%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU619^1 : 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 : n013.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 09:35:39 AM UTC 2026
% Result : Theorem 29.08s 5.36s
% Output : Refutation 29.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 52 ( 33 unt; 0 typ; 1 def)
% Number of atoms : 2569 ( 607 equ; 0 cnn)
% Maximal formula atoms : 139 ( 49 avg)
% Number of connectives : 1962 ( 16 ~; 12 |; 424 &; 941 @)
% ( 1 <=>; 541 =>; 0 <=; 0 <~>)
% Maximal formula depth : 146 ( 21 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 246 ( 241 usr; 143 con; 0-4 aty)
% ( 16 !!; 11 ??; 0 @@+; 0 @@-)
% Number of variables : 87 ( 38 ^; 39 !; 10 ?; 87 :)
% 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_177,type,
sK3: ( $i > $o ) > $i ).
thf(func_def_178,type,
sK4: ( $i > $o ) > $i > $i ).
thf(func_def_179,type,
sK5: ( $i > $o ) > $i > $i ).
thf(func_def_180,type,
sK6: $i > $i > $i ).
thf(func_def_181,type,
sK7: ( $i > $o ) > $i > $i ).
thf(func_def_182,type,
sK8: $i > $i > $i ).
thf(func_def_183,type,
sK9: $i > ( $i > $o ) > $i ).
thf(func_def_184,type,
sK10: ( $i > $o ) > $i ).
thf(func_def_185,type,
sK11: ( $i > $o ) > $i > $i ).
thf(func_def_186,type,
sK12: ( $i > $o ) > $i > $i ).
thf(func_def_187,type,
sK13: ( $i > $o ) > $i ).
thf(func_def_188,type,
sK14: $i > ( $i > $o ) > $i ).
thf(func_def_189,type,
sK15: $i > ( $i > $o ) > $i ).
thf(func_def_190,type,
sK16: $i > $i > $i ).
thf(func_def_191,type,
sK17: $i > $i ).
thf(func_def_192,type,
sK18: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_193,type,
sK19: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_194,type,
sK20: $i > ( $i > $o ) > $i ).
thf(func_def_195,type,
sK21: ( $i > $o ) > $i > $i ).
thf(func_def_196,type,
sK22: ( $i > $o ) > $i > $i ).
thf(func_def_197,type,
sK23: $i > ( $i > $o ) > $i ).
thf(func_def_198,type,
sK24: ( $i > $o ) > $i > $i ).
thf(func_def_199,type,
sK25: ( $i > $o ) > $i > $i ).
thf(func_def_200,type,
sK26: ( $i > $o ) > $i > $i ).
thf(func_def_201,type,
sK27: ( $i > $o ) > $i > $i ).
thf(func_def_202,type,
sK28: ( $i > $o ) > $i > $i ).
thf(func_def_203,type,
sK29: ( $i > $o ) > $i > $i ).
thf(func_def_204,type,
sK30: $i > $i ).
thf(func_def_205,type,
sK31: $i > $i > $i ).
thf(func_def_206,type,
sK32: $o > $i > $i > $i ).
thf(func_def_207,type,
sK33: ( $i > $o ) > $i > $i ).
thf(func_def_208,type,
sK34: $i > $i ).
thf(func_def_209,type,
sK35: $i > $i > $i ).
thf(func_def_210,type,
sK36: $i > $i > $i ).
thf(func_def_211,type,
sK37: $i > $i > $i ).
thf(func_def_212,type,
sK38: $i > $i > $i > $i ).
thf(func_def_213,type,
sK39: $i > ( $i > $o ) > $i ).
thf(func_def_214,type,
sK40: $i > ( $i > $i > $o ) > $i ).
thf(func_def_215,type,
sK41: $i > ( $i > $i > $o ) > $i ).
thf(func_def_216,type,
sK42: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_217,type,
sK43: $i > ( $i > $i > $o ) > $i ).
thf(func_def_218,type,
sK44: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_219,type,
sK45: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_220,type,
sK46: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_221,type,
sK47: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_222,type,
sK48: ( $i > $o ) > $i ).
thf(func_def_223,type,
sK49: ( $i > $o ) > $i ).
thf(func_def_224,type,
sK50: ( $i > $o ) > $i ).
thf(func_def_225,type,
sK51: ( $i > $o ) > $i ).
thf(func_def_226,type,
sK52: $i > $i > $i ).
thf(func_def_227,type,
sK53: $i > $i > $i ).
thf(func_def_228,type,
sK54: $i > $i ).
thf(func_def_229,type,
sK55: $i > $i ).
thf(func_def_230,type,
sK56: $i > $i ).
thf(func_def_231,type,
sK57: $i > $i > $i ).
thf(func_def_232,type,
sK58: $i > $i > $i ).
thf(func_def_233,type,
sK59: $i > ( $i > $o ) > $i ).
thf(func_def_234,type,
sK60: $i > $i ).
thf(func_def_235,type,
sK61: ( $i > $o ) > $i > $i ).
thf(func_def_236,type,
sK62: ( $i > $o ) > $i ).
thf(func_def_237,type,
sK63: ( $i > $o ) > $i > $i ).
thf(func_def_238,type,
sK64: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_239,type,
sK65: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_240,type,
sK66: ( $i > $o ) > $i ).
thf(func_def_241,type,
sK67: $i > ( $i > $o ) > $i ).
thf(func_def_242,type,
sK68: $i > ( $i > $o ) > $i ).
thf(func_def_243,type,
sK69: $i > ( $i > $o ) > $i ).
thf(func_def_244,type,
sK70: ( $i > $o ) > $i ).
thf(func_def_245,type,
sK71: $i > ( $i > $o ) > $i ).
thf(func_def_246,type,
sK72: ( $i > $o ) > $i ).
thf(func_def_247,type,
sK73: ( $i > $o ) > $i ).
thf(func_def_248,type,
sK74: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_249,type,
sK75: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_250,type,
sK76: $i > ( $i > $o ) > $i ).
thf(func_def_251,type,
sK77: $i > ( $i > $o ) > $i ).
thf(func_def_252,type,
sK78: $i > ( $i > $o ) > $i ).
thf(func_def_253,type,
sK79: $i > ( $i > $o ) > $i ).
thf(func_def_254,type,
sK80: $i > ( $i > $o ) > $i ).
thf(func_def_255,type,
sK81: $i > $i > $i ).
thf(func_def_256,type,
sK82: ( $i > $o ) > $i > ( $i > $o ) > $i > $i ).
thf(func_def_257,type,
sK83: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_258,type,
sK84: ( $i > $o ) > $i > $i ).
thf(func_def_259,type,
ph85:
!>[X0: $tType] : X0 ).
thf(f11762,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f11729,f11755]) ).
thf(f11755,plain,
~ spl2_31,
inference(avatar_contradiction_clause,[status(thm)],[f11754]) ).
thf(f11754,plain,
( $false
| ~ spl2_31 ),
inference(trivial_inequality_removal,[status(thm)],[f11747]) ).
thf(f11747,plain,
( ( $true = $false )
| ~ spl2_31 ),
inference(superposition,[status(thm)],[f938,f11728]) ).
thf(f11728,plain,
( ( ( in @ sK1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ~ spl2_31 ),
inference(avatar_component_clause,[status(thm)],[f11726]) ).
thf(f11726,definition,
( spl2_31
<=> ( ( in @ sK1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl2_31])],[avatar_definition]) ).
thf(f938,plain,
! [X2: $i,X1: $i] :
( ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f937]) ).
thf(f937,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f936]) ).
thf(f936,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f935]) ).
thf(f935,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f835]) ).
thf(f835,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f691,f593]) ).
thf(f593,plain,
setukpairIL = $true,
inference(cnf_transformation,[status(thm)],[f417]) ).
thf(f417,plain,
( ( subsetRefl = $true )
& ( dsetconstrER = $true )
& ( replAx = $true )
& ( dsetconstrEL = $true )
& ( subsetemptysetimpeq = $true )
& ( notequalI1 = $true )
& ( emptyInPowerset = $true )
& ( emptyinunitempty = $true )
& ( notdexE = $true )
& ( setadjoinOr = $true )
& ( dsetconstr__Cong = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( binunionE = $true )
& ( emptysetsubset = $true )
& ( binintersectRsub = $true )
& ( binunionLsub = $true )
& ( notinemptyset = $true )
& ( powerset__Cong = $true )
& ( powersetE = $true )
& ( symdiffIneg1 = $true )
& ( eqimpsubset2 = $true )
& ( powersetsubset = $true )
& ( setadjoinIL = $true )
& ( setadjoinSub = $true )
& ( nonemptyI1 = $true )
& ( symdiffE = $true )
& ( setukpairIL = $true )
& ( eqimpsubset1 = $true )
& ( symdiffI1 = $true )
& ( setoftrueEq = $true )
& ( emptyinPowerset = $true )
& ( quantDeMorgan2 = $true )
& ( notsubsetI = $true )
& ( exuE1 = $true )
& ( setadjoin__Cong = $true )
& ( upairset2IR = $true )
& ( exuE2 = $true )
& ( disjointsetsI1 = $true )
& ( secondinupair = $true )
& ( exuI2 = $true )
& ( subsetE2 = $true )
& ( binintersectSubset3 = $true )
& ( powersetAx = $true )
& ( setbeta = $true )
& ( setminusSubset2 = $true )
& ( setminusLsub = $true )
& ( emptyset__Cong = $true )
& ( binintersectLsub = $true )
& ( symdiffI2 = $true )
& ( inPowerset = $true )
& ( binintersectEL = $true )
& ( prop2setE = $true )
& ( binintersectI = $true )
& ( vacuousDall = $true )
& ( powersetE1 = $true )
& ( omega0Ax = $true )
& ( ( iskpair @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) )
!= $true )
& ( in__Cong = $true )
& ( subsetI1 = $true )
& ( binintersectSubset5 = $true )
& ( subsetTrans = $true )
& ( setadjoinE = $true )
& ( singletonsswitch = $true )
& ( emptyE1 = $true )
& ( noeltsimpempty = $true )
& ( descr__Cong = $true )
& ( setminusILneg = $true )
& ( emptysetAx = $true )
& ( prop2set2propI = $true )
& ( setminusSubset1 = $true )
& ( omegaIndAx = $true )
& ( nonemptyImpWitness = $true )
& ( emptyI = $true )
& ( inCongP = $true )
& ( setunionE = $true )
& ( bs114d = $true )
& ( exuI3 = $true )
& ( exuE3e = $true )
& ( binunionEcases = $true )
& ( exuI1 = $true )
& ( binintersectSubset4 = $true )
& ( foundationAx = $true )
& ( setminusELneg = $true )
& ( binunionIL = $true )
& ( setminusERneg = $true )
& ( setextAx = $true )
& ( subPowSU = $true )
& ( setminusER = $true )
& ( prop2setI = $true )
& ( emptysetimpfalse = $true )
& ( sepInPowerset = $true )
& ( subsetI2 = $true )
& ( setunion__Cong = $true )
& ( setextsub = $true )
& ( nonemptyI = $true )
& ( setext = $true )
& ( setadjoinSub2 = $true )
& ( binunionRsub = $true )
& ( exuEu = $true )
& ( quantDeMorgan3 = $true )
& ( binintersectER = $true )
& ( upairsetE = $true )
& ( subset2powerset = $true )
& ( nonemptyE1 = $true )
& ( quantDeMorgan4 = $true )
& ( upairsetIR = $true )
& ( powersetI1 = $true )
& ( symdiffIneg2 = $true )
& ( setminusEL = $true )
& ( setunionI = $true )
& ( notinsingleton = $true )
& ( exu__Cong = $true )
& ( omega__Cong = $true )
& ( setukpairIR = $true )
& ( notdallE = $true )
& ( setunionAx = $true )
& ( setminusI = $true )
& ( omegaSAx = $true )
& ( powersetI = $true )
& ( setadjoinIR = $true )
& ( setminusIRneg = $true )
& ( binintersectSubset2 = $true )
& ( wellorderingAx = $true )
& ( eqinunit = $true )
& ( quantDeMorgan1 = $true )
& ( binunionIR = $true )
& ( exuE3u = $true )
& ( uniqinunit = $true )
& ( setadjoinAx = $true )
& ( binintersectSubset1 = $true )
& ( notequalI2 = $true )
& ( sepSubset = $true )
& ( upairsetIL = $true )
& ( subsetE = $true )
& ( emptysetE = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f415,f416]) ).
thf(f416,plain,
( ? [X0: $i,X1: $i] :
( ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
!= $true )
=> ( ( iskpair @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f415,plain,
( ( subsetRefl = $true )
& ( dsetconstrER = $true )
& ( replAx = $true )
& ( dsetconstrEL = $true )
& ( subsetemptysetimpeq = $true )
& ( notequalI1 = $true )
& ( emptyInPowerset = $true )
& ( emptyinunitempty = $true )
& ( notdexE = $true )
& ( setadjoinOr = $true )
& ( dsetconstr__Cong = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( binunionE = $true )
& ( emptysetsubset = $true )
& ( binintersectRsub = $true )
& ( binunionLsub = $true )
& ( notinemptyset = $true )
& ( powerset__Cong = $true )
& ( powersetE = $true )
& ( symdiffIneg1 = $true )
& ( eqimpsubset2 = $true )
& ( powersetsubset = $true )
& ( setadjoinIL = $true )
& ( setadjoinSub = $true )
& ( nonemptyI1 = $true )
& ( symdiffE = $true )
& ( setukpairIL = $true )
& ( eqimpsubset1 = $true )
& ( symdiffI1 = $true )
& ( setoftrueEq = $true )
& ( emptyinPowerset = $true )
& ( quantDeMorgan2 = $true )
& ( notsubsetI = $true )
& ( exuE1 = $true )
& ( setadjoin__Cong = $true )
& ( upairset2IR = $true )
& ( exuE2 = $true )
& ( disjointsetsI1 = $true )
& ( secondinupair = $true )
& ( exuI2 = $true )
& ( subsetE2 = $true )
& ( binintersectSubset3 = $true )
& ( powersetAx = $true )
& ( setbeta = $true )
& ( setminusSubset2 = $true )
& ( setminusLsub = $true )
& ( emptyset__Cong = $true )
& ( binintersectLsub = $true )
& ( symdiffI2 = $true )
& ( inPowerset = $true )
& ( binintersectEL = $true )
& ( prop2setE = $true )
& ( binintersectI = $true )
& ( vacuousDall = $true )
& ( powersetE1 = $true )
& ( omega0Ax = $true )
& ? [X0: $i,X1: $i] :
( ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
!= $true )
& ( in__Cong = $true )
& ( subsetI1 = $true )
& ( binintersectSubset5 = $true )
& ( subsetTrans = $true )
& ( setadjoinE = $true )
& ( singletonsswitch = $true )
& ( emptyE1 = $true )
& ( noeltsimpempty = $true )
& ( descr__Cong = $true )
& ( setminusILneg = $true )
& ( emptysetAx = $true )
& ( prop2set2propI = $true )
& ( setminusSubset1 = $true )
& ( omegaIndAx = $true )
& ( nonemptyImpWitness = $true )
& ( emptyI = $true )
& ( inCongP = $true )
& ( setunionE = $true )
& ( bs114d = $true )
& ( exuI3 = $true )
& ( exuE3e = $true )
& ( binunionEcases = $true )
& ( exuI1 = $true )
& ( binintersectSubset4 = $true )
& ( foundationAx = $true )
& ( setminusELneg = $true )
& ( binunionIL = $true )
& ( setminusERneg = $true )
& ( setextAx = $true )
& ( subPowSU = $true )
& ( setminusER = $true )
& ( prop2setI = $true )
& ( emptysetimpfalse = $true )
& ( sepInPowerset = $true )
& ( subsetI2 = $true )
& ( setunion__Cong = $true )
& ( setextsub = $true )
& ( nonemptyI = $true )
& ( setext = $true )
& ( setadjoinSub2 = $true )
& ( binunionRsub = $true )
& ( exuEu = $true )
& ( quantDeMorgan3 = $true )
& ( binintersectER = $true )
& ( upairsetE = $true )
& ( subset2powerset = $true )
& ( nonemptyE1 = $true )
& ( quantDeMorgan4 = $true )
& ( upairsetIR = $true )
& ( powersetI1 = $true )
& ( symdiffIneg2 = $true )
& ( setminusEL = $true )
& ( setunionI = $true )
& ( notinsingleton = $true )
& ( exu__Cong = $true )
& ( omega__Cong = $true )
& ( setukpairIR = $true )
& ( notdallE = $true )
& ( setunionAx = $true )
& ( setminusI = $true )
& ( omegaSAx = $true )
& ( powersetI = $true )
& ( setadjoinIR = $true )
& ( setminusIRneg = $true )
& ( binintersectSubset2 = $true )
& ( wellorderingAx = $true )
& ( eqinunit = $true )
& ( quantDeMorgan1 = $true )
& ( binunionIR = $true )
& ( exuE3u = $true )
& ( uniqinunit = $true )
& ( setadjoinAx = $true )
& ( binintersectSubset1 = $true )
& ( notequalI2 = $true )
& ( sepSubset = $true )
& ( upairsetIL = $true )
& ( subsetE = $true )
& ( emptysetE = $true ) ),
inference(flattening,[status(thm)],[f414]) ).
thf(f414,plain,
( ? [X0: $i,X1: $i] :
( ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
!= $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)],[f207]) ).
thf(f207,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 )
=> ! [X0: $i,X1: $i] :
( ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f206]) ).
thf(f206,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
=> ! [X0: $i,X1: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f140]) ).
thf(f140,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
=> ! [X2: $i,X1: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f139]) ).
thf(f139,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
=> ! [X2: $i,X1: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CMzFP8z4xB/DTF2THF_22295.p',kpairiskpair) ).
thf(f691,plain,
( setukpairIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f335]) ).
thf(f335,plain,
( setukpairIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f334]) ).
thf(f334,plain,
! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) )
= setukpairIL ),
inference(rectify,[status(thm)],[f137]) ).
thf(f137,axiom,
! [X2: $i,X1: $i] :
( ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
= setukpairIL ),
file('/export/starexec/sandbox/tmp/tmp.CMzFP8z4xB/DTF2THF_22295.p',setukpairIL) ).
thf(f11729,plain,
spl2_31,
inference(avatar_split_clause,[status(thm)],[f11724,f11726]) ).
thf(f11724,plain,
( ( in @ sK1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f11723]) ).
thf(f11723,plain,
( ( $true = $false )
| ( ( in @ sK1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) )
= $false ) ),
inference(forward_demodulation,[status(thm)],[f11722,f934]) ).
thf(f934,plain,
! [X2: $i,X1: $i] :
( ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f933]) ).
thf(f933,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] : ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f932]) ).
thf(f932,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] : ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f931]) ).
thf(f931,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f752]) ).
thf(f752,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f506,f419]) ).
thf(f419,plain,
( setukpairIR
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f315]) ).
thf(f315,plain,
( setukpairIR
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f314]) ).
thf(f314,plain,
( setukpairIR
= ( ! [X0: $i,X1: $i] : ( in @ X0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(rectify,[status(thm)],[f138]) ).
thf(f138,axiom,
( setukpairIR
= ( ! [X2: $i,X1: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CMzFP8z4xB/DTF2THF_22295.p',setukpairIR) ).
thf(f506,plain,
setukpairIR = $true,
inference(cnf_transformation,[status(thm)],[f417]) ).
thf(f11722,plain,
( ( ( in @ sK0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( ( in @ sK1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) )
= $false ) ),
inference(equality_resolution,[status(thm)],[f1480]) ).
thf(f1480,plain,
! [X2: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) )
| ( ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) )
= $false )
| ( $false
= ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f1479]) ).
thf(f1479,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1478]) ).
thf(f1478,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( $false
= ( ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1477]) ).
thf(f1477,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) )
@ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f1476]) ).
thf(f1476,plain,
! [X1: $i] :
( ( $false
= ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1475]) ).
thf(f1475,plain,
! [X1: $i] :
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f1474]) ).
thf(f1474,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f1473]) ).
thf(f1473,plain,
( $true
!= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f719]) ).
thf(f719,plain,
( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y0 ) )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) )
& ( in @ Y1 @ ( setunion @ Y0 ) ) ) )
@ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f563,f650]) ).
thf(f650,plain,
( iskpair
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y0 ) )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) )
& ( in @ Y1 @ ( setunion @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f177]) ).
thf(f177,plain,
( iskpair
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y0 ) )
& ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) )
= Y0 ) ) )
& ( in @ Y1 @ ( setunion @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f176]) ).
thf(f176,plain,
( iskpair
= ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ ( setunion @ X0 ) )
& ? [X2: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= X0 )
& ( in @ X2 @ ( setunion @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f135]) ).
thf(f135,axiom,
( iskpair
= ( ^ [X3: $i] :
? [X1: $i] :
( ( in @ X1 @ ( setunion @ X3 ) )
& ? [X2: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= X3 )
& ( in @ X2 @ ( setunion @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.CMzFP8z4xB/DTF2THF_22295.p',iskpair) ).
thf(f563,plain,
( ( iskpair @ ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f417]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU619^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n013.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:28:23 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : SEU619^1 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.46 % Domain : Set Theory
% 0.20/0.46 % Problem : Ordered Pairs - Kuratowski Pairs
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English : (! x:i.! y:i.iskpair (setadjoin (setadjoin x emptyset) (setadjoin
% 0.20/0.46 % (setadjoin x (setadjoin y emptyset)) emptyset)))
% 0.20/0.46
% 0.20/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.20/0.46 % Source : [Bro08]
% 0.20/0.46 % Names : ZFC121g [Bro08]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v6.1.0, 0.43 v5.5.0, 0.33 v5.4.0, 0.60 v5.2.0, 1.00 v5.0.0, 0.80 v4.1.0, 1.00 v3.7.0
% 0.20/0.46 % Syntax : Number of formulae : 295 ( 138 unt; 156 typ; 138 def)
% 0.20/0.46 % Number of atoms : 734 ( 196 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 136 ( 5 avg)
% 0.20/0.46 % Number of connectives : 1216 ( 47 ~; 6 |; 30 &; 794 @)
% 0.20/0.46 % ( 14 <=>; 325 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 145 ( 2 avg)
% 0.20/0.46 % Number of types : 2 ( 0 usr)
% 0.20/0.46 % Number of type conns : 65 ( 65 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 159 ( 156 usr; 139 con; 0-2 aty)
% 0.20/0.46 % Number of variables : 397 ( 31 ^; 335 !; 31 ?; 397 :)
% 0.20/0.46 % SPC : TH0_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : http://mathgate.info/detsetitem.php?id=174
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(in_type,type,
% 0.20/0.46 in: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(exu_type,type,
% 0.20/0.46 exu: ( $i > $o ) > $o ).
% 0.20/0.46
% 0.20/0.46 thf(exu,definition,
% 0.20/0.46 ( exu
% 0.20/0.46 = ( ^ [Xphi: $i > $o] :
% 0.20/0.46 ? [Xx: $i] :
% 0.20/0.46 ( ( Xphi @ Xx )
% 0.20/0.46 & ! [Xy: $i] :
% 0.20/0.46 ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setextAx_type,type,
% 0.20/0.46 setextAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setextAx,definition,
% 0.20/0.46 ( setextAx
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 <=> ( in @ Xx @ B ) )
% 0.20/0.46 => ( A = B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptyset_type,type,
% 0.20/0.46 emptyset: $i ).
% 0.20/0.46
% 0.20/0.46 thf(emptysetAx_type,type,
% 0.20/0.46 emptysetAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptysetAx,definition,
% 0.20/0.46 ( emptysetAx
% 0.20/0.46 = ( ! [Xx: $i] :
% 0.20/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoin_type,type,
% 0.20/0.46 setadjoin: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinAx_type,type,
% 0.20/0.46 setadjoinAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinAx,definition,
% 0.20/0.46 ( setadjoinAx
% 0.20/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.20/0.46 <=> ( ( Xy = Xx )
% 0.20/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powerset_type,type,
% 0.20/0.46 powerset: $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(powersetAx_type,type,
% 0.20/0.46 powersetAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powersetAx,definition,
% 0.20/0.46 ( powersetAx
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.20/0.46 <=> ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setunion_type,type,
% 0.20/0.46 setunion: $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(setunionAx_type,type,
% 0.20/0.46 setunionAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setunionAx,definition,
% 0.20/0.46 ( setunionAx
% 0.20/0.46 = ( ! [A: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.20/0.46 <=> ? [B: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 & ( in @ B @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(omega_type,type,
% 0.20/0.46 omega: $i ).
% 0.20/0.46
% 0.20/0.46 thf(omega0Ax_type,type,
% 0.20/0.46 omega0Ax: $o ).
% 0.20/0.46
% 0.20/0.46 thf(omega0Ax,definition,
% 0.20/0.46 ( omega0Ax
% 0.20/0.46 = ( in @ emptyset @ omega ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(omegaSAx_type,type,
% 0.20/0.46 omegaSAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(omegaSAx,definition,
% 0.20/0.46 ( omegaSAx
% 0.20/0.46 = ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ omega )
% 0.20/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(omegaIndAx_type,type,
% 0.20/0.46 omegaIndAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(omegaIndAx,definition,
% 0.20/0.46 ( omegaIndAx
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ( ( in @ emptyset @ A )
% 0.20/0.46 & ! [Xx: $i] :
% 0.20/0.46 ( ( ( in @ Xx @ omega )
% 0.20/0.46 & ( in @ Xx @ A ) )
% 0.20/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ omega )
% 0.20/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(replAx_type,type,
% 0.20/0.46 replAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(replAx,definition,
% 0.20/0.46 ( replAx
% 0.20/0.46 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( exu
% 0.20/0.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.20/0.46 => ? [B: $i] :
% 0.20/0.46 ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 <=> ? [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(foundationAx_type,type,
% 0.20/0.46 foundationAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(foundationAx,definition,
% 0.20/0.46 ( foundationAx
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.20/0.46 => ? [B: $i] :
% 0.20/0.46 ( ( in @ B @ A )
% 0.20/0.46 & ~ ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(wellorderingAx_type,type,
% 0.20/0.46 wellorderingAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(wellorderingAx,definition,
% 0.20/0.46 ( wellorderingAx
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ? [B: $i] :
% 0.20/0.46 ( ! [C: $i] :
% 0.20/0.46 ( ( in @ C @ B )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ C )
% 0.20/0.47 => ( in @ Xx @ A ) ) )
% 0.20/0.47 & ! [Xx: $i,Xy: $i] :
% 0.20/0.47 ( ( ( in @ Xx @ A )
% 0.20/0.47 & ( in @ Xy @ A ) )
% 0.20/0.47 => ( ! [C: $i] :
% 0.20/0.47 ( ( in @ C @ B )
% 0.20/0.47 => ( ( in @ Xx @ C )
% 0.20/0.47 <=> ( in @ Xy @ C ) ) )
% 0.20/0.47 => ( Xx = Xy ) ) )
% 0.20/0.47 & ! [C: $i,D: $i] :
% 0.20/0.47 ( ( ( in @ C @ B )
% 0.20/0.47 & ( in @ D @ B ) )
% 0.20/0.47 => ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ C )
% 0.20/0.47 => ( in @ Xx @ D ) )
% 0.20/0.47 | ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ D )
% 0.20/0.47 => ( in @ Xx @ C ) ) ) )
% 0.20/0.47 & ! [C: $i] :
% 0.20/0.47 ( ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ C )
% 0.20/0.47 => ( in @ Xx @ A ) )
% 0.20/0.47 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.20/0.47 => ? [D: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ D @ B )
% 0.20/0.47 & ( in @ Xx @ C )
% 0.20/0.47 & ~ ? [Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ D )
% 0.20/0.47 & ( in @ Xy @ C ) )
% 0.20/0.47 & ! [E: $i] :
% 0.20/0.47 ( ( in @ E @ B )
% 0.20/0.47 => ( ! [Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ E )
% 0.20/0.47 => ( in @ Xy @ D ) )
% 0.20/0.47 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(descr_type,type,
% 0.20/0.47 descr: ( $i > $o ) > $i ).
% 0.20/0.47
% 0.20/0.47 thf(descrp_type,type,
% 0.20/0.47 descrp: $o ).
% 0.20/0.47
% 0.20/0.47 thf(descrp,definition,
% 0.20/0.47 ( descrp
% 0.20/0.47 = ( ! [Xphi: $i > $o] :
% 0.20/0.47 ( ( exu
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.47 => ( Xphi
% 0.20/0.47 @ ( descr
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(dsetconstr_type,type,
% 0.20/0.47 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.20/0.47
% 0.20/0.47 thf(dsetconstrI_type,type,
% 0.20/0.47 dsetconstrI: $o ).
% 0.20/0.47
% 0.20/0.47 thf(dsetconstrI,definition,
% 0.20/0.47 ( dsetconstrI
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( ( Xphi @ Xx )
% 0.20/0.47 => ( in @ Xx
% 0.20/0.47 @ ( dsetconstr @ A
% 0.20/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(dsetconstrEL_type,type,
% 0.20/0.47 dsetconstrEL: $o ).
% 0.20/0.47
% 0.20/0.47 thf(dsetconstrEL,definition,
% 0.20/0.47 ( dsetconstrEL
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx
% 0.20/0.47 @ ( dsetconstr @ A
% 0.20/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.20/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(dsetconstrER_type,type,
% 0.20/0.47 dsetconstrER: $o ).
% 0.20/0.47
% 0.20/0.47 thf(dsetconstrER,definition,
% 0.20/0.47 ( dsetconstrER
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx
% 0.20/0.47 @ ( dsetconstr @ A
% 0.20/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.20/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(exuE1_type,type,
% 0.20/0.47 exuE1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(exuE1,definition,
% 0.20/0.47 ( exuE1
% 0.20/0.47 = ( ! [Xphi: $i > $o] :
% 0.20/0.47 ( ( exu
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.47 => ? [Xx: $i] :
% 0.20/0.47 ( ( Xphi @ Xx )
% 0.20/0.47 & ! [Xy: $i] :
% 0.20/0.47 ( ( Xphi @ Xy )
% 0.20/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(prop2set_type,type,
% 0.20/0.47 prop2set: $o > $i ).
% 0.20/0.47
% 0.20/0.47 thf(prop2setE_type,type,
% 0.20/0.47 prop2setE: $o ).
% 0.20/0.47
% 0.20/0.47 thf(prop2setE,definition,
% 0.20/0.47 ( prop2setE
% 0.20/0.47 = ( ! [Xphi: $o,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.20/0.47 => Xphi ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(emptysetE_type,type,
% 0.20/0.47 emptysetE: $o ).
% 0.20/0.47
% 0.20/0.47 thf(emptysetE,definition,
% 0.20/0.47 ( emptysetE
% 0.20/0.47 = ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ emptyset )
% 0.20/0.47 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(emptysetimpfalse_type,type,
% 0.20/0.47 emptysetimpfalse: $o ).
% 0.20/0.47
% 0.20/0.47 thf(emptysetimpfalse,definition,
% 0.20/0.47 ( emptysetimpfalse
% 0.20/0.47 = ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ emptyset )
% 0.20/0.47 => $false ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(notinemptyset_type,type,
% 0.20/0.47 notinemptyset: $o ).
% 0.20/0.47
% 0.20/0.47 thf(notinemptyset,definition,
% 0.20/0.47 ( notinemptyset
% 0.20/0.47 = ( ! [Xx: $i] :
% 0.20/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(exuE3e_type,type,
% 0.20/0.47 exuE3e: $o ).
% 0.20/0.47
% 0.20/0.47 thf(exuE3e,definition,
% 0.20/0.47 ( exuE3e
% 0.20/0.47 = ( ! [Xphi: $i > $o] :
% 0.20/0.47 ( ( exu
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.47 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setext_type,type,
% 0.20/0.47 setext: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setext,definition,
% 0.20/0.47 ( setext
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( in @ Xx @ B ) )
% 0.20/0.47 => ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ B )
% 0.20/0.47 => ( in @ Xx @ A ) )
% 0.20/0.47 => ( A = B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(emptyI_type,type,
% 0.20/0.47 emptyI: $o ).
% 0.20/0.47
% 0.20/0.47 thf(emptyI,definition,
% 0.20/0.47 ( emptyI
% 0.20/0.47 = ( ! [A: $i] :
% 0.20/0.47 ( ! [Xx: $i] :
% 0.20/0.47 ~ ( in @ Xx @ A )
% 0.20/0.47 => ( A = emptyset ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(noeltsimpempty_type,type,
% 0.20/0.47 noeltsimpempty: $o ).
% 0.20/0.47
% 0.20/0.47 thf(noeltsimpempty,definition,
% 0.20/0.47 ( noeltsimpempty
% 0.20/0.47 = ( ! [A: $i] :
% 0.20/0.47 ( ! [Xx: $i] :
% 0.20/0.47 ~ ( in @ Xx @ A )
% 0.20/0.47 => ( A = emptyset ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setbeta_type,type,
% 0.20/0.47 setbeta: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setbeta,definition,
% 0.20/0.47 ( setbeta
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( ( in @ Xx
% 0.20/0.47 @ ( dsetconstr @ A
% 0.20/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.20/0.47 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(nonempty_type,type,
% 0.20/0.47 nonempty: $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(nonempty,definition,
% 0.20/0.47 ( nonempty
% 0.20/0.47 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(nonemptyE1_type,type,
% 0.20/0.47 nonemptyE1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(nonemptyE1,definition,
% 0.20/0.47 ( nonemptyE1
% 0.20/0.47 = ( ! [A: $i] :
% 0.20/0.47 ( ( nonempty @ A )
% 0.20/0.47 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(nonemptyI_type,type,
% 0.20/0.47 nonemptyI: $o ).
% 0.20/0.47
% 0.20/0.47 thf(nonemptyI,definition,
% 0.20/0.47 ( nonemptyI
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( ( Xphi @ Xx )
% 0.20/0.47 => ( nonempty
% 0.20/0.47 @ ( dsetconstr @ A
% 0.20/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(nonemptyI1_type,type,
% 0.20/0.47 nonemptyI1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(nonemptyI1,definition,
% 0.20/0.47 ( nonemptyI1
% 0.20/0.47 = ( ! [A: $i] :
% 0.20/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.20/0.47 => ( nonempty @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoinIL_type,type,
% 0.20/0.47 setadjoinIL: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoinIL,definition,
% 0.20/0.47 ( setadjoinIL
% 0.20/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(emptyinunitempty_type,type,
% 0.20/0.47 emptyinunitempty: $o ).
