06
% 11.71/3.06 % (30623)Memory used [KB]: 7291
% 11.71/3.06 % (30623)Time elapsed: 0.093 s
% 11.71/3.06 % (30623)Instructions burned: 204 (million)
% 11.71/3.06 % (30623)------------------------------
% 11.71/3.06 % (30623)------------------------------
% 11.71/3.07 % (30622)Instruction limit reached!
% 11.71/3.07 % (30622)------------------------------
% 11.71/3.07 % (30622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.71/3.07 % (30622)Termination reason: Unknown
% 11.71/3.07 % (30622)Termination phase: Saturation
% 11.71/3.07
% 11.71/3.07 % (30622)Memory used [KB]: 8699
% 11.71/3.07 % (30622)Time elapsed: 0.107 s
% 11.71/3.07 % (30622)Instructions burned: 269 (million)
% 11.71/3.07 % (30622)------------------------------
% 11.71/3.07 % (30622)------------------------------
% 11.71/3.07 % (30627)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_30432 for (2986ds/1539Mi)
% 11.71/3.09 % (30628)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_30432 for (2986ds/408Mi)
% 11.71/3.13 % (30609)Instruction limit reached!
% 11.71/3.13 % (30609)------------------------------
% 11.71/3.13 % (30609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.71/3.13 % (30609)Termination reason: Unknown
% 11.71/3.13 % (30609)Termination phase: Saturation
% 11.71/3.13
% 11.71/3.13 % (30609)Memory used [KB]: 9210
% 11.71/3.13 % (30609)Time elapsed: 0.381 s
% 11.71/3.13 % (30609)Instructions burned: 987 (million)
% 11.71/3.13 % (30609)------------------------------
% 11.71/3.13 % (30609)------------------------------
% 11.83/3.13 % (30620)Instruction limit reached!
% 11.83/3.13 % (30620)------------------------------
% 11.83/3.13 % (30620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.83/3.13 % (30620)Termination reason: Unknown
% 11.83/3.13 % (30620)Termination phase: Saturation
% 11.83/3.13
% 11.83/3.13 % (30620)Memory used [KB]: 7803
% 11.83/3.13 % (30620)Time elapsed: 0.182 s
% 11.83/3.13 % (30620)Instructions burned: 369 (million)
% 11.83/3.13 % (30620)------------------------------
% 11.83/3.13 % (30620)------------------------------
% 11.83/3.14 % (30629)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_30432 for (2986ds/5205Mi)
% 11.83/3.15 % (30630)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_30432 for (2986ds/1913Mi)
% 12.37/3.29 % (30628)Instruction limit reached!
% 12.37/3.29 % (30628)------------------------------
% 12.37/3.29 % (30628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.37/3.30 % (30628)Termination reason: Unknown
% 12.37/3.30 % (30628)Termination phase: Saturation
% 12.37/3.30
% 12.37/3.30 % (30628)Memory used [KB]: 9210
% 12.37/3.30 % (30628)Time elapsed: 0.211 s
% 12.37/3.30 % (30628)Instructions burned: 408 (million)
% 12.37/3.30 % (30628)------------------------------
% 12.37/3.30 % (30628)------------------------------
% 12.78/3.31 % (30631)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_30432 for (2984ds/4350Mi)
% 12.78/3.33 % (30616)Instruction limit reached!
% 12.78/3.33 % (30616)------------------------------
% 12.78/3.33 % (30616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.78/3.33 % (30616)Termination reason: Unknown
% 12.78/3.33 % (30616)Termination phase: Saturation
% 12.78/3.33
% 12.78/3.33 % (30616)Memory used [KB]: 9466
% 12.78/3.33 % (30616)Time elapsed: 0.469 s
% 12.78/3.33 % (30616)Instructions burned: 923 (million)
% 12.78/3.33 % (30616)------------------------------
% 12.78/3.33 % (30616)------------------------------
% 12.78/3.35 % (30632)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_30432 for (2984ds/68Mi)
% 12.78/3.38 % (30632)Instruction limit reached!
% 12.78/3.38 % (30632)------------------------------
% 12.78/3.38 % (30632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.78/3.38 % (30632)Termination reason: Unknown
% 12.78/3.38 % (30632)Termination phase: Property scanning
% 12.78/3.38
% 12.78/3.38 % (30632)Memory used [KB]: 1918
% 12.78/3.38 % (30632)Time elapsed: 0.031 s
% 12.78/3.38 % (30632)Instructions burned: 68 (million)
% 12.78/3.38 % (30632)------------------------------
% 12.78/3.38 % (30632)------------------------------
% 12.97/3.40 % (30633)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_30432 for (2983ds/358Mi)
% 12.97/3.46 % (30621)Instruction limit reached!
% 12.97/3.46 % (30621)------------------------------
% 12.97/3.46 % (30621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.97/3.46 % (30621)Termination reason: Unknown
% 12.97/3.46 % (30621)Termination phase: Saturation
% 12.97/3.46
% 12.97/3.46 % (30621)Memory used [KB]: 9722
% 12.97/3.46 % (30621)Time elapsed: 0.509 s
% 12.97/3.46 % (30621)Instructions burned: 1022 (million)
% 12.97/3.46 % (30621)------------------------------
% 12.97/3.46 % (30621)------------------------------
% 12.97/3.48 % (30635)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_30432 for (2982ds/31Mi)
% 12.97/3.49 % (30635)Instruction limit reached!
% 12.97/3.49 % (30635)------------------------------
% 12.97/3.49 % (30635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.97/3.49 % (30635)Termination reason: Unknown
% 12.97/3.49 % (30635)Termination phase: Property scanning
% 12.97/3.49
% 12.97/3.49 % (30635)Memory used [KB]: 1791
% 12.97/3.49 % (30635)Time elapsed: 0.016 s
% 12.97/3.49 % (30635)Instructions burned: 31 (million)
% 12.97/3.49 % (30635)------------------------------
% 12.97/3.49 % (30635)------------------------------
% 13.09/3.51 % (30636)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_30432 for (2982ds/279Mi)
% 13.09/3.57 % (30633)Instruction limit reached!
% 13.09/3.57 % (30633)------------------------------
% 13.09/3.57 % (30633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.09/3.57 % (30633)Termination reason: Unknown
% 13.09/3.57 % (30633)Termination phase: Saturation
% 13.09/3.57
% 13.09/3.57 % (30633)Memory used [KB]: 7675
% 13.09/3.57 % (30633)Time elapsed: 0.194 s
% 13.09/3.57 % (30633)Instructions burned: 359 (million)
% 13.09/3.57 % (30633)------------------------------
% 13.09/3.57 % (30633)------------------------------
% 13.09/3.59 % (30637)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_30432 for (2981ds/258Mi)
% 13.29/3.62 % (30636)Instruction limit reached!
% 13.29/3.62 % (30636)------------------------------
% 13.29/3.62 % (30636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.29/3.62 % (30636)Termination reason: Unknown
% 13.29/3.62 % (30636)Termination phase: Saturation
% 13.29/3.62
% 13.29/3.62 % (30636)Memory used [KB]: 6524
% 13.29/3.62 % (30636)Time elapsed: 0.110 s
% 13.29/3.62 % (30636)Instructions burned: 279 (million)
% 13.29/3.62 % (30636)------------------------------
% 13.29/3.62 % (30636)------------------------------
% 13.29/3.64 % (30638)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_30432 for (2981ds/26Mi)
% 13.29/3.65 % (30638)Instruction limit reached!
% 13.29/3.65 % (30638)------------------------------
% 13.29/3.65 % (30638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.29/3.65 % (30638)Termination reason: Unknown
% 13.29/3.65 % (30638)Termination phase: Property scanning
% 13.29/3.65
% 13.29/3.65 % (30638)Memory used [KB]: 1663
% 13.29/3.65 % (30638)Time elapsed: 0.014 s
% 13.29/3.65 % (30638)Instructions burned: 26 (million)
% 13.29/3.65 % (30638)------------------------------
% 13.29/3.65 % (30638)------------------------------
% 13.29/3.66 % (30639)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_30432 for (2981ds/995Mi)
% 13.44/3.70 % (30627)Instruction limit reached!
% 13.44/3.70 % (30627)------------------------------
% 13.44/3.70 % (30627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.44/3.70 % (30627)Termination reason: Unknown
% 13.44/3.70 % (30627)Termination phase: Saturation
% 13.44/3.70
% 13.44/3.70 % (30627)Memory used [KB]: 7931
% 13.44/3.70 % (30627)Time elapsed: 0.634 s
% 13.44/3.70 % (30627)Instructions burned: 1540 (million)
% 13.44/3.70 % (30627)------------------------------
% 13.44/3.70 % (30627)------------------------------
% 13.44/3.71 % (30637)Instruction limit reached!