% 0.20/0.47
% 0.20/0.47 thf(emptyinunitempty,definition,
% 0.20/0.47 ( emptyinunitempty
% 0.20/0.47 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoinIR_type,type,
% 0.20/0.47 setadjoinIR: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoinIR,definition,
% 0.20/0.47 ( setadjoinIR
% 0.20/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ A )
% 0.20/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoinE_type,type,
% 0.20/0.47 setadjoinE: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoinE,definition,
% 0.20/0.47 ( setadjoinE
% 0.20/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.20/0.47 => ! [Xphi: $o] :
% 0.20/0.47 ( ( ( Xy = Xx )
% 0.20/0.47 => Xphi )
% 0.20/0.47 => ( ( ( in @ Xy @ A )
% 0.20/0.47 => Xphi )
% 0.20/0.47 => Xphi ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoinOr_type,type,
% 0.20/0.47 setadjoinOr: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoinOr,definition,
% 0.20/0.47 ( setadjoinOr
% 0.20/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.20/0.47 => ( ( Xy = Xx )
% 0.20/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setoftrueEq_type,type,
% 0.20/0.47 setoftrueEq: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setoftrueEq,definition,
% 0.20/0.47 ( setoftrueEq
% 0.20/0.47 = ( ! [A: $i] :
% 0.20/0.47 ( ( dsetconstr @ A
% 0.20/0.47 @ ^ [Xx: $i] : $true )
% 0.20/0.47 = A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(powersetI_type,type,
% 0.20/0.47 powersetI: $o ).
% 0.20/0.47
% 0.20/0.47 thf(powersetI,definition,
% 0.20/0.47 ( powersetI
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ B )
% 0.20/0.47 => ( in @ Xx @ A ) )
% 0.20/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(emptyinPowerset_type,type,
% 0.20/0.47 emptyinPowerset: $o ).
% 0.20/0.47
% 0.20/0.47 thf(emptyinPowerset,definition,
% 0.20/0.47 ( emptyinPowerset
% 0.20/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(emptyInPowerset_type,type,
% 0.20/0.47 emptyInPowerset: $o ).
% 0.20/0.47
% 0.20/0.47 thf(emptyInPowerset,definition,
% 0.20/0.47 ( emptyInPowerset
% 0.20/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(powersetE_type,type,
% 0.20/0.47 powersetE: $o ).
% 0.20/0.47
% 0.20/0.47 thf(powersetE,definition,
% 0.20/0.47 ( powersetE
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.20/0.47 => ( ( in @ Xx @ B )
% 0.20/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setunionI_type,type,
% 0.20/0.47 setunionI: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setunionI,definition,
% 0.20/0.47 ( setunionI
% 0.20/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.20/0.47 ( ( in @ Xx @ B )
% 0.20/0.47 => ( ( in @ B @ A )
% 0.20/0.47 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setunionE_type,type,
% 0.20/0.47 setunionE: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setunionE,definition,
% 0.20/0.47 ( setunionE
% 0.20/0.47 = ( ! [A: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.20/0.47 => ! [Xphi: $o] :
% 0.20/0.47 ( ! [B: $i] :
% 0.20/0.47 ( ( in @ Xx @ B )
% 0.20/0.47 => ( ( in @ B @ A )
% 0.20/0.47 => Xphi ) )
% 0.20/0.47 => Xphi ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(subPowSU_type,type,
% 0.20/0.47 subPowSU: $o ).
% 0.20/0.47
% 0.20/0.47 thf(subPowSU,definition,
% 0.20/0.47 ( subPowSU
% 0.20/0.47 = ( ! [A: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(exuE2_type,type,
% 0.20/0.47 exuE2: $o ).
% 0.20/0.47
% 0.20/0.47 thf(exuE2,definition,
% 0.20/0.47 ( exuE2
% 0.20/0.47 = ( ! [Xphi: $i > $o] :
% 0.20/0.47 ( ( exu
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.47 => ? [Xx: $i] :
% 0.20/0.47 ! [Xy: $i] :
% 0.20/0.47 ( ( Xphi @ Xy )
% 0.20/0.47 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(nonemptyImpWitness_type,type,
% 0.20/0.47 nonemptyImpWitness: $o ).
% 0.20/0.47
% 0.20/0.47 thf(nonemptyImpWitness,definition,
% 0.20/0.47 ( nonemptyImpWitness
% 0.20/0.47 = ( ! [A: $i] :
% 0.20/0.47 ( ( nonempty @ A )
% 0.20/0.47 => ? [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 & $true ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(uniqinunit_type,type,
% 0.20/0.47 uniqinunit: $o ).
% 0.20/0.47
% 0.20/0.47 thf(uniqinunit,definition,
% 0.20/0.47 ( uniqinunit
% 0.20/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.20/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(notinsingleton_type,type,
% 0.20/0.47 notinsingleton: $o ).
% 0.20/0.47
% 0.20/0.47 thf(notinsingleton,definition,
% 0.20/0.47 ( notinsingleton
% 0.20/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.47 ( ( Xx != Xy )
% 0.20/0.47 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(eqinunit_type,type,
% 0.20/0.47 eqinunit: $o ).
% 0.20/0.47
% 0.20/0.47 thf(eqinunit,definition,
% 0.20/0.47 ( eqinunit
% 0.20/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.47 ( ( Xx = Xy )
% 0.20/0.47 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(singletonsswitch_type,type,
% 0.20/0.47 singletonsswitch: $o ).
% 0.20/0.47
% 0.20/0.47 thf(singletonsswitch,definition,
% 0.20/0.47 ( singletonsswitch
% 0.20/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.20/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(upairsetE_type,type,
% 0.20/0.47 upairsetE: $o ).
% 0.20/0.47
% 0.20/0.47 thf(upairsetE,definition,
% 0.20/0.47 ( upairsetE
% 0.20/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.20/0.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.20/0.47 => ( ( Xz = Xx )
% 0.20/0.47 | ( Xz = Xy ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(upairsetIL_type,type,
% 0.20/0.47 upairsetIL: $o ).
% 0.20/0.47
% 0.20/0.47 thf(upairsetIL,definition,
% 0.20/0.47 ( upairsetIL
% 0.20/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(upairsetIR_type,type,
% 0.20/0.47 upairsetIR: $o ).
% 0.20/0.47
% 0.20/0.47 thf(upairsetIR,definition,
% 0.20/0.47 ( upairsetIR
% 0.20/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(emptyE1_type,type,
% 0.20/0.47 emptyE1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(emptyE1,definition,
% 0.20/0.47 ( emptyE1
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.47 ( ? [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 & ( Xphi @ Xx ) )
% 0.20/0.47 => ( ( ( dsetconstr @ A
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.47 = emptyset )
% 0.20/0.47 => $false ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(vacuousDall_type,type,
% 0.20/0.47 vacuousDall: $o ).
% 0.20/0.47
% 0.20/0.47 thf(vacuousDall,definition,
% 0.20/0.47 ( vacuousDall
% 0.20/0.47 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ emptyset )
% 0.20/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(quantDeMorgan1_type,type,
% 0.20/0.47 quantDeMorgan1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(quantDeMorgan1,definition,
% 0.20/0.47 ( quantDeMorgan1
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.47 ( ~ ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( Xphi @ Xx ) )
% 0.20/0.47 => ? [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(quantDeMorgan2_type,type,
% 0.20/0.47 quantDeMorgan2: $o ).
% 0.20/0.47
% 0.20/0.47 thf(quantDeMorgan2,definition,
% 0.20/0.47 ( quantDeMorgan2
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.47 ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ~ ( Xphi @ Xx ) )
% 0.20/0.47 => ~ ? [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(quantDeMorgan3_type,type,
% 0.20/0.47 quantDeMorgan3: $o ).
% 0.20/0.47
% 0.20/0.47 thf(quantDeMorgan3,definition,
% 0.20/0.47 ( quantDeMorgan3
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.47 ( ~ ? [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 & ( Xphi @ Xx ) )
% 0.20/0.47 => ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(quantDeMorgan4_type,type,
% 0.20/0.47 quantDeMorgan4: $o ).
% 0.20/0.47
% 0.20/0.47 thf(quantDeMorgan4,definition,
% 0.20/0.47 ( quantDeMorgan4
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.47 ( ? [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 & ~ ( Xphi @ Xx ) )
% 0.20/0.47 => ~ ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(prop2setI_type,type,
% 0.20/0.47 prop2setI: $o ).
% 0.20/0.47
% 0.20/0.47 thf(prop2setI,definition,
% 0.20/0.47 ( prop2setI
% 0.20/0.47 = ( ! [Xphi: $o] :
% 0.20/0.47 ( Xphi
% 0.20/0.47 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(set2prop_type,type,
% 0.20/0.47 set2prop: $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(prop2set2propI_type,type,
% 0.20/0.47 prop2set2propI: $o ).
% 0.20/0.47
% 0.20/0.47 thf(prop2set2propI,definition,
% 0.20/0.47 ( prop2set2propI
% 0.20/0.47 = ( ! [Xphi: $o] :
% 0.20/0.47 ( Xphi
% 0.20/0.47 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(notdexE_type,type,
% 0.20/0.47 notdexE: $o ).
% 0.20/0.47
% 0.20/0.47 thf(notdexE,definition,
% 0.20/0.47 ( notdexE
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.47 ( ~ ? [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 & ( Xphi @ Xx ) )
% 0.20/0.47 => ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(notdallE_type,type,
% 0.20/0.47 notdallE: $o ).
% 0.20/0.47
% 0.20/0.47 thf(notdallE,definition,
% 0.20/0.47 ( notdallE
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.47 ( ~ ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( Xphi @ Xx ) )
% 0.20/0.47 => ? [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(exuI1_type,type,
% 0.20/0.47 exuI1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(exuI1,definition,
% 0.20/0.47 ( exuI1
% 0.20/0.47 = ( ! [Xphi: $i > $o] :
% 0.20/0.47 ( ? [Xx: $i] :
% 0.20/0.47 ( ( Xphi @ Xx )
% 0.20/0.47 & ! [Xy: $i] :
% 0.20/0.47 ( ( Xphi @ Xy )
% 0.20/0.47 => ( Xx = Xy ) ) )
% 0.20/0.47 => ( exu
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(exuI3_type,type,
% 0.20/0.47 exuI3: $o ).
% 0.20/0.47
% 0.20/0.47 thf(exuI3,definition,
% 0.20/0.47 ( exuI3
% 0.20/0.47 = ( ! [Xphi: $i > $o] :
% 0.20/0.47 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.20/0.47 => ( ! [Xx: $i,Xy: $i] :
% 0.20/0.47 ( ( Xphi @ Xx )
% 0.20/0.47 => ( ( Xphi @ Xy )
% 0.20/0.47 => ( Xx = Xy ) ) )
% 0.20/0.47 => ( exu
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(exuI2_type,type,
% 0.20/0.47 exuI2: $o ).
% 0.20/0.47
% 0.20/0.47 thf(exuI2,definition,
% 0.20/0.47 ( exuI2
% 0.20/0.47 = ( ! [Xphi: $i > $o] :
% 0.20/0.47 ( ? [Xx: $i] :
% 0.20/0.47 ! [Xy: $i] :
% 0.20/0.47 ( ( Xphi @ Xy )
% 0.20/0.47 <=> ( Xy = Xx ) )
% 0.20/0.47 => ( exu
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(inCongP_type,type,
% 0.20/0.47 inCongP: $o ).
% 0.20/0.47
% 0.20/0.47 thf(inCongP,definition,
% 0.20/0.47 ( inCongP
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( A = B )
% 0.20/0.47 => ! [Xx: $i,Xy: $i] :
% 0.20/0.47 ( ( Xx = Xy )
% 0.20/0.47 => ( ( in @ Xx @ A )
% 0.20/0.47 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(in__Cong_type,type,
% 0.20/0.47 in__Cong: $o ).
% 0.20/0.47
% 0.20/0.47 thf(in__Cong,definition,
% 0.20/0.47 ( in__Cong
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( A = B )
% 0.20/0.47 => ! [Xx: $i,Xy: $i] :
% 0.20/0.47 ( ( Xx = Xy )
% 0.20/0.47 => ( ( in @ Xx @ A )
% 0.20/0.47 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(exuE3u_type,type,
% 0.20/0.47 exuE3u: $o ).
% 0.20/0.47
% 0.20/0.47 thf(exuE3u,definition,
% 0.20/0.47 ( exuE3u
% 0.20/0.47 = ( ! [Xphi: $i > $o] :
% 0.20/0.47 ( ( exu
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.47 => ! [Xx: $i,Xy: $i] :
% 0.20/0.47 ( ( Xphi @ Xx )
% 0.20/0.47 => ( ( Xphi @ Xy )
% 0.20/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(exu__Cong_type,type,
% 0.20/0.47 exu__Cong: $o ).
% 0.20/0.47
% 0.20/0.47 thf(exu__Cong,definition,
% 0.20/0.47 ( exu__Cong
% 0.20/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.20/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.20/0.47 ( ( Xx = Xy )
% 0.20/0.47 => ( ( Xphi @ Xx )
% 0.20/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.20/0.47 => ( ( exu
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.47 <=> ( exu
% 0.20/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(emptyset__Cong_type,type,
% 0.20/0.47 emptyset__Cong: $o ).
% 0.20/0.47
% 0.20/0.47 thf(emptyset__Cong,definition,
% 0.20/0.47 ( emptyset__Cong
% 0.20/0.47 = ( emptyset = emptyset ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoin__Cong_type,type,
% 0.20/0.47 setadjoin__Cong: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoin__Cong,definition,
% 0.20/0.47 ( setadjoin__Cong
% 0.20/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.47 ( ( Xx = Xy )
% 0.20/0.47 => ! [Xz: $i,Xu: $i] :
% 0.20/0.47 ( ( Xz = Xu )
% 0.20/0.47 => ( ( setadjoin @ Xx @ Xz )
% 0.20/0.47 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(powerset__Cong_type,type,
% 0.20/0.47 powerset__Cong: $o ).
% 0.20/0.47
% 0.20/0.47 thf(powerset__Cong,definition,
% 0.20/0.47 ( powerset__Cong
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( A = B )
% 0.20/0.47 => ( ( powerset @ A )
% 0.20/0.47 = ( powerset @ B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setunion__Cong_type,type,
% 0.20/0.47 setunion__Cong: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setunion__Cong,definition,
% 0.20/0.47 ( setunion__Cong
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( A = B )
% 0.20/0.47 => ( ( setunion @ A )
% 0.20/0.47 = ( setunion @ B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(omega__Cong_type,type,
% 0.20/0.47 omega__Cong: $o ).
% 0.20/0.47
% 0.20/0.47 thf(omega__Cong,definition,
% 0.20/0.47 ( omega__Cong
% 0.20/0.47 = ( omega = omega ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(exuEu_type,type,
% 0.20/0.47 exuEu: $o ).
% 0.20/0.47
% 0.20/0.47 thf(exuEu,definition,
% 0.20/0.47 ( exuEu
% 0.20/0.47 = ( ! [Xphi: $i > $o] :
% 0.20/0.47 ( ( exu
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.47 => ! [Xx: $i,Xy: $i] :
% 0.20/0.47 ( ( Xphi @ Xx )
% 0.20/0.47 => ( ( Xphi @ Xy )
% 0.20/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(descr__Cong_type,type,
% 0.20/0.47 descr__Cong: $o ).
% 0.20/0.47
% 0.20/0.47 thf(descr__Cong,definition,
% 0.20/0.47 ( descr__Cong
% 0.20/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.20/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.20/0.47 ( ( Xx = Xy )
% 0.20/0.47 => ( ( Xphi @ Xx )
% 0.20/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.20/0.47 => ( ( exu
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.47 => ( ( exu
% 0.20/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.20/0.47 => ( ( descr
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.47 = ( descr
% 0.20/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(dsetconstr__Cong_type,type,
% 0.20/0.47 dsetconstr__Cong: $o ).
% 0.20/0.47
% 0.20/0.47 thf(dsetconstr__Cong,definition,
% 0.20/0.47 ( dsetconstr__Cong
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( A = B )
% 0.20/0.47 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.20/0.47 ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ! [Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ B )
% 0.20/0.47 => ( ( Xx = Xy )
% 0.20/0.47 => ( ( Xphi @ Xx )
% 0.20/0.47 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.20/0.47 => ( ( dsetconstr @ A
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.47 = ( dsetconstr @ B
% 0.20/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(subset_type,type,
% 0.20/0.47 subset: $i > $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(disjoint_type,type,
% 0.20/0.47 disjoint: $i > $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(setsmeet_type,type,
% 0.20/0.47 setsmeet: $i > $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(subsetI1_type,type,
% 0.20/0.47 subsetI1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(subsetI1,definition,
% 0.20/0.47 ( subsetI1
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( in @ Xx @ B ) )
% 0.20/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(eqimpsubset2_type,type,
% 0.20/0.47 eqimpsubset2: $o ).
% 0.20/0.47
% 0.20/0.47 thf(eqimpsubset2,definition,
% 0.20/0.47 ( eqimpsubset2
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( A = B )
% 0.20/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(eqimpsubset1_type,type,
% 0.20/0.47 eqimpsubset1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(eqimpsubset1,definition,
% 0.20/0.47 ( eqimpsubset1
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( A = B )
% 0.20/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(subsetI2_type,type,
% 0.20/0.47 subsetI2: $o ).
% 0.20/0.47
% 0.20/0.47 thf(subsetI2,definition,
% 0.20/0.47 ( subsetI2
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( in @ Xx @ B ) )
% 0.20/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(emptysetsubset_type,type,
% 0.20/0.47 emptysetsubset: $o ).
% 0.20/0.47
% 0.20/0.47 thf(emptysetsubset,definition,
% 0.20/0.47 ( emptysetsubset
% 0.20/0.47 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(subsetE_type,type,
% 0.20/0.47 subsetE: $o ).
% 0.20/0.47
% 0.20/0.47 thf(subsetE,definition,
% 0.20/0.47 ( subsetE
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( subset @ A @ B )
% 0.20/0.47 => ( ( in @ Xx @ A )
% 0.20/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(subsetE2_type,type,
% 0.20/0.47 subsetE2: $o ).
% 0.20/0.47
% 0.20/0.47 thf(subsetE2,definition,
% 0.20/0.47 ( subsetE2
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( subset @ A @ B )
% 0.20/0.47 => ( ~ ( in @ Xx @ B )
% 0.20/0.47 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(notsubsetI_type,type,
% 0.20/0.47 notsubsetI: $o ).
% 0.20/0.47
% 0.20/0.47 thf(notsubsetI,definition,
% 0.20/0.47 ( notsubsetI
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( ~ ( in @ Xx @ B )
% 0.20/0.47 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(notequalI1_type,type,
% 0.20/0.47 notequalI1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(notequalI1,definition,
% 0.20/0.47 ( notequalI1
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ~ ( subset @ A @ B )
% 0.20/0.47 => ( A != B ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(notequalI2_type,type,
% 0.20/0.47 notequalI2: $o ).
% 0.20/0.47
% 0.20/0.47 thf(notequalI2,definition,
% 0.20/0.47 ( notequalI2
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( ~ ( in @ Xx @ B )
% 0.20/0.47 => ( A != B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(subsetRefl_type,type,
% 0.20/0.47 subsetRefl: $o ).
% 0.20/0.47
% 0.20/0.47 thf(subsetRefl,definition,
% 0.20/0.47 ( subsetRefl
% 0.20/0.47 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(subsetTrans_type,type,
% 0.20/0.47 subsetTrans: $o ).
% 0.20/0.47
% 0.20/0.47 thf(subsetTrans,definition,
% 0.20/0.47 ( subsetTrans
% 0.20/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.20/0.47 ( ( subset @ A @ B )
% 0.20/0.47 => ( ( subset @ B @ C )
% 0.20/0.47 => ( subset @ A @ C ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoinSub_type,type,
% 0.20/0.47 setadjoinSub: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoinSub,definition,
% 0.20/0.47 ( setadjoinSub
% 0.20/0.47 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoinSub2_type,type,
% 0.20/0.47 setadjoinSub2: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoinSub2,definition,
% 0.20/0.47 ( setadjoinSub2
% 0.20/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.20/0.47 ( ( subset @ A @ B )
% 0.20/0.47 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(subset2powerset_type,type,
% 0.20/0.47 subset2powerset: $o ).
% 0.20/0.47
% 0.20/0.47 thf(subset2powerset,definition,
% 0.20/0.47 ( subset2powerset
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( subset @ A @ B )
% 0.20/0.47 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setextsub_type,type,
% 0.20/0.47 setextsub: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setextsub,definition,
% 0.20/0.47 ( setextsub
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( subset @ A @ B )
% 0.20/0.47 => ( ( subset @ B @ A )
% 0.20/0.47 => ( A = B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(subsetemptysetimpeq_type,type,
% 0.20/0.47 subsetemptysetimpeq: $o ).
% 0.20/0.47
% 0.20/0.47 thf(subsetemptysetimpeq,definition,
% 0.20/0.47 ( subsetemptysetimpeq
% 0.20/0.47 = ( ! [A: $i] :
% 0.20/0.47 ( ( subset @ A @ emptyset )
% 0.20/0.47 => ( A = emptyset ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(powersetI1_type,type,
% 0.20/0.47 powersetI1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(powersetI1,definition,
% 0.20/0.47 ( powersetI1
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( subset @ B @ A )
% 0.20/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(powersetE1_type,type,
% 0.20/0.47 powersetE1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(powersetE1,definition,
% 0.20/0.47 ( powersetE1
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.20/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(inPowerset_type,type,
% 0.20/0.47 inPowerset: $o ).
% 0.20/0.47
% 0.20/0.47 thf(inPowerset,definition,
% 0.20/0.47 ( inPowerset
% 0.20/0.47 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(powersetsubset_type,type,
% 0.20/0.47 powersetsubset: $o ).
% 0.20/0.47
% 0.20/0.47 thf(powersetsubset,definition,
% 0.20/0.47 ( powersetsubset
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( subset @ A @ B )
% 0.20/0.47 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(sepInPowerset_type,type,
% 0.20/0.47 sepInPowerset: $o ).
% 0.20/0.47
% 0.20/0.47 thf(sepInPowerset,definition,
% 0.20/0.47 ( sepInPowerset
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.47 ( in
% 0.20/0.47 @ ( dsetconstr @ A
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.47 @ ( powerset @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(sepSubset_type,type,
% 0.20/0.47 sepSubset: $o ).
% 0.20/0.47
% 0.20/0.47 thf(sepSubset,definition,
% 0.20/0.47 ( sepSubset
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.47 ( subset
% 0.20/0.47 @ ( dsetconstr @ A
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.47 @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(binunion_type,type,
% 0.20/0.47 binunion: $i > $i > $i ).
% 0.20/0.47
% 0.20/0.47 thf(binunionIL_type,type,
% 0.20/0.47 binunionIL: $o ).
% 0.20/0.47
% 0.20/0.47 thf(binunionIL,definition,
% 0.20/0.47 ( binunionIL
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(upairset2IR_type,type,
% 0.20/0.47 upairset2IR: $o ).
% 0.20/0.47
% 0.20/0.47 thf(upairset2IR,definition,
% 0.20/0.47 ( upairset2IR
% 0.20/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(binunionIR_type,type,
% 0.20/0.47 binunionIR: $o ).
% 0.20/0.47
% 0.20/0.47 thf(binunionIR,definition,
% 0.20/0.47 ( binunionIR
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ B )
% 0.20/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(binunionEcases_type,type,
% 0.20/0.47 binunionEcases: $o ).
% 0.20/0.47
% 0.20/0.47 thf(binunionEcases,definition,
% 0.20/0.47 ( binunionEcases
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.20/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.20/0.47 => ( ( ( in @ Xx @ A )
% 0.20/0.47 => Xphi )
% 0.20/0.47 => ( ( ( in @ Xx @ B )
% 0.20/0.47 => Xphi )
% 0.20/0.47 => Xphi ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(binunionE_type,type,
% 0.20/0.47 binunionE: $o ).
% 0.20/0.47
% 0.20/0.47 thf(binunionE,definition,
% 0.20/0.47 ( binunionE
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.20/0.47 => ( ( in @ Xx @ A )
% 0.20/0.47 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(binunionLsub_type,type,
% 0.20/0.47 binunionLsub: $o ).
% 0.20/0.47
% 0.20/0.47 thf(binunionLsub,definition,
% 0.20/0.47 ( binunionLsub
% 0.20/0.47 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(binunionRsub_type,type,
% 0.20/0.47 binunionRsub: $o ).
% 0.20/0.47
% 0.20/0.47 thf(binunionRsub,definition,
% 0.20/0.47 ( binunionRsub
% 0.20/0.47 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(binintersect_type,type,
% 0.20/0.47 binintersect: $i > $i > $i ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectI_type,type,
% 0.20/0.47 binintersectI: $o ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectI,definition,
% 0.20/0.47 ( binintersectI
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( ( in @ Xx @ B )
% 0.20/0.47 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectSubset5_type,type,
% 0.20/0.47 binintersectSubset5: $o ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectSubset5,definition,
% 0.20/0.47 ( binintersectSubset5
% 0.20/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.20/0.47 ( ( subset @ C @ A )
% 0.20/0.47 => ( ( subset @ C @ B )
% 0.20/0.47 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectEL_type,type,
% 0.20/0.47 binintersectEL: $o ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectEL,definition,
% 0.20/0.47 ( binintersectEL
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.20/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectLsub_type,type,
% 0.20/0.47 binintersectLsub: $o ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectLsub,definition,
% 0.20/0.47 ( binintersectLsub
% 0.20/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectSubset2_type,type,
% 0.20/0.47 binintersectSubset2: $o ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectSubset2,definition,
% 0.20/0.47 ( binintersectSubset2
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( subset @ A @ B )
% 0.20/0.47 => ( ( binintersect @ A @ B )
% 0.20/0.47 = A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectSubset3_type,type,
% 0.20/0.47 binintersectSubset3: $o ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectSubset3,definition,
% 0.20/0.47 ( binintersectSubset3
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( ( binintersect @ A @ B )
% 0.20/0.47 = B )
% 0.20/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectER_type,type,
% 0.20/0.47 binintersectER: $o ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectER,definition,
% 0.20/0.47 ( binintersectER
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.20/0.47 => ( in @ Xx @ B ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(disjointsetsI1_type,type,
% 0.20/0.47 disjointsetsI1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(disjointsetsI1,definition,
% 0.20/0.47 ( disjointsetsI1
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ~ ? [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 & ( in @ Xx @ B ) )
% 0.20/0.47 => ( ( binintersect @ A @ B )
% 0.20/0.47 = emptyset ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectRsub_type,type,
% 0.20/0.47 binintersectRsub: $o ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectRsub,definition,
% 0.20/0.47 ( binintersectRsub
% 0.20/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectSubset4_type,type,
% 0.20/0.47 binintersectSubset4: $o ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectSubset4,definition,
% 0.20/0.47 ( binintersectSubset4
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( subset @ B @ A )
% 0.20/0.47 => ( ( binintersect @ A @ B )
% 0.20/0.47 = B ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectSubset1_type,type,
% 0.20/0.47 binintersectSubset1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectSubset1,definition,
% 0.20/0.47 ( binintersectSubset1
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( ( binintersect @ A @ B )
% 0.20/0.47 = A )
% 0.20/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(bs114d_type,type,
% 0.20/0.47 bs114d: $o ).
% 0.20/0.47
% 0.20/0.47 thf(bs114d,definition,
% 0.20/0.47 ( bs114d
% 0.20/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.20/0.47 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.20/0.47 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(regular_type,type,
% 0.20/0.47 regular: $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(setminus_type,type,
% 0.20/0.47 setminus: $i > $i > $i ).
% 0.20/0.47
% 0.20/0.47 thf(setminusI_type,type,
% 0.20/0.47 setminusI: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setminusI,definition,
% 0.20/0.47 ( setminusI
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( ~ ( in @ Xx @ B )
% 0.20/0.47 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setminusEL_type,type,
% 0.20/0.47 setminusEL: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setminusEL,definition,
% 0.20/0.47 ( setminusEL
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.20/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setminusER_type,type,
% 0.20/0.47 setminusER: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setminusER,definition,
% 0.20/0.47 ( setminusER
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.20/0.47 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setminusSubset2_type,type,
% 0.20/0.47 setminusSubset2: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setminusSubset2,definition,
% 0.20/0.47 ( setminusSubset2
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( subset @ A @ B )
% 0.20/0.47 => ( ( setminus @ A @ B )
% 0.20/0.47 = emptyset ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setminusERneg_type,type,
% 0.20/0.47 setminusERneg: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setminusERneg,definition,
% 0.20/0.47 ( setminusERneg
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.20/0.47 => ( ( in @ Xx @ A )
% 0.20/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setminusELneg_type,type,
% 0.20/0.47 setminusELneg: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setminusELneg,definition,
% 0.20/0.47 ( setminusELneg
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.20/0.47 => ( ~ ( in @ Xx @ B )
% 0.20/0.47 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setminusILneg_type,type,
% 0.20/0.47 setminusILneg: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setminusILneg,definition,
% 0.20/0.47 ( setminusILneg
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ~ ( in @ Xx @ A )
% 0.20/0.47 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setminusIRneg_type,type,
% 0.20/0.47 setminusIRneg: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setminusIRneg,definition,
% 0.20/0.47 ( setminusIRneg
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ B )
% 0.20/0.47 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setminusLsub_type,type,
% 0.20/0.47 setminusLsub: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setminusLsub,definition,
% 0.20/0.47 ( setminusLsub
% 0.20/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setminusSubset1_type,type,
% 0.20/0.47 setminusSubset1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setminusSubset1,definition,
% 0.20/0.47 ( setminusSubset1
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( ( setminus @ A @ B )
% 0.20/0.47 = emptyset )
% 0.20/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(symdiff_type,type,
% 0.20/0.47 symdiff: $i > $i > $i ).
% 0.20/0.47
% 0.20/0.47 thf(symdiffE_type,type,
% 0.20/0.47 symdiffE: $o ).
% 0.20/0.47
% 0.20/0.47 thf(symdiffE,definition,
% 0.20/0.47 ( symdiffE
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.20/0.47 => ! [Xphi: $o] :
% 0.20/0.47 ( ( ( in @ Xx @ A )
% 0.20/0.47 => ( ~ ( in @ Xx @ B )
% 0.20/0.47 => Xphi ) )
% 0.20/0.47 => ( ( ~ ( in @ Xx @ A )
% 0.20/0.47 => ( ( in @ Xx @ B )
% 0.20/0.47 => Xphi ) )
% 0.20/0.47 => Xphi ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(symdiffI1_type,type,
% 0.20/0.47 symdiffI1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(symdiffI1,definition,
% 0.20/0.47 ( symdiffI1
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( ~ ( in @ Xx @ B )
% 0.20/0.47 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(symdiffI2_type,type,
% 0.20/0.47 symdiffI2: $o ).
% 0.20/0.47
% 0.20/0.47 thf(symdiffI2,definition,
% 0.20/0.47 ( symdiffI2
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ~ ( in @ Xx @ A )
% 0.20/0.47 => ( ( in @ Xx @ B )
% 0.20/0.47 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(symdiffIneg1_type,type,
% 0.20/0.47 symdiffIneg1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(symdiffIneg1,definition,
% 0.20/0.47 ( symdiffIneg1
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( ( in @ Xx @ B )
% 0.20/0.47 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(symdiffIneg2_type,type,
% 0.20/0.47 symdiffIneg2: $o ).
% 0.20/0.47
% 0.20/0.47 thf(symdiffIneg2,definition,
% 0.20/0.47 ( symdiffIneg2
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ~ ( in @ Xx @ A )
% 0.20/0.47 => ( ~ ( in @ Xx @ B )
% 0.20/0.47 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(iskpair_type,type,
% 0.20/0.47 iskpair: $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(iskpair,definition,
% 0.20/0.47 ( iskpair
% 0.20/0.47 = ( ^ [A: $i] :
% 0.20/0.47 ? [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.20/0.47 & ? [Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ ( setunion @ A ) )
% 0.20/0.47 & ( A
% 0.20/0.47 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(secondinupair_type,type,
% 0.20/0.47 secondinupair: $o ).