% 13.44/3.71 % (30637)------------------------------
% 13.44/3.71 % (30637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.44/3.71 % (30637)Termination reason: Unknown
% 13.44/3.71 % (30637)Termination phase: Saturation
% 13.44/3.71
% 13.44/3.71 % (30637)Memory used [KB]: 7931
% 13.44/3.71 % (30637)Time elapsed: 0.120 s
% 13.44/3.71 % (30637)Instructions burned: 259 (million)
% 13.44/3.71 % (30637)------------------------------
% 13.44/3.71 % (30637)------------------------------
% 13.44/3.72 % (30640)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_30432 for (2980ds/373Mi)
% 13.44/3.72 % (30641)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_30432 for (2980ds/253Mi)
% 14.22/3.82 % (30641)Instruction limit reached!
% 14.22/3.82 % (30641)------------------------------
% 14.22/3.82 % (30641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.22/3.82 % (30641)Termination reason: Unknown
% 14.22/3.82 % (30641)Termination phase: Saturation
% 14.22/3.82
% 14.22/3.82 % (30641)Memory used [KB]: 6652
% 14.22/3.82 % (30641)Time elapsed: 0.102 s
% 14.22/3.82 % (30641)Instructions burned: 253 (million)
% 14.22/3.82 % (30641)------------------------------
% 14.22/3.82 % (30641)------------------------------
% 14.22/3.84 % (30642)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_30432 for (2979ds/832Mi)
% 14.34/3.90 % (30640)Instruction limit reached!
% 14.34/3.90 % (30640)------------------------------
% 14.34/3.90 % (30640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.34/3.90 % (30640)Termination reason: Unknown
% 14.34/3.90 % (30640)Termination phase: Saturation
% 14.34/3.90
% 14.34/3.90 % (30640)Memory used [KB]: 7547
% 14.34/3.90 % (30640)Time elapsed: 0.183 s
% 14.34/3.90 % (30640)Instructions burned: 374 (million)
% 14.34/3.90 % (30640)------------------------------
% 14.34/3.90 % (30640)------------------------------
% 14.34/3.92 % (30643)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_30432 for (2978ds/668Mi)
% 18.68/4.04 % (30630)Instruction limit reached!
% 18.68/4.04 % (30630)------------------------------
% 18.68/4.04 % (30630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.68/4.04 % (30630)Termination reason: Unknown
% 18.68/4.04 % (30630)Termination phase: Saturation
% 18.68/4.04
% 18.68/4.04 % (30630)Memory used [KB]: 3965
% 18.68/4.04 % (30630)Time elapsed: 0.900 s
% 18.68/4.04 % (30630)Instructions burned: 1914 (million)
% 18.68/4.04 % (30630)------------------------------
% 18.68/4.04 % (30630)------------------------------
% 18.68/4.04 % (30639)Instruction limit reached!
% 18.68/4.04 % (30639)------------------------------
% 18.68/4.04 % (30639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.68/4.04 % (30639)Termination reason: Unknown
% 18.68/4.04 % (30639)Termination phase: Saturation
% 18.68/4.04
% 18.68/4.04 % (30639)Memory used [KB]: 8955
% 18.68/4.04 % (30639)Time elapsed: 0.406 s
% 18.68/4.04 % (30639)Instructions burned: 995 (million)
% 18.68/4.04 % (30639)------------------------------
% 18.68/4.04 % (30639)------------------------------
% 18.68/4.06 % (30645)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_30432 for (2976ds/294Mi)
% 18.68/4.06 % (30644)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_30432 for (2976ds/40Mi)
% 18.68/4.08 % (30644)Instruction limit reached!
% 18.68/4.08 % (30644)------------------------------
% 18.68/4.08 % (30644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.68/4.08 % (30644)Termination reason: Unknown
% 18.68/4.08 % (30644)Termination phase: Property scanning
% 18.68/4.08
% 18.68/4.08 % (30644)Memory used [KB]: 1791
% 18.68/4.08 % (30644)Time elapsed: 0.020 s
% 18.68/4.08 % (30644)Instructions burned: 40 (million)
% 18.68/4.08 % (30644)------------------------------
% 18.68/4.08 % (30644)------------------------------
% 18.68/4.10 % (30646)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_30432 for (2976ds/187Mi)
% 19.30/4.17 % (30643)Instruction limit reached!
% 19.30/4.17 % (30643)------------------------------
% 19.30/4.17 % (30643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.30/4.17 % (30643)Termination reason: Unknown
% 19.30/4.17 % (30643)Termination phase: Saturation
% 19.30/4.17
% 19.30/4.17 % (30643)Memory used [KB]: 13560
% 19.30/4.17 % (30643)Time elapsed: 0.250 s
% 19.30/4.17 % (30643)Instructions burned: 668 (million)
% 19.30/4.17 % (30643)------------------------------
% 19.30/4.17 % (30643)------------------------------
% 19.30/4.18 % (30645)Instruction limit reached!
% 19.30/4.18 % (30645)------------------------------
% 19.30/4.18 % (30645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.30/4.18 % (30645)Termination reason: Unknown
% 19.30/4.18 % (30645)Termination phase: Saturation
% 19.30/4.18
% 19.30/4.18 % (30645)Memory used [KB]: 6524
% 19.30/4.18 % (30645)Time elapsed: 0.122 s
% 19.30/4.18 % (30645)Instructions burned: 295 (million)
% 19.30/4.18 % (30645)------------------------------
% 19.30/4.18 % (30645)------------------------------
% 19.30/4.18 % (30646)Instruction limit reached!
% 19.30/4.18 % (30646)------------------------------
% 19.30/4.18 % (30646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.30/4.18 % (30646)Termination reason: Unknown
% 19.30/4.18 % (30646)Termination phase: Saturation
% 19.30/4.18
% 19.30/4.18 % (30646)Memory used [KB]: 7291
% 19.30/4.18 % (30646)Time elapsed: 0.088 s
% 19.30/4.18 % (30646)Instructions burned: 187 (million)
% 19.30/4.18 % (30646)------------------------------
% 19.30/4.18 % (30646)------------------------------
% 19.30/4.18 % (30647)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_30432 for (2975ds/371Mi)
% 19.30/4.20 % (30648)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_30432 for (2975ds/1827Mi)
% 19.86/4.20 % (30649)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_30432 for (2975ds/70Mi)
% 19.86/4.23 % (30649)Instruction limit reached!
% 19.86/4.23 % (30649)------------------------------
% 19.86/4.23 % (30649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.86/4.23 % (30649)Termination reason: Unknown
% 19.86/4.23 % (30649)Termination phase: Property scanning
% 19.86/4.23
% 19.86/4.23 % (30649)Memory used [KB]: 1791
% 19.86/4.23 % (30649)Time elapsed: 0.032 s
% 19.86/4.23 % (30649)Instructions burned: 70 (million)
% 19.86/4.23 % (30649)------------------------------
% 19.86/4.23 % (30649)------------------------------
% 19.86/4.24 % (30650)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_30432 for (2975ds/316Mi)
% 19.86/4.25 % (30642)Instruction limit reached!
% 19.86/4.25 % (30642)------------------------------
% 19.86/4.25 % (30642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.86/4.25 % (30642)Termination reason: Unknown
% 19.86/4.25 % (30642)Termination phase: Saturation
% 19.86/4.25
% 19.86/4.25 % (30642)Memory used [KB]: 9466
% 19.86/4.25 % (30642)Time elapsed: 0.417 s
% 19.86/4.25 % (30642)Instructions burned: 833 (million)
% 19.86/4.25 % (30642)------------------------------
% 19.86/4.25 % (30642)------------------------------
% 19.86/4.27 % (30651)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_30432 for (2974ds/932Mi)
% 20.29/4.36 % (30647)Instruction limit reached!
% 20.29/4.36 % (30647)------------------------------
% 20.29/4.36 % (30647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.29/4.36 % (30647)Termination reason: Unknown
% 20.29/4.36 % (30647)Termination phase: Saturation
% 20.29/4.36
% 20.29/4.36 % (30647)Memory used [KB]: 7675
% 20.29/4.36 % (30647)Time elapsed: 0.178 s
% 20.29/4.36 % (30647)Instructions burned: 371 (million)
% 20.29/4.36 % (30647)------------------------------
% 20.29/4.36 % (30647)------------------------------
% 20.29/4.38 % (30650)Instruction limit reached!
% 20.29/4.38 % (30650)------------------------------
% 20.29/4.38 % (30650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.29/4.38 % (30650)Termination reason: Unknown
% 20.29/4.38 % (30650)Termination phase: Saturation
% 20.29/4.38
% 20.29/4.38 % (30650)Memory used [KB]: 7419
% 20.29/4.38 % (30650)Time elapsed: 0.132 s
% 20.29/4.38 % (30650)Instructions burned: 317 (million)
% 20.29/4.38 % (30650)------------------------------
% 20.29/4.38 % (30650)------------------------------
% 20.29/4.38 % (30652)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_30432 for (2973ds/4714Mi)
% 20.29/4.39 % (30653)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_30432 for (2973ds/8250Mi)
% 21.54/4.64 % (30651)Instruction limit reached!
% 21.54/4.64 % (30651)------------------------------
% 21.54/4.64 % (30651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.54/4.64 % (30651)Termination reason: Unknown
% 21.54/4.64 % (30651)Termination phase: Saturation
% 21.54/4.64
% 21.54/4.64 % (30651)Memory used [KB]: 9850
% 21.54/4.64 % (30651)Time elapsed: 0.370 s
% 21.54/4.64 % (30651)Instructions burned: 932 (million)
% 21.54/4.64 % (30651)------------------------------
% 21.54/4.64 % (30651)------------------------------
% 21.54/4.66 % (30654)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_30432 for (2971ds/770Mi)
% 22.81/5.00 % (30654)Instruction limit reached!
% 22.81/5.00 % (30654)------------------------------
% 22.81/5.00 % (30654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.81/5.00 % (30654)Termination reason: Unknown
% 22.81/5.00 % (30654)Termination phase: Saturation
% 22.81/5.00
% 22.81/5.00 % (30654)Memory used [KB]: 6780
% 22.81/5.00 % (30654)Time elapsed: 0.341 s
% 22.81/5.00 % (30654)Instructions burned: 771 (million)
% 22.81/5.00 % (30654)------------------------------
% 22.81/5.00 % (30654)------------------------------
% 22.81/5.01 % (30655)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_30432 for (2967ds/794Mi)
% 25.67/5.05 % (30629)Instruction limit reached!
% 25.67/5.05 % (30629)------------------------------
% 25.67/5.05 % (30629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.67/5.05 % (30629)Termination reason: Unknown
% 25.67/5.05 % (30629)Termination phase: Saturation
% 25.67/5.05
% 25.67/5.05 % (30629)Memory used [KB]: 9338
% 25.67/5.05 % (30629)Time elapsed: 1.906 s
% 25.67/5.05 % (30629)Instructions burned: 5205 (million)
% 25.67/5.05 % (30629)------------------------------
% 25.67/5.05 % (30629)------------------------------
% 25.67/5.06 % (30656)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_30432 for (2966ds/464Mi)
% 25.67/5.07 % (30648)Instruction limit reached!
% 25.67/5.07 % (30648)------------------------------
% 25.67/5.07 % (30648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.67/5.07 % (30648)Termination reason: Unknown
% 25.67/5.07 % (30648)Termination phase: Saturation
% 25.67/5.07
% 25.67/5.07 % (30648)Memory used [KB]: 15479
% 25.67/5.07 % (30648)Time elapsed: 0.877 s
% 25.67/5.07 % (30648)Instructions burned: 1828 (million)
% 25.67/5.07 % (30648)------------------------------
% 25.67/5.07 % (30648)------------------------------
% 25.67/5.09 % (30657)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_30432 for (2966ds/1376Mi)
% 26.61/5.27 % (30626)Instruction limit reached!
% 26.61/5.27 % (30626)------------------------------
% 26.61/5.27 % (30626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.61/5.27 % (30626)Termination reason: Unknown
% 26.61/5.27 % (30626)Termination phase: Saturation
% 26.61/5.27
% 26.61/5.27 % (30626)Memory used [KB]: 16502
% 26.61/5.27 % (30626)Time elapsed: 2.230 s
% 26.61/5.27 % (30626)Instructions burned: 4436 (million)
% 26.61/5.27 % (30626)------------------------------
% 26.61/5.27 % (30626)------------------------------
% 26.61/5.29 % (30658)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_30432 for (2964ds/906Mi)
% 26.61/5.29 % (30656)Instruction limit reached!
% 26.61/5.29 % (30656)------------------------------
% 26.61/5.29 % (30656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.61/5.29 % (30656)Termination reason: Unknown
% 26.61/5.29 % (30656)Termination phase: Saturation
% 26.61/5.29
% 26.61/5.29 % (30656)Memory used [KB]: 7931
% 26.61/5.29 % (30656)Time elapsed: 0.226 s
% 26.61/5.29 % (30656)Instructions burned: 465 (million)
% 26.61/5.29 % (30656)------------------------------
% 26.61/5.29 % (30656)------------------------------
% 27.35/5.31 % (30659)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_30432 for (2964ds/434Mi)
% 27.35/5.36 % (30655)First to succeed.
% 27.35/5.36 % (30655)Refutation found. Thanks to Tanya!
% 27.35/5.36 % SZS status Theorem for DTF2THF_30432
% 27.35/5.36 % SZS output start Proof for DTF2THF_30432
% 27.35/5.36 thf(func_def_0, type, in: $i > $i > $o).
% 27.35/5.36 thf(func_def_1, type, exu: ($i > $o) > $o).
% 27.35/5.36 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 27.35/5.36 thf(func_def_8, type, powerset: $i > $i).
% 27.35/5.36 thf(func_def_10, type, setunion: $i > $i).
% 27.35/5.36 thf(func_def_19, type, descr: ($i > $o) > $i).
% 27.35/5.36 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 27.35/5.36 thf(func_def_26, type, prop2set: $o > $i).
% 27.35/5.36 thf(func_def_36, type, nonempty: $i > $o).
% 27.35/5.36 thf(func_def_69, type, set2prop: $i > $o).
% 27.35/5.36 thf(func_def_88, type, subset: $i > $i > $o).
% 27.35/5.36 thf(func_def_89, type, disjoint: $i > $i > $o).
% 27.35/5.36 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 27.35/5.36 thf(func_def_114, type, binunion: $i > $i > $i).
% 27.35/5.36 thf(func_def_122, type, binintersect: $i > $i > $i).
% 27.35/5.36 thf(func_def_135, type, regular: $i > $o).
% 27.35/5.36 thf(func_def_136, type, setminus: $i > $i > $i).
% 27.35/5.36 thf(func_def_147, type, symdiff: $i > $i > $i).
% 27.35/5.36 thf(func_def_153, type, iskpair: $i > $o).
% 27.35/5.36 thf(func_def_158, type, kpair: $i > $i > $i).
% 27.35/5.36 thf(func_def_160, type, cartprod: $i > $i > $i).
% 27.35/5.36 thf(func_def_190, type, sP3: $o > $o).
% 27.35/5.36 thf(func_def_191, type, sP4: $i > $o).
% 27.35/5.36 thf(func_def_192, type, sP5: $o > $o).
% 27.35/5.36 thf(func_def_193, type, sP6: $o > $o).
% 27.35/5.36 thf(func_def_194, type, sK7: $i > $i).
% 27.35/5.36 thf(func_def_195, type, sK8: $i > $i > $i).
% 27.35/5.36 thf(func_def_196, type, sK9: $i > $i > $i).
% 27.35/5.36 thf(func_def_197, type, sK10: $i > $i > $i).
% 27.35/5.36 thf(func_def_198, type, sK11: $i > $i > $i > $i).
% 27.35/5.36 thf(func_def_199, type, sK12: $i > ($i > $o) > $i).
% 27.35/5.36 thf(func_def_200, type, sK13: $i > $i > $i).
% 27.35/5.36 thf(func_def_201, type, sK14: $i > $i > $i).
% 27.35/5.36 thf(func_def_202, type, sK15: $i > ($i > $i > $o) > $i).
% 27.35/5.36 thf(func_def_203, type, sK16: $i > ($i > $i > $o) > $i).
% 27.35/5.36 thf(func_def_204, type, sK17: $i > $i > ($i > $i > $o) > $i).
% 27.35/5.36 thf(func_def_205, type, sK18: $i > $i > ($i > $i > $o) > $i).
% 27.35/5.36 thf(func_def_206, type, sK19: $i > $i > ($i > $i > $o) > $i).
% 27.35/5.36 thf(func_def_207, type, sK20: $i > $i > ($i > $i > $o) > $i).