% 0.20/0.47
% 0.20/0.47 thf(secondinupair,definition,
% 0.20/0.47 ( secondinupair
% 0.20/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setukpairIL_type,type,
% 0.20/0.47 setukpairIL: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setukpairIL,definition,
% 0.20/0.47 ( setukpairIL
% 0.20/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setukpairIR_type,type,
% 0.20/0.47 setukpairIR: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setukpairIR,definition,
% 0.20/0.47 ( setukpairIR
% 0.20/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(kpairiskpair,conjecture,
% 0.20/0.47 ( setextAx
% 0.20/0.47 => ( emptysetAx
% 0.20/0.47 => ( setadjoinAx
% 0.20/0.47 => ( powersetAx
% 0.20/0.47 => ( setunionAx
% 0.20/0.47 => ( omega0Ax
% 0.20/0.47 => ( omegaSAx
% 0.20/0.47 => ( omegaIndAx
% 0.20/0.47 => ( replAx
% 0.20/0.47 => ( foundationAx
% 0.20/0.47 => ( wellorderingAx
% 0.20/0.47 => ( descrp
% 0.20/0.47 => ( dsetconstrI
% 0.20/0.47 => ( dsetconstrEL
% 0.20/0.47 => ( dsetconstrER
% 0.20/0.47 => ( exuE1
% 0.20/0.47 => ( prop2setE
% 0.20/0.47 => ( emptysetE
% 0.20/0.47 => ( emptysetimpfalse
% 0.20/0.47 => ( notinemptyset
% 0.20/0.47 => ( exuE3e
% 0.20/0.47 => ( setext
% 0.20/0.47 => ( emptyI
% 0.20/0.47 => ( noeltsimpempty
% 0.20/0.47 => ( setbeta
% 0.20/0.47 => ( nonemptyE1
% 0.20/0.47 => ( nonemptyI
% 0.20/0.47 => ( nonemptyI1
% 0.20/0.47 => ( setadjoinIL
% 0.20/0.47 => ( emptyinunitempty
% 0.20/0.47 => ( setadjoinIR
% 0.20/0.47 => ( setadjoinE
% 0.20/0.47 => ( setadjoinOr
% 0.20/0.47 => ( setoftrueEq
% 0.20/0.47 => ( powersetI
% 0.20/0.47 => ( emptyinPowerset
% 0.20/0.47 => ( emptyInPowerset
% 0.20/0.47 => ( powersetE
% 0.20/0.47 => ( setunionI
% 0.20/0.47 => ( setunionE
% 0.20/0.47 => ( subPowSU
% 0.20/0.47 => ( exuE2
% 0.20/0.47 => ( nonemptyImpWitness
% 0.20/0.47 => ( uniqinunit
% 0.20/0.47 => ( notinsingleton
% 0.20/0.47 => ( eqinunit
% 0.20/0.47 => ( singletonsswitch
% 0.20/0.47 => ( upairsetE
% 0.20/0.47 => ( upairsetIL
% 0.20/0.47 => ( upairsetIR
% 0.20/0.47 => ( emptyE1
% 0.20/0.47 => ( vacuousDall
% 0.20/0.47 => ( quantDeMorgan1
% 0.20/0.47 => ( quantDeMorgan2
% 0.20/0.47 => ( quantDeMorgan3
% 0.20/0.47 => ( quantDeMorgan4
% 0.20/0.47 => ( prop2setI
% 0.20/0.47 => ( prop2set2propI
% 0.20/0.47 => ( notdexE
% 0.20/0.47 => ( notdallE
% 0.20/0.47 => ( exuI1
% 0.20/0.47 => ( exuI3
% 0.20/0.47 => ( exuI2
% 0.20/0.47 => ( inCongP
% 0.20/0.47 => ( in__Cong
% 0.20/0.47 => ( exuE3u
% 0.20/0.47 => ( exu__Cong
% 0.20/0.47 => ( emptyset__Cong
% 0.20/0.47 => ( setadjoin__Cong
% 0.20/0.47 => ( powerset__Cong
% 0.20/0.47 => ( setunion__Cong
% 0.20/0.47 => ( omega__Cong
% 0.20/0.47 => ( exuEu
% 0.20/0.47 => ( descr__Cong
% 0.20/0.47 => ( dsetconstr__Cong
% 0.20/0.47 => ( subsetI1
% 0.20/0.47 => ( eqimpsubset2
% 0.20/0.47 => ( eqimpsubset1
% 0.20/0.47 => ( subsetI2
% 0.20/0.47 => ( emptysetsubset
% 0.20/0.47 => ( subsetE
% 0.20/0.47 => ( subsetE2
% 0.20/0.47 => ( notsubsetI
% 0.20/0.47 => ( notequalI1
% 0.20/0.47 => ( notequalI2
% 0.20/0.47 => ( subsetRefl
% 0.20/0.47 => ( subsetTrans
% 0.20/0.47 => ( setadjoinSub
% 0.20/0.47 => ( setadjoinSub2
% 0.20/0.47 => ( subset2powerset
% 0.20/0.47 => ( setextsub
% 0.20/0.47 => ( subsetemptysetimpeq
% 0.20/0.47 => ( powersetI1
% 0.20/0.47 => ( powersetE1
% 0.20/0.47 => ( inPowerset
% 0.20/0.47 => ( powersetsubset
% 0.20/0.47 => ( sepInPowerset
% 0.20/0.47 => ( sepSubset
% 0.20/0.47 => ( binunionIL
% 0.20/0.47 => ( upairset2IR
% 0.20/0.47 => ( binunionIR
% 0.20/0.47 => ( binunionEcases
% 0.20/0.47 => ( binunionE
% 0.20/0.47 => ( binunionLsub
% 0.20/0.47 => ( binunionRsub
% 0.20/0.47 => ( binintersectI
% 0.20/0.47 => ( binintersectSubset5
% 0.20/0.47 => ( binintersectEL
% 0.20/0.47 => ( binintersectLsub
% 0.20/0.47 => ( binintersectSubset2
% 0.20/0.47 => ( binintersectSubset3
% 0.20/0.47 => ( binintersectER
% 0.20/0.47 => ( disjointsetsI1
% 0.20/0.47 => ( binintersectRsub
% 0.20/0.47 => ( binintersectSubset4
% 0.20/0.47 => ( binintersectSubset1
% 0.20/0.47 => ( bs114d
% 0.20/0.47 => ( setminusI
% 0.20/0.47 => ( setminusEL
% 0.20/0.47 => ( setminusER
% 0.20/0.47 => ( setminusSubset2
% 0.20/0.47 => ( setminusERneg
% 0.20/0.47 => ( setminusELneg
% 0.20/0.47 => ( setminusILneg
% 0.20/0.47 => ( setminusIRneg
% 0.20/0.47 => ( setminusLsub
% 0.20/0.47 => ( setminusSubset1
% 0.20/0.47 => ( symdiffE
% 0.20/0.47 => ( symdiffI1
% 0.20/0.47 => ( symdiffI2
% 0.20/0.47 => ( symdiffIneg1
% 0.20/0.47 => ( symdiffIneg2
% 0.20/0.47 => ( secondinupair
% 0.20/0.47 => ( setukpairIL
% 0.20/0.47 => ( setukpairIR
% 0.20/0.47 => ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 ------------------------
% 2.41/1.42 ---- Embedded in THF ---
% 2.41/1.42 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.41/1.42 %%% Generated on Tue Feb 24 12:28:24 EST 2026
% 2.41/1.42 %%% using '$$dhol' embedding, version 1.3.0.
% 2.41/1.42 %%% Logic specification used:
% 2.41/1.42 %%% thf(spec, logic, $$dhol).
% 2.41/1.42
% 2.41/1.42 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.CMzFP8z4xB/DTF2DTF22295.p
% See solution above
% 2.41/1.42 ------------------------
% 2.41/1.44 ---- Cleaned THF ---
% 2.41/1.44 thf(in_type,type,
% 2.41/1.44 in: $i > $i > $o ).
% 2.41/1.44
% 2.41/1.44 thf(exu_type,type,
% 2.41/1.44 exu: ( $i > $o ) > $o ).
% 2.41/1.44
% 2.41/1.44 thf(exu,definition,
% 2.41/1.44 ( exu
% 2.41/1.44 = ( ^ [Xphi: $i > $o] :
% 2.41/1.44 ? [Xx: $i] :
% 2.41/1.44 ( ( Xphi @ Xx )
% 2.41/1.44 & ! [Xy: $i] :
% 2.41/1.44 ( ( Xphi @ Xy )
% 2.41/1.44 => ( Xx = Xy ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(setextAx_type,type,
% 2.41/1.44 setextAx: $o ).
% 2.41/1.44
% 2.41/1.44 thf(setextAx,definition,
% 2.41/1.44 ( setextAx
% 2.41/1.44 = ( ! [A: $i,B: $i] :
% 2.41/1.44 ( ! [Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ A )
% 2.41/1.44 <=> ( in @ Xx @ B ) )
% 2.41/1.44 => ( A = B ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(emptyset_type,type,
% 2.41/1.44 emptyset: $i ).
% 2.41/1.44
% 2.41/1.44 thf(emptysetAx_type,type,
% 2.41/1.44 emptysetAx: $o ).
% 2.41/1.44
% 2.41/1.44 thf(emptysetAx,definition,
% 2.41/1.44 ( emptysetAx
% 2.41/1.44 = ( ! [Xx: $i] :
% 2.41/1.44 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(setadjoin_type,type,
% 2.41/1.44 setadjoin: $i > $i > $i ).
% 2.41/1.44
% 2.41/1.44 thf(setadjoinAx_type,type,
% 2.41/1.44 setadjoinAx: $o ).
% 2.41/1.44
% 2.41/1.44 thf(setadjoinAx,definition,
% 2.41/1.44 ( setadjoinAx
% 2.41/1.44 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.41/1.44 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.41/1.44 <=> ( ( Xy = Xx )
% 2.41/1.44 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(powerset_type,type,
% 2.41/1.44 powerset: $i > $i ).
% 2.41/1.44
% 2.41/1.44 thf(powersetAx_type,type,
% 2.41/1.44 powersetAx: $o ).
% 2.41/1.44
% 2.41/1.44 thf(powersetAx,definition,
% 2.41/1.44 ( powersetAx
% 2.41/1.44 = ( ! [A: $i,B: $i] :
% 2.41/1.44 ( ( in @ B @ ( powerset @ A ) )
% 2.41/1.44 <=> ! [Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ B )
% 2.41/1.44 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(setunion_type,type,
% 2.41/1.44 setunion: $i > $i ).
% 2.41/1.44
% 2.41/1.44 thf(setunionAx_type,type,
% 2.41/1.44 setunionAx: $o ).
% 2.41/1.44
% 2.41/1.44 thf(setunionAx,definition,
% 2.41/1.44 ( setunionAx
% 2.41/1.44 = ( ! [A: $i,Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ ( setunion @ A ) )
% 2.41/1.44 <=> ? [B: $i] :
% 2.41/1.44 ( ( in @ Xx @ B )
% 2.41/1.44 & ( in @ B @ A ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(omega_type,type,
% 2.41/1.44 omega: $i ).
% 2.41/1.44
% 2.41/1.44 thf(omega0Ax_type,type,
% 2.41/1.44 omega0Ax: $o ).
% 2.41/1.44
% 2.41/1.44 thf(omega0Ax,definition,
% 2.41/1.44 ( omega0Ax
% 2.41/1.44 = ( in @ emptyset @ omega ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(omegaSAx_type,type,
% 2.41/1.44 omegaSAx: $o ).
% 2.41/1.44
% 2.41/1.44 thf(omegaSAx,definition,
% 2.41/1.44 ( omegaSAx
% 2.41/1.44 = ( ! [Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ omega )
% 2.41/1.44 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(omegaIndAx_type,type,
% 2.41/1.44 omegaIndAx: $o ).
% 2.41/1.44
% 2.41/1.44 thf(omegaIndAx,definition,
% 2.41/1.44 ( omegaIndAx
% 2.41/1.44 = ( ! [A: $i] :
% 2.41/1.44 ( ( ( in @ emptyset @ A )
% 2.41/1.44 & ! [Xx: $i] :
% 2.41/1.44 ( ( ( in @ Xx @ omega )
% 2.41/1.44 & ( in @ Xx @ A ) )
% 2.41/1.44 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.41/1.44 => ! [Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ omega )
% 2.41/1.44 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(replAx_type,type,
% 2.41/1.44 replAx: $o ).
% 2.41/1.44
% 2.41/1.44 thf(replAx,definition,
% 2.41/1.44 ( replAx
% 2.41/1.44 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.41/1.44 ( ! [Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ A )
% 2.41/1.44 => ( exu
% 2.41/1.44 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.41/1.44 => ? [B: $i] :
% 2.41/1.44 ! [Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ B )
% 2.41/1.44 <=> ? [Xy: $i] :
% 2.41/1.44 ( ( in @ Xy @ A )
% 2.41/1.44 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(foundationAx_type,type,
% 2.41/1.44 foundationAx: $o ).
% 2.41/1.44
% 2.41/1.44 thf(foundationAx,definition,
% 2.41/1.44 ( foundationAx
% 2.41/1.44 = ( ! [A: $i] :
% 2.41/1.44 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.41/1.44 => ? [B: $i] :
% 2.41/1.44 ( ( in @ B @ A )
% 2.41/1.44 & ~ ? [Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ B )
% 2.41/1.44 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(wellorderingAx_type,type,
% 2.41/1.44 wellorderingAx: $o ).
% 2.41/1.44
% 2.41/1.44 thf(wellorderingAx,definition,
% 2.41/1.44 ( wellorderingAx
% 2.41/1.44 = ( ! [A: $i] :
% 2.41/1.44 ? [B: $i] :
% 2.41/1.44 ( ! [C: $i] :
% 2.41/1.44 ( ( in @ C @ B )
% 2.41/1.44 => ! [Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ C )
% 2.41/1.44 => ( in @ Xx @ A ) ) )
% 2.41/1.44 & ! [Xx: $i,Xy: $i] :
% 2.41/1.44 ( ( ( in @ Xx @ A )
% 2.41/1.44 & ( in @ Xy @ A ) )
% 2.41/1.44 => ( ! [C: $i] :
% 2.41/1.44 ( ( in @ C @ B )
% 2.41/1.44 => ( ( in @ Xx @ C )
% 2.41/1.44 <=> ( in @ Xy @ C ) ) )
% 2.41/1.44 => ( Xx = Xy ) ) )
% 2.41/1.44 & ! [C: $i,D: $i] :
% 2.41/1.44 ( ( ( in @ C @ B )
% 2.41/1.44 & ( in @ D @ B ) )
% 2.41/1.44 => ( ! [Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ C )
% 2.41/1.44 => ( in @ Xx @ D ) )
% 2.41/1.44 | ! [Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ D )
% 2.41/1.44 => ( in @ Xx @ C ) ) ) )
% 2.41/1.44 & ! [C: $i] :
% 2.41/1.44 ( ( ! [Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ C )
% 2.41/1.44 => ( in @ Xx @ A ) )
% 2.41/1.44 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.41/1.44 => ? [D: $i,Xx: $i] :
% 2.41/1.44 ( ( in @ D @ B )
% 2.41/1.44 & ( in @ Xx @ C )
% 2.41/1.44 & ~ ? [Xy: $i] :
% 2.41/1.44 ( ( in @ Xy @ D )
% 2.41/1.44 & ( in @ Xy @ C ) )
% 2.41/1.44 & ! [E: $i] :
% 2.41/1.44 ( ( in @ E @ B )
% 2.41/1.44 => ( ! [Xy: $i] :
% 2.41/1.44 ( ( in @ Xy @ E )
% 2.41/1.44 => ( in @ Xy @ D ) )
% 2.41/1.44 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(descr_type,type,
% 2.41/1.44 descr: ( $i > $o ) > $i ).
% 2.41/1.44
% 2.41/1.44 thf(descrp_type,type,
% 2.41/1.44 descrp: $o ).
% 2.41/1.44
% 2.41/1.44 thf(descrp,definition,
% 2.41/1.44 ( descrp
% 2.41/1.44 = ( ! [Xphi: $i > $o] :
% 2.41/1.44 ( ( exu
% 2.41/1.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.41/1.44 => ( Xphi
% 2.41/1.44 @ ( descr
% 2.41/1.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(dsetconstr_type,type,
% 2.41/1.44 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.41/1.44
% 2.41/1.44 thf(dsetconstrI_type,type,
% 2.41/1.44 dsetconstrI: $o ).
% 2.41/1.44
% 2.41/1.44 thf(dsetconstrI,definition,
% 2.41/1.44 ( dsetconstrI
% 2.41/1.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ A )
% 2.41/1.44 => ( ( Xphi @ Xx )
% 2.41/1.44 => ( in @ Xx
% 2.41/1.44 @ ( dsetconstr @ A
% 2.41/1.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(dsetconstrEL_type,type,
% 2.41/1.44 dsetconstrEL: $o ).
% 2.41/1.44
% 2.41/1.44 thf(dsetconstrEL,definition,
% 2.41/1.44 ( dsetconstrEL
% 2.41/1.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.41/1.44 ( ( in @ Xx
% 2.41/1.44 @ ( dsetconstr @ A
% 2.41/1.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.41/1.44 => ( in @ Xx @ A ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(dsetconstrER_type,type,
% 2.41/1.44 dsetconstrER: $o ).
% 2.41/1.44
% 2.41/1.44 thf(dsetconstrER,definition,
% 2.41/1.44 ( dsetconstrER
% 2.41/1.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.41/1.44 ( ( in @ Xx
% 2.41/1.44 @ ( dsetconstr @ A
% 2.41/1.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.41/1.44 => ( Xphi @ Xx ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(exuE1_type,type,
% 2.41/1.44 exuE1: $o ).
% 2.41/1.44
% 2.41/1.44 thf(exuE1,definition,
% 2.41/1.44 ( exuE1
% 2.41/1.44 = ( ! [Xphi: $i > $o] :
% 2.41/1.44 ( ( exu
% 2.41/1.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.41/1.44 => ? [Xx: $i] :
% 2.41/1.44 ( ( Xphi @ Xx )
% 2.41/1.44 & ! [Xy: $i] :
% 2.41/1.44 ( ( Xphi @ Xy )
% 2.41/1.44 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(prop2set_type,type,
% 2.41/1.44 prop2set: $o > $i ).
% 2.41/1.44
% 2.41/1.44 thf(prop2setE_type,type,
% 2.41/1.44 prop2setE: $o ).
% 2.41/1.44
% 2.41/1.44 thf(prop2setE,definition,
% 2.41/1.44 ( prop2setE
% 2.41/1.44 = ( ! [Xphi: $o,Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.41/1.44 => Xphi ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(emptysetE_type,type,
% 2.41/1.44 emptysetE: $o ).
% 2.41/1.44
% 2.41/1.44 thf(emptysetE,definition,
% 2.41/1.44 ( emptysetE
% 2.41/1.44 = ( ! [Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ emptyset )
% 2.41/1.44 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(emptysetimpfalse_type,type,
% 2.41/1.44 emptysetimpfalse: $o ).
% 2.41/1.44
% 2.41/1.44 thf(emptysetimpfalse,definition,
% 2.41/1.44 ( emptysetimpfalse
% 2.41/1.44 = ( ! [Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ emptyset )
% 2.41/1.44 => $false ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(notinemptyset_type,type,
% 2.41/1.44 notinemptyset: $o ).
% 2.41/1.44
% 2.41/1.44 thf(notinemptyset,definition,
% 2.41/1.44 ( notinemptyset
% 2.41/1.44 = ( ! [Xx: $i] :
% 2.41/1.44 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(exuE3e_type,type,
% 2.41/1.44 exuE3e: $o ).
% 2.41/1.44
% 2.41/1.44 thf(exuE3e,definition,
% 2.41/1.44 ( exuE3e
% 2.41/1.44 = ( ! [Xphi: $i > $o] :
% 2.41/1.44 ( ( exu
% 2.41/1.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.41/1.44 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(setext_type,type,
% 2.41/1.44 setext: $o ).
% 2.41/1.44
% 2.41/1.44 thf(setext,definition,
% 2.41/1.44 ( setext
% 2.41/1.44 = ( ! [A: $i,B: $i] :
% 2.41/1.44 ( ! [Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ A )
% 2.41/1.44 => ( in @ Xx @ B ) )
% 2.41/1.44 => ( ! [Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ B )
% 2.41/1.44 => ( in @ Xx @ A ) )
% 2.41/1.44 => ( A = B ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(emptyI_type,type,
% 2.41/1.44 emptyI: $o ).
% 2.41/1.44
% 2.41/1.44 thf(emptyI,definition,
% 2.41/1.44 ( emptyI
% 2.41/1.44 = ( ! [A: $i] :
% 2.41/1.44 ( ! [Xx: $i] :
% 2.41/1.44 ~ ( in @ Xx @ A )
% 2.41/1.44 => ( A = emptyset ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(noeltsimpempty_type,type,
% 2.41/1.44 noeltsimpempty: $o ).
% 2.41/1.44
% 2.41/1.44 thf(noeltsimpempty,definition,
% 2.41/1.44 ( noeltsimpempty
% 2.41/1.44 = ( ! [A: $i] :
% 2.41/1.44 ( ! [Xx: $i] :
% 2.41/1.44 ~ ( in @ Xx @ A )
% 2.41/1.44 => ( A = emptyset ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(setbeta_type,type,
% 2.41/1.44 setbeta: $o ).
% 2.41/1.44
% 2.41/1.44 thf(setbeta,definition,
% 2.41/1.44 ( setbeta
% 2.41/1.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ A )
% 2.41/1.44 => ( ( in @ Xx
% 2.41/1.44 @ ( dsetconstr @ A
% 2.41/1.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.41/1.44 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(nonempty_type,type,
% 2.41/1.44 nonempty: $i > $o ).
% 2.41/1.44
% 2.41/1.44 thf(nonempty,definition,
% 2.41/1.44 ( nonempty
% 2.41/1.44 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(nonemptyE1_type,type,
% 2.41/1.44 nonemptyE1: $o ).
% 2.41/1.44
% 2.41/1.44 thf(nonemptyE1,definition,
% 2.41/1.44 ( nonemptyE1
% 2.41/1.44 = ( ! [A: $i] :
% 2.41/1.44 ( ( nonempty @ A )
% 2.41/1.44 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(nonemptyI_type,type,
% 2.41/1.44 nonemptyI: $o ).
% 2.41/1.44
% 2.41/1.44 thf(nonemptyI,definition,
% 2.41/1.44 ( nonemptyI
% 2.41/1.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ A )
% 2.41/1.44 => ( ( Xphi @ Xx )
% 2.41/1.44 => ( nonempty
% 2.41/1.44 @ ( dsetconstr @ A
% 2.41/1.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(nonemptyI1_type,type,
% 2.41/1.44 nonemptyI1: $o ).
% 2.41/1.44
% 2.41/1.44 thf(nonemptyI1,definition,
% 2.41/1.44 ( nonemptyI1
% 2.41/1.44 = ( ! [A: $i] :
% 2.41/1.44 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.41/1.44 => ( nonempty @ A ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(setadjoinIL_type,type,
% 2.41/1.44 setadjoinIL: $o ).
% 2.41/1.44
% 2.41/1.44 thf(setadjoinIL,definition,
% 2.41/1.44 ( setadjoinIL
% 2.41/1.44 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(emptyinunitempty_type,type,
% 2.41/1.44 emptyinunitempty: $o ).
% 2.41/1.44
% 2.41/1.44 thf(emptyinunitempty,definition,
% 2.41/1.44 ( emptyinunitempty
% 2.41/1.44 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(setadjoinIR_type,type,
% 2.41/1.44 setadjoinIR: $o ).
% 2.41/1.44
% 2.41/1.44 thf(setadjoinIR,definition,
% 2.41/1.44 ( setadjoinIR
% 2.41/1.44 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.41/1.44 ( ( in @ Xy @ A )
% 2.41/1.44 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(setadjoinE_type,type,
% 2.41/1.44 setadjoinE: $o ).
% 2.41/1.44
% 2.41/1.44 thf(setadjoinE,definition,
% 2.41/1.44 ( setadjoinE
% 2.41/1.44 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.41/1.44 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.41/1.44 => ! [Xphi: $o] :
% 2.41/1.44 ( ( ( Xy = Xx )
% 2.41/1.44 => Xphi )
% 2.41/1.44 => ( ( ( in @ Xy @ A )
% 2.41/1.44 => Xphi )
% 2.41/1.44 => Xphi ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(setadjoinOr_type,type,
% 2.41/1.44 setadjoinOr: $o ).
% 2.41/1.44
% 2.41/1.44 thf(setadjoinOr,definition,
% 2.41/1.44 ( setadjoinOr
% 2.41/1.44 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.41/1.44 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.41/1.44 => ( ( Xy = Xx )
% 2.41/1.44 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(setoftrueEq_type,type,
% 2.41/1.44 setoftrueEq: $o ).
% 2.41/1.44
% 2.41/1.44 thf(setoftrueEq,definition,
% 2.41/1.44 ( setoftrueEq
% 2.41/1.44 = ( ! [A: $i] :
% 2.41/1.44 ( ( dsetconstr @ A
% 2.41/1.44 @ ^ [Xx: $i] : $true )
% 2.41/1.44 = A ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(powersetI_type,type,
% 2.41/1.44 powersetI: $o ).
% 2.41/1.44
% 2.41/1.44 thf(powersetI,definition,
% 2.41/1.44 ( powersetI
% 2.41/1.44 = ( ! [A: $i,B: $i] :
% 2.41/1.44 ( ! [Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ B )
% 2.41/1.44 => ( in @ Xx @ A ) )
% 2.41/1.44 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(emptyinPowerset_type,type,
% 2.41/1.44 emptyinPowerset: $o ).
% 2.41/1.44
% 2.41/1.44 thf(emptyinPowerset,definition,
% 2.41/1.44 ( emptyinPowerset
% 2.41/1.44 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(emptyInPowerset_type,type,
% 2.41/1.44 emptyInPowerset: $o ).
% 2.41/1.44
% 2.41/1.44 thf(emptyInPowerset,definition,
% 2.41/1.44 ( emptyInPowerset
% 2.41/1.44 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(powersetE_type,type,
% 2.41/1.44 powersetE: $o ).
% 2.41/1.44
% 2.41/1.44 thf(powersetE,definition,
% 2.41/1.44 ( powersetE
% 2.41/1.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.44 ( ( in @ B @ ( powerset @ A ) )
% 2.41/1.44 => ( ( in @ Xx @ B )
% 2.41/1.44 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(setunionI_type,type,
% 2.41/1.44 setunionI: $o ).
% 2.41/1.44
% 2.41/1.44 thf(setunionI,definition,
% 2.41/1.44 ( setunionI
% 2.41/1.44 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.41/1.44 ( ( in @ Xx @ B )
% 2.41/1.44 => ( ( in @ B @ A )
% 2.41/1.44 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(setunionE_type,type,
% 2.41/1.44 setunionE: $o ).
% 2.41/1.44
% 2.41/1.44 thf(setunionE,definition,
% 2.41/1.44 ( setunionE
% 2.41/1.44 = ( ! [A: $i,Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ ( setunion @ A ) )
% 2.41/1.44 => ! [Xphi: $o] :
% 2.41/1.44 ( ! [B: $i] :
% 2.41/1.44 ( ( in @ Xx @ B )
% 2.41/1.44 => ( ( in @ B @ A )
% 2.41/1.44 => Xphi ) )
% 2.41/1.44 => Xphi ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(subPowSU_type,type,
% 2.41/1.44 subPowSU: $o ).
% 2.41/1.44
% 2.41/1.44 thf(subPowSU,definition,
% 2.41/1.44 ( subPowSU
% 2.41/1.44 = ( ! [A: $i,Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ A )
% 2.41/1.44 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(exuE2_type,type,
% 2.41/1.44 exuE2: $o ).
% 2.41/1.44
% 2.41/1.44 thf(exuE2,definition,
% 2.41/1.44 ( exuE2
% 2.41/1.44 = ( ! [Xphi: $i > $o] :
% 2.41/1.44 ( ( exu
% 2.41/1.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.41/1.44 => ? [Xx: $i] :
% 2.41/1.44 ! [Xy: $i] :
% 2.41/1.44 ( ( Xphi @ Xy )
% 2.41/1.44 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(nonemptyImpWitness_type,type,
% 2.41/1.44 nonemptyImpWitness: $o ).
% 2.41/1.44
% 2.41/1.44 thf(nonemptyImpWitness,definition,
% 2.41/1.44 ( nonemptyImpWitness
% 2.41/1.44 = ( ! [A: $i] :
% 2.41/1.44 ( ( nonempty @ A )
% 2.41/1.44 => ? [Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ A )
% 2.41/1.44 & $true ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(uniqinunit_type,type,
% 2.41/1.44 uniqinunit: $o ).
% 2.41/1.44
% 2.41/1.44 thf(uniqinunit,definition,
% 2.41/1.44 ( uniqinunit
% 2.41/1.44 = ( ! [Xx: $i,Xy: $i] :
% 2.41/1.44 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.41/1.44 => ( Xx = Xy ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(notinsingleton_type,type,
% 2.41/1.44 notinsingleton: $o ).
% 2.41/1.44
% 2.41/1.44 thf(notinsingleton,definition,
% 2.41/1.44 ( notinsingleton
% 2.41/1.44 = ( ! [Xx: $i,Xy: $i] :
% 2.41/1.44 ( ( Xx != Xy )
% 2.41/1.44 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(eqinunit_type,type,
% 2.41/1.44 eqinunit: $o ).
% 2.41/1.44
% 2.41/1.44 thf(eqinunit,definition,
% 2.41/1.44 ( eqinunit
% 2.41/1.44 = ( ! [Xx: $i,Xy: $i] :
% 2.41/1.44 ( ( Xx = Xy )
% 2.41/1.44 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(singletonsswitch_type,type,
% 2.41/1.44 singletonsswitch: $o ).
% 2.41/1.44
% 2.41/1.44 thf(singletonsswitch,definition,
% 2.41/1.44 ( singletonsswitch
% 2.41/1.44 = ( ! [Xx: $i,Xy: $i] :
% 2.41/1.44 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.41/1.44 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(upairsetE_type,type,
% 2.41/1.44 upairsetE: $o ).
% 2.41/1.44
% 2.41/1.44 thf(upairsetE,definition,
% 2.41/1.44 ( upairsetE
% 2.41/1.44 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.41/1.44 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.41/1.44 => ( ( Xz = Xx )
% 2.41/1.44 | ( Xz = Xy ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(upairsetIL_type,type,
% 2.41/1.44 upairsetIL: $o ).
% 2.41/1.44
% 2.41/1.44 thf(upairsetIL,definition,
% 2.41/1.44 ( upairsetIL
% 2.41/1.44 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(upairsetIR_type,type,
% 2.41/1.44 upairsetIR: $o ).
% 2.41/1.44
% 2.41/1.44 thf(upairsetIR,definition,
% 2.41/1.44 ( upairsetIR
% 2.41/1.44 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(emptyE1_type,type,
% 2.41/1.44 emptyE1: $o ).
% 2.41/1.44
% 2.41/1.44 thf(emptyE1,definition,
% 2.41/1.44 ( emptyE1
% 2.41/1.44 = ( ! [A: $i,Xphi: $i > $o] :
% 2.41/1.44 ( ? [Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ A )
% 2.41/1.44 & ( Xphi @ Xx ) )
% 2.41/1.44 => ( ( ( dsetconstr @ A
% 2.41/1.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.41/1.44 = emptyset )
% 2.41/1.44 => $false ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(vacuousDall_type,type,
% 2.41/1.44 vacuousDall: $o ).
% 2.41/1.44
% 2.41/1.44 thf(vacuousDall,definition,
% 2.41/1.44 ( vacuousDall
% 2.41/1.44 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ emptyset )
% 2.41/1.44 => ( Xphi @ Xx ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(quantDeMorgan1_type,type,
% 2.41/1.44 quantDeMorgan1: $o ).
% 2.41/1.44
% 2.41/1.44 thf(quantDeMorgan1,definition,
% 2.41/1.44 ( quantDeMorgan1
% 2.41/1.44 = ( ! [A: $i,Xphi: $i > $o] :
% 2.41/1.44 ( ~ ! [Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ A )
% 2.41/1.44 => ( Xphi @ Xx ) )
% 2.41/1.44 => ? [Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ A )
% 2.41/1.44 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(quantDeMorgan2_type,type,
% 2.41/1.44 quantDeMorgan2: $o ).
% 2.41/1.44
% 2.41/1.44 thf(quantDeMorgan2,definition,
% 2.41/1.44 ( quantDeMorgan2
% 2.41/1.44 = ( ! [A: $i,Xphi: $i > $o] :
% 2.41/1.44 ( ! [Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ A )
% 2.41/1.44 => ~ ( Xphi @ Xx ) )
% 2.41/1.44 => ~ ? [Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ A )
% 2.41/1.44 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(quantDeMorgan3_type,type,
% 2.41/1.44 quantDeMorgan3: $o ).
% 2.41/1.44
% 2.41/1.44 thf(quantDeMorgan3,definition,
% 2.41/1.44 ( quantDeMorgan3
% 2.41/1.44 = ( ! [A: $i,Xphi: $i > $o] :
% 2.41/1.44 ( ~ ? [Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ A )
% 2.41/1.44 & ( Xphi @ Xx ) )
% 2.41/1.44 => ! [Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ A )
% 2.41/1.44 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(quantDeMorgan4_type,type,
% 2.41/1.44 quantDeMorgan4: $o ).
% 2.41/1.44
% 2.41/1.44 thf(quantDeMorgan4,definition,
% 2.41/1.44 ( quantDeMorgan4
% 2.41/1.44 = ( ! [A: $i,Xphi: $i > $o] :
% 2.41/1.44 ( ? [Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ A )
% 2.41/1.44 & ~ ( Xphi @ Xx ) )
% 2.41/1.44 => ~ ! [Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ A )
% 2.41/1.44 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(prop2setI_type,type,
% 2.41/1.44 prop2setI: $o ).
% 2.41/1.44
% 2.41/1.44 thf(prop2setI,definition,
% 2.41/1.44 ( prop2setI
% 2.41/1.44 = ( ! [Xphi: $o] :
% 2.41/1.44 ( Xphi
% 2.41/1.44 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(set2prop_type,type,
% 2.41/1.44 set2prop: $i > $o ).
% 2.41/1.44
% 2.41/1.44 thf(prop2set2propI_type,type,
% 2.41/1.44 prop2set2propI: $o ).
% 2.41/1.44
% 2.41/1.44 thf(prop2set2propI,definition,
% 2.41/1.44 ( prop2set2propI
% 2.41/1.44 = ( ! [Xphi: $o] :
% 2.41/1.44 ( Xphi
% 2.41/1.44 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(notdexE_type,type,
% 2.41/1.44 notdexE: $o ).
% 2.41/1.44
% 2.41/1.44 thf(notdexE,definition,
% 2.41/1.44 ( notdexE
% 2.41/1.44 = ( ! [A: $i,Xphi: $i > $o] :
% 2.41/1.44 ( ~ ? [Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ A )
% 2.41/1.44 & ( Xphi @ Xx ) )
% 2.41/1.44 => ! [Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ A )
% 2.41/1.44 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(notdallE_type,type,
% 2.41/1.44 notdallE: $o ).
% 2.41/1.44
% 2.41/1.44 thf(notdallE,definition,
% 2.41/1.44 ( notdallE
% 2.41/1.44 = ( ! [A: $i,Xphi: $i > $o] :
% 2.41/1.44 ( ~ ! [Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ A )
% 2.41/1.44 => ( Xphi @ Xx ) )
% 2.41/1.44 => ? [Xx: $i] :
% 2.41/1.44 ( ( in @ Xx @ A )
% 2.41/1.44 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.41/1.44
% 2.41/1.44 thf(exuI1_type,type,
% 2.41/1.45 exuI1: $o ).
% 2.41/1.45
% 2.41/1.45 thf(exuI1,definition,
% 2.41/1.45 ( exuI1
% 2.41/1.45 = ( ! [Xphi: $i > $o] :
% 2.41/1.45 ( ? [Xx: $i] :
% 2.41/1.45 ( ( Xphi @ Xx )
% 2.41/1.45 & ! [Xy: $i] :
% 2.41/1.45 ( ( Xphi @ Xy )
% 2.41/1.45 => ( Xx = Xy ) ) )
% 2.41/1.45 => ( exu
% 2.41/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(exuI3_type,type,
% 2.41/1.45 exuI3: $o ).