% 27.35/5.36 thf(func_def_208, type, sK21: $i > $i).
% 27.35/5.36 thf(func_def_211, type, sK22: $o > $i > $i > $i).
% 27.35/5.36 thf(func_def_212, type, sK23: $i > $i > $i).
% 27.35/5.36 thf(func_def_213, type, sK24: $i > $i > $i).
% 27.35/5.36 thf(func_def_214, type, sK25: $i > $i > $i).
% 27.35/5.36 thf(func_def_215, type, sK26: ($i > $o) > $i).
% 27.35/5.36 thf(func_def_216, type, sK27: ($i > $o) > $i > $i).
% 27.35/5.36 thf(func_def_217, type, sK28: ($i > $o) > $i > $i).
% 27.35/5.36 thf(func_def_218, type, sK29: $i > $i).
% 27.35/5.36 thf(func_def_219, type, sK30: $i > $i > $i).
% 27.35/5.36 thf(func_def_220, type, sK31: ($i > $o) > ($i > $o) > $i).
% 27.35/5.36 thf(func_def_221, type, sK32: ($i > $o) > ($i > $o) > $i).
% 27.35/5.36 thf(func_def_222, type, sK33: $i > ($i > $o) > $i).
% 27.35/5.36 thf(func_def_223, type, sK34: ($i > $o) > $i > $i).
% 27.35/5.36 thf(func_def_224, type, sK35: ($i > $o) > $i > $i).
% 27.35/5.36 thf(func_def_225, type, sK36: $i > ($i > $o) > $i).
% 27.35/5.36 thf(func_def_226, type, sK37: ($i > $o) > $i > $i).
% 27.35/5.36 thf(func_def_227, type, sK38: $i > ($i > $o) > $i).
% 27.35/5.36 thf(func_def_228, type, sK39: ($i > $o) > $i > $i).
% 27.35/5.36 thf(func_def_229, type, sK40: ($i > $o) > $i > $i).
% 27.35/5.36 thf(func_def_230, type, sK41: ($i > $o) > $i > $i).
% 27.35/5.36 thf(func_def_231, type, sK42: $i > ($i > $o) > $i).
% 27.35/5.36 thf(func_def_232, type, sK43: ($i > $o) > $i).
% 27.35/5.36 thf(func_def_233, type, sK44: ($i > $o) > $i > $i).
% 27.35/5.36 thf(func_def_234, type, sK45: ($i > $o) > $i).
% 27.35/5.36 thf(func_def_235, type, sK46: ($i > $o) > $i > $i).
% 27.35/5.36 thf(func_def_236, type, sK47: $i > $i > $i).
% 27.35/5.36 thf(func_def_237, type, sK48: $i > $i > $i).
% 27.35/5.36 thf(func_def_238, type, sK49: $i > $i > $i).
% 27.35/5.36 thf(func_def_239, type, sK50: $i > ($i > $o) > $i).
% 27.35/5.36 thf(func_def_240, type, sK51: $i > $i).
% 27.35/5.36 thf(func_def_241, type, sK52: $i > $i).
% 27.35/5.36 thf(func_def_242, type, sK53: $i > $i > $i).
% 27.35/5.36 thf(func_def_243, type, sK54: $i > ($i > $o) > $i).
% 27.35/5.36 thf(func_def_244, type, sK55: $i > $i > $i).
% 27.35/5.36 thf(func_def_245, type, sK56: ($i > $o) > $i > $i).
% 27.35/5.36 thf(func_def_246, type, sK57: ($i > $o) > $i > $i).
% 27.35/5.36 thf(func_def_247, type, sK58: $i > $i > $i).
% 27.35/5.36 thf(func_def_248, type, sK59: ($i > $o) > $i).
% 27.35/5.36 thf(func_def_249, type, sK60: $i > ($i > $o) > $i).
% 27.35/5.36 thf(func_def_250, type, sK61: ($i > $o) > ($i > $o) > $i).
% 27.35/5.36 thf(func_def_251, type, sK62: ($i > $o) > ($i > $o) > $i).
% 27.35/5.36 thf(func_def_252, type, sK63: ($i > $o) > ($i > $o) > $i).
% 27.35/5.36 thf(func_def_253, type, sK64: ($i > $o) > ($i > $o) > $i).
% 27.35/5.36 thf(func_def_254, type, sK65: ($i > $o) > ($i > $o) > $i).
% 27.35/5.36 thf(func_def_255, type, sK66: ($i > $o) > ($i > $o) > $i).
% 27.35/5.36 thf(func_def_256, type, sK67: ($i > $o) > ($i > $o) > $i).
% 27.35/5.36 thf(func_def_257, type, sK68: ($i > $o) > ($i > $o) > $i).
% 27.35/5.36 thf(func_def_258, type, sK69: ($i > $o) > $i).
% 27.35/5.36 thf(func_def_259, type, sK70: ($i > $o) > ($i > $o) > $i).
% 27.35/5.36 thf(func_def_260, type, sK71: $i > ($i > $o) > $i).
% 27.35/5.36 thf(func_def_261, type, sK72: ($i > $o) > ($i > $o) > $i).
% 27.35/5.36 thf(func_def_262, type, sK73: ($i > $o) > ($i > $o) > $i).
% 27.35/5.36 thf(func_def_263, type, sK74: ($i > $o) > $i > $i).
% 27.35/5.36 thf(func_def_264, type, sK75: ($i > $o) > ($i > $o) > $i).
% 27.35/5.36 thf(func_def_265, type, sK76: ($i > $o) > ($i > $o) > $i).
% 27.35/5.36 thf(func_def_266, type, sK77: $i > ($i > $o) > $i).
% 27.35/5.36 thf(func_def_267, type, sK78: $i > $i > $i).
% 27.35/5.36 thf(func_def_268, type, sK79: ($i > $o) > $i).
% 27.35/5.36 thf(func_def_269, type, sK80: ($i > $o) > $i).
% 27.35/5.36 thf(func_def_270, type, sK81: ($i > $o) > $i).
% 27.35/5.36 thf(func_def_271, type, sK82: ($i > $o) > $i).
% 27.35/5.36 thf(func_def_272, type, sK83: $i > $i).
% 27.35/5.36 thf(func_def_273, type, sK84: ($i > $o) > $i > ($i > $o) > $i > $i).
% 27.35/5.36 thf(func_def_274, type, sK85: $i > $i > ($i > $o) > ($i > $o) > $i).
% 27.35/5.36 thf(func_def_275, type, sK86: $i > $i).
% 27.35/5.36 thf(func_def_276, type, sK87: $i > $i > $i).
% 27.35/5.36 thf(func_def_277, type, sK88: $i > ($i > $o) > $i).
% 27.35/5.36 thf(func_def_278, type, ph89: !>[X0: $tType]:(X0)).
% 27.35/5.36 thf(f4046,plain,(
% 27.35/5.36 $false),
% 27.35/5.36 inference(trivial_inequality_removal,[status(thm)],[f4045])).
% 27.35/5.36 thf(f4045,plain,(
% 27.35/5.36 ($false = $true)),
% 27.35/5.36 inference(forward_demodulation,[status(thm)],[f4044,f932])).
% 27.35/5.36 thf(f932,plain,(
% 27.35/5.36 ((sP6 @ $true) = $false)),
% 27.35/5.36 introduced(definition,[new_symbols(naming,[sP6])],[inequality_splitting_name_introduction])).
% 27.35/5.36 thf(f4044,plain,(
% 27.35/5.36 ((sP6 @ $true) = $true)),
% 27.35/5.36 inference(trivial_inequality_removal,[status(thm)],[f4043])).
% 27.35/5.36 thf(f4043,plain,(
% 27.35/5.36 ((sP6 @ $true) = $true) | ($false = $true)),
% 27.35/5.36 inference(forward_demodulation,[status(thm)],[f4042,f931])).
% 27.35/5.36 thf(f931,plain,(
% 27.35/5.36 ((sP5 @ $true) = $false)),
% 27.35/5.36 introduced(definition,[new_symbols(naming,[sP5])],[inequality_splitting_name_introduction])).
% 27.35/5.36 thf(f4042,plain,(
% 27.35/5.36 ((sP5 @ $true) = $true) | ((sP6 @ $true) = $true)),
% 27.35/5.36 inference(forward_demodulation,[status(thm)],[f4041,f3971])).
% 27.35/5.36 thf(f3971,plain,(
% 27.35/5.36 ((in @ sK90 @ sK2) = $true)),
% 27.35/5.36 inference(binary_proxy_clausification,[status(thm)],[f3970])).
% 27.35/5.36 thf(f3970,plain,(
% 27.35/5.36 (((?? @ $i @ (^[Y0 : $i]: (((setadjoin @ (setadjoin @ sK90 @ emptyset) @ (setadjoin @ (setadjoin @ sK90 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK1) & (in @ Y0 @ sK0)))) & (in @ sK90 @ sK2)) = $true)),
% 27.35/5.36 inference(beta_eta_normalization,[status(thm)],[f3969])).
% 27.35/5.36 thf(f3969,plain,(
% 27.35/5.36 ($true = ((^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = sK1) & (in @ Y1 @ sK0)))) & (in @ Y0 @ sK2))) @ sK90))),
% 27.35/5.36 inference(sigma_clausification,[status(thm)],[f3968])).
% 27.35/5.36 thf(f3968,plain,(
% 27.35/5.36 ($true = (?? @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = sK1) & (in @ Y1 @ sK0)))) & (in @ Y0 @ sK2)))))),
% 27.35/5.36 inference(beta_eta_normalization,[status(thm)],[f3967])).
% 27.35/5.36 thf(f3967,plain,(
% 27.35/5.36 (((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ sK0)))) & (in @ Y1 @ sK2))))) @ sK1) = $true)),
% 27.35/5.36 inference(trivial_inequality_removal,[status(thm)],[f3958])).
% 27.35/5.36 thf(f3958,plain,(
% 27.35/5.36 (((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ sK0)))) & (in @ Y1 @ sK2))))) @ sK1) = $true) | ($false = $true)),
% 27.35/5.36 inference(superposition,[status(thm)],[f1893,f1249])).
% 27.35/5.36 thf(f1249,plain,(
% 27.35/5.36 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($false = (in @ X1 @ (dsetconstr @ X2 @ X3))) | ($true = (X3 @ X1))) )),
% 27.35/5.36 inference(binary_proxy_clausification,[status(thm)],[f1248])).
% 27.35/5.36 thf(f1248,plain,(
% 27.35/5.36 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($true = ((in @ X1 @ (dsetconstr @ X2 @ X3)) => (X3 @ X1)))) )),
% 27.35/5.36 inference(beta_eta_normalization,[status(thm)],[f1247])).
% 27.35/5.36 thf(f1247,plain,(
% 27.35/5.36 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : ((((^[Y0 : $i > $o]: ((in @ X1 @ (dsetconstr @ X2 @ Y0)) => (Y0 @ X1))) @ X3) = $true)) )),
% 27.35/5.36 inference(pi_clausification,[status(thm)],[f1246])).
% 27.35/5.36 thf(f1246,plain,(
% 27.35/5.36 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((in @ X1 @ (dsetconstr @ X2 @ Y0)) => (Y0 @ X1)))))) )),
% 27.35/5.36 inference(beta_eta_normalization,[status(thm)],[f1245])).
% 27.35/5.36 thf(f1245,plain,(
% 27.35/5.36 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ X1 @ (dsetconstr @ Y0 @ Y1)) => (Y1 @ X1))))) @ X2) = $true)) )),
% 27.35/5.36 inference(pi_clausification,[status(thm)],[f1244])).
% 27.35/5.36 thf(f1244,plain,(
% 27.35/5.36 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ X1 @ (dsetconstr @ Y0 @ Y1)) => (Y1 @ X1)))))) = $true)) )),
% 27.35/5.36 inference(beta_eta_normalization,[status(thm)],[f1243])).
% 27.35/5.36 thf(f1243,plain,(
% 27.35/5.36 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (Y2 @ Y0))))))) @ X1))) )),
% 27.35/5.36 inference(pi_clausification,[status(thm)],[f1242])).
% 27.35/5.36 thf(f1242,plain,(
% 27.35/5.36 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (Y2 @ Y0)))))))))),
% 27.35/5.36 inference(beta_eta_normalization,[status(thm)],[f881])).
% 27.35/5.36 thf(f881,plain,(
% 27.35/5.36 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (Y2 @ Y0)))))))) = $true)),
% 27.35/5.36 inference(definition_unfolding,[status(thm)],[f616,f584])).
% 27.35/5.36 thf(f584,plain,(
% 27.35/5.36 (dsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (Y2 @ Y0)))))))))),
% 27.35/5.36 inference(cnf_transformation,[status(thm)],[f405])).
% 27.35/5.36 thf(f405,plain,(
% 27.35/5.36 (dsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (Y2 @ Y0)))))))))),
% 27.35/5.36 inference(fool_elimination,[status(thm)],[f404])).
% 27.35/5.36 thf(f404,plain,(
% 27.35/5.36 (! [X0 : $i > $o,X1 : $i,X2 : $i] : ((in @ X2 @ (dsetconstr @ X1 @ (^[X3 : $i] : (X0 @ X3)))) => (X0 @ X2)) = dsetconstrER)),
% 27.35/5.36 inference(rectify,[status(thm)],[f16])).
% 27.35/5.36 thf(f16,axiom,(
% 27.35/5.36 (! [X0 : $i > $o,X3 : $i,X1 : $i] : ((in @ X1 @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))) => (X0 @ X1)) = dsetconstrER)),
% 27.35/5.36 file('/export/starexec/sandbox/tmp/tmp.X63vARrhRj/DTF2THF_30432.p',dsetconstrER)).
% 27.35/5.36 thf(f616,plain,(
% 27.35/5.36 (dsetconstrER = $true)),
% 27.35/5.36 inference(cnf_transformation,[status(thm)],[f459])).
% 27.35/5.36 thf(f459,plain,(
% 27.35/5.36 (singletoninpowunion = $true) & (setminusILneg = $true) & (kpairp = $true) & (binintersectEL = $true) & (binunionIL = $true) & (exuI1 = $true) & (upairinpowunion = $true) & (subPowSU = $true) & (secondinupair = $true) & (setadjoinE = $true) & (emptyinunitempty = $true) & (binintersectLsub = $true) & (notdallE = $true) & (emptysetimpfalse = $true) & (vacuousDall = $true) & (! [X3 : $i] : (! [X4 : $i] : ((sK1 != (kpair @ X3 @ X4)) | ((in @ X4 @ sK0) != $true)) | ((in @ X3 @ sK2) != $true)) & ((in @ sK1 @ (cartprod @ sK2 @ sK0)) = $true)) & (setextAx = $true) & (upairsetIL = $true) & (setunionE = $true) & (symdiffIneg1 = $true) & (prop2setI = $true) & (setminusEL = $true) & (setext = $true) & (nonemptyI = $true) & (dsetconstrEL = $true) & (binunionIR = $true) & (ubforcartprodlem2 = $true) & (subsetRefl = $true) & (nonemptyE1 = $true) & (quantDeMorgan1 = $true) & (upairsetE = $true) & (powerset__Cong = $true) & (notequalI1 = $true) & (subsetE2 = $true) & (setminusERneg = $true) & (nonemptyI1 = $true) & (quantDeMorgan4 = $true) & (subset2powerset = $true) & (quantDeMorgan2 = $true) & (symdiffI1 = $true) & (powersetI = $true) & (descrp = $true) & (powersetE = $true) & (setadjoinIL = $true) & (omegaSAx = $true) & (quantDeMorgan3 = $true) & (notsubsetI = $true) & (binintersectI = $true) & (binintersectSubset4 = $true) & (ubforcartprodlem1 = $true) & (emptysetAx = $true) & (kpairiskpair = $true) & (eqinunit = $true) & (setminusSubset2 = $true) & (setminusLsub = $true) & (binunionE = $true) & (setunionAx = $true) & (exu__Cong = $true) & (setminusELneg = $true) & (setminusER = $true) & (setbeta = $true) & (exuI3 = $true) & (binintersectSubset2 = $true) & (setukpairIL = $true) & (binintersectER = $true) & (prop2set2propI = $true) & (upairset2E = $true) & (binunionEcases = $true) & (notdexE = $true) & (cartprodpairin = $true) & (binintersectSubset3 = $true) & (emptyset__Cong = $true) & (exuE1 = $true) & (powersetAx = $true) & (setadjoin__Cong = $true) & (binunionLsub = $true) & (emptyinPowerset = $true) & (descr__Cong = $true) & (exuI2 = $true) & (setoftrueEq = $true) & (binintersectRsub = $true) & (setminusSubset1 = $true) & (singletoninpowerset = $true) & (binintersectSubset1 = $true) & (wellorderingAx = $true) & (in__Cong = $true) & (powersetI1 = $true) & (nonemptyImpWitness = $true) & (emptysetsubset = $true) & (setminusIRneg = $true) & (setukpairIR = $true) & (foundationAx = $true) & (setadjoinOr = $true) & (emptyInPowerset = $true) & (eqimpsubset1 = $true) & (eqimpsubset2 = $true) & (uniqinunit = $true) & (setadjoinSub = $true) & (powersetsubset = $true) & (omega__Cong = $true) & (singletonsubset = $true) & (setadjoinIR = $true) & (noeltsimpempty = $true) & (binunionRsub = $true) & (subsetI1 = $true) & (omegaIndAx = $true) & (sepInPowerset = $true) & (subsetI2 = $true) & (omega0Ax = $true) & (emptysetE = $true) & (binintersectSubset5 = $true) & (setunionI = $true) & (bs114d = $true) & (setunion__Cong = $true) & (symdiffIneg2 = $true) & (subsetemptysetimpeq = $true) & (exuE3u = $true) & (emptyI = $true) & (upairsubunion = $true) & (upairset2IR = $true) & (dsetconstrER = $true) & (sepSubset = $true) & (inCongP = $true) & (notinemptyset = $true) & (powersetE1 = $true) & (notinsingleton = $true) & (replAx = $true) & (notequalI2 = $true) & (singletonsswitch = $true) & (exuEu = $true) & (subsetTrans = $true) & (setminusI = $true) & (inPowerset = $true) & (emptyE1 = $true) & (upairsetIR = $true) & (setadjoinAx = $true) & (dsetconstrI = $true) & (ubforcartprodlem3 = $true) & (prop2setE = $true) & (setadjoinSub2 = $true) & (symdiffI2 = $true) & (dsetconstr__Cong = $true) & (subsetE = $true) & (setextsub = $true) & (exuE2 = $true) & (symdiffE = $true) & (disjointsetsI1 = $true) & (exuE3e = $true)),
% 27.35/5.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f457,f458])).