% 2.41/1.45
% 2.41/1.45 thf(exuI3,definition,
% 2.41/1.45 ( exuI3
% 2.41/1.45 = ( ! [Xphi: $i > $o] :
% 2.41/1.45 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.41/1.45 => ( ! [Xx: $i,Xy: $i] :
% 2.41/1.45 ( ( Xphi @ Xx )
% 2.41/1.45 => ( ( Xphi @ Xy )
% 2.41/1.45 => ( Xx = Xy ) ) )
% 2.41/1.45 => ( exu
% 2.41/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(exuI2_type,type,
% 2.41/1.45 exuI2: $o ).
% 2.41/1.45
% 2.41/1.45 thf(exuI2,definition,
% 2.41/1.45 ( exuI2
% 2.41/1.45 = ( ! [Xphi: $i > $o] :
% 2.41/1.45 ( ? [Xx: $i] :
% 2.41/1.45 ! [Xy: $i] :
% 2.41/1.45 ( ( Xphi @ Xy )
% 2.41/1.45 <=> ( Xy = Xx ) )
% 2.41/1.45 => ( exu
% 2.41/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(inCongP_type,type,
% 2.41/1.45 inCongP: $o ).
% 2.41/1.45
% 2.41/1.45 thf(inCongP,definition,
% 2.41/1.45 ( inCongP
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( A = B )
% 2.41/1.45 => ! [Xx: $i,Xy: $i] :
% 2.41/1.45 ( ( Xx = Xy )
% 2.41/1.45 => ( ( in @ Xx @ A )
% 2.41/1.45 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(in__Cong_type,type,
% 2.41/1.45 in__Cong: $o ).
% 2.41/1.45
% 2.41/1.45 thf(in__Cong,definition,
% 2.41/1.45 ( in__Cong
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( A = B )
% 2.41/1.45 => ! [Xx: $i,Xy: $i] :
% 2.41/1.45 ( ( Xx = Xy )
% 2.41/1.45 => ( ( in @ Xx @ A )
% 2.41/1.45 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(exuE3u_type,type,
% 2.41/1.45 exuE3u: $o ).
% 2.41/1.45
% 2.41/1.45 thf(exuE3u,definition,
% 2.41/1.45 ( exuE3u
% 2.41/1.45 = ( ! [Xphi: $i > $o] :
% 2.41/1.45 ( ( exu
% 2.41/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.41/1.45 => ! [Xx: $i,Xy: $i] :
% 2.41/1.45 ( ( Xphi @ Xx )
% 2.41/1.45 => ( ( Xphi @ Xy )
% 2.41/1.45 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(exu__Cong_type,type,
% 2.41/1.45 exu__Cong: $o ).
% 2.41/1.45
% 2.41/1.45 thf(exu__Cong,definition,
% 2.41/1.45 ( exu__Cong
% 2.41/1.45 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.41/1.45 ( ! [Xx: $i,Xy: $i] :
% 2.41/1.45 ( ( Xx = Xy )
% 2.41/1.45 => ( ( Xphi @ Xx )
% 2.41/1.45 <=> ( Xpsi @ Xy ) ) )
% 2.41/1.45 => ( ( exu
% 2.41/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.41/1.45 <=> ( exu
% 2.41/1.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(emptyset__Cong_type,type,
% 2.41/1.45 emptyset__Cong: $o ).
% 2.41/1.45
% 2.41/1.45 thf(emptyset__Cong,definition,
% 2.41/1.45 ( emptyset__Cong
% 2.41/1.45 = ( emptyset = emptyset ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setadjoin__Cong_type,type,
% 2.41/1.45 setadjoin__Cong: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setadjoin__Cong,definition,
% 2.41/1.45 ( setadjoin__Cong
% 2.41/1.45 = ( ! [Xx: $i,Xy: $i] :
% 2.41/1.45 ( ( Xx = Xy )
% 2.41/1.45 => ! [Xz: $i,Xu: $i] :
% 2.41/1.45 ( ( Xz = Xu )
% 2.41/1.45 => ( ( setadjoin @ Xx @ Xz )
% 2.41/1.45 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(powerset__Cong_type,type,
% 2.41/1.45 powerset__Cong: $o ).
% 2.41/1.45
% 2.41/1.45 thf(powerset__Cong,definition,
% 2.41/1.45 ( powerset__Cong
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( A = B )
% 2.41/1.45 => ( ( powerset @ A )
% 2.41/1.45 = ( powerset @ B ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setunion__Cong_type,type,
% 2.41/1.45 setunion__Cong: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setunion__Cong,definition,
% 2.41/1.45 ( setunion__Cong
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( A = B )
% 2.41/1.45 => ( ( setunion @ A )
% 2.41/1.45 = ( setunion @ B ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(omega__Cong_type,type,
% 2.41/1.45 omega__Cong: $o ).
% 2.41/1.45
% 2.41/1.45 thf(omega__Cong,definition,
% 2.41/1.45 ( omega__Cong
% 2.41/1.45 = ( omega = omega ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(exuEu_type,type,
% 2.41/1.45 exuEu: $o ).
% 2.41/1.45
% 2.41/1.45 thf(exuEu,definition,
% 2.41/1.45 ( exuEu
% 2.41/1.45 = ( ! [Xphi: $i > $o] :
% 2.41/1.45 ( ( exu
% 2.41/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.41/1.45 => ! [Xx: $i,Xy: $i] :
% 2.41/1.45 ( ( Xphi @ Xx )
% 2.41/1.45 => ( ( Xphi @ Xy )
% 2.41/1.45 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(descr__Cong_type,type,
% 2.41/1.45 descr__Cong: $o ).
% 2.41/1.45
% 2.41/1.45 thf(descr__Cong,definition,
% 2.41/1.45 ( descr__Cong
% 2.41/1.45 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.41/1.45 ( ! [Xx: $i,Xy: $i] :
% 2.41/1.45 ( ( Xx = Xy )
% 2.41/1.45 => ( ( Xphi @ Xx )
% 2.41/1.45 <=> ( Xpsi @ Xy ) ) )
% 2.41/1.45 => ( ( exu
% 2.41/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.41/1.45 => ( ( exu
% 2.41/1.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.41/1.45 => ( ( descr
% 2.41/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.41/1.45 = ( descr
% 2.41/1.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(dsetconstr__Cong_type,type,
% 2.41/1.45 dsetconstr__Cong: $o ).
% 2.41/1.45
% 2.41/1.45 thf(dsetconstr__Cong,definition,
% 2.41/1.45 ( dsetconstr__Cong
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( A = B )
% 2.41/1.45 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.41/1.45 ( ! [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ! [Xy: $i] :
% 2.41/1.45 ( ( in @ Xy @ B )
% 2.41/1.45 => ( ( Xx = Xy )
% 2.41/1.45 => ( ( Xphi @ Xx )
% 2.41/1.45 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.41/1.45 => ( ( dsetconstr @ A
% 2.41/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.41/1.45 = ( dsetconstr @ B
% 2.41/1.45 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(subset_type,type,
% 2.41/1.45 subset: $i > $i > $o ).
% 2.41/1.45
% 2.41/1.45 thf(disjoint_type,type,
% 2.41/1.45 disjoint: $i > $i > $o ).
% 2.41/1.45
% 2.41/1.45 thf(setsmeet_type,type,
% 2.41/1.45 setsmeet: $i > $i > $o ).
% 2.41/1.45
% 2.41/1.45 thf(subsetI1_type,type,
% 2.41/1.45 subsetI1: $o ).
% 2.41/1.45
% 2.41/1.45 thf(subsetI1,definition,
% 2.41/1.45 ( subsetI1
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ! [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ( in @ Xx @ B ) )
% 2.41/1.45 => ( subset @ A @ B ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(eqimpsubset2_type,type,
% 2.41/1.45 eqimpsubset2: $o ).
% 2.41/1.45
% 2.41/1.45 thf(eqimpsubset2,definition,
% 2.41/1.45 ( eqimpsubset2
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( A = B )
% 2.41/1.45 => ( subset @ B @ A ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(eqimpsubset1_type,type,
% 2.41/1.45 eqimpsubset1: $o ).
% 2.41/1.45
% 2.41/1.45 thf(eqimpsubset1,definition,
% 2.41/1.45 ( eqimpsubset1
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( A = B )
% 2.41/1.45 => ( subset @ A @ B ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(subsetI2_type,type,
% 2.41/1.45 subsetI2: $o ).
% 2.41/1.45
% 2.41/1.45 thf(subsetI2,definition,
% 2.41/1.45 ( subsetI2
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ! [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ( in @ Xx @ B ) )
% 2.41/1.45 => ( subset @ A @ B ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(emptysetsubset_type,type,
% 2.41/1.45 emptysetsubset: $o ).
% 2.41/1.45
% 2.41/1.45 thf(emptysetsubset,definition,
% 2.41/1.45 ( emptysetsubset
% 2.41/1.45 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(subsetE_type,type,
% 2.41/1.45 subsetE: $o ).
% 2.41/1.45
% 2.41/1.45 thf(subsetE,definition,
% 2.41/1.45 ( subsetE
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( subset @ A @ B )
% 2.41/1.45 => ( ( in @ Xx @ A )
% 2.41/1.45 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(subsetE2_type,type,
% 2.41/1.45 subsetE2: $o ).
% 2.41/1.45
% 2.41/1.45 thf(subsetE2,definition,
% 2.41/1.45 ( subsetE2
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( subset @ A @ B )
% 2.41/1.45 => ( ~ ( in @ Xx @ B )
% 2.41/1.45 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(notsubsetI_type,type,
% 2.41/1.45 notsubsetI: $o ).
% 2.41/1.45
% 2.41/1.45 thf(notsubsetI,definition,
% 2.41/1.45 ( notsubsetI
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ( ~ ( in @ Xx @ B )
% 2.41/1.45 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(notequalI1_type,type,
% 2.41/1.45 notequalI1: $o ).
% 2.41/1.45
% 2.41/1.45 thf(notequalI1,definition,
% 2.41/1.45 ( notequalI1
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ~ ( subset @ A @ B )
% 2.41/1.45 => ( A != B ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(notequalI2_type,type,
% 2.41/1.45 notequalI2: $o ).
% 2.41/1.45
% 2.41/1.45 thf(notequalI2,definition,
% 2.41/1.45 ( notequalI2
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ( ~ ( in @ Xx @ B )
% 2.41/1.45 => ( A != B ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(subsetRefl_type,type,
% 2.41/1.45 subsetRefl: $o ).
% 2.41/1.45
% 2.41/1.45 thf(subsetRefl,definition,
% 2.41/1.45 ( subsetRefl
% 2.41/1.45 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(subsetTrans_type,type,
% 2.41/1.45 subsetTrans: $o ).
% 2.41/1.45
% 2.41/1.45 thf(subsetTrans,definition,
% 2.41/1.45 ( subsetTrans
% 2.41/1.45 = ( ! [A: $i,B: $i,C: $i] :
% 2.41/1.45 ( ( subset @ A @ B )
% 2.41/1.45 => ( ( subset @ B @ C )
% 2.41/1.45 => ( subset @ A @ C ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setadjoinSub_type,type,
% 2.41/1.45 setadjoinSub: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setadjoinSub,definition,
% 2.41/1.45 ( setadjoinSub
% 2.41/1.45 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setadjoinSub2_type,type,
% 2.41/1.45 setadjoinSub2: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setadjoinSub2,definition,
% 2.41/1.45 ( setadjoinSub2
% 2.41/1.45 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.41/1.45 ( ( subset @ A @ B )
% 2.41/1.45 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(subset2powerset_type,type,
% 2.41/1.45 subset2powerset: $o ).
% 2.41/1.45
% 2.41/1.45 thf(subset2powerset,definition,
% 2.41/1.45 ( subset2powerset
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( subset @ A @ B )
% 2.41/1.45 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setextsub_type,type,
% 2.41/1.45 setextsub: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setextsub,definition,
% 2.41/1.45 ( setextsub
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( subset @ A @ B )
% 2.41/1.45 => ( ( subset @ B @ A )
% 2.41/1.45 => ( A = B ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(subsetemptysetimpeq_type,type,
% 2.41/1.45 subsetemptysetimpeq: $o ).
% 2.41/1.45
% 2.41/1.45 thf(subsetemptysetimpeq,definition,
% 2.41/1.45 ( subsetemptysetimpeq
% 2.41/1.45 = ( ! [A: $i] :
% 2.41/1.45 ( ( subset @ A @ emptyset )
% 2.41/1.45 => ( A = emptyset ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(powersetI1_type,type,
% 2.41/1.45 powersetI1: $o ).
% 2.41/1.45
% 2.41/1.45 thf(powersetI1,definition,
% 2.41/1.45 ( powersetI1
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( subset @ B @ A )
% 2.41/1.45 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(powersetE1_type,type,
% 2.41/1.45 powersetE1: $o ).
% 2.41/1.45
% 2.41/1.45 thf(powersetE1,definition,
% 2.41/1.45 ( powersetE1
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( in @ B @ ( powerset @ A ) )
% 2.41/1.45 => ( subset @ B @ A ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(inPowerset_type,type,
% 2.41/1.45 inPowerset: $o ).
% 2.41/1.45
% 2.41/1.45 thf(inPowerset,definition,
% 2.41/1.45 ( inPowerset
% 2.41/1.45 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(powersetsubset_type,type,
% 2.41/1.45 powersetsubset: $o ).
% 2.41/1.45
% 2.41/1.45 thf(powersetsubset,definition,
% 2.41/1.45 ( powersetsubset
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( subset @ A @ B )
% 2.41/1.45 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(sepInPowerset_type,type,
% 2.41/1.45 sepInPowerset: $o ).
% 2.41/1.45
% 2.41/1.45 thf(sepInPowerset,definition,
% 2.41/1.45 ( sepInPowerset
% 2.41/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.41/1.45 ( in
% 2.41/1.45 @ ( dsetconstr @ A
% 2.41/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.41/1.45 @ ( powerset @ A ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(sepSubset_type,type,
% 2.41/1.45 sepSubset: $o ).
% 2.41/1.45
% 2.41/1.45 thf(sepSubset,definition,
% 2.41/1.45 ( sepSubset
% 2.41/1.45 = ( ! [A: $i,Xphi: $i > $o] :
% 2.41/1.45 ( subset
% 2.41/1.45 @ ( dsetconstr @ A
% 2.41/1.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.41/1.45 @ A ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(binunion_type,type,
% 2.41/1.45 binunion: $i > $i > $i ).
% 2.41/1.45
% 2.41/1.45 thf(binunionIL_type,type,
% 2.41/1.45 binunionIL: $o ).
% 2.41/1.45
% 2.41/1.45 thf(binunionIL,definition,
% 2.41/1.45 ( binunionIL
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(upairset2IR_type,type,
% 2.41/1.45 upairset2IR: $o ).
% 2.41/1.45
% 2.41/1.45 thf(upairset2IR,definition,
% 2.41/1.45 ( upairset2IR
% 2.41/1.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(binunionIR_type,type,
% 2.41/1.45 binunionIR: $o ).
% 2.41/1.45
% 2.41/1.45 thf(binunionIR,definition,
% 2.41/1.45 ( binunionIR
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ B )
% 2.41/1.45 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(binunionEcases_type,type,
% 2.41/1.45 binunionEcases: $o ).
% 2.41/1.45
% 2.41/1.45 thf(binunionEcases,definition,
% 2.41/1.45 ( binunionEcases
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.41/1.45 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.41/1.45 => ( ( ( in @ Xx @ A )
% 2.41/1.45 => Xphi )
% 2.41/1.45 => ( ( ( in @ Xx @ B )
% 2.41/1.45 => Xphi )
% 2.41/1.45 => Xphi ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(binunionE_type,type,
% 2.41/1.45 binunionE: $o ).
% 2.41/1.45
% 2.41/1.45 thf(binunionE,definition,
% 2.41/1.45 ( binunionE
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.41/1.45 => ( ( in @ Xx @ A )
% 2.41/1.45 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(binunionLsub_type,type,
% 2.41/1.45 binunionLsub: $o ).
% 2.41/1.45
% 2.41/1.45 thf(binunionLsub,definition,
% 2.41/1.45 ( binunionLsub
% 2.41/1.45 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(binunionRsub_type,type,
% 2.41/1.45 binunionRsub: $o ).
% 2.41/1.45
% 2.41/1.45 thf(binunionRsub,definition,
% 2.41/1.45 ( binunionRsub
% 2.41/1.45 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(binintersect_type,type,
% 2.41/1.45 binintersect: $i > $i > $i ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectI_type,type,
% 2.41/1.45 binintersectI: $o ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectI,definition,
% 2.41/1.45 ( binintersectI
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ( ( in @ Xx @ B )
% 2.41/1.45 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectSubset5_type,type,
% 2.41/1.45 binintersectSubset5: $o ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectSubset5,definition,
% 2.41/1.45 ( binintersectSubset5
% 2.41/1.45 = ( ! [A: $i,B: $i,C: $i] :
% 2.41/1.45 ( ( subset @ C @ A )
% 2.41/1.45 => ( ( subset @ C @ B )
% 2.41/1.45 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectEL_type,type,
% 2.41/1.45 binintersectEL: $o ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectEL,definition,
% 2.41/1.45 ( binintersectEL
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.41/1.45 => ( in @ Xx @ A ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectLsub_type,type,
% 2.41/1.45 binintersectLsub: $o ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectLsub,definition,
% 2.41/1.45 ( binintersectLsub
% 2.41/1.45 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectSubset2_type,type,
% 2.41/1.45 binintersectSubset2: $o ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectSubset2,definition,
% 2.41/1.45 ( binintersectSubset2
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( subset @ A @ B )
% 2.41/1.45 => ( ( binintersect @ A @ B )
% 2.41/1.45 = A ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectSubset3_type,type,
% 2.41/1.45 binintersectSubset3: $o ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectSubset3,definition,
% 2.41/1.45 ( binintersectSubset3
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( ( binintersect @ A @ B )
% 2.41/1.45 = B )
% 2.41/1.45 => ( subset @ B @ A ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectER_type,type,
% 2.41/1.45 binintersectER: $o ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectER,definition,
% 2.41/1.45 ( binintersectER
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.41/1.45 => ( in @ Xx @ B ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(disjointsetsI1_type,type,
% 2.41/1.45 disjointsetsI1: $o ).
% 2.41/1.45
% 2.41/1.45 thf(disjointsetsI1,definition,
% 2.41/1.45 ( disjointsetsI1
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ~ ? [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 & ( in @ Xx @ B ) )
% 2.41/1.45 => ( ( binintersect @ A @ B )
% 2.41/1.45 = emptyset ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectRsub_type,type,
% 2.41/1.45 binintersectRsub: $o ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectRsub,definition,
% 2.41/1.45 ( binintersectRsub
% 2.41/1.45 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectSubset4_type,type,
% 2.41/1.45 binintersectSubset4: $o ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectSubset4,definition,
% 2.41/1.45 ( binintersectSubset4
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( subset @ B @ A )
% 2.41/1.45 => ( ( binintersect @ A @ B )
% 2.41/1.45 = B ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectSubset1_type,type,
% 2.41/1.45 binintersectSubset1: $o ).
% 2.41/1.45
% 2.41/1.45 thf(binintersectSubset1,definition,
% 2.41/1.45 ( binintersectSubset1
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( ( binintersect @ A @ B )
% 2.41/1.45 = A )
% 2.41/1.45 => ( subset @ A @ B ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(bs114d_type,type,
% 2.41/1.45 bs114d: $o ).
% 2.41/1.45
% 2.41/1.45 thf(bs114d,definition,
% 2.41/1.45 ( bs114d
% 2.41/1.45 = ( ! [A: $i,B: $i,C: $i] :
% 2.41/1.45 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.41/1.45 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(regular_type,type,
% 2.41/1.45 regular: $i > $o ).
% 2.41/1.45
% 2.41/1.45 thf(setminus_type,type,
% 2.41/1.45 setminus: $i > $i > $i ).
% 2.41/1.45
% 2.41/1.45 thf(setminusI_type,type,
% 2.41/1.45 setminusI: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setminusI,definition,
% 2.41/1.45 ( setminusI
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ( ~ ( in @ Xx @ B )
% 2.41/1.45 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setminusEL_type,type,
% 2.41/1.45 setminusEL: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setminusEL,definition,
% 2.41/1.45 ( setminusEL
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.41/1.45 => ( in @ Xx @ A ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setminusER_type,type,
% 2.41/1.45 setminusER: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setminusER,definition,
% 2.41/1.45 ( setminusER
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.41/1.45 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setminusSubset2_type,type,
% 2.41/1.45 setminusSubset2: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setminusSubset2,definition,
% 2.41/1.45 ( setminusSubset2
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( subset @ A @ B )
% 2.41/1.45 => ( ( setminus @ A @ B )
% 2.41/1.45 = emptyset ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setminusERneg_type,type,
% 2.41/1.45 setminusERneg: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setminusERneg,definition,
% 2.41/1.45 ( setminusERneg
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.41/1.45 => ( ( in @ Xx @ A )
% 2.41/1.45 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setminusELneg_type,type,
% 2.41/1.45 setminusELneg: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setminusELneg,definition,
% 2.41/1.45 ( setminusELneg
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.41/1.45 => ( ~ ( in @ Xx @ B )
% 2.41/1.45 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setminusILneg_type,type,
% 2.41/1.45 setminusILneg: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setminusILneg,definition,
% 2.41/1.45 ( setminusILneg
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ~ ( in @ Xx @ A )
% 2.41/1.45 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setminusIRneg_type,type,
% 2.41/1.45 setminusIRneg: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setminusIRneg,definition,
% 2.41/1.45 ( setminusIRneg
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ B )
% 2.41/1.45 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setminusLsub_type,type,
% 2.41/1.45 setminusLsub: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setminusLsub,definition,
% 2.41/1.45 ( setminusLsub
% 2.41/1.45 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setminusSubset1_type,type,
% 2.41/1.45 setminusSubset1: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setminusSubset1,definition,
% 2.41/1.45 ( setminusSubset1
% 2.41/1.45 = ( ! [A: $i,B: $i] :
% 2.41/1.45 ( ( ( setminus @ A @ B )
% 2.41/1.45 = emptyset )
% 2.41/1.45 => ( subset @ A @ B ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(symdiff_type,type,
% 2.41/1.45 symdiff: $i > $i > $i ).
% 2.41/1.45
% 2.41/1.45 thf(symdiffE_type,type,
% 2.41/1.45 symdiffE: $o ).
% 2.41/1.45
% 2.41/1.45 thf(symdiffE,definition,
% 2.41/1.45 ( symdiffE
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.41/1.45 => ! [Xphi: $o] :
% 2.41/1.45 ( ( ( in @ Xx @ A )
% 2.41/1.45 => ( ~ ( in @ Xx @ B )
% 2.41/1.45 => Xphi ) )
% 2.41/1.45 => ( ( ~ ( in @ Xx @ A )
% 2.41/1.45 => ( ( in @ Xx @ B )
% 2.41/1.45 => Xphi ) )
% 2.41/1.45 => Xphi ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(symdiffI1_type,type,
% 2.41/1.45 symdiffI1: $o ).
% 2.41/1.45
% 2.41/1.45 thf(symdiffI1,definition,
% 2.41/1.45 ( symdiffI1
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ( ~ ( in @ Xx @ B )
% 2.41/1.45 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(symdiffI2_type,type,
% 2.41/1.45 symdiffI2: $o ).
% 2.41/1.45
% 2.41/1.45 thf(symdiffI2,definition,
% 2.41/1.45 ( symdiffI2
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ~ ( in @ Xx @ A )
% 2.41/1.45 => ( ( in @ Xx @ B )
% 2.41/1.45 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(symdiffIneg1_type,type,
% 2.41/1.45 symdiffIneg1: $o ).
% 2.41/1.45
% 2.41/1.45 thf(symdiffIneg1,definition,
% 2.41/1.45 ( symdiffIneg1
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ A )
% 2.41/1.45 => ( ( in @ Xx @ B )
% 2.41/1.45 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(symdiffIneg2_type,type,
% 2.41/1.45 symdiffIneg2: $o ).
% 2.41/1.45
% 2.41/1.45 thf(symdiffIneg2,definition,
% 2.41/1.45 ( symdiffIneg2
% 2.41/1.45 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.41/1.45 ( ~ ( in @ Xx @ A )
% 2.41/1.45 => ( ~ ( in @ Xx @ B )
% 2.41/1.45 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(iskpair_type,type,
% 2.41/1.45 iskpair: $i > $o ).
% 2.41/1.45
% 2.41/1.45 thf(iskpair,definition,
% 2.41/1.45 ( iskpair
% 2.41/1.45 = ( ^ [A: $i] :
% 2.41/1.45 ? [Xx: $i] :
% 2.41/1.45 ( ( in @ Xx @ ( setunion @ A ) )
% 2.41/1.45 & ? [Xy: $i] :
% 2.41/1.45 ( ( in @ Xy @ ( setunion @ A ) )
% 2.41/1.45 & ( A
% 2.41/1.45 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(secondinupair_type,type,
% 2.41/1.45 secondinupair: $o ).
% 2.41/1.45
% 2.41/1.45 thf(secondinupair,definition,
% 2.41/1.45 ( secondinupair
% 2.41/1.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setukpairIL_type,type,
% 2.41/1.45 setukpairIL: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setukpairIL,definition,
% 2.41/1.45 ( setukpairIL
% 2.41/1.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(setukpairIR_type,type,
% 2.41/1.45 setukpairIR: $o ).
% 2.41/1.45
% 2.41/1.45 thf(setukpairIR,definition,
% 2.41/1.45 ( setukpairIR
% 2.41/1.45 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.41/1.45
% 2.41/1.45 thf(kpairiskpair,conjecture,
% 2.41/1.45 ( setextAx
% 2.41/1.45 => ( emptysetAx
% 2.41/1.45 => ( setadjoinAx
% 2.41/1.45 => ( powersetAx
% 2.41/1.45 => ( setunionAx
% 2.41/1.45 => ( omega0Ax
% 2.41/1.45 => ( omegaSAx
% 2.41/1.45 => ( omegaIndAx
% 2.41/1.45 => ( replAx
% 2.41/1.45 => ( foundationAx
% 2.41/1.45 => ( wellorderingAx
% 2.41/1.45 => ( descrp
% 2.41/1.45 => ( dsetconstrI
% 2.41/1.45 => ( dsetconstrEL
% 2.41/1.45 => ( dsetconstrER
% 2.41/1.45 => ( exuE1
% 2.41/1.45 => ( prop2setE
% 2.41/1.45 => ( emptysetE
% 2.41/1.45 => ( emptysetimpfalse
% 2.41/1.45 => ( notinemptyset
% 2.41/1.45 => ( exuE3e
% 2.41/1.45 => ( setext
% 2.41/1.45 => ( emptyI
% 2.41/1.45 => ( noeltsimpempty
% 2.41/1.45 => ( setbeta
% 2.41/1.45 => ( nonemptyE1
% 2.41/1.45 => ( nonemptyI
% 2.41/1.45 => ( nonemptyI1
% 2.41/1.45 => ( setadjoinIL
% 2.41/1.45 => ( emptyinunitempty
% 2.41/1.45 => ( setadjoinIR
% 2.41/1.45 => ( setadjoinE
% 2.41/1.45 => ( setadjoinOr
% 2.41/1.45 => ( setoftrueEq
% 2.41/1.45 => ( powersetI
% 2.41/1.45 => ( emptyinPowerset
% 2.41/1.45 => ( emptyInPowerset
% 2.41/1.45 => ( powersetE
% 2.41/1.45 => ( setunionI
% 2.41/1.45 => ( setunionE
% 2.41/1.45 => ( subPowSU
% 2.41/1.45 => ( exuE2
% 2.41/1.45 => ( nonemptyImpWitness
% 2.41/1.45 => ( uniqinunit
% 2.41/1.45 => ( notinsingleton
% 2.41/1.45 => ( eqinunit
% 2.41/1.45 => ( singletonsswitch
% 2.41/1.45 => ( upairsetE
% 2.41/1.45 => ( upairsetIL
% 2.41/1.45 => ( upairsetIR
% 2.41/1.45 => ( emptyE1
% 2.41/1.45 => ( vacuousDall
% 2.41/1.45 => ( quantDeMorgan1
% 2.41/1.45 => ( quantDeMorgan2
% 2.41/1.45 => ( quantDeMorgan3
% 2.41/1.45 => ( quantDeMorgan4
% 2.41/1.45 => ( prop2setI
% 2.41/1.45 => ( prop2set2propI
% 2.41/1.45 => ( notdexE
% 2.41/1.45 => ( notdallE
% 2.41/1.45 => ( exuI1
% 2.41/1.45 => ( exuI3
% 2.41/1.45 => ( exuI2
% 2.41/1.45 => ( inCongP
% 2.41/1.45 => ( in__Cong
% 2.41/1.45 => ( exuE3u
% 2.41/1.45 => ( exu__Cong
% 2.41/1.45 => ( emptyset__Cong
% 2.41/1.45 => ( setadjoin__Cong
% 2.41/1.45 => ( powerset__Cong
% 2.41/1.45 => ( setunion__Cong
% 2.41/1.45 => ( omega__Cong
% 2.41/1.45 => ( exuEu
% 2.41/1.45 => ( descr__Cong
% 2.41/1.45 => ( dsetconstr__Cong
% 2.41/1.45 => ( subsetI1
% 2.41/1.45 => ( eqimpsubset2
% 2.41/1.45 => ( eqimpsubset1
% 2.41/1.45 => ( subsetI2
% 2.41/1.45 => ( emptysetsubset
% 2.41/1.45 => ( subsetE
% 2.41/1.45 => ( subsetE2
% 2.41/1.45 => ( notsubsetI
% 2.41/1.45 => ( notequalI1
% 2.41/1.45 => ( notequalI2
% 2.41/1.45 => ( subsetRefl
% 2.41/1.45 => ( subsetTrans
% 2.41/1.45 => ( setadjoinSub
% 2.41/1.45 => ( setadjoinSub2
% 2.41/1.45 => ( subset2powerset
% 2.41/1.45 => ( setextsub
% 2.41/1.45 => ( subsetemptysetimpeq
% 2.41/1.45 => ( powersetI1
% 2.41/1.45 => ( powersetE1
% 2.41/1.45 => ( inPowerset
% 2.41/1.45 => ( powersetsubset
% 2.41/1.45 => ( sepInPowerset
% 2.41/1.45 => ( sepSubset
% 2.41/1.45 => ( binunionIL
% 2.41/1.45 => ( upairset2IR
% 2.41/1.45 => ( binunionIR
% 2.41/1.45 => ( binunionEcases
% 2.41/1.45 => ( binunionE
% 2.41/1.45 => ( binunionLsub
% 2.41/1.45 => ( binunionRsub
% 2.41/1.45 => ( binintersectI
% 2.41/1.45 => ( binintersectSubset5
% 2.41/1.45 => ( binintersectEL
% 2.41/1.45 => ( binintersectLsub
% 2.41/1.45 => ( binintersectSubset2
% 2.41/1.45 => ( binintersectSubset3
% 2.41/1.45 => ( binintersectER
% 2.41/1.45 => ( disjointsetsI1
% 2.41/1.45 => ( binintersectRsub
% 2.41/1.45 => ( binintersectSubset4
% 2.41/1.45 => ( binintersectSubset1
% 2.41/1.45 => ( bs114d
% 2.41/1.45 => ( setminusI
% 2.41/1.45 => ( setminusEL
% 2.41/1.45 => ( setminusER
% 2.41/1.45 => ( setminusSubset2
% 2.41/1.45 => ( setminusERneg
% 2.41/1.45 => ( setminusELneg
% 2.41/1.45 => ( setminusILneg
% 2.41/1.45 => ( setminusIRneg
% 2.41/1.45 => ( setminusLsub
% 2.41/1.45 => ( setminusSubset1
% 2.41/1.45 => ( symdiffE
% 2.41/1.45 => ( symdiffI1
% 2.41/1.45 => ( symdiffI2
% 2.41/1.45 => ( symdiffIneg1
% 2.41/1.45 => ( symdiffIneg2
% 2.41/1.45 => ( secondinupair
% 2.41/1.45 => ( setukpairIL
% 2.41/1.45 => ( setukpairIR
% 2.41/1.45 => ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.41/1.45 ------------------------
% 2.41/1.46 % (22491)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_22295 for (2999ds/2Mi)
% 2.41/1.46 % (22491)Instruction limit reached!
% 2.41/1.46 % (22491)------------------------------
% 2.41/1.46 % (22491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.46 % (22488)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_22295 for (2999ds/4Mi)
% 2.41/1.46 % (22491)Termination reason: Unknown
% 2.41/1.46 % (22491)Termination phase: shuffling
% 2.41/1.46
% 2.41/1.46 % (22491)Memory used [KB]: 1151
% 2.41/1.46 % (22491)Time elapsed: 0.002 s
% 2.41/1.46 % (22491)Instructions burned: 2 (million)
% 2.41/1.46 % (22491)------------------------------
% 2.41/1.46 % (22491)------------------------------
% 2.41/1.46 % (22492)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_22295 for (2999ds/275Mi)
% 2.41/1.46 % (22488)Instruction limit reached!
% 2.41/1.46 % (22488)------------------------------
% 2.41/1.46 % (22488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.46 % (22488)Termination reason: Unknown
% 2.41/1.46 % (22488)Termination phase: shuffling
% 2.41/1.46
% 2.41/1.46 % (22488)Memory used [KB]: 1279
% 2.41/1.46 % (22488)Time elapsed: 0.003 s
% 2.41/1.46 % (22488)Instructions burned: 7 (million)
% 2.41/1.46 % (22488)------------------------------
% 2.41/1.46 % (22488)------------------------------
% 2.41/1.46 % (22490)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22295 for (2999ds/2Mi)
% 2.41/1.46 % (22490)Instruction limit reached!
% 2.41/1.46 % (22490)------------------------------
% 2.41/1.46 % (22490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.46 % (22490)Termination reason: Unknown
% 2.41/1.46 % (22490)Termination phase: shuffling
% 2.41/1.46
% 2.41/1.46 % (22490)Memory used [KB]: 1151
% 2.41/1.46 % (22490)Time elapsed: 0.002 s
% 2.41/1.46 % (22490)Instructions burned: 2 (million)
% 2.41/1.47 % (22490)------------------------------
% 2.41/1.47 % (22490)------------------------------
% 2.41/1.47 % (22489)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_22295 for (2999ds/27Mi)
% 2.41/1.47 % (22493)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22295 for (2999ds/18Mi)
% 2.41/1.47 % (22495)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_22295 for (2999ds/37Mi)
% 2.41/1.47 % (22494)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_22295 for (2999ds/3Mi)
% 2.41/1.48 % (22494)Instruction limit reached!
% 2.41/1.48 % (22494)------------------------------
% 2.41/1.48 % (22494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.48 % (22494)Termination reason: Unknown
% 2.41/1.48 % (22494)Termination phase: shuffling
% 2.41/1.48
% 2.41/1.48 % (22494)Memory used [KB]: 1151
% 2.41/1.48 % (22494)Time elapsed: 0.003 s
% 2.41/1.48 % (22494)Instructions burned: 3 (million)
% 2.41/1.48 % (22494)------------------------------
% 2.41/1.48 % (22494)------------------------------
% 2.41/1.48 % (22493)Instruction limit reached!
% 2.41/1.48 % (22493)------------------------------
% 2.41/1.48 % (22493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.48 % (22493)Termination reason: Unknown
% 2.41/1.48 % (22493)Termination phase: Preprocessing 1
% 2.41/1.48
% 2.41/1.48 % (22493)Memory used [KB]: 1407
% 2.41/1.48 % (22493)Time elapsed: 0.011 s
% 2.41/1.48 % (22493)Instructions burned: 18 (million)
% 2.41/1.48 % (22493)------------------------------
% 2.41/1.48 % (22493)------------------------------
% 2.41/1.48 % (22487)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22295 for (2999ds/183Mi)
% 2.41/1.48 % (22489)Instruction limit reached!
% 2.41/1.48 % (22489)------------------------------
% 2.41/1.48 % (22489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.48 % (22489)Termination reason: Unknown
% 2.41/1.48 % (22489)Termination phase: Property scanning
% 2.41/1.48
% 2.41/1.48 % (22489)Memory used [KB]: 1663
% 2.41/1.48 % (22489)Time elapsed: 0.016 s
% 2.41/1.48 % (22489)Instructions burned: 27 (million)
% 2.41/1.48 % (22489)------------------------------
% 2.41/1.48 % (22489)------------------------------
% 2.41/1.48 % (22496)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_22295 for (2999ds/15Mi)
% 2.41/1.48 % (22495)Instruction limit reached!
% 2.41/1.48 % (22495)------------------------------
% 2.41/1.48 % (22495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.48 % (22495)Termination reason: Unknown
% 2.41/1.48 % (22495)Termination phase: Property scanning
% 2.41/1.48
% 2.41/1.48 % (22495)Memory used [KB]: 1663
% 2.41/1.48 % (22495)Time elapsed: 0.013 s
% 2.41/1.48 % (22495)Instructions burned: 40 (million)
% 2.41/1.48 % (22495)------------------------------
% 2.41/1.48 % (22495)------------------------------
% 2.41/1.49 % (22497)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_22295 for (2999ds/3Mi)
% 2.41/1.49 % (22496)Instruction limit reached!
% 2.41/1.49 % (22496)------------------------------
% 2.41/1.49 % (22496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.49 % (22496)Termination reason: Unknown
% 2.41/1.49 % (22496)Termination phase: Property scanning
% 2.41/1.49
% 2.41/1.49 % (22496)Memory used [KB]: 1407
% 2.41/1.49 % (22496)Time elapsed: 0.009 s
% 2.41/1.49 % (22496)Instructions burned: 16 (million)
% 2.41/1.49 % (22496)------------------------------
% 2.41/1.49 % (22496)------------------------------
% 2.41/1.49 % (22497)Instruction limit reached!
% 2.41/1.49 % (22497)------------------------------
% 2.41/1.49 % (22497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.49 % (22497)Termination reason: Unknown
% 2.41/1.49 % (22497)Termination phase: shuffling
% 2.41/1.49
% 2.41/1.49 % (22497)Memory used [KB]: 1279
% 2.41/1.49 % (22497)Time elapsed: 0.003 s
% 2.41/1.49 % (22497)Instructions burned: 5 (million)
% 2.41/1.49 % (22497)------------------------------
% 2.41/1.49 % (22497)------------------------------
% 2.41/1.49 % (22500)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_22295 for (2999ds/16Mi)
% 2.41/1.50 % (22498)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_22295 for (2999ds/1041Mi)
% 2.47/1.50 % (22499)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_22295 for (2999ds/7Mi)
% 2.47/1.50 % (22500)Instruction limit reached!
% 2.47/1.50 % (22500)------------------------------
% 2.47/1.50 % (22500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.50 % (22500)Termination reason: Unknown
% 2.47/1.50 % (22500)Termination phase: shuffling
% 2.47/1.50
% 2.47/1.50 % (22500)Memory used [KB]: 1535
% 2.47/1.50 % (22500)Time elapsed: 0.007 s
% 2.47/1.50 % (22500)Instructions burned: 17 (million)
% 2.47/1.50 % (22500)------------------------------
% 2.47/1.50 % (22500)------------------------------
% 2.47/1.50 % (22502)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_22295 for (2999ds/3Mi)
% 2.47/1.50 % (22502)Instruction limit reached!
% 2.47/1.50 % (22502)------------------------------
% 2.47/1.50 % (22502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.50 % (22502)Termination reason: Unknown
% 2.47/1.50 % (22502)Termination phase: shuffling
% 2.47/1.50
% 2.47/1.50 % (22502)Memory used [KB]: 1279
% 2.47/1.50 % (22502)Time elapsed: 0.003 s
% 2.47/1.50 % (22502)Instructions burned: 5 (million)
% 2.47/1.50 % (22502)------------------------------
% 2.47/1.50 % (22502)------------------------------
% 2.47/1.50 % (22499)Instruction limit reached!
% 2.47/1.50 % (22499)------------------------------
% 2.47/1.50 % (22499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.50 % (22499)Termination reason: Unknown
% 2.47/1.50 % (22499)Termination phase: shuffling
% 2.47/1.50
% 2.47/1.50 % (22499)Memory used [KB]: 1279
% 2.47/1.50 % (22499)Time elapsed: 0.006 s
% 2.47/1.50 % (22499)Instructions burned: 7 (million)
% 2.47/1.50 % (22499)------------------------------
% 2.47/1.50 % (22499)------------------------------
% 2.47/1.51 % (22501)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_22295 for (2999ds/3Mi)
% 2.47/1.51 % (22501)Instruction limit reached!
% 2.47/1.51 % (22501)------------------------------
% 2.47/1.51 % (22501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.51 % (22501)Termination reason: Unknown
% 2.47/1.51 % (22501)Termination phase: shuffling
% 2.47/1.51
% 2.47/1.51 % (22501)Memory used [KB]: 1279
% 2.47/1.51 % (22501)Time elapsed: 0.003 s
% 2.47/1.51 % (22501)Instructions burned: 3 (million)
% 2.47/1.51 % (22501)------------------------------
% 2.47/1.51 % (22501)------------------------------
% 2.47/1.51 % (22503)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_22295 for (2999ds/7Mi)
% 2.47/1.51 % (22504)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_22295 for (2999ds/3Mi)
% 2.47/1.51 % (22503)Instruction limit reached!
% 2.47/1.51 % (22503)------------------------------
% 2.47/1.51 % (22503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.51 % (22503)Termination reason: Unknown
% 2.47/1.51 % (22503)Termination phase: shuffling
% 2.47/1.51
% 2.47/1.51 % (22503)Memory used [KB]: 1407
% 2.47/1.51 % (22503)Time elapsed: 0.004 s
% 2.47/1.51 % (22503)Instructions burned: 9 (million)
% 2.47/1.51 % (22503)------------------------------
% 2.47/1.51 % (22503)------------------------------
% 2.47/1.51 % (22504)Instruction limit reached!
% 2.47/1.51 % (22504)------------------------------
% 2.47/1.51 % (22504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.51 % (22504)Termination reason: Unknown
% 2.47/1.51 % (22504)Termination phase: shuffling
% 2.47/1.51
% 2.47/1.51 % (22504)Memory used [KB]: 1279
% 2.47/1.51 % (22504)Time elapsed: 0.003 s
% 2.47/1.51 % (22504)Instructions burned: 6 (million)
% 2.47/1.51 % (22504)------------------------------
% 2.47/1.51 % (22504)------------------------------
% 2.47/1.52 % (22506)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_22295 for (2999ds/18Mi)
% 2.47/1.52 % (22505)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_22295 for (2999ds/4Mi)
% 2.47/1.52 % (22505)Instruction limit reached!
% 2.47/1.52 % (22505)------------------------------
% 2.47/1.52 % (22505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.52 % (22505)Termination reason: Unknown
% 2.47/1.52 % (22505)Termination phase: shuffling
% 2.47/1.52
% 2.47/1.52 % (22505)Memory used [KB]: 1279
% 2.47/1.52 % (22505)Time elapsed: 0.003 s
% 2.47/1.52 % (22505)Instructions burned: 4 (million)
% 2.47/1.52 % (22505)------------------------------
% 2.47/1.52 % (22505)------------------------------
% 2.47/1.52 % (22508)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_22295 for (2999ds/6Mi)
% 2.47/1.52 % (22507)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_22295 for (2999ds/710Mi)
% 2.47/1.52 % (22506)Instruction limit reached!
% 2.47/1.52 % (22506)------------------------------
% 2.47/1.52 % (22506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.52 % (22506)Termination reason: Unknown
% 2.47/1.52 % (22506)Termination phase: shuffling
% 2.47/1.52
% 2.47/1.52 % (22506)Memory used [KB]: 1663
% 2.47/1.52 % (22506)Time elapsed: 0.007 s
% 2.47/1.52 % (22506)Instructions burned: 20 (million)
% 2.47/1.52 % (22506)------------------------------
% 2.47/1.52 % (22506)------------------------------
% 2.47/1.52 % (22508)Instruction limit reached!
% 2.47/1.52 % (22508)------------------------------
% 2.47/1.52 % (22508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.52 % (22508)Termination reason: Unknown
% 2.47/1.52 % (22508)Termination phase: shuffling
% 2.47/1.52
% 2.47/1.52 % (22508)Memory used [KB]: 1279
% 2.47/1.52 % (22508)Time elapsed: 0.003 s
% 2.47/1.52 % (22508)Instructions burned: 7 (million)
% 2.47/1.52 % (22508)------------------------------
% 2.47/1.52 % (22508)------------------------------
% 2.47/1.53 % (22510)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_22295 for (2999ds/21Mi)
% 2.47/1.53 % (22511)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_22295 for (2999ds/5Mi)
% 2.47/1.54 % (22511)Instruction limit reached!
% 2.47/1.54 % (22511)------------------------------
% 2.47/1.54 % (22511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.54 % (22511)Termination reason: Unknown
% 2.47/1.54 % (22511)Termination phase: shuffling
% 2.47/1.54
% 2.47/1.54 % (22511)Memory used [KB]: 1279
% 2.47/1.54 % (22511)Time elapsed: 0.003 s
% 2.47/1.54 % (22511)Instructions burned: 7 (million)
% 2.47/1.54 % (22511)------------------------------
% 2.47/1.54 % (22511)------------------------------
% 2.47/1.54 % (22509)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_22295 for (2999ds/902Mi)
% 2.47/1.54 % (22510)Instruction limit reached!
% 2.47/1.54 % (22510)------------------------------
% 2.47/1.54 % (22510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.54 % (22510)Termination reason: Unknown
% 2.47/1.54 % (22510)Termination phase: Property scanning
% 2.47/1.54
% 2.47/1.54 % (22510)Memory used [KB]: 1663
% 2.47/1.54 % (22510)Time elapsed: 0.010 s
% 2.47/1.54 % (22510)Instructions burned: 21 (million)
% 2.47/1.54 % (22510)------------------------------
% 2.47/1.54 % (22510)------------------------------
% 2.47/1.55 % (22517)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_22295 for (2999ds/6Mi)
% 2.47/1.55 % (22517)Instruction limit reached!
% 2.47/1.55 % (22517)------------------------------
% 2.47/1.55 % (22517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.55 % (22517)Termination reason: Unknown
% 2.47/1.55 % (22517)Termination phase: shuffling
% 2.47/1.55
% 2.47/1.55 % (22517)Memory used [KB]: 1279
% 2.47/1.55 % (22517)Time elapsed: 0.003 s
% 2.47/1.55 % (22517)Instructions burned: 7 (million)
% 2.47/1.55 % (22517)------------------------------
% 2.47/1.55 % (22517)------------------------------
% 2.47/1.55 % (22487)Instruction limit reached!
% 2.47/1.55 % (22487)------------------------------
% 2.47/1.55 % (22487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.55 % (22487)Termination reason: Unknown
% 2.47/1.55 % (22487)Termination phase: Saturation
% 2.47/1.55
% 2.47/1.55 % (22487)Memory used [KB]: 7164
% 2.47/1.55 % (22487)Time elapsed: 0.073 s
% 2.47/1.55 % (22487)Instructions burned: 184 (million)
% 2.47/1.55 % (22487)------------------------------
% 2.47/1.55 % (22487)------------------------------
% 2.47/1.55 % (22518)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_22295 for (2999ds/377Mi)
% 2.47/1.56 % (22492)Instruction limit reached!
% 2.47/1.56 % (22492)------------------------------
% 2.47/1.56 % (22492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.56 % (22492)Termination reason: Unknown
% 2.47/1.56 % (22492)Termination phase: Saturation
% 2.47/1.56
% 2.47/1.56 % (22492)Memory used [KB]: 7803
% 2.47/1.56 % (22492)Time elapsed: 0.096 s
% 2.47/1.56 % (22492)Instructions burned: 275 (million)
% 2.47/1.56 % (22492)------------------------------
% 2.47/1.56 % (22492)------------------------------
% 2.47/1.56 % (22519)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_22295 for (2998ds/779Mi)
% 2.47/1.56 % (22520)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_22295 for (2998ds/19Mi)
% 2.47/1.57 % (22520)Instruction limit reached!
% 2.47/1.57 % (22520)------------------------------
% 2.47/1.57 % (22520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.57 % (22520)Termination reason: Unknown
% 2.47/1.57 % (22520)Termination phase: shuffling
% 2.47/1.57
% 2.47/1.57 % (22520)Memory used [KB]: 1663
% 2.47/1.57 % (22520)Time elapsed: 0.011 s
% 2.47/1.57 % (22520)Instructions burned: 20 (million)
% 2.47/1.57 % (22520)------------------------------
% 2.47/1.57 % (22520)------------------------------
% 2.47/1.57 % (22523)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_22295 for (2998ds/879Mi)
% 2.47/1.59 % (22531)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_22295 for (2998ds/17Mi)
% 2.47/1.60 % (22531)Instruction limit reached!
% 2.47/1.60 % (22531)------------------------------
% 2.47/1.60 % (22531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.60 % (22531)Termination reason: Unknown
% 2.47/1.60 % (22531)Termination phase: shuffling
% 2.47/1.60
% 2.47/1.60 % (22531)Memory used [KB]: 1535
% 2.47/1.60 % (22531)Time elapsed: 0.009 s
% 2.47/1.60 % (22531)Instructions burned: 18 (million)
% 2.47/1.60 % (22531)------------------------------
% 2.47/1.60 % (22531)------------------------------
% 2.47/1.62 % (22538)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_22295 for (2998ds/3Mi)
% 2.47/1.62 % (22538)Instruction limit reached!
% 2.47/1.62 % (22538)------------------------------
% 2.47/1.62 % (22538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.62 % (22538)Termination reason: Unknown
% 2.47/1.62 % (22538)Termination phase: shuffling
% 2.47/1.62
% 2.47/1.62 % (22538)Memory used [KB]: 1151
% 2.47/1.62 % (22538)Time elapsed: 0.003 s
% 2.47/1.62 % (22538)Instructions burned: 3 (million)
% 2.47/1.62 % (22538)------------------------------
% 2.47/1.62 % (22538)------------------------------
% 2.47/1.62 % (22509)Refutation not found, incomplete strategy
% 2.47/1.62 % (22509)------------------------------
% 2.47/1.62 % (22509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.62 % (22509)Termination reason: Refutation not found, incomplete strategy
% 2.47/1.62
% 2.47/1.62
% 2.47/1.62 % (22509)Memory used [KB]: 7291
% 2.47/1.62 % (22509)Time elapsed: 0.086 s
% 2.47/1.62 % (22509)Instructions burned: 135 (million)
% 2.47/1.62 % (22509)------------------------------
% 2.47/1.62 % (22509)------------------------------
% 2.47/1.63 % (22543)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_22295 for (2998ds/30Mi)
% 2.47/1.64 % (22544)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_22295 for (2998ds/127Mi)
% 2.47/1.64 % (22543)Instruction limit reached!
% 2.47/1.64 % (22543)------------------------------
% 2.47/1.64 % (22543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.64 % (22543)Termination reason: Unknown
% 2.47/1.64 % (22543)Termination phase: Preprocessing 3
% 2.47/1.64
% 2.47/1.64 % (22543)Memory used [KB]: 1663
% 2.47/1.64 % (22543)Time elapsed: 0.010 s
% 2.47/1.64 % (22543)Instructions burned: 33 (million)
% 2.47/1.64 % (22543)------------------------------
% 2.47/1.64 % (22543)------------------------------
% 2.47/1.65 % (22549)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_22295 for (2998ds/100Mi)
% 2.47/1.68 % (22544)Instruction limit reached!
% 2.47/1.68 % (22544)------------------------------
% 2.47/1.68 % (22544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.68 % (22544)Termination reason: Unknown
% 2.47/1.68 % (22544)Termination phase: Saturation
% 2.47/1.68
% 2.47/1.68 % (22544)Memory used [KB]: 6780
% 2.47/1.68 % (22544)Time elapsed: 0.038 s
% 2.47/1.68 % (22544)Instructions burned: 128 (million)
% 2.47/1.68 % (22544)------------------------------
% 2.47/1.68 % (22544)------------------------------
% 2.47/1.68 % (22549)Instruction limit reached!
% 2.47/1.68 % (22549)------------------------------
% 2.47/1.68 % (22549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.68 % (22549)Termination reason: Unknown
% 2.47/1.68 % (22549)Termination phase: Saturation
% 2.47/1.68
% 2.47/1.68 % (22549)Memory used [KB]: 6396
% 2.47/1.68 % (22549)Time elapsed: 0.030 s
% 2.47/1.68 % (22549)Instructions burned: 101 (million)
% 2.47/1.68 % (22549)------------------------------
% 2.47/1.68 % (22549)------------------------------
% 2.47/1.69 % (22550)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_22295 for (2997ds/3Mi)
% 2.47/1.69 % (22550)Instruction limit reached!
% 2.47/1.69 % (22550)------------------------------
% 2.47/1.69 % (22550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.69 % (22550)Termination reason: Unknown
% 2.47/1.69 % (22550)Termination phase: shuffling
% 2.47/1.69
% 2.47/1.69 % (22550)Memory used [KB]: 1279
% 2.47/1.69 % (22550)Time elapsed: 0.002 s
% 2.47/1.69 % (22550)Instructions burned: 4 (million)
% 2.47/1.69 % (22550)------------------------------
% 2.47/1.69 % (22550)------------------------------
% 2.47/1.69 % (22551)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_22295 for (2997ds/20Mi)
% 2.47/1.69 % (22518)Instruction limit reached!
% 2.47/1.69 % (22518)------------------------------
% 2.47/1.69 % (22518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.69 % (22518)Termination reason: Unknown
% 2.47/1.69 % (22518)Termination phase: Saturation
% 2.47/1.69
% 2.47/1.69 % (22518)Memory used [KB]: 7419
% 2.47/1.69 % (22518)Time elapsed: 0.139 s
% 2.47/1.69 % (22518)Instructions burned: 377 (million)
% 2.47/1.69 % (22518)------------------------------
% 2.47/1.69 % (22518)------------------------------
% 2.47/1.70 % (22551)Instruction limit reached!
% 2.47/1.70 % (22551)------------------------------
% 2.47/1.70 % (22551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.70 % (22551)Termination reason: Unknown
% 2.47/1.70 % (22551)Termination phase: SInE selection
% 2.47/1.70
% 2.47/1.70 % (22551)Memory used [KB]: 1407
% 2.47/1.70 % (22551)Time elapsed: 0.007 s
% 2.47/1.70 % (22551)Instructions burned: 20 (million)
% 2.47/1.70 % (22551)------------------------------
% 2.47/1.70 % (22551)------------------------------
% 2.47/1.70 % (22552)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_22295 for (2997ds/86Mi)
% 2.47/1.70 % (22553)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_22295 for (2997ds/107Mi)
% 2.47/1.71 % (22554)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_22295 for (2997ds/39Mi)
% 2.47/1.72 % (22554)Instruction limit reached!
% 2.47/1.72 % (22554)------------------------------
% 2.47/1.72 % (22554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.72 % (22554)Termination reason: Unknown
% 2.47/1.72 % (22554)Termination phase: Property scanning
% 2.47/1.72
% 2.47/1.72 % (22554)Memory used [KB]: 1663
% 2.47/1.72 % (22554)Time elapsed: 0.011 s
% 2.47/1.72 % (22554)Instructions burned: 40 (million)
% 2.47/1.72 % (22554)------------------------------
% 2.47/1.72 % (22554)------------------------------
% 2.47/1.72 % (22552)Instruction limit reached!
% 2.47/1.72 % (22552)------------------------------
% 2.47/1.72 % (22552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.72 % (22552)Termination reason: Unknown
% 2.47/1.72 % (22552)Termination phase: Saturation
% 2.47/1.72
% 2.47/1.72 % (22552)Memory used [KB]: 6396
% 2.47/1.72 % (22552)Time elapsed: 0.027 s
% 2.47/1.72 % (22552)Instructions burned: 89 (million)
% 2.47/1.72 % (22552)------------------------------
% 2.47/1.72 % (22552)------------------------------
% 2.47/1.72 % (22555)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_22295 for (2997ds/448Mi)
% 2.47/1.73 % (22553)Instruction limit reached!
% 2.47/1.73 % (22553)------------------------------
% 2.47/1.73 % (22553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.73 % (22553)Termination reason: Unknown
% 2.47/1.73 % (22553)Termination phase: Saturation
% 2.47/1.73
% 2.47/1.73 % (22553)Memory used [KB]: 6652
% 2.47/1.73 % (22553)Time elapsed: 0.030 s
% 2.47/1.73 % (22553)Instructions burned: 110 (million)
% 2.47/1.73 % (22553)------------------------------
% 2.47/1.73 % (22553)------------------------------
% 2.47/1.73 % (22556)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_22295 for (2997ds/46Mi)
% 2.47/1.74 % (22557)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_22295 for (2997ds/98Mi)
% 2.47/1.75 % (22556)Instruction limit reached!
% 2.47/1.75 % (22556)------------------------------
% 2.47/1.75 % (22556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.75 % (22556)Termination reason: Unknown
% 2.47/1.75 % (22556)Termination phase: Property scanning
% 2.47/1.75
% 2.47/1.75 % (22556)Memory used [KB]: 1663
% 2.47/1.75 % (22556)Time elapsed: 0.015 s
% 2.47/1.75 % (22556)Instructions burned: 48 (million)
% 2.47/1.75 % (22556)------------------------------
% 2.47/1.75 % (22556)------------------------------
% 2.47/1.76 % (22558)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_22295 for (2997ds/507Mi)
% 2.47/1.76 % (22519)Instruction limit reached!
% 2.47/1.76 % (22519)------------------------------
% 2.47/1.76 % (22519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.76 % (22519)Termination reason: Unknown
% 2.47/1.76 % (22519)Termination phase: Saturation
% 2.47/1.76
% 2.47/1.76 % (22519)Memory used [KB]: 6524
% 2.47/1.76 % (22519)Time elapsed: 0.203 s
% 2.47/1.76 % (22519)Instructions burned: 779 (million)
% 2.47/1.76 % (22519)------------------------------
% 2.47/1.76 % (22519)------------------------------
% 2.47/1.76 % (22557)Instruction limit reached!
% 2.47/1.76 % (22557)------------------------------
% 2.47/1.76 % (22557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.76 % (22557)Termination reason: Unknown
% 2.47/1.76 % (22557)Termination phase: Saturation
% 2.47/1.76
% 2.47/1.76 % (22557)Memory used [KB]: 1791
% 2.47/1.76 % (22557)Time elapsed: 0.026 s
% 2.47/1.76 % (22557)Instructions burned: 99 (million)
% 2.47/1.76 % (22557)------------------------------
% 2.47/1.76 % (22557)------------------------------
% 2.47/1.77 % (22560)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_22295 for (2996ds/149Mi)
% 2.47/1.77 % (22563)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_22295 for (2996ds/39Mi)
% 2.47/1.78 % (22563)Instruction limit reached!
% 2.47/1.78 % (22563)------------------------------
% 2.47/1.78 % (22563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.78 % (22563)Termination reason: Unknown
% 2.47/1.78 % (22563)Termination phase: Property scanning
% 2.47/1.78
% 2.47/1.78 % (22563)Memory used [KB]: 1791
% 2.47/1.78 % (22563)Time elapsed: 0.012 s
% 2.47/1.78 % (22563)Instructions burned: 40 (million)
% 2.47/1.78 % (22563)------------------------------
% 2.47/1.78 % (22563)------------------------------
% 2.47/1.79 % (22498)Instruction limit reached!
% 2.47/1.79 % (22498)------------------------------
% 2.47/1.79 % (22498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.79 % (22498)Termination reason: Unknown
% 2.47/1.79 % (22498)Termination phase: Saturation
% 2.47/1.79
% 2.47/1.79 % (22498)Memory used [KB]: 8955
% 2.47/1.79 % (22498)Time elapsed: 0.322 s
% 2.47/1.79 % (22498)Instructions burned: 1041 (million)
% 2.47/1.79 % (22498)------------------------------
% 2.47/1.79 % (22498)------------------------------
% 2.47/1.79 % (22572)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_22295 for (2996ds/6Mi)
% 2.47/1.79 % (22572)Instruction limit reached!
% 2.47/1.79 % (22572)------------------------------
% 2.47/1.79 % (22572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.79 % (22572)Termination reason: Unknown
% 2.47/1.79 % (22572)Termination phase: shuffling
% 2.47/1.79
% 2.47/1.79 % (22572)Memory used [KB]: 1279
% 2.47/1.79 % (22572)Time elapsed: 0.003 s
% 2.47/1.79 % (22572)Instructions burned: 8 (million)
% 2.47/1.79 % (22572)------------------------------
% 2.47/1.79 % (22572)------------------------------
% 2.47/1.80 % (22578)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_22295 for (2996ds/1087Mi)
% 2.47/1.80 % (22580)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_22295 for (2996ds/47Mi)
% 2.47/1.81 % (22507)Instruction limit reached!
% 2.47/1.81 % (22507)------------------------------
% 2.47/1.81 % (22507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.81 % (22507)Termination reason: Unknown
% 2.47/1.81 % (22507)Termination phase: Saturation
% 2.47/1.81
% 2.47/1.81 % (22507)Memory used [KB]: 8955
% 2.47/1.81 % (22507)Time elapsed: 0.285 s
% 2.47/1.81 % (22507)Instructions burned: 711 (million)
% 2.47/1.81 % (22507)------------------------------
% 2.47/1.81 % (22507)------------------------------
% 2.47/1.81 % (22560)Instruction limit reached!
% 2.47/1.81 % (22560)------------------------------
% 2.47/1.81 % (22560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.81 % (22560)Termination reason: Unknown
% 2.47/1.81 % (22560)Termination phase: Saturation
% 2.47/1.81
% 2.47/1.81 % (22560)Memory used [KB]: 7036
% 2.47/1.81 % (22560)Time elapsed: 0.045 s
% 2.47/1.81 % (22560)Instructions burned: 149 (million)
% 2.47/1.81 % (22560)------------------------------
% 2.47/1.81 % (22560)------------------------------
% 2.47/1.82 % (22586)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_22295 for (2996ds/44Mi)
% 2.47/1.82 % (22580)Instruction limit reached!
% 2.47/1.82 % (22580)------------------------------
% 2.47/1.82 % (22580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.82 % (22580)Termination reason: Unknown
% 2.47/1.82 % (22580)Termination phase: Property scanning
% 2.47/1.82
% 2.47/1.82 % (22580)Memory used [KB]: 1791
% 2.47/1.82 % (22580)Time elapsed: 0.014 s
% 2.47/1.82 % (22580)Instructions burned: 50 (million)
% 2.47/1.82 % (22580)------------------------------
% 2.47/1.82 % (22580)------------------------------
% 2.47/1.82 % (22589)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_22295 for (2996ds/432Mi)
% 2.47/1.83 % (22592)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_22295 for (2996ds/62Mi)
% 2.47/1.83 % (22586)Instruction limit reached!
% 2.47/1.83 % (22586)------------------------------
% 2.47/1.83 % (22586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.83 % (22586)Termination reason: Unknown
% 2.47/1.83 % (22586)Termination phase: Property scanning
% 2.47/1.83
% 2.47/1.83 % (22586)Memory used [KB]: 1663
% 2.47/1.83 % (22586)Time elapsed: 0.013 s
% 2.47/1.83 % (22586)Instructions burned: 46 (million)
% 2.47/1.83 % (22586)------------------------------
% 2.47/1.83 % (22586)------------------------------
% 2.47/1.83 % (22555)Instruction limit reached!
% 2.47/1.83 % (22555)------------------------------
% 2.47/1.83 % (22555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.83 % (22555)Termination reason: Unknown
% 2.47/1.83 % (22555)Termination phase: Saturation
% 2.47/1.83
% 2.47/1.83 % (22555)Memory used [KB]: 6524
% 2.47/1.83 % (22555)Time elapsed: 0.107 s
% 2.47/1.83 % (22555)Instructions burned: 450 (million)
% 2.47/1.83 % (22555)------------------------------
% 2.47/1.83 % (22555)------------------------------
% 2.47/1.84 % (22600)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_22295 for (2996ds/31Mi)
% 2.47/1.84 % (22603)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_22295 for (2996ds/96Mi)
% 2.47/1.84 % (22592)Instruction limit reached!
% 2.47/1.84 % (22592)------------------------------
% 2.47/1.84 % (22592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.84 % (22592)Termination reason: Unknown
% 2.47/1.84 % (22592)Termination phase: Property scanning
% 2.47/1.84
% 2.47/1.84 % (22592)Memory used [KB]: 1791
% 2.47/1.84 % (22592)Time elapsed: 0.017 s
% 2.47/1.84 % (22592)Instructions burned: 63 (million)
% 2.47/1.84 % (22592)------------------------------
% 2.47/1.84 % (22592)------------------------------
% 2.47/1.85 % (22600)Instruction limit reached!
% 2.47/1.85 % (22600)------------------------------
% 2.47/1.85 % (22600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.85 % (22600)Termination reason: Unknown
% 2.47/1.85 % (22600)Termination phase: Property scanning
% 2.47/1.85
% 2.47/1.85 % (22600)Memory used [KB]: 1663
% 2.47/1.85 % (22600)Time elapsed: 0.010 s
% 2.47/1.85 % (22600)Instructions burned: 34 (million)
% 2.47/1.85 % (22600)------------------------------
% 2.47/1.85 % (22600)------------------------------
% 2.47/1.85 % (22609)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_22295 for (2995ds/453Mi)
% 2.47/1.86 % (22610)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_22295 for (2995ds/71Mi)
% 2.47/1.87 % (22603)Instruction limit reached!
% 2.47/1.87 % (22603)------------------------------
% 2.47/1.87 % (22603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.87 % (22603)Termination reason: Unknown
% 2.47/1.87 % (22603)Termination phase: Saturation
% 2.47/1.87
% 2.47/1.87 % (22603)Memory used [KB]: 6652
% 2.47/1.87 % (22603)Time elapsed: 0.027 s
% 2.47/1.87 % (22603)Instructions burned: 98 (million)
% 2.47/1.87 % (22603)------------------------------
% 2.47/1.87 % (22603)------------------------------
% 2.47/1.87 % (22523)Instruction limit reached!
% 2.47/1.87 % (22523)------------------------------
% 2.47/1.87 % (22523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.87 % (22523)Termination reason: Unknown
% 2.47/1.87 % (22523)Termination phase: Saturation
% 2.47/1.87
% 2.47/1.87 % (22523)Memory used [KB]: 7931
% 2.47/1.87 % (22523)Time elapsed: 0.299 s
% 2.47/1.87 % (22523)Instructions burned: 880 (million)
% 2.47/1.87 % (22523)------------------------------
% 2.47/1.87 % (22523)------------------------------
% 2.47/1.88 % (22610)Instruction limit reached!
% 2.47/1.88 % (22610)------------------------------
% 2.47/1.88 % (22610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.88 % (22610)Termination reason: Unknown
% 2.47/1.88 % (22610)Termination phase: Saturation
% 2.47/1.88
% 2.47/1.88 % (22610)Memory used [KB]: 6268
% 2.47/1.88 % (22610)Time elapsed: 0.020 s
% 2.47/1.88 % (22610)Instructions burned: 73 (million)
% 2.47/1.88 % (22610)------------------------------
% 2.47/1.88 % (22610)------------------------------
% 2.47/1.88 % (22618)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_22295 for (2995ds/83Mi)
% 2.47/1.88 % (22621)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_22295 for (2995ds/11Mi)
% 2.47/1.88 % (22621)Instruction limit reached!
% 2.47/1.88 % (22621)------------------------------
% 2.47/1.88 % (22621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.88 % (22621)Termination reason: Unknown
% 2.47/1.88 % (22621)Termination phase: shuffling
% 2.47/1.88
% 2.47/1.88 % (22621)Memory used [KB]: 1407
% 2.47/1.88 % (22621)Time elapsed: 0.004 s
% 2.47/1.88 % (22621)Instructions burned: 11 (million)
% 2.47/1.88 % (22621)------------------------------
% 2.47/1.88 % (22621)------------------------------
% 2.47/1.88 % (22625)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_22295 for (2995ds/41Mi)
% 2.47/1.89 % (22628)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_22295 for (2995ds/6Mi)
% 2.47/1.89 % (22628)Instruction limit reached!