% 27.35/5.36 thf(f458,plain,(
% 27.35/5.36 ? [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (! [X4 : $i] : (((kpair @ X3 @ X4) != X1) | ((in @ X4 @ X0) != $true)) | ((in @ X3 @ X2) != $true)) & ((in @ X1 @ (cartprod @ X2 @ X0)) = $true)) => (! [X3 : $i] : (! [X4 : $i] : ((sK1 != (kpair @ X3 @ X4)) | ((in @ X4 @ sK0) != $true)) | ((in @ X3 @ sK2) != $true)) & ((in @ sK1 @ (cartprod @ sK2 @ sK0)) = $true))),
% 27.35/5.36 introduced(definition,[],[choice_axiom])).
% 27.35/5.36 thf(f457,plain,(
% 27.35/5.36 (singletoninpowunion = $true) & (setminusILneg = $true) & (kpairp = $true) & (binintersectEL = $true) & (binunionIL = $true) & (exuI1 = $true) & (upairinpowunion = $true) & (subPowSU = $true) & (secondinupair = $true) & (setadjoinE = $true) & (emptyinunitempty = $true) & (binintersectLsub = $true) & (notdallE = $true) & (emptysetimpfalse = $true) & (vacuousDall = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (! [X4 : $i] : (((kpair @ X3 @ X4) != X1) | ((in @ X4 @ X0) != $true)) | ((in @ X3 @ X2) != $true)) & ((in @ X1 @ (cartprod @ X2 @ X0)) = $true)) & (setextAx = $true) & (upairsetIL = $true) & (setunionE = $true) & (symdiffIneg1 = $true) & (prop2setI = $true) & (setminusEL = $true) & (setext = $true) & (nonemptyI = $true) & (dsetconstrEL = $true) & (binunionIR = $true) & (ubforcartprodlem2 = $true) & (subsetRefl = $true) & (nonemptyE1 = $true) & (quantDeMorgan1 = $true) & (upairsetE = $true) & (powerset__Cong = $true) & (notequalI1 = $true) & (subsetE2 = $true) & (setminusERneg = $true) & (nonemptyI1 = $true) & (quantDeMorgan4 = $true) & (subset2powerset = $true) & (quantDeMorgan2 = $true) & (symdiffI1 = $true) & (powersetI = $true) & (descrp = $true) & (powersetE = $true) & (setadjoinIL = $true) & (omegaSAx = $true) & (quantDeMorgan3 = $true) & (notsubsetI = $true) & (binintersectI = $true) & (binintersectSubset4 = $true) & (ubforcartprodlem1 = $true) & (emptysetAx = $true) & (kpairiskpair = $true) & (eqinunit = $true) & (setminusSubset2 = $true) & (setminusLsub = $true) & (binunionE = $true) & (setunionAx = $true) & (exu__Cong = $true) & (setminusELneg = $true) & (setminusER = $true) & (setbeta = $true) & (exuI3 = $true) & (binintersectSubset2 = $true) & (setukpairIL = $true) & (binintersectER = $true) & (prop2set2propI = $true) & (upairset2E = $true) & (binunionEcases = $true) & (notdexE = $true) & (cartprodpairin = $true) & (binintersectSubset3 = $true) & (emptyset__Cong = $true) & (exuE1 = $true) & (powersetAx = $true) & (setadjoin__Cong = $true) & (binunionLsub = $true) & (emptyinPowerset = $true) & (descr__Cong = $true) & (exuI2 = $true) & (setoftrueEq = $true) & (binintersectRsub = $true) & (setminusSubset1 = $true) & (singletoninpowerset = $true) & (binintersectSubset1 = $true) & (wellorderingAx = $true) & (in__Cong = $true) & (powersetI1 = $true) & (nonemptyImpWitness = $true) & (emptysetsubset = $true) & (setminusIRneg = $true) & (setukpairIR = $true) & (foundationAx = $true) & (setadjoinOr = $true) & (emptyInPowerset = $true) & (eqimpsubset1 = $true) & (eqimpsubset2 = $true) & (uniqinunit = $true) & (setadjoinSub = $true) & (powersetsubset = $true) & (omega__Cong = $true) & (singletonsubset = $true) & (setadjoinIR = $true) & (noeltsimpempty = $true) & (binunionRsub = $true) & (subsetI1 = $true) & (omegaIndAx = $true) & (sepInPowerset = $true) & (subsetI2 = $true) & (omega0Ax = $true) & (emptysetE = $true) & (binintersectSubset5 = $true) & (setunionI = $true) & (bs114d = $true) & (setunion__Cong = $true) & (symdiffIneg2 = $true) & (subsetemptysetimpeq = $true) & (exuE3u = $true) & (emptyI = $true) & (upairsubunion = $true) & (upairset2IR = $true) & (dsetconstrER = $true) & (sepSubset = $true) & (inCongP = $true) & (notinemptyset = $true) & (powersetE1 = $true) & (notinsingleton = $true) & (replAx = $true) & (notequalI2 = $true) & (singletonsswitch = $true) & (exuEu = $true) & (subsetTrans = $true) & (setminusI = $true) & (inPowerset = $true) & (emptyE1 = $true) & (upairsetIR = $true) & (setadjoinAx = $true) & (dsetconstrI = $true) & (ubforcartprodlem3 = $true) & (prop2setE = $true) & (setadjoinSub2 = $true) & (symdiffI2 = $true) & (dsetconstr__Cong = $true) & (subsetE = $true) & (setextsub = $true) & (exuE2 = $true) & (symdiffE = $true) & (disjointsetsI1 = $true) & (exuE3e = $true)),
% 27.35/5.36 inference(flattening,[status(thm)],[f456])).
% 27.35/5.36 thf(f456,plain,(
% 27.35/5.36 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (! [X4 : $i] : (((kpair @ X3 @ X4) != X1) | ((in @ X4 @ X0) != $true)) | ((in @ X3 @ X2) != $true)) & ((in @ X1 @ (cartprod @ X2 @ X0)) = $true)) & (cartprodpairin = $true)) & (ubforcartprodlem3 = $true)) & (ubforcartprodlem2 = $true)) & (ubforcartprodlem1 = $true)) & (upairinpowunion = $true)) & (upairsubunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (singletoninpowerset = $true)) & (singletonsubset = $true)) & (kpairp = $true)) & (kpairiskpair = $true)) & (setukpairIR = $true)) & (setukpairIL = $true)) & (secondinupair = $true)) & (symdiffIneg2 = $true)) & (symdiffIneg1 = $true)) & (symdiffI2 = $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 27.35/5.36 inference(ennf_transformation,[status(thm)],[f172])).