% 2.47/1.89 % (22628)------------------------------
% 2.47/1.89 % (22628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.89 % (22628)Termination reason: Unknown
% 2.47/1.89 % (22628)Termination phase: shuffling
% 2.47/1.89
% 2.47/1.89 % (22628)Memory used [KB]: 1279
% 2.47/1.89 % (22628)Time elapsed: 0.003 s
% 2.47/1.89 % (22628)Instructions burned: 6 (million)
% 2.47/1.89 % (22628)------------------------------
% 2.47/1.89 % (22628)------------------------------
% 2.47/1.90 % (22625)Instruction limit reached!
% 2.47/1.90 % (22625)------------------------------
% 2.47/1.90 % (22625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.90 % (22625)Termination reason: Unknown
% 2.47/1.90 % (22625)Termination phase: Property scanning
% 2.47/1.90
% 2.47/1.90 % (22625)Memory used [KB]: 1663
% 2.47/1.90 % (22625)Time elapsed: 0.012 s
% 2.47/1.90 % (22625)Instructions burned: 42 (million)
% 2.47/1.90 % (22625)------------------------------
% 2.47/1.90 % (22625)------------------------------
% 2.47/1.90 % (22618)Instruction limit reached!
% 2.47/1.90 % (22618)------------------------------
% 2.47/1.90 % (22618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.90 % (22618)Termination reason: Unknown
% 2.47/1.90 % (22618)Termination phase: Saturation
% 2.47/1.90
% 2.47/1.90 % (22618)Memory used [KB]: 6396
% 2.47/1.90 % (22618)Time elapsed: 0.023 s
% 2.47/1.90 % (22618)Instructions burned: 84 (million)
% 2.47/1.90 % (22618)------------------------------
% 2.47/1.90 % (22618)------------------------------
% 2.47/1.90 % (22632)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_22295 for (2995ds/150Mi)
% 2.47/1.91 % (22634)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_22295 for (2995ds/109Mi)
% 2.47/1.91 % (22633)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_22295 for (2995ds/343Mi)
% 2.47/1.92 % (22558)Instruction limit reached!
% 2.47/1.92 % (22558)------------------------------
% 2.47/1.92 % (22558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.92 % (22558)Termination reason: Unknown
% 2.47/1.92 % (22558)Termination phase: Saturation
% 2.47/1.92
% 2.47/1.92 % (22558)Memory used [KB]: 7164
% 2.47/1.92 % (22558)Time elapsed: 0.164 s
% 2.47/1.92 % (22558)Instructions burned: 509 (million)
% 2.47/1.92 % (22558)------------------------------
% 2.47/1.92 % (22558)------------------------------
% 2.47/1.93 % (22644)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_22295 for (2995ds/253Mi)
% 2.47/1.93 % (22589)Instruction limit reached!
% 2.47/1.93 % (22589)------------------------------
% 2.47/1.93 % (22589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.93 % (22589)Termination reason: Unknown
% 2.47/1.93 % (22589)Termination phase: Saturation
% 2.47/1.93
% 2.47/1.93 % (22589)Memory used [KB]: 2814
% 2.47/1.93 % (22589)Time elapsed: 0.109 s
% 2.47/1.93 % (22589)Instructions burned: 434 (million)
% 2.47/1.93 % (22589)------------------------------
% 2.47/1.93 % (22589)------------------------------
% 2.47/1.94 % (22634)Instruction limit reached!
% 2.47/1.94 % (22634)------------------------------
% 2.47/1.94 % (22634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.94 % (22634)Termination reason: Unknown
% 2.47/1.94 % (22634)Termination phase: Saturation
% 2.47/1.94
% 2.47/1.94 % (22634)Memory used [KB]: 6652
% 2.47/1.94 % (22634)Time elapsed: 0.030 s
% 2.47/1.94 % (22634)Instructions burned: 109 (million)
% 2.47/1.94 % (22634)------------------------------
% 2.47/1.94 % (22634)------------------------------
% 2.47/1.94 % (22645)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_22295 for (2995ds/140Mi)
% 2.47/1.95 % (22654)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_22295 for (2995ds/614Mi)
% 2.47/1.95 % (22632)Instruction limit reached!
% 2.47/1.95 % (22632)------------------------------
% 2.47/1.95 % (22632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.95 % (22632)Termination reason: Unknown
% 2.47/1.95 % (22632)Termination phase: Saturation
% 2.47/1.95
% 2.47/1.95 % (22632)Memory used [KB]: 7675
% 2.47/1.95 % (22632)Time elapsed: 0.046 s
% 2.47/1.95 % (22632)Instructions burned: 152 (million)
% 2.47/1.95 % (22632)------------------------------
% 2.47/1.95 % (22632)------------------------------
% 2.47/1.96 % (22660)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_22295 for (2995ds/202Mi)
% 2.47/1.96 % (22609)Instruction limit reached!
% 2.47/1.96 % (22609)------------------------------
% 2.47/1.96 % (22609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.96 % (22609)Termination reason: Unknown
% 2.47/1.96 % (22609)Termination phase: Saturation
% 2.47/1.96
% 2.47/1.96 % (22609)Memory used [KB]: 6524
% 2.47/1.96 % (22609)Time elapsed: 0.112 s
% 2.47/1.96 % (22609)Instructions burned: 456 (million)
% 2.47/1.96 % (22609)------------------------------
% 2.47/1.96 % (22609)------------------------------
% 2.47/1.97 % (22668)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_22295 for (2994ds/339Mi)
% 2.47/1.98 % (22645)Instruction limit reached!
% 2.47/1.98 % (22645)------------------------------
% 2.47/1.98 % (22645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.98 % (22645)Termination reason: Unknown
% 2.47/1.98 % (22645)Termination phase: Saturation
% 2.47/1.98
% 2.47/1.98 % (22645)Memory used [KB]: 6396
% 2.47/1.98 % (22645)Time elapsed: 0.040 s
% 2.47/1.98 % (22645)Instructions burned: 142 (million)
% 2.47/1.98 % (22645)------------------------------
% 2.47/1.98 % (22645)------------------------------
% 2.47/1.99 % (22675)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_22295 for (2994ds/283Mi)
% 2.47/2.00 % (22644)Instruction limit reached!
% 2.47/2.00 % (22644)------------------------------
% 2.47/2.00 % (22644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/2.00 % (22644)Termination reason: Unknown
% 2.47/2.00 % (22644)Termination phase: Saturation
% 2.47/2.00
% 2.47/2.00 % (22644)Memory used [KB]: 7931
% 2.47/2.00 % (22644)Time elapsed: 0.077 s
% 2.47/2.00 % (22644)Instructions burned: 254 (million)
% 2.47/2.00 % (22644)------------------------------
% 2.47/2.00 % (22644)------------------------------
% 6.32/2.01 % (22694)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_22295 for (2994ds/134Mi)
% 6.32/2.02 % (22660)Instruction limit reached!
% 6.32/2.02 % (22660)------------------------------
% 6.32/2.02 % (22660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.32/2.02 % (22660)Termination reason: Unknown
% 6.32/2.02 % (22660)Termination phase: Saturation
% 6.32/2.02
% 6.32/2.02 % (22660)Memory used [KB]: 8059
% 6.32/2.02 % (22660)Time elapsed: 0.062 s
% 6.32/2.02 % (22660)Instructions burned: 202 (million)
% 6.32/2.02 % (22660)------------------------------
% 6.32/2.02 % (22660)------------------------------
% 6.32/2.03 % (22695)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_22295 for (2994ds/298Mi)
% 6.32/2.05 % (22633)Instruction limit reached!
% 6.32/2.05 % (22633)------------------------------
% 6.32/2.05 % (22633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.32/2.05 % (22633)Termination reason: Unknown
% 6.32/2.05 % (22633)Termination phase: Saturation
% 6.32/2.05
% 6.32/2.05 % (22633)Memory used [KB]: 7291
% 6.32/2.05 % (22633)Time elapsed: 0.136 s
% 6.32/2.05 % (22633)Instructions burned: 345 (million)
% 6.32/2.05 % (22633)------------------------------
% 6.32/2.05 % (22633)------------------------------
% 6.32/2.05 % (22694)Instruction limit reached!
% 6.32/2.05 % (22694)------------------------------
% 6.32/2.05 % (22694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.32/2.05 % (22694)Termination reason: Unknown
% 6.32/2.05 % (22694)Termination phase: Saturation
% 6.32/2.05
% 6.32/2.05 % (22694)Memory used [KB]: 6780
% 6.32/2.05 % (22694)Time elapsed: 0.037 s
% 6.32/2.05 % (22694)Instructions burned: 136 (million)
% 6.32/2.05 % (22694)------------------------------
% 6.32/2.05 % (22694)------------------------------
% 6.32/2.06 % (22712)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_22295 for (2994ds/192Mi)
% 6.32/2.06 % (22675)Instruction limit reached!
% 6.32/2.06 % (22675)------------------------------
% 6.32/2.06 % (22675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.32/2.06 % (22675)Termination reason: Unknown
% 6.32/2.06 % (22675)Termination phase: Saturation
% 6.32/2.06
% 6.32/2.06 % (22675)Memory used [KB]: 9210
% 6.32/2.06 % (22675)Time elapsed: 0.071 s
% 6.32/2.06 % (22675)Instructions burned: 283 (million)
% 6.32/2.06 % (22675)------------------------------
% 6.32/2.06 % (22675)------------------------------
% 6.32/2.06 % (22714)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_22295 for (2994ds/258Mi)
% 6.32/2.07 % (22719)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_22295 for (2993ds/90Mi)
% 6.32/2.07 % (22668)Instruction limit reached!
% 6.32/2.07 % (22668)------------------------------
% 6.32/2.07 % (22668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.32/2.07 % (22668)Termination reason: Unknown
% 6.32/2.07 % (22668)Termination phase: Saturation
% 6.32/2.07
% 6.32/2.07 % (22668)Memory used [KB]: 7419
% 6.32/2.07 % (22668)Time elapsed: 0.098 s
% 6.32/2.07 % (22668)Instructions burned: 339 (million)
% 6.32/2.07 % (22668)------------------------------
% 6.32/2.07 % (22668)------------------------------
% 6.32/2.08 % (22727)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_22295 for (2993ds/231Mi)
% 6.32/2.09 % (22719)Instruction limit reached!
% 6.32/2.09 % (22719)------------------------------
% 6.32/2.09 % (22719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.32/2.09 % (22719)Termination reason: Unknown
% 6.32/2.09 % (22719)Termination phase: Saturation
% 6.32/2.09
% 6.32/2.09 % (22719)Memory used [KB]: 6652
% 6.32/2.09 % (22719)Time elapsed: 0.025 s
% 6.32/2.09 % (22719)Instructions burned: 91 (million)
% 6.32/2.09 % (22719)------------------------------
% 6.32/2.09 % (22719)------------------------------
% 6.32/2.10 % (22736)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_22295 for (2993ds/458Mi)
% 6.32/2.10 % (22695)Instruction limit reached!
% 6.32/2.10 % (22695)------------------------------
% 6.32/2.10 % (22695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.32/2.10 % (22695)Termination reason: Unknown
% 6.32/2.10 % (22695)Termination phase: Saturation
% 6.32/2.10
% 6.32/2.10 % (22695)Memory used [KB]: 6524
% 6.32/2.10 % (22695)Time elapsed: 0.076 s
% 6.32/2.10 % (22695)Instructions burned: 300 (million)
% 6.32/2.10 % (22695)------------------------------
% 6.32/2.10 % (22695)------------------------------
% 6.32/2.11 % (22740)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_22295 for (2993ds/31Mi)
% 6.86/2.12 % (22712)Instruction limit reached!
% 6.86/2.12 % (22712)------------------------------
% 6.86/2.12 % (22712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.12 % (22712)Termination reason: Unknown
% 6.86/2.12 % (22712)Termination phase: Saturation
% 6.86/2.12
% 6.86/2.12 % (22712)Memory used [KB]: 7164
% 6.86/2.12 % (22712)Time elapsed: 0.061 s
% 6.86/2.12 % (22712)Instructions burned: 194 (million)
% 6.86/2.12 % (22712)------------------------------
% 6.86/2.12 % (22712)------------------------------
% 6.86/2.12 % (22740)Instruction limit reached!
% 6.86/2.12 % (22740)------------------------------
% 6.86/2.12 % (22740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.12 % (22740)Termination reason: Unknown
% 6.86/2.12 % (22740)Termination phase: Preprocessing 1
% 6.86/2.12
% 6.86/2.12 % (22740)Memory used [KB]: 1663
% 6.86/2.12 % (22740)Time elapsed: 0.010 s
% 6.86/2.12 % (22740)Instructions burned: 32 (million)
% 6.86/2.12 % (22740)------------------------------
% 6.86/2.12 % (22740)------------------------------
% 6.86/2.13 % (22746)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_22295 for (2993ds/297Mi)
% 6.86/2.13 % (22747)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_22295 for (2993ds/987Mi)
% 6.86/2.13 % (22654)Instruction limit reached!
% 6.86/2.13 % (22654)------------------------------
% 6.86/2.13 % (22654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.13 % (22654)Termination reason: Unknown
% 6.86/2.13 % (22654)Termination phase: Saturation
% 6.86/2.13
% 6.86/2.13 % (22654)Memory used [KB]: 8059
% 6.86/2.13 % (22654)Time elapsed: 0.189 s
% 6.86/2.13 % (22654)Instructions burned: 616 (million)
% 6.86/2.13 % (22654)------------------------------
% 6.86/2.13 % (22654)------------------------------
% 6.86/2.14 % (22714)Instruction limit reached!
% 6.86/2.14 % (22714)------------------------------
% 6.86/2.14 % (22714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.14 % (22714)Termination reason: Unknown
% 6.86/2.14 % (22714)Termination phase: Saturation
% 6.86/2.14
% 6.86/2.14 % (22714)Memory used [KB]: 7164
% 6.86/2.14 % (22714)Time elapsed: 0.077 s
% 6.86/2.14 % (22714)Instructions burned: 260 (million)
% 6.86/2.14 % (22714)------------------------------
% 6.86/2.14 % (22714)------------------------------
% 6.86/2.14 % (22754)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_22295 for (2993ds/182Mi)
% 6.86/2.14 % (22727)Instruction limit reached!
% 6.86/2.14 % (22727)------------------------------
% 6.86/2.14 % (22727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.14 % (22727)Termination reason: Unknown
% 6.86/2.14 % (22727)Termination phase: Saturation
% 6.86/2.14
% 6.86/2.14 % (22727)Memory used [KB]: 10234
% 6.86/2.14 % (22727)Time elapsed: 0.067 s
% 6.86/2.14 % (22727)Instructions burned: 231 (million)
% 6.86/2.14 % (22727)------------------------------
% 6.86/2.14 % (22727)------------------------------
% 6.86/2.14 % (22756)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_22295 for (2993ds/182Mi)
% 6.86/2.15 % (22578)Instruction limit reached!
% 6.86/2.15 % (22578)------------------------------
% 6.86/2.15 % (22578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.15 % (22578)Termination reason: Unknown
% 6.86/2.15 % (22578)Termination phase: Saturation
% 6.86/2.15
% 6.86/2.15 % (22578)Memory used [KB]: 10234
% 6.86/2.15 % (22578)Time elapsed: 0.369 s
% 6.86/2.15 % (22578)Instructions burned: 1089 (million)
% 6.86/2.15 % (22578)------------------------------
% 6.86/2.15 % (22578)------------------------------
% 6.86/2.16 % (22762)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_22295 for (2993ds/154Mi)
% 6.86/2.16 % (22764)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_22295 for (2993ds/79Mi)
% 6.86/2.18 % (22764)Instruction limit reached!
% 6.86/2.18 % (22764)------------------------------
% 6.86/2.18 % (22764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.18 % (22764)Termination reason: Unknown
% 6.86/2.18 % (22764)Termination phase: Saturation
% 6.86/2.18
% 6.86/2.18 % (22764)Memory used [KB]: 6396
% 6.86/2.18 % (22764)Time elapsed: 0.023 s
% 6.86/2.18 % (22764)Instructions burned: 79 (million)
% 6.86/2.18 % (22764)------------------------------
% 6.86/2.18 % (22764)------------------------------
% 6.86/2.19 % (22772)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_22295 for (2992ds/216Mi)
% 6.86/2.19 % (22762)Instruction limit reached!
% 6.86/2.19 % (22762)------------------------------
% 6.86/2.19 % (22762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.19 % (22762)Termination reason: Unknown
% 6.86/2.19 % (22762)Termination phase: Saturation
% 6.86/2.19
% 6.86/2.19 % (22762)Memory used [KB]: 6524
% 6.86/2.19 % (22762)Time elapsed: 0.041 s
% 6.86/2.19 % (22762)Instructions burned: 157 (million)
% 6.86/2.19 % (22762)------------------------------
% 6.86/2.19 % (22762)------------------------------
% 6.86/2.19 % (22754)Instruction limit reached!
% 6.86/2.19 % (22754)------------------------------
% 6.86/2.19 % (22754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.19 % (22754)Termination reason: Unknown
% 6.86/2.19 % (22754)Termination phase: Saturation
% 6.86/2.19
% 6.86/2.19 % (22754)Memory used [KB]: 7036
% 6.86/2.19 % (22754)Time elapsed: 0.053 s
% 6.86/2.19 % (22754)Instructions burned: 182 (million)
% 6.86/2.19 % (22754)------------------------------
% 6.86/2.19 % (22754)------------------------------
% 7.32/2.20 % (22756)Instruction limit reached!
% 7.32/2.20 % (22756)------------------------------
% 7.32/2.20 % (22756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.32/2.20 % (22756)Termination reason: Unknown
% 7.32/2.20 % (22756)Termination phase: Saturation
% 7.32/2.20
% 7.32/2.20 % (22756)Memory used [KB]: 9083
% 7.32/2.20 % (22756)Time elapsed: 0.079 s
% 7.32/2.20 % (22756)Instructions burned: 183 (million)
% 7.32/2.20 % (22756)------------------------------
% 7.32/2.20 % (22756)------------------------------
% 7.32/2.20 % (22781)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_22295 for (2992ds/114Mi)
% 7.32/2.20 % (22782)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_22295 for (2992ds/922Mi)
% 7.32/2.21 % (22746)Instruction limit reached!
% 7.32/2.21 % (22746)------------------------------
% 7.32/2.21 % (22746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.32/2.21 % (22746)Termination reason: Unknown
% 7.32/2.21 % (22746)Termination phase: Saturation
% 7.32/2.21
% 7.32/2.21 % (22746)Memory used [KB]: 8187
% 7.32/2.21 % (22746)Time elapsed: 0.082 s
% 7.32/2.21 % (22746)Instructions burned: 297 (million)
% 7.32/2.21 % (22746)------------------------------
% 7.32/2.21 % (22746)------------------------------
% 7.32/2.21 % (22784)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_22295 for (2992ds/182Mi)
% 7.32/2.22 % (22788)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_22295 for (2992ds/164Mi)
% 7.32/2.24 % (22781)Instruction limit reached!
% 7.32/2.24 % (22781)------------------------------
% 7.32/2.24 % (22781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.32/2.24 % (22781)Termination reason: Unknown
% 7.32/2.24 % (22781)Termination phase: Saturation
% 7.32/2.24
% 7.32/2.24 % (22781)Memory used [KB]: 6780
% 7.32/2.24 % (22781)Time elapsed: 0.033 s
% 7.32/2.24 % (22781)Instructions burned: 116 (million)
% 7.32/2.24 % (22781)------------------------------
% 7.32/2.24 % (22781)------------------------------
% 7.32/2.24 % (22736)Instruction limit reached!
% 7.32/2.24 % (22736)------------------------------
% 7.32/2.24 % (22736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.32/2.24 % (22736)Termination reason: Unknown
% 7.32/2.24 % (22736)Termination phase: Saturation
% 7.32/2.24
% 7.32/2.24 % (22736)Memory used [KB]: 7803
% 7.32/2.24 % (22736)Time elapsed: 0.142 s
% 7.32/2.24 % (22736)Instructions burned: 459 (million)
% 7.32/2.24 % (22736)------------------------------
% 7.32/2.24 % (22736)------------------------------
% 7.32/2.25 % (22772)Instruction limit reached!
% 7.32/2.25 % (22772)------------------------------
% 7.32/2.25 % (22772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.32/2.25 % (22772)Termination reason: Unknown
% 7.32/2.25 % (22772)Termination phase: Saturation
% 7.32/2.25
% 7.32/2.25 % (22772)Memory used [KB]: 6780
% 7.32/2.25 % (22772)Time elapsed: 0.056 s
% 7.32/2.25 % (22772)Instructions burned: 218 (million)
% 7.32/2.25 % (22772)------------------------------
% 7.32/2.25 % (22772)------------------------------
% 7.32/2.25 % (22795)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_22295 for (2992ds/50Mi)
% 7.32/2.25 % (22799)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_22295 for (2991ds/368Mi)
% 7.32/2.26 % (22802)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_22295 for (2991ds/1021Mi)
% 7.32/2.26 % (22784)Instruction limit reached!
% 7.32/2.26 % (22784)------------------------------
% 7.32/2.26 % (22784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.32/2.26 % (22784)Termination reason: Unknown
% 7.32/2.26 % (22784)Termination phase: Saturation
% 7.32/2.26
% 7.32/2.26 % (22784)Memory used [KB]: 6524
% 7.32/2.26 % (22784)Time elapsed: 0.049 s
% 7.32/2.26 % (22784)Instructions burned: 185 (million)
% 7.32/2.26 % (22784)------------------------------
% 7.32/2.26 % (22784)------------------------------
% 7.32/2.26 % (22795)Instruction limit reached!
% 7.32/2.26 % (22795)------------------------------
% 7.32/2.26 % (22795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.32/2.26 % (22795)Termination reason: Unknown
% 7.32/2.26 % (22795)Termination phase: Property scanning
% 7.32/2.26
% 7.32/2.26 % (22795)Memory used [KB]: 1663
% 7.32/2.26 % (22795)Time elapsed: 0.015 s
% 7.32/2.26 % (22795)Instructions burned: 53 (million)
% 7.32/2.26 % (22795)------------------------------
% 7.32/2.26 % (22795)------------------------------
% 7.32/2.27 % (22788)Instruction limit reached!
% 7.32/2.27 % (22788)------------------------------
% 7.32/2.27 % (22788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.32/2.27 % (22788)Termination reason: Unknown
% 7.32/2.27 % (22788)Termination phase: Saturation
% 7.32/2.27
% 7.32/2.27 % (22788)Memory used [KB]: 2174
% 7.32/2.27 % (22788)Time elapsed: 0.052 s
% 7.32/2.27 % (22788)Instructions burned: 165 (million)
% 7.32/2.27 % (22788)------------------------------
% 7.32/2.27 % (22788)------------------------------
% 7.32/2.27 % (22812)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_22295 for (2991ds/267Mi)
% 7.32/2.27 % (22813)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_22295 for (2991ds/204Mi)
% 7.32/2.28 % (22819)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_22295 for (2991ds/26Mi)
% 7.32/2.29 % (22819)Instruction limit reached!
% 7.32/2.29 % (22819)------------------------------
% 7.32/2.29 % (22819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.32/2.29 % (22819)Termination reason: Unknown
% 7.32/2.29 % (22819)Termination phase: Property scanning
% 7.32/2.29
% 7.32/2.29 % (22819)Memory used [KB]: 1663
% 7.32/2.29 % (22819)Time elapsed: 0.010 s
% 7.32/2.29 % (22819)Instructions burned: 29 (million)
% 7.32/2.29 % (22819)------------------------------
% 7.32/2.29 % (22819)------------------------------
% 7.32/2.30 % (22832)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_22295 for (2991ds/53Mi)
% 7.90/2.31 % (22832)Instruction limit reached!
% 7.90/2.31 % (22832)------------------------------
% 7.90/2.31 % (22832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.90/2.31 % (22832)Termination reason: Unknown
% 7.90/2.31 % (22832)Termination phase: Property scanning
% 7.90/2.31
% 7.90/2.31 % (22832)Memory used [KB]: 1663
% 7.90/2.31 % (22832)Time elapsed: 0.017 s
% 7.90/2.31 % (22832)Instructions burned: 56 (million)
% 7.90/2.31 % (22832)------------------------------
% 7.90/2.31 % (22832)------------------------------
% 7.90/2.32 % (22841)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_22295 for (2991ds/4436Mi)
% 7.90/2.33 % (22813)Instruction limit reached!
% 7.90/2.33 % (22813)------------------------------
% 7.90/2.33 % (22813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.90/2.33 % (22813)Termination reason: Unknown
% 7.90/2.33 % (22813)Termination phase: Saturation
% 7.90/2.33
% 7.90/2.33 % (22813)Memory used [KB]: 7036
% 7.90/2.33 % (22813)Time elapsed: 0.059 s
% 7.90/2.33 % (22813)Instructions burned: 205 (million)
% 7.90/2.33 % (22813)------------------------------
% 7.90/2.33 % (22813)------------------------------
% 7.90/2.34 % (22812)Instruction limit reached!
% 7.90/2.34 % (22812)------------------------------
% 7.90/2.34 % (22812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.90/2.34 % (22812)Termination reason: Unknown
% 7.90/2.34 % (22812)Termination phase: Saturation
% 7.90/2.34
% 7.90/2.34 % (22812)Memory used [KB]: 9210
% 7.90/2.34 % (22812)Time elapsed: 0.068 s
% 7.90/2.34 % (22812)Instructions burned: 268 (million)
% 7.90/2.34 % (22812)------------------------------
% 7.90/2.34 % (22812)------------------------------
% 7.90/2.34 % (22842)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_22295 for (2991ds/1539Mi)
% 7.90/2.35 % (22843)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_22295 for (2991ds/408Mi)
% 7.90/2.36 % (22799)Instruction limit reached!
% 7.90/2.36 % (22799)------------------------------
% 7.90/2.36 % (22799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.90/2.36 % (22799)Termination reason: Unknown
% 7.90/2.36 % (22799)Termination phase: Saturation
% 7.90/2.36
% 7.90/2.36 % (22799)Memory used [KB]: 7419
% 7.90/2.36 % (22799)Time elapsed: 0.114 s
% 7.90/2.36 % (22799)Instructions burned: 368 (million)
% 7.90/2.36 % (22799)------------------------------
% 7.90/2.36 % (22799)------------------------------
% 7.90/2.37 % (22747)Instruction limit reached!
% 7.90/2.37 % (22747)------------------------------
% 7.90/2.37 % (22747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.90/2.37 % (22747)Termination reason: Unknown
% 7.90/2.37 % (22747)Termination phase: Saturation
% 7.90/2.37
% 7.90/2.37 % (22747)Memory used [KB]: 8699
% 7.90/2.37 % (22747)Time elapsed: 0.240 s
% 7.90/2.37 % (22747)Instructions burned: 988 (million)
% 7.90/2.37 % (22747)------------------------------
% 7.90/2.37 % (22747)------------------------------
% 7.90/2.37 % (22844)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_22295 for (2990ds/5205Mi)
% 7.90/2.38 % (22845)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_22295 for (2990ds/1913Mi)
% 8.45/2.48 % (22843)Instruction limit reached!
% 8.45/2.48 % (22843)------------------------------
% 8.45/2.48 % (22843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.45/2.48 % (22843)Termination reason: Unknown
% 8.45/2.48 % (22843)Termination phase: Saturation
% 8.45/2.48
% 8.45/2.48 % (22843)Memory used [KB]: 8955
% 8.45/2.48 % (22843)Time elapsed: 0.133 s
% 8.45/2.48 % (22843)Instructions burned: 410 (million)
% 8.45/2.48 % (22843)------------------------------
% 8.45/2.48 % (22843)------------------------------
% 8.45/2.49 % (22846)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_22295 for (2989ds/4350Mi)
% 8.58/2.50 % (22782)Instruction limit reached!
% 8.58/2.50 % (22782)------------------------------
% 8.58/2.50 % (22782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.58/2.50 % (22782)Termination reason: Unknown
% 8.58/2.50 % (22782)Termination phase: Saturation
% 8.58/2.50
% 8.58/2.50 % (22782)Memory used [KB]: 9210
% 8.58/2.50 % (22782)Time elapsed: 0.315 s
% 8.58/2.50 % (22782)Instructions burned: 922 (million)
% 8.58/2.50 % (22782)------------------------------
% 8.58/2.50 % (22782)------------------------------
% 8.58/2.51 % (22847)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_22295 for (2989ds/68Mi)
% 8.58/2.52 % (22847)Instruction limit reached!
% 8.58/2.52 % (22847)------------------------------
% 8.58/2.52 % (22847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.58/2.52 % (22847)Termination reason: Unknown
% 8.58/2.52 % (22847)Termination phase: Property scanning
% 8.58/2.52
% 8.58/2.52 % (22847)Memory used [KB]: 1791
% 8.58/2.52 % (22847)Time elapsed: 0.018 s
% 8.58/2.52 % (22847)Instructions burned: 68 (million)
% 8.58/2.52 % (22847)------------------------------
% 8.58/2.52 % (22847)------------------------------
% 8.58/2.53 % (22848)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_22295 for (2989ds/358Mi)
% 8.58/2.58 % (22802)Instruction limit reached!
% 8.58/2.58 % (22802)------------------------------
% 8.58/2.58 % (22802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.58/2.58 % (22802)Termination reason: Unknown
% 8.58/2.58 % (22802)Termination phase: Saturation
% 8.58/2.58
% 8.58/2.58 % (22802)Memory used [KB]: 9466
% 8.58/2.58 % (22802)Time elapsed: 0.326 s
% 8.58/2.58 % (22802)Instructions burned: 1023 (million)
% 8.58/2.58 % (22802)------------------------------
% 8.58/2.58 % (22802)------------------------------
% 8.58/2.59 % (22849)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_22295 for (2988ds/31Mi)
% 9.26/2.60 % (22849)Instruction limit reached!
% 9.26/2.60 % (22849)------------------------------
% 9.26/2.60 % (22849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/2.60 % (22849)Termination reason: Unknown
% 9.26/2.60 % (22849)Termination phase: Property scanning
% 9.26/2.60
% 9.26/2.60 % (22849)Memory used [KB]: 1663
% 9.26/2.60 % (22849)Time elapsed: 0.010 s
% 9.26/2.60 % (22849)Instructions burned: 32 (million)
% 9.26/2.60 % (22849)------------------------------
% 9.26/2.60 % (22849)------------------------------
% 9.26/2.61 % (22850)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_22295 for (2988ds/279Mi)
% 9.26/2.64 % (22848)Instruction limit reached!
% 9.26/2.64 % (22848)------------------------------
% 9.26/2.64 % (22848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/2.64 % (22848)Termination reason: Unknown
% 9.26/2.64 % (22848)Termination phase: Saturation
% 9.26/2.64
% 9.26/2.64 % (22848)Memory used [KB]: 7291
% 9.26/2.64 % (22848)Time elapsed: 0.108 s
% 9.26/2.64 % (22848)Instructions burned: 361 (million)
% 9.26/2.64 % (22848)------------------------------
% 9.26/2.64 % (22848)------------------------------
% 9.26/2.65 % (22851)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_22295 for (2988ds/258Mi)
% 9.26/2.68 % (22850)Instruction limit reached!
% 9.26/2.68 % (22850)------------------------------
% 9.26/2.68 % (22850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/2.68 % (22850)Termination reason: Unknown
% 9.26/2.68 % (22850)Termination phase: Saturation
% 9.26/2.68
% 9.26/2.68 % (22850)Memory used [KB]: 6524
% 9.26/2.68 % (22850)Time elapsed: 0.069 s
% 9.26/2.68 % (22850)Instructions burned: 281 (million)
% 9.26/2.68 % (22850)------------------------------
% 9.26/2.68 % (22850)------------------------------
% 9.26/2.69 % (22852)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_22295 for (2987ds/26Mi)
% 9.26/2.69 % (22852)Instruction limit reached!
% 9.26/2.69 % (22852)------------------------------
% 9.26/2.69 % (22852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/2.69 % (22852)Termination reason: Unknown
% 9.26/2.69 % (22852)Termination phase: Property scanning
% 9.26/2.69
% 9.26/2.69 % (22852)Memory used [KB]: 1663
% 9.26/2.69 % (22852)Time elapsed: 0.008 s
% 9.26/2.69 % (22852)Instructions burned: 27 (million)
% 9.26/2.69 % (22852)------------------------------
% 9.26/2.69 % (22852)------------------------------
% 9.50/2.70 % (22853)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_22295 for (2987ds/995Mi)
% 9.50/2.72 % (22851)Instruction limit reached!
% 9.50/2.72 % (22851)------------------------------
% 9.50/2.72 % (22851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.50/2.72 % (22851)Termination reason: Unknown
% 9.50/2.72 % (22851)Termination phase: Saturation
% 9.50/2.72
% 9.50/2.72 % (22851)Memory used [KB]: 7931
% 9.50/2.72 % (22851)Time elapsed: 0.072 s
% 9.50/2.72 % (22851)Instructions burned: 259 (million)
% 9.50/2.72 % (22851)------------------------------
% 9.50/2.72 % (22851)------------------------------
% 9.50/2.73 % (22854)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_22295 for (2987ds/373Mi)
% 9.58/2.82 % (22842)Instruction limit reached!
% 9.58/2.82 % (22842)------------------------------
% 9.58/2.82 % (22842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.58/2.82 % (22842)Termination reason: Unknown
% 9.58/2.82 % (22842)Termination phase: Saturation
% 9.58/2.82
% 9.58/2.82 % (22842)Memory used [KB]: 8699
% 9.58/2.82 % (22842)Time elapsed: 0.481 s
% 9.58/2.82 % (22842)Instructions burned: 1541 (million)
% 9.58/2.82 % (22842)------------------------------
% 9.58/2.82 % (22842)------------------------------
% 9.58/2.83 % (22855)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_22295 for (2986ds/253Mi)
% 9.58/2.84 % (22854)Instruction limit reached!
% 9.58/2.84 % (22854)------------------------------
% 9.58/2.84 % (22854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.58/2.84 % (22854)Termination reason: Unknown
% 9.58/2.84 % (22854)Termination phase: Saturation
% 9.58/2.84
% 9.58/2.84 % (22854)Memory used [KB]: 7419
% 9.58/2.84 % (22854)Time elapsed: 0.115 s
% 9.58/2.84 % (22854)Instructions burned: 374 (million)
% 9.58/2.84 % (22854)------------------------------
% 9.58/2.84 % (22854)------------------------------
% 9.58/2.85 % (22856)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_22295 for (2986ds/832Mi)
% 9.58/2.89 % (22855)Instruction limit reached!