% 27.35/5.36 thf(f172,plain,(
% 27.35/5.36 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ((ubforcartprodlem1 = $true) => ((ubforcartprodlem2 = $true) => ((ubforcartprodlem3 = $true) => ((cartprodpairin = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (cartprod @ X2 @ X0)) = $true) => ? [X3 : $i] : (((in @ X3 @ X2) = $true) & ? [X4 : $i] : (((kpair @ X3 @ X4) = X1) & ((in @ X4 @ X0) = $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 27.35/5.36 inference(fool_elimination,[status(thm)],[f171])).
% 27.35/5.36 thf(f171,plain,(
% 27.35/5.36 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (cartprod @ X2 @ X0)) => ? [X3 : $i] : ((in @ X3 @ X2) & ? [X4 : $i] : (((kpair @ X3 @ X4) = X1) & (in @ X4 @ X0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 27.35/5.36 inference(rectify,[status(thm)],[f154])).
% 27.35/5.36 thf(f154,negated_conjecture,(
% 27.35/5.36 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => ! [X4 : $i,X10 : $i,X3 : $i] : ((in @ X10 @ (cartprod @ X3 @ X4)) => ? [X1 : $i] : ((in @ X1 @ X3) & ? [X2 : $i] : (((kpair @ X1 @ X2) = X10) & (in @ X2 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 27.35/5.36 inference(negated_conjecture,[status(cth)],[f153])).
% 27.35/5.36 thf(f153,conjecture,(
% 27.35/5.36 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => ! [X4 : $i,X10 : $i,X3 : $i] : ((in @ X10 @ (cartprod @ X3 @ X4)) => ? [X1 : $i] : ((in @ X1 @ X3) & ? [X2 : $i] : (((kpair @ X1 @ X2) = X10) & (in @ X2 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 27.35/5.36 file('/export/starexec/sandbox/tmp/tmp.X63vARrhRj/DTF2THF_30432.p',cartprodmempair1)).
% 27.35/5.36 thf(f1893,plain,(
% 27.35/5.36 ((in @ sK1 @ (dsetconstr @ (powerset @ (powerset @ (binunion @ sK2 @ sK0))) @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ sK0)))) & (in @ Y1 @ sK2))))))) = $true)),
% 27.35/5.36 inference(beta_eta_normalization,[status(thm)],[f793])).
% 27.35/5.36 thf(f793,plain,(
% 27.35/5.36 ($true = (in @ sK1 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (powerset @ (binunion @ Y0 @ Y1))) @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((((^[Y5 : $i]: ((^[Y6 : $i]: (setadjoin @ (setadjoin @ Y5 @ emptyset) @ (setadjoin @ (setadjoin @ Y5 @ (setadjoin @ Y6 @ emptyset)) @ emptyset))))) @ Y3 @ Y4) = Y2) & (in @ Y4 @ Y1)))) & (in @ Y3 @ Y0))))))))) @ sK2 @ sK0)))),
% 27.35/5.36 inference(definition_unfolding,[status(thm)],[f721,f776])).
% 27.35/5.36 thf(f776,plain,(
% 27.35/5.36 (cartprod = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (powerset @ (binunion @ Y0 @ Y1))) @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((((^[Y5 : $i]: ((^[Y6 : $i]: (setadjoin @ (setadjoin @ Y5 @ emptyset) @ (setadjoin @ (setadjoin @ Y5 @ (setadjoin @ Y6 @ emptyset)) @ emptyset))))) @ Y3 @ Y4) = Y2) & (in @ Y4 @ Y1)))) & (in @ Y3 @ Y0))))))))))),
% 27.35/5.36 inference(definition_unfolding,[status(thm)],[f739,f563])).
% 27.35/5.36 thf(f563,plain,(
% 27.35/5.36 (kpair = (^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))),
% 27.35/5.36 inference(cnf_transformation,[status(thm)],[f311])).
% 27.35/5.36 thf(f311,plain,(
% 27.35/5.36 (kpair = (^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))),
% 27.35/5.36 inference(fool_elimination,[status(thm)],[f310])).
% 27.35/5.36 thf(f310,plain,(
% 27.35/5.36 (kpair = (^[X0 : $i, X1 : $i] : (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))),
% 27.35/5.36 inference(rectify,[status(thm)],[f140])).
% 27.35/5.36 thf(f140,axiom,(
% 27.35/5.36 (kpair = (^[X1 : $i, X2 : $i] : (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset))))),
% 27.35/5.36 file('/export/starexec/sandbox/tmp/tmp.X63vARrhRj/DTF2THF_30432.p',kpair)).
% 27.35/5.36 thf(f739,plain,(
% 27.35/5.36 (cartprod = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (powerset @ (binunion @ Y0 @ Y1))) @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y2) & (in @ Y4 @ Y1)))) & (in @ Y3 @ Y0))))))))))),
% 27.35/5.36 inference(cnf_transformation,[status(thm)],[f379])).
% 27.35/5.36 thf(f379,plain,(
% 27.35/5.36 (cartprod = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (powerset @ (binunion @ Y0 @ Y1))) @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y2) & (in @ Y4 @ Y1)))) & (in @ Y3 @ Y0))))))))))),
% 27.35/5.36 inference(fool_elimination,[status(thm)],[f378])).
% 27.35/5.36 thf(f378,plain,(
% 27.35/5.36 ((^[X0 : $i, X1 : $i] : (dsetconstr @ (powerset @ (powerset @ (binunion @ X0 @ X1))) @ (^[X2 : $i] : (? [X3 : $i] : ((in @ X3 @ X0) & ? [X4 : $i] : ((in @ X4 @ X1) & ((kpair @ X3 @ X4) = X2))))))) = cartprod)),
% 27.35/5.36 inference(rectify,[status(thm)],[f142])).
% 27.35/5.36 thf(f142,axiom,(
% 27.35/5.36 ((^[X3 : $i, X4 : $i] : (dsetconstr @ (powerset @ (powerset @ (binunion @ X3 @ X4))) @ (^[X1 : $i] : (? [X2 : $i] : ((in @ X2 @ X3) & ? [X8 : $i] : ((in @ X8 @ X4) & ((kpair @ X2 @ X8) = X1))))))) = cartprod)),
% 27.35/5.36 file('/export/starexec/sandbox/tmp/tmp.X63vARrhRj/DTF2THF_30432.p',cartprod)).
% 27.35/5.36 thf(f721,plain,(
% 27.35/5.36 ((in @ sK1 @ (cartprod @ sK2 @ sK0)) = $true)),
% 27.35/5.36 inference(cnf_transformation,[status(thm)],[f459])).
% 27.35/5.36 thf(f4041,plain,(
% 27.35/5.36 ((sP6 @ (in @ sK90 @ sK2)) = $true) | ((sP5 @ $true) = $true)),
% 27.35/5.36 inference(forward_demodulation,[status(thm)],[f4039,f3975])).
% 27.35/5.36 thf(f3975,plain,(
% 27.35/5.36 ((in @ sK91 @ sK0) = $true)),
% 27.35/5.36 inference(binary_proxy_clausification,[status(thm)],[f3974])).
% 27.35/5.36 thf(f3974,plain,(
% 27.35/5.36 ($true = (((setadjoin @ (setadjoin @ sK90 @ emptyset) @ (setadjoin @ (setadjoin @ sK90 @ (setadjoin @ sK91 @ emptyset)) @ emptyset)) = sK1) & (in @ sK91 @ sK0)))),
% 27.35/5.36 inference(beta_eta_normalization,[status(thm)],[f3973])).
% 27.35/5.36 thf(f3973,plain,(
% 27.35/5.36 (((^[Y0 : $i]: (((setadjoin @ (setadjoin @ sK90 @ emptyset) @ (setadjoin @ (setadjoin @ sK90 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK1) & (in @ Y0 @ sK0))) @ sK91) = $true)),
% 27.35/5.36 inference(sigma_clausification,[status(thm)],[f3972])).
% 27.35/5.36 thf(f3972,plain,(
% 27.35/5.36 ((?? @ $i @ (^[Y0 : $i]: (((setadjoin @ (setadjoin @ sK90 @ emptyset) @ (setadjoin @ (setadjoin @ sK90 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK1) & (in @ Y0 @ sK0)))) = $true)),
% 27.35/5.36 inference(binary_proxy_clausification,[status(thm)],[f3970])).
% 27.35/5.36 thf(f4039,plain,(
% 27.35/5.36 ((sP5 @ (in @ sK91 @ sK0)) = $true) | ((sP6 @ (in @ sK90 @ sK2)) = $true)),
% 27.35/5.36 inference(trivial_inequality_removal,[status(thm)],[f4037])).