% 9.58/2.89 % (22855)------------------------------
% 9.58/2.89 % (22855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.58/2.89 % (22855)Termination reason: Unknown
% 9.58/2.89 % (22855)Termination phase: Saturation
% 9.58/2.89
% 9.58/2.89 % (22855)Memory used [KB]: 6524
% 9.58/2.89 % (22855)Time elapsed: 0.063 s
% 9.58/2.89 % (22855)Instructions burned: 256 (million)
% 9.58/2.89 % (22855)------------------------------
% 9.58/2.89 % (22855)------------------------------
% 10.26/2.90 % (22857)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_22295 for (2985ds/668Mi)
% 10.26/2.90 % (22856)Refutation not found, incomplete strategy
% 10.26/2.90 % (22856)------------------------------
% 10.26/2.90 % (22856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.26/2.90 % (22856)Termination reason: Refutation not found, incomplete strategy
% 10.26/2.90
% 10.26/2.90
% 10.26/2.90 % (22856)Memory used [KB]: 7675
% 10.26/2.90 % (22856)Time elapsed: 0.045 s
% 10.26/2.90 % (22856)Instructions burned: 146 (million)
% 10.26/2.90 % (22856)------------------------------
% 10.26/2.90 % (22856)------------------------------
% 10.26/2.91 % (22858)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_22295 for (2985ds/40Mi)
% 10.26/2.92 % (22858)Instruction limit reached!
% 10.26/2.92 % (22858)------------------------------
% 10.26/2.92 % (22858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.26/2.92 % (22858)Termination reason: Unknown
% 10.26/2.92 % (22858)Termination phase: Property scanning
% 10.26/2.92
% 10.26/2.92 % (22858)Memory used [KB]: 1663
% 10.26/2.92 % (22858)Time elapsed: 0.012 s
% 10.26/2.92 % (22858)Instructions burned: 44 (million)
% 10.26/2.92 % (22858)------------------------------
% 10.26/2.92 % (22858)------------------------------
% 10.26/2.93 % (22859)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_22295 for (2985ds/294Mi)
% 10.26/2.95 % (22853)Instruction limit reached!
% 10.26/2.95 % (22853)------------------------------
% 10.26/2.95 % (22853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.26/2.95 % (22853)Termination reason: Unknown
% 10.26/2.95 % (22853)Termination phase: Saturation
% 10.26/2.95
% 10.26/2.95 % (22853)Memory used [KB]: 8699
% 10.26/2.95 % (22853)Time elapsed: 0.245 s
% 10.26/2.95 % (22853)Instructions burned: 999 (million)
% 10.26/2.95 % (22853)------------------------------
% 10.26/2.95 % (22853)------------------------------
% 10.26/2.95 % (22845)Instruction limit reached!
% 10.26/2.95 % (22845)------------------------------
% 10.26/2.95 % (22845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.26/2.95 % (22845)Termination reason: Unknown
% 10.26/2.95 % (22845)Termination phase: Saturation
% 10.26/2.95
% 10.26/2.95 % (22845)Memory used [KB]: 3454
% 10.26/2.95 % (22845)Time elapsed: 0.568 s
% 10.26/2.95 % (22845)Instructions burned: 1915 (million)
% 10.26/2.95 % (22845)------------------------------
% 10.26/2.95 % (22845)------------------------------
% 10.26/2.96 % (22860)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_22295 for (2985ds/187Mi)
% 10.26/2.96 % (22861)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_22295 for (2985ds/371Mi)
% 10.26/3.00 % (22859)Instruction limit reached!
% 10.26/3.00 % (22859)------------------------------
% 10.26/3.00 % (22859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.26/3.00 % (22859)Termination reason: Unknown
% 10.26/3.00 % (22859)Termination phase: Saturation
% 10.26/3.00
% 10.26/3.00 % (22859)Memory used [KB]: 6268
% 10.26/3.00 % (22859)Time elapsed: 0.074 s
% 10.26/3.00 % (22859)Instructions burned: 295 (million)
% 10.26/3.00 % (22859)------------------------------
% 10.26/3.00 % (22859)------------------------------
% 10.26/3.01 % (22860)Instruction limit reached!
% 10.26/3.01 % (22860)------------------------------
% 10.26/3.01 % (22860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.26/3.01 % (22860)Termination reason: Unknown
% 10.26/3.01 % (22860)Termination phase: Saturation
% 10.26/3.01
% 10.26/3.01 % (22860)Memory used [KB]: 7164
% 10.26/3.01 % (22860)Time elapsed: 0.054 s
% 10.26/3.01 % (22860)Instructions burned: 188 (million)
% 10.26/3.01 % (22860)------------------------------
% 10.26/3.01 % (22860)------------------------------
% 10.26/3.01 % (22862)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_22295 for (2984ds/1827Mi)
% 10.26/3.02 % (22863)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_22295 for (2984ds/70Mi)
% 13.40/3.04 % (22863)Instruction limit reached!
% 13.40/3.04 % (22863)------------------------------
% 13.40/3.04 % (22863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.40/3.04 % (22863)Termination reason: Unknown
% 13.40/3.04 % (22863)Termination phase: Saturation
% 13.40/3.04
% 13.40/3.04 % (22863)Memory used [KB]: 1791
% 13.40/3.04 % (22863)Time elapsed: 0.019 s
% 13.40/3.04 % (22863)Instructions burned: 72 (million)
% 13.40/3.04 % (22863)------------------------------
% 13.40/3.04 % (22863)------------------------------
% 13.40/3.05 % (22864)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_22295 for (2984ds/316Mi)
% 13.40/3.06 % (22857)Instruction limit reached!
% 13.40/3.06 % (22857)------------------------------
% 13.40/3.06 % (22857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.40/3.06 % (22857)Termination reason: Unknown
% 13.40/3.06 % (22857)Termination phase: Saturation
% 13.40/3.06
% 13.40/3.06 % (22857)Memory used [KB]: 13176
% 13.40/3.06 % (22857)Time elapsed: 0.166 s
% 13.40/3.06 % (22857)Instructions burned: 672 (million)
% 13.40/3.06 % (22857)------------------------------
% 13.40/3.06 % (22857)------------------------------
% 13.40/3.07 % (22861)Refutation not found, non-redundant clauses discarded% (22861)------------------------------
% 13.40/3.07 % (22861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.40/3.07 % (22861)Termination reason: Refutation not found, non-redundant clauses discarded
% 13.40/3.07
% 13.40/3.07 % (22861)Memory used [KB]: 7547
% 13.40/3.07 % (22861)Time elapsed: 0.111 s
% 13.40/3.07 % (22861)Instructions burned: 369 (million)
% 13.40/3.07 % (22861)------------------------------
% 13.40/3.07 % (22861)------------------------------
% 13.40/3.07 % (22865)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_22295 for (2983ds/932Mi)
% 13.40/3.08 % (22866)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_22295 for (2983ds/4714Mi)
% 13.82/3.12 % (22864)Instruction limit reached!
% 13.82/3.12 % (22864)------------------------------
% 13.82/3.12 % (22864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.82/3.12 % (22864)Termination reason: Unknown
% 13.82/3.12 % (22864)Termination phase: Saturation
% 13.82/3.12
% 13.82/3.12 % (22864)Memory used [KB]: 7164
% 13.82/3.12 % (22864)Time elapsed: 0.080 s
% 13.82/3.12 % (22864)Instructions burned: 318 (million)
% 13.82/3.12 % (22864)------------------------------
% 13.82/3.12 % (22864)------------------------------
% 13.82/3.13 % (22867)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_22295 for (2983ds/8250Mi)
% 14.44/3.30 % (22865)Instruction limit reached!
% 14.44/3.30 % (22865)------------------------------
% 14.44/3.30 % (22865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.44/3.30 % (22865)Termination reason: Unknown
% 14.44/3.30 % (22865)Termination phase: Saturation
% 14.44/3.30
% 14.44/3.30 % (22865)Memory used [KB]: 9466
% 14.44/3.30 % (22865)Time elapsed: 0.233 s
% 14.44/3.30 % (22865)Instructions burned: 932 (million)
% 14.44/3.30 % (22865)------------------------------
% 14.44/3.30 % (22865)------------------------------
% 14.44/3.31 % (22868)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_22295 for (2981ds/770Mi)
% 15.27/3.53 % (22868)Instruction limit reached!
% 15.27/3.53 % (22868)------------------------------
% 15.27/3.53 % (22868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.27/3.53 % (22868)Termination reason: Unknown
% 15.27/3.53 % (22868)Termination phase: Saturation
% 15.27/3.53
% 15.27/3.53 % (22868)Memory used [KB]: 6652
% 15.27/3.53 % (22868)Time elapsed: 0.220 s
% 15.27/3.53 % (22868)Instructions burned: 772 (million)
% 15.27/3.53 % (22868)------------------------------
% 15.27/3.53 % (22868)------------------------------
% 15.27/3.54 % (22869)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_22295 for (2979ds/794Mi)
% 15.27/3.55 % (22862)Instruction limit reached!
% 15.27/3.55 % (22862)------------------------------
% 15.27/3.55 % (22862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.27/3.55 % (22862)Termination reason: Unknown
% 15.27/3.55 % (22862)Termination phase: Saturation
% 15.27/3.55
% 15.27/3.55 % (22862)Memory used [KB]: 15607
% 15.27/3.55 % (22862)Time elapsed: 0.560 s
% 15.27/3.55 % (22862)Instructions burned: 1829 (million)
% 15.27/3.55 % (22862)------------------------------
% 15.27/3.55 % (22862)------------------------------
% 15.27/3.56 % (22870)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_22295 for (2978ds/464Mi)
% 16.35/3.62 % (22844)Instruction limit reached!
% 16.35/3.62 % (22844)------------------------------
% 16.35/3.62 % (22844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.35/3.62 % (22844)Termination reason: Unknown
% 16.35/3.62 % (22844)Termination phase: Saturation
% 16.35/3.62
% 16.35/3.62 % (22844)Memory used [KB]: 10490
% 16.35/3.62 % (22844)Time elapsed: 1.251 s
% 16.35/3.62 % (22844)Instructions burned: 5207 (million)
% 16.35/3.62 % (22844)------------------------------
% 16.35/3.62 % (22844)------------------------------
% 16.35/3.63 % (22871)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_22295 for (2978ds/1376Mi)
% 16.58/3.70 % (22870)Instruction limit reached!
% 16.58/3.70 % (22870)------------------------------
% 16.58/3.70 % (22870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.58/3.70 % (22870)Termination reason: Unknown
% 16.58/3.70 % (22870)Termination phase: Saturation
% 16.58/3.70
% 16.58/3.70 % (22870)Memory used [KB]: 7803
% 16.58/3.70 % (22870)Time elapsed: 0.140 s
% 16.58/3.70 % (22870)Instructions burned: 464 (million)
% 16.58/3.70 % (22870)------------------------------
% 16.58/3.70 % (22870)------------------------------
% 16.58/3.71 % (22872)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_22295 for (2977ds/906Mi)
% 16.58/3.73 % (22841)Instruction limit reached!
% 16.58/3.73 % (22841)------------------------------
% 16.58/3.73 % (22841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.58/3.73 % (22841)Termination reason: Unknown
% 16.58/3.73 % (22841)Termination phase: Saturation
% 16.58/3.73
% 16.58/3.73 % (22841)Memory used [KB]: 14711
% 16.58/3.73 % (22841)Time elapsed: 1.410 s
% 16.58/3.73 % (22841)Instructions burned: 4436 (million)
% 16.58/3.73 % (22841)------------------------------
% 16.58/3.73 % (22841)------------------------------
% 16.58/3.74 % (22873)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_22295 for (2977ds/434Mi)
% 16.58/3.79 % (22869)Instruction limit reached!
% 16.58/3.79 % (22869)------------------------------
% 16.58/3.79 % (22869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.58/3.79 % (22869)Termination reason: Unknown
% 16.58/3.79 % (22869)Termination phase: Saturation
% 16.58/3.79
% 16.58/3.79 % (22869)Memory used [KB]: 3837
% 16.58/3.79 % (22869)Time elapsed: 0.247 s
% 16.58/3.79 % (22869)Instructions burned: 795 (million)
% 16.58/3.79 % (22869)------------------------------
% 16.58/3.79 % (22869)------------------------------
% 17.15/3.80 % (22846)Instruction limit reached!
% 17.15/3.80 % (22846)------------------------------
% 17.15/3.80 % (22846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.15/3.80 % (22846)Termination reason: Unknown
% 17.15/3.80 % (22846)Termination phase: Saturation
% 17.15/3.80
% 17.15/3.80 % (22846)Memory used [KB]: 10234
% 17.15/3.80 % (22846)Time elapsed: 1.312 s
% 17.15/3.80 % (22846)Instructions burned: 4351 (million)
% 17.15/3.80 % (22846)------------------------------
% 17.15/3.80 % (22846)------------------------------
% 17.15/3.80 % (22874)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_22295 for (2976ds/865Mi)
% 17.15/3.81 % (22875)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_22295 for (2976ds/593Mi)
% 17.15/3.87 % (22873)Instruction limit reached!
% 17.15/3.87 % (22873)------------------------------
% 17.15/3.87 % (22873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.15/3.87 % (22873)Termination reason: Unknown
% 17.15/3.87 % (22873)Termination phase: Saturation
% 17.15/3.87
% 17.15/3.87 % (22873)Memory used [KB]: 8699
% 17.15/3.87 % (22873)Time elapsed: 0.131 s
% 17.15/3.87 % (22873)Instructions burned: 434 (million)
% 17.15/3.87 % (22873)------------------------------
% 17.15/3.87 % (22873)------------------------------
% 17.15/3.88 % (22876)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_22295 for (2975ds/443Mi)
% 17.30/3.95 % (22875)Instruction limit reached!
% 17.30/3.95 % (22875)------------------------------
% 17.30/3.95 % (22875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.30/3.95 % (22875)Termination reason: Unknown
% 17.30/3.95 % (22875)Termination phase: Saturation
% 17.30/3.95
% 17.30/3.95 % (22875)Memory used [KB]: 6524
% 17.30/3.95 % (22875)Time elapsed: 0.139 s
% 17.30/3.95 % (22875)Instructions burned: 594 (million)
% 17.30/3.95 % (22875)------------------------------
% 17.30/3.95 % (22875)------------------------------
% 17.30/3.96 % (22877)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_22295 for (2974ds/594Mi)
% 17.30/3.98 % (22871)Instruction limit reached!
% 17.30/3.98 % (22871)------------------------------
% 17.30/3.98 % (22871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.30/3.98 % (22871)Termination reason: Unknown
% 17.30/3.98 % (22871)Termination phase: Saturation
% 17.30/3.98
% 17.30/3.98 % (22871)Memory used [KB]: 8059
% 17.30/3.98 % (22871)Time elapsed: 0.346 s
% 17.30/3.98 % (22871)Instructions burned: 1380 (million)
% 17.30/3.98 % (22871)------------------------------
% 17.30/3.98 % (22871)------------------------------
% 17.30/3.98 % (22872)Instruction limit reached!
% 17.30/3.98 % (22872)------------------------------
% 17.30/3.98 % (22872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.30/3.98 % (22872)Termination reason: Unknown
% 17.30/3.98 % (22872)Termination phase: Saturation
% 17.30/3.98
% 17.30/3.98 % (22872)Memory used [KB]: 8699
% 17.30/3.98 % (22872)Time elapsed: 0.279 s
% 17.30/3.98 % (22872)Instructions burned: 906 (million)
% 17.30/3.98 % (22872)------------------------------
% 17.30/3.98 % (22872)------------------------------
% 17.30/3.99 % (22878)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_22295 for (2974ds/327Mi)
% 17.30/4.00 % (22879)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_22295 for (2974ds/5411Mi)
% 17.30/4.01 % (22876)Instruction limit reached!
% 17.30/4.01 % (22876)------------------------------
% 17.30/4.01 % (22876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.30/4.01 % (22876)Termination reason: Unknown
% 17.30/4.01 % (22876)Termination phase: Saturation
% 17.30/4.01
% 17.30/4.01 % (22876)Memory used [KB]: 7675
% 17.30/4.01 % (22876)Time elapsed: 0.134 s
% 17.30/4.01 % (22876)Instructions burned: 443 (million)
% 17.30/4.01 % (22876)------------------------------
% 17.30/4.01 % (22876)------------------------------
% 17.30/4.02 % (22880)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_22295 for (2974ds/1762Mi)
% 20.43/4.04 % (22874)Instruction limit reached!
% 20.43/4.04 % (22874)------------------------------
% 20.43/4.04 % (22874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.43/4.04 % (22874)Termination reason: Unknown
% 20.43/4.04 % (22874)Termination phase: Saturation
% 20.43/4.04
% 20.43/4.04 % (22874)Memory used [KB]: 7675
% 20.43/4.04 % (22874)Time elapsed: 0.239 s
% 20.43/4.04 % (22874)Instructions burned: 866 (million)
% 20.43/4.04 % (22874)------------------------------
% 20.43/4.04 % (22874)------------------------------
% 20.43/4.05 % (22881)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_22295 for (2974ds/96Mi)
% 20.43/4.07 % (22881)Instruction limit reached!
% 20.43/4.07 % (22881)------------------------------
% 20.43/4.07 % (22881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.43/4.07 % (22881)Termination reason: Unknown
% 20.43/4.07 % (22881)Termination phase: Saturation
% 20.43/4.07
% 20.43/4.07 % (22881)Memory used [KB]: 6396
% 20.43/4.07 % (22881)Time elapsed: 0.025 s
% 20.43/4.07 % (22881)Instructions burned: 96 (million)
% 20.43/4.07 % (22881)------------------------------
% 20.43/4.07 % (22881)------------------------------
% 20.43/4.08 % (22882)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_22295 for (2973ds/503Mi)
% 20.43/4.09 % (22878)Instruction limit reached!
% 20.43/4.09 % (22878)------------------------------
% 20.43/4.09 % (22878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.43/4.09 % (22878)Termination reason: Unknown
% 20.43/4.09 % (22878)Termination phase: Saturation
% 20.43/4.09
% 20.43/4.09 % (22878)Memory used [KB]: 8955
% 20.43/4.09 % (22878)Time elapsed: 0.106 s
% 20.43/4.09 % (22878)Instructions burned: 329 (million)
% 20.43/4.09 % (22878)------------------------------
% 20.43/4.09 % (22878)------------------------------
% 20.43/4.10 % (22866)Instruction limit reached!
% 20.43/4.10 % (22866)------------------------------
% 20.43/4.10 % (22866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.43/4.10 % (22866)Termination reason: Unknown
% 20.43/4.10 % (22866)Termination phase: Saturation
% 20.43/4.10
% 20.43/4.10 % (22866)Memory used [KB]: 6908
% 20.43/4.10 % (22866)Time elapsed: 1.022 s
% 20.43/4.10 % (22866)Instructions burned: 4716 (million)
% 20.43/4.10 % (22866)------------------------------
% 20.43/4.10 % (22866)------------------------------
% 20.43/4.10 % (22883)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_22295 for (2973ds/90Mi)
% 20.43/4.11 % (22884)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_22295 for (2973ds/593Mi)
% 20.95/4.13 % (22883)Instruction limit reached!
% 20.95/4.13 % (22883)------------------------------
% 20.95/4.13 % (22883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.95/4.13 % (22883)Termination reason: Unknown
% 20.95/4.13 % (22883)Termination phase: Saturation
% 20.95/4.13
% 20.95/4.13 % (22883)Memory used [KB]: 6652
% 20.95/4.13 % (22883)Time elapsed: 0.026 s
% 20.95/4.13 % (22883)Instructions burned: 90 (million)
% 20.95/4.13 % (22883)------------------------------
% 20.95/4.13 % (22883)------------------------------
% 20.95/4.14 % (22885)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_22295 for (2973ds/1512Mi)
% 20.95/4.14 % (22877)Instruction limit reached!
% 20.95/4.14 % (22877)------------------------------
% 20.95/4.14 % (22877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.95/4.14 % (22877)Termination reason: Unknown
% 20.95/4.14 % (22877)Termination phase: Saturation
% 20.95/4.14
% 20.95/4.14 % (22877)Memory used [KB]: 7803
% 20.95/4.14 % (22877)Time elapsed: 0.183 s
% 20.95/4.14 % (22877)Instructions burned: 596 (million)
% 20.95/4.14 % (22877)------------------------------
% 20.95/4.14 % (22877)------------------------------
% 20.95/4.15 % (22886)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_22295 for (2973ds/569Mi)
% 20.95/4.19 % (22885)Refutation not found, incomplete strategy
% 20.95/4.19 % (22885)------------------------------
% 20.95/4.19 % (22885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.95/4.19 % (22885)Termination reason: Refutation not found, incomplete strategy
% 20.95/4.19
% 20.95/4.19
% 20.95/4.19 % (22885)Memory used [KB]: 7675
% 20.95/4.19 % (22885)Time elapsed: 0.050 s
% 20.95/4.19 % (22885)Instructions burned: 163 (million)
% 20.95/4.19 % (22885)------------------------------
% 20.95/4.19 % (22885)------------------------------
% 20.95/4.20 % (22887)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_22295 for (2972ds/501Mi)
% 21.21/4.23 % (22882)Instruction limit reached!
% 21.21/4.23 % (22882)------------------------------
% 21.21/4.23 % (22882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.21/4.23 % (22882)Termination reason: Unknown
% 21.21/4.23 % (22882)Termination phase: Saturation
% 21.21/4.23
% 21.21/4.23 % (22882)Memory used [KB]: 7675
% 21.21/4.23 % (22882)Time elapsed: 0.154 s
% 21.21/4.23 % (22882)Instructions burned: 503 (million)
% 21.21/4.23 % (22882)------------------------------
% 21.21/4.23 % (22882)------------------------------
% 21.21/4.24 % (22888)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_22295 for (2972ds/562Mi)
% 21.21/4.29 % (22886)Instruction limit reached!
% 21.21/4.29 % (22886)------------------------------
% 21.21/4.29 % (22886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.21/4.29 % (22886)Termination reason: Unknown
% 21.21/4.29 % (22886)Termination phase: Saturation
% 21.21/4.29
% 21.21/4.29 % (22886)Memory used [KB]: 8571
% 21.21/4.29 % (22886)Time elapsed: 0.140 s
% 21.21/4.29 % (22886)Instructions burned: 571 (million)
% 21.21/4.29 % (22886)------------------------------
% 21.21/4.29 % (22886)------------------------------
% 21.21/4.29 % (22884)Instruction limit reached!
% 21.21/4.29 % (22884)------------------------------
% 21.21/4.29 % (22884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.21/4.29 % (22884)Termination reason: Unknown
% 21.21/4.29 % (22884)Termination phase: Saturation
% 21.21/4.29
% 21.21/4.29 % (22884)Memory used [KB]: 7419
% 21.21/4.29 % (22884)Time elapsed: 0.185 s
% 21.21/4.29 % (22884)Instructions burned: 595 (million)
% 21.21/4.29 % (22884)------------------------------
% 21.21/4.29 % (22884)------------------------------
% 21.21/4.30 % (22889)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_22295 for (2971ds/406Mi)
% 21.92/4.30 % (22890)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_22295 for (2971ds/582Mi)
% 21.92/4.35 % (22887)Instruction limit reached!
% 21.92/4.35 % (22887)------------------------------
% 21.92/4.35 % (22887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.92/4.35 % (22887)Termination reason: Unknown
% 21.92/4.35 % (22887)Termination phase: Saturation
% 21.92/4.35
% 21.92/4.35 % (22887)Memory used [KB]: 8571
% 21.92/4.35 % (22887)Time elapsed: 0.155 s
% 21.92/4.35 % (22887)Instructions burned: 504 (million)
% 21.92/4.35 % (22887)------------------------------
% 21.92/4.35 % (22887)------------------------------
% 21.92/4.36 % (22891)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_22295 for (2970ds/456Mi)
% 21.92/4.37 % (22889)Refutation not found, incomplete strategy
% 21.92/4.37 % (22889)------------------------------
% 21.92/4.37 % (22889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.92/4.37 % (22889)Termination reason: Refutation not found, incomplete strategy
% 21.92/4.37
% 21.92/4.37
% 21.92/4.37 % (22889)Memory used [KB]: 6652
% 21.92/4.37 % (22889)Time elapsed: 0.070 s
% 21.92/4.37 % (22889)Instructions burned: 254 (million)
% 21.92/4.37 % (22889)------------------------------
% 21.92/4.37 % (22889)------------------------------
% 21.92/4.38 % (22892)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_22295 for (2970ds/393Mi)
% 21.92/4.39 % (22888)Instruction limit reached!
% 21.92/4.39 % (22888)------------------------------
% 21.92/4.39 % (22888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.92/4.39 % (22888)Termination reason: Unknown
% 21.92/4.39 % (22888)Termination phase: Saturation
% 21.92/4.39
% 21.92/4.39 % (22888)Memory used [KB]: 6780
% 21.92/4.39 % (22888)Time elapsed: 0.144 s
% 21.92/4.39 % (22888)Instructions burned: 563 (million)
% 21.92/4.39 % (22888)------------------------------
% 21.92/4.39 % (22888)------------------------------
% 21.92/4.40 % (22893)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_22295 for (2970ds/1335Mi)
% 22.53/4.47 % (22880)Instruction limit reached!
% 22.53/4.47 % (22880)------------------------------
% 22.53/4.47 % (22880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.53/4.47 % (22880)Termination reason: Unknown
% 22.53/4.47 % (22880)Termination phase: Saturation
% 22.53/4.47
% 22.53/4.47 % (22880)Memory used [KB]: 10362
% 22.53/4.47 % (22880)Time elapsed: 0.444 s
% 22.53/4.47 % (22880)Instructions burned: 1762 (million)
% 22.53/4.47 % (22880)------------------------------
% 22.53/4.47 % (22880)------------------------------
% 22.53/4.48 % (22894)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_22295 for (2969ds/3373Mi)
% 22.53/4.49 % (22890)Instruction limit reached!
% 22.53/4.49 % (22890)------------------------------
% 22.53/4.49 % (22890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.53/4.49 % (22890)Termination reason: Unknown
% 22.53/4.49 % (22890)Termination phase: Saturation
% 22.53/4.49
% 22.53/4.49 % (22890)Memory used [KB]: 8699
% 22.53/4.49 % (22890)Time elapsed: 0.186 s
% 22.53/4.49 % (22890)Instructions burned: 584 (million)
% 22.53/4.49 % (22890)------------------------------
% 22.53/4.49 % (22890)------------------------------
% 22.53/4.50 % (22895)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_22295 for (2969ds/474Mi)
% 22.53/4.50 % (22892)Instruction limit reached!
% 22.53/4.50 % (22892)------------------------------
% 22.53/4.50 % (22892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.53/4.50 % (22892)Termination reason: Unknown
% 22.53/4.50 % (22892)Termination phase: Saturation
% 22.53/4.50
% 22.53/4.50 % (22892)Memory used [KB]: 8059
% 22.53/4.50 % (22892)Time elapsed: 0.121 s
% 22.53/4.50 % (22892)Instructions burned: 393 (million)
% 22.53/4.50 % (22892)------------------------------
% 22.53/4.50 % (22892)------------------------------
% 23.50/4.50 % (22891)Instruction limit reached!
% 23.50/4.50 % (22891)------------------------------
% 23.50/4.50 % (22891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.50/4.50 % (22891)Termination reason: Unknown
% 23.50/4.50 % (22891)Termination phase: Saturation
% 23.50/4.50
% 23.50/4.50 % (22891)Memory used [KB]: 7675
% 23.50/4.50 % (22891)Time elapsed: 0.140 s
% 23.50/4.50 % (22891)Instructions burned: 458 (million)
% 23.50/4.50 % (22891)------------------------------
% 23.50/4.50 % (22891)------------------------------
% 23.50/4.51 % (22896)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_22295 for (2969ds/157Mi)
% 23.50/4.51 % (22897)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_22295 for (2969ds/590Mi)
% 23.50/4.55 % (22896)Instruction limit reached!
% 23.50/4.55 % (22896)------------------------------
% 23.50/4.55 % (22896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.50/4.55 % (22896)Termination reason: Unknown
% 23.50/4.55 % (22896)Termination phase: Saturation
% 23.50/4.55
% 23.50/4.55 % (22896)Memory used [KB]: 6524
% 23.50/4.55 % (22896)Time elapsed: 0.042 s
% 23.50/4.55 % (22896)Instructions burned: 158 (million)
% 23.50/4.55 % (22896)------------------------------
% 23.50/4.55 % (22896)------------------------------
% 23.50/4.56 % (22898)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_22295 for (2969ds/104Mi)
% 23.50/4.58 % (22898)Instruction limit reached!
% 23.50/4.58 % (22898)------------------------------
% 23.50/4.58 % (22898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.50/4.58 % (22898)Termination reason: Unknown
% 23.50/4.58 % (22898)Termination phase: Saturation
% 23.50/4.58
% 23.50/4.58 % (22898)Memory used [KB]: 6652
% 23.50/4.58 % (22898)Time elapsed: 0.029 s
% 23.50/4.58 % (22898)Instructions burned: 106 (million)
% 23.50/4.58 % (22898)------------------------------
% 23.50/4.58 % (22898)------------------------------
% 23.50/4.59 % (22899)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_22295 for (2968ds/414Mi)
% 23.94/4.61 % (22895)Instruction limit reached!
% 23.94/4.61 % (22895)------------------------------
% 23.94/4.61 % (22895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.94/4.61 % (22895)Termination reason: Unknown
% 23.94/4.61 % (22895)Termination phase: Saturation
% 23.94/4.61
% 23.94/4.61 % (22895)Memory used [KB]: 8827
% 23.94/4.61 % (22895)Time elapsed: 0.118 s
% 23.94/4.61 % (22895)Instructions burned: 476 (million)
% 23.94/4.61 % (22895)------------------------------
% 23.94/4.61 % (22895)------------------------------
% 23.94/4.62 % (22900)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_22295 for (2968ds/715Mi)
% 23.94/4.69 % (22897)Instruction limit reached!
% 23.94/4.69 % (22897)------------------------------
% 23.94/4.69 % (22897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.94/4.69 % (22897)Termination reason: Unknown
% 23.94/4.69 % (22897)Termination phase: Saturation
% 23.94/4.69
% 23.94/4.69 % (22897)Memory used [KB]: 8699
% 23.94/4.69 % (22897)Time elapsed: 0.178 s
% 23.94/4.69 % (22897)Instructions burned: 590 (million)
% 23.94/4.69 % (22897)------------------------------
% 23.94/4.69 % (22897)------------------------------
% 23.94/4.69 % (22899)Instruction limit reached!
% 23.94/4.69 % (22899)------------------------------
% 23.94/4.69 % (22899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.94/4.69 % (22899)Termination reason: Unknown
% 23.94/4.69 % (22899)Termination phase: Saturation
% 23.94/4.69
% 23.94/4.69 % (22899)Memory used [KB]: 6524
% 23.94/4.69 % (22899)Time elapsed: 0.102 s
% 23.94/4.69 % (22899)Instructions burned: 414 (million)
% 23.94/4.69 % (22899)------------------------------
% 23.94/4.69 % (22899)------------------------------
% 23.94/4.70 % (22901)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_22295 for (2967ds/961Mi)
% 24.56/4.70 % (22902)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_22295 for (2967ds/1213Mi)
% 24.77/4.81 % (22893)Instruction limit reached!
% 24.77/4.81 % (22893)------------------------------
% 24.77/4.81 % (22893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.77/4.81 % (22893)Termination reason: Unknown
% 24.77/4.81 % (22893)Termination phase: Saturation
% 24.77/4.81
% 24.77/4.81 % (22893)Memory used [KB]: 7931
% 24.77/4.81 % (22893)Time elapsed: 0.416 s
% 24.77/4.81 % (22893)Instructions burned: 1338 (million)
% 24.77/4.81 % (22893)------------------------------
% 24.77/4.81 % (22893)------------------------------
% 24.77/4.82 % (22903)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_22295 for (2966ds/1979Mi)
% 24.77/4.84 % (22900)Instruction limit reached!
% 24.77/4.84 % (22900)------------------------------
% 24.77/4.84 % (22900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.77/4.84 % (22900)Termination reason: Unknown
% 24.77/4.84 % (22900)Termination phase: Saturation
% 24.77/4.84
% 24.77/4.84 % (22900)Memory used [KB]: 3582
% 24.77/4.84 % (22900)Time elapsed: 0.221 s
% 24.77/4.84 % (22900)Instructions burned: 715 (million)
% 24.77/4.84 % (22900)------------------------------
% 24.77/4.84 % (22900)------------------------------
% 24.77/4.85 % (22904)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_22295 for (2966ds/481Mi)
% 25.63/4.97 % (22904)Instruction limit reached!
% 25.63/4.97 % (22904)------------------------------
% 25.63/4.97 % (22904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.63/4.97 % (22904)Termination reason: Unknown
% 25.63/4.97 % (22904)Termination phase: Saturation
% 25.63/4.97
% 25.63/4.97 % (22904)Memory used [KB]: 8827
% 25.63/4.97 % (22904)Time elapsed: 0.116 s
% 25.63/4.97 % (22904)Instructions burned: 482 (million)
% 25.63/4.97 % (22904)------------------------------
% 25.63/4.97 % (22904)------------------------------
% 25.63/4.98 % (22905)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_22295 for (2964ds/783Mi)
% 25.63/4.99 % (22901)Instruction limit reached!
% 25.63/4.99 % (22901)------------------------------
% 25.63/4.99 % (22901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.63/4.99 % (22901)Termination reason: Unknown
% 25.63/4.99 % (22901)Termination phase: Saturation
% 25.63/4.99
% 25.63/4.99 % (22901)Memory used [KB]: 8187
% 25.63/4.99 % (22901)Time elapsed: 0.299 s
% 25.63/4.99 % (22901)Instructions burned: 964 (million)
% 25.63/4.99 % (22901)------------------------------
% 25.63/4.99 % (22901)------------------------------
% 25.63/5.00 % (22906)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_22295 for (2964ds/432Mi)
% 27.44/5.08 % (22902)Instruction limit reached!
% 27.44/5.08 % (22902)------------------------------
% 27.44/5.08 % (22902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.44/5.08 % (22902)Termination reason: Unknown
% 27.44/5.08 % (22902)Termination phase: Saturation
% 27.44/5.08
% 27.44/5.08 % (22902)Memory used [KB]: 11001
% 27.44/5.08 % (22902)Time elapsed: 0.379 s
% 27.44/5.08 % (22902)Instructions burned: 1216 (million)
% 27.44/5.08 % (22902)------------------------------
% 27.44/5.08 % (22902)------------------------------
% 27.44/5.09 % (22907)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_22295 for (2963ds/1670Mi)
% 28.12/5.13 % (22906)Instruction limit reached!
% 28.12/5.13 % (22906)------------------------------
% 28.12/5.13 % (22906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.12/5.13 % (22906)Termination reason: Unknown
% 28.12/5.13 % (22906)Termination phase: Saturation
% 28.12/5.13
% 28.12/5.13 % (22906)Memory used [KB]: 7547
% 28.12/5.13 % (22906)Time elapsed: 0.133 s
% 28.12/5.13 % (22906)Instructions burned: 434 (million)
% 28.12/5.13 % (22906)------------------------------
% 28.12/5.13 % (22906)------------------------------
% 28.12/5.14 % (22908)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_22295 for (2963ds/90Mi)
% 28.12/5.17 % (22908)Instruction limit reached!
% 28.12/5.17 % (22908)------------------------------
% 28.12/5.17 % (22908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.12/5.17 % (22908)Termination reason: Unknown
% 28.12/5.17 % (22908)Termination phase: Saturation
% 28.12/5.17
% 28.12/5.17 % (22908)Memory used [KB]: 6396
% 28.12/5.17 % (22908)Time elapsed: 0.025 s
% 28.12/5.17 % (22908)Instructions burned: 91 (million)
% 28.12/5.17 % (22908)------------------------------
% 28.12/5.17 % (22908)------------------------------
% 28.12/5.18 % (22909)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_22295 for (2962ds/346Mi)
% 28.54/5.22 % (22905)Instruction limit reached!
% 28.54/5.22 % (22905)------------------------------
% 28.54/5.22 % (22905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.54/5.22 % (22905)Termination reason: Unknown
% 28.54/5.22 % (22905)Termination phase: Saturation
% 28.54/5.22
% 28.54/5.22 % (22905)Memory used [KB]: 9850
% 28.54/5.22 % (22905)Time elapsed: 0.245 s
% 28.54/5.22 % (22905)Instructions burned: 783 (million)
% 28.54/5.22 % (22905)------------------------------
% 28.54/5.22 % (22905)------------------------------
% 28.54/5.23 % (22910)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_22295 for (2962ds/401Mi)
% 28.54/5.26 % (22909)Instruction limit reached!
% 28.54/5.26 % (22909)------------------------------
% 28.54/5.26 % (22909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.54/5.26 % (22909)Termination reason: Unknown
% 28.54/5.26 % (22909)Termination phase: Saturation
% 28.54/5.26
% 28.54/5.26 % (22909)Memory used [KB]: 8827
% 28.54/5.26 % (22909)Time elapsed: 0.088 s
% 28.54/5.26 % (22909)Instructions burned: 348 (million)
% 28.54/5.26 % (22909)------------------------------
% 28.54/5.26 % (22909)------------------------------
% 28.54/5.27 % (22911)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_22295 for (2961ds/6454Mi)
% 29.08/5.33 % (22910)Instruction limit reached!
% 29.08/5.33 % (22910)------------------------------
% 29.08/5.33 % (22910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.08/5.33 % (22910)Termination reason: Unknown
% 29.08/5.33 % (22910)Termination phase: Saturation
% 29.08/5.33
% 29.08/5.33 % (22910)Memory used [KB]: 6524
% 29.08/5.33 % (22910)Time elapsed: 0.098 s
% 29.08/5.33 % (22910)Instructions burned: 404 (million)
% 29.08/5.33 % (22910)------------------------------
% 29.08/5.33 % (22910)------------------------------
% 29.08/5.34 % (22912)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_22295 for (2961ds/283Mi)
% 29.08/5.35 % (22894)First to succeed.
% 29.08/5.36 % (22894)Refutation found. Thanks to Tanya!
% 29.08/5.36 % SZS status Theorem for DTF2THF_22295
% 29.08/5.36 % SZS output start Proof for DTF2THF_22295
% 29.08/5.36 thf(func_def_0, type, in: $i > $i > $o).
% 29.08/5.36 thf(func_def_1, type, exu: ($i > $o) > $o).
% 29.08/5.36 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 29.08/5.36 thf(func_def_8, type, powerset: $i > $i).
% 29.08/5.36 thf(func_def_10, type, setunion: $i > $i).
% 29.08/5.36 thf(func_def_19, type, descr: ($i > $o) > $i).
% 29.08/5.36 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 29.08/5.36 thf(func_def_26, type, prop2set: $o > $i).
% 29.08/5.36 thf(func_def_36, type, nonempty: $i > $o).
% 29.08/5.36 thf(func_def_69, type, set2prop: $i > $o).
% 29.08/5.36 thf(func_def_88, type, subset: $i > $i > $o).
% 29.08/5.36 thf(func_def_89, type, disjoint: $i > $i > $o).
% 29.08/5.36 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 29.08/5.36 thf(func_def_114, type, binunion: $i > $i > $i).
% 29.08/5.36 thf(func_def_122, type, binintersect: $i > $i > $i).
% 29.08/5.36 thf(func_def_135, type, regular: $i > $o).
% 29.08/5.36 thf(func_def_136, type, setminus: $i > $i > $i).
% 29.08/5.36 thf(func_def_147, type, symdiff: $i > $i > $i).
% 29.08/5.36 thf(func_def_153, type, iskpair: $i > $o).
% 29.08/5.36 thf(func_def_177, type, sK3: ($i > $o) > $i).
% 29.08/5.36 thf(func_def_178, type, sK4: ($i > $o) > $i > $i).
% 29.08/5.36 thf(func_def_179, type, sK5: ($i > $o) > $i > $i).
% 29.08/5.36 thf(func_def_180, type, sK6: $i > $i > $i).
% 29.08/5.36 thf(func_def_181, type, sK7: ($i > $o) > $i > $i).
% 29.08/5.36 thf(func_def_182, type, sK8: $i > $i > $i).
% 29.08/5.36 thf(func_def_183, type, sK9: $i > ($i > $o) > $i).
% 29.08/5.36 thf(func_def_184, type, sK10: ($i > $o) > $i).
% 29.08/5.36 thf(func_def_185, type, sK11: ($i > $o) > $i > $i).
% 29.08/5.36 thf(func_def_186, type, sK12: ($i > $o) > $i > $i).
% 29.08/5.36 thf(func_def_187, type, sK13: ($i > $o) > $i).
% 29.08/5.36 thf(func_def_188, type, sK14: $i > ($i > $o) > $i).
% 29.08/5.36 thf(func_def_189, type, sK15: $i > ($i > $o) > $i).
% 29.08/5.36 thf(func_def_190, type, sK16: $i > $i > $i).
% 29.08/5.36 thf(func_def_191, type, sK17: $i > $i).
% 29.08/5.36 thf(func_def_192, type, sK18: ($i > $o) > ($i > $o) > $i).
% 29.08/5.36 thf(func_def_193, type, sK19: ($i > $o) > ($i > $o) > $i).
% 29.08/5.36 thf(func_def_194, type, sK20: $i > ($i > $o) > $i).
% 29.08/5.36 thf(func_def_195, type, sK21: ($i > $o) > $i > $i).
% 29.08/5.36 thf(func_def_196, type, sK22: ($i > $o) > $i > $i).
% 29.08/5.36 thf(func_def_197, type, sK23: $i > ($i > $o) > $i).
% 29.08/5.36 thf(func_def_198, type, sK24: ($i > $o) > $i > $i).
% 29.08/5.36 thf(func_def_199, type, sK25: ($i > $o) > $i > $i).
% 29.08/5.36 thf(func_def_200, type, sK26: ($i > $o) > $i > $i).
% 29.08/5.36 thf(func_def_201, type, sK27: ($i > $o) > $i > $i).
% 29.08/5.36 thf(func_def_202, type, sK28: ($i > $o) > $i > $i).
% 29.08/5.36 thf(func_def_203, type, sK29: ($i > $o) > $i > $i).
% 29.08/5.36 thf(func_def_204, type, sK30: $i > $i).
% 29.08/5.36 thf(func_def_205, type, sK31: $i > $i > $i).
% 29.08/5.36 thf(func_def_206, type, sK32: $o > $i > $i > $i).
% 29.08/5.36 thf(func_def_207, type, sK33: ($i > $o) > $i > $i).
% 29.08/5.36 thf(func_def_208, type, sK34: $i > $i).
% 29.08/5.36 thf(func_def_209, type, sK35: $i > $i > $i).
% 29.08/5.36 thf(func_def_210, type, sK36: $i > $i > $i).
% 29.08/5.36 thf(func_def_211, type, sK37: $i > $i > $i).
% 29.08/5.36 thf(func_def_212, type, sK38: $i > $i > $i > $i).
% 29.08/5.36 thf(func_def_213, type, sK39: $i > ($i > $o) > $i).
% 29.08/5.36 thf(func_def_214, type, sK40: $i > ($i > $i > $o) > $i).
% 29.08/5.36 thf(func_def_215, type, sK41: $i > ($i > $i > $o) > $i).
% 29.08/5.36 thf(func_def_216, type, sK42: $i > $i > ($i > $i > $o) > $i).
% 29.08/5.36 thf(func_def_217, type, sK43: $i > ($i > $i > $o) > $i).
% 29.08/5.36 thf(func_def_218, type, sK44: $i > $i > ($i > $i > $o) > $i).
% 29.08/5.36 thf(func_def_219, type, sK45: $i > $i > ($i > $i > $o) > $i).
% 29.08/5.36 thf(func_def_220, type, sK46: $i > $i > ($i > $i > $o) > $i).
% 29.08/5.36 thf(func_def_221, type, sK47: $i > $i > ($i > $i > $o) > $i).
% 29.08/5.36 thf(func_def_222, type, sK48: ($i > $o) > $i).
% 29.08/5.36 thf(func_def_223, type, sK49: ($i > $o) > $i).
% 29.08/5.36 thf(func_def_224, type, sK50: ($i > $o) > $i).
% 29.08/5.36 thf(func_def_225, type, sK51: ($i > $o) > $i).
% 29.08/5.36 thf(func_def_226, type, sK52: $i > $i > $i).
% 29.08/5.36 thf(func_def_227, type, sK53: $i > $i > $i).
% 29.08/5.36 thf(func_def_228, type, sK54: $i > $i).
% 29.08/5.36 thf(func_def_229, type, sK55: $i > $i).
% 29.08/5.36 thf(func_def_230, type, sK56: $i > $i).
% 29.08/5.36 thf(func_def_231, type, sK57: $i > $i > $i).
% 29.08/5.36 thf(func_def_232, type, sK58: $i > $i > $i).
% 29.08/5.36 thf(func_def_233, type, sK59: $i > ($i > $o) > $i).
% 29.08/5.36 thf(func_def_234, type, sK60: $i > $i).
% 29.08/5.36 thf(func_def_235, type, sK61: ($i > $o) > $i > $i).
% 29.08/5.36 thf(func_def_236, type, sK62: ($i > $o) > $i).
% 29.08/5.36 thf(func_def_237, type, sK63: ($i > $o) > $i > $i).
% 29.08/5.36 thf(func_def_238, type, sK64: ($i > $o) > ($i > $o) > $i).
% 29.08/5.36 thf(func_def_239, type, sK65: ($i > $o) > ($i > $o) > $i).
% 29.08/5.36 thf(func_def_240, type, sK66: ($i > $o) > $i).
% 29.08/5.36 thf(func_def_241, type, sK67: $i > ($i > $o) > $i).
% 29.08/5.36 thf(func_def_242, type, sK68: $i > ($i > $o) > $i).
% 29.08/5.36 thf(func_def_243, type, sK69: $i > ($i > $o) > $i).
% 29.08/5.36 thf(func_def_244, type, sK70: ($i > $o) > $i).
% 29.08/5.36 thf(func_def_245, type, sK71: $i > ($i > $o) > $i).
% 29.08/5.36 thf(func_def_246, type, sK72: ($i > $o) > $i).
% 29.08/5.36 thf(func_def_247, type, sK73: ($i > $o) > $i).
% 29.08/5.36 thf(func_def_248, type, sK74: ($i > $o) > ($i > $o) > $i).
% 29.08/5.36 thf(func_def_249, type, sK75: ($i > $o) > ($i > $o) > $i).
% 29.08/5.36 thf(func_def_250, type, sK76: $i > ($i > $o) > $i).
% 29.08/5.36 thf(func_def_251, type, sK77: $i > ($i > $o) > $i).
% 29.08/5.36 thf(func_def_252, type, sK78: $i > ($i > $o) > $i).
% 29.08/5.36 thf(func_def_253, type, sK79: $i > ($i > $o) > $i).
% 29.08/5.36 thf(func_def_254, type, sK80: $i > ($i > $o) > $i).
% 29.08/5.36 thf(func_def_255, type, sK81: $i > $i > $i).
% 29.08/5.36 thf(func_def_256, type, sK82: ($i > $o) > $i > ($i > $o) > $i > $i).
% 29.08/5.36 thf(func_def_257, type, sK83: $i > $i > ($i > $o) > ($i > $o) > $i).
% 29.08/5.36 thf(func_def_258, type, sK84: ($i > $o) > $i > $i).
% 29.08/5.36 thf(func_def_259, type, ph85: !>[X0: $tType]:(X0)).
% 29.08/5.36 thf(f11762,plain,(
% 29.08/5.36 $false),
% 29.08/5.36 inference(avatar_sat_refutation,[status(thm)],[f11729,f11755])).
% 29.08/5.36 thf(f11755,plain,(
% 29.08/5.36 ~spl2_31),
% 29.08/5.36 inference(avatar_contradiction_clause,[status(thm)],[f11754])).
% 29.08/5.36 thf(f11754,plain,(
% 29.08/5.36 $false | ~spl2_31),
% 29.08/5.36 inference(trivial_inequality_removal,[status(thm)],[f11747])).
% 29.08/5.36 thf(f11747,plain,(
% 29.08/5.36 ($true = $false) | ~spl2_31),
% 29.08/5.36 inference(superposition,[status(thm)],[f938,f11728])).
% 29.08/5.36 thf(f11728,plain,(
% 29.08/5.36 ((in @ sK1 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) = $false) | ~spl2_31),
% 29.08/5.36 inference(avatar_component_clause,[status(thm)],[f11726])).
% 29.08/5.36 thf(f11726,definition,(
% 29.08/5.36 spl2_31 <=> ((in @ sK1 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) = $false)),
% 29.08/5.36 introduced(definition,[new_symbols(naming,[spl2_31])],[avatar_definition])).
% 29.08/5.36 thf(f938,plain,(
% 29.08/5.36 ( ! [X2 : $i,X1 : $i] : (((in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))) = $true)) )),
% 29.08/5.36 inference(beta_eta_normalization,[status(thm)],[f937])).
% 29.08/5.36 thf(f937,plain,(
% 29.08/5.36 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))) @ X2))) )),
% 29.08/5.36 inference(pi_clausification,[status(thm)],[f936])).
% 29.08/5.36 thf(f936,plain,(
% 29.08/5.36 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))) = $true)) )),
% 29.08/5.36 inference(beta_eta_normalization,[status(thm)],[f935])).
% 29.08/5.36 thf(f935,plain,(
% 29.08/5.36 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))) @ X1))) )),
% 29.08/5.36 inference(pi_clausification,[status(thm)],[f835])).
% 29.08/5.36 thf(f835,plain,(
% 29.08/5.36 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) = $true)),
% 29.08/5.36 inference(definition_unfolding,[status(thm)],[f691,f593])).
% 29.08/5.36 thf(f593,plain,(
% 29.08/5.36 (setukpairIL = $true)),
% 29.08/5.36 inference(cnf_transformation,[status(thm)],[f417])).
% 29.08/5.36 thf(f417,plain,(
% 29.08/5.36 (subsetRefl = $true) & (dsetconstrER = $true) & (replAx = $true) & (dsetconstrEL = $true) & (subsetemptysetimpeq = $true) & (notequalI1 = $true) & (emptyInPowerset = $true) & (emptyinunitempty = $true) & (notdexE = $true) & (setadjoinOr = $true) & (dsetconstr__Cong = $true) & (dsetconstrI = $true) & (descrp = $true) & (binunionE = $true) & (emptysetsubset = $true) & (binintersectRsub = $true) & (binunionLsub = $true) & (notinemptyset = $true) & (powerset__Cong = $true) & (powersetE = $true) & (symdiffIneg1 = $true) & (eqimpsubset2 = $true) & (powersetsubset = $true) & (setadjoinIL = $true) & (setadjoinSub = $true) & (nonemptyI1 = $true) & (symdiffE = $true) & (setukpairIL = $true) & (eqimpsubset1 = $true) & (symdiffI1 = $true) & (setoftrueEq = $true) & (emptyinPowerset = $true) & (quantDeMorgan2 = $true) & (notsubsetI = $true) & (exuE1 = $true) & (setadjoin__Cong = $true) & (upairset2IR = $true) & (exuE2 = $true) & (disjointsetsI1 = $true) & (secondinupair = $true) & (exuI2 = $true) & (subsetE2 = $true) & (binintersectSubset3 = $true) & (powersetAx = $true) & (setbeta = $true) & (setminusSubset2 = $true) & (setminusLsub = $true) & (emptyset__Cong = $true) & (binintersectLsub = $true) & (symdiffI2 = $true) & (inPowerset = $true) & (binintersectEL = $true) & (prop2setE = $true) & (binintersectI = $true) & (vacuousDall = $true) & (powersetE1 = $true) & (omega0Ax = $true) & ((iskpair @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))) != $true) & (in__Cong = $true) & (subsetI1 = $true) & (binintersectSubset5 = $true) & (subsetTrans = $true) & (setadjoinE = $true) & (singletonsswitch = $true) & (emptyE1 = $true) & (noeltsimpempty = $true) & (descr__Cong = $true) & (setminusILneg = $true) & (emptysetAx = $true) & (prop2set2propI = $true) & (setminusSubset1 = $true) & (omegaIndAx = $true) & (nonemptyImpWitness = $true) & (emptyI = $true) & (inCongP = $true) & (setunionE = $true) & (bs114d = $true) & (exuI3 = $true) & (exuE3e = $true) & (binunionEcases = $true) & (exuI1 = $true) & (binintersectSubset4 = $true) & (foundationAx = $true) & (setminusELneg = $true) & (binunionIL = $true) & (setminusERneg = $true) & (setextAx = $true) & (subPowSU = $true) & (setminusER = $true) & (prop2setI = $true) & (emptysetimpfalse = $true) & (sepInPowerset = $true) & (subsetI2 = $true) & (setunion__Cong = $true) & (setextsub = $true) & (nonemptyI = $true) & (setext = $true) & (setadjoinSub2 = $true) & (binunionRsub = $true) & (exuEu = $true) & (quantDeMorgan3 = $true) & (binintersectER = $true) & (upairsetE = $true) & (subset2powerset = $true) & (nonemptyE1 = $true) & (quantDeMorgan4 = $true) & (upairsetIR = $true) & (powersetI1 = $true) & (symdiffIneg2 = $true) & (setminusEL = $true) & (setunionI = $true) & (notinsingleton = $true) & (exu__Cong = $true) & (omega__Cong = $true) & (setukpairIR = $true) & (notdallE = $true) & (setunionAx = $true) & (setminusI = $true) & (omegaSAx = $true) & (powersetI = $true) & (setadjoinIR = $true) & (setminusIRneg = $true) & (binintersectSubset2 = $true) & (wellorderingAx = $true) & (eqinunit = $true) & (quantDeMorgan1 = $true) & (binunionIR = $true) & (exuE3u = $true) & (uniqinunit = $true) & (setadjoinAx = $true) & (binintersectSubset1 = $true) & (notequalI2 = $true) & (sepSubset = $true) & (upairsetIL = $true) & (subsetE = $true) & (emptysetE = $true)),
% 29.08/5.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f415,f416])).
% 29.08/5.36 thf(f416,plain,(
% 29.08/5.36 ? [X0 : $i,X1 : $i] : ((iskpair @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset))) != $true) => ((iskpair @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))) != $true)),
% 29.08/5.36 introduced(definition,[],[choice_axiom])).
% 29.08/5.36 thf(f415,plain,(
% 29.08/5.36 (subsetRefl = $true) & (dsetconstrER = $true) & (replAx = $true) & (dsetconstrEL = $true) & (subsetemptysetimpeq = $true) & (notequalI1 = $true) & (emptyInPowerset = $true) & (emptyinunitempty = $true) & (notdexE = $true) & (setadjoinOr = $true) & (dsetconstr__Cong = $true) & (dsetconstrI = $true) & (descrp = $true) & (binunionE = $true) & (emptysetsubset = $true) & (binintersectRsub = $true) & (binunionLsub = $true) & (notinemptyset = $true) & (powerset__Cong = $true) & (powersetE = $true) & (symdiffIneg1 = $true) & (eqimpsubset2 = $true) & (powersetsubset = $true) & (setadjoinIL = $true) & (setadjoinSub = $true) & (nonemptyI1 = $true) & (symdiffE = $true) & (setukpairIL = $true) & (eqimpsubset1 = $true) & (symdiffI1 = $true) & (setoftrueEq = $true) & (emptyinPowerset = $true) & (quantDeMorgan2 = $true) & (notsubsetI = $true) & (exuE1 = $true) & (setadjoin__Cong = $true) & (upairset2IR = $true) & (exuE2 = $true) & (disjointsetsI1 = $true) & (secondinupair = $true) & (exuI2 = $true) & (subsetE2 = $true) & (binintersectSubset3 = $true) & (powersetAx = $true) & (setbeta = $true) & (setminusSubset2 = $true) & (setminusLsub = $true) & (emptyset__Cong = $true) & (binintersectLsub = $true) & (symdiffI2 = $true) & (inPowerset = $true) & (binintersectEL = $true) & (prop2setE = $true) & (binintersectI = $true) & (vacuousDall = $true) & (powersetE1 = $true) & (omega0Ax = $true) & ? [X0 : $i,X1 : $i] : ((iskpair @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset))) != $true) & (in__Cong = $true) & (subsetI1 = $true) & (binintersectSubset5 = $true) & (subsetTrans = $true) & (setadjoinE = $true) & (singletonsswitch = $true) & (emptyE1 = $true) & (noeltsimpempty = $true) & (descr__Cong = $true) & (setminusILneg = $true) & (emptysetAx = $true) & (prop2set2propI = $true) & (setminusSubset1 = $true) & (omegaIndAx = $true) & (nonemptyImpWitness = $true) & (emptyI = $true) & (inCongP = $true) & (setunionE = $true) & (bs114d = $true) & (exuI3 = $true) & (exuE3e = $true) & (binunionEcases = $true) & (exuI1 = $true) & (binintersectSubset4 = $true) & (foundationAx = $true) & (setminusELneg = $true) & (binunionIL = $true) & (setminusERneg = $true) & (setextAx = $true) & (subPowSU = $true) & (setminusER = $true) & (prop2setI = $true) & (emptysetimpfalse = $true) & (sepInPowerset = $true) & (subsetI2 = $true) & (setunion__Cong = $true) & (setextsub = $true) & (nonemptyI = $true) & (setext = $true) & (setadjoinSub2 = $true) & (binunionRsub = $true) & (exuEu = $true) & (quantDeMorgan3 = $true) & (binintersectER = $true) & (upairsetE = $true) & (subset2powerset = $true) & (nonemptyE1 = $true) & (quantDeMorgan4 = $true) & (upairsetIR = $true) & (powersetI1 = $true) & (symdiffIneg2 = $true) & (setminusEL = $true) & (setunionI = $true) & (notinsingleton = $true) & (exu__Cong = $true) & (omega__Cong = $true) & (setukpairIR = $true) & (notdallE = $true) & (setunionAx = $true) & (setminusI = $true) & (omegaSAx = $true) & (powersetI = $true) & (setadjoinIR = $true) & (setminusIRneg = $true) & (binintersectSubset2 = $true) & (wellorderingAx = $true) & (eqinunit = $true) & (quantDeMorgan1 = $true) & (binunionIR = $true) & (exuE3u = $true) & (uniqinunit = $true) & (setadjoinAx = $true) & (binintersectSubset1 = $true) & (notequalI2 = $true) & (sepSubset = $true) & (upairsetIL = $true) & (subsetE = $true) & (emptysetE = $true)),
% 29.08/5.36 inference(flattening,[status(thm)],[f414])).
% 29.08/5.36 thf(f414,plain,(
% 29.08/5.36 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : ((iskpair @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset))) != $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)),
% 29.08/5.36 inference(ennf_transformation,[status(thm)],[f207])).
% 29.08/5.36 thf(f207,plain,(
% 29.08/5.36 ~((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) => ! [X0 : $i,X1 : $i] : ((iskpair @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset))) = $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 29.08/5.36 inference(fool_elimination,[status(thm)],[f206])).
% 29.08/5.36 thf(f206,plain,(
% 29.08/5.36 ~(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 => ! [X0 : $i,X1 : $i] : (iskpair @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 29.08/5.36 inference(rectify,[status(thm)],[f140])).
% 29.08/5.36 thf(f140,negated_conjecture,(
% 29.08/5.36 ~(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 => ! [X2 : $i,X1 : $i] : (iskpair @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 29.08/5.36 inference(negated_conjecture,[status(cth)],[f139])).
% 29.08/5.36 thf(f139,conjecture,(
% 29.08/5.36 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 => ! [X2 : $i,X1 : $i] : (iskpair @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 29.08/5.36 file('/export/starexec/sandbox/tmp/tmp.CMzFP8z4xB/DTF2THF_22295.p',kpairiskpair)).
% 29.08/5.36 thf(f691,plain,(
% 29.08/5.36 (setukpairIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))))),
% 29.08/5.36 inference(cnf_transformation,[status(thm)],[f335])).
% 29.08/5.36 thf(f335,plain,(
% 29.08/5.36 (setukpairIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))))),
% 29.08/5.36 inference(fool_elimination,[status(thm)],[f334])).
% 29.08/5.36 thf(f334,plain,(
% 29.08/5.36 (! [X0 : $i,X1 : $i] : (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset)))) = setukpairIL)),
% 29.08/5.36 inference(rectify,[status(thm)],[f137])).
% 29.08/5.36 thf(f137,axiom,(
% 29.08/5.36 (! [X2 : $i,X1 : $i] : (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))) = setukpairIL)),
% 29.08/5.36 file('/export/starexec/sandbox/tmp/tmp.CMzFP8z4xB/DTF2THF_22295.p',setukpairIL)).
% 29.08/5.36 thf(f11729,plain,(
% 29.08/5.36 spl2_31),
% 29.08/5.36 inference(avatar_split_clause,[status(thm)],[f11724,f11726])).
% 29.08/5.36 thf(f11724,plain,(
% 29.08/5.36 ((in @ sK1 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) = $false)),
% 29.08/5.36 inference(trivial_inequality_removal,[status(thm)],[f11723])).
% 29.08/5.36 thf(f11723,plain,(
% 29.08/5.36 ($true = $false) | ((in @ sK1 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) = $false)),
% 29.08/5.36 inference(forward_demodulation,[status(thm)],[f11722,f934])).
% 29.08/5.36 thf(f934,plain,(
% 29.08/5.36 ( ! [X2 : $i,X1 : $i] : (((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))) = $true)) )),
% 29.08/5.36 inference(beta_eta_normalization,[status(thm)],[f933])).
% 29.08/5.36 thf(f933,plain,(
% 29.08/5.36 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))) @ X2))) )),
% 29.08/5.36 inference(pi_clausification,[status(thm)],[f932])).
% 29.08/5.36 thf(f932,plain,(
% 29.08/5.36 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))) = $true)) )),
% 29.08/5.36 inference(beta_eta_normalization,[status(thm)],[f931])).
% 29.08/5.36 thf(f931,plain,(
% 29.08/5.36 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))) @ X1))) )),
% 29.08/5.36 inference(pi_clausification,[status(thm)],[f752])).
% 29.08/5.36 thf(f752,plain,(
% 29.08/5.36 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) = $true)),
% 29.08/5.36 inference(definition_unfolding,[status(thm)],[f506,f419])).
% 29.08/5.36 thf(f419,plain,(
% 29.08/5.36 (setukpairIR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))))),
% 29.08/5.36 inference(cnf_transformation,[status(thm)],[f315])).
% 29.08/5.36 thf(f315,plain,(
% 29.08/5.36 (setukpairIR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))))),
% 29.08/5.36 inference(fool_elimination,[status(thm)],[f314])).
% 29.08/5.36 thf(f314,plain,(
% 29.08/5.36 (setukpairIR = ! [X0 : $i,X1 : $i] : (in @ X0 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset)))))),
% 29.08/5.36 inference(rectify,[status(thm)],[f138])).
% 29.08/5.36 thf(f138,axiom,(
% 29.08/5.36 (setukpairIR = ! [X2 : $i,X1 : $i] : (in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))))),
% 29.08/5.36 file('/export/starexec/sandbox/tmp/tmp.CMzFP8z4xB/DTF2THF_22295.p',setukpairIR)).
% 29.08/5.36 thf(f506,plain,(
% 29.08/5.36 (setukpairIR = $true)),
% 29.08/5.36 inference(cnf_transformation,[status(thm)],[f417])).
% 29.08/5.36 thf(f11722,plain,(
% 29.08/5.36 ((in @ sK0 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) = $false) | ((in @ sK1 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) = $false)),
% 29.08/5.36 inference(equality_resolution,[status(thm)],[f1480])).
% 29.08/5.36 thf(f1480,plain,(
% 29.08/5.36 ( ! [X2 : $i,X1 : $i] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))) | ((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) = $false) | ($false = (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))))) )),
% 29.08/5.36 inference(equality_proxy_clausification,[status(thm)],[f1479])).
% 29.08/5.36 thf(f1479,plain,(
% 29.08/5.36 ( ! [X2 : $i,X1 : $i] : (($false = (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))))) | (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))) = $false) | ((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) = $false)) )),
% 29.08/5.36 inference(binary_proxy_clausification,[status(thm)],[f1478])).
% 29.08/5.36 thf(f1478,plain,(
% 29.08/5.36 ( ! [X2 : $i,X1 : $i] : (($false = (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))))) | ($false = ((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))))) )),
% 29.08/5.36 inference(beta_eta_normalization,[status(thm)],[f1477])).
% 29.08/5.36 thf(f1477,plain,(
% 29.08/5.36 ( ! [X2 : $i,X1 : $i] : (($false = (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))))) | ($false = ((^[Y0 : $i]: ((in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))))) @ X2))) )),
% 29.08/5.36 inference(pi_clausification,[status(thm)],[f1476])).
% 29.08/5.36 thf(f1476,plain,(
% 29.08/5.36 ( ! [X1 : $i] : (($false = (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))))) | ((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))))) = $false)) )),
% 29.08/5.36 inference(binary_proxy_clausification,[status(thm)],[f1475])).
% 29.08/5.36 thf(f1475,plain,(
% 29.08/5.36 ( ! [X1 : $i] : ((((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))))) & (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))))) = $false)) )),
% 29.08/5.36 inference(beta_eta_normalization,[status(thm)],[f1474])).
% 29.08/5.36 thf(f1474,plain,(
% 29.08/5.36 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))))) & (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))))) @ X1))) )),
% 29.08/5.36 inference(pi_clausification,[status(thm)],[f1473])).
% 29.08/5.36 thf(f1473,plain,(
% 29.08/5.36 ($true != (?? @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset)))))) & (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))))))))),
% 29.08/5.36 inference(beta_eta_normalization,[status(thm)],[f719])).
% 29.08/5.36 thf(f719,plain,(
% 29.08/5.36 (((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ Y0)) & ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))) & (in @ Y1 @ (setunion @ Y0)))))) @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))) != $true)),
% 29.08/5.36 inference(definition_unfolding,[status(thm)],[f563,f650])).
% 29.08/5.36 thf(f650,plain,(
% 29.08/5.36 (iskpair = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ Y0)) & ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))) & (in @ Y1 @ (setunion @ Y0)))))))),
% 29.08/5.36 inference(cnf_transformation,[status(thm)],[f177])).
% 29.08/5.36 thf(f177,plain,(
% 29.08/5.36 (iskpair = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ Y0)) & ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))) & (in @ Y1 @ (setunion @ Y0)))))))),
% 29.08/5.36 inference(fool_elimination,[status(thm)],[f176])).
% 29.08/5.36 thf(f176,plain,(
% 29.08/5.36 (iskpair = (^[X0 : $i] : (? [X1 : $i] : ((in @ X1 @ (setunion @ X0)) & ? [X2 : $i] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = X0) & (in @ X2 @ (setunion @ X0)))))))),
% 29.08/5.36 inference(rectify,[status(thm)],[f135])).
% 29.08/5.36 thf(f135,axiom,(
% 29.08/5.36 (iskpair = (^[X3 : $i] : (? [X1 : $i] : ((in @ X1 @ (setunion @ X3)) & ? [X2 : $i] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = X3) & (in @ X2 @ (setunion @ X3)))))))),
% 29.08/5.36 file('/export/starexec/sandbox/tmp/tmp.CMzFP8z4xB/DTF2THF_22295.p',iskpair)).
% 29.08/5.36 thf(f563,plain,(
% 29.08/5.36 ((iskpair @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK0 @ emptyset)) @ emptyset))) != $true)),
% 29.08/5.36 inference(cnf_transformation,[status(thm)],[f417])).
% 29.08/5.36 % SZS output end Proof for DTF2THF_22295
% 29.08/5.36 % (22894)------------------------------
% 29.08/5.36 % (22894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.08/5.36 % (22894)Termination reason: Refutation
% 29.08/5.36
% 29.08/5.36 % (22894)Memory used [KB]: 10362
% 29.08/5.36 % (22894)Time elapsed: 0.879 s
% 29.08/5.36 % (22894)Instructions burned: 2840 (million)
% 29.08/5.36 % (22894)------------------------------
% 29.08/5.36 % (22894)------------------------------
% 29.08/5.36 % (22486)Success in time 3.909 s
%------------------------------------------------------------------------------