% 27.35/5.36 thf(f4037,plain,(
% 27.35/5.36 ($false = $true) | ((sP5 @ (in @ sK91 @ sK0)) = $true) | ((sP6 @ (in @ sK90 @ sK2)) = $true)),
% 27.35/5.36 inference(superposition,[status(thm)],[f2260,f4005])).
% 27.35/5.36 thf(f4005,plain,(
% 27.35/5.36 ((sP4 @ (setadjoin @ (setadjoin @ sK90 @ emptyset) @ (setadjoin @ (setadjoin @ sK90 @ (setadjoin @ sK91 @ emptyset)) @ emptyset))) = $false)),
% 27.35/5.36 inference(backward_demodulation,[status(thm)],[f3993,f4004])).
% 27.35/5.36 thf(f4004,plain,(
% 27.35/5.36 ((setadjoin @ (setadjoin @ sK92 @ emptyset) @ (setadjoin @ (setadjoin @ sK92 @ (setadjoin @ sK93 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK90 @ emptyset) @ (setadjoin @ (setadjoin @ sK90 @ (setadjoin @ sK91 @ emptyset)) @ emptyset)))),
% 27.35/5.36 inference(backward_demodulation,[status(thm)],[f3989,f3977])).
% 27.35/5.36 thf(f3977,plain,(
% 27.35/5.36 (sK1 = (setadjoin @ (setadjoin @ sK90 @ emptyset) @ (setadjoin @ (setadjoin @ sK90 @ (setadjoin @ sK91 @ emptyset)) @ emptyset)))),
% 27.35/5.36 inference(equality_proxy_clausification,[status(thm)],[f3976])).
% 27.35/5.36 thf(f3976,plain,(
% 27.35/5.36 (((setadjoin @ (setadjoin @ sK90 @ emptyset) @ (setadjoin @ (setadjoin @ sK90 @ (setadjoin @ sK91 @ emptyset)) @ emptyset)) = sK1) = $true)),
% 27.35/5.36 inference(binary_proxy_clausification,[status(thm)],[f3974])).
% 27.35/5.36 thf(f3989,plain,(
% 27.35/5.36 ((setadjoin @ (setadjoin @ sK92 @ emptyset) @ (setadjoin @ (setadjoin @ sK92 @ (setadjoin @ sK93 @ emptyset)) @ emptyset)) = sK1)),
% 27.35/5.36 inference(equality_proxy_clausification,[status(thm)],[f3988])).
% 27.35/5.36 thf(f3988,plain,(
% 27.35/5.36 ($true = ((setadjoin @ (setadjoin @ sK92 @ emptyset) @ (setadjoin @ (setadjoin @ sK92 @ (setadjoin @ sK93 @ emptyset)) @ emptyset)) = sK1))),
% 27.35/5.36 inference(binary_proxy_clausification,[status(thm)],[f3986])).
% 27.35/5.36 thf(f3986,plain,(
% 27.35/5.36 ($true = (((setadjoin @ (setadjoin @ sK92 @ emptyset) @ (setadjoin @ (setadjoin @ sK92 @ (setadjoin @ sK93 @ emptyset)) @ emptyset)) = sK1) & (in @ sK93 @ sK0)))),
% 27.35/5.36 inference(beta_eta_normalization,[status(thm)],[f3985])).
% 27.35/5.36 thf(f3985,plain,(
% 27.35/5.36 ($true = ((^[Y0 : $i]: (((setadjoin @ (setadjoin @ sK92 @ emptyset) @ (setadjoin @ (setadjoin @ sK92 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK1) & (in @ Y0 @ sK0))) @ sK93))),
% 27.35/5.36 inference(sigma_clausification,[status(thm)],[f3984])).
% 27.35/5.36 thf(f3984,plain,(
% 27.35/5.36 ($true = (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ (setadjoin @ sK92 @ emptyset) @ (setadjoin @ (setadjoin @ sK92 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK1) & (in @ Y0 @ sK0)))))),
% 27.35/5.36 inference(binary_proxy_clausification,[status(thm)],[f3982])).
% 27.35/5.36 thf(f3982,plain,(
% 27.35/5.36 ($true = ((?? @ $i @ (^[Y0 : $i]: (((setadjoin @ (setadjoin @ sK92 @ emptyset) @ (setadjoin @ (setadjoin @ sK92 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = sK1) & (in @ Y0 @ sK0)))) & (in @ sK92 @ sK2)))),
% 27.35/5.36 inference(beta_eta_normalization,[status(thm)],[f3981])).
% 27.35/5.36 thf(f3981,plain,(
% 27.35/5.36 ($true = ((^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = sK1) & (in @ Y1 @ sK0)))) & (in @ Y0 @ sK2))) @ sK92))),
% 27.35/5.36 inference(sigma_clausification,[status(thm)],[f3980])).
% 27.35/5.36 thf(f3980,plain,(
% 27.35/5.36 ($true = (?? @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = sK1) & (in @ Y1 @ sK0)))) & (in @ Y0 @ sK2)))))),
% 27.35/5.36 inference(beta_eta_normalization,[status(thm)],[f3979])).
% 27.35/5.36 thf(f3979,plain,(
% 27.35/5.36 (((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ sK0)))) & (in @ Y1 @ sK2))))) @ sK1) = $true)),
% 27.35/5.36 inference(trivial_inequality_removal,[status(thm)],[f3962])).
% 27.35/5.36 thf(f3962,plain,(
% 27.35/5.36 ($false = $true) | (((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ sK0)))) & (in @ Y1 @ sK2))))) @ sK1) = $true)),
% 27.35/5.36 inference(superposition,[status(thm)],[f1249,f1893])).
% 27.35/5.36 thf(f3993,plain,(
% 27.35/5.36 ($false = (sP4 @ (setadjoin @ (setadjoin @ sK92 @ emptyset) @ (setadjoin @ (setadjoin @ sK92 @ (setadjoin @ sK93 @ emptyset)) @ emptyset))))),
% 27.35/5.36 inference(backward_demodulation,[status(thm)],[f930,f3989])).
% 27.35/5.36 thf(f930,plain,(
% 27.35/5.36 ($false = (sP4 @ sK1))),
% 27.35/5.36 introduced(definition,[new_symbols(naming,[sP4])],[inequality_splitting_name_introduction])).
% 27.35/5.36 thf(f2260,plain,(
% 27.35/5.36 ( ! [X3 : $i,X4 : $i] : (($true = (sP4 @ (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X4 @ emptyset)) @ emptyset)))) | ((sP5 @ (in @ X4 @ sK0)) = $true) | ($true = (sP6 @ (in @ X3 @ sK2)))) )),
% 27.35/5.36 inference(beta_eta_normalization,[status(thm)],[f933])).
% 27.35/5.36 thf(f933,plain,(
% 27.35/5.36 ( ! [X3 : $i,X4 : $i] : (($true = (sP4 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))) @ X3 @ X4))) | ($true = (sP6 @ (in @ X3 @ sK2))) | ((sP5 @ (in @ X4 @ sK0)) = $true)) )),
% 27.35/5.36 inference(inequality_splitting,[status(thm)],[f792,f932,f931,f930])).
% 27.35/5.36 thf(f792,plain,(
% 27.35/5.36 ( ! [X3 : $i,X4 : $i] : ((sK1 != ((^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))) @ X3 @ X4)) | ((in @ X4 @ sK0) != $true) | ((in @ X3 @ sK2) != $true)) )),
% 27.35/5.36 inference(definition_unfolding,[status(thm)],[f722,f563])).
% 27.35/5.36 thf(f722,plain,(
% 27.35/5.36 ( ! [X3 : $i,X4 : $i] : ((sK1 != (kpair @ X3 @ X4)) | ((in @ X4 @ sK0) != $true) | ((in @ X3 @ sK2) != $true)) )),
% 27.35/5.36 inference(cnf_transformation,[status(thm)],[f459])).
% 27.35/5.36 % SZS output end Proof for DTF2THF_30432
% 27.35/5.36 % (30655)------------------------------
% 27.35/5.36 % (30655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.35/5.36 % (30655)Termination reason: Refutation
% 27.35/5.36
% 27.35/5.36 % (30655)Memory used [KB]: 4221
% 27.35/5.36 % (30655)Time elapsed: 0.348 s
% 27.35/5.36 % (30655)Instructions burned: 702 (million)
% 27.35/5.36 % (30655)------------------------------
% 27.35/5.36 % (30655)------------------------------
% 27.35/5.36 % (30530)Success in time 3.613 s
%------------------------------------------------------------------------------